Aiming at the problem that the traditional causality extraction in natural language processing was mainly based  on  pattern matching methods
 or machine learning algorithms, and accuracy of the results was low, and only explicit causality with causal cue words could be extracted, we proposed an algorithm BERT-GCN using large-scale pretraining model combined with graph convolutional neural network. Firstly,  we used BERT （bidirectional encoder representation from transformers） to encode the corpus and generate word vectors. Secondly,  we put the generated word vectors into the graph convolutional neural network for training. Finally, we put them into the Softmax layer to complete the extraction of causality. The experimental results show that  the model obtains good results on the SEDR-CE dataset, and the effect of implicit causality is also good.

Aiming at the problem that the traditional relation extraction model relied on machine learning methods such as feature engineering, which had low accuracy and complicated rules, we proposed a BERT+BiLSTM+CRF method. Firstly,  bidirectional encoder representations from transformers (BERT) was used to pre-train the corpus. Secondly, by using BERT to dynamically generate word vectors according to context features, the generated word vectors were encoded through bidirectional long and short-term memory network (BiLSTM). Finally, we input it into the conditional random field (CRF) layer to complete the extraction of causality. The experimental result shows that the accuracy of the model on the SemEval-CE dataset is 0.054 1 higher than that of the BiLSTM+CRF+self-ATT model, which improves the performance of the deep learning method in the task of causality extraction.

Aiming at the problem that it was difficult to achieve high-precision and high frame rate tracking under limited computing resources, we proposed a lightweight  siamese network target  tracking algorithm based on ananchor free.   Firstly, the modified lightweight network MobileNetV3 was used as the backbone network to extract features, and reduced parameters and computation of the network  while maintaining deep feature expression capability. Secondly, for traditional cross-correlation operation, we proposed deep cross-correlation module for graph cascading optimization, which highlighted important information of target features through rich feature response graphs. Finally, feature sharing was used  to reduce parameters and computation to improve tracking speed in the anchor classification regression prediction network. Comparative experiments were conducted on two mainstream datasets OTB2015 and VOT2018, the experimental results show that the algorithm has a significant accuracy  advantages compared to  SiamFC tracker, and is more robust in complex tracking scenes. At the same time, the tracking frame rate can reach 175 frames/s.

By using Goswami’s method, we discussed the mean value problem of the composition of a class of arithmetic functions and the integral part function, and gave an asymptotic formula.

Aiming at the problem that existing ensemble clustering algorithms usually used K-means algorithm as the base clustering generator, although it could ensure the diversity of clustering members, it ignored that poor base clusterings might cause terrible disturbance to the final clustering result, we proposed a two stage ensemble algorithm based on clustering quality. Considering that K-means algorithm ran efficiently, but the clustering quality was relatively rough, firstly, we proposed to  use K-means algorithm to generate base clustering members in the generation stage, and then  selected clustering members with both high quality and strong diversity through  group aggrement measure to form candidate ensemble. Secondly, the information entropy knowledge was futher applied to construct the weighted-clustering co-association matrix in the ensemble stage. Finally, the final clustering result was obtained by using consensus function. Three indexes were used for comparative experiments on ten real datasets, and the experimantal results show that the algorithm can effectively improve the accuracy of clustering results while maintaining good robustness.

 The studies of reactions involving water radical cations and their cluster ion ((H₂O)⁺_n)  can  better understand the mechanisms of certain natural processes,  such as proton transfer in aqueous solutions,  the formation of hydrogen bonds,  the destruction of bio-molecules such as DNA,  and the discovery of novel gas phase reactions and products. In addition,  the potential of water radical cations in  radio-biology have broad application prospects and its use as a primary reactive ion have attracted much attention for efficient selective  chemical ionization as well as improving the analytical sensitivity. At present, there are many studies on the bonding properties and  structure  of protonated water clusters and hydrated electrons, but there are few studies on the isolation and physicochemical properties of (H₂O)⁺_n due to  their ultra-high reaction activity and extremely short lifetime. Since significant progress has been made in the  technology  of mass spectroscopy,  molecular spectrometry  and high-precision  theoretical calculation of quantum chemistry, we review the current knowledge of    (H₂O)⁺_n, including  the formation  methods  and generation mechanisms,  structural theoretical simulation and experimental verification,   chemical property analysis,  and their application research.

Aiming at the problem of high complexity in mask representation in the field of instance segmentation, we proposed a new mask representation method for instance segmentation, which used three repsesentation units that did not rely on any prior information  to represent and predict mask, and restored the mask in the form of nonlinear decoding. This method could significantly reduce the representation complexity and inference computation of image instance masks.   Based on the representation method, we constructed an efficient single-shot instance segmentation model. The experimental results show that compared to other single-shot instance segmentation models, the model can achieve better performance while ensuring that the  time cost is basically the same. Additionally, we embed the representation method with minimal modifications into the classic model BlendMask to reconstruct attention maps. The improved model has a  faster inference speed compared  to the original model, and the average accuracy of the mask is improved by 1.5%, indicating that the  representation method has good universality.

We constructed a three-stage representation learning model by combining convolutional neural network and transformer encoder with meta-learning as the core idea. In order to express the interaction between  entities and task relations in the reference set,  we used convolutional neural network to obtain relation-meta, applied the transformer encoder to enhance the entity representation in query set, and  designed a processor for calculating matching score of incomplete triples to  solve the problem of few-shot knowledge graph completion, i.e., the phenomenon that the large-scale knowledge graph was sparse, and the number of entity pairs corresponding to the long-tail relations with low frequency was large. The experimental results on the NELL-One and Wiki-One datasets show that the proposed model performs well  in predicting head and tail entities corresponding to long-tail relations in large-scale knowledge graphs, and can achieve efficient feature representation generation and missing entity completion for entities and relations in knowledge graphs.

We considered a  class of tumor-immune model, discussed the existence  conditions  of their equilibrium points, and used characteristic equations to analyze the local kinetic stability of each equilibrium point,  proving that the model underwent Hopf bifurcation under the corresponding conditions. By calculating the first Lyapunov coefficient, it can be concluded that if the coefficient is not zero, the model undergoes Hopf bifurcation,  the bifurcation is supercritical if the coefficient is less than zero, and the bifurcation is subcritical if the coefficient is greater than zero. Finally, numerical simulations are used to validate the theoretical analysis results.

For a three-dimensional T chaotic system with logarithmic term, on the basis of fractional-order stability theory, we used  differential 
method to design a more reasonable and concise sliding mode surface. The integer-order and fractional-order T chaotic systems were synchronized under the selected controller, and the MATLAB simulation program was used to verify the correctness of the method.

Aiming at the problem that the  existing HLA class Ⅰ  molecule-polypeptide binding affinity prediction algorithms rely on traditional sequence scoring functions in feature construction. In order to break through the limitations of using classical machine learning algorithms to construct  amino acid sequence features, we proposed a binding prediction algorithm ProHLAⅠ of HLA-Ⅰ and polypeptides based on protein pre-trained model ProtBert. The algorithm utilized the commonness of the composition of the living body language and the text language, compared the amino acid sequence with the sentence, and extracted the features of the HLA-Ⅰ sequence and the polypeptied sequence by integrating the network structure advantages of pre-trained model ProtBert, the BiLSTM coding and the attention mechanism, so as to realize the site\|independent polypeptide binding prediction of the HLA-Ⅰ.
The experimental results show that the model  achieves the optimal  performance on two independent test sets.

We solved the problem of low accuracy in car window recognition of the original YOLOX-S model by introducing deformable convolutional neural networks and Focal loss function (Focal loss) to the YOLOX-S model. Firstly, by introducing deformable convolutional neural networks into the backbone feature extraction network of the YOLOX-S model, offsets were introduced for each sampling point in the convolutional kernel to facilitate the extraction of more representative information from the original image, thereby improving the accuracy of car window recognition. Secondly, using Focal loss instead of binary cross entropy loss function in the original model, Focal loss could alleviate the impact of imbalance between positive and negative samples on training, and it paid  more attention to difficult samples during the training process, thereby improving the  recognition performance of the model for car window targets. Finally, in order to verify the performance of the improved algorithm, 15 627 images were collected and annotated for training and validation in the experiment. The experimental results show that the average target accuracy of the improved car window recognition algorithm increases by 3.88%.

We considered exponential attractor of Kirchhoff beam equation with linear memory and linear damping. Firstly, we gave the bounded absorbing sets in the strong-weak space by using the method of energy estimation. Secondly, we proved  the existence of exponential attractors for Kirchhoff type beam equations with linear memory term and linear damping term in weak topological space by using the method of operator decomposition.

Aiming at  the problem of few-shot relation extraction,  we proposed an induction network based on attention mechanism. Firstly, we used  dynamic routing algorithm in induction network to learn the class representation. Secondly, we proposed instance-level attention mechanism to  adjust support set and obtain high-level information between support set and query set samples, thereby obtaining  the support set samples that were more relevant to the query instances. The proposed  model effectively solved  the problem of how to extract relationships when the training data was insufficient. The experiment was conducted  on the few-shot relation extraction FewRel dataset, and the experimental results showed an  accuracy rate of (88.38±0.27)% in the 5-way 5-shot case,  (89.91±0.33)% in the 5-way 10-shot case, (77.92±0.44)% in the  10-way 5-shot case,  (81.21±0.39)% in the  10-way 10-shot case. The  experimental  results show that the model can adapt to tasks and outperforms other comparative  models, achieving better results than comparative  models in few-shot relation extraction.

We studied the asymptotic behavior of solutions for a class of  initial-boundary value problems of a semilinear parabolic equation with boundary degeneracy by using the methods of weighted energy estimates and constructing self-similar upper solutions. We obtained the global existence and blowing-up properties of solutions to the problem,  established Fujita type theorem, and characterized the quantitative relationship between the critical Fujita exponent and the degenerate diffusion term and the nonlinear source term.

By constructing the cohomologies complexes of Rota-Baxter Lie algebra homomorphisms, we discuss the formal deformation of Rota-Baxter Lie algebra homomorphisms and prove that Rota-Baxter Lie algebra homomorphism is rigid when the 2th-cohomology group of the deformation complex is zero.

Based on the knowledge graph embedding model, we proposed a scoring method combining knowledge graph embedding scoring and link scoring to solve multi-hop knowledge graph question answering task in the Chinese domain, which had wider applicability compared with the traditional single-hop knowledge question answering methods. The method constructed a query link while searching for the optimal answer, and gave the answer set by query, which effectively alleviated the situation of missing answers in existing methods. The experimental results on the NLPCC-MH dataset show that the average F₁ value of the method on multi-hop problems is 0.653, which is significantly better than the comparison method. Real knowledge graphs usually have missing links, and the experiments simulate the sparsity of knowledge graphs by randomly discarding 25% triples, the results show that the method is still effective in this case.

Let the strong product graph of path P_m and star graph S_1,n-1 be G=P_m*S_1,n-1. Firstly, by inducing assumptions and constructing internally vertex or edge disjoint paths, combined with the centrality of star graph, the vertex fault diameter D_w(G) and edge fault diameter D′_t(G) of the graph G were given. The results show that for any vertex or edge fault in the graph G, there holds D_w(G)≤d(G)+2 and D′_t(G)≤d(G)+1. Secondly, through the unequal relation between the number of vertices and the number of edges, the upper bound of the vertex fault diameter of the strong product graph of two maximally connected graphs and the 
upper bound of the edge fault diameter of the strong product graph of two nontrivial connected graph were given.

Firstly, we established a class of SEI₁I₂QR infectious disease models that included  transmission mode of asymptomatic infected individuals. Secondly, by using the next generation matrix method, we calculated the basic reproduction number of the model, performed the dynamic analysis of the model, and gave the threshold conditions for the extinction and outbreak of infectious disease. Finally, combined with  epidemic data, the sensitivity of the model parameters were analyzed through numerical simulations.

Under some conditions about corresponding principal eigenvalue of  linear operator, we prove the existence of nontrivial solutions and positive solutions of boundary value problem for the semipositive nonlinear Euler-Bernoulli beam equations with simply supported beam boundary condition by using the topological degree method and the fixed point theory.

Aiming at the problem that autoencoder  only extracted features from  the content information contained in a single data, ignoring 
the structure information of data, we proposed a deep graph clustering network based on heterogeneous fusion and discriminant loss. Firstly, the heterogeneous information obtained by two autoencoders was fused, and the problem of information loss was solved when a single autoencoder was used to extract features. Secondly, the discriminant loss function was designed in the clustering training module based on the consistency of distribution within the same cluster, so that the model could be trained end-to-end, and avoiding the mismatch between the feature extraction and the assumptions of the clustering algorithm in the two-stage training methods. Finally, experiments were carried out on six commonly used datasets to verify the effectiveness of the proposed method. The experimental results show that compared with most existing deep graph clustering models, the proposed method  significantly improves the clustering performance on both non-graph and graph datasets.

Let R S be a Frobenius extension of rings and M be an S-module. We prove that if R S is a separable Frobenius extension, then _SM is a projectively coresolved GorensteinFI_n-flat module (GorensteinFI_n-flat module) if and only if _RM is a projectively coresolved GorensteinFI_n-flat module (GorensteinFI_n-flat module).

Aiming at the problem of noise in non-continuous and non-stationary speech signals, we proposed a variational mode decomposition (VMD) denoising algorithm based on parameter optimization. Firstly, the grey wolf optimization algorithm was used to search the optimal decomposition parameter combination of the VMD algorithm: decomposition mode number K and penalty factor α. By using the combination of the obtained parameter combination to decompose the speech signal, K characteristic mode function components IMF were obtained. Secondly, the effective modal components were selected by the correlation coefficient, and the invalid modal components were processed by the wavelet threshold. Finally, the wavelet threshold processed modal component and effective modal component were reconstructed to denoise the speech signal. Experimental results show that compared with other classical algorithms, the proposed algorithm can effectively improve the signal-to-noise ratio (SNR), reduce the mean square error, and improve the quality of speech signals.

We considered the modeling problem of complex integer-valued time series data. Firstly, we  proposed a  class of first-order mixed integer-valued negative binomial autoregressive models, proved the strict stationary and ergodicity of the model, and discussed the probabilistic and statistical properties of the model such as transition probability, expectation, variance, etc. Secondly, we studied the  maximum likelihood estimation problem of the model, obtained the asymptotic normality of the estimator, and conducted empirical analysis on the basis of numerical simulations. The empirical analysis results show that the model performs well in fitting the drug offense count data.

Aiming at  the problem that the scale of relation extraction model was getting larger and larger, and the time consumption was getting longer and longer, we proposed a knowledge filtering mechanism to construct a lightweight relation extraction model by using the positive soft labels selected. Firstly, knowledge distillation was used to extract knowledge and store knowledge in soft labels. In order to avoid the problem of difficult  absorption of knowledge caused by the large gap between  teachers and  students in knowledge distillation, we used teacher assistant knowledge distillation pattern. Secondly,  the cosine similarity of labels was used to filter the positive soft labels and the positive soft labels were dynamically given  higher weight in each step of the distillation, so as to  weaken the influence caused by  the wrong labels in the knowledge transfer. The experimental results on SemEval-2010 Task 8 dataset show that the proposed  mode can not only complete the task of lightweight relation extraction, but also improve the extraction accuracy.

Firstly, by using the fractional order concentration-compactness principle, we proved the compactness conditions for a class of nonlinear Kirchhoff equations with electromagnetic fields and critical Hardy-Littlewood-Sobolev term in the whole space to overcome the problem of lack of compactness conditions caused by unbounded regions and critical term in this equation. Secondly, combined with the symmetric mountain path theorem, we proved that the equation satisfied the mountain path structure, and proved the multiplicity of the solution to the equation by using genus theory.

Aiming at the task of video action recognition, we proposed an action recognition method based on two-stream network. Firstly,
 a sparse sampling strategy was adopted to avoid the redundant information of adjacent frames from affecting the recognition effect. Secondly, the convolutional neural network was used to predict the optical flow map,  improve the acquisition efficiency of  the optical flow map and reduce the amount of calculation. Finally, the residual network was used to extract the completed video information and simplify the training process of neural networks simultaneously. In order to verify the effectiveness of the two-stream action recognition network, we carried out comparative experiments on two classical data sets. The experimental results show that the proposed two-stream action recognition network has good recognition effect and  can be applied to intelligent video surveillance, human-computer interaction, public security and other fields.

We gave some basic properties of the derivation algebra Der(A), generalized derivation algebra GDer(A), quasiderivation algebra QDer(A), centroid C(A), quasicentroid QC(A) and central derivation algebra ZDer(A) of a multiplicative BiHom-Poisson color algebras A, and proved that GDer(A)=QDer(A)+QC(A).

By using structural analysis method, we completely characterized the neighbor full sum distinguishing total coloring of unicyclic graph U, and obtained that ftndi_Σ(U)=Δ(U)+2 when U=C_n and n=0(mod 3),  ftndi_Σ(U)=Δ(U)+1 in other cases. This result  shows that the neighbor full sum distinguishing total coloring conjecture  holds on any unicyclic graph.

