We discuss  the existence of positive 2π-periodic solutions of the second-order ordinary differential equation with nonlinear derivative term by using positive operator perturbation method and fixed point index theory in cones. Under certain inequality conditions of the 
nonlinear term f(t,x,y), we obtain the existence of positive 2π-periodic solutions of the equation.

Based on the fact  that infected animals found in animal detection still had  infectious characteristics, we established a dynamic model to analyze the influence of detection behavior on the spread of animal brucellosis. Firstly, the basic reproduction number of the model was given, and the existence of the equilibrium point was analyzed. Secondly, through the discussion of the equilibrium point, it was found that the model occured backward bifurcation. Lyapunov function was used to prove that when R₀<1, the equilibrium point of disease-free was globally asymptotically stable under certain condition, when R₀>1, the model was uniformly persistent. Thirdly,  the optimal control strategy was formulated and solved according to Pontryagin maximum principle. Finally,  the theoretical analysis results were validated by numerical simulation, indicating that the control strategy can effectively control the spread of animal brucellosis.

By using T-weak continuous operator method and classical Galerkin technique, we discussed the initial boundary value problem of a class of incompressible magneto-micropolar fluid equations in a two-dimensional bounded smooth region, and obtained the existence and uniqueness theorems of the global weak solutions for the problem,   further improving the regularity of the weak solutions.

By considering the influence of various uncertain noises, we established an uncertain Logistic population model with Allee effect, which was characterized by an uncertain differential equation. Firstly, we obtained the solution of the model, and discussed the stability of the equilibrium state. Secondly, the unknown parameters in the model were estimated by using the generalized moment estimation method under the framework of uncertainty theory. Finally, the parameter estimations of the model and the properties of the solution were explained by an example analysis.

We considered  a class of Kirchhoff type viscoelastic wave equation with logarithmic nonlinear term of variable exponents. Firstly, the energy identity for the problem was given. Secondly, by constructing auxiliary functions and using Holder inequality and Gagliardo-Nirenberg inequality, we obtained the result of blow up of equation solutions in finite time in the case where  the logarithmic nonlinear term  contained variable exponents.

By using Holder’s inequality and the related properties of weighted functions, we gave the boundedness of fractional integral operators and BMO  commutator on generalized weighted Morrey spaces over RD (reverse doubling condition)-spaces, and gave the corresponding  endpoint estimates.

Firstly, by using  the method of weight functions, Euler-Maclaurin summation formula, Abel’s summation by parts formula, and the technique of real analysis, we gave a new half-discrete Hilbert-type inequality involving higher-order derivative function and partial sums. Secondly, as applications, we discussed the equivalent conditions of the best constant factor to connect multiple parameters in a  inequality with particular  parameter and several particular inequalities.

Using the weight coefficient method and real analysis techniques, we discussed the problems of constructing semi-discrete Hilbert-type inverse inequality with generalized homogeneous kernel, gave necessary and sufficient conditions for constructing such inequality,  the calculating formula of the best constant factor, and the  operator expression of the inequality.

Firstly,  by using the method of quasi-trace functions, the corresponding relationship between the cohomology group of the relative Rota-Baxter operator of a Lie representation pair and the cohomology group of the relative Rota-Baxter operator of the induced 3-Lie representation pair in the low-order cases was given. Secondly, by using the method of constructing chain maps, the homomorphism between the cohomology groups of the relative Rota-Baxter operator of a Lie representation pair and the induced 3-Lie representation pair with any order greater than or equal to 2 was obtained.

n-FI injective modules were generalized to the complex level. Firstly, we gave the definition of  n-FI injective complexes. Secondly, we proved that a complex C was n-FI injective complex if and only if each term was n-FI injective module  and Hom(X,C) was acyclic for any complex X with FP-id(X)≤n. Finally, n-FI injective complexes were characterized by covers of complexes.

