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.

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.

 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.

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.

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.

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%.

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.

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.

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.

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.

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.

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).

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.

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 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.

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.

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).

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.

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.

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.

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.

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 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.

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.

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 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.

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 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.

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  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 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.

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.

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 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.

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.

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.

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 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 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.

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 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 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 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.

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.

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.

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.

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). 

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.

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 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.

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.

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.

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.

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.

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.

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 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.

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.

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.

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 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.

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 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 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.

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.

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.

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.

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.

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.

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.

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.

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. 

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.

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.

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 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.

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.

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 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 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.

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.

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.

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.

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.

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 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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%.

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.

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.

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.

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.

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.

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 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.

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.

By using the time mapping principle, we prove the existence and multiplicity of positive solutions for the  boundary value problem with one-dimensional Minkowski mean curvature operator in the semipositive case of nonlinear terms and the nonlinear term is generalized from f(0)≥0 to f(0)<0.

By using the techniques of dealing with sublinear neutral terms, generalized Riccati transformation and integral averaging techniques, firstly, the author gave an analytical method for estimating Riccati transformation inequality. Secondly, the author considered a class of third-order damped differential equations with sublinear neutral terms and distributed delays, and obtained some sufficient conditions for the solution to oscillate or converge to zero. Finally, the results were verified by some examples.

Firstly, based on techniques such as  Taylor expansion and Chapman-Enskog multi-scale expansion,  the lattice Boltzmann method was used to accurately recover the discussed macroscopic equations, and  the equilibrium distribution function expressions of D1Q3 and D2Q9 models were derived. Secondly,  two numerical examples were used to verify the effectiveness of the proposed method. The results show that the lattice Boltzmann method can be used to solve the numerical solution of the Caputo type modified time fractional equation.

We considered  a class of Kirchhoff type viscoelastic wave equation with logarithmic nonlinear term of variable exponents. Firstly, the energy identity for the problem was given. Secondly, by constructing auxiliary functions and using Holder inequality and Gagliardo-Nirenberg inequality, we obtained the result of blow up of equation solutions in finite time in the case where  the logarithmic nonlinear term  contained variable exponents.

We used  finite element method to numerically solve the viscous Cahn-Hilliard equation. Firstly, the equivalent form of the viscous Cahn-Hilliard equation was obtained by introducing the Lagrange multiplier r of the auxiliary variable. Secondly, the second order linear finite element numerical scheme for the viscous Cahn-Hilliard equation was given by using the mixed finite element approximation  in space and the implicit backward differentiation formula (BDF)  for discretization in time, and the unconditional stability in energy and error estimation of the given scheme were analyzed in detail. Finally, a series of numerical examples were used to verify the accuracy and effectiveness of the given scheme. The results show that the proposed numerical scheme is ideal and has the characteristics of simultaneously satisfying linear, unconditional stability in energy and second order accuracy.

Aiming at the problem that the diagnosis of pleomorphic adenoma completely relied on manual labor, we proposed a computer
-assisted diagnostic method. Firstly, by  collecting data and constructing a pleomorphic adenoma dataset, the current dense connection nertwork was improved and fused with the channel attention mechanism for disease tissue classification feature extraction to obtain tissue categories and probabilities. Secondly, by using classification and regression trees (CART), we obtained diagnostic results and  provided manual assistance in the selection of difficult categories, thus achieving  computer-assisted work on pleomorphic adenomatous diseases. The experimental results show that the method  achieves  classification extraction accuracy of 97.7% in the classification recognition module, and decision tree inference diagnostic accyracy of 100%. In addition, the accuracy of classification recognition module  achieves 98.6%  in the field of blood cell classification, and the method has certain transferability and validity.

By using Leray-Schauder degree theory and Banach contraction mapping principle, we studied the existence and uniqueness of solutions for boundary value problems of conformable fractional delay differential equations when the nonlinear term satisfied the growth condition and the Lipschitz condition, we obtained the results of existence and uniqueness of solution for the boundary value problem respectively, and gave an example to illustrate the applicability of the obtained results.

