We studied the existence and multiplicity of solutions for a class of boundary value problems of nonlinear fractional differential equ
ations with p-Laplacian operator by using the properties of Green’s function and fixedpoint theorems on cone.

We considered the existence of positive solutions for a class of boundary value problems of fractional differential equations on infinite intervals, and  proved that there was at least one positive solution and unique positive solution for the boundary value problem by using the fixed point theorem of cone compression and cone expansion and the compressed image principle.

We gave the pullback Dasymptotic compactness for the weakly damped suspension bridge equations with linear memory by using the method of contraction function, and then proved the existence of pullback attractor.

Using some fixed point theorems of sum of two operators in semiordered Banach spaces, we proved the existence and uniqueness of positive solutions of the m-point boundary value problem for a class of fractional differential equations on an infinite interval and gave their applications by examples.

By using variational methods and the theory of fractional variable exponent Sobolev space, the author investigated the fractional differential equation with p(x)-Laplacian operator, under the condition of local superlinear growth nonlinearity, some sufficient conditions for the existence of multiple solutions for this problem were obtained.

We considered a nonlinear disturbed model for a class of singular perturbation trajectories of Fermi gases optical lattices. Firstly, the degenerate solution of the trajectories of the Fermi gases optical lattices model was given. Secondly, the outer solution of the system was given by using the singular perturbation method, and the layer type corrective term of the system was given by using a stretch variable methods. Finally, the arbitrary order asymptotic solution of the trajectory of nonlinear disturbed model for singular perturbation Fermi gases optical lattices and the uniformly valid asymptotic expansions of solution were given.

Firstly, the method of characteristic root was used to  analyze the  stability  of delayed oscillator with delaydependent parameters, and  a criterion for stability switches was given. Secondly, the  stability and periodicity of bifurcating periodic solutions were analyzed by using the center manifold and  the normal form theory.

Let R be a ring, cpD(R) stand for  the copure projective dimension of a ring R. We gave the change theorem of rings on the dimension of ring R based on the properties of cpD(R).

Let R be a commutative ring with identity, C be a semidualizing R-module and x be an exact zerodivisor over R. We considered the G_C-homological dimensions of modules under exact zerodivisors, and proved that if M was G_C-projective (injective, flat) R-module, then M/(xM) was G_C/(xC)-projective (injective, flat) R/(xR)-module. And the similar conclusions could be obtained for D_C-projective (injective) R-modules.

By using quasinilpotent part, analytic core and singlevalued extension property (SVEP) of operators, the author considered property (az) and property (z) of operator T, proved if H₀(T-λI) was closed for every λ∈σf(T), then T satisfied property (az), and gave two equivalent characterizations of T satisfying property (z).

By using the weight function method, the technique of the real analysis and the related theories of special functions, the author established a Hilberttype integral inequality with multiparameters related to some special functions and its equivalence, proved that its  constant factors were optimal, and  gave the operator expressions with the norm. 

The author gave the definition of generalized harmonically s-convex function on fractal sets ?^α(0<α≤1) of fractal real lines, established HermiteHadamard integral inequalities for generalized harmonically s-convex function and an identity for local fractional integral. Then some HermiteHadamard type local fractional integral inequalities for these classes of functions were obtained.

Firstly, the linear convergence of sequential minimal optimization (SMO) algorithm for solving the weighted minimum enclosing ball (WMEB) problem was established. Secondly, by incorporating the idea of column generation algorithm into the SMO algorithm, we proposed a column generation algorithm for solving the WMEB problem. The algorithm added the furthest point of weighted distance from the current ball center to  the core set at each iteration. The results of numerical experiments show that the proposed algorithm can effectively improve the computational efficiency of solving the WMEB problem on large
scale data sets.

