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31 December 1994, Volume 14 Issue S1 Previous Issue    Next Issue

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ABSOLUTE CONTINUITY OF THE OCCUPATION TIME PROCESSES WITH RESPECT TO LEBESGUE MEASURE FOR SUPER-BROWNIAN MOTION Wang Yongjin Acta mathematica scientia,Series B. 1994, 14 (S1):  1-7.  Abstract ( 116 )   RICH HTML   PDF (353KB) ( 50 )   Save Some properties of Super-Brownian motion have been approached by Dawson & Hochberg[1], Iscoe[2] &[3], Konnô & Shiga[4] and so on. In this paper, we limit our attention to the occupation time processes of the Super-Brownian motion,and try to give an intuitive proof for their absolute continuity with respect to the Lebesgue measure on Rd (d ≤ 3) when the initial measure of the Super-Brownian motion has the absolute continuity. Related Articles | Metrics

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CAVITATION OF NONLINEAR HYPERELASTICITY IN TOROIDAL BODY zhang Chengdian, Li Kaitai Acta mathematica scientia,Series B. 1994, 14 (S1):  8-22.  Abstract ( 103 )   RICH HTML   PDF (815KB) ( 48 )   Save Dealing with a class of isotropic material of hyperelasticity occupaying a "toroidal" body in R3, we give a proof of existence of the cavitating solutions. Related Articles | Metrics

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THE DISCUSSION ON THE NORMAL FUNDAMENTAL REGION OF FUCHS GROUP WITH NONEUCLIDEAN GEOMETRY Sun Zongyang Acta mathematica scientia,Series B. 1994, 14 (S1):  23-29.  Abstract ( 109 )   RICH HTML   PDF (419KB) ( 47 )   Save We define the fundamental region homeomorphic to the corresponding Riemann surface according to the methods on form-conserved circle of the fractional linear transformation in explaining that the form-conserved circle is the perpendicular bisector of noneuclidean segment limited by the end points both the origin and the equivalent point by the same transformation just mentioned and, consequently, its sense on noneuclidean geometry is clarified.The result does not appear in current literatures and is useful for the research of superstring. Related Articles | Metrics

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SYMMETRY IN FIELD THEORY FOR SINGULAR LAGRANGIAN WITH DERIVATIVES OF HIGHER ORDER Li Ziping Acta mathematica scientia,Series B. 1994, 14 (S1):  30-39.  Abstract ( 97 )   RICH HTML   PDF (588KB) ( 59 )   Save We have derived the first Noether theorem and Noether identities in canonical formalism for field theory with higher-order singular Lagrangian,which is a powerful tool to analyse Dirac constraint for such system. A gauge-variant system in canonical variables formalism must has Dirac constraint.For a system with first class constraint (FCC), we have developed an algorithm for construction of the gauge generator of such system. An application to the Podolsky generalized electromagnetic field was given. Related Articles | Metrics

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EXISTENCE OF POSITIVE SOLUTION TO-Δu=f(x,u) WHEN f CHANGES SIGNS Jiang Ming Acta mathematica scientia,Series B. 1994, 14 (S1):  40-45.  Abstract ( 149 )   RICH HTML   PDF (304KB) ( 53 )   Save The existence of positive solutions to the semlinear elliptic boundary value problem -Δ=f(x,u) in Ω and u=0 on ∂Ω is studied in this paper. The result obtained differs from the other known results in that the positivity of the solution does not follow from the positivity of f.Our result roughly says that if Ω is not too wide in some one direction, there is always a positive solution even if f changes signs, which is proved using the so-calles sub-super solution approach. Related Articles | Metrics

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ISOMETRIC APPROXIMATION FROM 2-DIM BANACH SPACE INTO L1[0,1] Zhang Qinghong Acta mathematica scientia,Series B. 1994, 14 (S1):  46-52.  Abstract ( 150 )   RICH HTML   PDF (353KB) ( 43 )   Save In this paper, some characterizations of isometric operators and ε-isometric opertors from 2-dim Banach Space E2 into L1[0, 1] are given, where E2 denotes a Banach Space whose unit ball is the union of a polygon C and the region enclosd by C in the plane. Also,the answer for IAP(Isometric Approximation Problem) on B(E2,L1[0, 1]) is obtained. Related Articles | Metrics

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DISCUSSION ON THE Cr-SOLUTIONS OF THE ITERATED EQUATION λ1f(x)+λ2f2(x)=F(x) Si Jianguo Acta mathematica scientia,Series B. 1994, 14 (S1):  53-63.  Abstract ( 149 )   RICH HTML   PDF (582KB) ( 48 )   Save In this paper, we consider the iterated equation λ1f(x) + λ2f2(x)=F(x) (*) where f2(x)=f(f(x)), F (x) denotes known function and f(x) denotes the unknown function. There are given conditions for the existence, uniqueness and stability of Cr-solutions of the iterated equation (*) and also there is a proved theorem for the continuous dependence of Cr-solutions of iterated equation (*) on the given function. Related Articles | Metrics

