We presented a characterization of the unitary operator with spread form. The operator can be considered as the operator induced by a bijection on N. Moreover, it can be resolved into orthogonal direct sum of bilateral shift and permutation on some orthonormal bases.

With the help of normalized integral of weak πentwined structure (A,C)π-ψ, a Maschketype theorem for weak πentwined modules is proved, that is, given a weak πentwined structure (A,C)π-ψ and supposed that there exists a normalized integral θ={θα:  Cα→Hom(Cα-1,Aα)}α∈π,then a monomorphism (resp. epimorphism) f={fα: Mα→Nα}α∈π  splits in Uπ-CA(ψ) if the monomorphism (resp. epimorphism) fe splits as an Aemodule morphism.

A type of third order functional differential equation with change delaysx(t)+∑2i=1［aix(i)(t)+bix(i)(t-τi(t))\]+cx(t)+g1(x(t))+g2(x(t-τ3(t)))=e(t)was considered by means of the theory of coincide degree. The sufficient condition for the existence of unique Tperiodic solution was obtained. The conclusion is relevant to three delays.

 With the help of the theory of integral equations and Schauder fixed-point theorem, nonlinear boundary value problem with shift for k hypermonogenic functions in Clifford analysis was investigated. The existence and uniqueness of the solution to the above problem were proved, and the integral representation of its solution was obtained.

 By means of nonlinear Leray-Schauder alternative theorem and fixed point theorem in cones, the authors proved the existence of the solutions for one-dimensional singular p-Laplacian three-point boundary value problems under assumptive conditions. There is at least one positive value in the interval from zero to one.

 By means of comparison and analysis, some equivalent conditions of  the maximal right ideal as a module being a projective module were given firstly; then a new definition: MQ ring was introduced;  and the properties of MQ ring were discussed by max-injectivity and max\|flatness. Finally, the related properties of max-IF ring were summarized.

 A non-autonomous multiple species Lotka-Volterra cooperative system with delayed biocontrols was investigated. With the aid of comparability theorem, constructing Lyapunov function and continuation theorem, a set of easily verifiable sufficient conditions were obtained to guarantee the permanent and positive periodic solution to be global attractivity of the system.

The present paper covers the Bayes estimation of the halfnormal distribution and compares the goodness of estimation under the quadratic loss function and the balance loss function. And it also proposes the similar result under Monte Carlo simulation and numerical simulation, and compares the differences of the estimations between different loss functions.

 A global convergence combined homotopy method for solving the extended horizontal linear complementarity problem was introduced. We gave the combined homotopy equation and proved in details the existence of the smooth path from almost any interior initial point to a solution of EHLCP(A,q). Numerical results were presented to show the effectiveness of this method.

 The authors proposed a numerical method to reconstruct  the grating profile. We considered the reconstrution of the grating profile by  the incident plane wave and the scattered waves measured on Γb, which is a straight line above the grating. First, we obtained the normal derivatives of the scattered waves on Γb via the Dirichlet-to-Neumann map. Then we got the total field below Γb by means of solving the Cauchy problem of the  Helmholtz equation, which is changed into an initial value problem. The initial value problem was solved by the spectral method which is used to solve the initial value problem of the elliptic equation. Finally, we used the curve, which is composed of the zeros of the total field, to approximate the grating profile. The numerical results show that the method is effective.

 We defined the weak quasi-normal cone condition and for solving the multiobjective programming problem by the combined homotopy interior\|point method. Under the weak quasi-normal cone condition, we proved the existence of the smooth path and  global convergence for almost all points in one subset of feasible region.

 Using Razumikhin-type method, we studied the pth moment exponent stability of impulsive stochastic delay differential systems. The results we got can be applied in a wider application scope than the existing results. Moreover, numerical simulations are provided to illustrate the effectiveness of the obtained results.

 The authors studied the totally real pseudo-umbilical submanifolds in quasi-complex projective space by means of moving frames, and obtained an integral inequality and some intrinsic rigidity theorems.

 We studied a class of operator-valued functions on time scales,  obtaining the largest one of those classes of operators to ensure  the functions defined on  any time scale and valued in  it are regressive. The  standard tools of operator approximation in Hilbert space were used to characterize the closure and interior of this class of operators.

We developed csupplemented subalgebras and Ealgebras for Lie supertriple systems, obtained some properties of Lie supertriple systems and gave a necessary conditions for solvable Lie superalgebras. Moreover, we obtained a necessary and sufficient condition for ELie supertriple systems and csupplemented Lie supertriple systems, respectively.

