数学物理学报(英文版)

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INTERSECTION OF PRIME SUBMODULES AND DIMENSION OF MODULES

A. Azizi

数学物理学报(英文版). 2005 (3): 385-394.

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The aim of this paper is to study the conditions by which a P-prime sub-
module can be expressed as a ¯nite intersection or union of P-prime submodules. Also
corresponding to dimension and rank of modules, some equivalent conditions for a ring to
be a Dedekind domain are given.

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ON THE PRODUCT OF G\^ATEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES

沈喜生|程立新

数学物理学报(英文版). 2005 (3): 395-400.

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A locally convex space is said to be a Gˆateaux differentiability space (GDS)
provided every continuous convex function defined on a nonempty convex open subset D
of the space is densely Gˆateaux differentiable in D.This paper shows that the product of
a GDS and a family of separable Fr´echet spaces is a GDS,and that the product of a GDS
and an arbitrary locally convex space endowed with the weak topology is a GDS.

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COINCIDENCE THEOREMS IN PRODUCT G-CONVEX SPACES

丁协平

数学物理学报(英文版). 2005 (3): 401-407.

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By applying the technique of continuous partition of unity, some new co-
incidence theorems for a better admissible mapping and a family of set-valued mappings
defined on the product G-convex spaces are proved. Theorems of this paper improve, unify
and generalize many important coincidence theorems and collectively fixed point theorems
in recent literature.

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(r,s)-STABILITY OF UNFOLDING OF |

$\Gamma$ -EQUIVARIANT PROBLEM

刘恒兴, 张散穆

数学物理学报(英文版). 2005 (3): 408-418.

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In this paper,the $\Gamma$ -equivariant $(s,t)$ -equivalence
relation and $\Gamma$ -equivariant infinitesimally
$(r,s)$ -stability of
$\Gamma$ -equivariant bifurcation problem are defined. The
criterion for $\Gamma$ -equivariant infinitesimally
$(r,s)$ -stability is proven when $\Gamma$ is a compact finite Lie
group . Transversality
condition is used to characterize the stability.

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ON THE BOREL SUMMABILITY OF FORMAL SOLUTIONS FOR SOME FIRST ORDER SINGULAR PDES WITH IRREGULAR SINGULARITY

陈化, 张志雄

数学物理学报(英文版). 2005 (3): 419-426.

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In this paper the authors consider the summability of formal solutions for
some first order singular PDEs with irregular singularity. They prove that in this case the
formal solutions will be divergent, but except a enumerable directions, the formal solutions
are Borel summable.

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FINITE DIFFERENCE FRACTIONAL STEP METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

袁益让

数学物理学报(英文版). 2005 (3): 427-438.

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Characteristic finite difference fractional step schemes are put forward. The
electric potential equation is described by a seven-point finite difference scheme, and the
electron and hole concentration equations are treated by a kind of characteristic finite dif-
ference fractional step methods. The temperature equation is described by a fractional step
method. Thick and thin grids are made use of to form a complete set. Piecewise threefold
quadratic interpolation, symmetrical extension, calculus of variations, commutativity of
operator product, decomposition of high order difference operators and prior estimates are
also made use of. Optimal order estimates in l2 norm are derived to determine the error of
the approximate solution. The well-known problem is thoroughly and completely solved.

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COMPUTATIONAL COMPLEXITY IN WORST, STOCHASTIC AND AVERAGE CASE SETTING ON FUNCTIONAL APPROXIMATION PROBLEM OF MULTIVARIATE

房艮孙,叶陪新

数学物理学报(英文版). 2005 (3): 439-448.

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The order of computational complexity of all bounded linear functional approximation
problem is determined for the generalized Sobolev class W
p (Id), Nikolskii
class Hk
1(Id) in the worst (deterministic), stochastic and average case setting, from which
it is concluded that the bounded linear functional approximation problem for the classes
W
p (Id) and Hk
1(Id) is intractable in worst case setting, but is tractable with respect to
stochastic and average case setting.

