We gave the equivalent canonical form of a upper triangular matrix over a field. As applications, we proved that a upper triangular rankr matrix could be decomposed into a sum of finitely many upper triangular ranks matrices; we also proved that each ideal of the ring of all upper triangular matrices over a field was a principal ideal, which was generated by a unique reduced canonical upper triangular matrix.

Let H be an infinitedimensional complex Hilbert space and B( H ) be the algebra of all bounded linear operators on H. We gave various characterizations of core partial order and dual core partial order. Then, using the method of operator block matrices, we gave the relationships between the core partial order, or the dual core partial order and minus partial order. Furthermore, we present the infimum A∧B of  A and B with respect to given orders.

Using the language of cogroupoids, we gave the relation between the global dimension of a Hopf algebra and the Hochschild dimensions of its HopfGalois objects. It is shown that the Hochschild dimensions of HopfGalois objects of H are at most d if H is a Hopf algebra with global dimension d.

A SIQRS epidemic model with saturating contact rate, isolation term and impulsive vaccination was established and analyzed. By means of Floquet theorem, impulsive differential inequality and limit system theory, the global asymptotic stable threshold conditions of diseasefree periodic solution in the SIQRS epidemic model were obtained. Comparing the effectiveness of the two control strategies of impulsive vaccination and isolation shows that using the two strategies concurrently is superior to only one strategy for eradicating the disease.

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Using the comparison of energy and constructing selfsimilar supersolutions, the author studied the homogeneous Neumann exterior problem of a coupled reactionconvectiondiffusion system with singular coefficients.The critical Fujita curve, which described whether solutions exist globally or not, was determined and the blowing up theorem of Fujita type was established. This critical Fujita curve depends on the spacial dimension, convection and reaction terms of the system.

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Three concepts of Novikov color algebra, Tortken color algebra and Jordan color algebra were defined, then the relations among three algebras were discussed. We gave the basic properties of Novikov color algebra and Tortken color algebra. Then we proved a Tortken color algebra with an identity
element is both associative and color commutative. We also showed how to use Novikov color algebra to construct a Tortken color algebra.

The author discussed the reducibility or semisimpleness of Doi Hom-Hopf modules. Given a Doi HomHopf datum (H,A,C), the forgetful functor was used to send the objects in the category M^C_A of Doi Hom-Hopf modules into the category M_A of right (A,β)-Hom-modules, and look for a deformation of a splitting map of a monomorphism in the category M_A so as to lead to the integral for Doi HomHopf datum (H,A,C). With the
 help of the integral introduced, the author  proved the Maschketype theorem for Doi Hom-Hopf modules. As an application, the author defined the category of Hom-Yetter-Drinfeld modules and  proved the category of HomYetterDrinfeld modules being a subcategory of our category of Doi HomHopf modules, then the author  obtained immediately the version of Maschke type theorem for Hom-Yetter-Drinfeld modules.

In order to further study DFIalgebra, firstly, the definition of a distance function in DFIalgebra was given. Its properties were discussed, and some special properties of the distance function of some kinds of special DFIalgebras, for example, linear DFIalgebras were given. Secondly, a new operation was introduced in DFIalgebra, and the equivalent definition of the distance function of DFIalgebras and some farther properties were given; finally, the corresponding metric space based on the distance function was introduced.

We gave the new concept of antisoft subinclines, and studied the relationship between antisoft subinclines and the antidual of soft sets and got some equivalent characterizations. Then we discussed some properties of the two operations ‘restricted union’ and ‘or’ on it. Using the antiextension principle, we obtained the properties of their antiimage and inverse image. Finally, we introduced the chain condition of H which consisted of all of the antisoft subinclines and gave a necessary and sufficient condition for H was Artinian or Noetherian.

Adding suspension points to those trees having setordered graceful labellings two times, and then using a split approach, we proved that a class of the super lobster trees S(P_2m) were strongly graceful tree, where m is an arbitrary positive integer. This method is called the suspensionsplit method.

Using the method of roundoff error analysis and the characteristics of computerfloatingpoint operation, we constructed a new kind of encryption and decryption algorithm based on rotation matrix. Then we proposed sufficient conditions for the validity of the algorithm. Finally, we used some numerical examples to verify the feasibility of the algorithm.

A class of disturbed system of nonlinear developed equation was studied via a specific undetermined functions and functional mapping methods. Firstly, using a travelling wave transform, we converted the developed equation into nonlinear differential equation, and obtained the solitary solution of a corresponding nondisturbed differential system via a set of undetermined functions. And then, the asymptotic solitary travelling wave solution for an original disturbed system of nonlinear developed equation was obtained by using the functional mapping iterative relational expressions.