Aiming at the uncertain mechanism  of node activation strategies and redundancy of feasible solution sets in the process of solving target coverage problem in wireless sensor networks, we proposed a deep Q learning based target coverage algorithm to learn the scheduling strategies of nodes in wireless sensor networks. Firstly, the algorithm abstracted the construction of feasible solution sets into  Markov decision process, and intelligently selected activated sensor nodes as discrete actions according to the network environment. Secondly, a reward function  evaluated the performance of the intelligent agent in selecting actions based on the 
 coverage capacity and its residual energy of the active node. The simulation  experiment result shows that the algorithm is effective in different network environments, and the network lifecycle is superior to the  three  greedy algorithms, the maximum lifetime  coverage algorithm and the adaptive learning automaton algorithm.

Aiming at the problems of overfitting and low classification accuracy in brain tumor magnetic resonance image classification, we proposed a brain tumor classification method based on an improved EfficientNetV2 network. The method  introduced the coordinate attention mechanism in the EfficientNetV2 network, which simultaneously obtained the feature information of brain tumor from both vertical and horizontal directions and accurately identified the lesion features of brain tumor. It helped the model to locate and identify the lesion area information more comprehensively and accurately, and effectively suppressed the influence of background information on the detection results, so that the model had higher classification accuracy. The problem of low classification accuracy caused by  insufficient acquisition of feature information was solved. In order to further improve the classification accuracy, the Hard-Swish activation function was introduced, which could not only improve the computational speed of the brain tumor classification network model, but also effectively improve the classification accuracy. Meanwhile, the improved model was equipped with Dropout layer and normalization layer, which could better suppress the occurrence of overfitting, accelerate the convergence speed of the model, improve the robustness of the model, and significantly improve the classification accuracy. The experimental results show that the improved model obtains classification accuracy of 98.4% in the validation set, and the effectiveness of the improved model in brain tumor classification task is verified by comparison experiments and ablation experiments.

By using the harmonic analysis method and Lagrangian method, we studied the Cauchy problem for the multi-dimensional inhomogeneous incompressible heat-conducting equations and  proved the global well-posedness of strong solutions for the system under small initial data conditions in the critical Besov spaces.

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 used the Faedo-Galerkin method to investigate the three-dimensional magnetofluid equations with nonlinear damping terms and  delay terms on a bounded domain  and solved the problem of well-posedness of the solutions. Firstly, the existence of strong solutions was proven when α≥16/5. Secondly, the uniqueness of strong solutions was proven by using the Gagliardo-Niernberg inequality.

Aiming at the shortcomings of incomplete multi-view clustering, we  proposed a unified framework that integrated self-representation and projection mapping. Firstly, self-representation and sample presence indication matrices were used to learn a uniform similarity graph, which reflected the common similarity relationship between samples. Secondly, the sample matrices were projected onto the hypersphere by using projection mapping to obtain a common low-dimensional representation. Finally, the two were embedded together through spectral representation to solve the incomplete multi-view clustering problem caused by missing multi-view data. The experimental results of this algorithm on real datasets are better than other algorithms, which proves the effectiveness of the proposed algorithm.

We considered the finite time blow-up to  a strongly damped  wave equation with variable-exponent nonlinear term. With the help of concave method and appropriately selected  parameters, we gave a new  blow-up criterion  for this problem and estimated the upper and lower bounds on  the blow-up time. The results show that the blow-up criterion contains special  implications for any high initial energy, and  the problem has a finite  time blow-up solutions.

We studied the control problem of third-order third-power nonlinear chaotic circuits. Firstly, we gave the Lyapunov exponent and chaotic attractor of the system to verify the existence of complex chaos in the system. Secondly, using adaptive feedback control method and H_∞ state feedback control method, we designed the adaptive feedback controller with known and unknown parameters and H_∞ state feedback controller to stabilize the chaotic system state to the equilibrium point. Finally, the effectiveness of the controller was verified through numerical simulation by using MATLAB software, and the control effect of the two controllers was compared.