Firstly, based on the Black-Scholes stock price model,  the neural stochastic differential equation (NSDE) model was established by parameterizing the asset return rate and volatility as a drift network and a diffusion network, respectively. Secondly, in the empirical analysis, the underlying asset as a single stock option was used as the research object, and real stock data was used for  the network training  and testing. The experimental results show that the NSDE model can overcome the defects of the constant assumption of the Black-Scholes model. Finally, for the case where the price of the underlying asset of the option was unobservable, we  proposed that the price of any target option and the price of a known option could be constrained within the Wasserstein distance of their risk-neutral equivalent martingale measure, and theoretically  proved the method.

Firstly, based on techniques such as  Taylor expansion and Chapman-Enskog multi-scale expansion,  the lattice Boltzmann method was used to accurately recover the discussed macroscopic equations, and  the equilibrium distribution function expressions of D1Q3 and D2Q9 models were derived. Secondly,  two numerical examples were used to verify the effectiveness of the proposed method. The results show that the lattice Boltzmann method can be used to solve the numerical solution of the Caputo type modified time fractional equation.

The Hopf bifurcation of predator-prey symbiotic model with double time delay was discussed  by using the normal form theory and the central manifold theorem. By analyzing the characteristic equation and taking the development time of the prey and the development time of the co-genitor as the parameters, the stability of equilibrium point, the existence of Hopf bifurcation, the stability of bifurcation direction and bifurcating periodic solution were given. The result that  time delay  affected the stability of the system was obtained. The correctness of obtained conclusions was verified through numerical simulation.

Aiming at the high-dimensional “big p small n” problem where the number of genes in biomics data (denoted as p) was far more than the number of samples (denoted as n), we proposd a graph attention network GATOr with local and global attention mechanisms. Firstly, the model used Pearson correlation coefficient to calculate the correlation between features on the omic data, and constructed a single sample network of the omic data. Secondly, we proposed a graph attention network which combined local and global attention mechanisms to learn graph-based omics feature representation from a single-sample network, thereby transforming the high-dimensional characteristics of the omics data into low-dimensional representations. The experimental results show that compared with other traditional classification algorithms, GATOr achieves better performance in classification task accuracy and other indexes.

Aiming at the problems of non-uniform experimental platforms and heterogeneous datasets faced in the field of vulnerability dete
ction, we  studied  the application of word vector models in C/C++ function vulnerability detection. Five word vector models were used for the knowledge representation of the abstract syntax tree structure generated by the source code, and six neural network models were used for vulnerability detection. The experimental results show that function-level code has shallow semantic relationships and tight connections within code blocks.

We analysed  the parametric accuracy of the generalized noise model estimated based on the maximum likelihood equation by using Fisher information and the associated asymptotic normality. The theoretical analysis results show that for standard pixel images, the parameter error of the additive noise estimated by using the maximum likelihood equation is larger than the error of signal-dependent noise parameter, while for the normalized images, the accuracy of the parameters is exactly the opposite. The experiments prove the correctness  of the theoretical analysis.

Aiming at the problem that the attention mechanism-based model ignored the  part-of-speech information of words in the aspect-level sentiment classification task, we proposed  an aspect-level sentiment classification method that incorporated a part-of-speech self-attention  mechanism. Firstly, the method  was based on the natural language processing part-of-speech tagging tool to obtain part-of-speech tagging sequence, and randomly initialized a part-of-speech embedding matrix to obtain part-of-speech embedding vector. Secondly,  the self-attention mechanism was used to learn the syntactic dependence between words. Finally the sentiment score of each word was calculated, the combination of word sentiment was used to express the polarity of sentiment in specific aspects.  The experimental results show that compared with baseline model with the best performance in 5 public datasets, this method improves the accuracy and macro F₁ score by 2% and 4.83% respectively, indicating  that the attention mechanism model incorporating part-of-speech information has better performance in aspect-level sentiment classification task.