 The problem of vertex-distinguishing total colorings of graphs was discussed via the methods of distributing color sets in advance, constructing concrete coloring with the help of matrices and recurrence method. The exact value of the vertex-distinguishing total chromatic number χvt(mK4) of the union mK4 of m vertex-disjoint K4 was given, that is “If k-14<4m≤k4, m≥2, k≥6, then χvt(mK4)=k”. This illustrates that  the VDTC conjecture is valid for mK4.

 Having introduced a homogeneous kernel of real number-degree with two independent parameters and estimating the weight function, we gave a new Hilbert-type integral inequality with a real number-degree with a best constant factor, it involves the equivalent inequality with reverse forms considered. It involves the ψ function. The reverse inequality and their corresponding equivalent forms were given.

 Optimality conditions of multi-objective programming problems for weak convex function were given via the abstract subdifferentiation on the basis of the  optimality conditions for the single objective optimization problem. New results were got.

 We investigated the Hopf bifurcation type of power system by the combining the center manifold theory with the direct periodic solution method and the subsequent function method, respectively. The theoretical analysis result is consistent with  the numerical simulation result based on the classical two-machine and three-bus model. Example shows that the proposed methods are valid.

 The variational iteration method was applied to solving functional differential equations with vanishing delays. After determining an appropriate Lagrange multiplier, the approximate solutions can be readily obtained. Sufficient conditions are given to guarantee the convergence of the method. Furthermore, the numerical experiment was also carried out to illustrate the main result.

 We investigated derivations with generalized Engel conditions in prime rings applying the theory of differential identities in prime rings. The main result is as follows. Let R be a prime ring, L a noncentral Lie ideal of R, d a nonzero derivation of R. Suppose that  xs［d(x),x］kxt=0 for all x∈L, where s,k,t ≥0 are fixed integers. Then char(R)=2. Moreover, if either s=0 or t=0, then RM2(F) for a field F.

 We first presented a  family of three\|parameter third\|order convergence iteration method for solving nonlinear equations and obtained different iteration methods by taking different values of the parameters.  We then proveed that the iteration methods have third-order convergence similar to those of existing methods, our methods also avoid computing the second derivative. Finally, we tested the methods on several numerical examples and illustrated that our methods are competitive with several other methods.

 We proved the existence and uniqueness of a class of evolution equation in Banach space  using  homotopy methods. We constructed a homotopy equation and made a priori estimate to this equation. Under the definition solution operator conditions, a sufficient condition of existence of solutions was obtained by means of  topological degree method.

 The definition of π-centers of finite groups was introduced, generalizing the definition of centers of finite groups, the relationships between π-center and center of π-Brauer characters were established and some group theoretical properties were obtained.

 We analyzed the relationship between the central mapping and the public key’s form for MPKCs. And we proved that only when the central mapping (x) of the MPKC contains the linear items,  choosing S for affine transformation is meaningful. When (x) does not contain any linear item, S should be selected for linear transformation so as to not reduce  the security of the system, and reduce the size of the public and private keys and improve the encryption and decryption efficiency of the system.

 A particle swarm optimization algorithm based on the solution space division was presented. On the premise of no impact on the particle swarm optimization, this algorithm can preprocess the solution space in order to get the optimal-intervals and improve the particle swarm optimization algorithm’s efficiency. Meanwhile, the checkpoints would be set up to update the solution space division dynamically. Experiments show that the algorithm can effectively improve the particle swarm optimization algorithm’s efficiency and solve the problem of trapping the local minimum. Furthermore, the algorithm can get minimum iteration times by designated precision and the results are satisfactory in the adaptive state.

 The merits and drawbacks of digital chaos and cellular automata used in cryptology were represented. On the basis of the analysis on the nonlinear features of 1-D cellular automata rules which have three neighbors  and periodic boundary, a method to design one-way hash function based on cellular automata dynamic parameters was proposed by considering the advantages of the cellular automata and the traditional one-way hash function together. In the iterative structure of MD5 algorithm, the output of the last iterative step was evolved only once according rule 198, and was used as the iterative parameter during the next iterative step, and the quadratic diffusion of the plaintext was implemented. A hash value with a  length of 128 bits was obtained as a result. It is shown that the proposed algorithm can resist differential cryptanalysis and linear cryptanalysis, and is sensitive to the initial message comparatively also. The confusion and diffusion properties of the proposed algorithm are pretty good. Moreover, it is easy to implement this algorithm under any platform by software and hardware. The practicability of the proposed algorithm is better.

