The linear maps preserving numerical range of linear operators were considered, and under certain conditions, the forms of linear maps  preserving q numerical range on block diagonal matrices, block upper triangular matrices, and general block matrices were given, respectively.

The auhtors presented an asymptotic procedure for the computation of wave fields in twodimensional inhomogeneous media. It is based on the simulation of the wave field by a system of Lagrangian Gaussian beams (LGB). Each beam is continued independently through an arbitrary inhomogeneous structure. The complete wave field is then obtained as an integral superposition of all Gaussian beams. Numerical results  presented verify the efficiency of our method.

An optimization method was used to calculate the periodic solutions of delay differential equations. The method transforms the computation of periodic solutions of delayed differential equation into an optimization problem with constraints. Using the optimization method, we can get the periodic solutions. Numerically, we proposed a method to get approximately the initial function via function fitting methods, and further used Newton’s method and penalty function method to locate the periodic solutions. Numerical experiments verify the effectiveness and efficiency of the proposed algorithm.

We investigated the rings with  semicommutative endomorphisms, referred to as the α-sc ring, by means of introducing the notion of semicommutative endomorphisms. A endomorphism α of a ring R is called semicommutative if α(a)b=0 implies  aRα(b)=0 for any a,b∈R.  We discussed the relations between αsc rings  and related rings  and present some extensions of αsc rings. It is proved
 that: 1) if α is a endomorphism of a reduced ring R, then R is αsc if and only if R［x］/〈xⁿ〉 is α-sc, where 〈xⁿ〉is the ideal by xⁿ generated in R and n is any positive integer;  2) if α is an automorphism of R, R is a symmetric right Ore ring, then R is αsc if and only if the classical right quotient ring Q(R) of R is α-sc.

We introduced the notion of nil powerserieswise McCoy rings and gave the corresponding examples. It was proved that the n×n matrix rings over reduced rings is not nil powerserieswise McCoy rings. Moreover, we investigated the extensions of nil powerserieswise McCoy rings. It was shown
 that the direct product of nil powerserieswise McCoy rings is nil powerserieswise McCoy rings.

Using the Mpembedding properties of some primary subgroup of Fitting subgroup and generalized Fitting subgroup to study the structure of finite groups, we obtained some sufficient conditions of supersolvable groups. At the same time, it was found that Mpembedding properties of subgroups have important influence on the structure of finite groups.

Analyzing the order of the group consisting of group\|like elements of a semisimple Hopf algebra, the authors obtained the structures of semisimple Hopf algebras of dimension pq³ over an algebraically closed field of characteristic 0: they are either semisolvable, or isomorphic to a Radford biproduR#A, where p,q are prime numbers to meet the needs of  p>q ², A is a semisimple Hopf algebra of dimension q ³, R is a semisimple Yetter-Drinfeld Hopf algebra in of dimension p.

We applied the automorphisms of Lie algebras to classifying the threedimensional Gel’fandDorfman bialgebras.

With the help of moving frams and Bochner skills, we discussed the totally real submanifolds with constant mean curvature in a complex projective space and obtained some Pinching results.

Using the singular value decomposition (SVD) and quotient singular value decomposition (QSVD) of a matrix and matrix pair, the authors established the necessary and sufficient conditions for the existence of the generalized reflexive solutions and the expressions for the inverse generalized eigenvalue problem of a matrix under a submatrix constraint. Moreover, the optimal approximation problem to a given matrix in the solution set was considered, and the optimal approximation generalized reflexive solution was obtained, and the perturbation analysis was made.

A leastsquares method was proposed for grating diffraction. Based on the partition of the computational domain, the local property of the solution is approximated by plane wave functions, and the property of the solution toward infinite is represented by a truncation of the Rayleigh expansion.
 The method with a fast convergence rate is easy to apply and needs few elements. It is appropriate to normal diffraction gratings and the cases with large wave number. Numerical examples show the effectiveness of the approach.

This paper deals with the extinction properties of solutions to a class of fast diffusion equations coupled with localized sources. Analyzing the effect of the diffusion term and the source term on the extinction properties of solutions and constructing some proper sub and supersolutions, the authors obtained the critical extinction exponents of the problem. The results show that when the exponent of the source term is suitably large any solution of the problem vanishes in finite time for appropriately small initial data, while the maximal solution will not vanish at any finite time provided that the exponent of the source term is suitably small.