Firstly, aiming at the uncertainty problem of electromagnetic pulse vulnerability assessment of engine system under the background of limited test data and incomplete information,  we proposed  a grey Bayesian network model  to improve the processing ability of Bayesian network for  uncertain information by introducing the interval grey number in grey system theory  to characterize the uncertainty of components sensitivity threshold and fault logic relationship of engine system. Secondly, taking wideband high power microwave as an example, the interval gray number failure probability of engine system and the interval gray
 number posterior failure probability of sensor were calculated. The former represented the survivability of the whole engine system under the action of strong electromagnetic pulse, and the latter reflected the vulnerable sequence of each sensor under the failure condition of the engine system. The evaluation conclusions could  provide reference for electromagnetic protection design of vehicles.

Aiming at the problem of privacy information security in mobile applications, the author proposed a security analysis method for mobile application based on user interface (UI) content. Firstly, this method  got the functions of mobile applications by mining the information of UI  products, and determined sensitive permissions that the application actually used by analyzing the code. Secondly,  the applications with similar functions were clustered together by using Mean shift algorithm. Finally, based on principle that products with similar functions should  use similar sensitive permissions, the anomaly detection algorithm iForest was used to determine whether the product was at risk of use.  Experimental results show that this method can effectively analyze the security of mobile applications.

Aiming at the problems of poor multiplexing, high routing overhead and average delay of Internet of Things (IoT) transport streams, we proposed a method for  transport stream multiplexing of IoT based on pheromone algorithm. Firstly, the method determined the necessity of multiplexing by analyzing the current situation and requirement of IoT. Secondly,  based on a network communication task, the basic idea of  transport stream multiplexing of IoT was outlined. Finally, on the basis of solving the single path problem existing in multiplexing, the pheromone algorithm was used to build a multiplexing model for the  transport stream of IoT, and the transport stream multiplexing of IoT was realized according to  output results of the model.  The experimental results show that the multiplexing result of the proposed method includes multiple signals, the signals are not missing, and the routing cost is only 3×10⁴ Mb, and the average delay is only 15 ms.

Aiming at the problems of yellowish tones, lack of color richness and low clarity of sand dust images acquired by outdoor imaging devices, we  proposesd a sand dust image clarity algorithm based on improved dark channel prior. For the problem of image color bias, firstly, we  improved the Gaussian model by adopting the adaptive normalization method  to adjust dark pixels of the image, and weighted fusion of a color correction method based on the gray world   to remove the color bias effect. Secondly,  the multi-scale retinal enhancement algorithm with color restoration was used for color restoration,  for the fog effect existing after processing, the atmospheric light value was re-selected and the dark pixels were compensated for brightness using the dark channel-based prior method. Finally, for the problems of insufficient image saturation and low contrast, the images were mapped  to HSI space and enhanced using the adaptive adjustment function and improved dual Gamma correction algorithm, respectively. The experimental results show that the method can not only effectively correct the color bias and better improve the image contrast and clarity, but also has a significant  effect on the image color richness enhancement, which can  improve the image quality of outdoor imaging equipment.

Aiming at the problem that traditional content-based clothing classification had high requirements for image features, and its accuracy was difficult to meet the application requirements of clothing classification when there were many clothing styles, we proposed a  parallel self-attention classification network based on deep learning methods. The network added a parallel self-attention compensation branch  on the basis of ResNet50, which could improve the quality of feature extraction in clothing classification tasks, and gradually supplement shallow detail information missing from  deep network. A comparative experiment was carried out on the DeepFashion dataset, and the experimental results proved the effectiveness of this method.

In order to achieve  more high-quality images in 3D digital image virtual scene  reconstruction, the author proposed  a 3D digital image virtual scene reconstruction algorithm based on machine learning. Firstly, the state information and presentation instructions of the scene were analyzed to obtain the vertex distribution positions of the mesh model for image reconstruction. The global image was approximately calculated by local coordinate method, and the local details were corrected to complete the rendering processing of 3D digital images. Secondly, taking space and scale as feature points, a window detection template was constructed on the image, and a classifier was used to suppress discrete feature points and remove redundant features. Finally, according to the fitting function method, the smoothed 3D coordinates were obtained  to reconstruct the 3D surface, and the local 2D triangle was segmented and mapped to the 3D space to realize the 3D digital image virtual scene reconstruction. The experimental results show that the proposed algorithm converges faster, the reconstructed image details and edge contours are complete, and the overall effect is good.

