We solved timedependent Brinkman equation by the weak Galerkin finite element method. Corresponding error equations and error estimates were established by using semidiscrete scheme only for the discrete space and fulldiscrete scheme for the time and space discretization. We obtained the optimal rate convergence in H¹ and L² norm for the velocity function, and in H¹ norm for the pressure function. So that the weak Galerkin finite element method was applied more widely.

We considered the density and temperature gradients of an inhomogeneous quantum plasma system in the atmospheric environment, and studied the two dimensional nonlinear fluid dynamics disturbed solitary wave model in the case of low collision frequency between the ions and neutrons. By using the hyperbolic function expansion method and perturbation theory and method, we obtained the potential function of the system in the astrophysical environment and gave its physical meaning.

By using fixedpoint theorems on a convex cone, we investigated the existence of positive solutions for boundary value problems of fractional differential equations with p-Laplace operator.

Using the corresponding characteristic equations (system of ODEs) of the first order quasilinear  partial differential equations (PDEs), we proved the existence and uniqueness of solutions for the first order quasilinear PDEs with the distributional HenstockKurzweil integral. Finally, we demonstrated that the result was more extensive by examples.

Using upper and lower solution method, we studied the existence of solution of fractionalorder periodic boundary value problem
x^(δ)(t)=f(t,x(t)),t∈［a,a+T］,a>0,
x(a)=x(a+T),
where f is a continuous function, f(a+T,x)=f(a,x), a>0, T>0 are constants and δ∈(0,1］. 

We considered the attainable sets of a class of two order differential inclusion, and the relationship between optimal control system and differential inclusions. We obtained the attainable sets of a class of two order affine control system and the range of attainable set of a two order differential inclusion. An example was given to illustrate the effectiveness of the proposed method.

The author considered the properties of solutions of initial boundary value problems for quasilinear parabolic systems from combustion theory, and obtained sufficient conditions for the existence and nonexistence of global solutions by using energy estimation method, Jensen inequality and Gronwall inequality. The results show that there is a global non negative solution to the problem if the parameter m in the equation is odd and the initial value satisfies appropriate integrability conditions; and the solution of the problem will blow up at a finite time if m is even and the integral of the initial value is suitably large.

By introducing independent parameters and intermediate variables of exponential function, and using the method of the weight functions, we established a Hilberttype integral inequality in the whole plane related to the Gamma function of the best constant factor, and considered  the  equivalent forms,  homogeneous and nonhomogeneous forms under particular parameters.

By introducing the ∞copure flat modules, we proved that R is a QF ring if and only if R is left Noetherian ring and every finitely presented left Rmodule is ∞copure flat; R is a right IF ring if and only if every left Rmodule is ∞copure flat; R is a left CFH ring if and only if ∞copure flat modules are closed to their submodules; a left coherent ring R is a semihereditary ring if and only if ∞copure flat left Rmodules are flat.

Suppose X_n={1,2,…,n}, with the usual order of natural number sequence, MC_n was the monotonic compression singular transformation semigroup on X_n. For any 3≤r≤n-1, we considered the semigroup MC(n,r)={α∈MC_n: |Im α|≤r}, and obtained the complete classification of the maximal subsemigroups of the semigroup MC(n,r) on X_n.

We considered the problem of the vertexdistinguishing total colorings of the disjoint union mC₇ of m cycles of length 7. By constructing a matrix which was composed of color sets as elements, the vertex distinguishing total coloring of mC₇ was determined by using the methods of distributing color sets in advance and induction. We obtained the exact value of vertexdistinguishing total chromatic number of mC₇. The results show that the VDTC conjecture is valid for mC₇.

We considered the generation and selection of Turing pattern of a class of two dimensional system with negative crossdiffusion. Firstly, the existence region of Turing pattern was obtained by using stability theory and Hopf bifurcation theory. Secondly, the amplitude equations of the system were derived by using multiscales analysis method, and the selection result of Turing pattern was given. Finally, we considered a specific ecosystem with a ratio dependent HollingTanner predatorprey model. MATLAB software was used to simulate the pattern generation and selection results of the model, and the different types of Turing patterns, such as dot, strip and the coexistence of the two types were obtained.

