Firstly, in view of characteristics of different infectivity of hepatitis B infectors and virus carriers in the process of hepatitis B transmission, we established an S^a_kSⁿ_kV_kE_kI_kC_kR_k epidemic model with stage-structured   on complex networks.  Secondly, we obained  the basic reproduction number R₀ by using the next generation matrix method, and  combined the matrix theory and the Lyapunov function method to prove the stability of the disease equilibrium point. We also discussed the optimal control problems of two strategies  by Pontryagin’s maximum principle. Finally, based on the scale-free network, the sensitivity analysis and numerical simulation were carried out to verify the theoretical results and find the optimal control.  The results show that reducing vaccine inefficacy rate and increasing vaccination rate can better control the spread of infectious diseases.

By using the Leray-Schauder fixed point theorem, we discuss the existence of radial symmetric solutions for the boundary value problem of the p-Laplace equation with nonlinear gradient term, where  p>1, f: ［r₁,r₂］×R×R⁺→R is continuous. When 1<p≤2, under the optimal inequality condition of the nonlinear term f which satisfy  the first eigenvalue λ_p,1 of the p-Laplace operator -Δ_pu under the boundary condition, an existence result of radial symmetric solutions is obtained.

By using the monotonic iterative method, we studied the existence and boundedness of p-k-convex radial solutions for a class of 
p-k-Hessian systems with singular gradient terms, and gave the range estimate of bounded solutions. Under appropriate assumptions about nonlinear terms, we obtained the existence and nonexistence of blow-up solutions, and gave several examples to verify the obtained conclusions.

Based on a new modified Gustafson-Schmitt type fixed point theorem, the author give sufficient conditions for the existence of radial solutions to the Dirichlet boundary value problem of the k-Hessian equation when the nonlinear term  satisfies the appropriate growth condition only at u=0.

By using Montel’s criterion and combining it with relevant theories  of differential equations, we studied the quasi-normal criterion and the order of quasi-normality for a class of meromorphic functions satisfying third-order linear differential inequalities with constant coefficients. The results show  that for all f∈F, when |f(z)+Af(z)|>Cand  F₁={f′(z)/f(z)|f(z)∈F} or F₂={f(z)/f(z)|f(z)∈F is normal,  the family F of meromorphic functions is quasi-normal.

By using methods such as the theory of variable exponent function spaces and hierarchical decomposition of function, we prove the boundedness of the intrinsic square function on variable grand Herz-Morrey space, where α(·) and q(·) are both variable exponents.

We considered the boundedness of generalized Hausdorff operators on local Morrey-type spaces and their complementary spaces. By using norm estimation and constructing test functions, we gave necessary and sufficient conditions for the boundedness of these operators and established their sharp constants.

Under the balanced loss function,  we discussed the statistical properties of two almost unbiased Liu estimators in linear models, gave the risks of the almost unbiased Liu estimator, the new Liu estimator and the new almost unbiased Liu estimator under the balanced loss function, and discussed  the relationships among  these risks  under different conditions.

A vertex reducible edge coloring of a graph G is an improper edge (total) coloring such that any two vertices with identical degree have the same color set. Based on the structural characters of the generalized Petersen graph G(n,k), we use combinatorial analysis method and constructive function method to give the vertex reducible edge (total) chromatic number of G(n,k) when its order is sufficiently large.

By using the theory of reduced rings, we studied the semicommutative and Armendariz properties of upper triangular matrix rings. Based on rings with compatible endomorphisms, we constructed and gave two classes of semicommutative Armendariz subrings of the fourth-order upper triangular matrix ring.

Based on the index properties of maximal subgroups, we constructed a set of maximal subgroups with non-prime-power indices, provided some classifications of the associated second maximal subgroups, and discussed the structure of the group in depth by combining  their strength and  parity of the orders, obtaining several sufficient conditions for a group to belong to the related formations.

Aiming at  the problems that traditional graph neural networks were difficult to handle large-scale complex data and it was difficult to 
 fully utilize the features of nodes and edges in the network as well as the connections between them, we proposed a feature-enhanced graph attention network (FEGAT). The method first modelled the data as a directed graph of nodes and edges. Then, a graph neural network model with an attention mechanism was designed to dynamically aggregate neighbor node information through edge feature weighting and attention coefficients, and fused multi-dimensional edge features by adopting an independent weighting and parallel concatenation strategy for multi-dimensional edge features. Finally, it combined XGBoost algorithm to complete node classification. To verify the effectiveness of the model, experiments were carried out on the anti-money laundering AMLSim dataset. The results show that the model significantly improves precision, recall and F₁-score in imbalanced data scenarios.

