By using Leray-Schauder fixed point theorem, the author studies existence of solutions for  second-order impulsive differential equations with Dirichlet boundary value problems.

By using the Rabinowitz global bifurcation theorem, the author studies the global structure of nodal solution set of second-order Dirichlet boundary problem, where r is a positive parameter, a: ［0,1］→［0,∞) is continuous and allowed to be constant at 0 in some proper subinterval of ［0,1］. f: R→R is continuous, asymptotically linear at 0 and ∞. There are two non-zero zero points of f.

The author considered  a class of singular nonlinear Riemann-Liouville boundary value problems of fractional differential equations, by using the Leggett-Williams fixed point theorem and constructing the  corresponding auxiliary problems with the help of regularization method, it is obtained that there are at least three positive solutions to the boundary value problem, and these positive solutions are also positive solutions to the auxiliary problem.

The author considered the traveling wave solutions of the SI epidemic model under different diffusion strategies with standard incidence rates. The susceptible individuals adopted the random diffusion strategy, and the infected individuals adopted the non-local diffusion strategy. By means of the upper and lower solution method combined with Schauder’s the fixed point theorem, the existence of the traveling wave solutions of the system was proved when R₀>1, R_d>1 and c>c*. The asymptotic behavior of traveling wave solutions of the model was discussed by applying  squeeze theorem, Lyapunov functional and Lebesgue dominated convergence theorem.

The author discussed the existence of solutions for a class of Caputo fractional derivative boundary value problems with p-Laplace operators by using the fixed-point theorem and analytical techniques. Existence results of one or three non-negative solutions of the problem were obtained, and two examples were given to illustrate the correctness of the results.

By using the method that a closed fuzzy matroid could be uniquely determined from the basic sequence and the derived matroid equence, the author proposed and proved that a subset family, a sequence, and a surjection from the subset family to the sequence could uniquely determine a closed fuzzy matroid under the conditions of normality,  inheritance, strong monotonic subtraction and growth, and vice versa. The equivalent description established the relationship between the family of ordinary sets and the family of fuzzy independent sets.

Firstly, a class of entanglement-assisted quantum codes with parameters ［［n+l,k-h,d′;n-k-h+l］］ are constructed by using an orthogonal basis of the linear complementary dual (LCD) linear subcode of the classical linear code C with parameters ［n,k,d］over a finite field F_q, where h=dim(Hull_E(C)), 0≤l≤k-h, d≤d′≤d+l. In particular, when the classical linear code C is Euclidean dual-containing linear code, there are entanglement-assisted quantum codes with parameters ［［n+l,2k-n,d′;l］］, where 0≤l≤2k-n, d≤d′≤d+l. Secondly, by making a kind of transformation on the parity check matrix H of Euclidean dual-containing linear code C with parameters ［n,k,d］, another kind of entanglement-assisted quantum codes with parameters ［［n+l,2k-n+l,d′;2l］］ are constructed, in which 0≤l≤n-k, d≤d′≤d+l.

Firstly, we considered a Crank-Nicolson fitted finite volume method for solving American options under Kou’s jump-diffusion models, and gave the convergence analysis. Secondly,  an iterative algorithm for the nonlinear algebraic system was designed and its convergence was proved. Finally,  the convergence, robustness and effectiveness of the new method are verified by numerical experiments.

We considered an inverse problem of simultaneous identification of the initial field and boundary heat flux for one-dimensional heat equation with Neumann boundary conditions. Firstly, the heat flux density and temperature at the right boundary and the terminal temperature were given, a model of Fredholm integral equation was established and the uniqueness of its solution was proved. Secondly, a regularization method for  simultaneous inversion of the heat flux density at the left boundary and initial temperature field was constructed. The results of numerical examples show that the data preprocessing algorithm and improved regularization method achieve higher accuracy of double-function inversion.

By using Fubini theorem and Holder inequality, we gave a class of maximal inequalities for nonnegative demisubmartingales, and gave some related inferences by using the obtained maximal inequality.

We considered the partly interval censored data, when the time variable obeyed the generalized exponential distribution, two models were established under whether the scale parameter was affected by covariates, then the model parameters were estimated by the maximum likelihood, and Newton-Raphson algorithm was used to solve the parameter estimation. The results of simulation experiments and example analysis verified the effectiveness of the model.

