Using the method of upper and lower solutions, we discuss the existence and uniqueness of positive radial solutions for elliptic boundary value problems with gradient term:When the coefficient function K(r)=O(1/r^2(N-1))(r→+∞), under the condition that the nonlinear term f(r,u,η） satisfies some appropriate inequality conditions and Nagumo condition on η, we prove the existence and uniqueness of the positive radial solution of the problem.

By using the theory of fixed-point index, we considered a class of  integral boundary value problems of fractional differential equations under the conditions related to the first eigenvalue of the corresponding linear operator. We obtained the result that there
 was at least one positive solution for the integral boundary value problem, and gave an example to illustrate the applicability of the theorem.

We consider a class of singularly perturbed quasilinear differential equation with Robin boundary value conditions and discontinuous right-hand side. Firstly, under the given conditions, the asymptotic expression of a smooth solution with an internal layer in the neighborhood of the discontinuous curve is constructed. Secondly, based on the matching technique, the existence of such solution is proved, and the remainder estimation is given. Finally, the effectiveness of the method is verified by a numerical example.

The selection mechanism (linear or nonlinear) of the minimum wave speed of traveling wave solutions for three species competition system was studied by using monotone iteration method combined with upper-lower solution method. We gave the sufficient conditions for linear selection of speed and some new results for the nonlinear selection of the minimum wave speed. The results expanded the parameter ranges of linear selection.

By introducing two real function classes Σ and Γ on ［1,∞)³, the author gave the existence theorems of unique fixed points for mappings with σ(γ)-contractive conditions on multiplicative metric spaces, and gave Banach type fixed point theorem, Kannan type fixed point theorem, Chatterjea type fixed point theorem and Ciric type fixed point theorem and their generalized fixed point theorems on multiplicative metric spaces.

Let U=Tri(A,M,B) be a 2-torsion free triangular algebra, and  {φ_n}_n∈N be a sequence of linear mappings from U to itself. By using the method of algebraic decomposition, we prove that  the specific form of higher ξ-Lie derivable maps on nest algebras by Jordan zero products is obtained.

Firstly, by using the time reparameterization method, we established and proved the Noether’s symmetry theorems of Hamilton s
ystem on time scales in event space. Secondly, through Hamilton principle on time scales in event space, we derived Hamilton canonical equations of the time scale, and then gave the Noether’s conserved quantity of the Hamilton system on time scales in event space. The results revealed the inherent relation between the symmetry of the system and the conserved quantity.

We discussed the rigidity of almost Ricci solitons by calculating the X-Laplacian for the module square of the trace-free curvature tensor. Under the assumption that the scalar curvature was nonnegative, we proved that a complete almost Ricci solitons were isometric to a finite quotient of Rⁿ or Sⁿ under a pointwise pinching condition. For a compact almost Ricci soliton, we gave an integral inequality and proved that the equal sign held if and only if the soliton was isometric to a finite quotient of Sⁿ under the assumption that the scalar curvature was positive.

We solved the problems of the optimal vertex-distinguishing Ⅰ-total colorings (VDITC) and the optimal vertex-distinguishing Ⅵ-total colorings (VDVITC) of graph mC₁₅ by constructing a matrix with color sets and empty set as its elements, and using the methods of distributing color sets in advance and describing coloring explicitly, and obtained vertex-distinguishing Ⅰ-total chromatic numbers and the vertex-distinguishing Ⅵ-total chromatic numbers of graph mC₁₅. The results  show that the VDITC conjecture and VDVITC conjecture are valid for graph mC₁₅.

Firstly, the definition of the representation of 3-Lie 2-algebras was given. Secondly, the definition of 2-cocycle of 3-Lie 2-algebras was given by using the representation. Finally, the necessary and sufficient conditions of 1-parameter infinitesimal deformations of 3-Lie 2-algebras were given.

Firstly, we used the linear transformation of real Clifford algebras to construct the faithful real matrix representations of unit groups of real Clifford algebras Cl*_0,3,Cl*_2,1,Cl*_3,0, and found that they were the subgroups of 8 order real matrix groups. Secondly, we constructed the faithful real matrix representations of real Clifford algebras Cl_2,1 and Cl_3,0 by the relations of basis elements of real Clifford algebras Cl_p,q(p+q=3) and their corresponding matrix relations, we found that they were the subalgebras of 4 order real matrix algebras, and gave their unfaithful real matrix representations.

