By using the method of upper and lower solutions, we discussed a class of elliptic equations with nonlinear terms of supercritical growth. We first proved the existence of solutions of the Dirichlet problem in the restricted region, and then proved that the local solutions in the restricted region could be extended to the whole region by combining a new  variational principle.

By using the ring decomposition, the commutator generated by the Bochner-Riesz operator and variable exponential Lipschitz function b(x) was decomposed into three parts, and its boundedness was estimated by using the properties of Lipschitz function with variable exponent, and the boundedness of the commutator of Bochner-Riesz operator and variable exponential Lispchitz function on the Herz-Morrey space with variable exponent was obtained.

By using the fixed point theorem of power contraction mapping, we discuss the existence and uniqueness of two kinds of fuzzy solutions for boundary value problems of second order delay fuzzy differential equations under the framework of generalized Hukuhara derivatives, and the existence and uniqueness of two kinds of fuzzy solutions of the problem are proved without limiting the Lipschitz condition coefficients of the nonlinear function.

The problem of the boundedness of fractional maximal operator and its commutator on generalized homogeneous Morrey spaces was solved by using function decomposition method, and the sufficient and necessary conditions for the boundedness of fractional maximal operator and its commutator on generalized homogeneous Morrey spaces were obtained. So some characteristics of fractional maximal operator on generalized Morrey spaces were generalized to generalized homogeneous Morrey spaces.

We considered the existence of solutions of differential equations for fractional Choquard type Kirchhoff critical problems. Firstly, Hardy-Littlewood-Sobolev embedding theorem was introduced, and combined with Nehari manifold method and fibbing maps of energy functional related to the problem, the existence of nontrivial solution of the equation was proved when the parameter λ was small enough. Secondly, the functional had (PS) sequence was obtained by Ekeland variational principle, and then the appropriate parameter λ was selected. Combined with the truncation method and mountain pass theorem, the compactness 
condition was proved to be true. Finally, the existence of nontrivial solutions of the above equations was established by using the fractional concentration-compactness principle.

The author considered the existence and multiplicity of positive solutions of nonhomogeneous second-order three-point boundary value problems by using topological degree theory and the method of upper and lower solutions when the nonlinear term f satisfied superlinear growth conditions. The results show that there are  at least two positive solutions, one positive solution and no solution of the problem  when the parameter b is in  different value ranges.

Based on the local well-posedness of the solution, we discussed  the non-uniformly continuous dependence of the solutions to the Cauchy problem associated with the periodic water wave system on initial value in Besov spaces by using the method of approximate solutions. The results show that the local well-posedness of the solutions to this problem in the corresponding Besov spaces can not be obtained only by  contraction mapping principle.

By using the Krein-Rutman theorem and Dancer global bifurcation theory, the author studies the global structure of positive solutions for nonlinear third-order three-point boundary value problem, where r>0 is a parameter, 0<η<1, α,β>0, and the nonlinear term f∈C(［0,1］×［0,∞),［0,∞)) satisfies asymptotic linear growth condition at 0 and ∞.

By using a new technique of treating neutral term and some results of first order impulsive delay differential inequalities, we investigated the oscillation problems for a class of nonlinear generalized elastic rod equations with impulse and neutral term, and established sufficient criteria for the oscillation of all solutions of this class of elastic rod equations under the third kind of boundary conditions. The obtained results reflect the decisive function of impulsive perturbation and delay effect in the oscillation of elastic rod structures.

We consider the existence of positive 2π-periodic solutions of the third-order ordinary differential equations with multiple delays,
where coefficient function a: R→(0,+∞) is  continuous, and the  period of  t is 2π, nonlinear term f: R×［0,+∞)ⁿ→［0,+∞) is  continuous, and the   period of  t is 2π, andτ₁,τ₂,…,τ_n are positive constants. Using fixed point index theory in cones, we give the existence results of positive 2π-periodic solutions of the problem under the inequality conditions that allow the nonlinear term f(t,x₁,x₂,…,x_n) to grow superlinearly or sublinearly on x₁,x₂,…,x_n.