The Richardson iterative method was extended to solve more general linear equations. First, the iterative process and the iterative matrix were reformulated by using the similar transformation matrix, based on minimizing spectral radius of the iterative matrix, and the method of selecting the optimal relaxation parameter was given. Then aiming at the problem that the smallest eigenvalue was difficult to calculate, an accelerated convergence strategy was proposed, which only depended on the largest eigenvalue.

We applied ultra weak variational method  to numerically solve a class of time harmonic scattering problem by medium. On the basis of truncation of the domain by artificial absorbing boundary, we derived ultra weak variational formula according to  the discontinuous Galerkin (DG)  method, and used the approximation property  of plane wave functions to approximate the local behavior of the field, then transformed the problem to the solution of the network boundary. The results show that  the algorithm can effectively simulate  the medium scattering problem, and is suitable for the case of big wave number with fast convergence rate. Numerical simulations verify the feasibility and  validity of the algorithm.

We considered a class of SISVS epidemic system with random perturbation,  applied the new Lyapunov function to study the ergodicity of the system, and obtained the sufficient conditions for the existence and ergodicity of the stationary distribution of the stochastic epidemic system. The results show that the construction method of Lyapunov function improves the existing results of endemic equilibrium and the mortality, which depend on the deterministic models, and obtains more applicable conditions.

A combined homotopy equation was constructed for solving the generalized linear complementarity problem， which was equivalent to the absolute value equation,  an existence condition of a solution of the generalized linear complementarity problem was obtained based on the homotopy equation,  and this condition was different from that of the usual interval matrix.  An example shows that this condition is not stronger than the regularity condition of the interval, so we obtain a new existence condition of a solution of absolute value equation.

The neighbor expanded sum distinguishing total coloring of join of two cycles was constructed, then the neighbor expanded sum distinguishing total colorings and neighbor expanded sum distinguishing total coloring indexes of joins of one cycle and one path, and two paths were obtained, respectively by deleting edges. The results illustrate that the neighbor expanded sum distinguishing total coloring index of several classes of graphs are all equal to 2; NESDTC conjecture is true for the joins of two cycles, one cycle and one path, and two paths.

According to the property of demi(sub)martingales, using the property of convex function and the indicative function, we gave a class of minimal inequalities for demi(sub)martingales under the condition that the product of the left derivative h(x) of the convex function g(x) and some of the indicative functions was a nonnegative function with respect to nondecreasing components.

By using the central limit theorem and the inequalities of the tail probability for the largest eigenvalue of β-Laguerre random matrix and  properties of the general β- Tracy-Wisdom distribution, we obtained a general result of precise asymptotics in complete moment convergence for the largest eigenvalue for more general boundary function and weighted function.

We considered a bivariate firstorder autoregressive time series model with Laplace marginal distribution, gave the properties of the model and conditional least squares estimation of parameters, and discussed the consistency and asymptotic normality of estimators. Finally, numerical simulation and example analysis were given.

The author considered the antiperiodic solutions for a class of nonlinear discrete systems with exponential dichotomy. Firstly, it was proved that if the homogeneous linear system had exponential dichotomy, then the corresponding nonhomogeneous linear system had an antiperiodic solution. Secondly, by means of this conclusion and the Banach fixed point theorem, a sufficient condition for the existence and uniqueness of antiperiodic solutions for nonlinear discrete systems was given. Finally, an application example was given.

We considered the stability of the weak Galerkin finite element method for solving the second order elliptic equations and Biharmonic equations. Firstly, we introduced  the weak functions and the weak gradient operators to approximate the standard functions and standard differential operators in the weak Galerkin method. Secondly,  we gave the definitions of  norms of |||·||| and |||·|||_-1in the weak  function space, and obtained  the stability of the weak Galerkin finite element method based on the two norms.

Aiming at the problem that visualization module of the selfdeveloped software AgriDEM (agricultural discrete element method) showed the vidio was not fluent  when the simulation data was huge, we proposed an accelerated visualization method of 3D discrete element software. From the point of view of display data reduction, the internal unit culling algorithm was used to simulate the visual depth of the human eye and occlusion feature of the object, and the data of the invisible particles in the object were removed. Thus, the load on the visual pipeline caused by the large data input was reduced, and 
the flicker and the vidio was not fluent problems of the simulation data visualization were solved.

