By means of the estimation on L^p space, and by using A_p weight inequality and function decomposition method, we gave the bounde
dness of the oscillation and variation operators for the commutators of the multilinear singlar integrals with bounded mean oscillation (BMO) functions on the weighted Morrey spaces.

By using the fixed-point theorem of Guo-Krasnoselskii, we give the existence and multiplicity of positive solution for semi-positone second-order discrete periodic boundary value problem, where λ>0 is the parameter, ［1,T］_z={1,2,…,T}, f:  ［［1,T］_z×［0,∞)→R is continuous and there exists constant  D>0,  such that  f(t,u)≥-D, (t,u)∈［1,T］_z×［0,∞),  a: ［［1,T］_z→(0,∞)  and  0<a(t)<4sin²(π/2T).

By using the connectivity theory of solution sets of compact vector field equation, we give the methods of upper and lower solutions for Neumann problem of one-dimensional discrete mean curvature equation.

By using Leray-Schauder fixed point theorem, the author discusses the existence of positive solutions for the elastic beam equations simply supported at both ends.

Firstly, by using Tikhonov regularization method to solve the inverse source problem of the fractional heat conduction equation with Riemann-Liouville derivative, we obtained a regularization solution with Mittag-Leffler function. Secondly, we analyzed the convergence of the regularization solution, gave the error estimate of the regularization and exact solutions under a priori parameter choice rule, and the range of regularization parameter under a posterior parameter choice rule. The numerical experiment results show the effectiveness of proposed regularization method.

Firstly, the author discussed the existence of radial positive solutions for a semipositone elliptic equation with the Dirichlet boundary condition by using the variational method, the results show that when the λ is sufficiently small, the equation has no nonnegative solution; when the λ is sufficiently large, the equation has a radial positive solution. Secondly, the author prove that the linearized operator at each solution of the equation has the nonnegative first eigenvalue. Where Ω is a ball or an annulus, the parameter λ>0, f∈C(［0,∞),R) and f(0)<0 (semipositone), k: ［a,b］→［0,∞) and k(|x|) is not always 0. Furthermore, when the Ω is a ball, the k is a linear map; when Ω is an annulus, the k is a monotone increasing function.

The lattice Boltzmann model was used to solve a class of third order partial differential equations with variable coefficients and source terms. By using Chapman-Enskog expansion technology, the macroscopic equation with the third order accuracy was recovered by selecting appropriate equilibrium distribution function and compensation function. Numerical simulation results verify the effectiveness of the proposed model.

By using 3-ary differential functions, we construct an infinite dimensional 3-Lie algebra T, discuss the structure of T, and prove that T is a non-3-solvable non-simple 3-Lie algebra, the inner derivation algebra ad T is an indecomposable unsolvable Lie algebra, and the ideals of ad T have only the derived sequence V⁽ⁿ⁾ of the maximal ideal V(n∈Z, n≥0).

We first gave the concept of Hom-LPNG algebras, and then solved some problems in the construction of Hom-LPNG algebras by using the newly defined operation method. We obtained the results of constructing Hom-LPNG algebras from Hom-commutative associative algebras, Novikov-Poisson algebras and LPNG algebras, and generating new Hom-LPNG algebras from known Hom-LPNG algebras.

Firstly, the author defined the Hom-Jacobi-Jordan algebras. Secondly, the author gave the isomorphism classes of low-dimensional Hom-Jacobi-Jordan algebras by using Jordan canonical form of linear mapping and undetermined coefficients method.

We considered the properties of zeros of analytic automorphisms on the unit disk. It is proved by calculation that the Blaschke product generated by the zeros of hyperbolic and parabolic analytic automorphism after iteration has the properties of interpolation and one-component, and the zeros of elliptic analytic automorphism after iteration does not tend to the boundary, so it can not generate Blaschke product.

Considering Logistic growth and saturated infection rate, we established a class of fractional-order time delay epidemic models with different orders. Firstly, by using Jacobi matrix and eigenvalue trajectory method, we analyzed the local stability of the model and gave the basic reproduction number. Secondly, we selected the bifurcation parameter as the time delay, and gave the sufficient condition for the occurrence of Hopf bifurcation at the endemic equilibrium point. Finally, the correctness of theoretical analysis was verified by numerical simulations. The research results show that the change of fractional-order may affect the stability of the system.

By using mathematical induction, reductio ad absurdum as well as construction of specific coloring function, together with Hall theorem, we discussed the D(2)-vertex-distinguishing edge coloring of unicyclic graphs, and gave their precise D(2)-vertex-distinguishing edge chromatic numbers.