Aiming at the problem of  the small sample size of high-resolution remote sensing images and  traditional optimized support vector machine (SVM) algorithms easily falling into local optima and slow optimization speed, we  proposed an algorithm based on deep transfer learning and lion swarm optimization SVM (LSO-SVM) to classify remote sensing image scene. Firstly, after enhancing the image through adaptive contrast,  color aggregation vectors were used to extract image color features. Secondly, three kinds of pretrained networks were used to extract the transfer learning depth features of images. Finally, the manually extracted image features and the features obtained using three pretrained networks were fused by using a series of feature fusion methods, and inputted them into LSO-SVM for image scene classification. The results show that the algorithm solves the problems of difficulty in deep learning training in small sample situations and the tendency of traditional optimized SVM algorithms to fall into local optima and slow search speed. Under 80% training conditions, the classification accuracy of UCM Land-Use and RSSCN7 datasets reaches 99.52% and 98.57%, respectively.

We proposed a new nonmonotonic adaptive accelerated Levenberg-Marquardt algorithm for solving nonlinear equations. The algorithm used a new adaptive function to update the Levenberg-Marquardt parameter, which could enhance the consistency between the model and objective function during too-successful iterations, thereby accelerating the convergence rate of the algorithm. Numerical experimental results show that the proposed algorithm has good numerical computational performance.

We used the physics-informed neural networks method to numerically solve the problem of discontinuous coefficient light wave diffraction. The results show that approximating the discontinuous coefficient with a smooth function can significantly improve the accuracy of the physics-informed neural network solution. Using physics-informed neural networks to solve the scattered field is better than directly solving the total field. Finally, the correctness of the theoretical results is verified through numerical experiments.

Aiming at the problem that it was difficult to eliminate tetracycline in wastewater and achieve water quality purification through self-purification of the environment, we developed and designed a  new type of sewage treatment agents. A novel metal-organic framework (MOF) material [Mn₂(TCPQ)(H₂O)₈]·xsolvent.  was synthesized by 4，4′，4″，4′′′-(quinoxalin-2,3,6,7-tetrayl)tetrabenzoic acid as the organic ligand and Mn(Ⅱ) as the metal center ion. The structure and stability of the material were studied by using powder X-ray diffraction,  X\|ray single crystal diffraction, Fourier transform infrared spectroscopy and thermogravimetry,  and its photocatalytic performance was analyzed. The experimental results show that the degradation rate of tetracycline by the prepared MOFs material can reach 97.5% when exposed to visible light for 30 min. The compound can be used as an excellent  material for the degradation of tetracycline.

By applying mathematics induction and combinatorial analysis, we gave D(2)-vertex-distinguishing total colorings of cactus graphs G_T with maximum degree of 3, and then obtained χ_2vt(G_T)≤6. The result shows that D(β)-VDTC conjecture holds for cactus graphs with maximum degree of 3.

We studied the robust control problem of three-dimensional Coullet system. Firstly, the complex dynamic behavior of the system was verified by drawing the time domain waveform, chaotic attractor and Lyapunov exponent diagram of the system. Secondly, the sliding mode control method, the sliding mode based high frequency robust control method and the high gain robust control method were used to design the controller and control the system. Finally, the effectiveness of the controller was verified by numerical simulation.

We considered a class of fourth-order thin-film equation with singular term and logarithmic source. Firstly, we obtained the local existence of weak solutions to the equation by  combining truncation function and  Galerkin approximation. Secondly, by virtue of the potential well method and Rellich inequality, we proved the global existence and decay estimate of weak solution to the equation under certain conditions. Finally, we proved the blow-up result of the  solution to the equation at a finite time by using the convex method, and gave the lower and upper bounds for blow-up time.

Aiming at  the problems of blurred details, large computer resource occupation, and slow image processing for the existing image deblurring algorithms, we proposd a lightweight image blind deblurring network. Firstly, the main framework of the network used a multi-scale architecture to input images of different resolutions into the network, and gradually optimized the datails through cyclic processing.  Secondly, the asymmetric structure was designed to enhance the feature extraction ability of the encoder and the feature fusion ability of decoder. In the encoder, the mixed multi-scale convolutional layer and residual pyramid module were proposed to enhance feature extraction and  reduce the number of network parameters. In the decoder stage, deep semantics were introduced  by using jump linkage, and the multi-scale joint structure  loss function was proposed for optimization. Finally, we used two evaluation indicators to compare the performance of the method with the other classical methods on two widely used 
 GoPro and Kohler datasets. The experimental results show that the effect of the network  is better than that of the traditional methods and other classical deep learning mehtods. It not only improves the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM), but also shortens the processing time.

By using the definition and properties of the coherence measure, we studied the state ordering of the pure state and the mixed state respectively in a single quantum system, and gave the state ordering results between C_max,C_vmax and C_r,C_I,C_l1 The results show that C_r,C_Ι, and C_H provide the same state ordering for pure states, but this state ordering result is not formed for mixed states. Unlike entanglement measures, the order relationship between two coherence measures in a pure state may not necessarily have the same result for any state.

Aiming at the problem that  the traditional object detection had poor feature extraction ability and low recognition rate for small targets, we proposed an improved object detection algorithm based on YOLOv4, which used the attention improved adaptive spatial feature fusion (AIASFF) strategy to generate a pyramid feature representation, and solved the challenges brought by changes in object detection scale. Through this new data-driven pyramid feature fusion strategy, the accuracy of medium and large targets was improved without affecting small target recognition. It combined attention learning image features with extracted features to improve the accuracy of feature detection. The new loss function was combined with the adaptive spatial feature fusion strategy and the exponential moving average,  the simulation results of multiple experiments on the MS COCO dataset based on YOLOv4 show that the algorithm achieves the best compromise between speed and accuracy. For the MS COCO dataset, mAP reaches 41.5% and AP₅₀ reaches 63.8%, which is 1.1% higher than the original algorithm. The improved algorithm has high robustness to MS COCO dataset, thereby  effectively improving the detection and recognition rate of the targets.

 A Ti/CoWO₄ photoanode with excellent semiconductor properties was prepared on a titanium substrate by using a one-step hydrothermal method. The number of CoWO₄ nanospheres attached to the substrate surface could be easily adjusted by changing the hydrothermal time,  where Ti/CoWO₄-6 h had a larger active area,  higher charge transfer ability and higher  intermediate active species (free radicals) generation efficiency. The materials were characterized by ultraviolet-visible spectroscopy (UV-Vis) and scanning electron microscopy (SEM) to investigate the photoelectrocatalytic (PEC) degradation activity of Ti/CoWO₄ photoanodes on reactive brilliant blue (KN-R). The results show that under PEC conditions, the decolorization rate of KN-R (60 mg/L) by Ti/CoWO₄-6 h  can reach 84.97%,  and the degradation rate can still reach 74.91% after 5 cycles.

Aiming at the problem of unstable clustering results and low solving accuracy of  I-k-means-+ algorithm, we proposed I-k-means-+ clustering algorithm based on min-max criterion and region division. Firstly, the min-max criterion was proposed to calculate the distance from each data point to the nearest center, and the data point with the largest distance was preferentially selected as the new clustering center to avoid multiple initial centers gathering in the same cluster. Secondly, the data points in the split cluster were divided into different regions, and a data point was selected as the candidate center in each region to increase the diversity of the candidate center. Finally, for the clusters that failed to pair, the new split cluster was re-selected by gain to pair with the original deleted cluster again, so as to improve the pairing success rate and further reduce the objective function value. The experimental results show that compared with the I-k-means-+ algorithm, the proposed algorithm improves the accuracy of the solution by 6.47% on average while maintaining similar operational efficiency, and the clustering results are more stable. Compared with k-means and k-means++ algorithms, the proposed algorithm has higher solving accuracy.

Based on the process theory in time-dependent space, we considered the long-time dynamic behavior of the solution for the non-damping suspension bridge equation with fading memory. Firstly, we obtained well-posedness of solution by using Faedo-Galerkin approximation method. Secondly, the non-autonomous dynamical system had pullback absorb set in the corresponding solution space was obtained by using energy estimation. Finally,  we proved the existence of time-dependent pullback attractors by using  the  contraction function method and cocyclic technique.

Aiming at the problem that the deep embedding clustering method only considerd the intra-class relationship and multi-view clust
ering had insufficient feature representation, we proposed a deep embedding clustering method based on inter-class loss and multi-view fusion. The method introduced a new regularization term into the loss function of deep embedding clustering to improve the class discrimination. Firstly, the feature representations of multi-view data were extracted by the auto-encoder, and the feature representations of different views were fused to obtain the public representation. Based on this, the soft allocation distribution and auxiliary target distribution of data were obtained. Secondly, the final clustering result was obtained by jointly optimizing the public representation and cluster allocation. The experimental results on multi-view datasets show that this method can effectively improve the clustering performance.

Let G=G(A,M,N,B) be a generalized matrix algebra, and a:G→G be a map (without the assumption of additivity). Using the  method of algebraic decomposition, we proved that if  a(XY)=a(X)Y+Xa(Y) held for any X,Y∈G and  at least one of X  and Y was idempotent, then a was an additive derivation on G.

We considered a class of sum of squares (SOS) convex polynomial optimization problems with spectrahedral uncertainty data in both objective and constraint functions. Firstly, an alternative theorem for SOS-convex polynomial system with uncertain data was established in terms of SOS conditions. Secondly, we introduced a SOS relaxation dual problem for this SOS polynomial optimization problem and characterized the robust weak and strong duality properties between them. Finally, a numerical example was used to demonstrate that the SOS relaxation dual problem could be reformulated as a semidefinite  programming problem.

Let (X,d,μ) be a non-homogeneous metric measure space which satisfies the upper doubling and geometrically doubling conditions, and T_α be the generalized fractional integral operator on (X,d,μ). By establishing pointwise inequality of sharp maximum function, we obtain that T_α is bounded from the weighted Lebesgue space L^p(ω) to the weighted weak Lebesgue space WL^p,κ,η(ω), and also from the weighted Morrey space L^p,κ,η(ω) to the weighted weak Morrey space WL^p,κ,η(ω).

Aiming at the problem that the operating pH range of  the conventional Fenton technique was relatively narrow，   increasing  pH  value significantly reduced the removal rate of tetracycline and led to secondary contaminztion,  Fe₃O₄@CF composite electrode was synthesized by loading Fe₃O₄ onto the surface of carbon felt (CF) electrode by using a solvent thermal synthesis method. The materials were characterised by scanning electron microscopy (SEM),  X-ray diffraction (XRD),  X-ray photoelectron spectroscopy (XPS),  Fourier transform infrared absorption spectroscopy (FTIR) and electrochemical impedance (EIS).  We investigated the degradation performance and mechanism of  tetracycline using it as electrode in a non-homogeneous electrically assisted Fenton (EF) system, and conducted cyclic experiments.  The results show that the Fe₃O₄ electrode exhibits the best degradation performance of tetracycline in a non-homogeneous electrically assisted Fenton system.  After 90 min at room temperature,  the initial mass   concentration of tetracycline is 20 mg/L,  an initial pH=3,  a distance between the two electrodes is 2 cm, and an applied current is 50 mA,  the removal rate of tetracycline by Fe₃O₄@CF electrode in the non-homogeneous electro-Fenton system can reach 96.7%. In addition,   the Fe₃O₄@CF electrode has good reusability. In the degradation of tetracycline in the non-homogeneous electro-Fenton system,  ^.OH plays a major role and  ^.O^-₂ plays an auxiliary role.

Aiming at  the problem that when the semantics of the input text were relatively complex, traditional end-to-end models generated questions with incomplete semantics,  we proposed a text encoder architecture based on semantic feature extraction. Firstly, we constructed bidirectional long short-term memory network to obtain  basic contextual information. Secondly,  self-attention mechanism was used to extract global features of semantics and bidirectional convolutional neural network model was used to extract local features of semantics respectively. Finally, we designed a hierarchical structure to merge the features and input their own information  to obtain the final text representation for question generation. Experimental results on the SQuAD dataset show that the question generation based on semantic feature extraction and hierarchical structure are significantly effective, and the results are better than the existing methods. Moreover, semantic feature extraction and hierarchical structure are improved  in each evaluation index of the task.

In order to effectively solve large-scale numerical calculation  problems, make full use of machine resources and improve computational efficiency, based on the linear element finite volume scheme, we proposed a parallel scheme suitable for computing on multi-core machines or parallel systems on triangular meshes by domain decomposition method. The results of numerical experiments show that the scheme can not only achieve the best convergence speed, but also have good parallel efficiency on various distorted meshes.

By using  variational methods and corresponding critical points theorems, we investigated a class of nonlocal elliptic equations Navier boundary value problems with p-biharmonic operators. We obtained two existence theorems for nontrivial generalized solutions 
 when nonlinear terms satisfied super-linear conditions.

Aiming at the problems existing in few-shot learning at present, we designed a new network structure and its training method to improve the few-shot learning. The  convolution network and multi-scale slide pooling method were used to enhance feature extraction in the feature embedding part of the network. The main structure  of the networks was the Siamese network  to facilitate learning semantics from small sample data through comparison between samples. The training method  of the framework adopted nested level parameter updating to ensure the stability of convergence. Compared with the common visual model and 
few-shot learning methods, the experimental results  on two classical few-shot learning datasets show that the method significantly improves the  accuracy of  few-shot learning, and  can be used as a solution  under the condition of insufficient sample.

Aiming at the problems of the limitations of  data sparsity and “cold start” on collaborative filtering and the inapplicability of the existing collaborative multi-armed Bandit algorithm to nonlinear reward functions, we proposed a neural Bandit recommendation algorithm COEENet, which combined collaborative filtering. Firstly, it adopted a dual neural network structure to learn expected  rewards and  potential gains. Secondly, we considered the collaborative effect of neighbors. Finally, a decision-maker was constructed to make the final decision. The experimental results show that the proposed method is superior to the four baseline algorithms in cumulative regret, and has a good recommendation effect.

We studied crushing performance and its analytical formula of the 3D printed Kagome honeycomb thin-walled stiffened structure, which was made of acrylonitrile butadiene styrene (ABS) plastics, and verified the crushing performance of isotropic Kagome honeycombs through experiments. According to the effective elastic modulus formula of orthogonally anisotropic Kagome honeycomb with plane structure, we gave the relationship among elastic modulus, relative density and shape anisotropy ratio of 3D printed Kagome honeycomb structure. Through analytical formulas and experimental results, we obtained the Kagome honeycomb structure with the best crushing performance. The method could be used to guide the design and processing of the stiffened structure of the rocket body.

Aiming at the problems of detail loss, color distortion and contrast reduction during image acquisition in foggy environments, we proposed an image dehazing algorithm based on attention feature fusion. Firstly, the algorithm adopted the principle of attention mechanism to design a feature fusion module that  combined channel attention and pixel attention. By using  the characteristics of different channel feature weighting information and uneven distribution of haze in different pixels,  different weights were assigned to the feature map according to the importance of the feature map, which solved the problems of fog residue and color distortion in the traditional  algorithms. Secondly, the enhancement strategy of “strength-operation-subtract” was added to the decoder of the network to solve the problem of image detail loss after dehazing. Finally,  in order to restore the image quality better,   the hybrid loss function was used to  train the network parameters. The experimental results show that the PSNR value of the proposed algorithm is improved by 1.88 dB compared with the comparison algorithm on the public  RESIDE dataset.

We considered the lower bound of VC (Vapnik-Chervonenkis) dimension for concept classes induced by general Bayesian networks where each random variable took any finite values. By analyzing the relationship between the number of parameters that could be freely set in a network and the corresponding VC dimension, we proved that adding 1 to the number of parameters that could be freely set in any discrete non-full Bayesian network was a lower bound of corresponding VC dimension.

We considered the effect of starvation-driven diffusion on the coexistence of a Holling-Ⅱ type predator-prey model under homogeneous Neumann boundary conditions. The eigenvalue theory was used to analyze the stability of semi-trivial solution under uniform diffusion and starvation-driven diffusion. By comparing the stability changes of semi-trivial solutions under two kinds of diffusion, we find that starvation-driven diffusion is conducive to the coexistence of species.

We considered  integral boundary value problem of a class of Riemann-Liouville fractional differential equations with multiple fractional derivative terms on infinite intervals. By constructing a new Banach space and using the nonlinear analysis theory, and under the condition that the nonlinear term satisfied the L¹-Carathéodory conditions, some conclusions  for existence and uniqueness of positive solutions to boundary value problems were obtained, and an example was used to illustrate the applicability and universality of the obtained results.

We considered the steady-state solutions of a B-D type predator-prey system with nonlinear cross-diffusion under homogeneous Dirichlet boundary conditions. Firstly, we analyzed the stability of trivial solution and semi-trivial solutions based on the spectral theory of linear operators. Secondly, the sufficient conditions for the existence of coexistence solutions were obtained by using the fixed point index theory in positive cones.

We used the extended Dirichlet-to-Neumann (DtN) map method to calculate the bandgap structures of two-dimensional gyroelectirc photonic crystals in terahertz band. Because the DtN map method only needed to discretize on the boundaries of the cell lattice and avoided discretization in its interior, so the number of discretization points was reduced, which made the calculation much faster. Firstly, the DtN map of a unit cell of gyroelectirc photonic crystals was constructed. Secondly, the bandgap structrue of photonic crystal was transformed into the eigenvalue problem of matrix. Finally, numerical simulation verified the effectiveness of using DtN map method to calculate the bandgap structure of gyroelectric photonic crystals.