Aiming at the problem that most of the current locationbased recommendation algorithms did not consider the user’s realtime location and time factors, which made the recommendation lack of realtime, we proposed a recommendation algorithm based on regional active users to solve the cold start problem in traditional locationbased recommendation algorithm. Firstly, the algorithm explored the active user in the area where the user was currently located, and used this as a standard to recommend for the user. Secondly, time factor was introduced into location recommendation to make the recommendation more accurate and realtime. The experimental results show that the number of active user’s friends in the algorithm can improve the realtime performance of the recommendation system, and the fusion of location information in the algorithm can make the recommendation more accurate.

Aiming at the problem that short text contained small words and various expressions, which led to ineffective clustering of the same category of text, we proposed a method to extend metaphorical words in short texts by using the rich lexical relationships in Chinese Wikipedia, which solved the shortages of the short text with less information and various lexical expressions. Experimental results show that the algorithm can effectively enhance the clustering effect of short text.

Aiming at the problem that the traditional method of image extraction of human motion could only obtain the local optimal solution, and the extracted feature sequence was discontinuous, which led to the poor contour extraction effect, we proposed an image attitude contour extraction algorithm of nonrigid human motion. First, the scaleinvariant feature transform (SIFT) in the human motion image sequence was extracted and preprocessed to obtain the human feature 
extraction graph, and a sequential probability graph model of the human motion sequence was designed to ensure the continuity of the feature sequence extraction. Then the exterior appearance model of human limbs was constructed. 
Based on the appearance model, the high precision contour extraction algorithm of sequential image was used to extract the contour line of the current human motion frame. The experimental results show that the proposed algorithm can extract
 continuous feature sequences, and the extracted human pose contours have high accuracy, high efficiency and robustness.

Aiming at the problem that the multidimensional multichoice knapsack problem (MMKP) couldnot find the optimal solution in polynomialtime. Besides, due to the strong constraint, the solving process would fall into the local optimization easily. We proposed an improved quantum particle swarm optimization (QPSO) algorithm to solve the problem. Firstly, in the process of quantum particle moving, the availability of the position information was determined by judging the position relationship between it and the next iteration individual, and the diversity of the particle was fully preserved by the information. Secondly, a new position disturbance method was proposed to avoid  population falling into local optimization. Finally, the algorithm was tested on the standard data set, and the convergence rate and running time of the algorithm were analyzed. Test results show that the algorithm is significantly improved in solving accuracy.

Aiming at the problem that value of d_c was difficult to select and the poor effect of neighborhood principle aggregation operation in low density area, we proposed a density peaks clustering (DPC) algorithm based on artificial bee colony and CDbw clustering index optimization, which realized automatic identification and reasonable clustering of data points between 
clusters, and solved the defect of DPC in class identification of data points between clusters. Experiment results show that the BeeDPC algorithm has advantages of automatic identification and reasonable clustering of data points between clusters, automatic identification of cluster centers and the number of clusters and dealing with arbitrary distributed data sets.

In view of the defects of the current clustering routing algorithm in wireless sensor network, such as the unaverage energy consumption and the premature death of nodes, we proposed an improved low energy adaptive clustering hierarchy (LEACH) routing algorithm for wireless sensor networks. Firstly, aiming at problem of the premature death of wireless sensor nodes, the dynamic determination of cluster radius was introduced, and the whole wireless sensor network was divided into multiple inhomogeneous clusters. Secondly, we considered the problem of fast energy consumption of cluster heads, and selected the cluster heads in each round according to the location of the cluster heads and the residual energy of the nodes. Finally, the data transmission mechanism was improved to ensure the balance of the energy consumption of nodes, and the performance of clustering routing algorithm in wireless sensor networks was tested on the MATLAB 2014 platform. The test results show that the improved LEACH algorithm solves the problem of premature death of nodes, prolongs the lifetime of the wireless sensor network and balances the energy consumption of each node. The performance of the whole wireless sensor network is significantly better than that of other comparison algorithms.