We discussed the dynamic properties of a class of bacterial toxin-dependent pathogenesis models. Firstly, by using the upper and lower solution method and the comparison theorem of parabolic equation, the global existence of solutions of the systems, dissipation, continuity and global asymptotic stability of boundary steady-state solutions were proved. Secondly, based on Lyapunov functional method, the global asymptotic stability of the positive normal steady-state solution was obtained. Finally, the effectiveness of results was verified by numerical simulation. The results show that proper regulation of the intrinsic growth rate of pathogens and the rate of elimination of pathogens by immune effectors can prevent disease outbreaks.

The finite element method was used to solve the probability density function with periodic properties to study the statistical properties of stochastic periodic solutions. We proved the integral conservation of the full space approximate solution and the spatial integral approximate conservation of the approximate solution truncated to a finite interval, and verified  the effectiveness of the method  by numerical experiments.

We  characterized strong Prüfer rings by using semi-regular flat modules. Namely, we proved that a ring R was strong Prüfer if and only if any ideal of R was semi-regular flat module, if and only if any submodule of a semi-regular flat module was semi-regular flat module, if and only if any R-module had an epimorphic semi-regular flat envelope.

We used the methods such as the analytical approximation, the subharmonic function, the Birkhoff ergodic theorem, the large deviation theorem and the avalanche principle to study the regularity of the Lyapunov exponent corresponding to  the quasi-periodic Jacobi operator model. Under the condition that the potential energy is a non-degenerate Gevrey function, if the frequency is a strong Diophantine  number and the coefficient of potential energy is  large enough, we obtain the results that  Lyapunov exponent is positive and continuous. Thus, the  result of the Schrodinger cocycle in SL(2,R) is extended to the Jacobi cocycle  in GL(2,R).

Firstly, the influence of the structure of the star network on synchronization was discussed by using the theory of rotating periodic solutions. The existence of various types of synchronization solutions in star networks was judged, and  the relationship between symmetry of the star network and synchronization solutions was given. Secondly, in the star network, all the rotating matrices satisfying the rotating periodic conditions formed some special groups. By using the conjugate classes of these groups and diagonalization method, we obtained various  types of synchronization solutions.

We considered the application of the  empirical likelihood (EL) method to the bivariate first-order integer-valued autoregressive (BINAR(1)) process. We first established the empirical likelihood ratio (ELR) statistics, discussed and found its limit distribution by using asymptotic normality of the conditional least squares (CLS) estimation of the process, thus constructed the confidence regions of the parameter and solved the problem of hypothesis test of the parameters. Then, the coverage probability of the confidence region of the parameters computed by EL methods and normal approximation (NA) methods was compared through numerical simulation.

We considered nonempty  boundness of solution sets for the quasiconvex function minimization problems in reflexive Banach spaces, gave the definition of q-asymptotic function of quasiconvex function on the nonempty closed convex set, and obtained the equivalent characterization of the existence of the solution set of the quasiconvex function minimization problems. The nonempty boundness of the solution set of the classical minimization problem of  convex function was extended to quasiconvex function, and a sufficient condition for the nonempty boundness of the solution set of equilibrium problems was given.

Aiming at the problem that the YOLO_v4 model would be gradually  diluted due to the features of serial connection of the neck network, which affected the performance of the model, we proposed a YOLO_v4 object detection method with improved multi-scale features. The method  reconstructed the YOLO_v4 neck network structure   by introducing an intermediate layer, and then used the intermediate layer to participate in the subsequent feature fusion to realize the cross-level connection of features, and used the parameters that could be learned through the network as the balance factor between the features to perform  feature weighted fusion. The experimental results on the VOC-2007 and VOC-2012 datasets show that the proposed  method  can improve the average accuracy of the model by 1.3%, which can effectively improve the detection ability of the model for different targets.

Aiming at the low accuracy of traditional instance segmentation methods in handling multi-object segmentation in unmanned driving technology, we proposed a deep learning method based on joint attention mechanism to achieve instance segmentation of urban traffic multi-object scenes. The method in tegrated channel attention and spatial attention by designing the joint attention module,  guided the neural network branches to process important feature information, so as to improve the performance of the network for multi-scale object segmentation, and solved the problem of poor segmentation effect of the current deep learning network for urban traffic multi-object scene. The  experimental results on cityscape dataset show that  the proposed method is effective and  can improve the accuracy of instance segmentation by unmanned driving technology in urban road traffic scenes.

