数学物理学报(英文版)

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MORE ABOUT MELLIN TRANSFORM IN WEAK FUNCTIONS AND M¨UNTS FORMULA

丁夏畦, 罗佩珠

数学物理学报(英文版). 2004 (1): 1-8.

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This paper is a further continuation of the paper [1]. In the present paper
Mellin transform and M¨unts formula of weak functions in complex domain will be treated.

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ON QUADRATURE FORMULAE FOR SINGULAR |INTEGRALS OF ARBITRARY ORDER

杜金元

数学物理学报(英文版). 2004 (1): 9-27.

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t Some quadrature formulae for the numerical evaluation of singular integrals
of arbitrary order are established and both the estimate of remainder and the convergence
of each quadrature formula derived here are also given.

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LOCAL MEDIAN ESTIMATION OF VARIANCE FUNCTION

杨瑛, W. C. Ip, Y. K. Kwan P

数学物理学报(英文版). 2004 (1): 28-38.

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This paper considers local median estimation in fixed design regression prob-
lems. The proposed method is employed to estimate the median function and the variance
function of a heteroscedastic regression model. Strong convergence rates of the proposed
estimators are obtained. Simulation results are given to show the performance of the
proposed methods.

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HYPERSURFACES IN SPACE FORMS WITH SCALAR CURVATURE CONDITIONS

徐森林, 张运涛

数学物理学报(英文版). 2004 (1): 39-44.

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Let $\ f:M^n$ $\hookrightarrow $ $S^{n+1}$
$\subset $ $R^{n+2}$ be an $n$-dimensional complete oriented
Riemannian manifold minimally immersed in an $(n+1)$-dimensional
unit sphere $S^{n+1}$. Denote by $S^{n+1}_+$ the upper closed
hemisphere.
If $f(M^n)\subseteq S_{+}^{n+1}$, then under some curvature
conditions the authors can get that the isometric immersion is a totally
embedding. They also generalize a theorem of Li Hai Zhong
on hypersurface of space form with costant scalar curvature.

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A RECOGNITION OF SIMPLE GROUPS PSL(3, q) BY THEIR ELEMENT ORDERS

M. R. Darafsheh;A. R. Moghaddamfar A.R. Zokay

数学物理学报(英文版). 2004 (1): 45-51.

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For any group G, denote by e(G) the set of orders of elements in G. Given
a finite group G, let h(e(G)) be the number of isomorphism classes of finite groups with
the same set e(G) of element orders. A group G is called k-recognizable if h(e(G)) =
k < 1, otherwise G is called non-recognizable. Also a 1-recognizable group is called a
recognizable (or characterizable) group. In this paper the authors show that the simple
groups PSL(3, q), where 3 < q ±2 (mod 5) and (6, (q − 1)/2) = 1, are recognizable.

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ON THE GROWTH OF SOLUTIONS OF A CLASS OF HIGHER ORDER DIFFERENTIAL EQUATIONS

陈宗煊, 孙光镐

数学物理学报(英文版). 2004 (1): 52-60.

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In this paper, authors investigate the order of growth and the hyper order of
solutions of a class of the higher order linear differential equation, and improve results of
M. Ozawa[6], G. Gundersen[7] and J.K. Langley[8], Li Chun-hong[11]

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BOOTSTRAP WAVELET IN THE NONPARAMETRIC REGRESSION MODEL WITH WEAKLY DEPENDENT PROCESSES

林路, 张润楚

数学物理学报(英文版). 2004 (1): 61-70.

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This paper introduces a method of bootstrap wavelet estimation in a non-
parametric regression model with weakly dependent processes for both fixed and random
designs. The asymptotic bounds for the bias and variance of the bootstrap wavelet estima-
tors are given in the fixed design model. The conditional normality for a modified version
of the bootstrap wavelet estimators is obtained in the fixed model. The consistency for
the bootstrap wavelet estimator is also proved in the random design model. These results
show that the bootstrap wavelet method is valid for the model with weakly dependent
processes.

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LOCAL REGULARITY RESULT FOR SOLUTIONS OF OBSTACLE PROBLEMS

高红亚, 田会英

数学物理学报(英文版). 2004 (1): 71-74.

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This paper gives the local regularity result for solutions
to obstacle problems of $A$-harmonic equation $\mbox {div} A(x,
\bigtriangledown u(x))=0$, $|A(x, \xi )|\approx |\xi|^{p-1}$, when
$1<p<n$ and the obstacle function $\psi \geq 0$.

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ON THE BOREL DIRECTION OF K-QUASIMEROMORPHIC MAPPINGS

杨燕, 刘名生

数学物理学报(英文版). 2004 (1): 75-82.

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For the K-quasimeromorphic mappings, a precise fundamental inequality for
the angular domain is established. From this, the Borel direction of the K-quasimeromorphic
mappings of zero order is derived.

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MEROMORPHIC FUNCTIONS THAT SHARE TWO SETS, II

仪洪勋, 吕巍然

数学物理学报(英文版). 2004 (1): 83-90.