Aiming at the interference power threshold of the primary user (PU) in the cognitive radio network (CRN), transmission rate limit of the secondary user (SU) and the signaltointerferencenoiseratio (SINR) requirement, we proposed a learning traditional particle swarm optimization (LTPSO) algorithm, in which the evaporation factor was set according to the particle swarm learning factor,  a new particle swarm memory form was established, and the fitness values were screened proportionally. The simulation results show that the LTPSO algorithm achieves better optimization results.

Aiming at the problems of low positioning accuracy of traditional DVhop algorithm and node positioning failure caused by objects blocking information dissemination in the positioning environment, we proposed an improved highprecision localization algorithm suitable for obstacle environment. Firstly, the algorithm introduced an error correction value that took into account the minimum number of hops of the positioning node. Through this parameter value, the anchor nodes participating in the positioning were screened, and then the average hop distance of the anchor nodes was optimized. Secondly, the distance between the unknown node and the anchor node was calculated by using the trigonometric function combined with the accurate distance between the two anchor nodes. Finally, through the convex optimization calculation of the location of unknown nodes, the data transmission between nodes had the optimal path, optimized the positioning process and improved the positioning accuracy. Simulation results show that the improved algorithm not only solves the problem of difficult localization in the obstacle environment of wireless sensor networks, but also effectively improves the positioning accuracy of unknown nodes.

Niche technology was used to enhance the identification ability and clustering ability of the algorithm for local optimal solution, 
improve the local search ability of the artificial bee colony algorithm, and improve the characteristics of rapid search for global optimal value of the scout bee. We proposed an artificial bee colony algorithm based on niche technology, and applied it to extract the character image edge on the bogie wheelset axle end. This algorithm improved the disadvantage of show 
recognition speed and poor recognition effect of character edge image caused by the large amount of operation. Neighborhood gray gradient value was used as the fitness function value of the algorithm, and the niche radius was used to maintain the diversity of the population, so as to improve the local search ability of the characters, and finally a high quality edge image of the character image was obtained. The experimental results show that the number of local character edge points can be increased 1.66 times by using niche algorithm.

The traditional proportional fairness wireless network resource scheduling strategy could not effectively guarantee the fairness of users, and had the shortcomings of low resource utilization of wireless network communication system, so we designed a resource scheduling optimization strategy based on spectrum coefficient and proportional fairness algorithm for wireless network communication system to solve the problems existing in the current resource optimization scheduling process of wireless network communication system. Firstly, the channel model of wireless network communication system was established, and the reasonable spectrum coefficient was determined by adaptive genetic algorithm. Secondly, according to proportional fairness algorithm, the scheduling priority was calculated, and the resources of wireless network communication system were allocated to users, and the shortcomings of traditional proportional fairness algorithm were improved accordingly. Finally, the performance of wireless network communication system was analyzed on the platform of MATLAB 2016. The resu
lts show that the proposed strategy can better ensure the fairness of users’ use of resources, improve throughput of wireless network communication system, and improve the resource utilization of wireless network communication system.

Using the NUSHELLX spherical shell model program, we considered the level structure of ⁹⁴Tc under two different configuration spaces. The calculation results show that the excitation mechanism of positiveparity spin states of ⁹⁴Tc is dominated by the excitation of protons from the p_1/2 orbit into the jg_9/2 orbit across the Z=40
 subshell closure and protons from the (f_5/2,p_3/2) into the (p_1/2,g_9/2) orbit across the Z=38 subshell closure. The negativeparity spin states are the excitation of neutrons from the d_5/2 orbit into the (g_7/2,h_11/2) orbits across the N=56 subshell closure.

