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26 December 1997, Volume 17 Issue S1 Previous Issue    Next Issue

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Frequecy Domain of Self-excited Oscillation of Deffct Concentration for Crystal Wafer in Irradiation by Ion-beam Hu Xianquan, Lin Zhenqi, Dai Teli Acta mathematica scientia,Series A. 1997, 17 (S1):  1-8.  Abstract ( 67 )   RICH HTML PDF (523KB) ( 65 )   Save By combining linear processing and topological mapping with numerical method,the non-linear differential equations for the defect Concentration and temperature in the case of locating the isotropy crystal wafer in irradiation by ion-beam have been solved. The paper has proved that when the defect production velocity and the temperature of the thermostat, the controllable parameters,are in some range, there are the defect concentration and temperature oscillate periodically with time-the time dissipative structure, studied the dependence of crystal properties on the frequency of self-excited oscillation and irradiation conditions. Take the silicon wafer as an example,the paper presented the frequency domain and the several specific frequencies and amplitudes of self-excited oscillation. Related Articles | Metrics

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Verifing of 1-loop Diagrams of GR Using W-T Identities Shao Changgui, Chen Zhongqiu, Chen Mengquan Acta mathematica scientia,Series A. 1997, 17 (S1):  9-14.  Abstract ( 64 )   RICH HTML PDF (353KB) ( 224 )   Save The Feynman rules for GR are given,the two-point functions are calculated,and the verification of 1-loop diagrams of GR is demonstrated using W-T identities. Related Articles | Metrics

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A Unified Approach to Method of Centers for Multiobjective Decision Making Shi Baochang, Chen Ting, Zhu Shijing Acta mathematica scientia,Series A. 1997, 17 (S1):  15-22.  Abstract ( 65 )   RICH HTML PDF (551KB) ( 62 )   Save This paper studies the structure and convergence of method of centers for solving multiobjective decision making problems. A general algorithm model is presented, in which three curvilinear search rules can be used. Under mild conditions the global convergence of the model is proved. On the basis the selection of search directions and other parameters in the model is discussed and two complementable algorithms are given. The results in the paper unify and extend the existing those on method of centers for single/multiobjective decision making. Numerical test indicates the effectiveness of the algorithm presented. Related Articles | Metrics

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The Conditions for the Cesaro Mean Convergence of a Class of Iterative Sequences Liu Wen, Wang Zikun Acta mathematica scientia,Series A. 1997, 17 (S1):  23-27.  Abstract ( 71 )   RICH HTML PDF (277KB) ( 200 )   Save In this paper the conditions for the Cesaro mean convergence of the iterative sequences generated by the tent map are given,and its relations with metric properties of the binary expansions of the real numbers are studied. Related Articles | Metrics

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Oscillation of the Solutions to a Parabolic Functional Differential Equations Chen Zhentao Acta mathematica scientia,Series A. 1997, 17 (S1):  28-32.  Abstract ( 58 )   RICH HTML PDF (291KB) ( 60 )   Save In this paper it is considered the oscillation behaviour of the solutions to a class of a parabolic functional differential equations. Sufficient conditions are obtained for the oscillation of the solutions satisfying different boundary conditons. Finally, two examples are given. Related Articles | Metrics

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α-Times Integrated Cosine Functions Zhang Jizhou Acta mathematica scientia,Series A. 1997, 17 (S1):  33-38.  Abstract ( 69 )   RICH HTML PDF (387KB) ( 196 )   Save In this paper, it is studied the some basic problems of α-times intgrated cosine functions. The purpose is to prove some basic properties, generation theorems and the relationships with α-times integrated semigroups. The results which we obtain improve and unify the the related results given by Arendt and Kellermann,Li and Shaw,Zheng. Related Articles | Metrics

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Singular Perturbation of Vector Boundary Value Problem with Nonlinear Boundary Conditions Huang WeiZhang Acta mathematica scientia,Series A. 1997, 17 (S1):  39-45.  Abstract ( 76 )   RICH HTML PDF (413KB) ( 56 )   Save Iu this paper, we prove, by the theory of differential inequality, the existance of the solution of nonlinear system with nonlinear boundary conditions by components,that is uniformly valid for the orders till O(εN+1). Related Articles | Metrics

