Table of Content

26 December 1998, Volume 18 Issue S1 Previous Issue    Next Issue

For Selected:

View Abstracts

Download Citations EndNote Reference Manager ProCite BibTeX RefWorks

Toggle Thumbnails

Select

Explicit Wavefront Solutions of a Reaction-diffusion Equation and Global Analysis of a Planar Cubic System Kang Dongsheng Acta mathematica scientia,Series A. 1998, 18 (S1):  1-12.  Abstract ( 60 )   RICH HTML PDF (639KB) ( 63 )   Save It this paper,author studies the traveiling-wave solutions of the reaction-diffusion e-quation ut=uxx+u(1-u)(u-a)(1)where 0 < a < 1,and c ≥ 0.Four types of traveiling-wave solutions are obtained with theirminimal or unique wave speeds c. Explicit form of some wave-front solutions including theHuxley wave are also established. The results are then applied to investigate the following pla-nar cubic system ζ=η, η=aξ+cη+(1+a)ξ2+ζ3.(2)It is well known that in the (U,U') phaes plane,the equation (1)is equivalent to the system(2). H. P. Mckean studied (1) by means of the traveiling-wave solution tnethod,and acquiredsome phase portraits for a∈(0,1/2) and c ≥ 0.Their results in this paper,however,glve allthe phase portraits for system (2) together with the bifurcation diagram. Related Articles | Metrics

Select

The Lp -integrability of Beltrami's Equations with Non-natural Exponents Zheng Shenzhou Acta mathematica scientia,Series A. 1998, 18 (S1):  13-20.  Abstract ( 69 )   RICH HTML PDF (451KB) ( 88 )   Save For Beltrami's equations in Rn,n ≥ 2,there exist two exponents r1,r2, which satisfy1 < r1 < n < r2 < ∞,such that every weakly solution f(x) of Beltrami's equations in Wloc1,r1(Ω,Rn) belongs to Wloc1,r2(Ω,Rn). Related Articles | Metrics

Select

On the Best Constants for Some Operator Inequalities Yang Changsen, Guo Qiuli Acta mathematica scientia,Series A. 1998, 18 (S1):  21-26.  Abstract ( 60 )   RICH HTML PDF (323KB) ( 69 )   Save Let △ be the unit disk,and H1(△) be the follwing set H1 (△)={φ(z):φ(z) is analytic in △,|φ(z)|<1, and there exists a θ∈[0,2π]such that|φ(eiθ<)|=1} Then all the proper contraction on H,we have φ∈H1sup(△) b2(φ)=2,φ∈H1sup(△)b2(φ)=1 where b2(φ)=supA(||φ'(A)||(1-||A||2)+||φ(A)||2) b2(φ)=supA(||φ'(A)||(1-||A||2)+infx∈H||x||=1||φ(A)x||2)On the other hand,if φ(z)=Σk=0n akzk,|φ(z)|<1, then ||φ'(A)||+||φ'(A)|| ≤ 2n where φ(z)=znφ(z-1), and 2 is the best constant for all the choices of n,φ(z) and A. Related Articles | Metrics

Select

The Convergence of The Cesaro Averages and The Strong Law of Large Numbers for Nonhomogeneous Markov Chains Yang Weiguo, Liu Kaidi, Dong Wei Acta mathematica scientia,Series A. 1998, 18 (S1):  27-34.  Abstract ( 74 )   RICH HTML PDF (446KB) ( 56 )   Save In this paper authers are to study the convergence of Cesaro averages and the stronglaw of large numbers for nonhomogeneous Markov chains,and to study the Shannon-McMillantheorem for nonhomogeneous Markov chaims by using above two concepts. Related Articles | Metrics

Select

The Concept of Group and Local Invariant Solution of Vacuum Einstein Equation Zhu Qingguo Acta mathematica scientia,Series A. 1998, 18 (S1):  35-43.  Abstract ( 75 )   RICH HTML PDF (521KB) ( 36 )   Save In the article, the author advances the concept of grolongation group of Lie transfor-mation group in a visual and pithy way,and resolve the coefficient problem of prolongation op-erator by using the method of fibre bundle,namely Lemma 1.1,Lemma 1.2 and Lamma 1.4. Related Articles | Metrics