In order to explore the principle of reflection of solar wind ions on lunar magnetic anomaly area, based on the detection data of the solar wind ion detector carried by Chang’E2 satellite, we inverted the motion of the solar wind ions by using single particle simulation, and analyzed incidence angles and reflection angles. The experimental results show that the solar wind ions are firstly scattered by lunar regolith in all directions, then accelerated upward by lunar surface electric field. There is a positive potential of 45—75 V on dayside lunar surface in solar wind, which has a significant effect on the solar wind ions reflected
 from the lunar surface.

We calculated the contributions of the natural atomic orbital (NAO) of the molecular orbital S-Leu system under different implicit solvents by using the Gaussian natural bond orbital (NBO) analysis program. The results show that the implicit solvent methanol and chloroform have great influence on the molecular orbital of S-Leu system according to the contribution of NAO. The contribution of NAO of implicit solvent methanol is closer to the calculation result of the implicit solvent H₂O. The total contribution value of NAO of carboxyl fragment under implicit solvent methanol is closer to 
the calculation result of the implicit solvent H₂O. The effect of contribution of NAO of carboxyl fragment under implicit solvent chloroform is different from implicit solvents methanol and H₂O.

The maximum power point tracking (MPPT) algorithm was invalid because the power characteristic curve of the photovoltaic array under partial shading condition was changed from a single peak curve to an overlapping peak curve, and other intelligent algorithms (such as particle swarm optimization (PSO) algorithm) had the disadvantages of more parameters, slow convergence speed and large amplitude of oscillation in the tracking process. The grey wolf optimization (GWO) algorithm with fast convergence speed and high precision was applied to multipeak MPPT algorithm of photovoltaic array. Firstly, a mathem
atical model of photovoltaic array under partial occlusion was established. Secondly, the principle of MPPT algorithm based on GWO algorithm was analyzed. Simulation results show that the GWO algorithm can track the maximum power point quickly, the tracking speed of the GWO algorithm is 1 times higher than that of the PSO algorithm, and the tracking efficiency is improved by 0.1%.

The author designed an ultrawideband antenna of a Ushaped floor semicircular ring feed terminal, and the effects on antenna performance of the parameters such as sector radius, inner diameter and the outer diameter of the semicircular ring, the length and width of the rectangle on the  Ushaped structure floor were analyzed. The antenna consisted of a semicircular ring feed terminal, a coplanar waveguide feeder and a Ushaped floor, coplanar waveguide was used to feed the antenna. The results show that the designed antenna has ultrawideband performance, the effective working bandwidth is 3—12.9 GHz, the design size is 20 mm×20 mm, the radiation characteristics and gain characteristics are good, so it can be used in ultrawideband wireless communication terminal system.

We investigated the mechanism of optical isomerism of valine catalyzed by hydroxyl water clusters of two conformations of valine molecules and the damage induced by hydroxy radicals in water environment by using MP2/6-311++G(2df,pd)//B3LYP/6-31+G(d,p) doubletheory and SMD model method for self consistent reaction field (SCRF) theory. The results show that the optical isomerism of valine can be  achieved in two channels a and b. In channel a, the substrate is formed by hydrogen bonds of hydroxyl water clusters with α-H and amino groups, hydroxyl abstracts α-H, and then α-C abstracts the hydrogen of water molecular at the other side. And in channel b, the substrate is formed by hydrogen bonds of hydroxyl water clusters with α-H and carbonyl groups, hydroxylabstracts α-H, and then α-C abstracts the hydrogen of water molecular at the other side. Water molecular assists abstraction of αH by hydroxy radicals can induce valine damage in channel b. The optical isomerism energy barriers of ratedetermining step of conformation Val1 (mono-hydrogen bond between aminoand carboxylgroup) and Val2 (dualhydrogen bond between aminoand carboxylgroup) are 6057, 6524 kJ/mol in channel a, while the energy barriers are 5676,64.11 kJ/mol in channel b. So the damage of valine by hydroxy radicalwater clusters of them in channel b was moderate exothermic reaction.