Aiming at the problems that how to accurately and quantitatively reveal and model the  network structure characteristics and sentiment evolution patterns of cultural public opinion in online communication, we  proposed a dynamic evolution model for cultural public opinion based on the integration of complex network  and affective computing. The model took the  data from the Douyin platform as the core, realized quantitative expression of  the public opinion communication network by constructing a multi-dimensional weighted relationship matrix, designed a sentiment-weighted community clustering algorithm  to identify sentiment resonance, obtained the fused features of emotional polarity and communication structure within the network, and  introduced a temporal prediction model of evolution of  a gated recurrent unit network combined with an attention mechanism to achieve dynamic modeling of sentiment fluctuations and communication trends. Experimental results show that the proposed model effectively characterizes the communication structure and sentiment distribution characteristics of Jilin cultural public opinion in cyberspace, and its fitting accuracy and predictive results  are superior to those of traditional Hegselmann-Krause (HK) opinion dynamics models and susceptible, infected, recovered (SIR) communication models, verifying that the model has strong generali
zation capability and can  provide effective theoretical support for analyzing the digital dissemination patterns of culture.

Aiming at the problem of insufficient extraction of 3D spatial features in 3D object detection models, we proposed an improved ICasA model. Firstly, we introduced focal sparse convolution to improve the 3D backbone network of CasA model, strengthening the extraction of information flow among non-empty voxel feature locations to obtain richer spatial features. Secondly, we constructed a multi-scale feature attention fusion module and embedded it into the 2D backbone network to enhance the model’s ability to handle multi-scale features. We adopted convolutions with different strides to deepen the structure of the 2D backbone network, improve the model’s ability to extract global features. We improved the attention fusion method to dynamically activate features of different scales and locations while preserving the original feature maps. The experimental results on the KITTI dataset show that compared with the CasA model, the ICasA model achieves 0.28 percentage points, 2.87 percentage points, and 1.03 percentage points increases in 3D average detection accuracy (AP@R40) for cars, pedestrians, and cyclists, respectively. Compared with existing advanced models, the ICasA model has more stable detection effect for all categories of objects, which helps to enhance the accuracy of 3D object detection.

Aiming at the problem that  the detail scales in X-ray images were diverse, it was difficult to meet the enhancement requirements of different scale details simultaneously using a single enhancement strategy, we proposed  a multi-level fuzzy enhancement method for X-ray images based on wavelet phase filtering. Firstly, by using histogram equalization to redistribute grayscale values to improve contrast, and utilizing linear interpolation to adjust the grayscale values of blurry local areas based on clear pixel information around them to restore details. Secondly, after optimizing the grayscale distribution, the noise points in the X-ray image were more significant, we first used  the Mallat algorithm to perform two-dimensional wavelet decomposition on the adjusted image, and then combined  wavelet phase filtering to achieve image denoising, enhance image clarity, and optimize image quality. Thirdly, we converted the clarity enhanced X-ray image into a histogram format to query peak gray levels, defined fuzzy sets and membership functions, used fuzzy subsets as enhancement levels, optimized membership using power functions and multi-level enhancement coefficients, and then traversed gray levels to complete membership optimization, and achieved image detail enhancement. Finally, we reverted the  fuzzy domain changes back to the grayscale domain to obtain grayscale update results, achieving multi-level fuzzy enhancement, highlighting image details and lesion areas, and improving diagnostic accuracy. The experimental results show that the proposed method can effectively highlight the detailed information in X-ray images. At different grayscale levels, the frequency of X-ray images remains between 18 Hz and 35 Hz, with relatively smooth frequency fluctuations. The mean gradient (MG) value can be maintained above 0.35. The proposed method has a significant enhancement effect on X-ray images, which helps to accurately and effectively analyze the lesion area, thereby improving the accuracy and efficiency of disease diagnosis.

