We considered an initial boundary value problem of a class of p-Kirchhoff equation with exponential nonlinearity and its 
steady state form. For the evolution equation, we adopted the potential well method. We characterized the asymptotic behaviors of the general global solutions to the problem and the depth of the potential well could be attained by using the properties of potential well and  estimates. For the steady state problem, we gave the existence of a ground state
solution by using Lagrange multiplier method.

Using the variational method, variable substitution and the Nehari manifold method, we obtained the existence of ground state solution for a class of quasilinear biharmonic equations by constructing the Nehari manifold and proving the properties of manifold when the nonlinearity term satisfied certain growth conditions.

We considered the finite time blowup of solutions to a class of parabolic type Kirchhoff equations with general nonlinearity. By using the first order differential inequality and convexity arguments, we gave some sufficient conditions for the solutions to blow
 up in finite time, and obtained the upper bound estimate of the blowup time.

We considered the first boundary value problems for a class of steadystate incompressible nonNewtonian Boussinesq equations in a threedimensional smooth bounded domain Ω. Under the conditions that the external force term was appropriately small, we proved the existence and uniqueness of regular solutions for the problem when the exponent p∈(1,2) by using the iterative method.

Firstly, based on Lax pairs of a class of differentialdifference equations, the N-fold Darboux transformation was constructed, and then we obtained the exact solutions of the equation by using  the  Darboux transformation.
 Through software drawing, we gave  the one, two, three and foursoliton solutions of the equation, and dicussed the 
elastic effect  among the three solitons and four solitons：  solitonic shapes and amplitudes do not change after  interaction.

With the help of the boundedness of commutators of Marcinkiewicz integral on Lebesgue space with variable exponents and the theory of atomic decomposition on HerzHardy space with variable exponents, the boundedness of commutator of Marcinkie
wicz integral with variable kernels μ^b_Ω on homogeneous and nohomogeneous HerzHardy space with variable exponents were given.

We considered two LotkaVolterra system with three degrees of freedom. Firstly, we introduced the generalized Poissonbracket and generalized Hamiltonian structures in threedimensional systems. Secondly,  we observed the first integral of the system by constructing local homeomorphism transformation and established the algebraic equation. The Hamiltonian function of the system was obtained by solving the algebraic equation. Finally, we gave  the sufficient conditions for the existence of BiHamiltonian structure of LotkaVolterra system.

For the onedimensional porous medium problem, wave front of the numerical solution could not propagate forward when  the standard mixed finite volume element method was used to solve them, we proposed  a new mixed finite volume element method for  solving the degradation problem, in which the  flux variable only included the derivative of the original variable  to spacial variable. The results show that the  method can avoid the phenomenon that wave front of the numerical solution can  not propagate forward, and can capture the interface of numerical solution well. The validity of the  method is verified by numerical experiments.

By using the analytical method of local fractional integrals, we gave a Hadamard type identity of generalized s-convex functions on fractal sets, and then obtained a class of Hadamard inequalities, some applications were given by combining numerical integration and several special means.

First, the author established a RiemannLiouville fractional integral identity with parameter. Then, according to the identity, some HermiteHadamard type fractional integral inequalities with parameter for harmonically quasiconvex functions involving RiemannLiouville fractional integral were established by using power mean inequality and Hlder inequality.

We discussed  the injectivity of the category of L-ordered algebras, and proved that M^≤-injective objects in the category of L-ordered algebras were exactly L-upalgebras, and  gave the concrete form of M^≤-injective hulls of a special class of L-ordered algebras in the category of L-ordered algebras.

Let {Xn, n≥1} be an m-widely orthant dependence (m-WOD) sequence with the same distribution, f_n(x) and r_n(x) were the kernel estimators of the density function f(x) and the failure rate function based on the sample X₁,X₂,…,X_n, respectively. Under some suitable assumptions, we proved the strong consistency and the uniform strong consistency of the kernel density estimator and failure rate function kernel estimator by using the moment inequality for m-WOD sequence and BorelCantelli lemma.