Firstly, by introducing the concept of filters in m-semilattices, some properties of filters in m-semilattices were discussed, then the filter topology on m-semilattices was constructed, and a series of properties of filter spaces were obtained. Secondly, we proved that each filter space was connected, and  the filter spaces on two-sided m-semilattices satisfied the first countability axiom. The necessary and sufficient conditions for them to be T₀ spaces and satisfied the second countability axiom were given respectively. Finally, by introducing  the concept of prime filters in m-semilattices, we discussed  the dual prime spectral spaces on m-semilattices, proved that the dual prime spectral spaces on two-sided m-semilattices were T₀ space, and gave its equivalent characterization as T₁ space.

Firstly, the Cline’s formula and Jacobson’s lemma for generalized n-strong Drazin inverse were given under the conditions of acd=dbd, bdb=bac. Secondly, the equivalent characterizations of generalized n-strong Drazin inverse idempotent elements equality were given. Finally, the equivalent characterizations of generalized n-strong Drazin invertible element similarity and the problem of multi-element similarity under the condition of acd=dbd, dba=aca were discussed.

By extending the theory of Killing form and adjoint representation over Hopf algebras to the weak Hopf algebras, the author gave the concepts and properties of Killing form and adjoint representation over weak Hopf algebras, and discussed the adjoint representations and Killing form of a weak Hopf algebras H₈,  so as to realize the application of the theory of Killing form and adjoint representation over the weak Hopf algebra.

We discussed the problems of the abstract representation of local automorphisms and local derivations by using matrix theory, and gave the matrix expressions of local automorphisms and local derivations of three-dimensional nilpotent Leibniz algebras that could not be decomposed in complex field as well as the representation of local automorphisms and local derivations.

Firstly, we properly divided the row index sets of the matrix by utilizing the theory of α-diagonally dominant matrices. Secondly, by selecting the progressive coefficients to construct the positive diagonal matrix, we gave some determination conditions of generalized strictly α-diagonally dominant matrices, and then some determination criteria for nonsingular H-matrices were obtained. A numerical example shows that these determination criteria are effective.

Firstly, we gave the definitions of the action and the crossed module of pre-Lie algebras, and studied the related properties of the 
crossed module. Secondly, a result was given that the isomorphism class of crossed modules of pre-Lie algebra was equivatent to that of cat¹-pre-Lie algebras by using the definition of the crossed modules and semidirect product of pre-Lie algebras. Finally, we showed that the homomorphisms and their homotopies of crossed module formed a groupoid structure.

Aiming at the problem of wide demand of  livestock facial recognition  in the breeding industry, we  proposed a  feature point detection method of pig face based on convolutional neural network, which solved the problem that it was difficult to detect feature points of pig face. Firstly, the pig face data was collected and the feature points were marked, and a new collection method was used to solve the problem that the pig mouth was usually invisible. Secondly, we calculated the structures of the pig face data and the human face data,  matched the pig face and human face with high similarity, and constructed the pig face and human face matching data set. Thirdly,  TPS (thin plate spline) deformed convolutional neural network was trained by matching data set,  and  the deformed pig face data set was obtained to fit the  feature point detection model of human face. Finally, the  feature point detection neural network model of human face was  fine-tuned by using the deformed pig face data set, and  feature point detection model of the pig face was obtained. The experimental results show that the error rate is only 5.60% by using the proposed method to defect feature points of pig face.

We realized the Marr-Hildreth edge detection in quantum images by designing quantum circuits of Gaussian filtering and zero-crossing extraction. In this method, the Gaussian filtering was realized by quantum adders and quantum multipliers, and the zero-crossing extraction was realized by quantum comparators and  auxiliary modules. The results of  theoretical analysis show that the method can achieve exponential acceleration of the classical algorithm, and simulation results on a classical computer verify the effectiveness of the proposed method.

In order to  improve the security and  capacity of quantum steganography, we  designed a steganography scheme based on Gray code rules. The scheme took the  color images as carrier,  firstly,  the secret information was divided into 3 bit segments, and then each  segment of secret information was embedded into the least significant bit (LSB) of the RGB channel of carrier pixel based on Gray code rule to complete the information embedding process. Extracting is the inverse process of embedding, firstly,  3 bit secret information segments were extracted from the RGB channel of the carrier pixel, and then they were spliced and restored  to the original secret information. Each carrier  pixel of the scheme could  contain 3 bits of secret information, which had a high embedding capacity. The embedding rules based on Gray code effectively improved the security of the embedding scheme. The simulation results show that the proposed scheme is superior to  other similar  schemes in terms of embedding capacity and security.