Select

Monotonic Trajectory of Differential Inclusions Qin Songxi, Wang Zhihua Acta mathematica scientia,Series A. 1998, 18 (S1):  44-50.  Abstract ( 78 )   RICH HTML PDF (403KB) ( 68 )   Save In this paper,the author study the existence of monotonic trajectories for differentialinclusions in Banach spaces. By using a new approximation method, an existence theorem isproved. As a special case,some viability theorems existed in references are generalized and improved. Related Articles | Metrics

Select

Positive Solution of Hammerstein Type Nonlinear Integral Equations in Banach Spaces and Application Zhang Qingzheng Acta mathematica scientia,Series A. 1998, 18 (S1):  51-56.  Abstract ( 68 )   RICH HTML PDF (390KB) ( 19 )   Save In this paper, with using the fixed point index theory,the existance of positive solu-tions of Hammerstein type nonlinear integral equations in Banach space E is investigated, andapplication is given. Even if E=RN these results are still new. Related Articles | Metrics

Select

Oscillation of First Order Nonhomogeneous Neutral Differential Difference Equations Gao Guozhu Acta mathematica scientia,Series A. 1998, 18 (S1):  57-63.  Abstract ( 70 )   RICH HTML PDF (371KB) ( 64 )   Save In this paper oscillation of the first order nonhomogeneous neutral differential difference equations (d)/dt[x(t)+cx(t-τ)]+P(t)x(t-σ)+f(t)=0,t ≥ t0 is discussed. The author gets some sufficient conditions for the equations to oscillate and gener-alizes the result of oscillation of some homogeneous equations. Related Articles | Metrics

Select

Linear Difference Coupled System of Poincaré Equation Chen Shihua, Du Nailin Wuhan Acta mathematica scientia,Series A. 1998, 18 (S1):  64-68.  Abstract ( 70 )   RICH HTML PDF (272KB) ( 21 )   Save It studies the in-phase solution and out-of-phase solution of linear difference coupledsystem of Poincare equation,gets the parameter domain in which the in-phase solution is sta-ble,and establishes the existence and stability theorem of out-of-phase solution in diagonal dif-ference coupling. Related Articles | Metrics

Select

The Existence and Uniqueness of Periodic Solution for a Class of High Dimensional Non-autonomous System Wu Xiaofei Acta mathematica scientia,Series A. 1998, 18 (S1):  69-75.  Abstract ( 67 )   RICH HTML PDF (395KB) ( 73 )   Save In this paper,using Schauder's and Roth's fixed point theorem,author discusses theexistence and uniqueness of periodic solution for a class of high dimensional non-autonomoussystem and has given some sufficient criteria for the existemce and uniqueness of periodic solu-tion. Related Articles | Metrics

Select

Stationary Oscillation for Higher Dimensions Functional Differential Systems Sun Jitao, Zhang Yinping Acta mathematica scientia,Series A. 1998, 18 (S1):  76-82.  Abstract ( 112 )   RICH HTML PDF (402KB) ( 76 )   Save This paper introduces a new concept of S-stability of the functional differential sys-tems and obtaines general stationary oscillation theorem. The results of papers[7-9] are im-proved and extended. Related Articles | Metrics

Select

The Exact Solution of the Integral-Differential Equation in Space W22 (*) of Reproducing Kernel Li Yunhui, Cui Minggeng, Liu Chunpu Acta mathematica scientia,Series A. 1998, 18 (S1):  83-92.  Abstract ( 64 )   RICH HTML PDF (489KB) ( 20 )   Save In this paper,authores discuss the definite solution problem of integral-differetial e-quation,give the exact solution to the definite solution problem of integral-differential equationin space W22(*) of reproducing kernel. Related Articles | Metrics