The full parabolic attraction-repulsion chemotaxis system defined on Ω was considered. By setting appropriate an auxiliary function and using the differential inequality technique, the differential inequality of the auxiliary function was derived, and the lower bound of the blow-up time was obtained.

The author considered a class of delayed predator-prey model with fear effect. Firstly, by using the characteristic equation and Lyapunov-LaSalle invariance principle, the global asymptotic stability of the boundary equilibrium was proved when R(τ)≤1. Secondly, by using the Hopf bifurcation theory of delay differential equation, the author discussed the stability of the coexistence equilibrium point and the existence of the global Hopf bifurcation when R(τ)>1, and obtained the results that fear effect and delay affected the stability of the system. Finally, the correctness of the theoretical results was verified by numerical simulations.

Aiming at the problems of scene details being covered up and image information being difficult to obtain in non-uniform illumination images, we proposed a non-uniform illumination image enhancement method based on simulated exposure fusion. Firstly, an improved adaptive Gamma correction algorithm was used in HSV color space to process the brightness component  as a medium exposure image. Secondly, the over-exposure pixel set was divided by dynamic threshold for the brightness component, and the simulated over-exposure image was synthesized by using maximum information entropy estimation and camera response model. Thirdly, the improved quality measurement method and the weight optimization method based on the guided filtering were used to obtain the fused image for the multi-exposure image sequences composed of the original images, the medium-exposure images and the over-exposure images.  Finally, the fusion result was processed by multi-scale detail enhancement to obtain the final image enhancement result. The experimental results show that the proposed algorithm can effectively improve the visual effect of non-uniform illumination images. The comparison of subjective and objective evaluation data shows that the proposed algorithm is superior to similar algorithms.

Aiming at the problem that  identifying  essential proteins in  biological experiments was time-consuming and laborious, and using
 computational methods to predict essential proteins could not effectively  integrate biological information,  we proposed  a deep learning framework. Firstly, a weighted protein interaction network was constructed by using network topology structure, gene expression data and gene ontology (GO) annotated data. Secondly, feature vectors were extracted from subcellular localization data, protein complex data and gene expression data by using feature graph network and bi-directional long short-term memory cells, respectively. Finally,  these feature vectors were input into the task learning layer to predict essential proteins. The experimental results show that, compared with  existing computational methods, the proposed method has better predictive performance.

Aiming at  the problems of missing data and small number of features in landslide disaster prediction around natural gas pipelines, 
the gradient boosting decision tree algorithm based on LightGBM framework was adopted to  supplement missing data by interpolation,  and short-term and long-term features were  generated by using the historical feature data to obtain the importance ranking of various factors affecting the slope evolution process and the optimal parameter set of the algorithm, so as to realize the effective prediction of landslide disasters around natural gas pipelines. The results show that  this method has higher accuracy and faster processing speed than XGBoost model  in the prediction of landslide disasters around the pipeline, which proves that LightGBM algorithm is feasible and effective in landslide disaster prediction.

We discuss  the existence of positive 2π-periodic solutions of the second-order ordinary differential equation with nonlinear derivative term by using positive operator perturbation method and fixed point index theory in cones. Under certain inequality conditions of the 
nonlinear term f(t,x,y), we obtain the existence of positive 2π-periodic solutions of the equation.

We designed and synthesized an inorganic-organic hybrid complex based on Keggin-type polyacids,  and obtained [SiW₁₂O₄₀][Ag(bpy)₂]₄·H₂O (1)(bpy=2,2′-bipyridine)  by using  hydrothermal in situ synthesis method. The bpy in complex 1 was obtained by in situ decarboxylation of 2,2′-bipyridine-6,6′-dicarboxylic acid. The structure of complex was characterized  by single crystal X-ray diffraction,  elemental analysis,  infrared spectrum and thermogravimetric analysis, and its   fluorescence,  photocatalytic degradation of organic dyes,  electrochemical and antibacterial properties were  studied.

Based on the polynomial feature generation method for one-dimensional feature data, we proposed a data augmentation algorithm that used the polynomial feature generation method to generate feature data for high-dimensional feature data. At the same time, we proposed an  algorithm  that combined the generated polynomial feature data with the neural network model during convolutional neural network training, which could organically combine the  generated polynomial feature data with the convolutional neural network model, and  improve the low recognition accuracy  and the limited generalization performance of model caused by data limitations such as limited data samples, fixed total number of data samples, and differences in available data samples  when modeling convolutional neural network models. Experimental results show that the accuracy of the convolutional neural network model using this method achieves significant improvement.

Based on the microbial degradation mechanism of petroleum contaminated groundwater and the characteristics of low temperature,  low oxygen,  and oligotrophic environments in a certain petroleum contaminated groundwater in Northeast China, we collected  petroleum contaminated groundwater and  studied the efficiency of  indigenous bacteria  degrading petroleum hydrocarbons in petroleum contaminated groundwater stimulated by microbial small molecule substances. The  results show that when petroleum hydrocarbons are used as the sole carbon source and biological small molecule substances such as amino acids and organic phosphorus sources are added to the inorganic salt based nutrient solution,   amino acid substances inhibit the degradation of petroleum hydrocarbons by indigenous bacteria,  with inhibitory ability of glycine (-20.49%)>glutamic acid (-7.81%)>alanine (-4.88%). Organic phosphate lipids promote the degradation of petroleum hydrocarbons by indigenous bacteria,  with promoting ability of lecithin (7.91%)>disodium glycerophosphate (7.01%)>triethyl phosphate (0.03%). Further supplementing biological small molecule carbon sources can improve the degradation efficiency of indigenous bacteria,  with the enhancement ability of sucrose (8.03%)>glucose (6.01%)>maltose (2.91%). Adding inorganic salts,  lecithin,  and sucrose to groundwater with an initial mass concentration   of 10 mg/L of petroleum hydrocarbon， after 7 d of stimulation,  the degradation rate can be increased to 77.26% due to the  stimulation of  biological small molecule substances. Combined with 16SrRNA amplicon sequencing,  high-throughput sequencing is performed on indigenous bacteria before and after the stimulation,  demonstrating that  there is a positive correlation between the abundance of dominant petroleum hydrocarbon genera and the expression of functional genes when biological small molecules promote the synergistic metabolism and degradation of petroleum hydrocarbons by indigenous bacterial communities.

Aiming at the problem that traditional algorithms were not suitable for image mosaic with large changes in appearance, we  proposed a remote sensing image mosaic method based on convolutional neural network, which enabled the model to realize the registration and mosaic of remote sensing images through deep learning. The algorithm was compared with the traditional algorithms through two experiments. Firstly, the Euclidean distance was used as the evaluation indicator, and statistics of two methods were performed on different remote sensing image data sets to evaluate their image registration abilities. Secondly, effects of remote sensing image mosaic realized by two algorithms in the real remote sensing image mosaic application scene were compared. The experimental results show that the convolutional neural network model has a better registration ability for images with large external deformations. Therefore, for the remote sensing images with large changes in appearance, the proposed algorithm can be used to replace the traditional algorithm to realize image mosaic and obtain a more accurate panoramic image.

Aiming at the problem that the attention mechanism-based model ignored the  part-of-speech information of words in the aspect-level sentiment classification task, we proposed  an aspect-level sentiment classification method that incorporated a part-of-speech self-attention  mechanism. Firstly, the method  was based on the natural language processing part-of-speech tagging tool to obtain part-of-speech tagging sequence, and randomly initialized a part-of-speech embedding matrix to obtain part-of-speech embedding vector. Secondly,  the self-attention mechanism was used to learn the syntactic dependence between words. Finally the sentiment score of each word was calculated, the combination of word sentiment was used to express the polarity of sentiment in specific aspects.  The experimental results show that compared with baseline model with the best performance in 5 public datasets, this method improves the accuracy and macro F₁ score by 2% and 4.83% respectively, indicating  that the attention mechanism model incorporating part-of-speech information has better performance in aspect-level sentiment classification task.

We designed a wearable wireless plantar pressure acquisition system and proposed a method for determining the stable state of the human body based on the center of pressure (CoP) of the human body. Firstly, the system was used to collect the plantar pressure data in the stable and critical instability states when the human body was standing and walking. Secondly, the area and boundary of the movement locus of the center of pressure in the stable walking state of the human body were obtained through the plantar pressure information. Finally, the CoP at the current moment was collected, and by comparing the trajectory area and boundary range of the CoP at the current moment with the maximum stable CoP of the human body, the stable state judgment of the human walking process was achieved. The results show that the designed wearable wireless plantar pressure acquisition system is wearable and convenient for measuring human plantar pressure data. The experimental verification shows that the human body steady state judgment method based on plantar pressure acquisition system and center of pressure is effective.

Aiming at the problem that the existing sequence recommendation model ignored the users’ long-term preference and short-term preference, resulting in the recommendation model not being able to  fully play its role and the recommendation effect being poor, we proposed a personalized recommendation model based on the users’ long- and short-term preferences. Firstly, for the characteristics of long and discontinuous long-term preference sequences, BERT （bidirectional encoder representations from transformers） was used to model the long-term preference, for the short-term preference sequences and the short interval time between interaction with the user, which was volatile, vertical and horizontal convolutional networks were used to model the short-term preference, after obtaining the users’ long-term preference and short-term preference, activation functions were used to model dynamically, and then a gated recurrent network was used to balance the long- and short-term preferences. Secondly, for the users’ mis-touching behavior in daily interaction, sparse attention network was used for modeling, and sparse attention network was used to process the users’ behavioral sequences before modeling the long- and short-term preferences. User feature preferences also had an impact on the recommendation results, and user features were extracted by using a multi-head attention mechanism with bias coding. Finally, the results obtained from each part were input into the fully connected layer to obtain the final output result. In order to verify the feasibility of the proposed model, experiments were conducted on Yelp and MovieLens-1M datasets, and the results show that the proposed model outperforms other baseline models.

We considered the coexistence solution problem of a class of Lotka-Volterra competitive systems with nonlinear cross-diffusion under homogeneous Dirichlet boundary conditions. Firstly, the stability of trivial solutions and semi-trivial solutions of the problem was analyzed by using spectral theory of linear operators. Secondly,  sufficient conditions for the existence of coexistence solutions of the problem were given by using the fixed point index theory on positive cone.

Aiming at the problem that existing methods could not fully capture the intrinsic structure of data without considering the higher-order neighborhood information of the data, we proposed an unsupervised feature selection algorithm based on graph filtering and self-representation. Firstly, a higher-order graph filter was applied to the data to obtain its smooth representation, and a regularizer was designed to combine the higher-order graph information for the self-representation matrix learning to capture the intrinsic structure of the data. Secondly, l_2,1 norm was used to reconstruct the error term and feature selection matrix to enhance the 
robustness and row sparsity of the model to select the discriminant features. Finally, an iterative algorithm was applied to effectively solve the proposed objective function and simulation experiments were carried out to verify the effectiveness of the proposed algorithm.

Aiming at the problems of yellowish tones, lack of color richness and low clarity of sand dust images acquired by outdoor imaging devices, we  proposesd a sand dust image clarity algorithm based on improved dark channel prior. For the problem of image color bias, firstly, we  improved the Gaussian model by adopting the adaptive normalization method  to adjust dark pixels of the image, and weighted fusion of a color correction method based on the gray world   to remove the color bias effect. Secondly,  the multi-scale retinal enhancement algorithm with color restoration was used for color restoration,  for the fog effect existing after processing, the atmospheric light value was re-selected and the dark pixels were compensated for brightness using the dark channel-based prior method. Finally, for the problems of insufficient image saturation and low contrast, the images were mapped  to HSI space and enhanced using the adaptive adjustment function and improved dual Gamma correction algorithm, respectively. The experimental results show that the method can not only effectively correct the color bias and better improve the image contrast and clarity, but also has a significant  effect on the image color richness enhancement, which can  improve the image quality of outdoor imaging equipment.

We studied the existence of the global smooth solutions for degenerate Gourset problem of a class of hyperbolic conversation law systems. Firstly, we introduced  characteristic angles α,β, and established characteristic decompositions for α,β and pressure 
P. Secondly, the characteristic decompositions of  α,β were used to obtain the invariant region, and then the maximum norm estimate of the characteristic angles were obtained. Finally, the gradient estimates of the solution were established by the characteristic decomposition of pressure P and continuity method, which proved the existence of the solutions to the degenerate Gourset problem.

Aiming at the problems of non-uniform experimental platforms and heterogeneous datasets faced in the field of vulnerability dete
ction, we  studied  the application of word vector models in C/C++ function vulnerability detection. Five word vector models were used for the knowledge representation of the abstract syntax tree structure generated by the source code, and six neural network models were used for vulnerability detection. The experimental results show that function-level code has shallow semantic relationships and tight connections within code blocks.

We proposed a recursive dichotomy algorithm to solve the graph partitioning problem with vertex weight constraint. Firstly, the interior point method was used to solve the semidefinite programming relaxation model without vertex weight constraint. Secondly, the initial feasible solution satisfying the vertex weight constraint was obtained by hyperplane rounding algorithm. Thirdly, the heuristic algorithm was further designed to locally improve the initial feasible partition to obtain the optimal partition result. The experimental results show that the proposed algorithm can obtain the high quality solution to the multi-constraint graph partitioning problem in a short time.

We considered the American put option pricing problem under Black-Scholes model. Firstly, based on the Black-Scholes model, we designed a neural network algorithm for the model, and gave the numerical approximation of the American option price. Secondly, the effectiveness of the algorithm was proved by comparing with the traditional binomial tree method.

Aiming at the problem of mixed noise in hyperspectral images, we proposd a method based on subspace representation and weighted low-rank tensor regularization to remove mixed noise from hyperspectral images. The subspace representation used the correlation between spectral bands to select an appropriate orthogonal matrix and project the hyperspectral image into a low-dimensional subspace, so that  the proposed algorithm had lower complexity and simplified the denoising process while  removing part of the noise in the image. The denoising process was based on the low-rank tensor extracted from the simplified image. The regularization term of the weighted low-rank tensor was introduced to represent the prior information of the simplified image subspace. A reasonable weighting mechanism was constructed based on the physical meaning of the nuclear norm in the Tucker decomposition, and the intrinsic structural correlation of the hyperspectral image was preserved. We designed  a method based on  iterative minimization to solve the proposed non-convex denoising model. The experimental results on simulated and real datasets show that the proposed subspace representation and weighted low-rank tensor regularization method achieve high denoising performance in both quantitative and qualitative analysis.

Aiming at the problems of low accuracy, under-detection, and missed detection in the vehicle target detection algorithm at traffic intersections, we proposed a target recognition algorithm of traffic intersection based on improved YOLOv7.  Firstly, the algorithm  used the feed-forward convolutional attention mechanism CBAM to enhance the network’s  attention to key features from both channel attention and spatial attention, improve the network’s running  speed, and optimize the network’s feature extraction capabilities. Secondly, a new learning module was formed by connecting the  spatial layer to depth  layers to form a  full-dimensional dynamic convolution, which improved the YOLOv7 feature learning method and enhanced the feature expression ability. Finally, the experiments were conducted on the actual collected traffic intersection dataset. The experimental results show that the proposed method  achieves an average accuracy of 96.1% on the corresponding dataset, and the training time is reduced to 16.71 h. Therefore, it has obvious recognition advantages  for small target detection at traffic intersections.

We considered the optimal control problem for a class of intraspecific competition with parabolic systems under Neumann boundary conditions. Firstly, we discussed  the competition relationships within the population and the interactions between the populations in the system, and defined the objective functional as the  profit obtained from harvesting. Secondly, we proved  the necessary condition for the existence of the optimal control in the system, and gave an expression for  the optimal contorl.

The structural problem of simple weight modules with a one-dimensional weight space in the quantum Loop algebra U_q(L(sl₂)) was solved by using a construction method, and it was obtained that any simple weight module with a one-dimensional weight space must be  isomorphic to one of the four classes of simple weight modules of U_q(L(sl₂)). In addition, a class of simple weight modules of  the quantum Loop algebra U_q(L(sl₂)) with  weight space dimension of 2, which was neither the highest weight nor the lowest weight, was constructed.

Aiming at the problem that MinMax k-means algorithm was easy to generate empty solutions, slow convergence speed and low computational efficiency, we proposed an incremental MinMax k-means clustering algorithm. The algorithm started from a given initial clustering number, and generated new cluster centers by increasing a fixed step length. The fast dividing method based on data balance was used to generate incremental cluster centers, so as to avoid the large amount of calculation problem caused by traversing data and too many running times of k-means clustering algorithm in traditional incremental clustering center selection. Compared with MinMax k-means and related algorithms, the experimental results show that the algorithm is superior to the comparison algorithm in calculation efficiency and accuracy, and effectively improves the sensitivity of MinMax k-means clustering to initialization center and easy to generate empty solutions.