The stochastic stability and stochastic bifurcation behavior  of Van der pol vibration damping system constructed based on fractional-order viscoelastic material was studied under external broadband noise excitation. Considering the influence of constraints condition, a non-smooth Zhuravlev transformation was introduced to transform the collision system into a collision-free dynamic system. A set of quasi-periodic functions was used to replace the fractional-order differential element approximately, the stochastic average method was used to obtain the Ito stochastic differential equation of the system. The stochastic stability of the system was classified and discussed based on the maximum Lyapunov exponent method and singular boundary theory. The stochastic bifurcation behavior of the system under the linear Ito equation was analyzed by using the pseudo Halmiton system stochastic average method, and the critical condition for D-bifurcation was obtained. Furthermore, the stationary probability density function related to the amplitude of the system was obtained. Using the steady-state probability density curves drawn by MATLAB to visually display the changes of steady state that occurred in the system. The results show that the system can generate P-bifurcation behavior when the fractional-order and noise intensity change within a certain threshold.

A multifunctional LiBr/MoO₃/PE composite separator was prepared by introducing molybdenum trioxide (MoO₃) and lithium bromide (LiBr) coatings onto polyethylene (PE) separators. The structure and morphology of the separator were characterized by X-ray diffraction and scanning electron microscope, and cyclic voltammetry, electrochemical impedance and charge discharge performance testing were used to investigate the effect of LiBr/MoO₃/PE separator coated with a modified layer on the stability of lithium metal negative electrodes and the performance of lithium sulfur batteries. The results show that LiBr increases the solubility of lithium polysulfide (LiPSs), and the MoO₃ layer has a chemical adsorption effect on LiPSs, which can improve the utilization rate of active substance sulfur and suppress the shuttle effect of Li-S batteries. The Li-Li symmetric battery with LiBr/MoO₃/PE as the separator has a stable cycle time of 1 600 h at a current density of 0.6 mA/cm² and a capacity of 1 (mA·h)/cm². The initial discharge specific capacity of the lithium sulfur battery at 0.2 C can reach 1 229.2 (mA·h)/g, and the specific capacity after 500 charge discharge cycles is 628 (mA·h)/g.

The first-principles pseudopotential plane wave method based on density functional theory was used to investigate the geometric structures and electronic properties of H,F,Zn,K,Al doped two-dimensional (2D) MgCl₂ monolayer materials. The results show that the crystal structures of these doped systems distort in different degrees. Due to the influence of s-state electrons of H,Al and Zn, the impurity levels of doped MgCl₂ appear in the forbidden bands, while the impurity levels of F and K doped systems appear in the valence bands. Compared with the 5.996 eV band gap of intrinsic MgCl₂ material, the band gap widths of H,F,Al,K and Zn doped systems decrease to 5.665,5.903,4.409,5.802,5.199  eV, respectively. The charges around the impurity atoms of five
 doped systems are redistributed. The charge transfers are consistent with the charge density difference results. Compared with the intrinsic work function 8.250 eV of MgCl₂, the work functions of H,F,Al,K and Zn doped systems decrease to 7.629,7.990,3.597,7.685,7.784 eV, respectively.

By using Rosenthal’s inequality, we discussed almost sure convergence of weighted sums for m-END (m-extended negatively dependent) random variable sequence. Almost sure convergence of weighted sums for END sequence in the classical probability space was extended to the almost sure convergence of weighted sums for m-END random variable sequence under the sub-linear expectations.