The author considered the polar factorization, generalized inverse and perturbation bound of quasirow (column) symmetric matrix, analyzed some perturbation bounds of the polar factorization of quasirow (column) symmetric matrix, and obtained the calculation formula of the polar factorization and generalized inverse of quasirow (column) symmetric matrix. The results show that the method can not only reduce the calculated amount and memory space, but also can not reduce the numerical accuracy.

Using Brauer’s theorem and sequences of upper bounds of the elements of inverse matrices, the author gave a monotone nonincreasing sequences of upper bounds of the spectral radius ρ(B·A^-1) for the Hadamard product of the inverse matrix A^-1 of a nonsingular Mmatrix A and a nonnegative
matrix B and gave some monotone nondecreasing sequences of lower bounds for the minimum eigenvalue τ(A) of Aby using this sequences of upper bounds. The obtained results were verified by several numerical examples. Numerical results show that these obtained estimates are more accurate than some existing results.

By the analysis of classical canonical correlation analysis criterion, we proposed a new criterion for source signal extraction. Using the online quasiNewton iteration algorithm to solve the new criterion, and then a new blind source extraction algorithm based on canonical correlation analysis was obtained and blind source separation was realized. Theoretical analysis show that the unique global minimum point of the new source signal extraction criterion is the maximum point of classical canonical correlation analysis criterion. Simulation results show that the convergence speed the new algorithm is faster.

Using diagonal similarity transformation of a matrix, we gave a numerical algorithm for the maximum eigenvalue and the corresponding eigenvector based on irreducible nonnegative matrix of power function, and the numerical examples show the feasibility of the algorithm and the influence of parameters on the convergence.

Using the information of the function value near the latest iteration point, we estimated simplex gradient of the point and calculated BarzilaiBorwein (BB) stepsize of the current point. We proposed an updating strategy of the grid stepsize based on adaptive BB stepsize, which could effectively solve the problem that the grid stepsize dropped too fast. Combined with the new updating strategy, we proposed a new direct search algorithm. The numerical results show that the algorithm has a great improvement in stability and efficiency.

We proposed a new numerical algorithm for scattering problem of multiple obstacles. The algorithm used the linear combination of single layer potential function and double layer potential function to approximate the scattering field, without need to truncate and partition the domain, and the application process was simple and the convergence rate was fast. Numerical examples show the algorithm is effective.

Using the method of Markov operator to measure function, we investigated the relationship between probability measure of the typical fractal sets and Dirac measure of Cantor division set, Sierpinski right triangle and Koch curve based on hyperbolic iterated function system under the condition of equal probability,  and obtained the relationship between probability measure and Dirac measure on the more general fractal sets under equal probability and unequal probability, respectively.

We proposed an uniaxial optimal perfectly matched layer (PML) method for solving timedomain acoustic scattering problem based on the Laplace transform and the complex coordinate stretching in the frequency domain. The uniaxial optimal PML was constructed by this method in a rectangular domain, which provided a flexible and effictive calculation method for the scattering problems of anisotropic scatters. A small parameter ε₀ was introduced into the absorption function, so that the calculation of the optimal PML method for scattering problem was no longer dependent on the thickness of the PML layer δ. The results show that the optimal PML solution converges exponentially to the solution of the original scattering problem if the parameter ε₀ is sufficiently small.

Based on the idea of single change point of Poisson distribution, we studied the risk model with change point claim process by using martingale method, obtained the upper bound of ruin probability before and after the change point, and gave the stochastic simulation result of ruin upper bound.

According to the cumulative number of shopping people in a mall, we established the poisson process model with periodic single change point, and studied the full conditional distributions of period and other parameters. Under the conditions of absolute loss and squared loss as the loss function, we discussed the Bayesian estimation of unknown parameters by using Gibbs and MetropolisHastings algorithms. The results of random simulation and example analysis show that Bayesian estimations of two kinds of loss functions have good accuracy.

The author considered the pseudoanti self adjoint property of compact normal operators in quaternion Hilbert spaces. The author used slice functional calculus of operators and the theory of spherical spectrum to characterize the spherical spectrum of compact normal pseudoanti self adjoint operators, and gave the relation between the self adjoint property and pseudoanti self adjoint property of the operators.