By using the Krasnosel’skii fixed-point theorem, the author give the existence and multiplicity of positive solutions of a singular third-order three-point boundary value problem, in the case that both the weight function h(t) and the nonlinear term f(t,u) are singular, where a is positive constant, η∈［π/2,π), h: (0,π)→［0,+∞) and f: (0,π)×(0,∞)→［0,+∞) are continuous functions.

We considered the boundary value problem of fractional differential equations at resonance, by defining a proper Banach space, norms and operators, the Mawhin’s coincidence degree theory was used to prove the existence of solutions for the  three-point boundary value problem of Conformable fractional differential equations at resonance, and a sufficient condition for the existence of its solution was obtained.

Firstly, by using the Banach contraction principle and Krasnoselskii fixed point theorem, we studied the existence of solutions for a class of nonlinear  fractional integro-differential equations, and obtained the result that there was at least one solution and there was a unique solution. Secondly, two examples were simulated by using the iterative method to verify the results.

We considered the first initial boundary value problem for a class of anisotropic non-Newtonian  fluid equations in a three-dimensional smooth bounded region Ω. Firstly, we constructed the approximate solution of the problem by using Galerkin method, and then obtained the uniform estimates of the approximate solution by using the energy estimation method. Finally, we proved the existence of the weak solution by using the compact method and the monotone method.

We considered the spatial properties of a class of thermoelastic plates with biharmonic operators. By constructing an energy function and using the technique of differential inequality, we derived a differential inequality in which the energy function could be controlled by its first derivative, and gave the Phragmén-Lindelof alternative result of the solution.

We first constructed T*-extensions of δ-Hom-Jordan Lie color algebras by 2-cocycle and co-adjoint representation, obtained the solvability and nilpotency of the T*-extension T^*_ωL, and then we gave sufficient condition of the decomposability of the trivial T*-extension T^*₀L.

By constructing a Lie coalgebra structurre of an infinite dimensional Lie algebra Witt algebra over the complex field C, we solved the problem whether the infinite dimensional Lie algebra Witt algebra was a weak co-split Lie algebra.

We proved the existence of nontrivial weak solution for a class of quasilinear Choquard equations with p-Laplacian operator as well as the convolution terms by using the mountain pass lemma.

Aiming at the parameterization problems for bounded and closed meshes, we proposed a mesh parameterization method based on local average  normal deformation. Taking the mean curvature flow as a reference, the vertices were pushed to the average position of their neighbors, thus deforming a mesh to a plane or a sphere. Firstly, the average normal of neighbor faces of each triangle was calculated and the rotation matrix of the normal was calculated. Secondly, based on Poisson system, the whole mesh were reconstructed by optimizing a stretching energy, the new coordinates of vertices were calculated. By alternating the above two steps, the original mesh was deformed to a constant mean curvature surface. The algorithm was different from the general methods based on energy optimization, which noly needed to solve a sparse linear system in each iteration, therefore, it could process large data sets quickly. By adding a penalty function during the deformation to dynamically adjust the weights of global average normals, the problem of triangle degeneration or flipping in the deformation process was avoided. The experimental results show that compared with other parameterization methods, the proposed method has the advantages of practical reliability and high efficiency, and can compute low-distortion plane parameterization and spherical parameterization in the same frame.

Aiming at the problem that traditional iris classification required manual design of filters to extract iris features, which was single, and usually required a large number of manual parameters adjustment, so the generalization ability was poor, we proposed an iris classification algorithm based on multiple features in residual network. On the one hand, the iris image was combined with Gabor features, on the other hand, multi-scale convolution kernels were used in the network structure, which made the learned iris features more abundant, and improved the representation ability of image features. The experimental results show that in the fixed category, using Softmax classifier for multi-classification, the classification accuracy of the algorithm in JLU iris database can be more than 98.90%, which is not lower than the network structure such as DeepIrisNet and Resnet, and the network structure of the algorithm has fewer parameters and faster learning speed.

Aiming at the problem that the existing models rarely designed face features and the face features were weak in discrimination, we proposed a deep face representation algorithm based on dual attention mechanism. The algorithm adopted network structure of dual attention mechanism, designed low-level features through detail attention mechanism, and paid attention to local features through automatic and adaptive learning of hierarchical features, semantic attention mechanism was used to design high-level features, and pay attention to semantic features through adaptive semantic grouping. The experimental results on LFW,YTF,MegaFace,IJB-B and IJB-C datasets show that the recognition accuracy of the dual attention mechanism method is as high as 99.87%,97.9%,98.91%,95.02% and 96.28% respectively, which is 0.02%,0.1%,0.2%,1% and 1% higher than that of similar algorithm Groupface. The comparative experiments show  the advantages of dual attention mechanism network.

