This paper concerns the existence of antiperiodic solutions of first order ordinary differential equations. Under the commonly used condition in the literature, via the homotopy method, a global method for finding those solutions is proved. Numerical examples show this mthod is effective.

The paper concerns the regularity of weak solutions for nonlinear subelliptic systems under elliptic and controllable structure conditions on Carnot groups of step two. By the superposition technique of fractional difference quotients, the local HW^2,2estimate of weak solutions is established.

The authors investigated the singular limits of stiff relaxation and dominant diffusion for general 2×2nonlinear systems of balance laws, that is, τ=o(ε), ε→ 0, the relaxation time τtends to zero faster than the diffusion parameter ε. If there exists a priori L^∞ bound that is uniformly with respect to ε for the solutionsof a system, then the solution sequence converges to the corresponding equilibrium solution of the system. This framework can be applied to some important nonlinear systems with relaxation terms and inhomogeneous terms, such as the system of quadratic flux, the LeRoux system, the system of elasticity and the extended models of traffic flows.

KKM type of theorem in general topological space without any convexity structure was obtained, from which we obtain many fixed point theorems or existence theorem of maximal element for FanBrowder type map in noncompact general topological space without any convexity structure.

Using the relation between homogeneous Morrey-Herz spaces MK^α,λ_p,q(Rⁿ) and homogeneous Herz spaces K^α,p_q(Rⁿ), some results on K^α,p_q(Rⁿ) were extended. The CBMO estimates on MK^α,λ_p,q(Rⁿ) were established for the commutator T^b_Ω,l and multilinear operators T^A_Ω,l of fractional integrals with rough kernel. In the meanwhile, the corresponding results for maximal commutators M^b_Ω,l and multilinear maximal operators M^A_Ω,l of fractional integrals were obtained.

This paper deals with the dynamical properties of the Hopf bifurcation diagram of the price Reyleigh equation model with delay, and the stability of equilibrium point and the existence of Hopf bifurcation by the method of τ-Dpartitioning approach of exponential polynomial. Furthermore, we gained the computational forumla of the direction of the Hopf bifurcation and the stability of the periodic solutions with the Hopf bifurcation formula of Liénard equation with finite delay and completely gave the Hopf bifurcat ion diagram in the parameterplane of r-γ. Finally we found an important conclusion that delay reflects that price has an hysteresis on supply , by which we can explain the shake phenomenon of price in economy life.

Using the Leray-Schauder degree theory, we studied the existence of two nonnegative solutions to a type of p-Laplacian two point b oundary value problems with sign changing of nonlinear term, and obtained sufficient conditions for the existence of the solution under weaker conditions.

A class of merit functions for describing the nonlinear complementarity problems (NCP) was extended to that for describing the symmetric cone complementarity (SCCP) problems by the tool of Euclidean-Jordan algebras. And then it was shown that the SCCP is equivalent to an unconstrained smooth minimizationvia this new merit function and two examples of the class of merit function are given. Moreover, the conditions under which the new merit function provides a global error bound were studied with a weak condition given under which the new merit function has bounded level sets.

By means of mixed monotone fixed point theorem, singular second order threepoint continuous and discrete boundary value problems were studied. First, the existence and uniqueness were established for the threepoint continuous boundary value problems of singular second order differential equations. Second, the existence and uniqueness were established for the threepoint discrete boundary value problems of singular second order difference equations.

The number of codewords with weight 4 in one open problem on a class of binary cyclic codes is discussed by means of cyclotomic numbers, three elementary rules of criterion on the open problem and a formula to compute A₄ with only cyclotomic numbers involved is given under certain conditions.

Stable homotopy regular morphism is defined in this paper by using suspension functor. Its existenceand properties are also presented. The main conclusion is as follows. Letf: X→Y be a map of stable standard decomposition (g,Z,h). Supposing that there exist A,B and i: A→X, p: Y→B such that gi and phare all stable homotopy equivalences, then fis a stable homotopy regular morphism, and f is uniquenessin the sence of kstable homotopy.

