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 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.

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.

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.

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.

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.

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.

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.

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.

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 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.

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.

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.

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.

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

Aiming at the problem that 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.

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.

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 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.

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.

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.

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.

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 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.

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.

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

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

Aiming at the problem 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.

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.

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.

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.

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.