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

We considered the existence of invariant tori for nearly integrable small twist mappings whose dimensional numbers of angles and actions variables were different. By constructing KAM iteration method, we proved that the nearly integrable small twist mappings with high dimension possessed a family of invariant tori under the Rüssmann non-degeneracy condition and the intersection condition.

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

We discussed a class of centralizer of the general linear Lie superalgebra by using homological method. Firstly, the general linear Lie superalgebras were divided into three cases for structural analysis, namely, gl(m,n),gl(m,0) and gl(0,n), where m and n were not zero. Secondly, the centralizers of the even and odd situation of the three cases in the generalized Witt Lie superalgebras were calculated respectively. Finally, the structure of this kind of centralizer was given.

Firstly, by introducing the concept of 3-Lie-Rinehart color algebra and using the representation of 3-Lie-Rinehart color algebras,  we
 discussed its cohomology. Secondly, we gave relationship between 1-cocycle and 2-cocycle of 3-Lie-Rinehart color algebras. Finally, as an application, we characterized the deformations of 3-Lie-Rinehart color algebras by the cohomology theory.

We considered the problem of the neighbor full sum distinguishing total coloring of three types of join graphs which consisting of paths and paths, paths and cycles, cycles  and cycles. By constructing edge coloring matrix, using  the methods of combinatorial analysis and categorical discussion, we obtained the exact value of the neighbor full sum distinguishing total chromatic number of  three types of join graphs: paths and paths, paths and cycles, cycles and cycles.

LetS*_l denote the class of analytic functions f(z) in the open unit disk D={z: |z|<1} normalized by f(0)=f′(0)-1=0. We investigated the forth\|order Toeplitz determinant T₄(2) for this function class S*_l and gave the upper bound estimate of the determinant T₄(2).

By introducing a class of real function G on ［1,∞)⁴, the author gave the existence theorems of unique fixed point for  a class of implicit contractive mappings on multiplicative metric spaces, and gave an example to illustrate the correctness of the given result.

We proposed a new modified three terms Hestenes-Stiefel conjugate gradient projection algorithm to solve the problems of 
large-scale nonlinear equations and signal recovery. This algorithm was constructed by a new modified three terms Hestenes-Stiefel search direction as well as a classical line search method and the hybrid plane projection technique. The new search direction automatically satisfied  sufficient descent property without any line search condition. Under conventional assumptions, the new algorthm had global convergence. Numerical results show that the new algorithm is efficient and stable.

We gave a discretized form of edge-averaged finite element for a class of three-dimensional Poisson-Nernst-Planck equations. Under appropriate grid conditions, the total stiffness matrix obtained by the discrete form was an M-matrix, which ensured the non-negative properties of the numerical solution. The numerical experimental results show that compared with the standard finite element method, the edge-averaged finite element method has shorter CPU time and less error.

We solved a semi-interior point combined homotopy equation for variational Inequality problems with inequality and inequality constraints. Under weak conditions, we proved the existence, boundedness and convergence of homotopy paths starting from any point in Rⁿ, and verified the feasibility and effectiveness of the semi-interior point combined homotopy method for solving variational inequality problems with equality and inequality constraints by using numerical examples.

Based on the fixed point index theorem, we discuss the uniqueness of positive radial solutions of Dirichlet problem for quasilinear differential system with mean curvature operator.

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

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

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

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

Aiming at the problems of chaotic storage allocation and low storage efficiency in automated three-dimensional warehouse, we proposed a combinatorial optimization model solved by a multi population space mapping genetic algorithm. The method improved the basic genetic algorithm and optimized the objective function composed of goods demand, shelf center of gravity and goods correlation. The MATLAB simulation results show that the method obtains better results than the existing algorithms, the values of the three objective functions are improved, and the task capacity can affect the optimization ability of the improved method.

Firstly, aiming at the problems that the existing technology could not automatically extract software repository, mark data, build quality analysis model and analyze software quality, we proposed a just-in-time quality analysis framework GIF for Python projects. Secondly, based on GIF, the top 10 most popular Python projects on GitHub were extracted and labeled, and three classical classifiers (logistic regression, naive Bayes and random forest) were used for experimental verification on the evaluation indexes of AUC and F₁ values. The experimental results show that GIF framework can identify software defects in Python projects immediately and effectively, it is an easy-to-use just-in-time software quality analysis framework.