Advanced oxidation technology based on persulfate had important potential value in treating antibiotic pollution. We  used MnSO₄,  MnCl₂  and Mn(NO₃)₂ as raw materials to prepare three kinds of MnO₂ by hydrothermal method. The prepared MnO₂ was characterized by an X-ray diffractometer (XRD),  scanning electron microscope (SEM)  and X-ray photoelectron spectroscopy (XPS). The effects of three kinds of MnO₂  catalysts on the removal of tetracycline (TC)  by peroxymonosulfate (PMS) were compared and analyzed, and  the catalytic mechanism was studied by quenching experiments. The results show that the MnO₂ prepared by MnSO₄ has a nanorod structure and the best catalytic effect on PMS. The removal rate of 50 mg/L TC is 56.8% within 60 min. There is an Mn(Ⅳ)/Mn(Ⅲ) cycle in the catalytic process,  and SO^-₄.,  .OH,  and ¹O₂ all contribute to the removal of TC. The MnO₂/PMS system has a high removal rate for  tetracycline when   pH>7,  10 mmol/L NO^-₃ and Cl^- have no affect on the  degradation efficiency of TC,  and 10 mmol/L HCO^-₃  can promote the  degradation of TC. The order of removal  of three tetracycline antibiotics by this method is  chlortetracycline>TC>oxytetracycline，  which  can be used for the treatment of antibiotic pollution.

We proposed a scheme of injecting chaotic laser into semiconductor ring lasers (SRL) to otain the time delay signature (TDS) of chaotic laser and increase its bandwidth. In this scheme, the master lasers was a distributed feedback semiconductor lasers with double phase modulation optical feedback in the outer cavity, and chaotic laser output was simultaneously injected into both clockwise and counterclockwise modes of the SRL, thus forming a SRL system with dual modes optical injection from external chaos light （SRL-DMOIECL）. We numerically studied the influence of parameters such as external light injection coefficient and feedback coefficient on the TDS of the output chaotic laser of the system. The maximum value of the time delay signature peak in the autocorrelation function curve was used to represent the time delay signature value. The suppression effect of this system on TDS was compared with that of the SRL system with single mode optical injection from external chaos light (SRL-SMOIECL), and the bandwidth of chaotic laser from the system was studied. The results show that the scheme has a better suppression effect on TDS, which  can effectively suppress the TDS of the output chaotic laser and increase its bandwidth, the maximum 3 dB bandwidth can reach 19 GHz.

Firstly, aiming at the uncertainty problem of electromagnetic pulse vulnerability assessment of engine system under the background of limited test data and incomplete information,  we proposed  a grey Bayesian network model  to improve the processing ability of Bayesian network for  uncertain information by introducing the interval grey number in grey system theory  to characterize the uncertainty of components sensitivity threshold and fault logic relationship of engine system. Secondly, taking wideband high power microwave as an example, the interval gray number failure probability of engine system and the interval gray
 number posterior failure probability of sensor were calculated. The former represented the survivability of the whole engine system under the action of strong electromagnetic pulse, and the latter reflected the vulnerable sequence of each sensor under the failure condition of the engine system. The evaluation conclusions could  provide reference for electromagnetic protection design of vehicles.

In order to grasp the phase transformation mechanical behaviour of shape memory alloy beam with variable cross section during bending deformation, based on the bending deformation theory, the non-linear control equations of shape memory alloy beam with variable cross section was derived by combined with constitutive relationship of shape memory alloy,  the phase transformation process of variable cross section beam was analysed by using a step-by-step method,  the effects of mechanical load, the tension-compression asymmetry coefficient and the variable cross section coefficients on neutral axis displacement, 
curvature and phase boundary were studied and compared them with the finite element results. The results show that the effect of the variable cross section coefficient on the phase boundary and curvature is more obvious, the larger its value, the smaller the maximum value of neutral axis displacement, and the position of each phase boundary is further away from the section edge. The effects of the tension-compression asymmetry coefficient on the maximum displacement of the neutral axis is greater than that of load and variable cross section coefficient, but it has the smallest effect on the position of the cross section where the maximum value occurs. The tension-compression asymmetry coefficient has a greater effect on the phase boundary of compression side than on the tension side. The larger the tension-compression asymmetry coefficient, the more likely the phase transformation occurs on the compression side of the cross section.

We considered the convergence problem of the Jamison type weighted sums of extended negatively dependent (END) random variable sequences in a sub-linear expectation space by using the truncation method, and obtained the convergence of the Jamison type weighted sums of END random variable sequences in a sub-linear expectation space. We extended  almost sure  convergence of Jamison type weighted sums of END  random variable sequences  in probability spaces to sub-linear expectation spaces, and the Jamison theorem was generalized.

Aiming at the high-dimensional “big p small n” problem where the number of genes in biomics data (denoted as p) was far more than the number of samples (denoted as n), we proposd a graph attention network GATOr with local and global attention mechanisms. Firstly, the model used Pearson correlation coefficient to calculate the correlation between features on the omic data, and constructed a single sample network of the omic data. Secondly, we proposed a graph attention network which combined local and global attention mechanisms to learn graph-based omics feature representation from a single-sample network, thereby transforming the high-dimensional characteristics of the omics data into low-dimensional representations. The experimental results show that compared with other traditional classification algorithms, GATOr achieves better performance in classification task accuracy and other indexes.

With the development of deep learning technology,  the number of parameters in automatic speech recognition task  models was becoming  increasingly  large, which gradually increased  the computing overhead, storage requirements and power consumption of the models, and it was difficult to deploy on resource-constrained devices. Therefore, it was of great  value to compress the automatic speech recognition models based on deep learning to reduce the size of the modes while maintaining the original performance as much as possible. Aiming at the above problems,  a comprehensive survey was conducted on  the main works in this field in recent years, which was summarized as several methods, including knowledge distillation, model quantization, low-rank decomposition, network pruning, parameter sharing and combination models, and  conducted a systematic review  to  provide alternative solutions for the deployment of models on resource-constrained devices.

Let (L,A) be a fixed complete duality pair. Firstly, the author introduced the Gorenstein (L,A)-injective dimension of complexes, gave its  characterization, and proved that Gorenstein (L,A)-injective dimension of complexes was not larger than injective dimension. Secondly, the author also discussed relative cohomology and  Tate cohomology of complexes, and obtained the long exact sequence connecting absolute, relative and Tate cohomology.

The  maltase-glucoamylase (MGAM) from the large fungus Ganoderma lucidum  as the research object,  and a mutant D246A with significantly reduced enzyme activity was successfully constructed by using methods such as homologous sequence alignment,  homologous modeling,  substrate docking,  and site-specific mutation. The characterization results of enzymatic properties show that  the optimal reaction temperature decreases from 65 ℃ for wild type (WT) to 60 ℃， and the heat tolerance of the mutant decreases. The optimal pH value increases from 6.0 for WT to 7.0,  which is beneficial for the growth of engineering bacteria.  The half-life decreases from 2.0 h for WT to 1.5 h,  the stability of enzyme decreases. The enzyme kinetics results show that  the enzyme kinetics curve of mutant D246A conforms to the Michaelis equation, and   compared with the WT, the K_m value increases,  indicating a decrease in affinity of enzyme and substrate.  V_max decreases to 1/4 of its original value.

We considered the problem of neighbor sum distinguishing total colorings of gragh and its related 1-2 conjecture. Firstly, by using the independent decycling set method, we obtained the neighbor sum distinguishing total chromatic numbers of the subdivision graph S(G) and the triangular extension graph R(G). Secondly, when G was an arbitrary simple connected graph and T was a given special graph, we proved that the edge-replaced graph G［T］ satisfied the 1-2 conjecture.

Aiming at the  characteristics of  subtle, uneven, imperceptible inter-class differences between classes and real-world data distribution in  fine-grained image classification, we proposed a fine-grained image classification model based on attention mechanism. Firstly, the preliminary feature extraction of the image was carried out  by introducing the fusion of a two-way channel attention and residual network. Secondly,  the multi-head self-attention mechanism was applied to extract fine-grained relationships between  deep feature data. Thirdly, the training of loss function measurement system was designed by combining cross entropy loss and center loss. The experimental results show that the test accuracy of the model on two standard datasets 102 Category Flower and CUB200-2011 is  94.42% and 89.43%, respectively. Compared with other mainstream classification models, the classification effect is better.

Aming at the problem that  the lignocellulose had a  complex structure and was difficult to  degrade and utilize,  resulting in environmental pollution when it burned,  we used cellulase to  hydrolyze  cellulose from lignocellulose into glucose. Firstly, the rice straw was pretreated using sodium hydroxide solution. Secondly,  the rice straw before and after the pretreatment was analyzed by scanning electron microscopy,  Fourier transform infrared spectroscopy,  and X-ray diffraction. Finally, the cellulase produced by Aspergillus niger Q7 was used to hydrolyze and pretreat rice straw. The results show that after pretreatment, the fiber structure of rice straw is opened, the surface area increases, and the crystallinity increases.  The cellulose content in rice straw increases after pretreatment,  while the content of hemicellulose and lignin decreases.  The glucose content of pretreated rice straw is higher than that of unpretreated rice straw. 

Aiming at the problem of  static resource allocation of the Storm platform, we proposed a distributed adaptive elastic resource allocation strategy,  which could  optimally meet the resource requirements of applications. Based on this strategy, combined with the resource allocation mechanism, application programming interface and user interface parameters of Storm, an elastic resource allocation component deployed in Storm was implemented to support adaptive and dynamic adjustment of application resources. The experimental results show that on the real stream data set, compared with the middle-value dynamic resource allocation strategy and the static resource allocation strategy of Storm, this distributed optimal strategy has advantages in throughput, loss rate and resource utilization. Meanwhile, this adaptive elastic resource allocation component can well interact with the Storm system, providing a reference solution for the development of other elastic resource scheduling components.

Aiming at the problem of the difficulty in collecting noiseless point clouds and the low generalisation performance of  training on synthetic datasets using simulated noise,  we proposed a self-supervised denoising method that only required  noisy point clouds to complete  training in order  to achieve point cloud denoising in different environments. The method first performed downsampling on  the noisy point cloud by designing and implementing a special sampler to obtain the paired point cloud required for training the network, and then the problem of noise perturbation in network training was solved by designing a lightweight multi-scale denoising network. The experimental results on multiple datasets show that the method is effective and can obtain the same effect as supervised training in different scenarios.

Aiming at the problem of insufficient feature extraction resulting in low classification accuracy of the traditional encrypted traffic classification model, we  proposd an encrypted traffic classification model based on an improved convolutional neural network combined with Transformer by using deep learning techniques.  In order to improve the classification accuracy, firstly, we cut and filled the dataset,  and completed standardization processing. Secondly, the multi-head attention mechanism in the Transformer network model was used to capture long-distance feature dependencies, and the convolutional neural network was used to extract local features. Finally, the Inception module was added to achieve multi-dimensional feature extraction and feature fusion, and the model training and encrypted traffic classification were completed. The experimental verification was conducted on the 
ISCX VPN-non-VPN 2016 public dataset, the experimental results show that the classification accuracy of the proposed  model reaches 98.5%, with the precision rate, recall rate and F₁ value  all exceeding  98.2%, which show better classification effect compared with other models.

Sunflower straw was used as a biological template, a novel graded porous structure of nickel oxide doped zinc oxidenanocomposite (Bio NiO/ZnO) was synthesised.  The composition and structure of the composite were characterised by using X-ray diffraction (XRD),  scanning electron microscopy (SEM),  transmission electron microscopy (TEM) and X-ray photoelectron spectroscopy (XPS). The experimental results show that the synthesised Bio NiO/ZnO preserves the original graded porous structure of the sunflower straw material,  which consists of a large number of hexagonal crystalline fibrillated ZnO-type structures of uniform size and shape stacked with spherical particles of nickel oxide in a cubic crystalline aragonal phase structure.  Compared with the undoped ZnO material,   a gas sensor made of Bio NiO/ZnO composite  material has enhanced gas sensitivity to formaldehyde.  The response of the gas sensor to formaldehyde of 10^-4   is 42 at an operating temperature of 240 ℃， the response time and recovery time are 7 s and 6 s respectively. The lower limit of detection is 1.48×10^-4, which is  related to the increased concentration of oxygen vacancies in the complex and the existence  of p-n type heterojunctions between the two phases.

Aming at  the problem that traditional clothing classification algorithms based on convolutional neural networks could not meet the needs of massive and diverse clothing classification, we  proposed a clothing classification network based on convolutional attention fusion.  The network adopted a parallel structure, including a ResNet branch and a Transformer branch, and  fullly utilizing  the local features extracted by the convolution operation and the global features extracted by the self-attention mechanism to enhance the representation learning ability of the network, thereby improving the performance and generalization ability of the clothing classification algorithm.  In order to verify the effectiveness of the method, we conducted comparative experiments on the Fashion-MNIST and DeepFashion datasets.   The results show that on the Fashion-MNIST dataset, the method achieves an accuracy rate of 93.58%, and on the DeepFashion dataset, the method  achieves an accuracy rate of 71.1%, which is superior to the  experimental results of other methods.

We synthesized a   metal-organic framework complex  [Cu₃(L)₃·2DMF]·2DMF modified by isoquinoline. The  structure of the complex was characterized by elemental analysis,  thermogravimetric analysis,   infrared spectroscopy,   X-crystal diffraction and powder X-ray diffraction. The results show that this complex  has a new  topology network structure with {3,4,6}-connectivity, which can selectively separate carbon dioxide from methane and has good adsorption performance for iodine in solution with a   maximum adsorption capacity of 661.84 mg/g.

Aiming at  the blurring problem of remote sensing images, we designed an image restoration algorithm based on non-subsampled shearlet  transformation and sparse prior. Firstly, the image recovery model was created by setting the sparse a priori condition of remote sensing image under non-subsampled shearlet decomposition of the high-frequency image. Secondly, the model was solved by using the alternating direction multiplier method. Thirdly, the high-frequency image was restricted by the soft thresholding method, and the guided filtering was conducted in the low-frequency image to maintain the detailed information of the image as much as possible. Finally, the high-frequency image and the low-frequency image were reconstructed, the  
 reconstructed image was subjected to deep denoising by  using  convolutional neural networks, ultimately restoring a clear image. The deblurring algorithm was compared with H-PNP, GSR, and L2TV algorithms through experiments. The experimental results show that the algorithm can effectively remove  blurring and noise in remote sensing images, preserve the edge details of the image, and  the objective evaluation indexes are higher than the other three comparative experimental algorithms.

Based on the advantages of   high sensitivity,  simple operation and time-saving in   the detection of metal ions by fluorescent analysis.  We designed and synthesized a porous metal-organic framework  crystal fluorescent probe with amino modification. The experimental results show that the   compound is a two-fold interpenetrating  structure  of pcu framework,  and the amino groups on the organic ligands are freely distributed in the channels. The compound has excellent thermal  stability and water stability, and can be used as fluorescence enhanced probe to detect Ag⁺ in aqueous solutions,  with the detection limit of 0.76 μmol/L.

We studied the long-time dynamic behavior of solution to non-autonomous beam equation with  nonlocal structural damping by using the process theory in the time-dependent space. Firstly, we obtained the well-posedness of solution  by using Faedo-Galerkin approximation method. Secondly, the existence of pullback absorption set of the dynamical system  in the corresponding solution space was obtained by using energy estimation. Finally, we proved the existence of time-dependent pullback attractors by using the cocyclic technique and contraction function method.

By using Schaefer fixed point theorem, we discussed a class of parametric type anti-periodic boundary value problems of fractional La
ngevin equation with p(t)-Laplace operator, the existence result of solution was obtained by giving reasonable assumptions for nonlinear term, and the application of the main result was illustrated with an example.

The geometries of S₀ and T₁ states of a series of iridium(Ⅲ) complexes (C^N)₂Ir(pic-X)（C^N=ppy(1),  dfpmpy(2),  cyppy(3),  dfpmpy(4),  ocfppy(5),  ppy=Phenylpyridine,  dfpmpy=2-(2,4-difluorophenyl)-4-methylpyri-dine,  cyppy=2-(3-cyanophenyl)- pyridine,  ocfppy=2-(2-octyl-3-cyano-4-fluorophenyl)pyridine;  pic=2-carboxyl-pyridine;  X=H(1,2,3,5), EO₂(4),  EO₂=4-diethyloxy）were optimized by the B3LYP and  UB3LYP methods,  respectively. Time dependent density functional theory (TD-DFT) method together with the solvation model in Gauss program were used to obtain their spectral properties in CHCl₃  solvent. The results show that the structural parameters and spectral datas are close to their experimental values. The lowest energy absorptions and phosphorescence emissions are at 459,415,412,397,393 nm, and 567,532,544，491,490 nm,  respectively. The highest occupied molecular orbital (HOMOs) of complexes 1—5 are mainly localized on the Ir atom and C^N ligands,   the lowest unoccupied molecular orbital (LUMOs) are mainly contributed by the pic ligand for complexes  1,2,3,5,  and dominantly localized on the C^N and pic ligands for complex 4. Therefore,  they have different transition characteristics of metal to ligand and ligand to ligand charge transfer (MLCT/LLCT). The calculation results show that the phosphorescence color can be changed by altering the π electron-donating ability of substituent group.

Based on the stability analysis theory, by using linear matrix inequality method and cross term definition method, the author designed a dynamic output feedback H_∞ controllers without memory and memory, constructed a new Lyapunov-Krasovskii(L-K) functional, and derived a sufficient criterion for the asymptotic stability of dynamic output feedback control under the condition of meeting H_∞ performance index, the obtained theorem was suitable for standard and non-standard cases. The effectiveness of the control method was verified by numerical example.

We discussed a class of Schnakenberg models with homogeneous Neumann boundary conditions in view of the periodic oscillation phenomenon in biochemical reactions. By using the  methods of Hopf bifurcating theory, center manifold theory, normal form method and perturbation theory, we gave  the existence, stability and Turing instability of the Hopf bifurcating periodic solutions of the reaction-diffusion Schnakenberg system.