This paper deals with large time behavior of solutions to multidimensional nonlinear heat equation. Using the prior estimation and constructing an approximate Green function, we proved that the planar diffusion wave was nonlinearly stable for the nonlinear heat equation. Besides, the optimal time decay rates are established.

We gave a new integervalued time series model, which could describe both the strong correlation data and the weak correlation data. We gave a sufficient condition for stability of the model, and studied the problem of the maximum likelihood estimation and the asymptotic properties of the estimator.

Using stochastic differential equation and Monte Carlo simulation, we established and verified a stock price model with Poisson jumps when the volatility obeyed CIR process. The price formula of stock was given and we also computed the mean and variance of stock yield. Numerical result indicates that the model can better reflect the characteristics of high kurtosis and fat tail of stock yields distribution.

We used the empirical likelihood method to obtain estimators of the population parameters and cumulative distribution function (CDF) for measurement error model with multiple populations. Our estimator of CDF is asymptotically unbiased and utilizes all the available sample information. Then we
applied the empirical likelihood to the NS sampling model and obtained the efficient estimation of the common mean and CDF. Simulation study further demonstrates the good properties of our estimators.

The author obtains  the existence of solutions for a class of onedimensional nonconvex variational problems with thirdorder Lagrangian functions by using the integral minimax methods.

The author gave a class of composite vector valued invariant invex function, and applied it to the nonsmooth multiobjective programming problem. The author established a general Craven type of duality and proved weak, strong and converse duality theorems under the nonsmooth composite multiobjective programming.

We studied the totally real pseudoumbilical submanifolds in quasicomplex projective space by means of the method of moving frams. Based  on the Stokes theorem and the Lapalacian of the square of the length of the second fundamental form, an integral inequality and a instrinsic rigidity theorem were obtained, which makes the study of the totally real pseudoumbilical submanifolds extend from the complex projective to the quasicomplex projective.

Using Sobolev embedding theorem, Lusin theorem and Egoroff theorem, we proved nonexistence of solutions to singular elliptic problems. At the same time, we also obtained a sufficient and necessary condition of existence of finite energy solutions.

This paper dealt with the uniqueness of positive stationary solutions for Sel’kov model with Neumann boundary conditions. Firstly, we  established a new integral identity, which proved that there was only one positive solution to the problem for 0<p≤1. Secondly, we discussed the uniqueness of positive solutions for the problem with p>1 by means of a priori estimate technique.

Based on the tree decomposition backtracking search algorithm, combined with the separator decomposition operator, we proposed a new search algorithm BTD⁺-MAC. The algorithm first selected the variables in separator to carry on the consistency checks and instantiation during search, so the efficiency of constraint propagation could be improved by reducing the width of the tree and further improved the efficiency of solving problems. We tested several sets of benchmark problems. The results show that the algorithm is more efficient than the MAC3rm and BTD-MAC algorithm in solving the problem.

The author proposed an iterative algorithm for complex linear equations of   symmetric positive definite sparse matrices based on GPU. First, the author used the conjugate gradient method and double conjugate gradient algorithm based on GPU to achieve  the operation of matrix vector multiplication, and  optimized the corresponding algorithm steps fully. Second, in order to realize the 3 pretreatment methods, which were  diagonal element preprocessing step based on GPU, incomplete Cholesky decomposition and symmetric super relaxation, the author proposed  a parallel algorithm for solving triangular systems based on GPU. Finally, the advantage and disadvantage of various pretreatment methods were analyzed through experiments. The experimental results show that the speed of the algorithm is higher than the  CPU serial iterative algorithm and the classical direct method, and the maximum speed is up to 76 times faster than that of two methods.

Aiming at the problem of structural damage identification, we proposed an intelligent algorithm for structural damage identification based on multiobjective optimization strategy. The algorithm used the extreme learning machine as the damage parameter index, and established the nonlinear function expression between damage parameters and every frequency. We first had the structure of the actual structural frequency  minus the function expression, and then took the formation of each expression as a optimization objective to obtain a highdimension multiobjective optimization model based on structural damage identification. In order to improve the solution accuracy of the model, we proposed a grey multi particle swarm coevolutionary algorithm for multi-objective optimization. The experimental results show that these methods can deal with the problem of structural damage identification.

