Using the spherical harmonic decompositions method on the unit sphere, we obtained a class of  singular integral operators T with variale kernel and corresponding adjoint operator T^* and pseudoadjoint operator T^# and the boundedness of fractional differentiation operator D^γ on the weighted MorreyHerz spaces.

For a class of cooperative systems with three discrete time delays, with two combinations of three time delays τ₁,τ₂,τ as bifurcation parameters, based on the analysis of the root of the characteristic equation and the standard theory, we investigated the stability of equilibrium points and the sufficient conditions of local Hopf bifurcation in two cases, and obtained the algorithms and calculation formulas for determining the stability and bifurcation direction of the bifurcation periodic solutions. We gave the theoretical proof of the existence of global Hopf bifurcation, and the existence of bifurcation periodic solutions from local to global can be verified by numerical simulations.

For multiobjective game problem of the plurality players of multiple payment function, we studied the existence of optimal value of each player’s payment function based on equilibrium coordination. We proved the existence of equilibrium solution in the equilibrium coordination sense of game system, and gave the equilibrium coordination algorithm to solve the problem of multiobjective game. The rationality and validity of the algorithm were tested by example analysis.

The author proposed an optimal perfectly matched layer (PML) method with small parameter ε₀ for solving timeharmonic scattering problem. The results show that the proposed method makes the calculation of the scattering problem of optimal PML method do not depend on the thickness δ  of  the PML, and the exponential convergence of the optimal PML is the solution of the original problem.

By introducing a class of optimization problems with uncertainty information both in the objective functions and constraints, and then using the robusttype subdifferential constraint qualification, we characterized MondWeir type robust duality between the uncertain optimization problem and its uncertain dual problem, in other words, the duality between the robust counterpart of the primal problem and the optimistic counterpart of its dual problem.

Using matrix splitting method and some existing infinity norm estimates of the inverse of strictly diagonally dominant Mmatrices， we gave a monotone non-increasing sequence for the upper bounds of ‖A^-1‖_∞  of a strictly αdiagonally dominant Mmatrix A. The obtained results were verified by several numerical examples. Numerical results show that the method is feasible and more accurate than some existing results.

We discussed the perturbation analysis for the weighted QR factorization by using the classical matrix equation method, the refined matrix equation method and the matrixvector equation method, and obtained the firstorder normwise  perturbation bounds with normwise perturbations.

Based on local convergence of neighborhoodfollowing algorithm, we investigated convex quadratic programming problem, and proved  linear programming neighborhoodfollowing algorithm has local quadratic convergence in the more general case (there is no need to assume that the problem is non-degenerate), and theoretically explained numerical convergence characteristics of the proposed algorithm.

By introducing a class of complex functions A and constructing convergent sequences on complex valued metric spaces, we proved that the limits of the given sequences are the unique fixed point of the mappings satisfying a Aimplicit contractive condition, and gave the existence theorems of common fixed points for two mappings satisfying a Aimplicit contractive condition on a nonempty set with two complex valued metrics.

By introducing the independent parameters, the method of applying the weight functions and HermiteHadamard’s inequality, we established a strengthened semi discrete HardyHilberttype inequality with a best constant factor, and gave its strengthened equivalent forms.

Let p,q be odd primes such that p>q, let G be a finite group of order p³q³ with extraspecial Sylow q-subgroups with order q³ and exponent q. Using local analysis of finite groups, through the analysis of the different actions among the subgroups, the author completely classified the group G, and obtained its whole struture.

Using the combined method, we investigated the treecoritivity of Cartesian products graphs of path and path, and path and cycle. In particular, we gave the exact value of treecoritivities for Cartesian products of path and path, and path and cycle, and characterized a relation between the treecoritivity of Cartesian product and that of its original graphs.

We obtained the generalized characteristic polynomial of two classes of composite graphs by using block matrix, the coronal of matrix and Schur complement, and then gave the adjacency, Laplacian, signless Laplacian and normalized Laplacian characteristic polynomial of these two classes of compo
site graphs, respectively. We extended the scope of generalized cospectral graphs by proving some generalized cospectral graphs.

Aiming at the mechanical centrifugal flywheel governor system, we studied the type of Hopf bifurcation and the stability of periodic solution by using the method of multiple scales. A nonlinear controller was designed to restrain the flutter caused by Hopf bifurcation. The nonlinear control gain could be determined to transform subcritical Hopf bifurcation into supercritical one and transform large amplitude of supercritical Hopf bifurcation into small
amplitude of supercritical one. The results of the theoretic analysis and numerical simulation show that the designed controller is valid.