Aiming at the problems that the existing video association tracking methods could  not accurately extract the association motion trajectory, which led to large deviation in the video association motion  tracking results and low tracking rate, the author proposed a video association motion tracking method based on trajectory extraction algorithm. Firstly, according to the idea of multivariate group, a multivariate group trajectory extraction model was established, the feature distribution vectorization set of moving video image was divided, and the critical value of video image segmentation support vector machine was calculated. Secondly, the pixel features were separated by the color system, and the extracted values of association motion trajectory were output by virtual scene reconstruction. Thirdly, the expected output value was set in the multi granularity filter training, and the Fourier transform was used to transform convolution calculation into point multiplication operation to calculate the minimum rectangular overlap rate of the boundary under each granularity. Finally, the minimum matrix transformation of two boundaries was obtained by Euclidean distance, the trajectory fluctuation degree of each granularity was defined, and the whole process of video association motion tracking was completed. The experimental results show that the video association motion tracking rate of the proposed method is 14.9 frame/s, which can effectively improve the target tracking rate and achieve accurate video association motion tracking.

Aiming at  the problem that the accuracy of feature point matching was low when  image changed, we proposed an improved AKAZE (accelerated-KAZE) algorithm based on perceptual Hash and epipolar constraint. The algorithm  divided feature point matching into two stages: rough matching and fine matching. In the rough matching stage,  ratio of the nearest neighbor and next nearest neighbor of feature points and the perceptual Hash algorithm were used to screen the matching pairs in  the fine matching stage,  the random sample consensus algorithm and epipolar constraint were used to further screen the matching pairs. The simulation results show that, compared with the original algorithm after the random sample consensus algorithm  eliminates the wrong matching pairs, the feature point matching accuracy is still improved by 12.9% on average, and the speed is only 2.4% slower, which can effectively improve the accuracy of matching pairs when the  image changes on the premise of  ensuring the efficiency of the algorithm.

Aiming at the problem of effective information loss and lossy quality detection caused by unclear near infrared hyperspectral feature contour of rice, we proposed a combined model of rice hyperspectral typical feature region extraction algorithm based on energy functional active contour wave under mask. The method compared and optimized the hyperspectral segment information between the morphological region and geometric centroid of target samples, and made a generalization visual discrimination for  four producing areas and three kinds of quality rice. The results of MATLAB experiment show that the recognition accuracy of morphological regions of interest is higher, and the accuracy of generalization prediction set is 94.84% by modeling and comparing the spectral information of typical characteristic regions of different quality rice.  The optimal modeling problem of typical characteristic regions of near infrared hyperspectral rice is optimized, and the rapid nondestructive[JP] quality detection of rice is realized.

Aiming at the problem that the traditional methods for solving  high-dimensional multi-objective optimization problems had the defects of convergence and distribution uniformity of solution sets. We   proposed to design a novel high-dimensional multi-objective optimization algorithm based on the combination of global sorting method and  grey association analysis. By designing the parent sequence of minimum function values and the subsequence of individual objective function values, the grey association analysis method  was used to calculate  the association degree, and  combined with  the individual objective  fitness calculation strategy, the problem of uneven distribution of solution sets was solved. The algorithm could not only improve the selection ability of non-dominant individuals, but also had good convergence. In order to test the  performance of the algorithm, we chose three classical multi-objective evolution algorithms to carry out  comparative experiments on the standard test function set DTLZ {2,4,5,6}. Experimental results show that the proposed algorithm has better convergence and uniform distribution of solution set than  the other three algorithms in  solving the high-dimensional multi-objective problems.

Aiming at the problems of  ignoring local structure, the high dependence of low rank representation tensor and affinity matrix, 
we proposed a multiple view clustering method based on graph regularization， low rank representation tensor and affinity matrix. Firstly, we proposed a unified framework to learn the graph regular low rank representation tensor and affinity matrix of multiple view subspace. Secondly, furthermore, the correlation of high-order cross views was analyzed by tensor singular value decomposition based on tensor kernel norm, and the local structure embedded in high-dimensional space was preserved by graph regularization. Finally, constrained quadratic programming was used to assign adaptive weights to each view. Experimental results on seven data sets show that the  clustering effect of the proposed method is better.