Firstly, based on the Black-Scholes stock price model,  the neural stochastic differential equation (NSDE) model was established by parameterizing the asset return rate and volatility as a drift network and a diffusion network, respectively. Secondly, in the empirical analysis, the underlying asset as a single stock option was used as the research object, and real stock data was used for  the network training  and testing. The experimental results show that the NSDE model can overcome the defects of the constant assumption of the Black-Scholes model. Finally, for the case where the price of the underlying asset of the option was unobservable, we  proposed that the price of any target option and the price of a known option could be constrained within the Wasserstein distance of their risk-neutral equivalent martingale measure, and theoretically  proved the method.

By using T-weak continuous operator method and classical Galerkin technique, we discussed the initial boundary value problem of a class of incompressible magneto-micropolar fluid equations in a two-dimensional bounded smooth region, and obtained the existence and uniqueness theorems of the global weak solutions for the problem,   further improving the regularity of the weak solutions.

Based on the fact  that infected animals found in animal detection still had  infectious characteristics, we established a dynamic model to analyze the influence of detection behavior on the spread of animal brucellosis. Firstly, the basic reproduction number of the model was given, and the existence of the equilibrium point was analyzed. Secondly, through the discussion of the equilibrium point, it was found that the model occured backward bifurcation. Lyapunov function was used to prove that when R₀<1, the equilibrium point of disease-free was globally asymptotically stable under certain condition, when R₀>1, the model was uniformly persistent. Thirdly,  the optimal control strategy was formulated and solved according to Pontryagin maximum principle. Finally,  the theoretical analysis results were validated by numerical simulation, indicating that the control strategy can effectively control the spread of animal brucellosis.

We gave a Dai-Liao conjugate gradient method based on regularization model. Firstly,  a new Dai-Liao parameter t was obtained by minimizing the 3-degree regularization model, and based  on this, an adaptive Dai-Liao parameter was generated according to  the properties of the  function near  the iterative point. Secondly, combined with improved Wolfe line search, we proposed a Dai-Liao conjugate gradient method based on regularization model. Finally, we proved that the search direction of the proposed 
method satisfied sufficient descent, and established the global convergence of the proposed algorithm under the general assumption. Numerical results show that the proposed algorithm is effective.

Aiming at  the problem of unknown words in speech recognition tasks, we proposed a threshold based-BPE-dropout multi-task learning speech recognition method. This method adopted a random byte pair coding algorithm. When forming sub-words, a strategy with word number threshold was introduced. The sub-words were used as modeling units, and the encoder part adopted Conformer structure, which was combined with link timing classification and attention mechanism. In order to further improve the performance of the model,  dynamic parameters were  introduced to dynamically adjust the loss function, and  multi-task training and decoding were performed simultaneously. The experimental results show that the proposed method can effectively solve the problem of unknown words by using sub-words as modeling units, and further improve the recognition performance of the model under the multi-task learning framework. On the public datasets THCHS30 and ST-CMDS, the model achieves more than 95% recognition accuracy.

We used the methods of conservative energy estimation and characteristic line estimation to solve the Sobolev norm growth estimation problem of the solution of the (1+1)-dimensional Maxwell-Chern-Simons-Higgs model, gave the L^∞ estimation of the first derivative of the finite energy solution of the model, and obtained the polynomial growth of the H² norm of the solution by improving the exponential growth.

Aiming at the problems that the existing mainstream target detection algorithms had  low detection accuracy and incomplete segmentation in the  image edge regions, we proposed a region of interest pooling algorithm based on Mask RCNN model. Firstly, the feature maps of the regions of interest were divided into edge regions and non-edge regions by the Otsu threshold segmentation method. Secondly, the edge gradient interpolation algorithm was used to interpolate for the edge regions, 
and the bilinear interpolation algorithm was used to interpolate for the non-edge regions so that the discrete feature map was mapped into a continuous space. Thirdly,  the interpolated feature maps were evenly divided into k×k units. Finally, the double integral was used to calculate the average value of each unit to complete the pooling operation. The comparative experimental results show that the proposed algorithm, based on the Mask RCNN model, has a certain improvement in detection accuracy  compared with existing algorithms on COCO(2014) dataset, and has a good segmentation effect on the details of the image edge regions.