The existence of the positive solutions of the following Fredholm integral equation u(t)=∫¹₀k(t,s)f(s,u(s))ds was investigated by applying the fixed point theorem in cones. The main results show that the problem has a positive solution at least provided growth rates of nonlinear term are appropriate.

This paper deals with the multiplicity of positive solutions to singular superlinear equations with periodic boundary value problems. It is proved that such a problem has at least two positive solutions under our r easonable conditions when the nonlinear term possesses singularity and super-linearity. The proof relies on a nonlinear alternative of LeraySchauder theorem and Krasnoselskii on fixed point theorem in cones.

Let (M,T) be a smooth closed manifold with a smooth involution T and F={x|T(x)=x, x∈M}the fixed point set of Ton M, the authors studied the closed mainfold (M,T) with involution Tof F=RP⁵×RP^2s, and determined the possible dimensions and equivariant cobordism classification of (M,T).

he subproblem generates trail step size d^k always in trust region. d^k is updated at every iter ation. Nonmonotone line search is used to solve subproblem when d^k is not accepted. Global convergence is proved under some suitable conditions.

A new algorithm was derived for determining a parameterization of multivariate osculatory rational functions a(X)/b(X) interpolating an arbitrary sequence of points by means of Groebner bases of submodules of the free module over the polynomial ring in multivariate variable. For Cauchy multivariate rational interpolation, the algorithm is a Newton algorithm.

The authors considered the unconstraint global optimization and presented a conjugate gradient method to solve under a condition of a special inexact line search. According the test function it is shown that the method is efficient and feasible.

The purpose of this paper is to investigate the characterization of a compactly supported spline function φdefined on simplex in Rⁿ. We give the equivalent condition of φbeing M-refinable, where M. the dilation matrix of the refinement function, is an n×ninteger matrix with the norms of all its eigenvalues greaterthan 1. Furthermore, we give a necessary and sufficient condition of the shifts of φ forming Riesz basis.

Using the singular value decomposition (SVD) of a matrix and the canonical correction decomposition (CCD) of matrices, this paper establishes the necessary and sufficient conditions for the existence of the doubly center solutions and presents the expressions for the inverse problem of a matrix under a submatrix constraint. Moreover, the optimal approximation problem to a given matrix in the solution set is considered, and the optimal approximation solution is obtained.

The authors studied singularly perturbed initial value problem for a class of system of nonlinear equations. According to the problem, the corresponding solution is expanded as the series form with small parameterε. With the aid of the corrective method of initial layer, the approximate of outer solution and corre ctive terms of initial layer are constructed successively. Uniformly valid asymptotic solutions of the problemand their asymptotic behavior are obtained.

The authors investigated the weak viability property of backward stochastic differential equations(shortened by BSWVP). By means of sto chastic Lyapunov’s method and Chebychev’s inequality, the authors give a sufficient condition for BSWVP holds on a nonempty closed set. As application, the authors obtaineda decision condition for the weak viability for the viscosity solution of quasilinear parabolic partial differential equations in a closed set.

c-Supplement is generalized and weak c-supple ment is introduced. Let Gbe a finite group and H a subgroup ofG.H is called weakly c supplemented in G if there exists a subgroup K of Gsuch that G=HK is the maximal quasinormal subgroup of Gcontained in H. Kis called a weak csupplement of Hin G. It is shown that for the least prime divisor p of the order of a finite group G and for a Sylow psubgroup P of G, if every 2maximal subgroup of P is  csupplemented in G and if G is not involved with A4, then G  is pnilpotent.

This paper deals with the existence of single and multiple positive solutions to second order by means of the fixed point theorem in cones.

Operational and denotational semantics are defined in connection with different paradigms of programming languages, including a simple functional programming language, a simple procedural programming language and a simple object oriented language. A visual teaching assistant system was designed to demonstrate the visual procedure of running programs of different programming languages. With the assistance of the system students can easily understand and grasp the formal semantics of programming languages and their implementation.