By using the Rosenthal type moment inequalities of φmixing random variables, we considered the strong convergence properties of φmixing random variables arrays with different distributions under certain weight, and obtained some new results.

Let {X_n, n≥1} be a strictly stationary sequence of ρ^--mixing random variables. By using moment inequality and the central limit theorem of weighted sums, we obtained almost sure central limit theorem for product of some partial sums of ρ^--mixing sequences under general weights.

Using the method of partition, summation and rerecursion, we gave the counting formula of the perfect matching number for graphs 2-nRO₈ and 2-F_2n+1,4. Further, we used the method to calculate the number of all the perfect matching of many graph classes.

Using  improved Jacobi elliptic function method, we obtained  new  Jacobi elliptic function periodic solutions of Davey-Stewartson equation. The results show that some of these solutions can be degenerated into the corresponding soliton  solutions and triangular function solutions in the limit cases. This method can also be applied to solve the exact travelling wave solutions of other nonlinear evolution equations.

By using critical point theory and the generalized Nehari manifold method, we considered a class of periodic discrete nonlinear Schrdinger systems
and obtained the existence of infinitely many geometrically distinct solutions of the systems. Moreover, we used this method to obtain the multiplicity of solutions for single periodic discrete nonlinear Schrdinger equation.

Considering the quasiArmendariz property of the subring S_n(R) of n×n matrix ring M_n(R), the author proved that if R is a semiprime ring with compatible endomorphisms α₁,α₂,…,α_n, then S_n(R) is a quasiArmendariz ring for any positive integer n≥2, and that if R is a commutative ring and α₁,α₂,…,α_n are compatible endomorphisms of R such that α₁=α_n, then R is a semiprime ring if and only if Sn(R) is a quasiArmendariz ring.

Based on the extension of C language, we defined a new domainspecific programming language MISPC, which described the characteristics of mainstream scene in the field of multimedia and wireless network, and used BackusNaur form to describe the data type. In view of the language features, we proposed a compiling framework for heterogeneous platforms to produce highperformance source codes. The experimental results indicate the domainspecific language and its compiling framework significantly improve development efficiency of the domains, and achieve a maximum speedup of 5.59 times compared with corresponding program versions of different inputs. By defining the highlevel language and constructing the compiling framework, we provide domainspecific programming framework of system solution and technology to effectively decrease the programming and debugging difficulty, and increase development efficiency and application performance.

Based on subjective Bayes method, we predicted user trust relation in social networks. The method utilized the existing trust relationships and rating relationships between users, took a rating record from user to another user as evidence and calculated the quantity representation of “trust” and “distrust” by merging the evidences based on a rule set obtained by supervised learning, thus predicting and spreading the trust relationship among users by using multi-valued logic method. The comparative experimental result shows that the proposed method can solve the usertrustprediction problem in social networks with high accuracy.

In view of the problem that how to add the personalized information to the search result ranking, we proposed a method based on decision tree to quantify the user’s personalized information. According to the user’s search keywords and user’s personalized information, the method predicted the user’s search intention, and fused the predicted results in ranking results. It can effectively solve the defect of traditional retrieval model by adding user’s personalization information. The experimental results show that accuracy of the ranking results is significantly improved after adding the personalized information, thereby improving the user’s experience of the search engine.

We used the modified Shamir’s threshold recursive algorithm to construct a multisecret sharing model with hierarchical structure. We used a secret distribution algorithm to share a subsecret in each layer, and then achieved huge data storage with short secret shares. Furthermore, the proposed scheme employed a twovariable resistant collision Hash function, so that the participants could dynamically  join or exit. At the same time, any participant could verify the authenticity of other participants  by exposing the Hash values of secret shares. The results show that the secret sharing scheme is dynamic and verifiable, and can achieve unconditional security.

We proposed a Skyline query algorithm based on Rtree index in MapReduce parallel computing model, which solved the low execution efficiency problems of Skyline query in the massive spatial data sets. Through the establishment of Rtree index to realize spatial data of different size range pruning, the algorithm effectively reduced the size of the data required to scan the distributed Skyline query, and improved the execution efficiency of Skyline query in MapReduce model. Comparative tests in different data distribution shows the proposed method has more advantages on efficiency than the existing algorithms.

Aiming at the problem of high precision modelling of multi contour 3D stereo model, it was necessary to carry out the projection detection and separation to improve the image quality, because of the speckle and projection of the visual switching and attenuation of the light intensity, we proposed a projection detection algorithm based on the similarity characteristics of texture segmentation of multi contour 3D stereo vision images. Firstly, according to the known multi contour 3D model, the proposed algorithm made traversal modelling analysis for all the modelling point. Secondly, the model for modelling point
after traversal were reconstructed, and planar control basis functions with integral recursion polynomial were constructed. Finally, an improved  3D stereo vision image projection detection iterative equation was obtained by using the curve mixed function initialization detection model of multi contour image. We used similarity feature texture segmentation method to improve the projection detection of visual image, which solved the problem of inaccurate image projection detection. The simulation results show that the algorithm can effectively realize the separation of image projection detection, image retention is better, and improve the image quality.