We discussed the existence and multiplicity of the positive solutions of the following Neumann boundary value problems({u″(t)+a(t)u′(t)+b(t)u(t)+ f(t,u(t))=0,t∈(0,1),u′(0)=u′(1)=0,)where a∈C［0,1］, b∈C(［0,1］, (-∞,0)), f∈C(［0,1］×［0,+∞), ［0,+∞))  using fixed point theorem on cones and the LeggettWilliams fixedpoint theorem.

We discussed the solution of complete singular integral equation with Cauchy and convolution kernels and  variable limit. Based on  the Fourier transform and the theory of Riemann boundary value problem and Fredholm integral equation, the equation was transfered to the equivalent Fredholm integral equation in {{0}} undering some conditions. Then  solving the equivalent Fredholm integral equation, we got solvable conditions and general solution on the equation  discussed in {{0}}.

Most existing approximate methods for solving generalized D.C.programming problems may sometimes provide an infeasible solution, or a solution far from the true optimum. To overcome these limitations, a nonisolated global optimal solution algorithm was proposed for solving generalized D.C.programming problem. Numerical results show the effectiveness of this method.

The homotopy method was used to solve the linear complementarity problem LCP(M,q), the relationship between the existence of a solution of the semimonotone nonhomogeneous complementarity problem and the uniqueness of the solution of the homogeneous complementarity problem LCP(M,0) was given. And an existence condition of a solution of the problem was also obtained when the strictly feasible condition held.

A nonlinear weak separation function and a nonlinear regular weak separation function were first introduced by virtue of a nonlinear scalarization function. Then image space analysis approach was applied to the discussion of vector optimization problem with constraints.

The authors proposed a combined homotopy interior point algorithm to solve a class of unbounded nonconvex optimization problems. Under suitable conditions, we obtained the existence of the homotopy path. By tracking this homotopy path, we can get a K-K-T point of the nonconvex optimization problem. The results provide an efficient globally convergent algorithm for the nonconvex unbounded optimization problems.

The authors studied blowup properties of solutions to a polytropic filtration equation with variable exponent of nonlinearity. By constructing a suitable control function, applying energy estimates method and Gronwall’s inequalities, we proved that the solution of the above problem blows up in finite time when the initial energy is positive.

Authors discussed the stochastic SIQS epidemic system with environmental white noise. When the basic reproduction number was not more than 1, we gave the asymptotic behavior of the stochastic system around the diseasefree equilibrium point of the deterministic model by stochastic Lyapunov analysis method. The result shows that the disease will die out when the white noises are small. When the basic reproduction number is more than 1, it is shown that
 there is a stationary distribution based on the Hasminskii’s ergodic theory and it is ergodic, which reveals that the disease will prevail under some conditions.

Let {X_n,n≥1} be an identically distributed NOD random sequence or a strict stationary sequence of m dependent random variables, and f(x) is a probability density function of random variable X₁. Based on NOD samples or m dependent samples, under suitable conditions the kernel estimator for density function f(x) was investigated, and the pointwise strong consistency, the consistency in r order mean and uniform consistency in L₁ were obtained via Fourier transform, the related properties for NOD random sequences and the exponential inequality.

We proved that the existence of antiperiodic extremal solutions when the mutilfuction G(t,x) takes a bounded, weakly compact, convex value, and is measurable about variable t, and continuous about variable x, using the Tolstonogov extremal continuous selection theorem and the Schauder fixed point theory.

We proposed the maximum likelihood method to estimate the parameters in a special timevarying parameter autoregression model (TVPAR(p) model). The maximum likelihood estimate results of all the unknown parameters were given.The stability of the TVPAR model was discussed. Simulation was used to illustrate the proposed estimation method.

The authors mainly discussed the certification of the square structure matrix with rank deficiency one. For a square structure matrix M, it is given an algorithm which outputs an interval squarematrix M(E) with the same algebraic structure such that M(E) contains a structure matrix M(ε^)with rank deficiency one, where each element of M(E) is a small interval perturbation of the corresponding element of M.