Aiming at the problems of  texture blurring such as speckle noise, region blurring, and weak boundaries in the image caused  by factors such as noise and artifacts during utrasound imaging,  which led to a decrease in the quality of ultrasound image segmentation, we proposed  an ultrasound image segmentation algorithm based on improved attention W-Net. Firstly, we constructed texture feature factors based on the correlation between pixel intensity and edge texture, and applied texture factors to improve the guided filtering algorithm. The improved guided filtering algorithm could smooth the image while better preserving the texture features in the image. Secondly, by extending U-Net to W-Net through attention mechanism, an improved attention mechanism was integrated into W-Net. The improved attention W-Net was used to segment ultrasound images with texture preservation, which could better preserve the texture information of the image during the segmentation process, thereby improving the accuracy and robustness of segmentation. Experimental results show that the proposed method has a relatively high cumulative probability of blur detection (CPBD) value, a low percentage of area difference, and good ultrasound image segmentation effect, which can be widely applied in the field of ultrasound image segmentation.

Aiming at the problems of insufficient modeling of trigger word contexts, inability to utilize historical event information, and difficulty in capturing complex semantic structures in generative event extraction models in complex scenarios, we proposed a generative event extraction model enhanced by event-aware memory graph network. The model enhanced its ability to focus on trigger word related contexts through an event-aware attention mechanism, utilized dynamic event memory network to achieve cross-text historical information reuse, and displayed semantic associations among modeling event arguments through an event graph structure. Experimental results on two standard datasets show that the proposed model outperforms existing baseline models in both event argument identification and classification tasks, effectively improving the extraction accuracy and generalization capability of generative models in multi-event and complex context scenarios.

Aiming at the problem that it was  difficult to achieve real time processing of distance-based outlier detection in high speed data stream environments within an effective time, we  proposed a θ-approximate outlier detection algorithm over data stream. The algorithm was based on the local uniformity of object distributions. It constructed a summary structure of local uniform distribution to identify and maintain regional nodes that satisfied  approximate  uniform distribution characteristics. By using the positional  relationship between the query object and these regional nodes, it  estimated the number of neighbors and determined the outlier state of the object under the  guarantee of probability error. Unlike traditional methods that required frequent execution of precise range queries, the algorithm prioritized object state determination through estimating the number of neighbors under probability guarantee, and only performed exact neighbor computation when necessary, thereby reducing the cost of range queries and distance calculations. The experimental results on real and synthetic datasets show that the proposed algorithm  can significantly reduce processing time while maintaining good detection accuracy. The use of local distribution characteristics for probabilistic approximation judgment can effectively improve the real time processing capability of outlier detection in high-speed  data stream environments, providing an efficient and quality guaranteed solution for large-scale data stream management and analysis.

Aiming at the problems that there were  difficultes in dynamic optimization and lack of theoretical guidance for resource regulation in the collaborative development among comples enterprise entities, we proposed an improved Lotka-Volterra collaborative work model. Firstly, by introducing resource input as a control variable, we derived the conditions for the collaborative system to achieve stability in a finite time and the stability time function, and used the Pontryagin’s maximum principle and the Hamilton function method to obtain the optimal resource regulation strategy for maximizing the collaborative economic benefits. Secondly, by comparing the effectiveness and feasibility of simulation algorithm, we calculated the resource input ratio for two types of enterprise entities to achieve maximum economic benefits. The experimental results show that the proposed algorithm not only provides a new idea for predicting the collaborative work path among different enterprise entities, but also provides theoretical basis for formulating scientific industrial regulation strategies.

Aiming at the security issue of integrated sensing and communication systems in unmanned aerial vehicle, we proposed an artificial noise assisted secure beamforming scheme to enhance the security performance of the system. Firstly, in the case where the unmanned aerial vehicle base station only had statistical channel state information, we minimized the signal-to-noise ratio of a potential eavesdropper, ensured the communication service quality of legitimate users and met the similarity constraint of radar beam pattern. Secondly, in order to solve the non-convex optimization problem in this solution, semidefinite relaxation technique was used to relax the rank constraint in the original problem, and combining with a parametric reformulation method to handle the fractional objective function, it was transformed into an iteratively solvable convex semidefinite programming problem. Subsequently, an interior-point method was used to construct a barrier function, achieving efficient solution under feasible conditions. Simulation experiment results show that, compared with the conventional scheme without artificial noise, the proposed scheme significantly improves the security performance of the system while ensuring the communication service quality of legitimate users.

