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

We considered the existence of uniform  random attractors for a class of delay parabolic equations with additive noise and non-autonomous external force terms on the smooth  bounded domains. Firstly, through the uniform estimation of the solution, we obtained  that the solution of the equation had a closed uniform pullback absorbing set with respect to the symbol space. Secondly, by Sobolev imbedding theorem and Arzela-Ascoli theorem,
the uniform pullback compactness of the solution was obtained.  Finally, the existence and uniqueness of uniform random attractor was proved.

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

By using the Schauder fixed point theorem and topological degree theory, the author studies the existence of positive solutions of Neumann boundary value problems for second order ordinary differential systems with variable coefficients, where f,g: [0,1]×R→R are continuous functions, and f(x,0)<0, g(x,0)<0; a,b∈C([0,1],[0,∞)) are not always 0 on any subinterval of [0,1]. The result shows that under suitable conditions, there exists λ₀>0 such that the problem has at least one positive solution for 0<λ<λ₀.

By using fixed point theorem of cone expansion-compression, the author studies the existence, nonexistence and multiplicity of positive solutions for the elastic beam problem with sliding supports at both ends, where ρ∈(0,π/2) is a constant, λ is a positive parameter, f∈C(［0,1］×［0,+∞),［0,+∞)).

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

Based on  a new 2×2 discrete matrix spectral problem, we  studied conservation law and Darboux transformation of generalized Ablowitz-Ladik (AL) equation. Firstly, we gave infinite  conservation law of the generalized AL equation and obtained its explicit representation by using Riccati  method. Secondly, Darboux transformation (DT) of the generalized AL equation was constructed by means of the Lax pair and gauge  transformation. Finally,  by choosing the appropriate seed solution, we gave the explicit exact solutions of the generalized AL equation,  obtained 2-kink soliton, and analyzed the dynamic properties of the solution.

Firstly, using extrapolation method of one-sided weights, we established the boundedness of multilinear commutators generated by singular integral
and fractional integral  with function in BMO on weighted Lebesgue spaces. Secondly,  on this basis, we further studied the weighted boundedness of this kind of  commutators of one-sided oscillatory integrals on one-sided  Morrey spaces.

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

We considered the continuous up-and-out Paris option pricing problem. Firstly, an implicit difference scheme with the first order in time and the second order in space was given for this type of Paris option. Secondly, the inequality amplification method and Fourier expansion method were used to discuss the stability, solvability and convergence of the difference scheme, respectively. Finally, the numerical pricing results of continuous up-and-out Paris options were analyzed by using the difference scheme.

Aiming at the modeling problem of nonlinear integer-valued time series data with upper limit and dependent structure between data, we proposed a self-exciting generalized binomial threshold autoregressive model. Firstly, we proved the strictly stationary and ergodicity of the model, and discussed some statistical properties of the model, including the expectation, variance, aoto-covariance and the transition probability. Secondly, we gave the conditional maximum likelihood estimation method of the model parameters in the case of known and unknown threshold variable. Finally, we applied the model to a set of real data for fitting verification.

Let {X_n, n≥1} be an independent and identically distributed continuous random variables， let {L_n, n≥1} and {μ_n, n≥1} be the record times sequence and corresponding counting process. By using the central limit theorem, the moment inequalities and the Berry-Esseen inequalities of the record times and its counting process, a general result of precise asymptotics for the record times and corresponding counting process were obtained for the boundary function and quasi-weight function.

Aiming at the problem of estimating the failure parameters of the Poisson censored δ-shock model, under the principle of minimum mean square error and different priori assumptions, the Bayesian estimations of the failure parameters δ of the Possion censored δ-shock model were given  based on the  two kinds of sample data of  total number of shocks in the end of life and the  arrival time of shock by using the Bayesian estimation method.

Firstly, the variable limit integral method and the fourth-order Runge-Kutta method were used to discretize the spatial and temporal variables of a nonlinear Schrodinger equation with a fifth order term, respectively, and a fully-discrete scheme for the initial boundary value problem was constructed. Secondly, we theoretically proved the boundedness, existence, uniqueness and the order of convergence of the numerical solution. Finally, the numerical simulations verified the validity of the theoretical analysis.

By introducing a real function class Φ on ［1,∞)⁴, we gave the existence theorems of unique common fixed point for two mappings satisfying the Φ-implicit condition on multiplicative metric spaces, and gave some (common) fixed point theorems. The conclusions generalized and improved the existing common fixed point theorems (in particular, the Banach-Chateajia type common fixed point theorems on multiplicative metric spaces). Finally, two examples were used to verify the correctness of the conclusions.

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

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

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

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

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

Aiming at the complexity and diversity of current network intrusion, the traditional model was insufficient to extract traffic characteristics, and had low accuracy, we proposed an intrusion detection method based on CR-BiGRU hybrid model improved by merging residual network. Firstly, the dataset was normalized and one-hot encoding treatment in the model. Secondly, the convolutional neural network based on the residual network was used to extract the spatial features. Finally,   the bidirectional gated neural network was used to extract the temporal features,  complete the training of the model and realize the intrusion detection of the abnormal network. In order to illustrate the applicability of the model, comparative analysis experiments were conducted based on NSL-KDD and UNSW-NB15 datasets. The results show that the accuracy of the method based on the above datasets is 99.40% and 83.79% respectively, which is obviously superior to the classical network intrusion detection algorithm, and can effectively improve the accuracy of network intrusion detection, so as to  better ensure the  communication security of network data.

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

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

In order to clarify the texture thickness and tissue distribution of the X-ray image, enhance the presentation of body structure information, and reduce the wrong judgment of fuzzy image on doctors’  diagnosis results, we proposed an adaptive enhancement algorithm of digital X-ray image based on Markov random field model. Firstly, the algorithm counted the pixels with the same brightness in the whole range of X-ray image, and the histogram equalization method was used to transform the original image into gray level distribution image  to eliminate light interference. Secondly, we analyzed the organization attributes, extracted the texture features of X-ray image through gray level co-occurrence matrix, and obtained the gray level information of image texture thickness and layout structure. Finally, the average brightness was calculated by the mapping function and logarithmic function, the Markov random field model was used to adjust the brightness of the image, supplement the brightness of small parts of the texture, then the smooth image was divided by the random field function, and the  secondary reconstruction was adopted to ensure the balance of image sharpening and enhancement effect. The simulation results show that the proposed algorithm can improve the internal information clarity of the image.

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

In order to reduce the delay of data transmission in banded wireless sensor networks, the author proposed a real-time intelligent data collection algorithm based on data compression and line scheduling. Firstly, through the transformation training of the collected data, the correlation of the data was evaluated, and the longest scale of segmentation coding was determined, so that the redundant information was compressed by recoding. Secondly, the author calculated the maximum time slot length occupied by data collection, scheduled network collection links, and minimized time delay.  Finally, the transmission energy consumption model was built by multi-path transmission mechanism, and solved by Lagrange function algorithm to complete data collection. The simulation results show that the proposed algorithm has the advantages of network load balancing, small data collection  transmission delay, low energy consumption and good robustness.

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

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

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

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

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

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