Let S=S(a₁,a₂,…,a_t,b₁,b₂,…,b_s) be a star-like tree, where a_i is odd, b_j is even for 1≤i≤t, 1≤j≤s. Firstly, under different values of t and s, we discuss whether the product graph SP of a star-like tree S and a path P_l is arbitrarily partitionable graph. We give some sufficient conditions for S such that SP is not arbitrarily partitionable graph by contradiction and the method of graphs without perfect matching. Secondly, by analyzing the Hamiltonian property of graphs SP_l and using arbitrary partition of star-like trees, we give some sufficient conditions for S such that SP is arbitrarily partitionable graph. The results show that if t=1 and s≤2, then SP_l is arbitrarily partitionable graph; if t≥2 or t=0, or t=1, s≥3, b₁=b₂=…=b_s, t+s≥l+2, then SP_l is not arbitrarily partitionable graph.

Using the  different  research methods than the probability space, under the condition that the Choquet integrals existed, we studied the almost sure convergence of weighted sums for extended negatively dependent（END）random variable sequences in the sub-linear expectation spaces, and obtained the almost sure convergence theorem, which extended the theorem from the traditional probability space to the sub-linear expectation spaces.

We investigated the existence of solutions for tensor variational inequality problems by using convex analysis. Firstly, we gave a necessary condition for the solution set of tensor variational inequality problems to be empty. Secondly, when the tensor was  positive definite on the asymptotic cone of the set, we proved that the solution set of the tensor variational inequality problems was nonempty and compact, and gave several coercivity conditions  for the solution set of tensor variational inequality problems to be nonempty and compact, and gave a necessary condition for the solution set of tensor variational inequality problems to be nonempty and compact.

The number of entangled bits was determined by a decomposition of defining sets of constacyclic codes over finite fields F_^q2. Two classes of the entanglement-assisted quantum maximum distance separable codes (entanglement-assisted quantum MDS codes for brevity) were constructed by using constacyclic codes.

We first used Galerkin approximation and potential well method to prove the global existence of the solution for a class of fourth order hyperbolic equations with superlinear source terms at small initial values, and then we proved the solution blew up at finite time by using Levine convex method when the initial energy was negative.

We considered the periodic problem of a class of nonlinear iterative differential equation in the sense of Caputo type fractional derivative. Under one sided-Lipschtiz conditions on nonlinear term, the existence and uniqueness of solution for the nonlinear fractional iterative differential equations is proved by applying the Leray-Schauder fixed point theorem and topological degree theory.

Based on the fixed point index theorem of cone, by constructing a proper cone, we discuss the existence and multiplicity of positive solutions for Robin problem of one-dimensional prescribed mean curvature equation in Minkowski space and obtain relationship between the number of the zeros of the nonlinear term f and the number of positive solutions of the Robin problems, where λ is a positive parameter, a∈C［0,1］, f∈C(［0,∞),［0,∞)) and there exist two sequences of positive numbers a_i and b_i with f(a_i)=0, f(b_i)=0 and f(s)>0 in s∈(a_i,b_i), and a_i<b_i≤a_i+1<b_i+1 for i=1,2,…,n.

We proved the approximate controllability of a class of one-dimensional semilinear degenerate parabolic equations with boundary control functions by using the Kakutani fixed point theorem. The boundary condition of the problem at the degenerate point x=0 to be controlled is the second boundary condition in the sense of limit, and the boundary condition is the homogeneous Dirichlet condition at the non degenerate point x=1.

In order to meet the requirements of positioning accuracy and real-time in robot servo grasping, we proposed a fast algorithm of feature matching and target location based on Harris and improved local binary pattern (LBP). Firstly, Harris detection algorithm was adopted to extract the image feature points. Secondly, we proposed a new definition method of feature point descriptor. The Hu momen was used to determine the  feature directions, and then the local images were standardized according to the feature directions, and the LBP features of the standardized local image were extracted as the feature point descriptors. Finally, The features matching were realized by calculating the Hamming distance between the descriptors of each feature point in the two images, and then according to the matching results, the homography matrix was estimated to locate the position of target in the scene image. Experimental results show that the algorithm has fast matching speed and high positioning accuracy.

