数学物理学报(英文版)

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1. A NOTE ON SINGULAR VALUE DECOMPOSITION FOR RADON TRANSFORM IN R^N

王金平, 杜金元

数学物理学报(英文版) 2002, 22 (3): 311-318.

摘要（708）

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The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in Rn with respect to the weight W(x). It fulfilles mainly by means of the projection-slice theorem.The range of the Radon transform is spanned by products of Gegenbauer polynomials and spherical harmonics. The inverse transform of the those basis functions are given. This immediately
leads to an inversion formula by series expansion and range characterizations.

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2. EXISTENCE OF SOLUTION FOR A BOUNDARY VALUE PROBLEM OF FRACTIONAL ORDER

张淑琴

数学物理学报(英文版) DOI: 10.1016/S0252-9602(06)60044-1

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3. MULTI-DIMENSIONAL GEOMETRIC BROWNIAN MOTIONS, ONSAGER-MACHLUP FUNCTIONS, AND APPLICATIONS TO MATHEMATICAL FINANCE

胡耀忠

数学物理学报(英文版) 2000, 20 (3): 341-358.

摘要（958）

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The solutions of the following bilinear stochastic differential equation are stud-
ied
dxt =
Xm
k=1
Ak
t xtdwk(t) + Btxtdt
where Ak
t , Bt are (deterministic) continuous matrix-valued functions of t and w1(t), · · ·,
wm(t) are m independent standard Brownian motions. Conditions are given such that the
solution is positive if the initial condition is positive. The equation the most probable path
must satisfy is also derived and applied to a mathematical finance problem.

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4. INTERSECTION OF PRIME SUBMODULES AND DIMENSION OF MODULES

A. Azizi

数学物理学报(英文版) 2005, 25 (3): 385-394.

摘要（815）

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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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5. GLOBAL DYNAMICS OF AN SEIR EPIDEMIC MODEL WITH IMMIGRATION OF DIFFERENT COMPARTMENTS

张娟; 李建全; 马知恩

数学物理学报(英文版) DOI: 10.1016/S0252-9602(06)60081-7

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6. RIESZ IDEMPOTENT AND BROWDER´S THEOREM FOR ABSOLUTE-(p, r)-PARANORMAL OPERATORS

Salah Mecheri

数学物理学报(英文版) 2012, 32 (6): 2259-2264. DOI: 10.1016/S0252-9602(12)60175-1

摘要（572）

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An operator T is said to be paranormal if ||T²x|| ≥ ||Tx||² holds for every unit vector x. Several extensions of paranormal operators are considered until now, for example absolute-k-paranormal and p-paranormal introduced in [10], [14], respectively. Yamazaki and Yanagida [38] introduced the class of absolute-(p, r)-paranormal operators as a further generalization of the classes of both absolute-k-paranormal and p-paranormal operators. An operator T ∈B(H) is called absolute-(p, r)-paranormal operator if |||T|^p|T*|^rx||^r ≥ |||T*|rx||^p+r for every unit vector x ∈ H and for positive real numbers p > 0 and r > 0. The famous result of Browder, that self adjoint operators satisfy Browder´s theorem, is extended to several classes of operators. In this paper we show that for any absolute-(p, r)-paranormal operator T, T satisfies Browder´s theorem and a-Browder´s theorem. It is also shown that if E is the Riesz idempotent for a nonzero isolated point μ of the spectrum of a absolute-(p, r)-paranormal operator T, then E is self-adjoint if and only if the null space of T − μ, N(T − μ) N(T* − μ).

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7. FORMATION OF NECROTIC CORES IN THE GROWTH OF TUMORS: ANALYTIC RESULTS

崔尚斌

数学物理学报(英文版) DOI: 10.1016/S0252-9602(06)60104-5

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8. SOLVING SECOND ORDER DIFFERENTIAL EQUATIONS IN QUANTUM MECHANICS BY ORDER REDUCTION

C. Ted Chen

数学物理学报(英文版) 2003, 23 (2): 274-.

