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

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

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

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

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

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

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

By using topological degree theory, the author studies the existence of positive radial solutions of 2m order semipositone elliptic equations in the annulus, where λ>0 is a parameter, m≥1 is a positive integer,  Ω={x∈Rⁿ; a<|x|<b}(n>2m), 0<a<b<∞, f∈C(［a,b］×［0,∞),R).  The results show that there exists λ₀>0, so that the above problem 
has at least one positive radial solution when λ₀ under suitable conditions.

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

Firstly, we study the Dirichlet forms (ε,Dom ε) in continuous-time Guichardet-Fock space L²(Γ;η) by means of multiple integral of bounded operator, and obtain the relation. Secondly, we consider a class of operator semigroups and prove the relation.

We considered the influence of discontinuous noise on the disease transmission process with an incubation period, and established a stochastic SEIQR epidemic model driven by Lévy noise. Based on the relevant theory of stochastic differential equations, we proved the existence and uniqueness of the global positive solution of the stochastic SEIQR epidemic model by using the Lyapunov analysis method, and discussed the asymptotic behavior of the solutions for stochastic system at the disease-free equilibrium point and the endemic equilibrium point of the corresponding deterministic model respectively by constructing the appropriate Lyapunov functions.

We considered a class of sum of squares convex polynomial optimization problems with uncertain parameters. Firstly, we proposed a robust counterpart optimization model for the uncertain sum of squares convex polynomial optimization problem with the help of robust optimization method. Secondly, by using a class of robust type characteristic cone constraint qualifications, we established exact SDP relaxation problem for this optimization problem. Finally, we introduced a Lagrangian function of this uncertain sum of squares convex polynomial optimization problem, and gave robust saddle point theorems of this uncertain sum of squares convex polynomial optimization problem with the help of sum of squares conditions.

By using the maximum likelihood estimation method, we considered the parameter estimation of a class of nonlinear stochastic differential equations driven by Lévy process. Firstly, the unbiasedness, the asymptotic consistency and the asymptotic normality of the estimator as T→∞ were discussed under time-continuous observations. Secondly, the continuous martingale part was approximated by a threshold method, and the unbiasedness and asymptotic normality of the estimator as n→∞ were obtained under the condition of high-frequency discrete observations and finite activity. Finally, the unbiasedness and asymptotic normality of estimator were verified by numerical simulation results.

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

Let a,b be two generalized Drazin invertible elements  in a Banach algebra A with unity 1, a^d be the generalized  Drazin inverse of a. The generalized Drazin inverse of the sum and product of two elements in a Banach algebra was considered by means of the system of idempotents. The expressions for the generalized Drazin inverse of the sum and product of a and b were given under some conditions such as ab²=bab, b^πba²=b^πaba, a^db²=ba^db etc.

By using the method of geometric analysis and some important inequalities,  we studied the local characterization of four-dimensional complete gradient almost Ricci solitons satisfying certain conditions involving either the anti-self-dual or self-dual part of the Weyl tensor, and proved that such solitons were locally warped product structure with three-dimensional  constant sectional curvature fibers or three-dimensional Einstein fibers.

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

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

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

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

Aiming at the problem of poor robustness of color image watermarking algorithms under filtering attacks, we proposed a dual-color robust watermarking algorithm based on tensor decomposition and joint entropy. Firstly, the color carrier image was tensor-decomposed as a whole to obtain its tensor feature map and divided into blocks. Secondly, joint entropy was used to extract the feature map sub-blocks with better shadowing. Finally, the watermark information was embedded into the U matrix of the selected block after singular value decomposition (SVD). The experimental results show that the peak signal-to-noise ratio of Lena images is more than 39 dB. The algorithm  can not only effectively resist image filtering attacks, with a maximum NC value of 1.000 0, but also has strong robustness against other conventional image attacks and geometric attacks.