Aiming at the problems  of mode collapse in the application of single texture expansion model to multiple texture expansion, and the user could not control the output texture mode and style, we proposed a novel network  for controllable multi-texture extended synthesis  and transfer. Firstly, by adding  classification training in the discrimination  training of generative adversarial network (GAN),  the discriminator could distinguish the generated data from the real data, and could further correctly identify the input texture came from which training image, so as to improve the problem of  mode collapse. Secondly, in order to achieve the user’s control of texture mode in texture transfer, we modified the generator to a two-stream data input, in which one stream provided structure-guiding features, and the other one provided texture mode features. The final texture image was generated by decoding after  fusing  the two features. The experimental results show   that the proposed model can not only correctly  learn the  texture modes of multi-texture images with one network,  but also has better and  controllable texture transfer function.

Aiming at the problem that the  current convolution kernel initialization method was easy to lead to network instability and the limitation of principal component analysis algorithm on network structure, we proposed a convolution kernel initialization method based on image features. Firstly, the method combined fuzzy processing technology and edge processing technology to sample images, and then the sampled data were randomly divided into groups. Principal component analysis algorithm was used to extract the principal components of each group of data, and the convolution kernel was initialized. We applied the method to Cifar-10 and Corel-1000 datasets, and compared it with Gaussian initialization method and He initialization method. The experimental results show that the performance of the method is superior to other convolution kernel initialization methods.

In order to better preserve the rich details of the visible image, we proposed a dynamic image compression enhancement method based on directional guided wave to fuse visible image and infrared image. Firstly, the directional guided wave enhancement method was used to enhance the visible image. Secondly, a low-frequency subband and a series of high-frequency subbands were obtained by decomposing the enhanced visible image and the corresponding infrared image with the nonsubsampled contourlet. A sparse representation theory was used to fuse the low-frequency subband. The parametric adaptive impulse coupled neural network was used to fuse each high-frequency subband. Finally, the fused image was obtained by the inverse transform of nonsubsampled contourlet. The experimental results show that the proposed method is superior to the traditional methods in objective quality evaluation and visual inspection.

Aiming at solving  problems of  high parameter dimension, complex calculation and the fitness depended on  other tools with GA, we proposed an aggregation operator to accelerate the convergence of genetic algorithm. Firstly, the affinity propagation (AP) clustering was used to divide the population into sub-clusters, and then the dimension of each cluster was reduced by principal component analysis (PCA). Secondly, the population distribution was fitted to quadric surfaces by weighted least square method in lower dimensional space. Finally, the calculated extreme points were returned to the original space as the dominant individuals. The experimental results show that compared with the traditional genetic algorithm, aggregation operator can effectively improve the convergence speed and ensure the optimization accuracy.

Aiming at the problem that the current multiple object tracking algorithm had poor tracking effect in the face of frequent target occlusion, using Mask R-CNN as a detector, according to the detection results, the Kalman filter was used to predict the position of the tracking target in the next frame image and the improved Hungarian algorithm was used for data association, and the trajectory correction scheme was used to deal with the problem of trajectory interruption. The algorithm was experimented on each test set of MOT16 dataset, the experimental results show that the tracking accuracy of the algorithm is 55.1%, and the effect of target occlusion is better.

Aiming at the parameter optimization problem of deep learning network in the process of network traffic prediction modeling, in order to improve the network traffic prediction results, we proposed a network traffic prediction model based on improved gray wolf algorithm to optimize the deep learning network. Firstly, the historical data of network traffic was collected and preprocessed by phase space reconstruction and normalization. Secondly, gray wolf algorithm was introduced to quickly search the relevant parameters of the global optimal deep learning network, the preprocessed historical data of network traffic was learned according to the optimal parameters, and a prediction model that could mine the change law of historical data of network traffic was established. Finally, the network traffic prediction model of deep learning network optimized by other algorithms was compared and analyzed. The experimental results show that the network traffic prediction accuracy based on improved gray wolf algorithm to optimize deep learning network is more than 90%, which is much higher than other comparison models, and the modeling time of prediction modeling process is less than that of comparison model, which can meet the requirements of high accuracy and real-time of network traffic management.

Aiming at the problem of single feature evaluation criteria in feature selection process, we proposed a new feature selection algorithm based on the extreme gradient boosting algorithm in ensemble learning. Firstly, the metrics of building ensemble tree model in the extreme gradient boosting algorithm were used as the importance measures of features in feature selection, and then a new bidirectional search strategy was used to balance the influence of multiple feature importance on the results, and optimize the efficiency of evaluation process. Through the test of 11 different dimensions of standard datasets, the experimental results show that the algorithm can increase the diversity of feature subsets, accelerate the speed of feature selection, and has high computational efficiency on both medium and low dimensional datasets, and can deal with high-dimensional datasets.