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Chaos in the Semi-Flows and its Inverse Limit systems He Lianfa, Zhang Zhenguo Acta mathematica scientia,Series A. 1997, 17 (S1):  46-51.  Abstract ( 74 )   RICH HTML PDF (453KB) ( 77 )   Save In this paper,we study the invariants of the chaos in the sense of Devaney for continuous dynamical systems. The followings is proved:(1) a semi-flow is chaotic (resp. ω-chaotic) iff inverse limit system of it is chaotic (resp. ω-chaotic); (2) a continuous mcap is chaotic (resp. ω-chaotic) iff suspension semi-flow of it is chaotic (resp. ω-chaotic); (3) suspension flow of inverse limit system of a continuous map is conjugate to inverse limit system of suspension semi-flow of it. It follows from (2) and (3)that (1) is a generalizafion of those obtained for discrete dynamical systems in[4]. Related Articles | Metrics

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Global Smooth Solution for P-System with Dissipation Guo Changquan Acta mathematica scientia,Series A. 1997, 17 (S1):  52-56.  Abstract ( 61 )   RICH HTML PDF (306KB) ( 9 )   Save In this paper, the global smooth solution to the initial value problem of p-system with dissipation are considered. Results of existence of global smooth solution with large amplitude and small derivation initial data are obtained. Related Articles | Metrics

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A New Lax Integrable System and Its Liouville Integrability Xu Xixiang Acta mathematica scientia,Series A. 1997, 17 (S1):  57-61.  Abstract ( 57 )   RICH HTML PDF (283KB) ( 11 )   Save A new isospectral problem is discussed,according to Tu Guizhang scheme, the corresponding hierarchy of Lax integrable nonlinear evolution equations is derived,and their Hamiltonian struture are given by means of trace identity method. It is shown that this hierarchy is Liouville integrable. Related Articles | Metrics

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The Probability Density and Uncertainty Relation of any one of Stars with Random Motion in Irregular Galactic System Lan Chengrong, Shi Wenyia, Lai Sanzhi, Lan Xin Acta mathematica scientia,Series A. 1997, 17 (S1):  62-65.  Abstract ( 67 )   RICH HTML PDF (238KB) ( 36 )   Save In this pater,we describe the random motion of any one of stars in irregular galactic system by using Langevin equation.Using the represent points in phase space X,Ẋ,we can describe each random state of the star with random motion. From Fokker-Planck equation, we have calculated the probability density fs(X,Ẋ) of these random states.#br#According to fs(X,Ẋ), we have calculated the square of the standard deviation and fluctuation corresponding to the position and velocity of these stars with random motion.Hence,we discover that any one of stars with random motion in irregular galactic system should satisfy the uncertainty relation of celestial body. Related Articles | Metrics

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Global Attractivity in a Periodic Delay-Logistic Equation Li Yongkun Acta mathematica scientia,Series A. 1997, 17 (S1):  66-69.  Abstract ( 68 )   RICH HTML PDF (242KB) ( 61 )   Save In this paper,we establish the existence of a positive periodic solution for#br#N'(t)=r(t)N(t)[1-N(t-τ)/k(t)],#br#and we obtain sufficient conditions for uniqueness and global attractivity of the positive periodic solution. Our results extend and improve the correspond ones in[1]. Related Articles | Metrics

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On the Dirichlet Eigenvalue Problem of the Folland-Stein Operator on the Heisenberg Group Luo Xuebo, Niu Pengcheng Acta mathematica scientia,Series A. 1997, 17 (S1):  70-75.  Abstract ( 77 )   RICH HTML PDF (341KB) ( 20 )   Save We study the Dirichlet eigenvalue problem of the Folland-Stein operator Lα which has discrete eigenvalues as|Reα|<n and positive eigenvalues as α∈(-n,n). Then by establishing the Rayleigh Theorem and the Min-Max Theorem we give the estimates for the differences of the consecutive eigenvalues. Related Articles | Metrics

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Complete Convergence for Sums of B-valued Random Elements Liang Hanying, Niu Sili Acta mathematica scientia,Series A. 1997, 17 (S1):  76-82.  Abstract ( 67 )   RICH HTML PDF (393KB) ( 145 )   Save We discuss the complete convergence for the partial sums of B-valued random element sequences which are bounded by a non-negative random variable. As an application we obtain corresponding results for randomly indexed partial sums of B-valued random element sequences. Some results in[5] are extended to sequences of B-valued independent random elements,and the results in[3] (d=1),[4],[6]are particular case of these results. Related Articles | Metrics