Through the discussing  the necessary characteristics that fractal dimension should possess, we drew the stretching criterion and local criterion on fractal dimension, which are a universal standard for the characterization of dimension. We also analysed the normal dimension with accuracy, and proved that
 the dimension satisfies both stretching and local criterions.

We built 12intersection matrix model which appropriately represents these topological relations, and gave the relevantly restricted conditions, showed that there are at most 53 possible topological relations between the region with holes of mutual inclusion and a simple region by programs. Furthermore, we checked up that all these 53 topological relations are possible. We proved that these topological relations are exclusive and complete.

This paper describes the design of a fast index for distributed storage of forestry resource data. According to the load data request of a large number of independent data nodes to reduce the mutual exclusion during data access, parallel access was realized for distributed storage of spatial and attributive data. Based on the common application server cluster, this fast index can be used by making the minor modifications of data access process so as to improve the performance of statistics and update of the whole data cluster with low cost.

Aiming at the semi\|structured characteristics of XML document and the traditional tf\|idf method only considering the frequency of keyword in the document, not considering the lack of semantic information of the nodes in the XML document, we designed the relevance ranking strategies that were designed based on XML keyword searching results via the vector space model. To improve the accuracy of the measure of the node weights, correlation calculation fully considers the distinctive degree of the nodes in the XML document, the clear and direct degree of nodes describing the document so as to provide the most relevant information to users. Experimental results show that the proposed method is effective.

Based on the analysis of virtual reality\|oriented hydraulic turbine system, the problem of time delay in conventional collision of various hydraulic structures under different working conditions was solved by using the method of decomposing collision bounding box. Particle boundary computation was conducted by the method of polygonal boundary construction to realize the collision between particle system and hydraulic structure, which produces a verisimilar effect of flow rebound. Decomposition of bounding box through surface reconstruction and collision test of particle boundary structure were carried out on hydraulic turbine blades, and a proper equilibrium point between running speed and fidelity was found out through tests. The simulated effect of the stable operation of hydraulic turbine underwater was realized.

A daily behavior recognition algorithm based on spectral clustering algorithm and hidden Markov model was proposed by utilizing sensor data of smart phones. After the acceleration, GPS and RSSI data were obtained, our method combined spectral clustering algorithm with hidden Markov model can automatically and effectively identify user behavior. Experimental results show that the proposed method achieved higher recognition accuracy from the reality data.

Since in the application of digit data index, establishing index needs a long time, B+ tree was applied to the index. The storage model was established based on B+ tree, then B+ tree node was stored in the storage medium with the help of the storage bitmap. Through the index storage, the data can be read according to the path when B+ tree is used. The time of building index is thus saved, and the stability of B+ tree is improved. The results of experiment show the theory of B+ tree can be applied to digit books data and indexing speed is greatly improved in accessing to key information.

A scheme for controlling hyperchaos in the RCLSJJ array is presented by applying periodic perturbations to the external bias current. Numerical investigations show that this scheme can be effectively used to control hyperchaos states in this array and to make them enter into stable periodic states. And the different stable period states with different period numbers can be obtained by appropriately adjusting the amplitude and frequency of the
 perturbation signal. Moreover, the inphase states were discussed in the controlled array system.

FePt thin films of different thicknesses were prepared by magnetron sputtering on thermally oxidized Si substrates and annealed at 600 ℃ for 1 h in hydr
ogen to obtain L1₀-FePt films. The results of Xray diffraction show that L1₀-FePt films have a (001) texture or obvious growth in (001) orientation. The grain size of FePt and the degree of ordering increase, and (001) orientation decreases with the increased deposition thickness. Magnetic data exhibit
the inplane coercivity increases, while the outofplane coercivity first increases and then decreases with the increased film thickness. When the film thickness is 10 nm, the sample has the most perpendicular magnetic anisotropy.

