数学物理学报(英文版)

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MULTIPLE SOLUTIONS FOR AN INHOMOGENEOUS SEMILINEAR ELLIPTIC EQUATION IN RN

邓引斌, 李亦, 赵学进

数学物理学报(英文版). 2003 (1): 1-15.

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In this paper, the authors study the existence and nonexistence of multiple positive solutions for problem (− △u + u = f(x, u) + μh(x), x ∈ RN, u ∈ H1(RN),(∗)μ where h ∈ H−1(RN), N ≥ 3, |f(x, u)| ≤ C1up−1 + C2u with C1 > 0, C2 ∈ [0, 1) being some constants and 2 < p < +∞. Under some assumptions on f and h, they prove that there exists a positive constant μ < +∞ such that problem (∗)μ has at least one positive solution uμ if μ ∈ (0, μ), there are no solutions for (∗)μ if μ > μ and uμ is increasing with respect to μ ∈ (0, μ); furthermore, problem (∗)μ has at least two positive solution for μ ∈ (0, μ) and a unique positive solution for μ = μ if p ≤ 2N N−2 .

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REMARKS ON THE LIFESPAN FOR THE SOLUTION TO NONLINEAR WAVE EQUATIONS IN THREE SPACE DIMENSIONS

杨晗, 刘法贵

数学物理学报(英文版). 2003 (1): 16-22.

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The authors consider the Cauchy problem for the following nonlinear wave equations
?????
utt − u = |∇v|2,
vtt − v = (u)2,
u(0, x) = "u0(x), ut(0, x) = "u1(x),
v(0, x) = "v0(x), vt(0, x) = "v1(x),
where x ∈ R3, t ≥ 0, " > 0 is a small parameter, and obtain the sharp bounds for the lifespan of solution to (0.1). Specially, it is proved that there exist two constants C1 and C2, which are independent of ", then the lifespan T(") satisfies the folowing inequalities C1 ≤ lim"!0 " ln T(") ≤ C2.

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TWO ENTIRE FUNCTIONS SHARING FOUR SMALL FUNCTIONS IN THE SENSE OF Ek)(B, f) = Ek)(B, g)

姚卫红

数学物理学报(英文版). 2003 (1): 23-32.

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This paper proves a result that if two entire functions f(z) and g(z) share four small functions aj(z) (j = 1, 2, 3, 4) in the sense of Ek)(aj , f) = Ek)(aj , g), (j = 1, 2, 3, 4) (k 11), then there exists f(z) g(z).

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A NEW FORMULA WITHOUT BOUNDARY INTEGRALS ON A STEIN MANIFOLD

邱春晖

数学物理学报(英文版). 2003 (1): 33-40.

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A new Koppelman-Leray-Norguet formula of (p, q) differential forms for a strictly pseudoconvex polyhedron with not necessarily smooth boundary on a Stein man-ifold is obtained, and an integral representation for the solution of @-equation on this domain which does not involve integrals on boundary is given, so one can avoid complex estimates of boundary integrals.

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QUANTUM PHENOMENON OF THE ENERGY DENSITY OF A HARMONIC MAP TO A SPHERE

周振荣

数学物理学报(英文版). 2003 (1): 41-45.

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This paper proves that if the energy density of a harmonic map to a unit sphere varies between two successive half eigenvalues, then it must be one of them. Applying this result to the Gaussian maps of some submanifolds, the quantum phenomena of the squarelength of the second fundamental forms of these submanifolds is obtained. Some related topics are discussed in this note.

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QUALITATIVE ANALYSIS OF BOBWHITE QUAIL POPULATION MODEL

李先义, 朱德明

数学物理学报(英文版). 2003 (1): 46-52.

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In this paper, the qualitative behavior of solutions of the bobwhite quail pop-ulation model
xn+1 = axn +bxn(1 + xpn−k)c, n = 0, 1, · · · ,
where 0 < a < 1 < a + b, p, c 2 (0,1) and k is a nonnegative integer, is investigated.Some necessary and sufficient as well as sufficient conditions for all solutions of the modelto oscillate and some sufficient conditions for all positive solutions of the model to be nonoscillatory and the convergence of nonoscillatory solutions are derived. Furthermore,the permanence of every positive solution of the model is also showed. Many known results are improved and extended and some new results are obtained for G. Ladas’ open problems.

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EXPLICIT EXPRESSIONS FOR SOME DISTRIBUTIONS RELATED TO RUIN PROBLEMS

党兰芬, 杨丽明

数学物理学报(英文版). 2003 (1): 53-60.

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The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim amount distribution is a finite mixture of exponential distributions or a Gamma (2, ) distribution.

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QUASI-CONFORMING FINITE ELEMENT APPROXIMATION FOR A FOURTH ORDER VARIATIONAL INEQUALITY WITH DISPLACEMENT OBSTACLE

石东洋, 陈绍春

数学物理学报(英文版). 2003 (1): 61-66.

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In this paper, unconventional quasi-conforming finite element approximation for a fourth order variational inequality with displacement obstacle is considered, the op-timal order of error estimate O(h) is obtained which is as same as that of the conventional finite elements.

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INITIAL-OBLIQUE DERIVATIVE PROBLEMS FOR NONLINEAR PARABOLIC SYSTEMS WITH MEASURABLE COEFFICIENTS

闻国椿, 许作良

数学物理学报(英文版). 2003 (1): 67-73.

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This paper deals with some initial-oblique derivative boundary value problems for nonlinear nondivergent parabolic systems of several second order equations with mea-surable coefficients in multiply connected domains. Firstly, a priori estimates of solutions for the initial-boundary value problems are given, and then by using the above estimates of solutions and the Leray-Schauder theorem, the existence and uniqueness of solutions for
the problems are proved.