The authors extended the representing framework Rof the KRA model so as to divide the perception into primary perception and abstraction perception. In the process of primary perception,Wunder the primary perception system P is mapped as P(W) where the attributes of the objects in Wdo not change. In the process of abstraction perception, Wunder the abstraction perception system P^* is mapped as P^*(W). The objects in P^*(W)are abstraction objects, the types of which are related to the abstraction objects database predefined by the agent. The specified modeling process can generate various abstraction models of W, making the reasoning simplified.

Aiming at the efficiency of knowledge fusion, the authors extended the structure of conventionaltopicmaps. This new structure embodied the multilevel, multi-granularity and inherent relevant characteristics of knowledge. A new distributed knowledge fusion architecture based on extended topic maps was built up, and a novel algorithm of the similarity of topic maps based on comprehensive information was proposed by integrating syntactic similarity, semantic similarity and pragmatic similarity. It gave full consideration to the meaning and context of the compared elements so as to improve the accuracy of the similarity algorithm. The fusion rules and algorithm for extended topic maps were presented, implementing the effective knowledge fusion in distributed environment.

Based on the principle of virtual instrument, a virtual spectrum analyzer was constructed via the software platform of LabVIEW. The instrument can implement the analysis of timedomain and frequencydomain process the complex signal via adding windows and filtration, getting the parameter, such as frequency, frequency response with the display of digital, the plot of figure, the save and examine of data etc, which makes high cost lower, long development circle shorter, and manual record replaced.

A kind of software and hardware design was studied for a complete set of timing system based on PCI bus. To realize the design, two theories were adopted, which were remote longline transmission theory and a newest device driver program theory. This timing system owns lots of merits, such as high precision, strong ability of signal drive, convenience for use and so on. It not only was realized synchronization for more than one remote computer in the simulation process of driving simulators in State Key Laboratory of Automobile Dynamic Simulation, but also was applicable to getting synchronization for remote computers in other industry control process.

Web service combination, as a technique to fulfill the user’s requirements by means of reusing existing webs, has become a pop topic in the researches of Service Oriented Computing(SOC). The current combination approaches based on three Semantic Web services frameworks are described and their lim itations in regard to main requirements of SWS combination that need to be resolved are summed up. Therefore the clear issues for SWS composition is given, it is of a certain significance for research work in this area.

A parallel information processing system was implemented based on existing multicore microprocessor, in order to solve the difficult of the traditional highperformance parallel computing system, which is expensive and high maintenance costs, so as to provide a lowcost strategy for parallel information processing. The experiment shows that the parallel information proces sing system based on the microprocessor is suitable for parallel information processing and science calculation.

The derivative Lorenz chaotic system was studied on its basic dynamical behavior, such as Lyapunov exponent spectrum, bifurcation diagram, power spectrum, Poincare mapping and the phase portrait. Numerical simulations show that the Lorenz chaotic evolution system’s behavior can be stable, periodic, half periodic and chaotic as the parameter varies.

High coercivity magnetic nanoparticles (CoFe2O4) were synthesized by the combustion method with glycine as fuel followed by proper thermal annealing treatment to induce the crystallization. Structural and magnetic properties of the products were investigated via X\|ray diffractometry, a scanning electron microscopy, and a vibrating sample magnetometer, respectively. The magnetic properties of the products were greatly affected by the average crystalline size of the nanoparticles. By controlling the thermal annealing treatment, the coercivity (H_c) and saturation magnetization (σ_s) of the nanoparticles can be well tuned as a function of temperature. The range of the annealing temperature is from 500 ℃ to 900 ℃.

Hyperbolic complex space is corresponding to Minkowski space. We introduced Dirac operator into hyperboloid half linearity space. Then, we established a theoretical framework which can describe the relativity theory and the quantum mechanics in a unified way.