In the object detection of aerial remote sensing images, aerial images were arranged in any direction under the overhead view, which had problems  such as large image size, arbitrary direction and complex background. In order to get better detection results in aerial images with complex backgrounds, we proposed a rotated object detection model in aerial images based on the attention mechanism. Firstly, RetinaNet was used as the baseline model, on the basis of  the original detector structure, additional  angle parameter was added to adapt to the  rotated object detection. Secondly, we proposed  a new channel semantic extracting (CSE)  attention module to  capture global semantic information and the channel relationship, and predicted the coarse bounding box and classification score.  Finally, the feature alignment and the improved Fast R-CNN detector head were used for fine processing to  further improve the detection accuracy and obtain the final classification and regression results. The experimental results show that the detection accuracy of this method on the public aerial remote sensing  DOTA dataset reaches 77.71%, which is superior to  other advanced rotated object detection methods.

Aiming at the problem of weak robustness of encoder-decoder networks in feature extraction from complex medical images, such as complex textures, blurred boundaries, low contrast with surrounding tissues, and background noise interference, which led to low segmentation accuracy of lesion region, we proposed a medical image segmentation network based on multi-scale semantic representation. Firstly, a multi-scale context-aware module was used to enhance the representation ability of different scale contexts. Secondly, by calculating the feature difference between adjacent layers, the difference in semantic features between different layers was highlighted and the redundancy of feature information was reduced. Finally, a hybrid attention module was used to enhance the boundary information of the lesion region and the semantic perception ability of complex features by the network. Experimental results show that the network has high segmentation accuracy and strong robustness in  complex medical image segmentation.

Aiming at the  illumination correction problem of the image interfered by the same illumination conditions, we proposed an image illumination correction algorithm based on principal component analysis.  Firstly, a covariance matrix was constructed by using given multiple images, and the eigenvalues and eigenvectors were calculated. Secondly,  a set of normal orthogonal bases was constructed according to  the eigenvectors. Finally, a part of substrate principal component was selected to reconstruct the image. 
 The experimental results show that the algorithm can eliminate the influence of illumination and retain the main features of the image.  Compared with the  classical algorithm,  the effectiveness of the algorithm is verified.

Aiming at the problems  of low target segmentation rate and feeble correlation of image context feature information under multi-scale categories in image semantic segmentation, we proposed an image semantic segmentation model that fused attention mechanism and multi-scale features. The model used the improved  atrous spatial pyramid pooling to increase the segmentation of multi-scale targets, used the attention refinement module to capture context information to guide feature learning, and added feature fusion  based on attention mechanism to  supervise the learning of important channel features, guide the fusion of high-order and low-order features, so as to improve  the generalization capability of the model. The simulation results on the Cityscapes dataset show that the mean intersection over union of the model is 1.14% higher than that of DeepLab v3+, which proves that the model has good robustness.

Aiming at the problem that image texture filtering need to preserve structures while filtering multi-scale texture details, we proposed a  weighted least squares texture filtering based on structure tensor. The method used anisotropy of structure tensors and local gradient to extract the structure information in the image, so as  to optimize the smoothing weights of each pixel in the 
traditional weighted least squares filtering, which determined the smoothness degree of each pixel. In the global optimization framework of minimization, the constraints of the pixels at the structures were relatively small, so smaller weights were assigned,  the constraints of the pixels in the texture regions were relatively large, so larger weights were assigned. The constructed multi-scale edge-preserving smoothing algorithm framework could decompose the image into a segmented smooth base layer and texture detail layer to obtain the edge-preserving smoothing result of natural image, so as to realize the purpose of structure-aware adaptive texture filtering. The experimental results of  subjective and objective comparison with the common methods show that the proposed algorithm can effectively maintain the structure edges while smoothing out multi-scale textures, and has obvious advantages in terms of structure similarity and visual perception quality.