 Based on the improved Canny operator, the modified templates of size 3×3 were extended to the ones of size 5×5 via half-pixel interpolation method, and the method of maximum value of normalized autocorrelation was used to determine the edge direction so as to mitigate the broken edges or false edges due to the effects of noise. In the experiment, we used receiver operating characteristic curves to evaluate the performance of the algorithm. The results show that the modified Canny operator improves the effect of the detection, for it can accurate the edge direction while reducing the probability of false edge points, especially for that of the images rich in line edge.

 The authors proposed a power spectrum autofocusing method based on defocus iris images. Firstly, we gave the relation curve  between autofocusing evaluation function value PS and blur radius of each iris image. Experiments show that the power spectrum evaluation function could find the location of system focusing mirror when the image is clearest. Moreover, we dealt with evaluation function curve by means of Gaussian fitting, and the relation number of the curve could reach 0.994 7(close to 1),  verifying the accuracy of the power spectrum autofocusing evaluation function.

 As the current stochastic optimization algorithms almost simulate evolutional process to solve the real optimization problems and  the searching result can’t reach the optimum solution, and it is difficult to use them in the real-time application,  a novel, fast and direct random optimization algorithm was proposed. The random search was directly used to find the optimum to cut off the additional time, and the random search process was divided into two different phases. In the first one a global optimizer was created through connecting three sub-optimizers including increasing parameters in serials and a global optimization module was formed with the paralleling optimizers to get a global solution; in the second one local optimization module was created to obtain  more precise an optimum. The tests for quite a few complicated functions indicate that the proposed optimization algorithm is rapid and effective and outperforms the current global optimization algorithms.

 Based on WINNA abstract model and ZigBee characteristics, a novel WSN management framework was proposed. An embedded framework of WSN node based on agent was given, which is usable to heterogeneous networks. Furthermore, a visual network management platform was designed, which can improve the efficiency of the WSN management. It proves that this WSN management system can fully use the limited network resources and greatly improve the service quality.

 With the application of CCD, the enlarged non-circular spinneret holes image was captured, followed by edge detection and preprocessing of thresholding and edge thinning. In the measurement of non-circular degree parameter,  the basic circular and linear elements were first detected, then  the method of least square was used to fit circular and linear for obtaining more accurate parameter. This method can achieve the judgment of  block and detection of shaped degree for non-circular spinneret hole. Experimental results show that this method has the high precision and speed detection. Meanwhile, it is suitable for non-circular spinneret holes detection in synthetic fiber industry.

 We reviewed the back ground, motivation and state of arts about learning information diffusion network. On the basis of  comparing and analyzing the existing approaches, such as approximate reasoning and convex programming, we discussed their respective advantages and disadvantages. And we summarized the main issues currently faced and presented the future prospect of developing direction.

 The properties of strange quark matter and strange stars were studied by means of  Nambu\|Jona\|Lasinio (NJL) model to describe the strange quark matter. Dynamical mass and number density of consisent quarks versus baryon number density were given by means of solving the gap\|equations. The equations of states for strange quark matter and corresponding mass\|radius relation of strange star were also investigated. The numerical results show that the mass and radius of the strange stars described by NJL model are smaller than that of EMBM within the scope of observational data.

 Based on the nonlinear characteristics of BoseEinstein condensed body in moving optical lattices and Lyapunov stability theory, and the combination with the sine coupling chaotic synchronization method, chaotic synchronization of Einstein condensed body in moving optical lattices was realized. With the help of  theoretical analysis and numerical calculation, the authors proved the effectiveness of the method on  the sine coupling chaotic synchronization and respectively realized the chaotic synchronization of the single variable coupling and double variable coupling. On the basis of the numerical calculation to determine the parameters range in which the chaotic synchronization can be realized, we proved that  chaotic synchronization double variable coupling is faster than single variable coupling and small coupling coefficient can achieve chaotic synchronization. We also analysed the relationship between the synchronization time and the coupling coefficient.

The mixed powder samples of α-quartz and silicon   with different mass ratios were used as raw materials.   The influence of silicon content on coesite formation conditions was investigated by means of combining the high\|energy mechanical ball-milling with  high temperature high pressure (HTHP) method. The experimental products were characterized by X-ray diffraction (XRD) and Raman spectrometry. The results show that Si atom on α-quartz grain surface has a strong affinity for oxygen atom under sealing environment with HTHP,  prevents neighbor atoms  from displacement and thereby the Markov-type homogeneous change from hexagonal α-quartz to monoclinic coesite is constrained.