Aiming at the problem of network intrusion feature optimization, we proposed a network intrusion detection model based on hybrid particle swarm optimization algorithm selecting features to improve the network intrusion detection rate. Firstly, we took the detection rate of network intrusion as
the objective function for feature selection, and the network state features as the constraint conditions to establish the corresponding mathematical model. Secondly, we used the hybrid particle swarm optimization algorithm to find the optimal feature subset. Finally, we took support vector machine as classifier to build intrusion detection model, and carried out the verification experiment by using KDD1999 data on MATLAB2012 platform. The results show that the model can efficiently query the optimal features subset, and intrusion detection rate and efficiency are better than the classical intrusion detection model.

Aiming at the problem of the abnormal change of the related parameters in the mathematical model of neuron, we first made a real time estimation of these key parameters by unscented Kalman filter (UKF), and then took these parameters as feedback signal of the controller to complete closed loop control of the neuron discharge. With this method, the MATLAB simulation was carried out for the abnormal discharge caused by the key parameters (the conductance
between cell bodies and dendrites gc, and the stimulated currents of dendrites Ic) of PinskyRinzel （PR）neuron, and the control of abnormal discharge caused by single parameter and two parameters were achieved respectively. The experimental results show the proposed method is effective.

For the global image feature could not describe the image category information, we proposed an image feature retrieval method based on interest points features. Firstly, we converted the image to affine scale invariant feature, and used the probability density gradient to extract the interest point. Secondly, we mapped these interest points back to the orginal image, and used the color histogram as the image feature. Finally, we used similarity measure model to realize image retrieval, and selected the image of the Corel image database to analyze the performance of the algorithm. The experimental results show that this method can effectively improve the accuracy and efficiency of image retrieval, and quickly find the user need image.

In view of the relevant data of 100 ECommerce demonstration enterprises in China, we first used factor analysis method to reduce the dimension of high dimensional data, then we processed the uneven density data of reduced dimension by using improved DBSCAN (densitybased spatial clustering of applications with noise) algorithm, and obtained more reasonable clustering results. Finally, according to the clustering results, we put forward some suggestions to the relevant enterprises.

We proposed an improved shuffled frog leaping algorithm based on cellular automaton theory. In the algorithm, the cellular automaton was embedded into the shuffled frog leaping algorithm to improve the grouping strategy. We used cloud model and chaos theory to improve the individual update mode, and used dynamic characteristics of biological evolution to simulate the evolution rules. Simulation results of the six kinds of basic test functions show that the algorithm has better convergence precision and computing speed, and it is suitable for multi peak function optimization.

Aiming at the problems of high time complexity and low accuracy of traditional medical image segmentation algorithm, we proposed a segmentation algorithm based on onedimensional Otsu automatic multiple threshold. Taking into account the complexity of medical image information, we introduced a
 comprehensive information histogram based on gradient, gray scale and distance to replace the traditional gray histogram, and gave the corresponding weights of the 3 information respectively. Kdtree was used as a framework to quickly determine the number of threshold automatically, and then to realize the automatic threshold segmentation of medical images by Otsu. Compared with the maximum entropy and Otsu based on particle swarm optimization algorithm, experimental results show that the segmentation performance of the proposed algorithm is superior to other algorithms.

In view of the disadvantages of the classic Apriori algorithm with multiple scan the database and generation of redundant candidate, we proposed an improved VMApriori algorithm. The algorithm combined with transaction data vector matrix and row candidate vectors representation method. We used
 quick sort of frequent item sets by individual frequency ascending rearrangement to enhance the efficiency of the algorithm. The experimental results show that the improved VMApriori algorithm can mining association rules correctly, and greatly improve the efficiency of execution.

Based on the research of homogeneous academic network and citation network optimal\|path, we proposed a heterogeneous network optimal-path
algorithm and two evaluation indexes of the importance of path, and solved the problem that homogeneous network optimal\|path algorithm could not be applied to the real academic network. Taking the transfer learning domain data from Microsoft as dataset, we verified the correctness in heterogen
eous academic network optimal\|path detection of important literatures and their similarity in transfer learning domain and the development of transfer learning. The experimental result shows that the algorithm and indexes are more consistent with the real academic network.

Based on the matrix theory, combined with active control method, we designed a suitable controller. Controller applied to the different systems by changing switches, the switching synchronization between new fractionalorder hyperchaotic system and fractionalorder hyperchaotic Lorenz system was realized. Applying frequency domain approximation method based on Bode diagram, we designed synchronization circuits of fractionalorder hyperchaotic systems. The results of circuit simulation further verify the correctness of theoretical analysis and numerical simulation.