Firstly, based on the form of the balanced loss function, we gave a  weighted balanced entropy loss function and applied it to the Poisson distribution, and  the Bayesian estimation of the parameter under the  loss function was obtained. Secondly, under the condition that the prior distribution was Gamma distribution, we gave the explicit expression of the estimator, proved  the consistency of the estimator, and tested the asymptotic normality of the estimator by using the QQ plot method.

By using the central limit theorem and the inequalities of the tail probability for the length of the longest increasing subsequence and properties of the TracyWisdom distribution, the author gave a general result of precise asymptotics in complete moment convergence for the length of the longest increasing subsequence for more general boundary functions and quasiweight functions.

By splitting a complex square matrix A=sI-B, where s is an arbitrary complex number, I is the identity matrix and B is a complex square matrix, and by using an existing method of determination of nonsingularity for matrices, some eigenvalue inclusion sets and some methods of determination of nonsingularity for A with two parameters (s and a positive integer k) are obtained and proved to be more accurate and more general than some existing results. Numerical results show that by adjusting s and k, the eigenvalues of A  can be located  more accurate, and  the nonsingularity of A can be determined.

A smooth activation function with a parameter was constructed for the deep learning neural networks. The online correction formula for this parameter was established based on the error back propagation algorithm, which avoided the problems of gradients losing, nonsmooth and overfitting. Compared with some popular activation functions, the results show that the new activation function works well on many data sets.

First, we introduced the concept of the nondeterministic public key cryptography (PKC) and decryption success rate (DSR),
 and gave its implementation scheme NHFMS based on the difficulty of the multivariate problem over finite field
. Then， we analyzed the number of nonsingular matrices in F_q［M］ and deduced the accurate counting formula of nonsingular matrices in F_q［M］ by using Euler-φ_q function. The results show that the method can not only accurately estimate the DSR of any specific instance of NHFSM, but also deduce the the lower limit of DSR of NHFSM scheme, which theoretically proves the feasibility of NHFMS. By using NHFSM scheme, the session key can be agreed, thus secure communication can be realized.

Based on the metaheuristic algorithm： crow search algorithm (CrSA), we proposed an improved feature selection based on crow search algorithm (IFSCrSA) to solve the shortcomings of the current feature selection problem. Compared with traditional machine learning feature selection algorithms and feature selection algorithm based on evolutionary computing. The results show that IFSCrSA can select features with strong recognition in the data set, which not only greatly reduces the size of the feature subset, but also improves the classification accuracy.

Aiming at the problem that the traditional discontinuous edge detection algorithm was used to detect the edge contrast of the enhanced image, but it was only suitable for detecting the edge of the image with no strong change of gray value and ordinary noise, and the detection performance had the limitation, we proposed an improved algorithm for intelligent detection of discontinuous edges of blurred images. Firstly, the estimation of the noise variance of the image was obtained by the gene
ralized cross validation criterion to discriminate the Gauss noise in the image, and the adaptive fuzzy filter was used to make fuzzy filtering of the noisy image. Secondly, the improved image edge detection algorithm of blurred image was used to acquire the edge of the blurred image by formulating the image edge detection strategy according to the situation of image noise. Finally, the discontinuous edge detection algorithm of blurred image of gray morphology was used to detect the expansion, corrosion and morphologic gradient discontinuous edges of the blurred image edge caused by the uneven change of gray value. The experimental results show that the proposed algorithm has high noise immunity, and the results of discontinuous edge detection of the blurred image are clearer and more complete.

Aiming at the problem that the traditional image denoising algorithm had poor denoising effect and stability, we proposed an image denoising algorithm based on partial differential equation combined with multiscale analysis method. Firstly, the high frequency and low frequency bands of the image were processed by the second order partial differential diffusion equation and the fourth order partial differential equation, and the processed image was denoised as a whole by using the inverse transform of nondown sampling profile wave. Secondly, the contour wave transform method was used to decompose the whole image into different subbands,  the kernel principal component analysis algorithm was used to reduce the dimension of the whole image, and the different subbands were managed by blocks to complete the local denoising of the whole image. Finally, the image denoising based on partial differential equation and multiscale analysis method was realized. The experimental results show that the proposed algorithm has high image denoising effect and stability.