Select

Necessary and Sufficient Condition of Existence and Uniqueness of the Periodic Solution For a Class of Equation of High Order of Compound Type Yang Qigui Acta mathematica scientia,Series A. 1998, 18 (S1):  93-100.  Abstract ( 53 )   RICH HTML PDF (429KB) ( 98 )   Save In this paper the periodic solution of linear functional equation of compound type ofarbitary order with constant coefficients and two constant delays is considered by Fourier seriestheory,and necessary and sufficient condition characterized by coefficients and delays is ob-tained, under which periodic solution of compound equation will be existence and uniqueness. Related Articles | Metrics

Select

Corner and Shock Layer Bahaviors in Singularly Perturbed Nonlinear Systems Huang Weizhang Acta mathematica scientia,Series A. 1998, 18 (S1):  101-106.  Abstract ( 56 )   RICH HTML PDF (323KB) ( 89 )   Save In this paper,the author studies the corner and the shock layer bahaviors in secondorder nonlinear systems. Under the appropriate condions, using the theory of differential in-equality, the author gets the existence of the solution and its componentwise uniformly validasymptotic estimation. Related Articles | Metrics

Select

On the Renewal Theorem for Random Compact Convex Sets Qian Nengsheng Acta mathematica scientia,Series A. 1998, 18 (S1):  107-114.  Abstract ( 56 )   RICH HTML PDF (439KB) ( 79 )   Save In this paper, the author first proves the multidimensional renewal theorem and thenconsiders the renewal theorem for Minkowski sums of random compact convex sets. Some im-portant results are obtained. Related Articles | Metrics

Select

Positive Solutions of Singular Superlinear Emden-Fowler Boundary Value Problems Wei Zhongli Acta mathematica scientia,Series A. 1998, 18 (S1):  115-118.  Abstract ( 66 )   RICH HTML PDF (215KB) ( 23 )   Save This paper is about the Dirichlet boundary value problems of singular superlinear Emden-Fowler equations. A sufficient condition for the existence of positive solutions to thisproblem has been obtained by using the fixed point theorems on cones. Related Articles | Metrics

Select

Asymptotic Behavior of Solutions for Neutral Differential Equation with Several Delay Arguments and Positive-negative Coefficients Tao Youshan, Gao Guozhu Acta mathematica scientia,Series A. 1998, 18 (S1):  119-124.  Abstract ( 53 )   RICH HTML PDF (302KB) ( 63 )   Save In this paper authors obtain sufficient conditions under which every solution of theneutral differential equations with several delay arguments and positive-negative coefficients [x(t)-Σ k=1lCk(t)x(t-rk)]+Σi=1mPi(t)x(t-τi)-Σj=1nQj(t)x(t-σj)=0,t ≥ t0,tends to a constant as t→∞.This paper extends the result of[5] to the case of several delayarguments. Related Articles | Metrics

Select

The Analysize of the Over-Voltage Models During Transition Process Ji Guojun Acta mathematica scientia,Series A. 1998, 18 (S1):  125-132.  Abstract ( 59 )   RICH HTML PDF (465KB) ( 27 )   Save This paper analyse the math' models of unsimultaneous three-phase closed in thepower system during transition process. Simultaneously the author studies these models theoryresults that are identical with the practical background and the models are first given. Related Articles | Metrics

Select

Quasi Likelihood Estimation and Constrained Quasi Likelihood Estimation in Nonlinear Regression Model Lin Lu Acta mathematica scientia,Series A. 1998, 18 (S1):  133-138.  Abstract ( 78 )   RICH HTML PDF (373KB) ( 88 )   Save In nonlinear regression model, the optimality of quasi likelihood estimatiom in theclass of normal generalized quasi likelihood estirnation is proved.The relation between the opti-mality of quasi score function and quasi likelihood estimation is discussed. To improve on quasilikelihood estimation,a constrained quasi likelihood estimation is presented. For this estimation,the superiority over quasi likelihood estimation is proved. Related Articles | Metrics