The infrared spectra of p-benzoquinone were measured in 13 solvents. The rule of Fermi resonance was validated by Bertvan changing solvent method. The Fermi resonance mechanism studied by changing solvent method was explained by means of KBM equation and electron donor-receptor model. The relationship between Fermi resonance intensity ratio (R) and the solvent dielectric constant (ε) was given.

Self-consistent field model was used to study the phase separation and gelation of physically associating polymer solution. The variations of the locations of the phase separation point and the gelation point with the polymer concentration and interaction parameter were investigated. The effect of polymerization on the transition was also studied. The formation of the gel network has a significant effect on the phase separation of the system.

In-situ high-pressure Raman study of β-Ga₂O₃ was carried out from 0 to 23.4 GPa with a diamond anvil cell (DAC). The authors determined the pressure dependences of the Raman bands of β-Ga₂O₃. The external vibrational modes at 144 cm^{-1 and 169 cm-1 were assigned according to the high-pressure Raman spectra. Two new Raman peaks at 232 cm-1 and 483 cm-1 are near 18 GPa, and their intensity is strengthened with increasing pressure. So we can determine the occurrence of pressure-induced phase transition near 18 GPa.}

An adaptive update method of noise covariance is given. This method needn’t input the noise parameters, the noise parameter can automatically renew according the change of the noise in recursion. This method was checked with origin measure data of UTC(NTSC) and the time of rubidium atomic clock. The experiment results show that this method is better than general Kalman filter. 

The method of fitting hyperbola with singular value decomposition(SVD) was used to measure the laser beam quality parameters. The advan tages and disadvantages of using the normal equations to fit a hyperbola were an alyzed. The hyperbola fitted by SVD was used to express the change of the laser beam’s width, and the rules for estimating the goodnessoffit were offered. The fitting precisions of hyperbolas fit with the normal equations and the SVD were compared. The result showed that the precisions and the goodness-of-fit were affected better in the fitting hyperbola with SVD for laser measure.

Zealite 4A was synthesized by a onestep alkalidissolved hydrothermal method with bentonite as raw material. The effects of n_Na2O∶n_SiO2, n_H2O∶n_{Na2O, nSiO2∶nAl2O3, synthesis time and temperature on the properties of the products were investigated by means of XRD, SEM and calciu m ion exchange capacity. The optimum conditions for synthesizing zeolite 4A are nNa2O∶nSiO2=2, nH2O∶nNa2O=60和nSiO2∶nAl2O3=1.5, a crystallization temperature of 90 ℃ and a reaction time of 6 h. Under the optimal conditions, zeolite 4A with a high degree of crystallinity, a small granularity of particles (most of the particle size of zeolite 4A was less than 2 μm) and a high calcium ion(CaCO3)exchange capacity (293 mg/g) was obtained.}

The authors demonstrate that hexagonal nanodisks of Cd(OH)₂ could be fabricated by a facile hydrothermal treatment. The product obtained showed a good crystallization and regular shape. The compositions and morphologies of the samples were characterized by XRD, SEM, TEM and SEAD. The effects of experimental conditions such as temperature and mineralizer on the structure and morphology of the product were investigated in detail. Furthermore, possible formation mechanism was discussed.

Onestep synthesis of phenol via the hydroxylation of benzene is an important synthesis route. A novel catalyst Cu₂(OH)PO₄ shows a very good catalytic activity for benzene hydyoxylation to phenol. Herein, some impact factors, such as the kind and amount of solvent, catalyst amount, reaction temperature and time have been studied in detail.

An improved method was presented for the synthesis of birnessite, and single-phase layered birnessite was obtained. Birnessite samples synthesized by this method were characterized by the XRD and SEM. The results indicate that the crystallinity of the birnessite synthesized by this method is increased greatly by increasing the concentration of Mn(Ⅱ) solution.