Based on the modified Cambridge model, an elasto-plastic model was established to describe the physical-mechanical behavior of unsaturated granite residual soils by adjusting the yield surface, and the basic incremental format of the modified Cambridge model was derived. The interface program of ABAQUS was developed to realize the stress and deformation analysis of unsaturated granite residual soil. Compared the simulation results with test data of unsaturated granite residual soils measured by GDS (global digital system) triaxial apparatus. The results show that the simulation results are consistent with the experimental results.

Aiming at the problem of location privacy leakage of workers in traditional mobile crowd sensing, we proposed a two-stage location privacy protection method. Firstly, a system model combining blockchain and edge computing was designed to replace the third-party platform. Secondly, a ciphertext time worker selection algorithm based on homomorphic encryption was proposed in the task allocation stage, which efficiently completed the task allocation through the cooperation of edge nodes. Finally, in the data upload stage, a two disturbance local differential privacy algorithm was given, workers perturbed location data locally, and the interference factor ω was added to balance the protection strength and the quality  loss. Simulation experimental results show that compared with the existing algorithms, the proposed method improves the task completion rate, reduces the  service quality loss, and effectively protects the location privacy of workers.

We considered the generalized anti-periodic boundary value problem for a class of nonlinear Caputo fractional q-difference equations, gave the existence and uniqueness results of solutions for the generalized anti-periodic boundary value problem  by using the Banach fixed point theorem, and  gave an application example.

Aiming at the problem of unreasonable traffic-path allocation and elephant flow collision in data center networks, we proposed a 
software defined network (SDN) flow scheduling algorithm based on discrete partical swarm optimization. The algorithm redefined the search  process within the partical swarm with the goal of optimizing  network performance,  dynamically allocated optimal paths for  data center traffic to reduce elephant flow collision, and introduced Metropolis to design  diversified optimal  scheduling scheme to ensure reasonable scheduling of data center traffic. The experimental results of  comparing and verifying with other flow scheduling algorithms show that the algorithm improves network quality, reduces  elephant flow delay, and achieves a better
 load balancing of network.

Aiming at the problem that the initial number of clusters and cluster centers derived from the clustering layer in the original deep embedding clustering (DEC) algorithm had  strong randomness and thus affected the effectiveness of the  DEC algorithm, we proposed a review text clustering algorithm based on improved DEC for unsupervised clustering of category-free labeled e-commerce review data. Firstly, we  obtained a vectorized representation of the BERT-LDA dataset incorporating the sentence embedding vector and the topic distribution vector.  Secondly, we improved DEC algorithm, reduced the dimensionality by the autoencoder, and stacked the clustering layers  after the encoder, where the number of clusters in the clustering layers was selected based on the topic coherence. Meanwhile,  the topic feature vector was used as the custom clustering center, and then the joint training of encoder and clustering layers was performed to improve the accuracy of clustering. Finally, the visualization tool was used to visually  display the clustering effect. In order to verify the effectiveness of the proposed algorithm, unsupervised clustering  training was conducted  on an unlabeled product review dataset by using the algorithm and six comparison algorithms. The results show that the algorithm  achieves the best results of 0.213 5 and 2 958.18 in the contour coefficient  and Calinski-Harabaz (CH) index, indicating that the algorithm  can effectively handle ecommerce review data and reflect users’ attention to the products.

In order to suppress the transformation of amyloid β polypeptide (Aβ)  from random curling or α-helix to β-folding structure, we studied the conformational changes of wild type Aβ and its array mutants. Combining Markov model and molecular dynamics simulation, we studied the conformational change precess  of the wild type,  A4 type and D7N type Aβ, and identified the  conformational transformation path of three Aβ types. The experimental results show that one region of β-folding is found in the wild type Aβ, and the conformation of the A4 type Aβ is almost unchanged, while two regions of β-folding are found in the D7N type Aβ, indicating that the D7N type mutant has the characteristic of promoting β-folding. The results provide a theoretical baisis for exploring treatment methods for Alzheimer’s disease.