The nanocrystal ε-Fe₃N thin films were deposited at a N₂ pressure of 10% by DC magnetron sputtering. The films were annealed at different temperatures of 500,600,700,800 ℃ in vaccum. The structure and magnetic properties of the films were characterized via an Xray diffractometer (XRD) and vibrating sample magnetometer (VSM). The results show that the structures of ε-Fe₃N films were still stable under the annealing temperature of 600 ℃. The saturation magnetization (M_s) of the films  did not change significantly. The coercivity of the films decreased at first and then increased. The soft magnetic properties were the most optimal when the ε-Fe₃N films were heattreated at 500 ℃.

The wave equation of light and the differential equation, which describes the amplitude of electric or magnetic field vectors when the ray of light is “moving” in the medium with varying refractive index, were derived by the Maxwell’s equations. The differential equation shows that transformation from “wave” in the view of wave optics to “line” in the view of geometrical optics is a conditional change of physical character. It is also shown that both therepresentations of the concept of wave and method of simple harmonic vibration or concept of light ray and method of geometry,  are opposite but actually are unified, i.e, reaching the same goal of comprehensive understanding on the propagation characteristics of light by different means.

Si/C composite anode material was successfully fabricated by electrospinning with PAN as macromolecule polymer collocation and carbon source. Decomposition process of the precursor was investigated by thermal gravimetric analysis (TG), and the structure and morphology of the asprepared samples were characterized by Xray diffraction (XRD), Raman spectrum and scanning electron microscope (SEM). The result shows that Si/C composite anode material is nanofiber structure. The fiber diameter is about 350 nm with distributing interlaced mesh. PAN decomposition products are mostly amorphous carbon at a high temperature. The electrochemical test results demonstrate that battery discharge capacities are respectively 735.6,712.1,685.4,492.3 and 367.9 mA·h/g at 0.1,0.2,0.5,1.0 and 2.0 C, and this material has very excellent rate performance.

The electronic properties of boron nitridegraphene hybrid single atomic layers were investigated with the help of the first principle based on density functional theory. The calculation results show that midgap states will be induced in the band structures when the triangular h-BN or triangular graphene is embedded in graphene or h-BN. The midgap states are closely related with the configuration of hybrid nanostructures, and these hybrid nanostructures produce the semiconducting  conducting transition. Hence, the electronic structures can be tuned by controlling the hybrid ways.

The grapheneAuNPs hybrid was achieved with sodium citrate as a reductant and stabilizer and was functionalized by carboxyl group. DNA was successfully bound to the surface of the hybrid through a condensation reaction between the terminal amino group on the lysine residues of DNA and carboxyl group on  AuNPs. A novel model of the DNA biosensor based on the grapheneAuNPs hybrid electrode was fabricated. The sodium 9, 10dihydro 9, 10dioxoanthracene2sulphonate (AQMS) was used as the hybridization indicator for the target DNA detection. The results show that the DNA biosensors fabricated with the grapheneAuNPs  selectively distinguishs the singlebase mismatch of target DNA sequence and shows a higher specific selectivity.

With 2,4-dichlorophenol (2,4-DCP) as the target contaminant, in an electrolytic cell with diaphragm, the effects of different ion exchange membranes on the 2,4-DCP degradation were investigated by the biofilmelectrode. It was found that the anion exchange membrane has the better results for the conversion of 2,4-DCP and the removal of intermediaters compared to the cation exchange membrane. The longer the time of the biofilmelectrode kept is, the worse  the effect of 2,4-DCP degradation is. The service life of the biofilmelectrode gradually declines in.

Supermicroporous carbon with stable network has been successfully synthesized by the self assembly of carbonfluorine surfactant ［FSOCF₃CF₂CF₂CF₂CF₂-(CH₂CH₂O)_10］(FSO) with resol under high temperature hydrothermal conditions. After the carbonization of the sample at a high tempreture, which results in the shrinkage of the network, the small mesopore size carbon in the range of supermicroporous was obtained. XRD patterns show that the sample exhibits a certain order. N2 isotherm shows that the sample has a large BET surface area (600 m2/g) and obviously supermicropore (1.2 nm). Adsorption test shows that the resulted sample shows much better adsorption properties and a good recyclability, and the maximal adsorption capacity of organic dye RhB is 120 mg/g.