We considered the problem of chaos synchronization of a class of fractional order DufflingVan der pol systems, and gave two sufficient conditions for the synchronization of the system based on Lyapunov stability theory. The results show that systems obtain chaos synchronization under appropriate controlling law.

Using the first principles method, the author studied the crystal structure, electronic properties and superconductivity of Li₃S and Li₂S at 0—50 GPa. The results show that Li₃S can be synthesized at pressure above 16 GPa from Li₂S+Li, and the high pressure phase transition sequence of Li₃S is
 P6₃/m→P6₃/mmc→Pm-3m. Li₃S is metallic, but the electronphonon interaction in Li₃S is very weak indicating Li₃S is not a superconductor. The predicted high pressure phase transition sequence of Li₂S is in agreement with the existing results. Li2S is still not metallization at 50 GPa.

Vanadium carbide (VC) nano thin films were deposited by magnetron sputtering technology. We investigated the effect of deposition temperature on the microstructure, mechanical and tribological properties of VC thin films, and analyzed their intrinsic relationship. Results show that the increase of deposition temperature has little effect on the phase structure and friction coefficient of VC thin films. However, it is beneficial to reduce the stress and roughness of the film, which can improve the hardness of the film.

Adding 4,4′-(phenylazanediyl)dibenzoic acid (H₂L) ligand and cadmium(Ⅱ) ions to 1,4-bis-(imidazol-1-yl)benzene (bimb) and 1,4-bis(pyridine-4-ylmethoxy)benzene (bpmb), we synthesized two new types of metal cadmium organicinorganic coordination polymers {［CdL(bimb)_0.5］·2H₂O}_n(1) and ［Cd(HL)2(bpmb)_0.5］_n(2) under the hydrothermal conditions. We determined the structure of the two polymers by means of XRD, and characterized their structures with the help of elemental analysis, IR spectroscopy, TG and powder Xray diffraction(PXRD). The fluorescence properties of two kinds of coordination polymers were tested at room temperature. The experimental results show that coordination polymer 1 crystallizes in the triclinic space group P1, and its framework is a twodimensional layered structure. Coordination polymer 2 crystallizes in the monoclinic space group C2/c, and it’s a threedimensional supramolecular polymer formed by the Hbond of onedimensional zigzag chains.

Using Ni(NO₃)₂·6H₂O and FeCl₃·6H₂O mixed hydrothermal method, we synthesized nanometer NiFe₂O₄ powders, and characterized the samples by X-ray diffraction (XRD) and transmission electron microscopy (TEM). Meanwhile, in order to evaluate the stability of product, we tested the samples for charge and discharge cycle. The experimental results show that the nanometer NiFe₂O₄ power is spherical quasi\|crystal structure, high degree of crystallinity, crystalline intact and uniform particle size distribution; the 1st,30th,50th,70th specific capacity of the charge and discharge are （997,1 019）,(726,750.2),(560.9,578.4),(514.8,528.2)(mA·h)/g, which show that NiFe₂O₄ has good electrochemical stability.

Using synthetic biology and metabolic engineering techniques, we screened and cloned 5 key enzyme gene atoB,hbd,crt,adhE2 and ter with relatively high activity in butanol synthesis pathway. Firstly, we constructed the pUC18-atoB-hbd-crt-ter plasmid by recombinant PCR, and then coloned tandem gene atoB-hbd-crt-ter and gene adhE2 into the plasmid pET21b and eventually constructed the expression vector of pET-21b-atoB-hbd-crt-ter-adhE2 containing butanol synthesis pathway, and transferred it into E.coli BL21 (DE3) for the preparation of engineering strains. We performed IPTG induced expression detection and gas chromatograph (GC) analysis of samples. The results show that key enzyme proteins have been synthesized and produced a certain amount of butanol.

Genomic DNA was extracted from peripheral blood of 91 patients with myeloproliferative neoplasms (MPNs) and 1 028 healthy volunteers (both Chinese). Using allele specific PCR (ASP) technique, we detected the genotype of rs12343867 and rs10974944 loci of the JAK2 haplotype 46/1 as protein tyrosine
 kinase. And combined with clinical data, we used SNPstats software for statistical analysis. Experimental results show that the probability of JAK2 haplotype 46/1 in MPNs patients was significantly higher than that in healthy volunteers (P<0.000 1); MPNs patients with JAK2 haplotype 46/1 are more likely to appear in the JAK2V617F mutation positive MPNs patients (n=70, P<0.000 1); the risk of MPNs in the Chinese population with JAK2 haplotype 46/1 is significantly increased, which is consistent with the results of the test in Europe and the United States.