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Extension of Solution on Nonlinear Singular Lntegal Differential Eguation Wu Haoshen, Liu Jun Acta mathematica scientia,Series A. 1997, 17 (S1):  83-89.  Abstract ( 81 )   RICH HTML PDF (452KB) ( 61 )   Save In this paper,it is investigated the following with Cauchy's kernel Lu(t)=Σj=0m[a1(t)u(j)(t)+(1/(πj))∫(K1(t,τ)u(j)(τ)/(τ-1))dτ]=(1/(πi))∫((φ[t,τ,U(τ),λ])/(τ-t))dτ.(1) u(j)(t0)=u0j (t0∈Γ,j=0,…,m-1) (1). Where Γ is a simple Liapunov's closed path, u (t) is a nonknown function u(t)={u(t), u(t),…, u(n) (t)}, u0j are some real or complex number. Ref.[1]-[s] applied the interpolation and topological method for the equation (1). By using the Liapunov's method,Ref、[6],[7],studied the solution of equation (1). Related Articles | Metrics

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Global Solutions of the Cubic Autocatalytic Model Wu Jianhua, Zhang Quande Acta mathematica scientia,Series A. 1997, 17 (S1):  90-96.  Abstract ( 60 )   RICH HTML PDF (414KB) ( 152 )   Save The paper first obtains the L2-apriori estimates for the solutions of two kinds of autocatalytic models under Dirichlet boundary conditions, and then, using the properties of linear semigroup and delicate calculations, the estimates of the maximal norms are obtained, therefore, the global existence of the solutions is proved. In the meantime, the existence of the maximal attractor is also given. Related Articles | Metrics

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Maluta Coefficients of Quotients Spaces of lp(1 ≤ p<∞) Hu Changsong Acta mathematica scientia,Series A. 1997, 17 (S1):  97-101.  Abstract ( 43 )   RICH HTML PDF (277KB) ( 12 )   Save For a Banach space X. Maluta introduced the Maluta coefficient of X denoted as D(X). In this paper, we study the Maluta coefficient of quotients spaces of lp and show that D(X/M)=D(X), if M is complemented subspace in X and has schur property. Related Articles | Metrics

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One Necessary and Sufficient Condition on Convex Sets Being Strongly Separated and its Applications Yang Ganshang Acta mathematica scientia,Series A. 1997, 17 (S1):  102-107.  Abstract ( 71 )   RICH HTML PDF (419KB) ( 61 )   Save In this paper,first step,we have obtained one necessary and sufficent condition on noncompact convex sets being strongly separated, it is an improvement of some theorems in[1,2]. Second step, by using the results obtained in first step, we have improved some theorems in[4-7] and one result in[8]. Related Articles | Metrics

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On Non-Oscillation and Asymptotic Behavior of the Solutions of a Class of Nonlinear Equation With Periodic Coefficients Feng Zhaosheng, Fei Shumin Acta mathematica scientia,Series A. 1997, 17 (S1):  108-113.  Abstract ( 53 )   RICH HTML PDF (378KB) ( 75 )   Save In the paper, it is investigated the following nonlinear differential equation.with periodic coefficients y'=Σi=0mAi(t)y' (m > 2,m∈N) (1) Obtained a few theorens for non-oscillation and by the method of cross-ratio of solutions and the Brouwer fined point theorem and asymptotic of the solutions of equation (1). Related Articles | Metrics

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Method of Determing Irreducible Paths Zhang Bingru Acta mathematica scientia,Series A. 1997, 17 (S1):  114-119.  Abstract ( 48 )   RICH HTML PDF (364KB) ( 12 )   Save let un=Σk ≤ nn-kk and Pn denote the path with n vertices. In this paper, it is proved that Pn are shown to be irreducible path if n=3 of n=q-1, where q ≥ 3 are prime and[(uq-1-1) + 1]/uq-1 are positive integer. Related Articles | Metrics