Aiming at the problem of color cast and blur in the process of acquisition and transmission of underwater images, we proposed an enhancement method of underwater color cast image based on deep convolutional neural network, and gave the convergence analysis of the proposed method. Firstly, on the basis of the traditional U-Net model, a convolutional neural network model based on color cast images was constructed to continuously learn the color cast between the input image and the output image. Secondly, by using the loss function of structural similarity, the enhanced underwater image was highly similar to the input underwater image in the details of the content structure. The model solved the problem of color cast and distortion of underwater images. By verifying a large number of real underwater data sets, and compared with other algorithms, the experimental results show that the underwater image enhanced by the method not only improves the visual effect effectively, but also retains the texture structure contained in the original image, which proves that the model has high practicability in the field of underwater image enhancement.

In order to improve the effect of medical ultrasonic image in clinical diagnosis, it was necessary to optimize the detection and recognition of images, we proposed a multi-scale edge detection algorithm for medical ultrasonic images based on deep residual network. Firstly, the gray scale distribution matrix of medical ultrasonic image was constructed by automatically tagging the original medical ultrasonic image, and the multi-scale segmentation of medical ultrasonic image was completed by using the distribution matrix. Secondly, the contour model of multi-scale edge of medical ultrasonic image was constructed to extract the edge features of multi-scale image. Thirdly, the deep residual network structure was constructed, and the deep residual learning algorithm was used to fuse the underlying image information of ultrasonic image. Finally, multi-scale edge detection was performed on the fused edge image data. The experimental results show that the proposed algorithm has high accuracy of image segmentation, the accuracy of feature extraction is more than 80%, the detection effect of discontinuous area in the image boundary is good, the edge point checking is high, the detection time of the algorithm is short, and the convergence is strong.

Aiming at the problem of adaptive threshold calculation for open set voiceprint recognition, we proposed a threshold calculation method based on Otsu algorithm and deep learning. Firstly, deep features of speech were extracted from Mel cepstrum coefficients by using deep confidence network stacked by three layers of restricted Boltzmann machines. Secondly, the similarity value of features was calculated by Gaussian mixture model, and Otsu algorithm was used to calculate the threshold value of the similarity value of the features. The experimental results show that the proposed method has a better recognition effect, compared with the method of calculating the threshold value with equal error rate, the method has higher recognition accuracy.

The MATLAB platform was used for modeling and simulation, the position loop/current loop double closed-loop proportional-integral-differential (PID) control system, and the combination of fuzzy control were used to solve the problem of the rotary direct drive valve (RDDV) of the aero-engine fuel regulation system. The servo system had hydraulic load disturbance, which seriously affected the dynamic characteristics and stability of the system. The simulation results show that under the same input conditions, the fuzzy double closed-loop control method can significantly shorten the response time under the premise of ensuring that the system has no overshoot, when there is a disturbance, the system can be restored to a steady state faster.

The classification methods based on regular expressions and traditional machine learning had the problems of manual extraction of patterns and performance bottleneck, we proposed deep learning-based classification methods for question post, the deep text mining model TextCNN and integrating attention mechanism—TextRNN were used to construct a classification model. The experimental results show that the classification performance of deep learning-based methods is better than the existing benchmark methods on most of the question purpose categories, and the Adam optimizer is better than the SGD optimizer, and the Glove pre-trained word vector is better than randomly generated word vectors. The method classifies posts for the purpose of asking question, which can add a new dimension to the analysis of post discussion topics on Stack Overflow (SO).

Aiming at the  problem that class imbalance generally existed less negative comments but more influence in the network comments, we proposed a sentiment analysis method based on class imbalance learning. This method used the probability output in the process of deep learning training to calculate the information entropy of the sample. The information entropy was used as the influence factor to construct the cross information entropy loss function. The experimental results on the IMDB public dataset show that the bidirectional long short-term memory network based on the integrated information entropy loss function can deal with class imbalance problem. The statistical analysis of the data shows that this strategy can improve performance of sentiment polarity classification based on the bidirectional long short-term memory network. For the AUC (area under curve) indicator, the median of bidirectional long short-term memory network model with the integrated information entropy loss function is 15.3% higer than that of the deep learning model that does not consider class imbalance.