An improved phase unwrapping algorithm was proposed to sovle the problem of phase jumping and timeconsuming in phase unwrapping of complex wrapping phase image. Firstly, the wrapped phase image was obtained by fourstep phase shift method, and the quality map was generated from the wrapped phase image. Secondly, the quality map was divided into high quality area and low quality area, the high quality area was unwrapped by simple path algorithm, and the low quality area was constructed the horizontal and vertical weighted edges by the quality values of two adjacent pixels. Finally, phase unwrapping was performed according to the constructed edge weights from small to large. The unwrapping process took the edges of two pixel points as unit. Discontinuous unwrapping paths were used to unwrap all the pixels one by one. The experimental results show that compared with other algorithms, the proposed algorithm has faster unwrapping speed and better effect of unwrapping.

In order to overcome the shortcomings of current image segmentation algorithms, such as large segmentation error and long segmentation time and inability to segment online image, we proposed an image segmentation algorithm based on combination of clustering analysis and active contour model. Firstly, the original image was denoised and roughly segmented by clustering analysis algorithm. The roughly segmented result was taken as the initial contour line of the active contour model. Secondly, the active contour model was used to fit the contour of different regions of the image according to the initial contour line to realize the fine segmentation of the image. Finally, it was compared with clustering analysis algorithm, active contour model and the current classical image segmentation algorithm. The experimental results show that the proposed algorithm overcomes the shortcomings of the current image segmentation algorithm, improves the efficiency and accuracy of image segmentation, it is insensitive to noise and has strong robustness. The overall image segmentation effect is significantly better than that of the contrast algorithm.

Aiming at the problem that the traditional communication node selection algorithm could not accurately perform the optimal node selection, and could not effectively guarantee the effective communication of the Internet of Things, we proposed an optimal communication node selection algorithm for intrusion of Internet of Things based on node information redundancy. Firstly, the transfer characteristics model of communication node was constructed, and the frequency hopping node and noise node under network intrusion were calculated. Secondly, the communication distribution sequence analysis model was designed to calculate the node information redundancy and the extremum of the communication node. According to the node information redundancy calculation results, the interference nodes were eliminated and the optimal communication node was selected according to the extremum. Finally, the simulation experiment of the optimal communication node selection algorithm was carried out. The experimental results show that the proposed algorithm can quickly and accurately select the optimal node under the intrusion of Internet of Things,  has strong antijamming ability, and the comprehensive performance of the algorithm is better than other optimal communication node selection algorithms.

Aiming at the problem that the image contaminated by high intensity salt and pepper noise, the author proposed a nonlocal switchable denoising algorithm. First, the noisy image was cut into several local blocks as the basic processing unit of the algorithm, and the prerepairing process of the blocks was designed to avoid the interference of the local blocks caused by the high noise pollution and ensure the similarity measure and the accuracy of the model estimation process. Then, a nonlocal filter was constructed in the nonlocal range, the author measured the similarity and calculated the repair weights to restore the noise, and obtained the omnidirectional image denoising effect. The experimental results show that compared with the traditional method of constructing filter based on local information, the proposed algorithm improves the performance and image measurement index of both lowpollution and highpollution images.

Aiming at the problem of inaccuracy of attack path prediction caused by incomplete node analysis in traditional attack graph, we proposed a prediction method of attack path based on attack graph attack behavior analysis. First, the traditional attack graph was optimized by the node attack distance weight, the possible attack path was decided, and the node attack behavior cost of the path was calculated. Then, the priority attack path was determined based on the estimation function. The experimental results show that the method can effectively eliminate the path redundancy of the attack graph and filter out reliable attack path, which improves the accuracy of the attack graph attack path prediction.

We constructed a psychological assessment model based on text emotional characteristics. Firstly, acording to the emotional polarity and part of speech of words, word features were designed, and each word in the text was mapped into an emotional word vector, which was then used as the input of convolutional neural network. Attention mechanism was added to optimize the output results, the text vector representation containing emotional features was obtained. Secondly, the Bayesian regularization algorithm was used to optimize the weights, control and balance the fitting degree of the neural network, and improve the generalization ability of the BP neural network algorithm. Finally, the text vector was used as the input of Bayesian regularization neural network to predict the students’ psychological state. Compared with the results of psychological assessment, the experimental results show that the effect of the model is ideal.