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Oscillatory Properties of Solutions of Impulsive Delay Differential Equations With Positive and Negative Coefficients Zhang Yuzhu, Yan Jurang Acta mathematica scientia,Series A. 1997, 17 (S1):  120-124.  Abstract ( 55 )   RICH HTML PDF (270KB) ( 61 )   Save In this paper, we consider the first order impulsive delay differential equations with positive and negative coefficients, two sufficient conditions are obtained for the oscillation of all of its solutions. Related Articles | Metrics

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A NEW RESULT ON ERDÖS-SÓS CONJECTURE Wang Min, Zhao Yanqing, Li Guojun Acta mathematica scientia,Series A. 1997, 17 (S1):  125-131.  Abstract ( 52 )   RICH HTML PDF (453KB) ( 10 )   Save Erdös and Sós conjectured in 1963 that if G is a graph of order q and size q with q>(1/2)p(k-1), then G contains every tree of size k. It is shown in this paper that the conjecture is true if the complement G of G contains no a copy of K3 as an induced subgraph of G. Related Articles | Metrics

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ORTHONORMAL POLYNOMIAL BASSES AND WAVELET-PACKETS Han Bin Acta mathematica scientia,Series A. 1997, 17 (S1):  132-139.  Abstract ( 54 )   RICH HTML PDF (490KB) ( 11 )   Save For any fixed ε > 0, an explicit construction of anorthonormal trigonometric polynomial basis {Tk}k=1∞ in L2[0,1) with deg Tk ≤ 0.5(1 +ε)k is presented. Thus weimprove the results obtained by D. Offin and K. Oskolkov in[4] and by Al. A. Privalov in[6]. and practically solve the open problemasked in[4],[8] and[9]. Moreover, as in[4], Fourier sums with respectto this polynomial basis are projectors onto subspaces of trigonometricpolynomials of high degree, which implies almost best approximation-properties. Related Articles | Metrics

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THE INITIAL TRACE OF SOLUTIONS FOR POROUS MEDIUM EQUATION WITH CONVECTION Lu Guofu Acta mathematica scientia,Series A. 1997, 17 (S1):  140-153.  Abstract ( 45 )   RICH HTML PDF (739KB) ( 10 )   Save In this paper author consider the following problem ut=△um+bi(un)xi Let u=u(x.t) be a continuous weak solution of the equation in RN×(O,T] for some T >O.Then author conclude:corresponding to u there is a unique nonnegative Borel measure v on RN which is the initial trace of u; there is the global inequality of Harnack type for u; the initial trace must belong to a certain growth class; consequently, by combining the results mentioned above a uniqueness conclusion is established. Related Articles | Metrics

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SOME CLASSES OF UPPER EMBEDDABLE GRAPHS Hyang Yuangqiu, Liu Yanpei Acta mathematica scientia,Series A. 1997, 17 (S1):  154-161.  Abstract ( 47 )   RICH HTML PDF (534KB) ( 9 )   Save In this paper, we provide a number of new classes of upper embeddable graphs which are with specific degrees, specific edges. Related Articles | Metrics

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THE HAUSDORFF DIMENSION AND MEASURE IN GENERALIZED GEOMETRIC GRAPH DIRECTED CONSTRUCTION Su Feng, Zhao Xingqiu Acta mathematica scientia,Series A. 1997, 17 (S1):  162-167.  Abstract ( 51 )   RICH HTML PDF (312KB) ( 10 )   Save Abthors introduce the notation of generalized geometric constructions in Rm generated by a directed graph G and by a sequence of similarity ratios which are labelled with the edges of this graph. In this paper, it is obtained the Hausdorff dimension and measure of this construction object for some cases. Related Articles | Metrics

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EXPLICIT EXACT SOLUTIONS TO A GENERALIZED KDV EQUAFION Ma Wenxiu, Zhou Detang Acta mathematica scientia,Series A. 1997, 17 (S1):  168-174.  Abstract ( 53 )   RICH HTML PDF (415KB) ( 17 )   Save This paper carefully analyses the possibility of that a generalized KdV equation possesses a family of solutions of the finite series form,and thus a kind of its explicit complex exact solutions is cxhibited.These complex solutions constitute real exact solutions to the system of complex form of the above generalized KdV equation. Related Articles | Metrics