Aiming at the problem that FBCM (FUP (fast update algorithm) based on matrix compression) algorithm frequently scanned the original frequent itemset library and generated a large number of candidate sets in the process of item set mining. We proposed a method to extract the most frequent items from the database to reduce the scanning times on the original frequent itemset library, and through a candidate set pruning idea, it reduced the generation of candidate sets in the whole running process of the algorithm, so as to improve the speed of frequent itemset mining. Experimental results show that the efficiency of the algorithm is 15% higher than that of FBCM algorithm, and the highest is 60% under the same experimental conditions.

Aiming at the problem that traditional time relationships were only applied in the direction of machine learning, we proposed a relationship extraction method based on sequence labeling entity recognition. We first constructed Bi-LSTM model for feature extraction, and then input time relationship as a characteristic matrix for graph convolution. The experimental results show that the time relationship can improve the effect of causality extraction, and the Bi-LSTM+GCN model containing time relationship can effectively extract causal events, and the results of causality extraction of the Bi-LSTM+GCN model with time relationship are better than those of traditional methods.

Based on tendency analysis of time series data, the author proposed a method of insulation abnormality detection  based on tendency analysis for power equipment  to solve the problem of real-time detection of abnormal capacitive power equipment in the substation. Firstly, the data of dielectric loss factor obtained from on-line monitoring was used to divide the monitoring data stream reasonably, and the method of least square was used to fit it into a straight line. Secondly, based on the characteristic value of fitting line, the abnormal tendency was detected and analyzed. Finally, the insulation abnormality detection results of capacitive equipment were obtained. According to the analysis and judgement of the measured data of capacitive equipement in the substation, the effectiveness and practicability of the method were verified.

Based on the Melnikov method for non-smooth systems, we studied the chaotic motion of a shape memory alloy beam with bilateral constraints under harmonic excitation, and obtained the  necessary conditions for the occurrence of Smale horseshoe chaos. The phase diagram, Poincaré section diagram and maximum Lyapunov exponent of the system were studied by numerical simulation. The results show that the numerical simulation results are consistent with the analytical results under Melnikov criterion. When parameters take specific values, the larger impact recovery coefficient can suppress chaos, and the larger harmonic excitation amplitude can promote the generation of chaos.

By designing logarithmic type sliding mode surface, the self-adaptive sliding mode synchronization of uncertain fractional-order Rucklidge chaotic system was studied. Two sufficient conditions for self-adaptive sliding mode synchronization of uncertain fractional-order and integer-order Rucklidge chaotic systems were obtained.

The effects of different linear functional forms of dielectric column dielectric constant of two-dimensional functional photonic crystals on transverse electric (TE) wave and transverse magnetic (TM) wave band structures were studied by using plane wave expansion method. The results of numerical calculation show that the band gaps of two-dimensional functional photonic crystals are wider than that of two-dimensional conventional photonic crystals. By changing the different functional forms of dielectric column dielectric constant, the number, position and width of band gaps of the two-dimensional functional photonic crystals can be changed, so as to adjust the band gap of two-dimensional functional photonic crystals.

Based on the first-principles calculation method of density functional theory, we studied the adsorption, migration and storage of alkali metal sodium atoms on two-dimensional carbon materials—M-graphene. The calculation results show that the best adsorption site of sodium atom is the center of seven-rings in M-graphene, which has the characteristics of low migration potential barrier, large storage capacity and low average open-circuit voltage. Therefore， M-graphene can be used as an anode material for Na-ion batteries.

Using methylmercaptotetrazole and mercaptopyrimidine as sulfur sources,  two pure inorganic hydroxysulfate frameworks were obtained through in situ reaction under the solvo-thermal conditions： [Cu₃(SO₄)(OH)₄]_n(1) and [K₂Co₃(OH)₂(SO₄)₃(H₂O)₂]_n (2). In compound 1,  the puckered cationic —Cu₃(OH)₄— chain with one-dimensional ribbon was connected by sulfate to form a three-dimensional copper hydroxysulfate framework.  In compound 2,  the one-dimensional puckered cationic Co₃(OH)₂ chain was joined by sulfate to form a two-dimensional anionic cobalt hydroxysulfate layer,  which was further connected by K⁺ to form a three-dimensional pure inorganic framework with bimetallic centers. There was  K⁺ transport channels in the 3D structure. The experimental results show that organic sulfur as sulfur sources provides a new strategy for the synthesis of hydroxyl sulfate.