Aiming at  the problem that the current traditional method of analyzing target background difference using polarization parametric images did not fully consider the unique polarization properties generated by light acting on objects, we proposed a target background difference feature analysis method based on the statistical characteristics of polarization direction features, from a new  polarization direction information to analyze target background difference. Firstly, the polarization direction vector image was constructed by extracting the polarization direction information from the polarization angle image, which solved the problem that the polarization angle image could not be used effectively and directly due to too much noise. Secondly, the orthogonal difference calculation was carried out for the four polarization direction intensity images respectively to obtain the polarization orthogonal difference component images, and the information of the polarization angle intensity images around the ±α polarization direction was supplemented to obtain the polarization direction statistical images. By extracting the three polarization feature images of the four polarization directions, the problem of traditional polarization parametric images with less prominent target in the complex background was solved. The experimental results show that objects of different materials have different polarization directions, and the polarization direction feature image obtained by extracting the polarization direction information can more clearly identify the target in the complex background. The objective evaluation index show that the polarization direction feature image corresponding to the polarization direction orientation of the target area in the polarization direction vector image is richer in expressing the information of the target, and is more informative than the polarization direction feature image corresponding to other polarization directions.  Therefore, the polarization vector image can be used to quickly extract the polarization feature image with prominent target features.

By using Holder’s inequality and the related properties of weighted functions, we gave the boundedness of fractional integral operators and BMO  commutator on generalized weighted Morrey spaces over RD (reverse doubling condition)-spaces, and gave the corresponding  endpoint estimates.

Aiming at the problems that the classical deep learning algorithm was difficult to extract facial features effectively and the accuracy of character identification was difficult to reach the ideal accuracy due to factors such as illumination, shooting angle and image quality, we proposed an  age recognition algorithm based on strong facial semantics. Firstly, the feature weights of facial regions were enhanced by the attention matrix to achieve the purpose of extracting feature regions. Secondly, a cascaded bi-directional long short-term memory (Bi-LSTM) network was used to learn the feature dependency relationships between temporal frames 
and  compensate for the influence of missing features on recognition accuracy. When tested on IMDB-WIKI facial dataset and Adience dataset, the age recognition accuracy of the algorithm reached 78.34% and 77.89%, respectively. Experimental results show that compared with other methods based on deep learning algorithms, the proposed algorithm has higher accuracy in the task of person age recognition based on image datasets.

The Hopf bifurcation of predator-prey symbiotic model with double time delay was discussed  by using the normal form theory and the central manifold theorem. By analyzing the characteristic equation and taking the development time of the prey and the development time of the co-genitor as the parameters, the stability of equilibrium point, the existence of Hopf bifurcation, the stability of bifurcation direction and bifurcating periodic solution were given. The result that  time delay  affected the stability of the system was obtained. The correctness of obtained conclusions was verified through numerical simulation.

By using the compactness method, we gaved the existence of solutions to the Cauchy problem of the energy-critical fractional  nonlinear Schrodinger equation and proved the existence of global solution to the Cauchy problem. By constructing the approximation equation and taking the limit of the solution sequence satisfying the approximation equation, the obtained limit function was the global weak solution of the energy-critical fractional nonlinear Schrodinger equation, and it was proved that the weak solution satisfied the energy inequality and mass conservation property.

By considering the influence of various uncertain noises, we established an uncertain Logistic population model with Allee effect, which was characterized by an uncertain differential equation. Firstly, we obtained the solution of the model, and discussed the stability of the equilibrium state. Secondly, the unknown parameters in the model were estimated by using the generalized moment estimation method under the framework of uncertainty theory. Finally, the parameter estimations of the model and the properties of the solution were explained by an example analysis.

Using the weight coefficient method and real analysis techniques, we discussed the problems of constructing semi-discrete Hilbert-type inverse inequality with generalized homogeneous kernel, gave necessary and sufficient conditions for constructing such inequality,  the calculating formula of the best constant factor, and the  operator expression of the inequality.