In view of diversity and variability of the current network intrusion, and it was difficult to obtain ideal network intrusion detection results by a single method. In order to improve the accuracy of network intrusion detection and effectively intercept all kinds of network intrusion, we proposed a network intrusion detection method based on combination of semi-supervised technology and active learning. Firstly, the network intrusion data was collected, the network intrusion features were extracted, and the semi-supervised technology was used to cluster the network intrusion data according to the features. Secondly, the active learning algorithm was used to train the clustered data, the classifier of network intrusion detection was constructed, and the ant colony algorithm was introduced to optimize the classifier of network intrusion detection. Finally, the standard data set was used to simulate and test the network intrusion detection. The text results show that this method solves the defects of the current intrusion detection methods, improves the accuracy of network intrusion detection, and the missed detection rate and false detectio
n rate are significantly less than the classical network intrusion detection methods. At the same time, it shortens the network intrusion detection time, improves the efficiency of network intrusion detection, and can better ensure the security of network communication and data transmission.

In order to realize the smooth optimal path planning of differential drive robot in obstacle avoidance environment, the author proposed a path planning algorithm for hybrid obstacle avoidance of differential drive robot based on Bézier curve. Firstly, the motion model of differential drive robot was established, which was used to control the linear speed of the left and right driving wheels to complete the turning and non-uniform motion of the robot. Secondly, by using Bézier curve to describe the path state, the path planning problem was transformed into the problem of generating Bézier curve finite point orientation optimization, which improved the motion smoothness of robot. Finally, genetic algorithm was introduced to simplify the two-dimensional path coding problem into one-dimensional coding problem, and the roadside constraints, dynamic obstacle avoidance requirements and shortest path requirements were mixed into fitness function. The robot could get rid of the local minima as soon as possible and successfully bypass the obstacles to reach the target point. The simulation results show that the obstacle avoidance path planning effect of this method is better, the distance of the obstacle avoidance path is 30.19 m, and the obstacle avoidance time is lower than that of the comparison methods, the longest obstacle avoidance time is 5.3 min.

Aiming at the problem of high energy consumption and unbalanced load in traditional LEACH protocol and its improved methods, we proposed an improved LEACH protocol based on chaotic genetic algorithm called CGA-LEACH to minimize the energy consumption for wireless sensor networks (WSNs). By constructing a new fitness function considering the energy consumption and load, the algorithm used conditional chaotic mapping to generate real coded chromosomes, and used the chaotic genetic selection, crossover and mutation operations to improve the convergence speed and find the optimal cluster heads, so as to form a cluster structure with uniform distribution, energy consumption and balanced load . Simulation results show that CGA-LEACH algorithm can effectively prolong network lifetime, balance network load and improve network energy efficiency.

In order to prolong the network lifetime and timeliness of data transmission, we proposed a routing algorithm based on improved short-chain aggregation strategy for wireless sensor network. Firstly, we analyzed the protocol structure of wireless sensor networks. Considering the energy consumption of nodes in the operation process of wireless sensor networks, we designed an improved routing algorithm according to the chain data acquisition protocol. Secondly, the greedy algorithm was used to find the neighbor nodes, and the distance threshold equation was introduced to realize the establishment of the chain. After the establishment of the chain, the routing cluster head was selected by comprehensively considering the energy consumption and residual energy of the node transmission data, so as to prolong the network life and improve the data transmission efficiency. Finally, the effectiveness of the algorithm was verified by MATLAB software simulation experiment. The simulation results show that the algorithm can effectively control the energy balance of the network, prolong the network lifetime, and the operation effect is good.

In order to study the uncertainty relations for triple components of angular momentum for spin -1, the uncertainty relations of product and sum of three components were established by using Heisenberg-Robertson uncertainty relation inequality. The results show that the inequality becomes tight by introducing a triple constant τ, and the triple constant in the tight inequality is the same in the case for spin -1/2.

We proposed a grid multi-scroll hyper-chaotic system. The number of scrolls can be generated by extending saddle focal equilibrium points in x and y directions. Through dynamic analysis of Lyapunov exponential spectrum, equilibrium point, bifurcation diagram, complexity, the system exhibits hyper-chaotic state in a large parameter interval. With the increase of the number of scrolls, the complexity and largest Lyapunov exponent of the system increase obviously, and the dynamic behaviors of the system become more complicated. Based on the Lyapunov stability theory, we studied adaptive synchronization of the grid multi-scroll hyper-chaotic system with unknown parameters. The results of numerical experiments show that the syschronization time is short, and the synchronization effect is better.