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ON CHOVER’S LIL FOR THE WEIGHTED SUMS OF STABLE RANDOM VARIABLES

陈平炎, 余旌胡

数学物理学报(英文版). 2003 (1): 74-82.

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Let {Xn, n 1} be a sequence of -stable random variables(0 < < 2),{ani, 1 i n, n 1} be an array of constant real numbers. Under some restrictionof {ani, 1 i n, n 1}, the authors discuss the integral test for the weighted partial sums {Pn i=1 aniXi, n 1}, and obtain the Chover’s laws of iterated logarithm(LIL) as corollaries.

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LENTICULAR NONCOMMUTATIVE TORI

Chun-Gil Park

数学物理学报(英文版). 2003 (1): 83-94.

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All C-algebras of sections of locally trivial C-algebra bundles overQsi=1 Lki (ni) with fibres A! Mc(C) are constructed, under the assumption that every completely irra-tional noncommutative torus A! is realized as an inductive limit of circle algebras, where Lki (ni) are lens spaces. Let Lcd be a cd-homogeneous C-algebra overQsi=1 Lki (ni)×Tr+2 whose cd-homogeneous C-subalgebra restricted to the subspace Tr × T2 is realized as
C(Tr) A l d Mc(C), and of which no non-trivial matrix algebra can be factored out.The lenticular noncommutative torus Lcd is defined by twisting C(dTr+2) C(Zm−2)in Lcd C(Zm−2) by a totally skew multiplier ρ on dTr+2 × Zm−2. It is shown that Lcd Mp∞ is isomorphic to C(Qsi=1 Lki (ni))
AMcd(C) Mp∞ if and only if the set of prime factors of cd is a subset of the set of prime factors of p, and that Lcd is not stablyisomorphic to C(Qs
i=1 Lki (ni)) A Mcd(C) if the cd-homogeneous C-subalgebra o fLcd restricted to some subspace Lki (ni) ?! Qsi=1 Lki (ni) is realized as the crossed productby the obvious non-trivial action of Zki on a cd ki -homogeneous C-algebra over S2ni+1 for ki an integer greater than 1.

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ON CAUCHY-POMPEIU FORMULA FOR FUNCTIONS WITH VALUES IN A UNIVERSAL CLIFFORD ALGEBRA

Heinrich Begehr, 张忠祥, 杜金元

数学物理学报(英文版). 2003 (1): 95-103.

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This paper obtains the Cauchy-Pompeiu formula on certain distinguished boundary for functions with values in a universal Clifford algebra. This formula is just anextension of the Cauchy’s integral formula obtained in [11].

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INVERSE PROBLEMS FOR A GENERAL MULTI-CONNECTED BOUNDED DRUM WITH APPLICATIONS IN PHYSICS

E.M.E.Zayed

数学物理学报(英文版). 2003 (1): 104-116.

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This paper studies the influence of a finite container on an ideal gas.The trace of the heat kernel (t) =P1 μ=1 exp(−tμ), where {μ}1 μ=1 are the eigenvalues of the negative Laplacian −n = −Pn p=1( @ @xp )2 in Rn(n = 2 or 3), is studied for a general multi-connected bounded drum which is surrounded by simply connected bounded domainsi with smooth boundaries @ i(i = 1, · · · ,m) where the Dirichlet, Neumann and Robin
boundary conditions on @i(i = 1, · · · ,m) are considered. Some geometrical properties of are determined. The thermodynamic quantities for an ideal gas enclosed in are examined by using the asymptotic expansions of (t) for short-time t. It is shown that the ideal gas can not feel the shape of its container , although it can feel some geometrical properties of it.

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REPRESENTATION OF ADDITIVE FUNCTIONALS AND LOCAL TIMES FOR JUMP MARKOV PROCESSES AND THEIR FUNCTIONAL LIMIT THEOREM

蒋义文, 刘禄勤

数学物理学报(英文版). 2003 (1): 117-123.

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The representation of additive functionals and local times for jump Markov processes are obtained. The results of uniformly functional moderate deviation and their applications to birth-death processes are also presented

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HETEROGENEOUS INFORMATION ARRIVAL AND R&D OPTION PRICING

薛明皋, 李楚霖

数学物理学报(英文版). 2003 (1): 124-132.

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The paper models the arrival of heterogeneous information during R&D stages
as a doubly stochastic Poisson process(DSPP). The new product market introduction is
considered as a timing option(an American perpetual option). Investment in R&D can be
thought of as option on an option(a compound option). This paper derives an analytic
approximation valuation formula for the R&D option, and demonstrates that the accounts
for heterogeneous information arrival may reduce the pricing biases. This way, the gap
between real option theory and the practice of decision making with respect to investment
in R&D is diminished.

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A NOTE ON MARCINKIEWICZ INTEGRALS WITH H1 KERNELS

徐罕, 陈杰诚, 应益明

数学物理学报(英文版). 2003 (1): 133-138.

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This paper shows that for 2 H1(Sn−1), Marcinkiewicz integral operator μ is Lp(Rn) bounded for 1 < p < 1, which improves some known results.

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THE CHARACTERISTTHE CHARACTERISTICS OF HYPERSPHERES IN MINKOWSKI SPACE

程新跃, 杨文茂

数学物理学报(英文版). 2003 (1): 139-144.

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Y -Riemannian metric gY is an important tool in Finsler geometry, where Y is a smooth non-zero vector field on Finsler manifold. If Y is a geodesic field, it is very effective to study flag curvature using Y -Riemann metric. In this paper, using a special Y -Riemann metric ( that is, so called -Riemann metric ), we study hyperspheres in a Minkowski space and give some characteristics of hyperspheres in a Minkowski space.

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