Aiming at the redundant relations and entity overpalling problems in  the task of relational triple extraction,  we proposd a 2D entity pair tagging scheme based on the relation filter (RF2DTagging).  RF2DTagging model consisted of two parts: 1) A relation filter for filtering redundant relations, and 2) a 2D entity pair tagging scheme that could effectively solve various entity overlapping problems. To further validate the RF2DTagging model, we conducted experiments on three public Chinese relation extraction datasets CCKS2019-Task3, CMeIE and DuIE2.0. The experimental results show that the  model can effectively solve the above two problems,  and the overall performance is better than the comparison model.

We considered the extreme problem of the Randic energy of unicyclic graphs C_g∪S_t composed of sticking a star graph S_t at a certain vertex on the circle C_g. Using the definition and properties of the Randic energy, and combined with graph transformations, we found the graph that obtained the minimum Randic energy in this class of unicyclic graphs C_g∪S_t.

By using the method of contradiction,  the method of constructing concrete coloring and distributing the color sets in advance, we discussed the general total colorings of complete 4-partite graph K_n1,_n2,_n3,_n4n₁≤n₂=n₃<n₄ or n₁=n₂=n₃=n₄) that were vertex-distinguished by multisets. We gave an  optimal coloring scheme and determined the chromatic numbers of the corresponding colorings.

By using  Jensen’s inequality of nonnegative upper convex function and the fixed point index theory, we discuss the existence of positive solutions of the boundary value problem for a class of nonlinear difference equations, and obtain sufficient conditions for the existence of positive solutions of the Dirichlet boundary value problem for the second order difference equations, where ［1,T］_Z∶={1,2,…,T}, T≥2 is the integer, Δu(t)=u(t+1)-u(t) is the forward difference operator, f,g: ［1,T］_Z×［0,∞)×［0,∞)→［0,∞) are continuous.

Aiming at the problem of water pollution caused by the antibiotic sulfadiazine (SDZ), a three-dimensional layered Co₃Mn-LDHs/rGO dual-action catalyst with both photocatalysis and persulfate activation functions based on graphene (rGO) was prepared by a hydrothermal method,  and a visible light/persulfate coupled degradation system (Vis-PMS) was constructed to degrade SDZ in water. The experimental results show that Co₃Mn-LDHs are successfully loaded on rGO and the attachment of Co₃Mn-LDHs prevents the stacking of rGO sheets.  The optimal conditions for the degradation of SDZ in the visible-light-coupled non-homogeneous-phase-activated PMS system are Co₃Mn-LDHs/rGO mass concentration of 20 mg/L,  PMS mass concentration of 200 mg/L,  and an initial pH=7,  and the removal rate of SDZ reaches 87.58% after 60 min of reaction.   Co₃Mn-LDHs/rGO still has a high removal rate for SDZ with good reusability after 10 cycle tests.  The free radicals that play a major role  in this system are sulfate radicals (SO^-₄),  hydroxyl radicals (.OH),  and singlet-linear oxygen (¹O₂). 

By systematically changing the geometric parameters such as pore size and porosity of large and small pores in hierarchically porous membranes, we used finite element simulation method to study the linear or nonlinear quantitative relationships between membrane flux and related geometric parameters. The simulation results show that after addition spherical cavities to the curved channel matrix to form a hierarchical porous structure, the water flux of the film can be increased by about 171% of the original. For the curved channels, simply increasing their number can lead to a linear increase in water flux, and simply increasing their pore size can lead to an exponential function increase in water flux. For spherical cavities,  simply increasing their number or simply increasing their pore size results in an exponential function increase in water flux. In addition, the water flux enhancement effect of spherical cavities also depends on their relative size with the matrix grid of curved channels. The performance of separation membrane materials can be improved by adjusting the preparation conditions.

Aiming at the problem that the cellular Internet of Things involved large-scale device connection and identity authentication management, and attackers cuold use various methods  to forge identity information, which made the difficulty of  anonymous access  user identity authentication increase, the author proposed  an  anonymous access user identity authentication algorithm for cellular Internet of Things. Firstly, the 5G network was used as the dynamic application scenario of the cellular Internet of Things system, and the system parameters were preseted. Secondly, according to the user’s identification number and public key, the forged name was used to generate the user’s anonymous access information, and the registration was anonymously saved to the local. Finally, based on the concept of decentralization, the decryption results of the unit public key and the adjacent group key, the random number encryption information and the unit Hash value were compared to authenticate the user identity. The experimental results show that the proposed algorithm effectively shortens the time required for identity authentication and batch message authentication, reduces the number of bytes required for data transmission, with a time cost of only 13 ms, a computational cost of only 4 ms,  and a communication cost of only 210 bytes. Moreover, it can successfully resist 15 types of identity authentication attacks.

We established a class of measles epidemic model based on secondary vaccine failure induced by vaccination. By using the next generation matrix method, we first obtained the basic reproduction number R₀ of the model and gave its biological meaning, and then proved that R₀ was a sharp threshold parameter by constructing an appropriate Laypunov function. When R₀≤1, the disea
se-free equilibrium is globally asymptotically stable; when R₀>1, the diseasefree equilibrium is unstable and the endemic equilibrium is globally asymptotically stable.

By using Schauder fixed point theorem, the author study the  existence and uniqueness of solutions for second-order iterative differential system satisfying the boundary conditions x(a)=y(a)=a, x(b)=y(b)=b或x(a)=y(a)=b, x(b)=y(b)=a, where x^［2］(t)=x(x(t)).

In order to study the effects of human to human diffusion, spatial heterogeneity and different concentrations of Vibrio in static water source environment on cholera transmission, we established  a partially degenerated reaction-diffusion cholera model. Firstly, we defined the basic reproduction number R₀ of the model. Secondly, the global threshold dynamics of the model was determined by the sign of R₀-1. Finally, we discussed  the effects of key model parameters on R₀ through numerical simulation experiments. The results show that moderate urbanization is beneficial to disease control.

We used the adaptive penalized likelihood method to solve the structure learning problem of Gaussian graphical models with latent variables. The simulation results show that the adaptive penalties are significantly superior to the non-adaptive penalties, which can effectively reduce the estimation bias and more accurately estimate the conditional independence relationships among observed variables given latent variables.

Using ascorbic acid as reducing agent, Cu₂O crystal was synthesized by low temperature aqueous phase method, and the different samples were prepared by controlling the mass of surfactant polyvinylpyrrolidone. The structure and morphology of the samples were characterized by X-ray diffraction, scanning electron microscope, ultraviolet visible spectrophotometer and Fourier transform infrared spectroscopy. The experimental results show that increasing the mass of PVP can change the crystal morphology and increase the exposure ratio of (111)/(200) crystal surface. The crystal plane heterojunction formed between (111) and (200) crystal planes can enhance the separation ability of photogenerated electrons and hole pairs in the photocatalytic process, thus imporving the photocatalytic efficiency of Cu₂OO crystal. Spherical Cu₂O crystal can be used as templates for the compound synthesis.

In order to achieve  more high-quality images in 3D digital image virtual scene  reconstruction, the author proposed  a 3D digital image virtual scene reconstruction algorithm based on machine learning. Firstly, the state information and presentation instructions of the scene were analyzed to obtain the vertex distribution positions of the mesh model for image reconstruction. The global image was approximately calculated by local coordinate method, and the local details were corrected to complete the rendering processing of 3D digital images. Secondly, taking space and scale as feature points, a window detection template was constructed on the image, and a classifier was used to suppress discrete feature points and remove redundant features. Finally, according to the fitting function method, the smoothed 3D coordinates were obtained  to reconstruct the 3D surface, and the local 2D triangle was segmented and mapped to the 3D space to realize the 3D digital image virtual scene reconstruction. The experimental results show that the proposed algorithm converges faster, the reconstructed image details and edge contours are complete, and the overall effect is good.

Aiming at the problem of  the performance degradation of the automatic operator selection algorithm in convolutional neural network training under high memory pressure, we modelled offloading, recomputing and convolutional operator selecting in a unified manner and proposed an intelligent operator selection algorithm. The algorithm weighed the time overhead introduced by offloading and recomputing against the time saved by faster convolutional operators, found the scheduling of offloading, recomputing and convolutional operator selecting, and solved the performance degradation problem of the automatic operator selection algorithm. The experimental results  show that the intelligent operator selection algorithm reduces training time by 13.53% over the recomputing-automatic operator selection algorithm and by 4.36% over the existing offloading/recomputing-automatic operator selection algorithm.

We investigated the adsorption and dissociation behaviors of NO molecules on the surface of TM-MoS₂ (TM=Fe,Ir) doped systems by  using the PW91 method under the generalized gradient approximation in density functional theory in combination with periodic plate model. The results show that,  unlike the physical adsorption  on the intact MoS₂ surface (-0.05 eV),  the adsorption energies of NO on the surface of Fe and Ir doped MoS₂ are -3.30,-3.17 eV respectively,  indicating  that  the doped  surface exhibits more excellent adsorption performance for NO.  Differential charge density analysis shows that after adsorption of NO molecules,  there is an increase in charge  between the N atoms and the doped atoms Fe and Ir,  covalent bonds are formed,  and the charge around the doped atoms decreases.  The  calculation results of the density of states show that the adsorption of NO on the surface of doped TM-MoS₂ (TM=Fe,Ir) is mainly consisted of strong interactions between2p_y and 2p_x of N atoms, and 3d_xy,3d_yz,3d_xz of doped atom Fe as well as 5d_xy,5d_yz, and 5d_xz orbitals of Ir.  Comparative analysis of the activation energy of the dissociation reaction, the results show that, compared to the noble metal Ir,  the activation energy of NO dissociation on the Fe-MoS₂ surface  is smaller than that on the Ir-MoS₂ surface after doping with inexpensive Fe,   and the adsorption energy on  the Fe-MoS₂ surface is nearly close to the activation energy,  with only a difference of   0.08 eV,  indicating that there is a mutual competition between the adsorption and dissociation of NO in this system. 

Aiming at the problem of privacy information security in mobile applications, the author proposed a security analysis method for mobile application based on user interface (UI) content. Firstly, this method  got the functions of mobile applications by mining the information of UI  products, and determined sensitive permissions that the application actually used by analyzing the code. Secondly,  the applications with similar functions were clustered together by using Mean shift algorithm. Finally, based on principle that products with similar functions should  use similar sensitive permissions, the anomaly detection algorithm iForest was used to determine whether the product was at risk of use.  Experimental results show that this method can effectively analyze the security of mobile applications.

By using the quantum Bernoulli noise method, we investigated the one-dimensional space-time inhomogeneous open quantum walk, and gave the evolution properties and limit probability distribution of the walk. It was also shown that the one-dimensional space-time inhomogeneous open quantum walk based on quantum Bernoulli noises had the same limit probability distribution as the classical random walk when the localized ground state was used as the initial state.

The SnS thin films with bundle-like nanostructure were prepared by chemical bath deposition at 70 ℃, using fluorine-doped tin oxide conductive glass (FTO) and ordinary glass as substrates, respectively. By studying the effect of reaction time on the bundle-like nanostructure SnS thin films, we proposed the possible forming mechanism of the bundle-like nanostructure SnS thin films, and tested the photocatalytic degradation performance of the bundle-like nanostructure SnS thin films on rhodamine B. The results show that the SnS thin film with bundle-like nanostructure grown on FTO substrate has better photocatalytic performance.

In order to solve the environmental pollution caused by the stacking of furfural residue and expand the high-value utilization of waste resources, the furfural residue based lignin/cellulose composite was prepared through the pretreatment processes such as ultra-fine grinding and high-pressure homogenization. The sample morphology was characterized by using scanning electron microscopy (SEM) and atomic force microscopy (AFM), the composition and elemental content of the composite were analyzed by using normal form washing method and elemental analysis, the surface functional groups of the composite were analyzed by using Fourier transform infrared spectroscopy (FTIR) and ultraviolet spectroscopy (UV), and the thermokinetic analysis was performed by using multiple heating rate thermogravimetry (TG) under non-isothermal conditions. The results show that the mass fraction of C in furfural residue based lignin/cellulose composite is high (55.95%), which can be used as an ideal carbon source. The material contains abundant lignin (53.18%) and cellulose (39.48%), and has high utilization value. The overall apparent activation energy is low (30 kJ/mol), and the half-wave potential (E_1/2=0.83 V) in 0.1 mol/L KOH alkaline electrolyte reaches 96.5% of commercial Pt/C (E_1/2=0.86 V). Therefore, carbon materials prepared by using furfural residue based lignin/cellulose composites as biomass precursors can be used as ideal oxygen reduction catalysts for fuel cells.

Aiming at the problem of difficulty in obtaining images for local examination of potential lesions in endoscopic surgery, we proposed an optical design system for an optical zoom endoscope based on variable focal power lens. This system was based on the Gaussian bracket method and the principle of endoscopic zoom, we derived and analyzed the first-order optical control equation of a zoom endoscope with variable focal power lens. Using the analytical solution of the first-order zoom optical theory and the optical design software ZEMAX, the optimal design and imaging evaluation of three typical zoom positions of the endoscope were performed to analyze its optical imaging capabilities. The results show that the zoom endoscope based on variable focal power lens has the ability to distinguish the inner wall tissue of the human body after zooming and magnifying it. This optical system has advantages such as no component movement, fast response frequency, and small size, which can improve the accuracy of endoscopic treatment technology in surgical treatment and diagnosis.

Based on scalar diffraction theory, the aberration function was constructed by using Zernike polynomial method, and the aberration function was applied to ZEMAX to study the spherical aberration of Gaussian laser beam in Fraunhofer circular aperture diffraction imaging when the distance between lens and circular aperture was large. The experimental and theoretical simulation results show that the lens and the distance between lens and circular aperture have significant effects on spherical aberration. When selecting optimized aspheric lens, lens materials with higher refractive index and small field-of-view, it can effectively reduce the spherical aberration caused by large  distance between lens and circular aperture, thereby effectively improving the diffraction imaging quality.

Aiming at  the problem that marine controlled-source electromagnetic (MCSEM) signals were prone to be interfered by various noises in exploration, which  affected the accuracy of later inversion and data processing, we proposed an attention mechanism-guided convolutional autoencoder marine controlled-source electromagnetic data denoising method. Firstly, based on  the  autoencoder, we constructed a noise suppression network based on convolutional autoencoder for marine controlled-source electromagnetic data. Secondly, we opimized it according to the characteristics of noise in the data, deepened the depth of the network, introduced attention mechanism to make the network pay more attention to the effective signal features in the data, enhanced the feature extraction ability, constructed the network model, and realized the noise suppression of marine controlled-source electromagnetic data. The experimental results show that this method has higher signal-to-noise ratio and lower mean square error than the db8 wavelet noise suppression method and the variational mode decomposition noise suppression method. Meanwhile, it can still retain the signal features and increase the interpretable range of offset distance in the measured data, which proves the effectiveness of this method in the noise suppression of marine controlled\|source electromagnetic data.

By using the transmission matrix method, the matching matrix and transmission matrix of one-dimensional functional composite structure photonic crystal were given. On this basis, we studied the interface state of one-dimensional functional photonic crystals, and studied the influence of refractive index endpoint value, thickness of medium and incident angle on the position of interface state. The results show that interface state appears at the position where the imaginary part of the total impedance is 0. For functional media, when the initial endpoint value of refractive index increases, the position of interface state shifts red with the band gap, when the endpoint value of refractive index increases, the position of interface state shifts red  with the band gap. When the thickness of the medium increases, the position of the interface state shifts red with the band gap. When the incidence angle increases, the position of interface state shifts blue with the band gap. Therefore, the position of interface states can be adjusted by functional photonic crystals.

We discussed the E-total coloring of complete bipartite graphs K_4,n which were vertex-distinguished by multiple sets by using
 the method of proof by contradiction, the method of pre-assignment of color sets and the method of constructing specific coloring, and determined E-total chromatic numbers of K_4,n which were vertex-distinguished by multiple sets.

Aiming at the problem that the interpretable method based on class activation mapping (CAM) was disturbed by features unrelated to the target class, which led to more noise in the visualization results and lower localization accuracy of target objects, we proposed a convolutional neural network (CNN) visualization method based on ablation analysis. Firstly, the correlation between deep network features and target classes was investigated and feature fusion weights were calculated through ablation experiments. Secondly,  the feature fusion weights were corrected by ReLU or Softmax functions to reduce the interference of irrelevant features and obtain  class activation map with higher localization accuracy, so as to make an effective description of network decisions. A variety of evaluation metrics were used for verification on the ILSVRC 2012 validation set, the experimental results show that the method achieves better model interpretation capability in all indicators.

We used an ideal convergence structure to solve the characterization problem of directed topology, and provided necessary and  sufficient conditions for the topological transformation of ideal S limits and ideal generalized S limits. The results show that the directed topology, the ideal S limit topology and the ideal generalized S limit topology are the same  in T₀ topological spaces.  The ideal S convergence in a directed space is topological if and only if it is a c-space. The ideal generalized S convergence in a directed space is topological if and only if it is a locally strongly compact space.