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

We proposed an improved model of metal surface defect detection method. Firstly,  based on the YOLOv3(you only look once v3) object detection model, a multi-scale convolution parallel structure was used to extract and fuse multi-scale features. Secondly, efficient downsampling was used to maintain the feature information and reduce the computation caused by feature dimension raising. Finally, spatial separable convolution was used to  increase the width and depth of the model while keeping the receptive field unchanged, so that an  improved model YOLOv3I (you only look once v3 inception) with  reduced the amount of model parameters and improved  the performance of the model was obtained. The improved model improved the feature  extraction ability for  complex defects and further reduced the requirements for hardware configuration. The experimental results show that the improved model has significantly improved both accuracy  and calculation efficiency, with an  average accuracy  increase of  about 5% on the public dataset, and about 3% on the bearing dataset provided by the enterprise. The amount of model parameters decreases by more than 20%, and the  floating point computation of the model  reduces by 1.6×10⁹ and 1.2×10¹⁰ times on both two datasets respectively.

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

Aiming at the problem of low clustering accuracy caused by redundant text features, we proposed a feature selection and text clustering algorithm based on binary mayfly optimization. Firstly, we improved the strategy of location update, mating, and mutation of the traditional mayfly algorithm.  Secondly, we  combined it with a feature selection model to select text features using the inverse document frequency as the objective function. Finally,  on the basis of new feature subset, K-means++ algorithm was used to cluster text and obtain the optimal text clustering results. The results of experiments conducted on multiple datasets show that the proposed algorithm can effectively shorten the feature dimension and improve the efficiency of text clustering.

Aiming at the problem of effectively protecting user privacy data,  we proposed a privacy-preserving logistic regression training scheme based on two-party secure computation  to complete the  joint modeling work of multiple data parties.  Firstly, the scheme  optimized the  generation process of the multiplicative triplet to reduce the time required in  the offline phase. Secondly, we replaced  the activation functions that were difficult to calculate in secure multi-party computation with approximate functions. 
Finally, we vectorized the proposed protocols  and accelerated the local matrix computation by using  CUDA (compute unified device architecture).  The experimental results of using different datasets to test the privacy-preserving logistic regression  performance in both local and wide area networks show that the scheme can enable the model to converge in a  short time and  increase the possibility of solving privacy-preserving machine learning related problems in real world.

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

Aiming at the problem of inaccurate information collected by a single sensor, we proposed a data fusion algorithm for confined space detection based on Bayesian estimation. Firstly, by analyzing the composition structure of the detection signal,  filtering, amplitude limiting, step signal removal and other methods were used to solve the problem of signal interference and improve the significance of characteristic parameters. Secondly, based on  the dynamic characteristics of the data fusion architecture, reasonable assumptions were given, and a dynamic Bayesian network model was jointly established by combining a prior network and the transfer network to obtain the fusion objective function. Finally, by introducing  normal distribution  to study the uncertainty of detection value, the detection node was regarded as the likelihood function, and the maximum a posteriori probability after fusion was deived. Taking the fusion weighted average error ratio as the index, multi type detection data fusion was realized by “two-two encounter”. The results of simulation experiments show that the proposed algorithm solves the problem of signal redundancy, the data fusion effect is better, the overall number of fire missed reports is less, and the highest value of the data fusion time is only 2.4 s.

Aiming at the problem that the integration difficulty was relatively high caused by the low similarity and uncertainty of multi-source information data source domain, we proposed an integration method based on K-medoids clustering algorithm. First,  the clustering process of multi-source data was regarded as a transfer learning process, the weight value of the initial sample was determined, the learning characteristics of the weight and loss expectation value of the training sample in each iteration were recorded, and then the characteristic parameters were used to determine whether the data belongs to the source domain or the target domain. Then the clustering of the integration algorithm was transformed into a diversified domain value marking problem. After the data had the clustering characteristics, the weight factors between the data to be integrated in the source domain and the target domain were calculated respectively, the amount of interactive information between them was determined by using  the coverage characteristics of the weight factors, and the data with high amount of information was integrated to ensure the success rate of integration. The simulation experiment results show that the proposed algorithm  can achieve efficient integration, less secondary integration times and low overall consumption under stable and less datasets, or disordered and more and more complex datasets.

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

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

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

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

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

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