Aiming at the problems of the difficulty of identification casused by a  large number of noise interference in microseismic signals, we proposed a deep bidirectional gated recurrent unit recurrent neural network model and applied to microseismic data denoising. Firstly, we constructed a multi-layer bidirectional gated recurrent unit recurrent neural network model, and designed the network structure and training algorithm of the model. Secondly,  the validity of the model was verified by using Ricker wavelet forward modeling microseismic data, and  the proposed method was compared with the other four methods. Finally, by inputting the real microseismic data with noise into the trained model, the microseismic data without noise could be obtained. The simulation results show that the peak signal-to-noise ratio of the signal after denoising by the proposed method is about 36 dB higher than that before denoising, and the correlation coefficient value between the signals increases from 0.088 6 to 0.933 5. The practical application results also show that the proposed method can effectively reduce the noise in the actual microseismic data.

Aiming at the  problems that there were feature deviation for  the minority class in massive open online course (MOOC) reviews, we proposed a deep intelligent teaching evaluation method based on compensation for feature deviation. Firstly, this method used the Glove pre-training model to obtain the distributed word vectors of MOOC reviews. Secondly, the shallow convolutional neural networks were used to learn the semantics of teaching evaluation  through multiple convolution kernels. The number of different types of reviews was introduced to design influence  factors,  which was  normalized and applied to  the cross-entropy loss function. Finally,  the data set of undergraduate teaching reviews based on Coursera was compared with other loss functions on F₁,gmean,balance,gmeasure and other evaluation indicators. The experimental results show that the  loss function based on normalized  feature deviation compensation has  a performance improvement of up to 15.40% on gmeasure than the base loss function, and  the classification model using this loss function also shows strong stability.

Aiming at the problem that people with audio-visual disabilities could not obtain the information of mobile devices through tactile interaction, we proposed a method to encode the information on mobile devices by using vibrotactile signals with multiple perceptual intensities, which was used to distinguish the types or contents of information. Firstly, the sensing intensity of the frequency, duration and interval of the vibrotactile signal were determined by testing the sensing threshold, and the signal was adjusted to an acceptable level. Secondly, according to the difference of subjective perception intensity and the encoding combination mode, equal-length code and variable-length code were proposed  for the tactile coding transmission of information. Finally,  the recognition results of limited coding information were evaluated by information theory. Experimental results show that this method can improve the accuracy of information tactile judgment, and the variable-length code has better recognition rate and transmission efficiency than the equal-length code.

Aiming at  the influence of distance error on the location results, we proposed a location algorithm based on Gaussian mixture model  (GMM) in wireless sensor network (WSN). In this algorithm, the GMM  method was introduced into the location problem of WSN. The  distance information with large error was found by using the analysis of GMM and eliminated. The remaining distance information was solved by  trilateral measurement location method, and the position was  estimated combined with wighted location algorithm. Simulation results show  that the improved  algorithm can improve positioning accuracy and the positioning  results are  more stable.

We proposed a fast and stable numerical method to solve the two-dimensional Cahn-Hilliard equation with constant mobility. The second order finite difference method was used in spatial discretization and Crank-Nicolson method was used in time discretization. We proved theoretically that the discrete energy had the property of dissipation with time evolving. The fixed point iteration method was used to solve the nonlinear algebraic equations in the fully discrete scheme, and the fast discrete cosine transform (FDCT) was used to improve the computational efficiency. The numerical results show that the discrete free energy is non increasing with respect to time, and the method has the advantaes of good stability, small storage and fast computation speed.

Bayesian method was used to simultaneously reconstruct inhomogeneous medium and embedded sound-soft obstacle. Firstly, we parameterized inhomogeneous medium and embedded obstacles, and gave a prior information of parameters. Secondly, we used Markov chain Monte Carlo (MCMC) method and a prior information of parameters to solve a posteriori information of parameters. Finally, the feasibility and effectiveness of Bayesian method were verified by some numerical examples.