 Sm2Fe17N3/Fe3N/BN  composite magnetic material was prepared by means of high\|energy ball\|milling and vacuum annealing treatment. Solid\|state phase transformation  and magnetic performance were investigated. The results show that the conditions  of the generation of Sm2Fe17N3 and Fe3N are the   grain size of Fe comes up to  nanometre (D＜80 nm) and forms Fe(Sm) solid solution. The crystal substance of  Sm2Fe17N3/Fe3N/BN in the ball\|milling material vacuum annealing at 300 ℃ was increased and   coercivity was increased with increasing annealing time. That is magnetic property of the sample has something to do with the degree of crystallinity of Sm2Fe17N3.

 Generalized Gauss density model was employed for the blind separation of the mixtures of sub- and super-Gauss sources, and the local stability analysis was performed for independent component analysis algorithm in the framework of the natural gradient in Stiefel manifold. We presented some new results about its local stability analysis and verified their correctness and applicability.

 The influence of molecular architecture of a triblock copolymer on the self-assembly morphology was investigated by dissipative particle dynamics simulation. Tuning the architecture of the triblock copolymer, we obtained different self-assembly morphologies, e.g., ordered layered structure, small-domain disorderly-aggregated structure and distorted stage structure, etc. To reduce the system free energy as much as possible, the triblock copolymer systems with different molecular structures would spontaneously self-assemble into different ordered morphologies.

 Quantum chemistry density functional theory (DFT) method was used to simulate the pre-organization of template and functional monomer, the geometry optimization, the bonding situation, the NBO charge and the binding energies of the imprinted molecule with the functional monomer at different proportions by means of B3LYP/6\|31G(d,p) with atrazine as template molecule and trifluoromethacrylic acid (TFMAA) as functional monomer. The molecular imprinting mechanism and interaction strength of atrazine and TFMAA were discussed. Results indicate that generally, atrazine and TFMAA form ordered compounds via the hydrogen bonding interactions. The compounds were mutual remedy in the molecular structure. The polymer with a ratio of atrazine-TFMAA (1 ∶6) had the lowest binding energy and the maximum charge transfer trend. The compounds had seven active sites of hydrogen bonds.

 Soluble ginsenosides with gradient concentrations were added into the culture environment of Caenorhabditis elegans. The effects of ginsenosides on C.elegans were further investigated including lifespan, broodsize, and locomotion. Our results show that 200 μg/mL ginsenosides can increase the lifespan and slow the aging of C.elegans. However, 500 μg/mL ginsenosides induced toxicity to C.elegans.

 Rich low-grade diatomite mineral was modified with calcium carbonate so as to improve the adsorption properties of diatomite for heavy metal ions. The results show that in a single component system, the dynamic laws for the adsorption of Cu2+,Pb2+ ,Cd2+and Zn2+ on the diatomite modified by calcium carbonate obey the pseudo-second-order model and the adsorption thermodynamics laws obey the Langmuir model. In a mixed component system, because of the effect of coexisting components, the adsorption rate of Pb2+,Cd2+ and Zn2+ was decreased respectively and the adsorption rate of Cu2+ was increased, but the adsorption dynamic laws of four kinds of metal ions still obey the pseudo-second-order model; at the same time, the adsorption capacities of four kinds of metal ions on the modified diatomite were decreased obviously and only the adsorption thermodynamics law of Pb2+ obeys the Langmuir model.

The influence of co\|existing heavy metals on the adsorption of cadmium and copper onto solid phases was investigated by simulating aquatic multiphase system comprising three types of solid phases, including biofilms, suspended particulate materials and sediments, in the absence and presence of co\|existing heavy metals. The results indicate that co\|existing metals (copper and lead) reduced the adsorption of cadmium to all solid phases remarkably. Under  the conditions of the adsorption of cadmium onto suspended particulate materials, the reduction effects increased as the initial concentration of copper and le
ad increased. Under the conditions of the adsorption of cadmium to biofilm and sediments, increasing lead initial concentration enhanced the reduction effects on cadmium adsorption, but increasing copper initial concentration had little influence on the reduction effects. The co-existing lead reduced the adsorption of c
opper to solid materials and these reduction effects increased with the increase of lead concentration for all the solid materials, while the co-existing cadmium had only a little effect on copper adsorption. Overall, the mpetitive adsorption between heavy metals was insignificant at low concentrations, and enhanced with the increasing of the concentration of co-existing heavy metals. The concentration of co-existing metals influenced the reduction of the adsorption of copper and cadmium to suspended particulate materials. The greater the concentrations of co-existing heavy metals were, the stronger the reduction of the adsorption of
 cadmium and copper to suspended particulate materials was.