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LINEAR ¤-DERIVATIONS ON JB¤-ALGEBRAS

Park Chun-Gil

数学物理学报(英文版). 2005 (3): 449-454.

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It is shown that for a derivation $f(x_1 \circ \cdots \circ x_{j-1}\circ x_j\circ x_{j+1} \circ \cdots \circ x_k)= \sum_{j=1}^k x_1\circ \cdots \circ x_{j-1}\circ x_{j+1}\circ \cdots\circ x_k \circ f(x_j)$ on a $JB^*$ -algebra ${\cal B}$ , there
exists a unique ${\Bbb C}$ -linear $*$ -derivation $D : {\cal B} \rightarrow {\cal B}$ near the derivation.

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EXISTENCE OF MINIMISERS FOR A CLASS OF FREE DISCONTINUITY PROBLEMS IN THE HEISENBERG GROUP Hn 1

宋迎清, 杨孝平, 秦姣华

数学物理学报(英文版). 2005 (3): 455-469.

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The purpose of this paper is to prove existence of minimisers of
the functional
$J(K,u):=\int_{\Omega\setminus K}f(L_u){\rm d}x+\alpha \int_{\Omega\setminus K}|u-g|^q {\rm d}x+\beta \sdqe(K\cap\Omega),$
where $\Omega$ is an open set of the Heisenberg group
$\hn$ , $K$ runs over all closed sets of $\hn$ , $u$ varies in
$C_H^1(\Omega\setminus K)$ , $\alpha$ , $\beta >0,q\ge 1,g\in L^q(\Omega)\cap L^\infty(\Omega)$ and $f:R^{2n} \rightarrow R$ is a
convex function satisfying some
structure conditions (H $_1$ )(H $_2)$ (H $_3)$ (see below).

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THE COMPARISON OF GREEN FUNCTION |FOR QUASI-LINEAR ELLIPTIC EQUATION

郑神州, 康秀英

数学物理学报(英文版). 2005 (3): 470-480.

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A generalization of the usual Green function to a kind of nonlinear elliptic
equation of divergence form is discussed. The regularity and comparison principle of Green
function in the sense of distribution are shown.

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PERSISTENCE OF RESONANT INVARIANT TORI WITH NON-HAMILTONIAN PERTURBATION

白玉真, 朱德明

数学物理学报(英文版). 2005 (3): 481-491.

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A persistence theorem for resonant invariant tori with non-Hamiltonian per-
turbation is proved. The method is a combination of the theory of normally hyperbolic
invariant manifolds and an appropriate continuation method. The results obtained are
extensions of Chicone’s for the three dimensional non-Hamiltonian systems.

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THE BI-SELF-CONJUGATE AND NONNEGATIVE DEFINITE SOLUTIONS TO THE INVERSE EIGENVALUE PROBLEM OF QUATERNION MATRICES

储玉明

数学物理学报(英文版). 2005 (3): 492-504.

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The main aim of this paper is to discuss the following two problems: \\
Problem I: Given $X\in H^{n\times m}$ (the set of all $n\times m$ quaternion matrices),
$\Lambda={\rm diag}(\lambda_1, \cdots$ , $\lambda_m)\in H^{m\times m}$ ,
find $A\in BSH_\geq^{n\times n}$ such that $AX=X\Lambda$ , where $BSH_\geq^{n\times n}$
denotes the set of all $n\times n$ quaternion matrices which are bi-self-conjugate and nonnegative definite.\\
ProblemⅡ: Given $B\in H^{n\times m}$ , find $\overline{B}\in S_E$ such that
$\|B-\overline{B}\|_Q=\min_{A\in S_E}\|B-A\|_{Q},$
where $S_{E}$ is the solution set of problem Ⅰ, $\|\cdot\|_Q$ is the
quaternion matrix norm. The necessary and sufficient conditions for $S_E$ being nonempty are obtained.
The general form of elements in $S_E$ and the expression of the unique solution $\overline{B}$
of problem Ⅱ are given.