Aiming at the uncertain mechanism  of node activation strategies and redundancy of feasible solution sets in the process of solving target coverage problem in wireless sensor networks, we proposed a deep Q learning based target coverage algorithm to learn the scheduling strategies of nodes in wireless sensor networks. Firstly, the algorithm abstracted the construction of feasible solution sets into  Markov decision process, and intelligently selected activated sensor nodes as discrete actions according to the network environment. Secondly, a reward function  evaluated the performance of the intelligent agent in selecting actions based on the 
 coverage capacity and its residual energy of the active node. The simulation  experiment result shows that the algorithm is effective in different network environments, and the network lifecycle is superior to the  three  greedy algorithms, the maximum lifetime  coverage algorithm and the adaptive learning automaton algorithm.

Aiming at the problem of large number of data transmission node deaths and high transmission energy output during energy-saving clustering routing communication in wireless sensor networks, we proposed an energy efficient clustering routing algorithm for heterogeneous wireless sensor networks based on energy iterative model and bee colony optimization. Firstly, a network communication energy consumption model was constructed, with the goal of reducing energy consumption and combining differential bee colony algorithm to timely optimize the distribution of network nodes. Secondly, based on the optimization results of network node distribution, an energy efficient clustering method for heterogeneous wireless sensor networks was developed, the energy iterative clustering selection method was used to determine the cluster head to obtain the cluster head radius and complete the energy efficient clustering of communication nodes in heterogeneous wireless sensor networks. Finally, we set the distance between the communication cluster head node and the base station, determined the routing level of node communication, and combined multi hop routing communication to achieve energy efficient routing communication in heterogeneous wireless sensor networks. The experimental results show that when using the proposed method for network energy efficient clustering routing communication, the maximum number of dead data transmission nodes is 22, and the maximum energy consumption of node transmission is 21 nJ/bit, indicating that the method has good energy efficient effect on node communication.

We designed four simple forms of sliding mode surfaces and control inputs, studied the sliding mode synchronization of the fractio
nal-order atmospheric chaotic systems, obtained four sufficient conditions for sliding mode synchronization of the fractional-order atmospheric chaotic systems, and verified the conclusions through numerical simulation. The results show that the master-slave system of the fractional-order atmospheric chaotic systems can achieve sliding mode synchronization under certain conditions.

Based on the modified Cambridge model, an elasto-plastic model was established to describe the physical-mechanical behavior of unsaturated granite residual soils by adjusting the yield surface, and the basic incremental format of the modified Cambridge model was derived. The interface program of ABAQUS was developed to realize the stress and deformation analysis of unsaturated granite residual soil. Compared the simulation results with test data of unsaturated granite residual soils measured by GDS (global digital system) triaxial apparatus. The results show that the simulation results are consistent with the experimental results.

Ultra-fine SnO₂ nanoparticles were prepared by hydrothermal method using glucose and SnCl₄·5H₂O solution as raw materials. During the synthesis process, different amounts of phosphoric acid(PA) were added into the solution. X-ray diffraction (XRD), scanning electron microscope (SEM), and specific surface area tester were used to characterize the SnO₂ products. We studied the effect of adding PA on the gas sensing properties and analyzed its gas sensing mechanism. The results show that the final products have the ultra-fine particle size and large specific surface area, among which the gas sensor prepared by SnO₂ doped with 0.6 mmol PA has the best gas sensing performance, at the optimal operating temperature of 200 ℃, the sensitivity reaches 7.5 and has good stability. The improvement of its gas sensing properties is attributed to the ultra-fine particle size and large specific surface area, which is beneficial to the adsorption of ethanol gas.