The author considered a complete minimal submanifold in hyperbolic space by using the theory of harmonic functions, and proved that there was only one end of the submanifold, if supremum of the length of the second fundamental form was less than n(n-4)/4, either infimum of Ricci curvature of the submanifold was greater than -n(n-1)/4.

We considered the existence condition of solution for a class of stochastic Riccati equation. Based on the characteristics of the stochastic Riccati equation, we constructed a backward stochastic differential equation without constraints by using It formula. The solution of backward stochastic differential equations satisfied the algebraic constraints corresponding stochastic Riccati equation during the construction. Thus we gave the existence condition of the solution of the stochastic Riccati equation by using the relation of them.

We proposed a new revised rectified activation function. The new rectified activation function has a changeable parameter, and the logarithmic function was used to rectify the gradient in positive region, which solved the problem of low accuracy of prediction. The improved activation function used two different parameters to control the gradient in positive region and negative region, respectively. The results of simulation experiments on two different data sets show that the effectiveness of the two new methods is better than that of the original rectified linear units. With the improvement of two parameters, the verification error rate is reduced by 014% and 533%, respectively.

In order to improve detection effect of illegal users intrusion behavior in cloud computing environment, we designed a new detection model of illegal users intrusion behavior in cloud computing environment. Firstly, the features of illegal users intrusion behaviors in cloud computing environment were extracted, and features were selected by using principal component analysis. Secondly, least square support vector machine was used to classify and detect the intrusion behavior of illegal users, which parameters of least square support vector machine were determined by using particle swarm optimization algorithm. Finally, the validity of the model was verified by selecting specific illegal users intrusion data set. The results show that the proposed model can obtain higher accuracy rate of intrusion detection results of illegal users, and accelerate detection speed of illegal users intrusion behavior.

Aiming at the shortcomings of the traditional watershed segmentation algorithm, such as noise sensitivity and high rate of false segmentation, we proposed a novel image segmentation method based on improved watershed algorithm in order to obtain better image segmentation result. Firstly, the original image was filtered to eliminate the interference of noise to image segmentation, and the edge information of target was effectively protected. Secondly, image was transformed to enhance contrast of the image, and then image was segmented by watershed algorithm. Finally, several types of images were tested on the MATLAB2014 platform. Simulation results show that the proposed method can avoid effect of noise on image segmentation results, and can obtain better  image segmentation results, moreover, the segmentation accuracy and efficiency are better than other image segmentation methods.

Aiming at the problem of single objective optimization of topology control algorithm in wireless sensor networks, we proposed a faulttolerant topology control algorithm for k-disjoint paths, which could not only optimize the network energy efficiency but also guarantee the network fault tolerance. Fristly, k-disjoint paths were constructed from sensor nodes to the sink node, and  improving network fault tolerance by adding redundant links. Secondly, we selected energy consumption of the path, the standard deviation of the power of nodes in the path and the number of path hops as a measure of the path quality. Finally, a multiobjective programming was established, and intelligent optimization algorithm was used to solve the problem. According to the different k- values, the path was selected to achieve the purpose of reducing the network energy consumption and prolonging the network lifetime. Simulation experiment results show that the network topology constructed by this algorithm can effectively reduce the network energy consumption, prolong the network lifetime and improve the network fault tolerance.

In order to solve the problem of parameter perturbation of power allocation in cognitive radio networks, we proposed a robust power allocation algorithm based on protection factor for cognitive radio. According to the disturbance of the channel parameters in the actual system, the algorithm introduced the protection mechanism of the authorized user’s interference power threshold into robust programming, and then used the Lagrange dual algorithm and convex optimization theory to obtain the optimal power allocation. The algorithm could solve the problem of channel parameter perturbation in the underlay cognitive radio networks. The simulation results show that the proposed algorithm has good robustness, reduces the complexity of the algorithm and improves the system capacity of cognitive radio networks.

In order to improve the localization effect of sensor nodes, aiming at the parameters optimization problem of support vector machine, we designed a sensor node localization model based on artificial bee colony algorithm optimizing support vector mathine. Firstly, relevant data of sensor nodes were collected, and the effective parameters were extracted. Secondly, support vector machine was used to establish sensor node localization model, and artificial bee colony algorithm was used to solve the parameter selection problem of support vector machine. Finally, sensor node localization experiment was implemented on MATLAB2014 platform. The experimental results show that the proposed model can reflect the position of current sensor nodes, and obtain the accurate positioning results of the sensor nodes.