Using sodium cetyl m-xylene sulfonate as the surfactant and benzene,  naphthalene,  phenanthrene,  and pyrene as the aromatic hydrocarbon phases,  we used all-atom molecular dynamics simulation methods to study the effect of aromatic hydrocarbon phase changes on the properties of aromatic hydrocarbon/water interface, and analyzed interfacial thickness,  interfacial formation energy (IFE),  interfacial tension,  the radial distribution function and coordination number between surfactant molecules and aromatic hydrocarbon molecules,  and the diffusion coefficient of aromatic hydrocarbon phase and water phase. The results show that when the aromatic hydrocarbon phase is phenanthrene,  the interfacial thickness,  the interfacial formation energy  and the coordination number are the largest,  the interfacial tension and the diffusion coefficient between the aromatic hydrocarbon phase and the water phase are the smallest,  which has better solubilization and compatibility,  but the elution rate is the slowest.

The electrochemical detection method based on graphene oxide quantum dots/multi walled carbon nanotubes/screen printed electrode (GOQDs/MWCNTs/SPCE*) was used to simultaneously detect thymine and cytosine in BALB/c 3T3 cells. The effects of enrichment potential, enrichment time and pH values on the electrochemical behavior of thymine and cytosine were investigated. The experimental results show that   the optimal detection conditions are as follows：  enrichment potential  is 0, enrichment time is 150 s, pH=7.4.  The detection limits of  thymine and cytosine are 0.69,0.95 μmol/L, respectively. The electrochemical detection method can be used to  detect thymine and cytosine in BALB/c 3T3 cells simultaneously.

We established a method based on liquid  chromatography-high resolution tandem mass spectrometry (LC-HRMS/MS) to detect A1 and A2 β-casein in milk. Caseins were extracted from milk by isoelectric point precipitation method,  after trypsin hydrolysis,  the hydrolysates were analyzed by LC-HRMS/MS method. The peptide containing varied amino acid moiety at the 67th position was selected as characteristic species to  distinguish A1 and A2 β-casein. Casein was fully dissolved in Tris-HCl buffer solution. The  acetonitrile was added to the enzymatic hydrolysis system to improve the enzymtic hydrolysis efficiency.  High resolution mass spectrometry and tandem mass spectrometry were used to eliminate the interference signal of impurity. Four kinds of common milk  and two kinds of  A2 milk  were tested by this method. The results show that the content of A1 β-casein is about 2—4 times that of  A2 β-casein in common milk,  while a small amount of  A2 milk samples contain trace A1 β-casein. This method can detect A1 and A2 β-casein in milk with advantages of high reliability and sensitivity,  which provides support for A2 milk source screening and quality control.

Taking Caenorhabditis elegans (C.elegans)  as a model, we studied the effect of mint extracts on the stress resistance, and further studied the mechanism of mint extract against ultraviolet (UV) irradiation. The results show that  mint extracts can significantly increase the resistance of C.elegans to  UV-irradiation，P.Aeruginosa infection， 35 ℃ heat shock，  and juglone oxidation. The mint extracts can significantly reduce the level of reactive oxygen species (ROS)  and increase activity of superoxide dismutase (SOD) in C.elegans   after UV-irradiation. It can also play a role  through insulin/IGF-1-like signaling pathway, increase the mRNA expression  levels of the sod-3，hsp-12.6，hsp-16.1， and hsp-16.49  of the downstream transcription factor of the pathway, and increase the number of nuclear localization of transcription factor daf-16. The mint extracts can increase the motility and swallowing ability of C.elegans, but do not affect their lifespan and fertility.

A new type  of TiO_2-graphene oxide (TiO₂-GO) composite was prepared by  one-pot ultrasonic reflux method，and its structure was characterized by X-ray diffraction (XRD)， infrared spectrum (IR) and Raman spectrum, and  the removal effect of the material as an adsorbent on phenol wastewater was studied at different pH values， adsorption temperature， adsorption time and initial mass concentration of the solution. The experimental results show that when the mass concentration of  phenol solution is 400 mg/L， the adsorption capacity of phenol is 80 mg/g at room temperature with  pH=5. The adsorption process is  in accordance with the Langmuir model， and the kinetic experimental data are in accordance with the quasi-second\|order kinetic curves.  TiO₂-GO  can effectively purify phenol wastewater within 30 min， which has a certain  application prospect.