A crossdomain dictionary learning algorithm was applied to the recognition of human actions. By introducing the auxiliary domain data set, the algorithm learned from the original training set (target domain) together with the dictionary to obtain the dictionary pair, and then obtain the sparse coding of the action class, and effectively expanded diversity of training set. The algorithm is a combination of learning framework of dictionary learing and training classification, which can be used to classify the reconstruction errors in the learning process. The experiment was carried out under the condition of MATLAB simulation. The UCF YouTube data sets were regarded as the original training set, and the HMDB51 data sets were regarded as an auxiliary domain data set. 7 coherent human actions of the two data sets were selected to do the work of recognition according to the flow chart of the proposed algorithm. The crossdomain dictionary learning algorithm was compared with another two kinds of human actions recognition algorithms. The results show that the recognition rate of the proposed algorithm is significantly improved. It is proved that the crossdomain dictionary learning algorithm is effective in human actions recognition.

Based on the localization technology and adjustable grid to improve the existing routing algorithm, we proposed an improved routing algorithm based on adjustable grid and crossregion transmission, and solved the problem of energy  imbalance and high energy consumption of perimeter stateless
 greedy routing algorithm in wireless sensor network. Using a localization algorithm of relative position of nodes, adjustable grid, greedy algorithm and right
hand rule, the algorithm established routing path of regional level  coarseness, and the network used different methods to transmit data according to the density of sensor nodes in different regions. Simulation experiment results show that the improved algorithm reduces the energy consumption of network  and extends the lifecycle of network.

Aiming at the unknown and dynamic path planning in complex scene, the traditional method could not solve the problem of path planning, we designed an improved shuffled frog leaping algorithm for robot path planning in order to improve the accuracy of path planning in dynamic environment. Firstly, we analyzed the research status of dynamic environment path planning, and established its mathematical model. Secondly, we used the shuffled frog leaping al
gorithm to solve the model, and improved the shortage of basic shuffled frog leaping algorithm. Finally, we tested effectiveness of the path planning  by simulation experiments. The results show that the proposed algorithm can accurately find the optimal path planning scenarios, and can be used in more complex scene path planning, and its performance is better than that of other path planning methods.

Aiming at the feature selection problem in image classification, we proposed a multiple feature selection and support vector machine for an image classification model. Firstly, we extracted a varity of features of the image and normalized the features. Secondly, we selected a set of optimal feature subset according to the average impact value of features. Finally, the multi classifier was built by using support vector machine, and the simulation experiments were carried out to verify the validity of the model by using image data set SIMPLIcity. The experimental results show that the proposed model can reduce the cost of image classification and improve the performance of image classification.

Aiming at the problem of information security of the uplink and downlink in the full duplex system, we proposed a secret rate balancing algorithm for both uplink and downlink full duplex communication links based on the design parameters with secure rate. The proposed algorithm could guarantee information security of uplink and downlink full duplex communication links by joint design of information beamforming vector and noise beamforming vector. Under the full duplex base station transmit power constraint, the security rate of the full duplex uplink and downlink communication link is greater than zero. Simulation results verify the effectiveness of the proposed algorithm.

We considered influences of quantum channels on robustness of multi\|body entanglement. Firstly, we proved that the infimum in the definition of the robustness of entanglement (RoE) could be attained based on the fact that the set of all separable states was a convex closed set. Secondly, we proved that a convex combination of two different optimal states of the same entanglement state ρ was still the optimal state, and the RoE was a lower semicontinuous function on the set of all quantum states. Finally, we gave  necessary and sufficient conditions for the RoE of a quantum channel, which did not increase, did not reduce and maintained all quantum states.

CdSe nanorods arrays were grown on ITO substrate by electrochemical deposition method at room temperature. Using Xray diffraction (XRD), energy dispersive Xray (EDX), field emission scanning electron microscopy (FESEM) and UVVis absorption spectroscopy, we characterized the CdSe nanorods
array, and studied its photoelectric chemical properties. We tested the photoelectric properties of CdSe nanorods array electrodes under the standard three electrode system. The results show that the sample is preferentially grown along \[001\] direction, and has obvious light response properties. When the light intensity is 100 mW/cm², the optical current density (J_sc), open circuit voltage (V_oc), the fill factor (FF) are 2.93 mA/cm², 116 V, 0278, and the photoelectric conversion efficiency of the battery η=0.947%.