Aiming at the problem that the current resource scheduling algorithm could not meet the requirements of business diversification, we proposed a cloud computing resource scheduling algorithm based on unified deployment and business management. Firstly, business was classified and unified management according to business change in real time to adjust resource requirements. Secondly, transformation between soft constraints and hard constraints of business was used to adapt to requirements of business diversification. Finally, the validity and superiority of the algorithm was tested by simulation experiment. The experimental results show that compared with other algorithms, the proposed algorithm can greatly improve utilization rate of cloud computing system resources, and  meet the requirements of practical applications.

In order to improve the security of image, aiming at the defects of traditional image analysis algorithm, such as weak ability resistance attacks and small key space, we proposed an image security analysis algorithm based on the fusion of chaotic system and shift register. Firstly, we analyzed security of image to find the limitations of single shift register and chaotic system. Secondly, initial value of chaotic system was determined by sequence generated by shiftregister, and a new pseudorandom sequece was generated by continuous iteration, and using pseudorandom sequence as key stream to encrypt image. Finally, we simulated image encryption effect and security analysis. The results show that proposed algorithm improves work efficiency of the image encryption system, can resist a variety of attacks, and obtains the ideal image encryption effect and can ensure the security of image transmission on the network.

Aiming at the problem that the supervised information was not sufficient and the information content of supervision information was low in semi-supervised clustering algorithm, we proposed a semi\|supervised clustering algorithm based on active learning. Firstly, we designed a semi\|supervised clustering algorithm based on Seeds set and pairwise constraints (SC\|Kmeans) to guide the clustering process of the Kmeans algorithm by using the labeled data a
nd pairwise constraints. Secondly, we introduced the active learning algorithm into SC\|Kmeans, in order to select a higher amount of supervision information with a small cost and improve the clustering accuracy of SC\|Kmeans algorithm. Finally, the simulation experiments were performed on machine learning repository (UCI) standard data sets. The experimental results show that the proposed algorithm can achieve better clustering effect, and effectively improve the clustering accuracy.

Based on the method of hierarchical tree and the spatialtemporal correlation theory, we studied the problem of fast processing of big data and the fast application of optimization algorithm in the agricultural Internet of things, and proposed an improved hybrid hierarchical bounding box tree and collision detection algorithm. The experimental results show that the optimization algorithm has a certain promotion value  in the field of agricultural Internet of things.

Aiming at the defects of low resource utilization rate and serious waste of the resource scheduling algorithm in cloud computing system, in order to obtain a more ideal cloud computing resource scheduling scheme, we proposed an improved ant colony optimization algorithm for cloud computing resource scheduling. Firstly, the working principle of cloud computing resource scheduling was analyzed, and the objective function of cloud computing resource scheduling optimization was established. Secondly, ant colony optimization algorithm was used to simulate the ant colony to find a path from the starting point to the destination, which was the optimal solution of objective function for cloud computing resource scheduling, and ant colony algorithm was improved according to the objective function. Finally, the MATLAB2014R programming was used to optimize resource scheduling model of cloud computing. The experimental results show that the proposed model can find the optimal solution of cloud computing resource scheduling in a short time, which can improve  the resource utilization rate.

We proposed a new onedimensional variable frequency photonic crystals (VFPCs), and gave the expression of transmission matrix and electric field distribution. On this basis, we calculated transmissivity and the electric field distribution of onedimensional VFPCs and studied the effect of variable frequency function, variable frequency medium refractive index, thickness, period numbers and defect layer on the transmissivity and the electric field distribution of the VFPCs. The results show that the photonic band gap of the VFPCs is wither than that of the conventional photonic crystals.

Firstly, we gave characterization of the pure state in the PTsymmetric quantum theory based on the relationship between the PTinner product and the original inner product of PTsymmetric quantum system. Secondly, we gave the characterization of the mixed state in the PTsymmetric quantum system. Finally, we studied the evolution of state in PTsymmetric quantum system, and gave a necessary and sufficient condition for the unitary evolution.