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SOME INEQUALITIES ABOUT DUAL MIXED VOLUMES OF STAR BODIES

李小燕,冷岗松

数学物理学报(英文版). 2005 (3): 505-510.

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The authors establish some inequalities about the dual mixed volumes of star
bodies in Rn. These inequalities are the analogue in the Brunn-Minkowski theory of the
inequalities of Marcus-Lopes and Bergstrom about symmetric functions of positive reals.

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EXPLICIT DESCRIPTION OF A CLASS OF INDECOMPOSABLE INJECTIVE MODULES

M.R. Pournaki,M. Tousi

数学物理学报(英文版). 2005 (3): 511-514.

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Let R be a commutative Noetherian ring and p be a prime ideal of R such
that the ideal pRp is principal and ht(p) 6= 0. In this note, the anthors describe the explicit
structure of the injective envelope of the R-module R=p.

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TWO PROBLEMS ABOUT COMPOSITION OPERATORS ON HARDY SPACE

吴树宏, 王茂发, 刘陪德

数学物理学报(英文版). 2005 (3): 515-524.

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In this paper, two problems about composition operator on Hardy space are
considered. Firstly, a new estimation of the norm of a class of composition operators is
given. Secondly, the cyclic behavior of the adjoint operator of a composition operator is
discussed.

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ON THE STRONG LAW OF LARGE NUMBERS

邱德华,甘师兴

数学物理学报(英文版). 2005 (3): 525-532.

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This paper introduces the concept of BC sequences and investigates some
conditions which imply the strong law of large numbers for these sequences. The authors
also study the strong law of large numbers for general random variable sequences. As
applications of the result the authors characterize p-smoothableness of Banach space. Some
generalizations of Petrov theorem, the Marcinkiewicz-Zygmund theorem and Hoffmann-
Jørgensen and Pisier theorem are obtained.

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EXISTENCE OF SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS AND HARDY TERMS

韩丕功

数学物理学报(英文版). 2005 (3): 533-544.

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This paper deals with the existence of solutions to the elliptic equation −u−
µ u
|x|2 = u + |u|2∗−2u + f(x, u) in
, u = 0 on @
, where
is a bounded domain in
RN(N ≥ 3), 0 ∈
, 2 = 2N
N−2 , > 0, 6∈ µ, µ is the spectrum of the operator
− − µI
|x|2 with zero Dirichlet boundary condition, 0 < µ < ¯µ, ¯µ = (N−2)2
4 , f(x, u) is
an asymmetric lower order perturbation of |u|2∗−1 at infinity. Using the dual variational
methods, the existence of nontrivial solutions is proved.

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ON THE COMMUTATORS OF SINGULAR INTEGRAL OPERATORS

胡国恩

数学物理学报(英文版). 2005 (3): 545-554.

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Lp(Rn) (1 < p < 1) boundedness and a weak type endpoint estimate are
considered for the commutators of singular integral operators. A condition on the associated
kernel is given under which the L2(Rn) boundedness of the singular integral operators
implies the Lp(Rn) boundedness (1 < p < 1) and the weak type (H1(Rn), L1(Rn))
boundedness for the corresponding commutators. A new interpolation theorem is also
established.

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THE DECOMPOSITION OF STATE SPACE FOR MARKOV CHAIN IN RANDOM ENVIRONMENT

胡笛鹤

数学物理学报(英文版). 2005 (3): 555-568.

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This paper is a continuation of [8] and [9]. The author obtains the decomposition
of state space X of an Markov chain in random environment by making use of the
results in [8] and [9], gives three examples, random walk in random environment, renewal
process in random environment and queue process in random environment, and obtains
the decompositions of the state spaces of these three special examples.

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MULTIPLICATION OF WEAK FUNCTIONS

丁夏畦, 王振

数学物理学报(英文版). 2005 (3): 569-576.

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This paper is a contionuation of [1] and is concerned with multiplication of
weak functions. Here the weak functions are treated as generalized expansions in Hermite
functions in [2].

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