Aiming at the problem that the pre-training model would cut off part of text when dealing with long text such as news, which led to the loss of text infomation, we  proposed a  method to build a model by combining  TextRank algorithm, implicit Dirichlet distribution topic model and pre-training model on the basis of integrating news title information, and  compared the model with other  semantic similarity calculation methods. The results show that the accuracy rate of the model is 82.46%, the recall rate is 87.43%, the accuracy rate is 82.68%, and the F₁ value is 84.99%,  the optimal results are obtained, which effectively improves the performance of semantic similarity calculation between news texts and comments.

Aiming at the problem that the accuracy of the network model would drop sharply with the imbalance of the network structure when the traditional layer-wise  pruning method was in the later stage of the pruning process， we proposed a layer-wise pruning method based on network characteristics. Firstly, the pruning coefficient of each iteration was calculated according to the network depth, network width and inter-layer importance index. Secondly,  the dynamic pruning rate of each layer parameter was obtained by combining the basic pruning rate. Finally, pruned and fine tuned the pre-trained network, and repeated the above process to the end of iteration. The experimental results show that the layer-wise pruning method based on network characteristics performs 
well on VGG-16 model. When the compression rate is about double, the accuracy is still 3.6% higher than that of the layer-wise pruning method with single pruning rate, and the overall performance is better than that of the global pruning method. When the compression rate reaches more than 98.85%, the accuracy on the Resnet-20 model is 20% higher than that of the layer-wise method with single pruning rate, which is close to the global pruning method. It shows that  the performance of layer-wise pruning method can be improved by making full use of network characteristics.

Aiming at  the problem that the traditional fuzzy C-means (FCM) algorithm  produced a large amount of computation  when dealing with high-dimensional data sets with complex structures, which led to the decline of clustering effect, we proposed a modified fuzzy clustering algorithm based on non-negative matrix factorization. Firstly, the algorithm proposed a new objective function, which was solved by alternating iterations. Secondly, in the iterative process, triangular inequalities were used to filter out samples that met the inequality conditions, and at the same time,  a new membership updating formula was used to reduce the amount of calculation and  improve the clustering performance. Finally,  experiments were carried ou on the UCI dataset and image dataset, and compared with other classical FCM algorithms. The experimental results show that the algorithm  improves the clustering effect.

Aiming at the problem that the trust model of wireless sensor network (WSN)  usually only resisted external attacks on the network, and ignored how to resist attacks on the trust model itself, we proposed a fast identification model for trust attacks in WSN  based on trust to improve the recognition speed of trust attacks. Firstly, a penalty factor was introduced into the direct trust value to adaptively adjust the decline speed of malicious node trust value,  and at the same time, a volatilization factor was introduced to change the weight of historical trust value in the comprehensive trust value. Secondly, we filtered the direct trust value recommended by the third party node to reduce the adverse impact caused by  malicious evaluation. Finally, we weighted the direct and indirect trust values to obtain a comprehensive trust value to determine whether the node was malicious. The experimental results show that this method can effectively improve the speed of identifying trust attacks when identifying different number of trust attacks.

The Rayleigh-Marangoni convective instability of a non-Newtonian fluid in a fluid-porous medium two-layer system was studied. The linear stability analysis and Chebyshev tau-QZ algorithm were used to obtain the numerical results, and the neutral curves of the critical Rayleigh number and the critical Marangoni number were obtained. The instability variation trend of the coupling modes of the critical Rayleigh number for different Marangoni numbers was analyzed, and the instability of the Rayleigh convection and Marangoni convection under the oscillatory convection was discussed. The results show that the Rayleigh convection and the Marangoni convection under the oscillatory convection become more unstable when the stress relaxation time increases, the instability of the two types of convection has the opposite effects when the strain retardation time increases. The two types of convections become more stable when the thermal conductivity of the upper surface (the corresponding Biot number) increases, and the Rayleigh convection instability mode converts with the increase of Biot number when the depth ratio changes. The coupling instability mode of the Rayleigh-Marangoni convection for a given depth ratio is obtained.

In an asymmetric double quantum well with tunneling induced quantum interference, we designed a controllable spatial vortex four-wave mixing scheme. The spiral phase and intensity distribution of vortex four-wave mixing can be effectively controlled by tuning the detuning of the probe field and the Rabi frequency of coupling field as well as vortex field, and the numerical results can be interpreted by using the dispersion relation.