Using density functional theory B3P86 and time\|dependent density functional theory (TD\|DFT) method, we calculated excitation energy, transition wavelengths and oscillator strength of chiral C₁₃H₁₀N₂O₄ molecules from ground state to the excited states of 1—8 at the level of 6-311++G(2-df
-) basis sets, and studied the influence of the excited states of chiral C₁₃H₁₀N₂O₄ molecules under different external electric fields. The results show that the excitation energies Δ E of each excited state of C₁₃H₁₀N₂O₄ molecule increases with the increase of the electric field intensity, that is, the electron  isn’t easy to be excited under the limited external electric field.

By using the method of twobeam interference of nanosecond laser, we fabricated sample of periodic onedimensional grating structure  on the photoresist layer, and studied its shapememory characteristics. The results show that the grating morphology of developed sample is changed under the ambient temperature of 195 ℃ and pressure, as well as the vertical height of grating reduced, and the diffraction intensity weakened. When
 the sample is cooled to room temperature, the grating morphology can remain unchanged. When ambient temperature of the sample is 120 ℃, the morphology of the grating is restored to the original shape, and microshapememory function is realized.

Na₂Co₂TeO₆ was synthesized by solid state reaction and its structural and valence state of elements were investigated by X-ray diffraction (XRD), scanning electron microscopy (SEM) and X-ray photoelectron spectroscopy (XPS). Furthermore, the electrochemical and kinetic properties of the materials were tested by means of galvanostatic chargedischarge cycling, rate performance and cyclic voltammetry measurements between 30 V and 001 V. The results show that, as negative electrode material, Na₂Co₂TeO₆ demonstrates good cycle performance with a reversible capacity of 200 mA·h/g and high coulombic efficiency of 95%. Meanwhile, the material shows good rate performance, and the stable capacity can still be maintained 50 mA·h/g under the current density of 500 mA/g.

Using density functional theory B3LYP, we investigated the second reaction channel process of the chiral transition of the nonrestricted area monomer asparagine (Asn) molecule at the level of 6-311-+G(2-df-) basis sets. We drawed a complete chiral transition path reaction potential energy surface by finding structures of the extreme value points including the transition states and intermediates, and analyzed the geometric and electronic structure properties of extreme value points. The results show that the 4H atom on the chiral carbon atom of SAsn molecule can transfer to the other side of the carbon atom via the 10O atom of carboxyl atoms as a bridge, and achieve the chiral transition of Asn molecule from Stype to Rtype. On this path there are two transition states and three intermediates. The maximum reaction energy barrier is 313.222 1 kJ/mol.

We studied optical isomerism mechanism and water solvation effect from gaseous phase S-isoleucine to R-allo-isoleucine by using the B3LYP method of density functional theory, the MP2 method of perturbation theory, and SMD model method of self\|consistent reaction field (SCRF) theory. The results show that there are three channels a,b and c in the reaction. The optical isomerism reaction requires three elementary reactions in the channel a and c, four elementary reactions in the channel b. Channel a is the main reaction channel and the stepdetermining Gibbs free energy barrier is 255.0 kJ/mol, which is generated by the transition state of proton transfer from the chiral carbon to the amino N. The stepdetermining reaction rate constant is 1.25×10^-32 s^-1. The water solvation effect enables the stepdetermining energy barrier to reduce to 114.1 kJ/mol and the reaction rate constant to increase to 2.73×10^-7 s^-1. It shows that water environment has better catalytic effect on Sisoleucine optical isomerization.