Three spin polarized currents with the direction of (-1,1-1) were passed through the nanometer disk. The effects of the magnitude and position of the spin polarized currents on the dynamical behavior of magnetic vortex were analyzed by OOMMF 
(object oriented micromagnetic framework） software. The results show that the  position of the maximum velocity on the trajectory is relatively fixed when the magnetic vortex core experiences gyrotropic motion. According to this property, we can import defect at the position of the maximum velocity, moving to which the magnetic vortex core can be pinned and 
inverted, thus realizing the controllable polarity switching of the magnetic vortex core. The frequency of the gyrotropic motion of the magnetic vortex core can be adjusted by changing the magnitude and position of the spin polarized currents. The chirality switching of the magnetic vortex at the region of high current density, and the inversion time is shorter. Compared with the symmetrical position of polarized currents, the current range of chirality switching is enlarged and the time to the transient state is shortened with the asymmetrical current position.

By using the fractionalorder finitetime stability theory, and constructing a proper fractionalorder slidingmode hyper surface, a fractionalorder controller with finitetime control was designed to realize the slidingmode synchronization control of generalized driveresponse Sprott-C systems. Combined with adaptive control strategy, the unknown parameters and the upper bounds of disturbance were accurately estimated by using parameter update laws. The correctness and validity of the results were verified by MATLAB numerical simulation with appropriate control and system parameters.

Monte Carlo program was used to simulate the output spectrum of a welltype antiCompton spectrometer with the main probe wrapped with NaI(Tl) crystal. We gave the antiCompton suppression spectrum and Compton electron spectrum by adjusting the parameters of the FU card to screen the pulse height of the external detector. The usage method of FU card
 of MCNP in anticoincidence measurement was verified, and the effect of the thickness of external detector on antiCompton spectrum was analyzed.

The charge transfer between molecular fragments was calculated based on components of molecular orbit (MO) and natural transition orbit (NTO), we first optimized the geometric configuration of threonine (Thr) molecule at 6-31G(d) basis set under implicit solvent H₂O by using the CAMB3LYP method of density functional theory. Then, we calculated the electron excitation of time dependent density functional theory (TDDFT) under the same theoretical method, and gave the results of comparing the charge transfer characteristics between fragments during the electron excitation of Thr molecular system under implicit solvent H₂O. The results show that in the S1—S5 excited state, only a pair of MO32→MO33 transition orbits are dominant in the S2, and the charge transfer can be discussed by analyzing the orbital components of the orbit, 
charge transfer of other excited states can be discussed by NTO analysis method. The main contribution of charge transfer from S0 to excited states S1,S3 and S4 is NTO32→NTO33 orbit, which is consistent with the qualitative results of 
Hirshfeld and Becke methods, and the quantitative results are slightly different.

Using the method of density functional B3LYP, we optimized the ground state stable configuration of gas phase lysine (Lys) molecules and Lys^2- at the level of the 6-311+G(2df) basis set. The method of time dependent density functiona
l theory (TD-DFT) was used to investigate the characteristics of single excited state of gas phase Lys molecule and chargedion system. The results show that the energy of the system increases when the Lys molecular system captures dual electrons, the energy difference between the S1 and S0 decreases, the fluorescence wavelength of the molecular system increases, and the number of electron transition orbits of the S7 single excited state decreases.

Using the dispersion correction density functional WB97XD method, the MP2 method of perturbation theory and the SMD model method of selfconsistent reaction field, we studied the chiral enantiomer transition of two aspartic acid (Asp) molecule in dominant reaction channels, the catalysis and the solvent effect of water molecules.  The results show that the chiral enantiomer transition is realized by a series of Asp transition states of the rotation of αcarboxyhydroxyl, βcarboxyhydroxyl,  βcarboxyl and Rgroup and proton transport from αcarbon to amino nitrogen, from amino nitrogen to αcarbon and in carboxyl groups, and several kinds of optical isomerism products with different configurations are obtained. The intrinsic energy barriers of Asp molecules with two strong single hydrogen bonds and two moderate strength single hydrogen bonds in the dominant channel are 2585, 2538 kJ/mol, respectively, which are derived from the transition states of transfer of αhydrogen to aminonitrogen, and that are reduced to 133.3, 134.3 kJ/mol by the catalysis of two water clusters, and to 106.3,  107.8 kJ/mol in water solvent environment, respectively. 
Therefore, the chiral enantiomer transition of Asp molecules can be realized slowly by the catalysis of water molecular clusters, and the reaction rate can be accelerated by the water solvent effect.