We considered the well-posedness of solution to the initial-boundary value problem for a class of non-Newtonian double-diffusive convection models. Under periodic boundary conditions in three-dimensional space, by using the Galerkin method combined with a priori estimates, we prove the existence of global regular solutions to the system when the initial data are appropriately small and the power-law index satisfies 5/3≤p＜2. 

In order to obtain a complex scroll chaotic system, a new system was constructed by applying the Julia fractal with a scroll structure to the deformed Liu system. The main characteristics such as phase diagram, equilibrium point, Lyapunov exponent spectrum and bifurcation diagram were analyzed. The power and fractional unit circuits of the system were designed on the Multisim platform, and the digital circuit of the new system was implemented using a microcontroller. The results show that the new system produces a more diverse form of four-winged double-scroll attractor, and the introduction of the coefficient k of the quadratic term does not change the shape of the attractor, only affecting the size of the attractor. Corresponding to the same parameter a, changing the coefficient k, the value of the maximum Lyapunov exponent remains unchanged, the coefficient k does not affect chaotic state of the system. Adopting modular circuit design can make the circuit more clear and the parameter adjustment more convenient. The results of the circuit simulation and the digital circuit implementation are consistent with the numerical calculation results performed in MATLAB, thus validating the feasibility of the combination of fractal and chaos.

Based on the unique chemical properties and broad application prospects of high electron affinity (EA) of superhalogens, we constructed a hetero-binuclear superhalogen anions MXO^-₄(M=Be,Mg,Ca; X=N,P) with alkaline earth metals (Be,Mg,Ca) and pnictogen nonmetals (N,P) as central atoms, and oxygen atoms as ligands, and studied its geometric structures, relative stabilities, and vertical detachment energies (VDE) through theoretical calculations. The results show that the MXO^-₄ can be classified into four geometric configurations containing zero, one, two or three bridged oxygen atoms (0,1,2,3), with structure 2 having the highest VDE values, and structure 0 having the lowest VDE values. The radius and type of central atoms significantly influence the VDE values, the smaller radii of the metal central atom M, the greater the electronegativity of the nonmetal central atom X, and the higher the VDE value of the anions.

We investigated the molecular mechanism of Poria inhibition through network pharmacology and molecular docking technology, and verified the antibacterial effect of Poria in vitro through experiments. The results show that the antibacterial effect of Poria mainly relies on the regulation of tumor necrosis factor (TNF) and other targets and signaling pathways such as PI3K-Akt, and Poria extracts have inhibitory effect on the growth of Escherichia coli and Staphylococcus aureus, with the minimum inhibitory concentrations of 0.5,0.25 g/mL, respectively. The Poria contains triterpenoids such as oleanolic acid. The Poria is rich in polysaccharides that can exert antibacterial effect. The morphological structure of Staphylococcus aureus and Escherichia coli under the action of Poria is obviously damaged, and Poria can interfere with the synthesis process of the bacterial cell walls, and inhibit the formation of the cell membranes, thereby suppressing the growth of the bacterial strains.

In order to study the mechanism by which nitrogen-containing organic compounds (NOCs) produced during straw burning affected the formation of secondary aerosols,  a self-built smog-chamber system was used to simulate the aging processes of straw burning aerosol (SBA) under light (UV) and no light (dark) conditions. High-resolution electrospray ionization mass spectrometry (HRESI-MS) combined with Van Krevelen (VK) diagram analysis was used  to characterize the molecular composition and oxidation features of NOCs in SBA. The results show that more than 60% of the organic compounds produced by straw burning are NOCs,  including CHN (compounds containing C,H,N elements, 9.61%—58.63%),  CHON (compounds containing C,H,O,N elements, 22.38%—62.89%),  and CHONS (compounds containing C,H,O，N，S elements, 6.48%—29.90%). The overall oxidation state of the organic compounds under UV light is higher than that under dark conditions. The combination of HRESI-MS and VK diagram can achieve accurate qualitative and oxidation state characterization of NOCs components in SBA, effectively tracking dynamic changes of  molecular composition and elemental ratio parameters  at different aging stages, and  providing a reliable analytical approach for molecular-level research on NOC aging process in biomass burning aerosols.