Using nearedge Xray absorption fine structure (NEXAFS) spectrum combined with the quantitative analysis method, we carried on the system analysis to the organic carbon functional groups of albic soil with corn straw based on the application of equal nitrogen amount and different nitrogen forms of n(NH⁺⁴)∶n(NO^-3)=4,1,1∶4. The results show that the addition of nitrogen in any form is helpful to the microbial mineralization of soil organic carbon (SOC) of albic soil with corn straw. The n(NH⁺⁴)∶n(NO^-3)=1 is more advantageous in promoting the mineralization and decomposition of SOC, which is beneficial to the formation and accumulation of fulvic acid extracted from the albic soil, and to enhance its physiological activity of humic acid to a larger degree; the N supply mainly dominated by NO^-3-N is more beneficial to the microbial decomposition and transformation of SOC in a short period of time, and most of the microorganisms can obtain energy from consuming the C—OH groups, which also has a cumulative effect on aromatic carbon, and increasing the complexity degree of SOC molecules. Influenced by the NH⁺⁴N that served as the main N form, the microorganisms are more inclined to consume much more carboxyl functional groups of SOC and make them decomposed and transformed into much more alcoholic hydroxyl groups (C—OH). There are some main types of SOC functional groups existing in the albic soil with corn straw, such as aromatic hydrocarbon C〖CDS1〗C and C—H, aliphatic hydrocarbon, carboxyl group C---O, alcoholic hydroxyl group C—OH and graphite type C---C.

By using the technology of threedimensional fluorescence spectroscopy, we studied the effects of fluorescence characteristics on water extractable organic matter in soda saline\|alkali soil (grassland, dry farmland, paddy field) under different land use patterns  in the west of Jilin Province.
 The results show that the mass ratio of organic matter in paddy field is the highest, 2708 g/kg, while the mass ratio of organic matter in grassland is the lowest, 21.63 g/kg. The mass ratio of water extractable organic matter (WEOM) is paddy field>dry farmland>grassland. The aromatic concentration is grassland>paddy field>dry farmland, and the values are 390,379,331 L/(mg·m). The fluorescence intensity of region Ⅲ and region Ⅴ is the highest in threedimensional fluorescence spectra of WEOM. The integral values of WEOM fluorescence region are humic acidlike>fulvi acid like>soluble microbial byproductlike substance>tyrosinelike protein>tryptophanlike protein. The mass ratios  of fulvic acidlike are grassland>dry farmland>paddy field,  the mass ratios of soluble microbial byproductlike substance are paddy field>dry farmland>grassland, [JP+1]and the mass ratios of humic acidlike are dry farmland>grassland>paddy field. It indicated that different land use had significant effect on the mass ratio and compos
ition of WEOM in soil.

Using CANOCO45 software, we investigated the difference of the structure of phytoplankton communities in Xianghai and Chagan Lake wetlands,  combined with the difference of water environmental chemical factors in wetland water supplement, and analyzed the causes of the difference of phytoplan
kton community structure. The results show that the geographical and climatic conditions are similar to those of Xianghai and Chagan Lake wetlands, there are pollution phenomena of the water environmental chemical factors in Xianghai and Chagan Lake wetlands, and the pollution degree of water environment in the Chagan Lake wetland is more serious than that in Xianghai wetland. Furthermore, the structure of phytoplankton communities is similar in the two wetlands, and the abundance of Cyanophyta is the largest, the species and dominant species of phytoplankton in Chagan Lake wetland are less than those in Xianghai wetland, and the number of detected species in each phylum exist certain differences.  pH, total phosphorus (TP), biochemical oxygen demand (BOD5) and bicarbonate are the main water environmental chemical factors affecting the distribution of phytoplankton in the Xianghai wetland, while pH, TP, total nitrogen (TN), dissolved oxygen(DO) and BOD5 are the main water environmental chemical factors affecting the distribution of phytoplankton in the Chagan Lake wetland. The significant differences of characteristics of water environment and structure characteristics of phytoplankton community between Xianghai wetland and Chagan Lake wetland are mainly caused by land use degree and the characteristics of supplementary water.

Using planar optode technology, we prepared fluorescence sensing membrane of pH, dissolved oxygen (DO) and partial presure of CO₂ (p_CO2), constructed 3 kinds of membrane in the simulated water/sediment system, and studied the twodimensional distributions and coordinated variation of pH, DO and p_CO2 in the system of the disturbance of the tubificid. The results show that there are hardly any changes in the parameters of overlying water and sediment system without the presence of bioturbation. On the contrary, there is obvious and coordinated variation in various parameters of system
of the disturbance of the tubificid with time. The pH,DO and p_CO2 in the system tend to be uniform with the extension of the disturbance time. There exists a certain coordinated variation tendency and interactions among three environmental parameters in the system with the presence of bioturbation.