A multifunctional LiBr/MoO₃/PE composite separator was prepared by introducing molybdenum trioxide (MoO₃) and lithium bromide (LiBr) coatings onto polyethylene (PE) separators. The structure and morphology of the separator were characterized by X-ray diffraction and scanning electron microscope, and cyclic voltammetry, electrochemical impedance and charge discharge performance testing were used to investigate the effect of LiBr/MoO₃/PE separator coated with a modified layer on the stability of lithium metal negative electrodes and the performance of lithium sulfur batteries. The results show that LiBr increases the solubility of lithium polysulfide (LiPSs), and the MoO₃ layer has a chemical adsorption effect on LiPSs, which can improve the utilization rate of active substance sulfur and suppress the shuttle effect of Li-S batteries. The Li-Li symmetric battery with LiBr/MoO₃/PE as the separator has a stable cycle time of 1 600 h at a current density of 0.6 mA/cm² and a capacity of 1 (mA·h)/cm². The initial discharge specific capacity of the lithium sulfur battery at 0.2 C can reach 1 229.2 (mA·h)/g, and the specific capacity after 500 charge discharge cycles is 628 (mA·h)/g.

We proposed an improved square root unscented Kalman filtering (SRUKF) algorithm to reduce motor speed error in the presence of interference. The interference was added to affect  the motor operation in simulation experiments, we used information such as d-q axis current, electrical angular velocity, and rotor position of the motor to predict the motor speed value, and used improved algorithms to control the speed to reduce the error caused by interference on the motor speed. Compared it with the traditional unscented Kalman filtering algorithm. The results show that the algorithm has less system operation, and the error of the interfered motor speed controlled by the algorithm is smaller compared to the true value without interference, and it has better robustness.

The 1,3-dione boron difluoride compounds were used as the research object based on the advantages of high molar absorption coefficient,  high fluorescence quantum yield,  good planar six-member ring and so on. The author designed and synthesized an asymmetric  1,3-dione boron difluoride compound, detected   its changes in solution  by using ultraviolet visible absorption spectrum and fluorescence emission spectrum,  and observed its morphology by using atomic force microscopy and measured the size of its assembly. The experimental results show that there is a significant  assembly behavior of 1,3-dione boron difluoride with an increase in  water ratio, and its assembly body exhibits a regular and ordered banded  structure. 

We studied  the reaction mechanism of Edaravone (Eda) scavenging superoxide anion free radical (O·^-₂) in aqueous liquid phase by using M06-2X and MN15 methods of DFT (density functional theory) and SMD (solvation model density) model method of self-consistent reaction field theory. The results show that the reaction of Eda scavenging O·^-₂ has three channels,  which are extraction of H atom by O·^-₂,  addition of O·^-₂ to unsaturated C and single electron transfer from Eda to O·^-₂. The lowest energy barrier of O·^-₂ extracting H reaction is 12.2 kJ/mol, the lowest energy barrier of O·^-₂ addition reaction is 110.2 kJ/mol, the energy barrier of single electron transfer from Eda to O·^-₂ is 408.5 kJ/mol, and the reaction of extracting H has the most advantage. The  reaction of Eda scavenging O·^-₂ is mainly achieved in channel of extracting H in aqueous liquid phase,  and Eda can be used as O·^-₂ free radical scavenger.

Aiming at the problem of water pollution caused by the antibiotic sulfadiazine (SDZ), a three-dimensional layered Co₃Mn-LDHs/rGO dual-action catalyst with both photocatalysis and persulfate activation functions based on graphene (rGO) was prepared by a hydrothermal method,  and a visible light/persulfate coupled degradation system (Vis-PMS) was constructed to degrade SDZ in water. The experimental results show that Co₃Mn-LDHs are successfully loaded on rGO and the attachment of Co₃Mn-LDHs prevents the stacking of rGO sheets.  The optimal conditions for the degradation of SDZ in the visible-light-coupled non-homogeneous-phase-activated PMS system are Co₃Mn-LDHs/rGO mass concentration of 20 mg/L,  PMS mass concentration of 200 mg/L,  and an initial pH=7,  and the removal rate of SDZ reaches 87.58% after 60 min of reaction.   Co₃Mn-LDHs/rGO still has a high removal rate for SDZ with good reusability after 10 cycle tests.  The free radicals that play a major role  in this system are sulfate radicals (SO^-₄),  hydroxyl radicals (.OH),  and singlet-linear oxygen (¹O₂).