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WELL-POSEDNESS AND CONTROLLABILITY AND OBSERVABILITY OF A COUPLED VIBRATING SYSTEM Xu Yanqin, Hu Shunju Acta mathematica scientia,Series B. 1994, 14 (S1):  64-72.  Abstract ( 118 )   RICH HTML   PDF (513KB) ( 52 )   Save In this paper, we derive a new description form of coupled bending and torsional vibrating system with boundary control and observation through Green's formula and prove that it is equivalent to the original form. On the basis of this. we prove the control system is well-posed in time and frequency domain and completely controllable and observable. Related Articles | Metrics

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THE LOCUS OF SHOCK FRONT OF SPHERICAL BLAST WAVES WITH BACK PRESSURE Wu Shourong Acta mathematica scientia,Series B. 1994, 14 (S1):  73-77.  Abstract ( 112 )   RICH HTML   PDF (261KB) ( 48 )   Save This papaer presents an analytic formula for the locus of shock front of spherical blast waves with back pressure. Meanwhile, it is shown that the wave velocity is inversely proportions to the area of shock wave in the Lagrangian coordinate space. If shock wave is propagating into the gas at rest, the wave velocity is also inversely propagating into the gas at rest, the wave velocity is also inversely proportional to the area of shock front in the Eulerian coordinate space. The results obtained are generally applicable and may be suited to the wave velocity of contracting spherical shock wave. Related Articles | Metrics

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OPTIMAL CONTROL OF A CLASS OF INFINTIE DIMENSIONAL UNCERTAIN SYSTEMS Xiang Xiaoling Acta mathematica scientia,Series B. 1994, 14 (S1):  78-87.  Abstract ( 100 )   RICH HTML   PDF (561KB) ( 48 )   Save In this paper, we use relaxation theory to study a class of relaxed infinite dimensional uncertain systems.We obtained the exisence and some important properties of solutions of relaxed systems first. Then the existence of optimal control of relaxed systems with a correspondingly relaxed cost functional was proved. Lastly, we showed that under some assumptions the set of original trajectories is dense in the set of relaxed trajectories and the relaxed control problem is equivalent to the original one. Related Articles | Metrics

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ON SOME MULTIVARIATE DISTRIBUTIONS Xia Mingyuan Acta mathematica scientia,Series B. 1994, 14 (S1):  88-90.  Abstract ( 95 )   RICH HTML   PDF (180KB) ( 47 )   Save In this Paper we generalized the Wishart matrix and the Hotelling's T2 statistic and investigated their distrbutions. Related Articles | Metrics

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SOME CONDITIONS FOR f-COVERED GRAPHS Liu Guizhen Acta mathematica scientia,Series B. 1994, 14 (S1):  91-97.  Abstract ( 100 )   RICH HTML   PDF (421KB) ( 44 )   Save A graph G is f-covered if each edge of G belongs to an f-factor. Some sufficient conditions for a graph to be f-covered are given.Katerinis' and Bermond's results are generalized. Related Articles | Metrics

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THE STATIONARY DISTRIBUTION OF A CONTINUOUS-TIME RANDOM GRAPH PROCESS WITH INTERACTING EDGES Han Dong Acta mathematica scientia,Series B. 1994, 14 (S1):  98-102.  Abstract ( 157 )   RICH HTML   PDF (312KB) ( 49 )   Save In previous papers, the stationary distributions of a class of discrete and continuous time random graph processes with state space consisting of the simple and directed graphs on N venices were studied. In this paper, the random graph graph process is extended one impotent step further by allowing interaction of edges. Similarly, We obtha the expressions of the stationary distributions and prove that the process is ergodic under different editions. Related Articles | Metrics

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THE RELATIVE EFFICIENCIES OF LEAST SQUARES IN LINEAR MODELS Chen Jianbao, Zhan Jinlong Acta mathematica scientia,Series B. 1994, 14 (S1):  103-109.  Abstract ( 122 )   RICH HTML   PDF (413KB) ( 45 )   Save The present paper discusses the relative efficiencies of the least square estimates in linear models. For Gauss-Markoff model:Y=Xe + e,E(e)=0, Cov(e)=σ2V, an new efficiency of least square estimate for linearly estimable function c' τ is proposed and its lower bound is given. For variance component model:Y=Xτ+ e, E(e)=0, Cov(e)=∑i=1mσ2V, an new efficiency of least square estimate for linearly estimable function c' τ is introduced for the first time and its lower bound, which is independent of unknown parameters, is also obtained. Related Articles | Metrics

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BOUNDEDNESS PROPERTIES OF SOLUTIONS OF DOUBLY NONLINEAR PARABOLIC EQUATIONS Liang Xiting, Liang Xuexin Acta mathematica scientia,Series B. 1994, 14 (S1):  110-117.  Abstract ( 103 )   RICH HTML   PDF (447KB) ( 50 )   Save Consider a doubly nonlinear parabolic equation and prove the boundedness of its generalized solutions. Related Articles | Metrics

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SOME ESTIMATES ABOUT WHITE NOISE FUNCTIONALS AND APPLICATIONS Liao Y. L., Liu Kai Acta mathematica scientia,Series B. 1994, 14 (S1):  118-126.  Abstract ( 111 )   RICH HTML   PDF (506KB) ( 47 )   Save Some estimate results about translation, scaling transform and pointwise product within the Meyer-Yan's framework are obtained. Some applications of there adults to wiener product and Gateaux differentiation are also proposed. Related Articles | Metrics