To construct the short hairpin RNA (shRNA) interference expression plasmid vectors of human HER2/neu gene, the recombinant plasmid was identified by PCR coupled with sequencing. The vector was transfected into SK-BR-3 cells, HER2/neu mRNA, protein, and the cell migration were assayed.
 The result indicated that the construction of recombinant plasmid was successful. Transfection of shRNA plasmid significantly downregulated HER2/neu mRNA and protein; at the same time, the migration ability of SKBR3 cell was obviously inhibited. Recombinant plasmid 1 had the strongest effect, with the inhibition ratios of 84.65% at the mRNA level and 74.98% at the protein level.

Gene phosphotriesterase from archeaon Thermaerobacter subterraneus DSM13965 was cloned and expressed at high levels in E.coli BL21. The recombinant enzyme was purified to homogeneity via ultrasonic, heating and histag in Nisepharose chromatography. With the help of SDSPAGE and Westernblotting, the phosphotriesterase was identified as a homooligomer existed in dimer form. The enzyme was characterized with ethylparaoxon, its optimum temperature and pH were 70 ℃ and 10.0, respectively. The enzyme has a favourable heat resistance.

Typical farmland soil samples of Changchun, Dehui, Fuyu, Gongzhuling, Yongji were collected with grid method. The residues of organochlorine pesticides(OCPs) in soil and the distribution were measured and the composition and sources of organochlorine pesticide residues were discussed. The results show that HCHs and DDTs of the study areas had higher detection rate. The total OCPs content of the residues was in a range of 1.45~83.88 ng/g. HCHs and DDTs were found widely in all the samples with a range of 1.17~27.83 ng/g and 1.45~81.75 ng/g respectively. The residue levels in different lands were in the order as follows: Changchun>Gongzhuling>Yongji>Dehui>Fuyu. A significant positive correlation existed between the total amount of OCPs and that of TOC was showed. The source analysis shows that the average value of α-HCH/γ-HCH of survey region was 0.37, indicating that there was a large number of lindane imported recently. The DDTs pesticide composition displays that P,P′-DDT/(P,P′-DDD+P,P′DDE) values of each sampling site except Gongzhuling were less than 1, indicating the sources of DDTs were residues historically. Gongzhuling was likely contaminated by industrial DDTs. From the results of factor analysis and cluster analysis, we conclude that the content of organochlorine pesticides causing Changchun area pollution is significantly higher than those of other regions. From the analysis of pollutant factor, γ-HCH and P,P′-DDT are the major pollutants.

A BP neural network of ultrasonicassisted biodegradation of EE2 and BPA was established, the amount of carbon source, amount of nitrogen source, inoculum dose, ultrasonic time, and degradation time were set as input, and the degradation rates of ethinyl estradiol (EE2) and bisphenol A (BPA) were set as output. The BP neural network model was employed for predicting the response for the factorial design of ultrasonicassisted biodegradation of EE2 and BPA. The primary effects and interaction effect on the ultrasonicassisted biodegradation were analyzed by factorial design. The optimum conditions for EE2 and BPA degradation were obtained. The correlation coefficient between experimental and predictive values were 0.952 5 and 0.983 1 for EE2 and BPA, Nash Suttclife coefficient values were 0.956 5 and 0.957 2, which indicated the accuracy prediction of the models. The results of factorial design analysis suggest that the amount of carbon source×the amount of nitrogen source, and the amount of carbon source × inoculum dose both had a synergistic effect on the degradation of EE2 and BPA. The maximum degradation rates of EE2 and BPA arrived at 87.13% and 69.27%, respectively. The optimum conditions for the degradation were as follow: 10% of carbon source, 10% of nitrogen source, 20 mL of inoculum dose, 1 min of ultrasonic time, and 168 h of degradation time. The biodegradation difference analysis shows the degradation rate of EE2 and BPA were proportional to mobility, while inversely proportional to the persistence.

A new catalyst CeAC was prepared by impregnating activated carbon (AC) into the solution of cerium nitrate. CeAC catalyst was characterized by XRF. During the CeAC  heterogeneous catalyzed ozonation, the different removal effcts of pyrene and fluoranthene in different treatment processes and a series of different conditions  were compared. The biotoxicity of the treated water was detected. The mechanism of the reaction was also discussed.