CdTe@SiO₂ microspheres were synthesized by modified Stber method, and then CdTe@SiO₂@GdF₃fluorescence/magnetic resonance imaging dual functional microsphere with core/shell structure were prepared by direct precipitation method. Furthermore the structure, magnetic resonance imaging and fluorescence property were characterized by transmission electron microscope (TEM), energy dispersive Xray analysis (EDXA),  magnetic resonance imaging (MRI), Fourier transform infrared spectroscopy (FT-IR) and fluorescence spectrum. The experimental results show that the synthesized microsphere has obvious spherical core/shell structure, a large number of GdF3 dispersed well on the surface of silica in the form of small particles, and the particle sizes are 5—8 nm. Si,O and Gd elements can be detected on the surface of CdTe@SiO₂@GdF₃ microsphere, and Gd has been doped into the CdTe@SiO₂ materials. Compared with CdTe quantum dots, the fluorescence emission spectra of CdTe@SiO₂@GdF₃ microspheres have a red shift, but still have good fluorescence property. The relaxation parameter r₁ of CdTe@SiO₂@GdF₃ microspheres is 3.48 s^-1/(mmol·L^-1), so the synthesized CdTe@SiO2@GdF3 microspheres can be used for T₁weighted magnetic resonance imaging. When mass concentration of CdTe@SiO₂@GdF₃ is 200 μg/mL, the cell viability is still above 90%, indicating that the toxicity of the microphere on cells is weak.

α-Fe₂O₃ with spindle or hexagonal morphologies were prepared by hydrothermal method, we investigated the photocatalytic properties of methyl orange and rhodamine B under visible light irradiation. The results show that all samples are rhombohedral phase of hematite with uniform sizes. The energy gap of hexagonal α-Fe₂O₃ is less than that of spindle α-Fe₂O₃,meaning that it can absorb visible light with larger wavelength range. The hexagonal α-Fe₂O₃ has higher degradation rate and degradation rate constant, and has higher photocatalytic activity.

Using 3aminopropyltriethoxysilanes (APTES) as soft template, we prepared mesoprous ZSM-5 zeolite molecular sieve by soft template method. The samples were characterized by Fourier transform infrared spectroscopy (FT-IR), X-ray diffraction (XRD), N₂ adsorptiondesorption and transmission electron microscope (TEM), etc. The effect of adding amount of APTES on the pore structure of the synthesized samples was investigated. The acid catalytic performance of the synthesized sample
s was analyzed by model reaction of phenol.

We used a computer aided molecular isomer construction algorithm STRU^auto to solve the difficult problem of judging the uniqueness of the molecular structure in Gaussian calculation. With the help of the iterative comparison of energy and bond length, the algorithm completed the batch deduplication of the molecular structure, avoided the error of the judgment of uniqueness of the molecular structure under normal conditions, and obtained accurate molecular isomer. Experimental results on several types of typical molecular structures show that the algorithm STRU^auto can significantly improve the efficiency of judging the uniqueness of molecular structure.

The effect of nanoTiO₂ on the mass ratio of nitrate nitrogen and activity of nitrate reductase (NR) in soils were investigated by laboratory simulation experiments. The results show that the nanoTiO₂ can reduce the mass ratio of nitrate nitrogen and the activity of NR in soil, with the increase of time, the degree of reduction increased first and then decreased. Under the same sampling time, the mass ratio of nitrate nitrogen and NR activity of nano-TiO^-2 in different types of soil decrease as follows: sandy soil>black soil>peat soil, and the degree of reduction increases with the increase of nanoTiO₂ addition. In the presence of alfalfa, nanoTiO₂ decreases the mass ratio of nitrate nitrogen and NR activity in the soil. Therefore, the nanoTiO₂ can reduce the intensity and rate of soil denitrification, and alfalfa can reduce the biological toxicity of nanoTiO₂.