Highperfomance liquid chromatography was used to study how to control solasedine hydrochloride quality. Column was Agilent ZORBAX Eclipse XDB-C₁₈ column (150 mm×4.6 mm, 5 μm), mobile phase was V_methanol∶V_acetonitrile∶V_{0.020 mol·L^-1lammonium acetate}=60 ∶35 ∶5, flow rate was 1 mL/min, detection wavelength 205 nm, injection volume 10 μL, the solasodine hydrochloride quality separated from other impurities in a good linear range of 5~500 μg/mL (r=0.999 3), numder of theoretical plates n＞12 000(R>1.5); the average recovery for the sample 98.6% (n=9). Relative standard deviation of reproducibility (RSD) was 0618%.

To investigate the antiproliferative effect of betulin and betulinic acid on 3 kinds of human cancer cells and the mechanism of betul inic acid induced cytotoxicity in MCF7 cell line, crystal violet dyeing was used to screen the cytotoxicity effect of betulin and betulinic acid in the cancer cells. RTPCR was operated to determine the expression of p21 mRNA, p53 mRNA, Bcl2 mRNA and Bax mRNA. This study shows that the growth of tumor cells is significantly inhibited by betulin and betulinic acid in dosedependence. The study alsoindicates that betulinic acid induces the apoptosis of MCF7 cells. So a s to make the expression of p21 mRNA and p53 mRNA increased but make the express ion of Bcl2 mRNA and Bax mRNA unchanged.

Distribution of heavy metals (Fe,Mn,Cu,Zn and Pb) surficial sediments with water phase in the simulated system in a period of 45 d w as investigated via a modified sequential extraction procedure, and pH, Eh and enzymes (protease, dyhydrogenas, sucrase and phosphatase) were monitored simultaneously. The resultsindicate that exchangeable manganese was converted into carbonateassociated fractions (10.2%) and Fe/Mnoxides fraction (32.1%), respectively, 11.5% zinc was found to exist from exchangeable to Fe/Mnoxides fraction, and organic matterassociated Pb was observed to increase by 20.1%. pH was variable in the first 20 d while Eh was fluctuated during the whole experiment. The activities of protease and dyhydrogenase were raised by a factor of 88.9% and that of 71.4%, respectively. The correlation analysis shows that pH was signifi cantly positively correlated with carbonateassociated Fe,Cu. Noticeable correlation was found between protease activity and Mn of carbonateassociated Fe/Mnoxide fraction, Zn of exchangeable Fe/Mnoxide fraction as well as Pb of organic mattersassociated fraction (n=8, p=0.05), and the similarcorrelative phenomenon was obtained between dyhydrogenase and Pb of carbonateassociated fraction, implying that the enzyme is one of the most important factors in transforma tion and cycling of heavy metals in surficial sediments besides pH.

Absorption and transportation of methyltertbutylether(MTBE) in water by Eichhornia crassipes were studied. Results show that concentrations of MTBE in treatments Ⅰ,Ⅱ, and Ⅲ(control) were decreased by 94.25％, 50％, and 7.3％, respectively when they were exposed to MTBE for 5 d. This illustrates that the transpiration of the leaves of Eichhornia crassipes was the major cause for the reduction in concentration of MTBE in water solution. Regression analysis of the experimental data was performed, showing that the disappearance of MTBE in water solution was fitted to first order kinetic equation. Disappearance rate of MTBE in water in treatment Ⅲ was obviously lower than that in treatment Ⅰor Ⅱ. This further demonstrates that transpiration plays a crucial role in the elimination of MTBE in water solution. No harm was observed and no difference in the ratio of transpiration quantity to biomass emerged when Eichhornia crassipes was exposed to MTBE at a concentration less than 1 110 mg/L for 5 d. Ratio of transpiration quantity to biomass reduced obviously and leaf edge was dried up and became etiolate when Eichhornia crassipes was exposed to MTBE at concentration 1 480 mg/L. By measuring the contents of MTBE in the root, stalk, and leaf of Eichhornia crassipes, it was found that concentration ratio of MTBE in root, stalk, and leaf was 1 ∶1.5 ∶0.5, which showed that the order of MTBE concentration in the tissues was stalk>root>leaf.