Aiming at the posture control problem of three-joint biomimetic robotic fish, firstly, the hardware structure and motion control system of three-joint biomimetic robotic fish was introduced. Secondly, the coordinate system was established based on the expected posture to construct the posture error model of robotic fish. Thirdly, on the basis of cascade proportional-integral
-differential (PID) control system, the posture control algorithm of biomimetic robotic fish based on cascade PID was proposed. Finally, the algorithm simulation experiment and the entity experiment were carried out on the URWPGSim2D simulation platform and the multi-underwater robots cooperative control system platform respectively. The experimental results show that, compared with the time-varying feedback control algorithm, the simulation robotic fish based on cascade PID algorithm takes longer to reach the target posture, but the position error and direction angle error decrease, which improves the accuracy of posture control. It takes 14.4 s for the biomimetic robot fish to reach the expected posture, and the posture error is (-3 px,-4 px,0.062 rad), which basically meets the application requirements such as tracking and handling, and verifies the effectiveness of the algorithm.

The micro-mesoporous aluminosilicate molecular sieves were prepared by mixing aluminosilicate sol precursor with polyethylene glycol (PEG) soft template under hydrothermal condition. X-ray diffraction (XRD),  Fourier transform infrared (FT-IR) spectroscopy,  N₂ adsorption desorption,  transmission electron microscopy (TEM) and NH₃-temperature programmed desorption （NH₃-TPD） were used to characterize the physicochemical properties of the micro\|mesoporous aluminosilicate molecular sieves. The obtained micro\|mesoporous aluminosilicate molecular sieves were used as catalyst for alkylation of phenol with tert butyl alcohol.  The catalytic performance of the material was tested by the conversion of phenol. The results show that polyethylene glycol as a soft template produces mesoporous structure,  and the amount of polyethylene glycol can affect the crystallinity of aluminosilicate molecular sieves. The conversion of phenol is affected when the amount of PEG is different. When the dosage of polyethylene glycol is 8 g,  the conversion of phenol is the highest,  which can reach 95.5%.

The soluble dietary fiber (SDF) was extracted from brown algae by complex enzyme extraction. Firstly, the effects of different extraction conditions on the extraction rate of brown algae SDF were studied  by single-factor experiment,  and then the  response surface analysis was carried out to determine  the optimal conditions for enzyme extraction of brown algae SDF,  and  the physicochemical properties of obtained brown algae  SDF and its antioxidant activity were determined. The results show that  the optimal extraction conditions are  m(solid)∶V（liquid）=1∶25, enzymatic hydrolysis temperature of  55 ℃, enzymatic hydrolysis time of 75 min and 2.2% enzyme addition, the maximum  extraction rate of brown algae SDF is  38.15%, and the relative deviation is 2.23%. The water holding capacity and swelling capacity  of brown algae SDF are 24.6 g/g and 53.7 mL/g respectively,  1,1-diphenyl-2-picrylhydrazyl  radical 2,2-diphenyl-1-(2,4,6-trinitrophenyl)hydrazyl（DPPH.） radical clearance rate is  75.77%, and there is no significant difference between the control group and 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid）（ABTS.） radical clearance rate when brown algae SDF mass ratio is 160 μg/g. 

The survival characteristics and main influencing factors of common Enterobacteriaceae such as Escherichia coli (Ec10538),  Salmonella enterica subsp. Enterica (sd-51) and Enterobacter cloacae subsp. Cloacae (Ec7256) in river water under freeze-thaw cycles were studied by indoor  simulation experiment method, and the mechanism of freeze-thaw cycle influencing bacterial survival was analyzed. The  results show that the three Enterobacteriaceae in river water is significantly inhibited by freeze-thaw cycles,  and the inhibitory effects gradually stronger with the increase of freeze-thaw frequency. The survival characteristics  of Enterobacteriaceae in river water under freeze-thaw cycle are  related to its tolerance to freeze-thaw stress and water quality. EC7256 is stronger  than the Ec10538 and sd-51  to freeze-thaw stress.   The  better river water quality, the stronger its tolerance  to freeze-thaw cycles. The electrical conductance (EC),  pH value and total organic carbon (TOC) of river water have significant effect on survival of Enterobacteriaceae (P<0.05). The freeze-thaw cycles lead to increase of cell surface hydrophobicity (CSH),  and reach the peak at last freeze-thaw cycles,  which is conducive to the   bacterial agglomeration and resistance to  the freeze-thaw stress. The activities of superoxide dismutase (SOD) and catalase from micrococcus lysodeikticus (CAT) increase with the increase of freeze-thaw frequency,  so as to  reduce the damage of the active oxygen generated by freeze-thaw stress to the bacteria, and then improve the tolerance of bacteria to freeze-thaw stress.