Using magnetron sputtering technique, VC thin films were prepared by changing the substrate bias at room temperature. We investigated the effect of substrate bias on the crystal structure, hardness and friction properties of VC thin films, and established the intrinsic relationship between them. The
 results show that with the increase of substrate bias, the grain is refined,  the hardness and wear resistance of films are increased, and the change of the friction coefficient is slight.

Using SBA15 as carrier and tetrabutyl titanate as titanium source, the SBA15 molecular sieve loaded with TiO₂ was prepared by solgel method. The different mass concentrations of lanthanum nitrate were loaded onto TiO₂-SBA-15 by impregnation method, and TiO₂-SDA-15 catalysts with different lanthanum loading were prepared by high temperature calcination method. The series of catalysts were characterized by X-ray diffraction (XRD), infrared spectrum (FTIR), inductively coupled plasma (ICP) emission spectrum, transmission electron microscopy (TEM) and N₂ adsorptiondesorption isotherm. The TiO₂-SBA-15 catalysts with different La mass contents were used as photocatalysts to degrade the solution of methyl orange. We investigated the effect of La loading mass content on the degradation rate of methyl orange. The experimental results show that the degradation rate of methyl orange is 100% when La loading mass content is 0.14% and UV lamp irradiation for 140 min.

We investigated chiral transition mechanism of α-Ala molecule under complex environment of singlewalled carbon nanotubes and water based on amidogen as H transfer bridge by using the method of quantum chemistry ONIOM. The results show that there are two shift reaction channels a and b based on amidogen as a bridge of hydrogen transfer process in chiral transformation. The channel a is the most advantage way. Armchair SWCNT/water complex environment provide a preferable catalytic effect for hydrogen transfer reaction. Under the confined environment of SWCNT(8,8), compared with the primary reaction, the rate determining step energy barrier drops from 266.1 kJ/mol of naked reaction to 117.8 kJ/mol using chain of three water molecules. Thus the SWCNT (8,8)/water complex can used as an ideal nano reactor of implementation α-Ala chiral shift, and α-Ala molecule will also make this optical isomerism reacion reality in a similar nano environment in organisms.

Using density functional theory at the level of B3LYP/6-311+G(2df), we investigated the chiral transition process of the nonrestricted area monomer asparagine molecule. We drawed a complete asparagine molecule chiral transition path reaction potential energy surface by finding stuctures of the extreme value points of recation process of transition states and intermediates, and analyzed the geometric and electronic structure characteristics of extreme value points. The results show that the hydrogen atom on the chiral carbon atom of Sasparagine molecule can transfer to the other side of the carbon atom via the oxygen atoms of carboxyl atoms as a bridge, and achieve the chiral transition of asparagine molecule from S-type to R-type. On this path there are four intermediate and five transition states. The maximum reaction energy barrier is 316.372 8 kJ/mol, which comes from the fourth transition states TS-_2-R-Asn.

Based on the method of mechanochemistry and density functional theory (DFT), we calculated the bond order and dissociation energy of all the C—Cl bonds in the structure of dechlorane plus (DP) with Al and quartz sand as additives. We speculated the possible dechlorination position, and gave the main degradation pathway of DP.

Using microwave digestiongraphite furnace atomic absorption spectrometry (GFAAS), we determined the mass ratio of Pb,Cu,Ni and Mn in four kinds of traditional Chinese medicines (Psychotria rubra, Spotted ardisia, Caulis et folium schefflerae arboricolae, acanthopanax senticosus), selected and optimized matrix modifier, ashing temperature and atomization temperature. Under the selected experimental conditions, we used standard curve method to analyze the mass ratio of Pb,Cu,Ni and Mn in traditional Chinese medicines. Experimental results show that the standard curves of four kinds of heavy metal elements have good linear relationship (r>0.999). The average recovery rates are 94.6%—103.4%.

Using rabbit polyclonal antibody against SA11 as the primary antibody and Alexa488 labeled the goat antirabbit antibody as the secondary antibody, we established an indirect immunofluorescence assay (IFA) for detection of Rotavirus （RV） through the optimization of reaction conditions. Experimental results show that the optimum conditions of IFA are as follows: the best density of MA104 cells is 2×104 cells per well, the best mass concentration of trypsin activation rotavirus is 1 μg/mL, the best time of incubate Rotavirus is 18 h, and the optimum working dilutions of the rabbit polyclonal antibody against SA11 and Alexa488 labeled the goat antirabbit antibody are 1∶800 and 1∶500, respectively.