A new complex (Ph3Sn)(L)·C₁₂H₆O₃ (complex 1) was prepared with triphenyltin hydroxide as substrate and amide acid as ligand. Its composition and structure were characterized by elemental analysis, Xray single crystal diffraction, infrared spectroscopy and nuclear magnetic resonance, and the antitumor activity of the complex was tested by MTT assay. The experimental results show that the crystal structure of complex 1 belongs to monoclinic syngony and P21/c space group. The cell parameters are as follows: a=2238 50(17) nm, b=1202 30(14) nm, c =1441 0(3) nm, α=90000(0)°, β=101217(2)°, γ=90.000(0)°, V=3804 1(9) nm3, Z=4, Dc=
1.509 g/cm3. The complexl  is a monomer structure. The central Sn atom coordinates with O atom in the ligand  carboxyl group to form a distorted tetrahedral geometric coordination configuration with coordination number 4. In the crystal structure of complex 1, there is π…π interaction betwwen ligand and free anhydride naphthalene molecule. The complex 1 has strong inhibitory effect on cancer cells MCF-7 and Hepg2.

Hybrid particlefield molecular dynamics simulation method was used to simulate the selfassembly of block copolymer in bulk with large system (about 56 nm) and long time (100 μs) in order to avoid the finite size effect of the small system. The selfassembled structure of  diblock copolymer and triblock copolymer in bulk has been obtained by adjusting the number of blocks, the block ratio, and the interaction parameters between different blocks. The results show that the simulation results are consistent with the results of the selfconsistent field theory (SCFT), the Monte Carlo method (MC), and the dissipative particle dynamics method (DPD).

The silica microspheres were used as carriers to absorb and reduce silver ions automatically on the surface of microspheres, and a new type of composite material of silica@silver nanoparticle microspheres (SiO₂@Ag NPs) was obtained. The silver nanoparticles were characterized by transmission electron microscopy (TEM), Raman spectroscopy and Xray photoelectron s
pectroscopy (XPS), and the bacteriostasis of Escherichia coli was tested. The results show that the antibacterial rate of the composite is 99.8% when the mass concentration of SiO2@Ag NPs is 2.0 mg/mL, and the antibacterial rate decreases when the surface of silver nanoparticles contains stabilizer (polyvinyl pyrrolidone). Therefore, the stabilizer can protect the monodispersity of silver nanoparticles, but it is not conducive to its bacteriostatic effect.

We constructed a T7 phage display of antigenic variability gene fragment library of bird flu virus. Firstly, we searched and scree
ned the antigenic variability gene of bird flu virus from Gene Bank, truncated, modified and degenerated the gene to obtain the microarray of antigenic variability gene of bird flu virus. Secondly, the recombinant phages DNA were constructed by amplifying and digesting the synthesized antigenic variability gene frament library of bird flu virus and linking it to the T7 phage vector gene. Finally,  T7 phage display library was obtained by packaging and amplification of the recombinant phage DNA in vitro. The titer, recombination rate and immune activity of T7 phase display library were determined. The experimental results show that a total of 96 258 sequences are obtained by searching, screening, cutting and modifying gene bank. T7 phage display library is constructed with original library titer of 3.6×107 colonies/mL. The recombination rate is more than 90%. The bird flu virus H5N1 antibody is used for capture and the ideal target band is obtained and identified by polymerase chain reaction (PCR). The display proteins on the surface of phages have antigenic activities, and can be used for rapid d
etection of bird flu virus infection patients and screening of antigenic epitopes of antibodies.