Aiming at the problem of large number of data transmission node deaths and high transmission energy output during energy-saving clustering routing communication in wireless sensor networks, we proposed an energy efficient clustering routing algorithm for heterogeneous wireless sensor networks based on energy iterative model and bee colony optimization. Firstly, a network communication energy consumption model was constructed, with the goal of reducing energy consumption and combining differential bee colony algorithm to timely optimize the distribution of network nodes. Secondly, based on the optimization results of network node distribution, an energy efficient clustering method for heterogeneous wireless sensor networks was developed, the energy iterative clustering selection method was used to determine the cluster head to obtain the cluster head radius and complete the energy efficient clustering of communication nodes in heterogeneous wireless sensor networks. Finally, we set the distance between the communication cluster head node and the base station, determined the routing level of node communication, and combined multi hop routing communication to achieve energy efficient routing communication in heterogeneous wireless sensor networks. The experimental results show that when using the proposed method for network energy efficient clustering routing communication, the maximum number of dead data transmission nodes is 22, and the maximum energy consumption of node transmission is 21 nJ/bit, indicating that the method has good energy efficient effect on node communication.

Firstly, we introduced the definition of Gorenstein AC flat dimension for complexes and gave some characterizations of GFacdim M≤n for any complex M. Secondly, we proved that if the complex M had finite Gorenstein AC flat dimension, then M had a complete AC resolution.

Aiming at the problem of low mapping accuracy and efficiency caused by semantic heterogeneity in ontology mapping, especially in large-scale heterogeneous ontology mapping, we  proposed an  ontology mapping method based on node semantic similarity (NSS). Firstly, we studied  key technologies such as web-based ontology parsing and representation, automatic ontology partitioning, rapid recognition of similar sub ontologies, and node semantic based sub ontology mapping. Secondly, the experiments were conducted on the conference ontology set in the ontology alignment evaluation initiative (OAEI) evaluation datasets. The results show that the proposed method outperforms traditional mapping methods in performance and has higher accuracy than fragment based mapping methods.

Aiming at the problem  of nitrate pollution in water, we synthesized a novel polymer vinylimidazole/dibromodecane/ethylene glycol dimethacrylate (VDE),  its structure was characterized by scanning electron microscopy (SEM),  Fourier transform infrared spectroscopy (FT-IR),  X-ray photoelectron spectroscopy (XPS),  and its optimal dose ratio,  pH value,  adsorption temperature,  and reusability in aqueous solutions containing nitrate were investigated. The results show that the adsorption capacity of nitrate nitrogen on VDE at 15 ℃ and pH=4 is 28.31 mg/g by Langmuir model,  and this adsorption process can reach the equilibrium in 10 min,  and it is in accordance with the quasi-primary and quasi-secondary kinetic fitting model,  and its adsorption capacity can still reach 95.5% of the first use after five adsorption/desorption experiments,  which indicates that this material can effectively  purify  nitrate wastewater with low mass concentration.

We considered a class of dynamic fuzzy systems, which consisted of fuzzy Atangana-Baleanu fractional differential inclusion and variational inequalities, called fuzzy fractional differential variational inequalities (FFDVI). It included the two fields of fuzzy fractional differential inclusion and variational inequalities, expanding the researchable problems in fuzzy environments. The model captured the desired features of the fuzzy fractional differential inclusion and fractional differential variational inequalities within the same framework. By using Krasnoselskii fixed point theorem, the existence of solutions of FFDVI under some mild conditions was obtained.

By using the method of upper and lower solutions, we discussed a class of elliptic equations with nonlinear terms of supercritical growth. We first proved the existence of solutions of the Dirichlet problem in the restricted region, and then proved that the local solutions in the restricted region could be extended to the whole region by combining a new  variational principle.

Aiming at the problem that the connected temporal classification model needed to have output independence assumption, and there was strong dependence on language model and long training period, we proposed  a speech recognition method based on connected temporal classification model. Firstly, based on the framework of traditional acoustic model, spectrogram feature extraction network based on attention mechanism was trained by using prior knowledge, which effectively improved the discrimination and robustness of speech features. Secondly, the spectrogram feature extraction network was spliced in the 
front of the connected temporal  classification model, and the number of layers of the recurrent neural network in the model was reduced for retraining. The test analysis results show that the improved model shortens the training time, and effectively improves the  accuracy of speech recognition.

By introducing the notion of cyclic pure phantom morphisms, we gave  some equivalent characterizations of cyclic pure phantom morphisms,  proved that every R-module had an epic cyclic pure phantom cover with the kernel cyclic pure injective modules, and discussed the transitivity of cyclic pure phantom precover under change of rings.

Aiming at the time-consuming and labor-intensive problem of obtaining large-scale multi-hop question and answer training dataset, we  proposed a multi-hop question generation model based on the contrastive learning idea. The model was divided into the generation phase and the contrastive learning scoring phase. In the generation phase, candidate multi-hop questions were generated by executing the inference graph. In the contrastive  learning scoring phase, candidate questions were scored and sorted through a candidate question scoring model without reference question based on the contrastive learning idea, and the best candidate question was selected. This model had to some extent narrowed the gap between unsupervised methods and manual annotation methods, effectively alleviating the problem of lacking a multi-hop question and answer dataset. The experimental results on HotpotQA dataset show that the multi-hop question generation model based on contrastive learning can effectively expand the training data and greatly reduce the cost of manually labeling data.

In order to realize the effective precipitation of power transformer operation and maintenance knowledge, taking the operation and
 maintenance text as the research object, we proposed a framework for deep construction of power transformer operation and maintenance knowledge graph with fusion rules. We  first constructed the concept layer of the knowledge graph from top to bottom according to the guidance of experts, and then  integrated rules and deep neural network models to extract knowledge and construct the data layer of the knowledge graph. Aiming at the blurred boundaries of entities and insufficient utilization of contextual information in operation and maintenance texts, we proposed a method for obtaining extended Span lables by extending contextual information and bidirectional encoder representations from transformers  for entity and relation extraction. The example analysis shows that  the proposed method performs well in  knowledge extraction from  power transformer operation and maintenance data.

Aiming at the problem of  the navigational challenges for visually impaired users on diverse webpages, we proposed a method for automatically identifying navigation bars to improve  webpage accessibility. Firstly, by designing heuristic rules, elements within the navigation bars were  autonomously extracted based on the ordered element arrangement within the navigation bar, as well as rules such as hyperlinks and succinct textual content within sub-elements. Secondly, a decision tree binary classification algorithm was used to categorize elements with pronounced feature disparities in the navigation bars. Finally, the identified navigation bar elements were subject to the injection of Landmark attributes. In experimental evaluations of  100 websites, the method successfully identified  92.6% of navigation bar elements, and the infusion of Landmark attributes significantly improves website accessibility, thereby ameliorating the user experience for visually impaired individuals.

The 1,3-dione boron difluoride compounds were used as the research object based on the advantages of high molar absorption coefficient,  high fluorescence quantum yield,  good planar six-member ring and so on. The author designed and synthesized an asymmetric  1,3-dione boron difluoride compound, detected   its changes in solution  by using ultraviolet visible absorption spectrum and fluorescence emission spectrum,  and observed its morphology by using atomic force microscopy and measured the size of its assembly. The experimental results show that there is a significant  assembly behavior of 1,3-dione boron difluoride with an increase in  water ratio, and its assembly body exhibits a regular and ordered banded  structure. 

Aiming at the problems of poor multiplexing, high routing overhead and average delay of Internet of Things (IoT) transport streams, we proposed a method for  transport stream multiplexing of IoT based on pheromone algorithm. Firstly, the method determined the necessity of multiplexing by analyzing the current situation and requirement of IoT. Secondly,  based on a network communication task, the basic idea of  transport stream multiplexing of IoT was outlined. Finally, on the basis of solving the single path problem existing in multiplexing, the pheromone algorithm was used to build a multiplexing model for the  transport stream of IoT, and the transport stream multiplexing of IoT was realized according to  output results of the model.  The experimental results show that the multiplexing result of the proposed method includes multiple signals, the signals are not missing, and the routing cost is only 3×10⁴ Mb, and the average delay is only 15 ms.

With the help of the boundedness of the Lebesgue spaces, by applying the decomposition method of function and real variable
 techniques, the boundedness of Marcinkiewicz integral with rough kernel was proved on Morrey-Adams spaces. Meanwhile, the corresponding result of its commutator with Lipschitz and BMO functions was given.

We proposed an improved approximate optimal gradient method to solve the unconstrained objective function in the graph partition problem. We first used  the modified BFGS updating formula and selected the linear combination of BB class step sizes as scalar matrices to obtain  the approximate optimal step sizes, then we introduced parameters to improve the classical Zhang-Hager line search form, construced the algorithm framework  and gave the proof of R-linear convergence. The experimental results show that the improved algorithm improves the performance of the original algorithm.

Aiming at the bottleneck of solving efficiency of existing Chinese postman problem solving methods on large-scale sparse road network graph, we proposed a fast solution method based on ant colony optimization to obtain feasible solutions in an acceptable time range. This method used ant colony algorithms to solve the second stage of the odd even point graph operation method for Euler’s loop solution. At the same time, we improved the method based on density peak clustering algorithm according to the characteristics of large-scale sparse road network graph. Firstly, we clustered and segmented the large-scale sparse road network graph before using the ant colony algorithm to solve the problem. Secondly, we merged the segmented node groups according to the coverage of adjacent nodes. Finally, by changing the clustering of some nodes, the number of internal nodes in each node group was even. The experimental results show that: under the node size supported by the homework method on the odd even point graph, the proposed method can obtain the same optimal solution as the deterministic algorithm and achieve the efficiency optimization of about 10 times in the operation time. The proposed method can effectively improve computational efficiency in large-scale sparse road network graphs and obtain optimized feasible solutions within a controllable time range. When facing road network graphs with a scale of 5 000 nodes, the fastest solution can be completed within 60 s.

Aiming at the problem that complex segmentation networks could not converge on small sample iris datasets, we proposed an iris segmentation model based on lightweight convolutional neural network. Firstly, the model used a feature extraction module based on depth-wise separable convolution to extract iris image features, which could  significantly reduce model parameters while maintaining segmentation accuracy. Secondly, an efficient attention mechanism module was introduced between the encoder and the decoder, which could effectively obtain rich context information and improve the discriminability of iris region pixels. Finally, the experimental results on the iris database UBIRIS.V2 show that the proposed method not only has significant performance advantages on small sample databases, but also has high segmentation accuracy on large sample databases.

By using the fixed point theorem on expansion and  compression of cones, we study the existence of positive solutions for a class of periodic boundary value problems of third-order ordinary differential equations. The  results show that there exists  at least one positive solution to the above problem when the nonlinear term f satisfies appropriate conditions.

Aiming at the problem that computational and storage resources of embedded and mobile devices were limited, and the compact  network optimization was easy to  converge to poor local optimal solutions,  we proposed an  activation map adaptation model for knowledge distillation,  which was composed  of an activation map adapter and an activation map adaptation knowledge distillation strategy. Firstly, the activation map adapter realized activation map size matching, synchronous transformation of teacher-student network features, and adaptive semantic information matching by heterogeneous convolution and stacking of visual feature expression modules. Secondly, the activation map adaptation knowledge distillation strategy embedded the adapter into the teacher network to reconstruct it, and realized adaptively search suitable for the  supervision features of the hidden layer of the student network  during training process,  the front output  of the adapter was used to prompt the front training of the 
student network, so as to realize knowledge transfer from the teacher to the student network, and further optimize it  under the constraint of learning rate. Finally, experimental verification was carried out on the image classification task  dataset cifar-10. The results show  that the classification accuracy of the activation map adaptive knowledge distillation model is improved by 0.6%, the inference loss is reduced by 6.5%, and  the time to converge to 78.2% accuracy is reduced to 5.6% when it is not migrated.

Aiming at the problems that the traditional  hierarchical matching algorithm of visual image for mobile robot could only complete rough matching, resulting in low final matching accuracy and long matching time, we proposed a  hierarchical matching algorithm of visual image for mobile robot based on deep reinforcement learning.  Firstly, the strategy network and value network in the deep reinforcement learning network structure were used to guide the floating image to move to the reference image in the correct direction. Secondly, in the process of rough matching, the reward function was designed to realize the rough matching of color features. Finally, on the basis of rough matching, the improved scale invariant feature transformation algorithm was used to extract  the local features of the image to be matched, and the mobile robot visual image was graded matched according to the similarity. The experimental results show that the algorithm can effectively realize the coarse matching and fine matching of images. The stability of feature detection is high under different viewing angles and scales. The matching accuracy is high, the time is short, and the matched image quality is good, which improves the actual application effect of mobile robot.

Aiming at the problem that extraction accuracy and speed were limited when using principal component analysis (PCA) algorithm only in face image high-dimensional data dimensionality reduction, we proposed a hybrid feature extraction algorithm based on wavelet transform and improved PCA. Firstly, the face image was decomposed by wavelet, and low-frequency component was selected for feature extraction. Secondly, the improved PCA algorithm was used for principal component extraction to obtain the feature vectors representing face features. Finally, the algorithm was applied to the image classification of Olivetti Faces  dataset. The experimental results show that the recognition accuracy is improved by 10% and the recognition speed is improved by about 37% when the image feature data processed by the hybrid algorithm are classified and recognized by convolutional neural network (CNN) algorithm.

We studied  the antioxidant active components and mechanism of  dandelion based on  high performance liquid chromatograph (HPLC) method and network pharmacology method.   The effective components of Chinese herbal medicine dandelion were extracted by  organic reagents,  such as petroleum ether,  ethyl acetate,  dichloromethane and n-butanol,  and their antioxidant effects were studied. Multiple online databases of network pharmacology were used to obtain  common targets of dandelion antioxidant construct PPI network,  and conduct GO enrichment analysis and KEGG signal pathway enrichment analysis. The results show that the  extracts of each phase of dandelion have a certain scavenging ability to hydroxy radical (.OH),  superoxide anion radical (O^2-.) and 1,1-diphenyl-2-picrylhydrazyl radical (DPPH.),  the ethyl acetate phase extract of dandelion and the dichloromethane phase extract of dandelion have better scavenging effects,  and the main antioxidant active components are isorhamnetin and oleanolic acid. There are 137 dandelion antioxidant targets screened from the online database. The common targets are mainly concentrated on membrane rafts,  which are resistant to the response of cells to inorganic substances,  nitrogen compounds,  and nutrient levels oxidation. The common targets are closely related to cancer signal pathway,  NF-kappa B signal pathway,  and PPAR signal pathway. 

The feasibility of remediation of Cr(Ⅵ)-contaminated soil by combining pure water extraction and freezing method was studied through laboratory simulation. The results show that for 1 000 mg/kg  Cr(Ⅵ)-contaminated soil,  the extraction rate of total chromium is about 35% by using pure water for extraction, which is   similar to the conventional oxalic acid extraction method. After freezing and icing，  oxalic acid was added to the pure water, extraction solution at a  500 μmol/L,  the reduction rate of Cr(Ⅵ) in the extraction solution reaches 97%. NaCl,  NaNO₃,  and Na₂SO₄ have a weak inhibitory effect on removal efficiency of  Cr(Ⅵ). The ultraviolet absorption spectrum,  X-ray photoelectron spectroscopy,  infrared spectra,  and 3D fluorescence spectroscopy tests show that the working principle of  the method is that oxalic acid provides  H⁺,  and dissolved organic matter (DOM) in the soil acts as a reducing agent,  hexavalent chromium in the soil extract is reduced through the freeze-concentration effect.  Therefore,  the combination of pure water extraction and oxalic acid freezing method can be used for the ex-situ remediation of Cr(Ⅵ)-contaminated soil, and can decrease the usage of chemical reagents,  which is conducive to maintaining the stability of soil physicochemical properties.

Aiming at the problem that the traditional Yinyang algorithm did not use the data structure, resulting in low computational efficiency, we proposed an efficient Yinyang k-means clustering algorithm. The algorithm decomposed the original data layer by layer according to the data similarity, and established a full m-tree structure to store the data of each layer. The weighted data was established based on the data information stored in each leaf node of the tree structure, and the weighted Yinyang k-means algorithm was run to obtain the convergence center. In the original data, the convergence centers of the weighted data were taken as the initial condition to run the traditional Yinyang k-means algorithm to further optimize the objective function value. Comparative experiments with k-means, traditional Yinyang k-means and other two acceleration algorithms on five UCI data sets show that the proposed algorithm has a high acceleration ratio, and the solution accuracy is basically equivalent to Yinyang k-means clustering.

We analysed  the parametric accuracy of the generalized noise model estimated based on the maximum likelihood equation by using Fisher information and the associated asymptotic normality. The theoretical analysis results show that for standard pixel images, the parameter error of the additive noise estimated by using the maximum likelihood equation is larger than the error of signal-dependent noise parameter, while for the normalized images, the accuracy of the parameters is exactly the opposite. The experiments prove the correctness  of the theoretical analysis.

We studied the one-dimensional non-Newtonian fluid model with gravitational potential and damping terms. The singularity and strong nonlinearity were solved by using the method of regularization equations and constructing  approximate solutions. The existence of the positive density solution was obtained by assuming the compatibility condition. Furthermore, the existence and uniqueness of local solutions for coupled equations under vacuum conditions were obtained.