Select

The Thermal Effect of Kerr Black Hole after Considering The Effect of Evaporation Zhao Ren, Zhang Yusheng, Zhang Lichun Acta mathematica scientia,Series A. 1998, 18 (S1):  139-143.  Abstract ( 70 )   RICH HTML PDF (226KB) ( 17 )   Save After using the new generalized tortoise coordinate transformation,authors obtainthe location of horizon and radiation temperature of axis symmetric Kerr black hole with coor-dinate (t,r) as variable,through directly solving K-G equation near the event horison. The re-sult of calculating indicate that on the condition that the effect of evaporation is considered,thehorison surface of Kerr black hole is a elliptic spherical.surface which changes with time,Hawking radiation temperature is not only relative to time.but also the azimuth. Further the re-sults indicate that Hawking radiation temperature can be regarded as a compensate effect underthe time-scale transformation. Related Articles | Metrics

Select

Wavelet Properties of Linear Stochastic System Xia Xuewen Acta mathematica scientia,Series A. 1998, 18 (S1):  144-148.  Abstract ( 42 )   RICH HTML PDF (237KB) ( 90 )   Save In this paper, the author studies some wavelet properties of linear system, and ob-taines some new results. Related Articles | Metrics

Select

Asymptotic Expansion of Solution of Mixed Boundary Value Problem for a Class Sixth Order Elliptic Equation when the Limit Equation Has Singularity Lin Surong Acta mathematica scientia,Series A. 1998, 18 (S1):  149-156.  Abstract ( 64 )   RICH HTML PDF (461KB) ( 78 )   Save In this paper, the author considered the singular perturbation of mixed boundaryvalue problem for a class sixth order elliptic equation when the limit equation is degenearatedelliptic equation (elliptic-parabolic) at the partial boundary. Under suitable assumptions, usingthe improving method of multiple scale, the uniformly valid asymptotic expansion of solutioninvolving boundary layer and cover layer of arbitrary order at the whole half-circle region is ob-tained except two corner point at the half-circle region. Related Articles | Metrics

Select

Bounded Solutions and Almost Periodic Solutions for Differential Equations with Reflection of the Argument Feng Chunhua, Yang Xitao Acta mathematica scientia,Series A. 1998, 18 (S1):  157-162.  Abstract ( 68 )   RICH HTML PDF (320KB) ( 70 )   Save By using the method of exponential dichotomy and fixed point theorem,this paperinvestigated the existence and uniqueness of bounded solutions and almost periodic solutions fordifferential equations with reflecition of the argument. Related Articles | Metrics

Select

Improvements on the Prior Estimate of Sturm-Liouville Problem Li Fuyi Acta mathematica scientia,Series A. 1998, 18 (S1):  163-166.  Abstract ( 58 )   RICH HTML PDF (234KB) ( 25 )   Save In this paper,one important condition used to make the prior estimate in[1] is e-liminated,so the existence results for nontrivial solutions of the superlinear Sturm-Liouville twopoint boundary value problems are essentially improved. Related Articles | Metrics

Select

The Positive Entire Solutions of Class of Singular Nonlinear Biharmonic Equations Xu Xingye Acta mathematica scientia,Series A. 1998, 18 (S1):  167-173.  Abstract ( 61 )   RICH HTML PDF (382KB) ( 109 )   Save In this paper,author's aim is singular to establish the theorems of exsitence of posi-tive radial symmetry entire solutions of a class of nonlinear biharmonic equations on R2 and pre-sents about the properties of the solutions. It enrichs and develops the theory and apply of paper[1] and[2]. Related Articles | Metrics

Select

Bargmann Coordinate for Stationary Coupled Harry-Dym Equation and Poisson Structure for the Restricted System DU Dianlou Acta mathematica scientia,Series A. 1998, 18 (S1):  174-180.  Abstract ( 62 )   RICH HTML PDF (356KB) ( 31 )   Save In this paper, the polynomial solution of the Lenard's recurise equation associatedwith coupled Harry-Dym (CHD) hierarchy is derived,and it is proved that every solution ofstationary CHD equation has a integrable Bargmann coordinate. Finally Poisson structure anddynamical r-matrix for the restricted system are presented. Related Articles | Metrics