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GLOBAL ATTRACTIVITY FOR A MULTIPLICATIVE DELAY DIFFERENTIAL POPULATION MODEL Hou Zhenting, Luo Jiaowan, Yu Jianshe Acta mathematica scientia,Series A. 1997, 17 (S1):  175-183.  Abstract ( 43 )   RICH HTML PDF (450KB) ( 12 )   Save Sufficient conditions are presented for the asymptotic behavior of all positive solutions of the multiplicative delay Logistic equation ((dN(t))/dt)=r(t)N(t)(1-Πj=1m(N(gj(t))/K)) about the positive equilibrium K. The case when r(t)=r and gj(t)=t-τj or gj(t)=[t-kj],[·] denoting the greatest integer function,where r, τj and kj are positive constants, j=1, 2,… m, ale also included. Related Articles | Metrics

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ASSESSMENT OF LOCAL INFLUENCE IN MULTIVARIATE REGRESSION MODEL Shi Lei, Ren Shiquan Acta mathematica scientia,Series A. 1997, 17 (S1):  184-194.  Abstract ( 42 )   RICH HTML PDF (677KB) ( 8 )   Save In this article, authors introduce a method to assess local influence of observations on the parameter estimates and prediction in multivariate regression model. The diagnostics under the perturbations of error variance, response variables and explanatory variables are derived, and the results are compared with those of casedeletion. Two examples are analyzed for illustration. Related Articles | Metrics

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THE SINGULARLY PERTURBED NONLINEAR ELLIPTIC SYSTEMS IN A HALF SPACE Zhang Hanlin, Mo Jiaqi Acta mathematica scientia,Series A. 1997, 17 (S1):  195-199.  Abstract ( 50 )   RICH HTML PDF (284KB) ( 12 )   Save The singularly perturbed problems for elliptic systems in a half space are considered. Under suitable conditions, and by using the comparison theorem the existence and asymptotic behavior of solution for the boundary value problems are studied. Related Articles | Metrics

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ON THE NONAUTONOMOUS PREDATOR-PREY LOTKA-VOLTERRA DIFFUSION SYSTEMS Song Xinyu Acta mathematica scientia,Series A. 1997, 17 (S1):  200-205.  Abstract ( 55 )   RICH HTML PDF (317KB) ( 9 )   Save In the present paper,the nonautonomous two-species Predator-Prey models with diffusion are considered. Prey species can diffuse between two patches, while the predator species is confined to one patch and cannot diffuse. It is proved that if the coefficients satisfy certain inequalities,then the system can be made persistent and have a strictly positive periodic orbit which is glotally asymptotically stable. Related Articles | Metrics

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INTEGRATED BISEMIGROUP AND APPLICATIONS TO IMPULSIVE DIFFERENTIAL EQUATIONS Xu Genqi Acta mathematica scientia,Series A. 1997, 17 (S1):  206-210.  Abstract ( 48 )   RICH HTML PDF (280KB) ( 8 )   Save In this paper author studies the solvability of abstract impulsive differential equations on Banach space X. By terms of integrated bisemigroup, author obtains the existence of abstract impulsive differential equations with finite contant impulses and gives a condition which makes the impulsive equation be solvable for a Variable impuls. Related Articles | Metrics

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SEMIGROUPS OF POSITIVE CONTRACTIONS AND APPLICAfIONS TO LINEAR TRANSPORT THEORY Zhang Xianwen Acta mathematica scientia,Series A. 1997, 17 (S1):  211-216.  Abstract ( 44 )   RICH HTML PDF (337KB) ( 9 )   Save In this paper, author abtains a group of characteristic conditions for the infinitesimal generators of positive contraction semigroups and stochastic semigroups.Furthermore, Applications of them to linear transport theory are discussed. Related Articles | Metrics

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THE SPECTRUM OF THE LAPLACE OPERATION ON COMPACT SUBMANIFOLDS Ni Yiliong, Xu Senlin Acta mathematica scientia,Series A. 1997, 17 (S1):  217-224.  Abstract ( 58 )   RICH HTML PDF (411KB) ( 14 )   Save Let M be a compct submanifold of sphere SN, and M be Cliford torus imbedding in SN. If Spec0(M)=Spec0(M), and Specq(M)=Specq(M), then author can obtaid that M is isometric to M. Related Articles | Metrics