Aiming at the problem that when the local linear embedding algorithm used Euclidean distance to calculate the similarity of unaligned samples, it was greatly affected by data position difference, resulting in low measurement accuracy and affecting the accuracy of the algorithm feature extraction, we proposed a local linear embedding algorithm based on information entropy measurement. Firstly, the degree of confusion among sample features was counted by information entropy to improve the accuracy of dividing local neighborhoods. Secondly, a local reconstruction model was established to dig out the essential structure of the manifold. Finally, the local structure was used to build a low-dimensional reconstruction model to obtain the salientfeatures of the samples. The experiment on the bearing data set proves the effectiveness of the algorithm in feature extraction.

Based on the M06-2X theoretical method, the electronic excitation was calculated by time-dependent density functional theory (TDDFT) at the level of the aug-cc-pVTZ base group with dispersion function, we gave the isosurface diagrams of hole-electron, natural transition orbit (NTO) and charge density difference (CDD) of the first elementary reaction intermediate INT₁-S-Met-CHCl₃+H₂O molecular system in the chiral transition of the Met(methionine)+H₂O composite system under implicit solvent chloroform, and analyzed the properties and electronic structure of the excited states of the intermediates. The results show that: H atoms migrate to form intermediates, resulting in significant changes in the structure of Met molecular system, based on NTO, hole-electron and CDD isosurfaces, the mutual recognition of excitation types of excited states of INT₁-S-Met-CHCl₃+H₂O molecular system is consistent with the hole-electron data analysis.

Based on the third-order aberration theory of plane-symmetric optical system, we studied the aberration analytical analysis method of the plane-parallel plate with a large field of view incident. Firstly, the third-order aberration calculation method of several parallel refraction planes was studied, and the corresponding aperture-ray transformation equations and aberration coefficients expressions were derived. Secondly, on the basis, the wave aberration and aberration calculation expressions of a single plane-parallel plate were derived. Finally, the aberration calculation expressions and optical design software Zemax were applied to calculate the aberration of an example of the large field of view optical system including the plane-parallel plate. The results show that the results calculated by aberration expressions have high accuracy.

We studied the adsorption of three groups of H,O and F on the surface of Ti₃C₂, the electronic properties and quantum capacita
nce of the adsorbed structure were calculated by density functional theory simulation. The results show that the best adsorption
 site is directly above the center of three adjacent carbon atoms, the electronic structure of Ti₃C₂ can be modulated by the adsorption of the groups. The quantum capacitance enhancement effect of adsorbing H group on Ti₃C₂ surface is the best, and it has higher charge accumulation ability under negative bias voltage.

The artificially cultivated meat-like Ganoderma lucidum (MGL) extracts were applied to the oxidative damage model of Caenorhabditis elegans  to evaluate their toxicity and antioxidant efficacy.  The ultraviolet (UV) full wavelength scanning method was used to determine the main components of the extracts, the life span and spawning quantity were used to evaluate the toxicity of the extracts, the free radical content was detected by active oxygen detection (DCF) method to evaluate the antioxidant efficacy of the extracts, the potential acting target of the extracts was explored by the transcriptome analysis. The experimental results show that the main components of the MGL extracts are quinones and proteins, the extracts have no obvious toxic effects, 2.5 mg/mL extracts have significant antioxidant capacity against damaged nematodes and can effectively regulate the expression of  related genes to the heat shock protein family (hsp-16.1,16.11,16.48,16.49), superoxide dismutase (sod-5), inner mitochondrial membrane (timm-23), metal sulphurin-1 (mtl-1), and the Skp1 protein family.The artificially cultivated MGL extracts can exert obvious antioxidant efficacy through the life\|regulating signal pathway, and  have the potential ability to regulate fat metabolism and promote protein synthesis.

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

In order to realize the high sensitivity detection of glassy carbon electrode in the field of electrochemical sensors,  the glassy carbon electrode was electrochemically activated by constant potential method in phosphate buffer solution at pH=5.0. The effects of pH value,  accumulation potential and accumulation time on the detection effect of Pb²⁺ were investigated, and the detection performance of activated electrode for Pb²⁺ was investigated under the optimal experimental conditions. The experimental results show that the activated electrode can enhance the response current of electrochemical detection of Pb²⁺, and has the characteristics of short detection time and high sensitivity. The detection linear range of Pb²⁺ is 1×10^-10—5×10^-6 mol/L,  the minimum detection limit is 3×10^-11 mol/L,  and the limit of quantification is 1.0×10^-10 mol/L. The activated electrode has a high recovery in the determination of  Pb²⁺ in tap water, and can be used in the actual water quality detection.