Aiming at the shortcomings  of gradient-domain tone mapping methods in subjective display performance, we proposed a luminance-gradient co-guidance tone mapping algorithm based on Retinex theory by  using the perceptual ability of the human visual system  and the gradient-domain method. Firstly, a domain-aware adaptive  normalization  method was proposed to construct normalized mappings for different domain algorithms. Secondly, a Retinex luminance guidance term was introduced to estimate the background luminance, and the dynamic range of the image was compressed based on the gradient guidance term. Finally, the luminance and gradient guidance terms were combined for unified modeling, and the exponential mean local variance weight was used to suppress halos. The experimental results show that the algorithm suppresses oversaturation and artifacts while compressing the dynamic range, and  has good visual effects and robustness.

Aiming at the problem that the traditional matrix-completion unconstrained optimization model had poor robustness in dealing with missing matrices damaged by singular noise, we proposed an adaptive robust matrix completion method. In this method, truncated kernel norm was used as the low-rank approximation of the rank function in the objective function, and the F-norm robust to singular noise was used as the loss term to recover the missing values in the matrix, so as to reduce the influence of outliers on the algorithm and improve the recovery accuracy. In the process of solving this model, a dynamic weight parameter was introduced by using convex optimization technique, which could be used to adjust the next update adaptively according to the current recovery error when updating the recovery value, and then an effective iteration method was established to solve the optimization problem. The experimental results show that the algorithm has better robustness and accuracy when dealing with matrices damaged by singular noise, so that better image restoration effects can be obtained.

Let T be a formal triangular matrix ring. Using Hom functors and adjoint isomorphism  theory, we describe the structure of the F-Gorenstein flat modules over formal triangular matrix ring T.

We used the differential complex to calculate the standard cohomology of 4-dimensional even centers and 3-dimensional odd centers Heisenberg Lie superalgebras with coefficients in the 1-dimensional trivial modules. Firstly, we calculated the differential operators of these two classes of Heisenberg Lie superalgebras. Secondly, we calculated the standard cohomology of these two types of Heisenberg Lie superalgebras with coefficients in the 1-dimensional trivial modules. In particular, we obtained the basis and dimension of the standard cohomology for these two types of Heisenberg Lie superalgebras.

We considered a class of boundary value problems for fractional differential equations with Ψ-Caputo fractional derivative, the boundary conditions included a Stieltjes integral and multiple Ψ-Riemann-Liouville fractional integral operators. Firstly, the expression of solution of corresponding auxiliary boundary value problem was given. Secondly, the existence and uniqueness of solution of the boundary value problem were proved by using Banach compression mapping principle and Schaefer fixed point theorem. Finally, we gave an example to illustrate the validity of the obtained results.

In order to study the key genes and key metabolic pathways after the sgf73 gene was knocked out in Schizosaccharomyces pombe,  the wild\|type yeast strains and sgf73Δ  gene-deficient strains were sequenced and bioinformatics analyzed by RNA-Seq sequencing technology, and the GO and KEGG functional enrichment analysis were carried out.  The results show that in the sgf73Δ gene-deficient strains,  there are 1 834 highly expressed genes,  including 6 extremely highly expressed genes,  and 1 714 differentially expressed genes,  of which 934 genes are up-regulated and 780 genes are down-regulated. The  sgf73 gene knockout leads to  abnormal changes in cellular metabolism and transmembrane transport. The  down-regulation of cki1,cki2 and cdc25 genes involved in cycle regulation in the MAPK signaling pathway leads to prolongation of mitotic time in sgf73Δ strain,  the down-regulation of regulatory cytoskeleton rgf2,rho1 and stt4 genes leads to abnormal contraction  of actin ring of  sgf73Δ strain.

Aiming at the problems of the complicated underwater image imaging environment resulted in the subsequent image analysis often being affected by color bias and other factors, we proposed a deep convolutional neural network image restoration method based on multi-scale features and triple attention multimodal fusion. Firstly, the deep convolutional neural network introduced the image multi-scale transformation feature on the basis of extracting the image spatial feature. Secondly, by using channel attention, supervised attention and non-local attention, the scale correlation and feature correlation of image features were mined. Finally, by designing a multimodal feature fusion mechanism, the above two types of features could be effectively fused. The proposed method was tested on the open underwater image test set and compared with the current mainstream methods. The results show that this method is superior to the comparison method in quantitative comparison such as peak signal-to-noise ratio and structural similarity, as well as qualitative comparison such as color and details.

Inspired by attention mechanism and transductive learning method, we proposed a node classification algorithm based on weighted meta-learning. Firstly, Euclidean distance was used to calculate the difference of data distribution between subtasks in meta-learning. Secondly, adjacency matrices of subgraph was used  to calculate and capture structural difference of data points  between subtasks. Finally, the captured information above between subtasks were converted into weights  to weight the process of updating the  meta-learner in the meta-training procedure, and  an optimized meta-learning model was constructed to solve the problem that the loss of all meta-training subtasks in meta-training procedure of classical meta-learning algorithms was equal-weight to update the parameters of meta-learners. The experimental results of this algorithm on Citeseer and Cora datasets are superior to other classical algorithms, which demonstrates the effectiveness of the algorithm on few-shot node classification task.

By using the method of proof by contradiction, the method of pre-assignment of color sets and the method of constructing coloring, we discussed the general total coloring of  complete p-partite graphs which were vertex-distinguished by multiple sets, gave the coloring scheme for optimal coloring and determined the chormatic numbers of the corresponding colorings.

Aiming at white Gaussian noise in remote sensing images, we proposed a remote sensing images denoising algorithm based on shearlet transform and goodness of fit test. Firstly, the noisy remote sensing image was decomposed into different sub-bands through shearlet transform at multiple scales, and  the denoising threshold was estimated using the statistical relationship of white Gaussian noise coefficients in the shearlet domain. Secondly, we calculated the goodness of fit test statistics of high-frequency sub-bands  and compared it with the denoising threshold for denoising. Finally, shearlet  inverse transform on the coefficient matrix was performed to reconstruct the denoised  images. The simulation experiment results show that this algorithm can effectively remove Gaussian noise in remote sensing images, maintain the edge texture information of images, and achieve  high peak signal-to-noise ratio under different noise levels, among which the  average increase is  0.33 dB compared with  the shearlet threshold denoising algorithm.

Aiming at the problem that traditional content-based clothing classification had high requirements for image features, and its accuracy was difficult to meet the application requirements of clothing classification when there were many clothing styles, we proposed a  parallel self-attention classification network based on deep learning methods. The network added a parallel self-attention compensation branch  on the basis of ResNet50, which could improve the quality of feature extraction in clothing classification tasks, and gradually supplement shallow detail information missing from  deep network. A comparative experiment was carried out on the DeepFashion dataset, and the experimental results proved the effectiveness of this method.

By using the method that the determinant of the adjacency matrix of the singular graph was equal to zero, we discussed the singularity of the generalized θ-graphs and the generalized plum blossom φ-graphs, and gave the necessary and sufficient conditions for the generalized θ-graph θ(a₁,a₂,…,a_k) and the generalized plum blossom graph φ(a₁,a₂,…,a_k) to be a singular graph, respectively. The probability values of singular graph occurring in these two types of graphs were calculated.

Nanoparticles of CoFe₂O₄ were prepared by thermal decomposition method. The crystal structure, microstructure and magnetic properties of samples were analyzed by using X-ray diffraction (XRD), scanning electron microscope (SEM) and vibrating sample magnetometer (VSM). The effects of different heating rates on the microstructure and magnetic properties of CoFe₂O₄ nanoparticles during the preparation process were investigated. The results show that increasing the heating rate can increase the growth momentum of crystal nuclei, which is beneficial for the grain growth of the sample, thereby increasing saturation magnetization and coercivity of the sample.

We used SBA-15 hard template replication technology to prepare In₂O₃ series samples with nanowire array structures at different temperatures. The crystal structure, grain size, unit cell parameters, morphology and band gap width of the samples were characterized by X-ray diffractometer, field scanning electron microscope and UV-Vis spectrophotometer, and the gas sensitivity of the samples to ethanol gas was tested and analyzed. The results show that the samples are all three-dimensional nanowire array structures formed by the orderly arrangement and growth of spherical nano In₂O₃ grains. With the increase of sintering temperature, the grain size and nanowire diameter of the samples increase, and the nanowire spacing decreases. The unit cell parameters and the band gap width of the samples show  an increasing and decreasing trend respectively  with the increase of sintering temperature in the range of sintering temperature from 450 ℃ to 650 ℃. When the mass concentration of ethanol gas is 1×10^-4 mg/L and the test temperature is 320 ℃, the sensitivity of the In₂O₃ sample sintered at 450 ℃ is the maximum of 50.59.

Flower-like ZnO (ZnO-F) structure was prepared by chemical precipitation method. The sample structure was characterized by scanning electron microscope (SEM) and transmission electron microscope (TEM), the composition of sample was analyzed by X-ray powder diffraction (XRD), X-ray photoelectron spectroscopy (XPS) and energy dispersive spectroscopy (EDS), the photoelectric performance of the sample was analyzed by UV-visible diffuse reflectance spectroscopy (DRS) and fluorescence spectroscopy (PL), and the photocatalytic activity of ZnO-F was studied by photocatalytic degradation of methylene blue (MB). The results show that the product is ZnO with a diameter of about 1 μm, and its flower-like structure is formed by cross assembly of nanosheets with a diameter of about 17 nm. The sample has high photocatalytic activity, and the photocatalytic degradation efficiency of MB exceeds 90% within 240 min.

By using the variational method, the proof of the existence of the solution of the equation was transformed into finding the critical point of the corresponding energy functional of the equation, and the existence of infinitely many nontrivial solutions of the Kirchhoff-Schrodinger-Poisson system was obtained.

Ganoderma lucidum spore powder was used as raw material,  ethanol  with a volume fraction of  70%  as extractant.  We adopted a combination of enzymatic  hydrolysis and ultrasound assisted extraction method,  set different liquid-solid ratios,  ultrasound time,  enzymatic hydrolysis time,  and enzyme dosage  as  four factors for a one-way test and designed a response surface experiment to  determine the optimal extraction method and its influencing factors. The   Ganoderma triterpene were separated and purified by using macroporous resin chromatography. By optimizing the  separation and purification process, the optimal elution resin,   eluent volume fraction,  flow rate of the upper sample solution and the mass ratio of the upper sample solution were determined. The compositional differences of the total  Ganoderma triterpenes were analysed by high performance liquid chromatography (HPLC). Though the pre-experimental analysis, the results show that the enzyme + ultrasound assisted extraction is more efficient compared to the single extraction method. Ethanol is used as an extractant to extract triterpenoids from Ganoderma lucidum can enhance the purity of triterpenoids. Under optimal conditions, the  rapid and accurate determination of the triterpene content can be achieved, providing a theoretical basis for the separation and purification of Ganoderma triterpenes.

By using the divergence theorem and some important inequalities on Riemannian manifolds, combined with  the method of geometric analysis, we studied rigidity problems of compact gradient Ricci-Yamabe solitons, and obtained rigidity result of the nontrivial compact gradient Ricci-Yamabe solitons being equidistant from Euclidean sphere under appropriate conditions. In addition, under the assumption of positive scalar curvature, we proved that n(4≤n≤6) dimensional compact gradient shrinking Ricci-Yamabe solitons that satisfied L^n/2 integral pinched condition must be Einstein manifolds.

By using the fixed point theorem, we investigated the existence and uniqueness of mild solutions for a class of  delay stochastic evolution equations with α∈(0,1) order Riemann-Liouville fractional derivatives in Hilbert spaces, and proved the Ulam-Hyers stability of the solution. Finally, an example was given to illustrate the applicability of the obtained conclusions.

Firstly, the correlation estimates of temperature and velocity were obtained by using differential inequality technique, especially the fourth-order norm estimates of temperature and the gradient estimates of velocity. Secondly, with the help of a priori bound, the energy expression was constructed and the differential inequality satisfied by the expression was derived. Finally, the continuous dependence of solutions of Brinkman-Darcy fluid equations on the boundary coefficients α was established.

Aiming at the problem of poor adaptability of soil background estimation algorithm after parameter determination, we  proposed a soil background estimation algorithm based on radial basis function (RBF) neural network model, which could effectively improve
 the background deduction effect and element quantitative accuracy of energy-dispersive X-ray fluorescence detection for soil. We first  analyzed the commonly used background estimation models, and proposed an algorithm model based on improved RBF neural network for the deduction effect and problem of continuous peak-stripping method and wavelet transform on background estimation， then we theoretically proved the validity of the algorithm model and  applied it to the actual soil energy-dispersive X-ray fluorescence detection system to detect the national standard soil samples, and the quantitative detection of heavy metal elements such as Cr,Zn and As was analyzed in depth. The experimental results show that the soil background estimation algorithm can better extract the energy eigenvalues of elements, reduce the influence of background on the characteristic peaks and mass fractions of elements, and effectively improve the quantitative accuracy of soil elements.

The dithiocarbamate modified graphene oxide (GO) material (GO-TETA-DTC) based on triethylenetetramine (TETA) was prepared by grafting TETA onto the surface of GO firstly and then reacting it with CS₂. The GO-TETA-DTC was characterized and analyzed by infrared spectrometer,  element analyzer and scanning electron microscope. We studied the adsorption performance of the material on Cu²⁺, and investigated the effects of pH values of solution, initial  mass concentration of Cu²⁺, adsorption time and temperature on adsorption effects. The  results show  that the adsorption process of Cu²⁺ in water by GO-TETA-DTC follows the quasi-second order kinetic equation,  the intra-particle diffusion equation and Langmuir equation.  The maximum adsorption capacity of GO-TETA-DTC for Cu²⁺ calculated from Langmuir equation is 294.12 mg/g. The  adsorption process takes place in the form of heat absorption and  entropy increase.

Ultra-fine SnO₂ nanoparticles were prepared by hydrothermal method using glucose and SnCl₄·5H₂O solution as raw materials. During the synthesis process, different amounts of phosphoric acid(PA) were added into the solution. X-ray diffraction (XRD), scanning electron microscope (SEM), and specific surface area tester were used to characterize the SnO₂ products. We studied the effect of adding PA on the gas sensing properties and analyzed its gas sensing mechanism. The results show that the final products have the ultra-fine particle size and large specific surface area, among which the gas sensor prepared by SnO₂ doped with 0.6 mmol PA has the best gas sensing performance, at the optimal operating temperature of 200 ℃, the sensitivity reaches 7.5 and has good stability. The improvement of its gas sensing properties is attributed to the ultra-fine particle size and large specific surface area, which is beneficial to the adsorption of ethanol gas.

The ADCBAR(1) model was extended to case of the random coefficient,  we proposed a class of first-order random coefficient binomial autoregressive model RCADCBAR(1) with dependent thinning operator, which could be used to characterize the finite-range integer-valued time series data with dependence and zero stacking properties. Firstly, some statistical properties of the model were derived. Secondly, the unknown parameters in the model were estimated by the conditional maximum likelihood method, and the asymptotic properties of estimators were discussed. Finally, the model was applied to a group of real data to illustrate the applicability of the model.

By studying  a class of three-species cooperating models on periodically evolving domain, we discussed  the effect of periodic evolution of domain on the persistence and  extinction of species. The existence and stability of the positive periodic solution of the model were studied by using the upper and lower solutions method, the comparison principle, the theory of quasi-monotone system and the priori estimates of parabolic equations. We recorded  ρ as the domain evolution rate. The results show that the effect of periodically  evolving domain on the persistence of species is negative when ρ^-2>1, it is positive when ρ^-2<1, and  there is no effect when ρ^-2=1.

We studied  the reaction mechanism of Edaravone (Eda) scavenging superoxide anion free radical (O·^-₂) in aqueous liquid phase by using M06-2X and MN15 methods of DFT (density functional theory) and SMD (solvation model density) model method of self-consistent reaction field theory. The results show that the reaction of Eda scavenging O·^-₂ has three channels,  which are extraction of H atom by O·^-₂,  addition of O·^-₂ to unsaturated C and single electron transfer from Eda to O·^-₂. The lowest energy barrier of O·^-₂ extracting H reaction is 12.2 kJ/mol, the lowest energy barrier of O·^-₂ addition reaction is 110.2 kJ/mol, the energy barrier of single electron transfer from Eda to O·^-₂ is 408.5 kJ/mol, and the reaction of extracting H has the most advantage. The  reaction of Eda scavenging O·^-₂ is mainly achieved in channel of extracting H in aqueous liquid phase,  and Eda can be used as O·^-₂ free radical scavenger.

M2-like macrophages induced from human macrophages THP-1 were used as the model, we studied  inhibitory effects of β-1,6-glucan   isolated and purified from Armilla melariella (AAMP-A70) on its polarization and analyzed the role and mechanism of AAMP-A70 in inhibiting DLD-1 proliferation of colon cancer cells by regulating macrophage polarization.   The enzyme linked immunosorbent assay (ELISA) and quantitative real-time PCR (qRT-PCR)  were used to detect the expression of M1-like and M2-like macrophage markers in M2 macrophages induced by THP-1 before and after AAMP-A70 treatment, DLD-1 cells were treated with cell culture medium of each treatment group, and the proliferation of DLD1 cells was detected by MTT assay and crystal violet staining assay, and the expression of apoptosis protein in DLD-1 cells was detected by Western-blot test.  The experimental results show that AAMP-A70 can significantly inhibit the expression of M2-like macrophages markers including VEGF,Arg-1 and TGF-β, and promote the expression of M1-like macrophages markers including TNF-α,IL-1-β and CCR7. The  culture medium of AAMP-A70 treated cells can significantly inhibit the  proliferation of DLD-1 in a concentration-dependent manner.  The supernatant of AAMP-A70 treated cells can induce up regulation of cleaved-PARP and cleaved-Caspase-3 expressed in DLD-1 cells.