Using the B3LYP mehtod of density functional theory (DFT), the author optimized the geometry of gas phase methionine (Met) molecule at the level of the 6-311+G(2df) base set, and analyzed the characteristics of each elementary reaction in the process of chiral transformation of the Met+2H₂O molecular system. Under M06-2X/def2-TZVP, the time-dependent density functional theory (TDDFT) was used to obtain the molecular orbitals (MO), natural transition orbitals (NTO) and isosurface maps of hole-electron distribution of a transition state system in the process of the chiral transition of the Met+2H₂O molecular system in the implicit solvent methanol, and the electronic excitation characteristics were studied. The results show that with the help of double water molecules, H atom migrates to form transition states, which makes the Met molecular system structure and reactants change significantly, as well as the molecular function changes.

Using self-consistent field theory lattice model, we studied the effect of polymer concentration and polymer chain model on micelle formation in amphiphilic diblock copolymer solutions by calculating phase diagram and specific heat. The results show that the temperature of micelle formation increases gradually with the increase of polymer concentration. Compared with direct backfolding polymer chain model, the non-direct backfolding polymer chain model increases the excluded volume effect, which is favorable to unimer-micelle transition. However, the excluded volume effect limits the increase of micelle aggregation to a certain extent.

Under the solvothermal system，  5-(hydroxymethyl) isophthalic acid and nitrogen heterocyclic ligand 4，4′-di(1H-imidazol-1-yl)-1，1′-biphenyl(4，4′-DIB) reacted with Mn(Ⅱ) ions to obtain complex Mn[(HIPA)(4，4′-DIB)](1). Crystallographic analysis indicates that complex 1 crystallizes in the monoclinic   P2₁/c space group. In the complex 1,  HIPA^2- ligands connect dinuclear Mn₂(CO₂)₄ units to form a two-dimensional (2D)  structure，  and then the adjacent layers are further connected together by 4，4′-DIB to obtain a three-dimensional (3D) pillar-layered framework with six connected pcu net. When auxiliary ligand 4，4′-DIB is replaced by (E)-1，2-di(pyridin-4-yl)ethene (DPEE)，  another complex Mn[(HIPA)(DPEE)]·xGuest (2) is obtained in the same reaction system. Complex 2 crystallizes in monoclinic P2₁/c space group with Mn₂(CO₂)₄ units. The structure of complex 2  is a 2D structure with sql net,  Mn₂(CO₂)₄ unit is stereoscopic in complex 1，  and planar structure in complex  2.  The different configurations of Mn₂(CO₂)₄ lead to different structural characteristics of complexes 1 and 2.

Based on the helical character of Exendin-4,  we modified the N terminal α-helix and C terminal α-helix by deleting helix,  replacing the helix with 3 Alas and changing Gln13 with Tyr13， and  designed 4 structral mimetics. Combined with the bioactivity experiment of the mimetics, we analyzed the relationship between the helical structure and bioactivity of Exendin-4 by  circular dichroism analysis and fluorescent spectroscopy analysis. The results show that N terminal α-helix is more important than C terminal α-helix to promote the bioactivity of Exendin-4；  C terminal α-helix is more effective than N terminal α-helix to maitain the stability of Exendin-4 to DPPⅣ；  Tyr13 in the helical structure can be used as an important optimized site to improve the bioactivity of Exendin-4.

To solve the problem of comprehensive utilization of agricultural resources waste and pesticide pollution. The hydrothermal carbon was prepared by the hydrothermal carbonization method from cornstalks and characterized by scanning electron microscope (SEM) and Fourier transform infrared spectroscopy.The effects of  different pH values,  ionic strength,  initial concentration  and different prepared temperatures on the adsorption of Atrazine by hydrothermal carbon of cornstalks  were  studied by laboratory simulation.The results show that with the increase of temperature,  hydrothermal carbon produced carbon microsphere structure and abundant oxygen-containing functional groups. The adsorption kinetics of hydrothermal carbon on Atrazine conforms to  the quasi-second-order kinetic equation (R²≥0.970,  P≤0.001), and the adsorption thermodynamics conforms to the Langmuir  equation (R²≥0.992,  P≤0.001 ), which is  a nonlinear adsorption and  spontaneous  endothermic reaction. The maximum adsorption capacity of hydrothermal carbon is   8.862 mg/g,  and the maximum removal rate is 69.74% at 298 K. The adsorption capacity of  Atrazine by hydrothermal carbon increases with the increase of prepared temperature, but decreases with the increase of pH value and ionic strength. Therefore, the hydrothemal carbon prepared from cornstalk can effectively adsorb Atrazine in water, which has a good application prospect. The experimental results provide theoretical basis and data support for reuse of  cornstalk and water purification.