Multilayer triangular WS₂ films with a maximum size of 74.22 μm were prepared by atmospheric chemical vapor deposition (APCVD) method on SiO₂/Si(300 nm) substrate, and WS₂ films with clear edge, regular shape and a maximum size of 41.89 μm were synthesized on sapphire substrate. The prepared samples were characterized by optical microscope (OM), scanning electron microscope (SEM), Raman spectrometer and photo-emission spectrometer (PL). Combined with the morphology and size of the sample, the effects of experimental parameters such as growth temperature, dosage ratio of tungsten source and sodium chloride, and different substrates on the growth of WS₂ thin films were analyzed. The experimental results show that temperature has the greatest influence on the growth of WS₂ films by APCVD, and high temperature is conducive to the growth of WS₂ films with high crystal quality. The higher the temperature is, the more regular the film shape is. At the optimum temperature, the smaller the wave number difference is, the fewer the film layers are, the fewer the grain defects are, and the higher the luminous intensity is. The dosage ratio of tungsten source and sodium chloride corresponding to different temperatures is different. The addition of proper amount of sodium chloride can improve the supersaturation of tungsten source in the reaction system, promote the smooth progress of the reaction, and is more conducive to the growth of WS₂ thin film. The growth temperature required by the growth system for preparing WS₂ thin films on different substrates is different, and the growth temperature required on sapphire substrate is higher under the same experimental conditions.

One-dimensional (1D) rod-like, two-dimensional (2D) sheet-like and three-dimensional (3D) flower like ZnO were prepared by direct precipitation method in the same system, and the phase, morphology and optical properties of the synthesized materials were characterized. The photocatalytic performance of different morphological ZnO was tested  by degradation of Rhodamine B, and the photocatalytic efficiency differences were analyzed by combining the performance of ZnO with different morphologies. The results show that all samples have a hexagonal wurtzite structure and  uniform in size. The specific surface area of 2D sheet-like ZnO is the largest, and there are a lot of holes on the surface of  2D sheet-like and 3D flower-like ZnO.  The 2D sheet-like ZnO has the largest band gap width. The   2D sheet-like ZnO has the highest photocatalytic efficiency, and the 1D rod-like ZnO has the  lowest photocatalytic efficiency. 

Based on the advantages of   high sensitivity,  simple operation and time-saving in   the detection of metal ions by fluorescent analysis.  We designed and synthesized a porous metal-organic framework  crystal fluorescent probe with amino modification. The experimental results show that the   compound is a two-fold interpenetrating  structure  of pcu framework,  and the amino groups on the organic ligands are freely distributed in the channels. The compound has excellent thermal  stability and water stability, and can be used as fluorescence enhanced probe to detect Ag⁺ in aqueous solutions,  with the detection limit of 0.76 μmol/L.

We proposed a surface enhanced Raman spectroscopy (SERS)  method using nano gold (AuNP) as enhanced signal, which could be used  for rapid and sensitive quantitative analysis of hydrogen peroxide (H₂O₂),  and applied it to monitor the change of glycerol content in the process of yeast fermentation. The experimental results show that the  method is based on the positive correlation between enzymatically hydrolyzed glycerol and the concentration of hydrogen peroxide. When 3,3′,5,5′-tetramethylbenzidine (TMB) is used as substrate,  TMB²⁺ final product with strong SERS activity is produced through the catalytic H₂O₂ action of peroxidase. The H₂O₂ content can be  sensitively detected through AuNP enhanced signal,  and the glycerol content can be monitored according to the quantity  ratio of equivalent substances. The TMB²⁺ is  linear relationship with natural logarithm of SERS signal  intensity when  H₂O₂ concentration is 2.75—22 μmol/L,  and the detection limit LOD=2.75 μmol/L,  R² =0.995,  average CV=5.38%,  average recovery 96.05%. The method has high sensitivity,  precision and accuracy, and can be used to detect the concentration of H₂O₂ and monitor the change of glycerol content in the fermentation process.