We designed and screened  αvβ6 polypeptide ligands with new structure by using computer-aided drug design strategy and solid-phase synthesis method,  and determined  the binding affinity between  the polypeptide ligands and αvβ6 by using enzyme-linked immunosorbent assay (ELISA) to establish a screening scheme for αvβ6 polypeptide ligands.  Firstly,  Sybyl-X 1.3 was used to perform molecular docking of the  αvβ6 polypeptide ligands and natural ligands. Secondly, Amber 16 was used to perform molecular dynamics simulation to determine the binding mode between the polypeptide ligands and αvβ6 protein,  and RGDLXXL (X was any amino acid) was used as the core structure of the polypeptide ligand, the virtual peptide library was constructed by gradual extension of amino acids,  polypeptide ligands with a length of 7—10 amino acids were screened， and new polypeptide ligands different from the core of RGDLXXL were designed and screened by similar amino acid substitution method. Finally,  the newly designed polypeptide ligands were synthesized by solid-phase synthesis method, and  the binding affinity of polypeptide ligand-αvβ6 was determined by indirect ELISA method.   The molecular docking and molecular dynamics simulation results of polypeptide ligands and natural ligands show that the binding of αvβ6 to the ligand is mainly achieved through the hydrogen bond formation between Asp218 and the polypeptide ligand,  and the metal chelation between Mg²⁺ and the polypeptide ligand. Combined with virtual combination screening and similar amino acid substitution,  we find that polypeptides such as GRTDLGTLLFR，GRRTDLATIHG，RTDVGRVRGRG and RGDVGRVGR all meet this binding pattern, and  the affinity between  RTDVGRVRGRG and αvβ6 is 10.76 μmol/L. Therefore,  RTDVGRVRGRG  and αvβ6  have a good affinity and are a new   αvβ6 polypeptide ligand.

Chloromethylated polysulfone with high degree of substitution was prepared from polysulfone as raw materials by chloromethylation reaction,  after reacting with trimethylamine solution,  the quaternary ammonium polysulfone  with bacteriostatic properties and water-soluble was obtained by  dialysis and freeze-drying. The  quaternary ammonium polysulfone  reacted with  polyvinyl alcohol aqueous solution,  the  quaternary ammonium polysulfone/polyvinyl alcohol hydrogels could be obtained by  cross-linking γ-ray radiation without addition of  cross-linking agent. The problem of residual organic solvents and other auxiliary reagents in the polysulfone hydrogels was solved,  at the same time, the  hydrogels had bacteriostatic properties and could be used for preparing medical wound dressings.

We considered the r-hued chromatic number of Cartesian product of complete graph K_n and complete bipartite graph K_n□K_m,s. Firstly, we classified the positive integer r according to its different values, and combined with the properties of K_n□K_m,s, we characterized a lower bound of the r-hued chromatic number of the graph. Secondly, we found a specific (k,r)-coloring of K_n□K_m,s, so we characterized an upper bound of the r-hued chromatic number of the graph. Finally, we determined the r-hued chromatic number of K_n□K_m,s.

Aiming at the problem that the current convolutional neural network could not make full use of the shallow feature information, 
and it was difficult to capture the dependency between each feature channel, resulting in the loss of high-frequency information, we proposed a new generative adversarial network for image super-resolution reconstruction. Firstly, the WDSR-B residual block was introduced into the generator to fully extract the shallow feature information. Secondly, the GCNet module and pixel attention mechanism were combined into the generator and discriminator to learn the importance and high-frequency information of each feature channel. Finally, using spectral normalization instead of batch normalization that was not conducive to image super-resolution, and reduced computational overhead and stabilize training. Experimental results show that compared with other classical algorithms, the proposed algorithm can effectively improve the utilization of shallow feature information, better reconstruct the detailed information and geometric features of the image, and improve the quality of super-resolution images.

Aiming at the problems that using regular square patches for denoising might cause artifacts, or when the image suffered from af
fine deformation, the number of similar patches found by square patches would be reduced, we proposed a BM3D (block matching and 3D filtering) image denoising algorithm based on an affine invariant patch similarity measure. Firstly, in the process of block matching, elliptical patches were used to replace regular square patches for grouping by block matching to form three-dimensional elliptical patch groups. Secondly, an affine invariant patch similarity measure was used to calculate the distance between two elliptical patches and judge their similarity. This measure performed a patch comparison by automatically adjusting the size and shape of the patches, and more similar patches could be found and used for image denoising. Experimental results show that the algorithm can effectively improve the denoising effect and obtain good visual effects. Compared with the original BM3D algorithm, 
this algorithm has better peak signal-to-noise ratio.

Aiming at the problem that the existing sequence recommendation algorithms did not make full use of time information, we proposed  a multi-time embedding mode,  which used  dynamic fusion strategy to alleviate the problem of insufficient long-term preference modeling in existing sequence recommendation algorithms. The multi-time embedding mode could simultaneously model the absolute time information and relative time information of user-item interaction, and fully capture various rules of user-item interaction about time. The dynamic fusion network dynamically integrated the users’ long-term preference and recent preference according to the users’ intentions,  accurately depicted the users’ interest, and improved the diversity of recommendation results.  The proposed time embedding sequence recommendation algorithm based on  long-term memory enhancement was compared with the existing  algorithms on the public datasets MovieLens-1M and Amazon-Beauty. The results show that the proposed algorithm is better than the comparison method in the evaluation indicators HR@N and NDCG@N. Experimental results show that the accuracy of the time embedding sequence recommendation algorithm based on  long-term memory enhancement is higher than that of other  comparison sequence recommendation algorithms.

Aiming at the problem that convolutional neural network (CNN) could only be applied to Euclidean data and could not effectively 
obtain global relationship features between pixels and long-distance contextual information, we constructed a superpixel segmentation-based graph attention network (SSGAT). The network treated the segmented superpixel blocks as graph nodes in the graph structure, effectively reducing the complexity of the graph structure and reducing the noise of the classification graph.  
The classification accuracy of SSGAT and the comparison algorithm were tested on three datasets, and overall classification accuracy of 94.11%, 95.22%, and 96.37% were obtained, respectively. The results show that the method has excellent performance and significant advantages in dealing with classification problems in large-scale regions.

In order to optimize the deployment of wireless sensor networks, we proposed  a new  3D deployment optimization method of wireless sensor networks. On the basis of enhanced gray wolf optimization algorithm, an adaptive weight method was introduced in the outer position update strategy to  balance the search between the development and exploration of the enhanced gray wolf optimization algorithm. Simulation experiments were carried out on the saddle-shaped curved slope, and the experimental results 
show that under 50 nodes, the proposed method can achieve the highest coverage rate of 97.58%, and the average coverage rate can reach 96.74% while ensuring connectivity, which is an increase of 1.64%—3.87% compared with other algorithms. It can effectively improve the coverage of wireless sensor networks and enhance the service quality of wireless sensor networks.

By using the Leray-Schauder fixed point theorem, we discuss the solvability of the fourth-order boundary value problem.  The existence and uniqueness of solutions to the problem are obtained under the condition that the nonlinear term f(x,u,v) is allowed to grow superlinearly with respect to  u,v.

We designed four simple forms of sliding mode surfaces and control inputs, studied the sliding mode synchronization of the fractio
nal-order atmospheric chaotic systems, obtained four sufficient conditions for sliding mode synchronization of the fractional-order atmospheric chaotic systems, and verified the conclusions through numerical simulation. The results show that the master-slave system of the fractional-order atmospheric chaotic systems can achieve sliding mode synchronization under certain conditions.

n-FI injective modules were generalized to the complex level. Firstly, we gave the definition of  n-FI injective complexes. Secondly, we proved that a complex C was n-FI injective complex if and only if each term was n-FI injective module  and Hom(X,C) was acyclic for any complex X with FP-id(X)≤n. Finally, n-FI injective complexes were characterized by covers of complexes.

Aiming at the problem that   multi-source heterogeneous data had the complex sources and unique structure, resulting in a greater difficulty in its fusion. In order to improve the efficiency and accuracy of data fusion, we proposed a multi-source heterogeneous data fusion model based on fuzzy mathematics. Firstly, by utilizing a federated weighted average fusion strategy, the metadata transmitted from various sensors to the data level fusion layer was integrated to obtain the data level fusion results. Secondly, combined with the principal component analysis method and canonical correlation analysis method, the features of data unified by Web Ontology Language were extracted to complete the  feature level data fusion. Thirdly, a fuzzy rule library established and updated based on fuzzy mathematics theory was used to obtain decision level fusion results through decision fusion algorithms. Finally, we combined the data fusion results of above different levels to establish a data fusion model, and obtained the final data fusion result. The experimental results show that the maximum covariance value and absolute error value of the proposed method do not exceed 0.15, and the shortest fusion time is only 12.6 ms. The fusion accuracy and stability of this method are good, and both timeliness and anti-interference have significant advantages.

We designed and synthesized  a novel imidazole ionic liquid crystal compound containing azobenzene group,    its structure was characterized by  ¹H nuclear magnetic resonance,  mass spectrum and infrared spectrum,  and its thermal properties  were characterized by thermogravimetry and differential scanning calorimetry. The results show that compound  remains stable before 190 ℃,  the melting point is 142.96 ℃,  and the liquid crystal range is 124.37—134.04 ℃  upon cooling. The spherical texture of compound can be observed by using polarization microscope,  and confirmed to be the layered structure of compound by X-ray diffraction test. The photo-responsive time of compound  from trans to cis isomerization is 205 s when it is irradiated by ultraviolet light,   the photo-responsive time of compound from cis to trans isomerization is  595 s when it is irradiated by  visible light,  and the degree of trans-cis isomerization reaches 80.4%.

Aiming at the problem of high ranking of commodity views and lagging sales in online shopping, based on purchasing intention of users, we proposed a collaborative filtering recommendation algorithm merged with enhanced rating matrix. Firstly, the penalty factor was used as the evaluation weight of the enhanced matrix, and the commodity portrait representing the user’s purchasing intention was weighted to obtain the prediction score of the enhanced matrix. Secondly, the basic rating matrix was obtained by combining the item-based collaborative filtering recommendation to establish the item similarity matrix between the potentially interested commodities. Finally, TOP-N result was used to recommend the top ranked commodities to target users with strong purchasing intention. The experimental results show that, compared with the traditional item-based collaborative filtering recommendation algorithm, the recommendation accuracy of the enhanced rating matrix collaborative filtering recommendation algorithm is improved by 2.48%, the recall rate is improved by 4.31%, and the comprehensive value F₁ is improved by 3.19%, which effectively solves the problem that the commodities of interest to users are ranked low and are not purchased or purchased less times, so as to achieve recommendation purpose of more accurate target users with strong purchasing intention, and then improve the recommendation accuracy.

In order to improve the speed, accuracy and efficiency of web data query, we proposed a dynamic web data interactive query algorithm based on user preferences. The user preference model was built to increase the evolutionary individual adaptability of the preference combinations, and the adaptive value was  comprehensively calculated. Secondly, in order to prevent data redundancy and duplication, based on interest similarity, query data and duplicate data with high similarity were separated to identify the properties of network data. Finally, the particle swarm optimization algorithm was used to find the optimal interactive query scheme of dynamic web page data. The experimental results show that the quality of the query result set of the proposed algorithm is above 0.95 under the influence of the dataset cardinality, under the influence of the maximum dimension of the query, the quality of the query result set of the proposed algorithm is above 0.96, indicating  that the proposed algorithm has short query time, high precision of the result set and strong adaptability.

We used taking condition method, probability method and moment generating function method to research the lifetime problem of Yule-Furry classical δ shock model, and gave the explicit expressions of the lifetime properties such as reliability, moment generating function and moment of lifetime of the model. The mean lifetime of the model was applied to the problem of cell carcinogenesis and numerically verified.

Aiming at the problems existing in the process of iris quality evaluation, such as how to select appropriate evaluation factors, how to reduce the calculation amount of evaluation factors, and how to effectively integrate evaluation factors, we proposed an iris image quality evaluation method based on genetic algorithm-support vector machine (GA-SVM) model and multi-measure evaluation indexes. Firstly, the definition quality of iris images was evaluated, and fuzzy images were roughly screened out. Secondly, four evaluation indexes were selected and GA-SVM model was used to effectively fuse the evaluation index values to comprehensively evaluate the quality of iris images. Finally, the method was verified in JLU-6.0 iris library and compared with other classical evaluation methods. Experimental results show that this method can improve the survival rate of available iris images, achieve better recognition accuracy, and improve the running speed of the system.

By using Mawhin’s coincidence degree theory, we  study the existence of  solutions for the φ-Hilfer fractional order Riemman-Stieltjes integral boundary value problem. The results show that the solutions of φ-Hilfer fractional differential equation exist under the Riemann-Stieltjes integral boundary value conditions in suitable Banach spaces.

Aiming at the problem of high location precision and real-time in robot servo grasping, we proposed a fast algorithm for feature matching and target location. Firstly, Shi-Tomasi detection algorithm was adopted to extract the feature points. Secondly, a new definition method of feature descriptors was proposed, the sub-image was intercepted with the feature point as a center, and the feature direction was determined by the partial derivative of two-dimensional Gaussian function, the local image was rotated according to the feature direction, and the local binary pattern of the standard local image after rotation was extracted as the feature descriptor, which had good locality as well as invariance of translation and rotation. Finally, the feature matching was realized by calculating the Hamming distance between the feature descriptors, the homography matrix was estimated to locate the position and direction of the target in the scene. The experimental results show that the algorithm has the advantages of fast 
matching speed, high location precision and good stability, and can meet the requirements of location precision and real-time in robot servo grasping.

The extraction conditions of kaempferol were optimized by a two-phase acid hydrolysis method,  and the effects of acid concentration,  extraction time and solid-liquid ratio on the extraction yield of kaempferol were investigated by a single factor experiment combined with high performance liquid chromatography (HPLC). The  response surface Box-Behnken experiment was used to optimize the extraction process of kaempferol. The experimental results show that the optimum extraction conditions are  the concentration of hydrochloric acid of 6.1×10^-2 mmol/L,  the extraction time of 12.87 min,  the solid-liquid  ratio of 1∶137.46,  and the extraction yield is 1.11%. Kaempferol has a certain antioxidant effect,  and has certain scavenging ability on superoxide free radical (·O^2-) and 1,1-diphenyl-2-picrylhydrazyl radical 2,2-diphenyl-1-(2,4,6-trinitrophenyl)hydrazyl (DPPH·),  especially on DPPH·,  and the scavenging ability  increases with the increase of concentration.

The virtual element method was used to solve a three-dimensional steady-state Poisson-Nernst-Planck (PNP) equations on polyhedral meshes. The virtual element discrete forms of the PNP equations were given, and the matrix expressions of the stiffness matrix and the load vector of the electric potential equation and ion concentration equation were derived. The numerical experimental results show that the virtual element computation of PNP equations is realized in three different polyhedral meshes, and the numerical solutions reach the optimal order in both L² and H² norms.

We considered a Stackelberg stochastic differential game problem with an ambiguity-averse reinsurance company as the leader and an ambiguity-neutral insurance company  as the follower. By solving the extended HJB (Hamilton-Jacobi-Bellman) equation systems, we gave the robust optimal investment-reinsurance strategies and the corresponding value function under the time-consistent mean-variance criterion. Finally, we gave some numerical examples and sensitivity analyses to illustrate the relationship between the optimal strategies and the main parameters.

Firstly,  by using the method of quasi-trace functions, the corresponding relationship between the cohomology group of the relative Rota-Baxter operator of a Lie representation pair and the cohomology group of the relative Rota-Baxter operator of the induced 3-Lie representation pair in the low-order cases was given. Secondly, by using the method of constructing chain maps, the homomorphism between the cohomology groups of the relative Rota-Baxter operator of a Lie representation pair and the induced 3-Lie representation pair with any order greater than or equal to 2 was obtained.

Aiming at the problem of frequent identity exchange in multi-target tracking due to target occlusion, we proposed a pedestrian multi-target tracking algorithm. Firtsly, the algorithm used YOLOv4 as the detector to detect the target and determine the coordinates of the detection frame, the extended Kalman filter was used to predict the trajectory. Secondly, the Hungarian algorithm was used as the data association module, the detection frame predicted by extended Kalman filter was matched with the detection frame of target detection by cascade matching method, and the trajectory anomaly correction algorithm was added for the occluded target. Finally, the experiments were carried out on the test set of the MOT16 data set. The experimental results show that the algorithm achieves 56.5% tracking accuracy, and has a good effect on the occlusion phenomenon, which effectively improves the problem of frequent identity switching and target loss caused by occlusion.

Based on the Black-Scholes-Merton option pricing model, we first gave a simplified algorithm of European option pricing equation under Vasicek model by using the method of conversion of valuation units, and then based on the simplified equation, we gave the iterative scheme for the numerical solution of the European option price by using the explicit difference method and the Crank-Nicolson difference method, and verified the stability of the iterative scheme.