Based on non Markov chain denoising diffusion implicit model (DDIM), we proposed  probability method of denoising diffusion based on  rough sets. The rough set theory was used to equivalently partition the sampled original sequence, construct the upper and lower approximation sets and roughness of the subsequences on the original sequence, and obtain the effective subsequences of the non Markov chain DDIM when the roughness was the lowest. The comparative experiments were conducted by the denoising diffusion probability model (DDPM) and DDIM,  and the experimental results  show that the sequence obtained by proposed method is an effective subsequence, and the sampling efficiency on this sequence is better than that of the DDPM.

Aiming at the problems of the limitation of obtaining global features in image recognition and the difficulty in improving recognition accuracy, we proposed  an image recognition method based on the lightweight model of random augmentation Swin-Tiny Transformer.  The method combined the random data augmentation based enhancement (RDABE) algorithm to enhance image features in the preprocessing stage, and adopted the Transformer’s self-attention mechanism to obtain more comprehensive 
high-level visual semantic information. By optimizing the Swin-Tiny Transformer model and fine-tuning the parameters on a maize disease dataset, the applicability of the algorithm was verified on maize diseases in the agricultural field, and more accurate disease detection was achieved. The experimental results show that the lightweight Swin-Tiny+RDABE model based on stochastic 
enhancement has an accuracy of 93.586 7% for maize disease image recognition. The experimental results compared with the excellent performance lightweight Transformer and convolutional neural network (CNN) series models with consistent parameter weights show that  the accuracy of the improved model is higher than that of the  Swin-Tiny Transformer, Deit3_Small, Vit Small, 
Mobilenet_V3_Small, ShufflenetV2 and Efficientnet_B1_Pruned models by 1.187 7% to 4.988 1%, and can converge rapidly.

Firstly, by using  the method of weight functions, Euler-Maclaurin summation formula, Abel’s summation by parts formula, and the technique of real analysis, we gave a new half-discrete Hilbert-type inequality involving higher-order derivative function and partial sums. Secondly, as applications, we discussed the equivalent conditions of the best constant factor to connect multiple parameters in a  inequality with particular  parameter and several particular inequalities.

Aiming at  the problems that  the whale optimization algorithm was prone to getting stuck in local optima and had drawbacks such as slow  speed control response and large overshoot of brushless DC motor, we  proposed an improved whale optimization algorithm (IWOA) for optimizing proportional integral derivative (PID) parameters in brushless DC motor speed control. The algorithm combined Gaussian mutation factor, adaptive weight factor, and dynamic threshold to optimize the whale optimization algorithm. The simulation experiment results show that the  improved whale optimization  PID speed control algorithm of brushless DC motor has faster  convergence rate, smaller overshoot phenomenon, and better robustness.

Aiming at the problems of insufficient training data and low accuracy of long-tail entity alignment  in the task of knowledge graph entity alignment, we  proposed an iterative entity alignment method based on an adaptive feature fusion strategy and designed an iterative strategy to automatically expand the scale of the training data. This method utilized the structural information of the knowledge graph and utilized  relationships, attributes, and entity name information as  semantic information to assist  alignment 
and  improve alignment effectiveness. The experimental results on the dataset show that the proposed model  performs well in the task of knowledge graph entity alignment.

We considered the characterization problem of weighted right core inverses and weighted right pseudo core inverses over *-rings by 
using algebraic methods. Firstly, the concept of weighted right core inverse was introduced. Secondly,  three equations and right invertible elements were used to give its characterization. Finally, the definition and characterization of weighted right pseudo core inverse were given.