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his paper deals with the problem of uniqueness
of meromorphic functions, and gets the following result:
There exists a set $S$ with $13$ elements such that any two
non-constant meromorphic functions
$f$ and $g$ satisfying $\overline{E}(S,f)=\overline{E}(S,g)$ and
$\overline{E}(\{\infty\},f)=\overline{E}(\{\infty\},g)$
must be identical. This is the best result
on this question until now.

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FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH STOPPING TIME

吴臻

数学物理学报(英文版). 2004 (1): 91-99.

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The existence and uniqueness results of fully coupled forward-backward sto-
chastic differential equations with stopping time (unbounded) is obtained. One kind of
comparison theorem for this kind of equations is also proved.

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BILINEAR FORMS AND LINEAR CODES

高莹

数学物理学报(英文版). 2004 (1): 100-106.

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Abraham Lempel et al[1] made a connection between linear codes and systems
of bilinear forms over finite fields. In this correspondence, a new simple proof of a theorem
in [1] is presented; in addition, the encoding process and the decoding procedure of RS codes
are simplified via circulant matrices. Finally, the results show that the correspondence
between bilinear forms and linear codes is not unique.

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CONFIDENCE REGIONS IN TERMS OF STATISTICAL CURVATURE FOR AR(q) NONLINEAR REGRESSION MODELS 1

刘应安, 韦博成

数学物理学报(英文版). 2004 (1): 107-117.

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This paper constructs a set of confidence regions of parameters in terms of
statistical curvatures for AR(q) nonlinear regression models. The geometric frameworks
are proposed for the model. Then several confidence regions for parameters and parameter
subsets in terms of statistical curvatures are given based on the likelihood ratio statistics
and score statistics. Several previous results, such as [1] and [2] are extended to AR(q)
nonlinear regression models.

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NON-NEWTON FILTRATION EQUATION WITH SPECIAL MEDIUM VOID

谭忠

数学物理学报(英文版). 2004 (1): 118-128.

摘要 ( 585 )

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This paper considers the existence and asymptotic
estimates of global solutions and finite time blowup of
local solution of non-Newton filtration equation with special
medium void of the following form:
$$ \left\{
\begin{array}{ll}
\displaystyle \frac{u_t}{|x|^2}-\bigtriangleup_p u=u^q, & (x,t)\in\Omega\times (0,T),\\[2mm]
u(x,t)=0, & (x,t)\in\partial\Omega\times (0,T),\\
u(x,0)=u_0(x), & u_0(x)\geq 0, u_0(x)\not\equiv 0,
\end{array}\right.$$
where $\bigtriangleup_pu={\rm div}
\left(|\bigtriangledown u|^{p-2}\bigtriangledown u\right)$,
$\Omega$ is a smooth bounded domain in $R^N(N\geq 3$), $0\in\Omega$,
$2<p<N$, $p-1<q<\frac{Np}{N-p}-1$. The result of asymptotic estimate of
global solution depends on the best constant in Hardy inequality.

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A FINITE VOLUME ELEMENT METHOD FOR THERMAL CONVECTION PROBLEMS

芮洪兴

数学物理学报(英文版). 2004 (1): 129-138.

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Consider the finite volume element method for the thermal convection problem
with the infinite Prandtl number. The author uses a conforming piecewise linear function
on a fine triangulation for velocity and temperature, and a piecewise constant function on
a coarse triangulation for pressure. For general triangulation the optimal order H1 norm
error estimates are given.

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A CLASS OF STATIONARY MODELS OF SINGULAR STOCHASTIC CONTROL

刘坤会, 秦明达, 陆传赉

数学物理学报(英文版). 2004 (1): 139-150.

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A class of stationary models of singular stochastic control has been studied,
in which the state is extended to solution of a class of S.D.E. from Wiener process. The
existence of optimal control has been proved in all cases under some weaker conditions,
and the structure of optimal control may be characterized.

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PERIODIC SOLUTIONS FOR GENERALIZED PREDATOR-PREY SYSTEMS WITH TIME DELAY AND DIFFUSION

李必文

数学物理学报(英文版). 2004 (1): 151-160.

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A set of easily verifiable sufficient
conditions are derived for the existence of positive
periodic solutions for delayed generalized predator-prey dispersion system
$$
\begin{array}{l}
x'_{1}(t)=x_1(t)g_1(t,x_1(t))-a_1(t)y(t)p_1(x_1(t))+ D_1(t)(x_2(t)-x_1(t)),\\
x'_{2}(t)=x_2(t)g_2(t,x_2(t))-a_2(t)y(t)p_2(x_2(t))+ D_2(t)(x_1(t)-x_2(t)),\\
y'(t)=y(t)\left[-h(t,y(t))+b_1(t)p_1(x_1(t-\tau_1))+ b_2(t)p_2(x_2(t-\tau_2))
\right],
\end{array}
$$
where $a_i(t),b_i(t)$ and $D_i(t)(i=1,2)$
are positive continuous $T$-periodic functions,
$g_i(t,x_i)$
$(i=1,2)$ and $h(t,y)$ are continuous and
$T$-periodic with respect to $t$ and $h(t,y)>0$
for $y>0,t,y\in R,p_i(x)(i=1,2)$ are continuous and
monotonously increasing functions, and
$p_i(x_i)>0$ for $x_i>0$.

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