Aiming at the problem that the control of link load was affected by the search space of the Internet of Things, a small  search space could reduce the load balancing degree， we proposed a load balancing control method of the Internet of Things  link based on  improved genetic algorithm. Firstly, the frequency band transmission model of the Internet of Things link was constructed, and tap interval sampling was used to control the transmission of the Internet of Things link, the frequency band model of the Internet of Things link was established  to obtain the balanced scheduling function, and the frequency band was integrated to complete the load balancing configuration. Secondly, we added  fractional interval equalization to design the link, used the frequency band allocation principle to obtain the frequency band matching probability, adjusted the tap value of the equalizer, and set the inter symbol interference term constraint of the link. Thirdly, we gave the parameter code of genetic algorithm, arranged all requests  in one-dimensional order, and  transformed  linear scale on the fitness function to complete the improvement of genetic algorithm. Finally, we combined  gene evolution chromosomes to expand the search space of the Internet of Things, made the number of iterations less than the maximum coefficient, and realized the balancing control of link transmission load. The experimental results show that the proposed method can effectively  control the load balancing of the Internet of Things link, the link load balancing degree can reach 92%, and can reduce energy consumption.

We considered the representation of the Drazin inverses of the sum for two matrices. For n-|th order matrices P and Q, the expression  of the Drazin inverse of the sum for two matrices P+Q was given by using the Cline formula and the properties of Drazin inverse under the conditions such as  P²QP²=0, P³QP=0, PQ³=0, PQ²P=0, P²QPQ=0, etc.

Firstly, by using the power function method, we discussed the half-discrete Hilbert-type inverse inequality with non-homogeneous kernel K(n,x)=G(n^λ1x^λ2)(λ₁λ₂>0), gave equivalent conditions for the best half-discrete Hilbert-type inverse inequality and the relationship  between the parameters. Secondly,  as an application, we gave  the equivalent operator expressions and some special cases.

Aiming at the problem of equipment heterogeneity and the change of Bluetooth beacon nodes in indoor location based on Bluetooth fingerprint, we proposed an indoor location algorithm for heterogeneous devices and environmental changes. Firstly, we used Procrustes analysis method to standardize the received signal strength, and used kernel extreme learning machine (KELM) to model the standardized fingerprint database to reduce the signal strength differences caused by the differences of users’ mobile terminals. Secondly, when the access point (AP) signal changed, the access point signal was recalibrated by Gaussian process regression (GPR), and the fingerprint database was updated to eliminate the positioning error caused by the weak signal, position movement or environmental change of the access point. Test analysis results show that the algorithm can effectively overcome the impact of heterogeneous equipment, and better adapt to the environmental changes.

In order to improve the accuracy of short text semantic similarity measurement, we designed a short text semantic similarity measurement algorithm based on a hybrid machine learning model. Firstly, we preprocessed the short text, constructed a word vector model of the short text based on the hybrid machine learning model, and extended the  features of the short text. Secondly, we  combined the various metric features of the short text, implemented dimensional reduction on the various metric features. Finally, we constructed an ensemble learning  model to calculate the semantic similarity results and achieve the  semantic similarity measurement. We tested the performance of the method by using the “Quora Question Pairs” competition dataset, the test results show that the accuracy of the  method is high, the logarithmic loss, and the measurement mean square error are both low, indicating that the similarity measurement accuracy of the method is high.

We  gave necessary and sufficient conditions for bounded linear operators and their operator functions to satisfy the property
 (UW_Π) by using the spectrum sets defined by topological uniform descent property, commonly used spectrum sets and some properties of operators themselves, and discussed  the perturbation problems of property (UW_Π).

We proposed an improved square root unscented Kalman filtering (SRUKF) algorithm to reduce motor speed error in the presence of interference. The interference was added to affect  the motor operation in simulation experiments, we used information such as d-q axis current, electrical angular velocity, and rotor position of the motor to predict the motor speed value, and used improved algorithms to control the speed to reduce the error caused by interference on the motor speed. Compared it with the traditional unscented Kalman filtering algorithm. The results show that the algorithm has less system operation, and the error of the interfered motor speed controlled by the algorithm is smaller compared to the true value without interference, and it has better robustness.