摘要（880）

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t Solving the famous Hermite, Legendre, Laguerre and Chebyshev equations
requires different techniques of unique character for each equation. By reducing these
differential equations of second order to a common solvable differential equation of first
order, a simple common solution is provided to cover all the existing standard solutions
of these named equations. It is easier than the method of generating functions and more
powerful than the Frobenius method of power series.

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9. GLOBAL STABILITY OF AN SIRS EPIDEMIC MODEL WITH DELAYS

靳祯; 马知恩; 韩茂安

数学物理学报(英文版) DOI: 10.1016/S0252-9602(06)60051-9

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10. CONE--DIRECTED CONTINGENT DERIVATIVES AND GENERALIZED PREINVEX SET-VALUED OPTIMIZATION

丘京辉;

数学物理学报(英文版) DOI: 10.1016/S0252-9602(07)60019-8

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11. COMPRESSIBLE NAVIER-STOKES-POISSON EQUATIONS

肖玲, 李海梁

数学物理学报(英文版) 2010, 30 (6): 1937-1948. DOI: 10.1016/S0252-9602(10)60184-1

摘要（1128）

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This is a survey paper on the study of compressible Navier-Stokes-Poisson equations. The emphasis is on the long time behavior of global solutions to multi-dimensional compressible Navier-Stokes-Poisson equations, and the optimal decay rates for both unipolar and bipolar compressible Navier-Stokes-Poisson equations are discussed.

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12. SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m

Harun Polat; Feyzi Basar

数学物理学报(英文版) DOI: 10.1016/S0252-9602(07)60024-1

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13. ON MULTIPLICATION AND COMULTIPLICATION MODULES

H. Ansari-Toroghy, F. Farshadifar

数学物理学报(英文版) 2011, 31 (2): 694-700. DOI: 10.1016/S0252-9602(11)60269-5

摘要（717）

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This article deals with some results concerning multiplication and comultiplication modules over a commutative ring.

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14. RECURSIVE FORMULA FOR CALCULATING THE
CHROMATIC POLYNOMIAL OF A GRAPH BY
VERTEX DELETION

许进

数学物理学报(英文版) 2004, 24 (4): 577-582.

摘要（622）

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new recursive vertex-deleting formula for the computation of the chromatic
polynomial of a graph is obtained in this paper. This algorithm is not only a good tool for
further studying chromatic polynomials but also the fastest among all the algorithms for
the computation of chromatic polynomials.

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15. NONLINEAR EVOLUTION SYSTEMS AND GREEN'S FUNCTION

王维克

数学物理学报(英文版) 2010, 30 (6): 2051-2063. DOI: 10.1016/S0252-9602(10)60190-7

摘要（776）

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In this paper, we will introduce how to apply Green's function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative structure. First of all, we introduce the pointwise estimates of the time-asymptotic shape of the solutions of the isentropic Navier-Stokes equations and show to exhibit the generalized Huygen's principle. Then, for other nonlinear
dissipative evolution equations, we will only introduce the result and give some brief explanations. Our approach is based on the detailed analysis of the Green's function of the linearized system and micro-local analysis, such as frequency decomposition and so on.

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16. ON ALMOST PRIME SUBMODULES

Hani A. Khashan

数学物理学报(英文版) 2012, 32 (2): 645-651. DOI: 10.1016/S0252-9602(12)60045-9

摘要（586）

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In this article, we define almost prime submodules as a new generalization of prime and weakly prime submodules of unitary modules over a commutative ring with identity. We study some basic properties of almost prime submodules and give some char-acterizations of them, especially for (finitely generated faithful) multiplication modules.

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17. VARIOUS NOTIONS OF ORTHOGONALITY IN NORMED SPACES

N.B. OKELO, J.O. AGURE, P.O. OLECHE

数学物理学报(英文版) 2013, 33 (5): 1387-1397. DOI: 10.1016/S0252-9602(13)60090-9

摘要（241）

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In this paper, we present various notions and aspects of orthogonality in normed spaces. Characterizations and generalizations of orthogonality are also consid-ered. Results on orthogonality of the range and the kernel of elementary operators and the operators implementing them also are given.

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18. THE CARBUNCLE PHENOMENON IS INCURABLE

Volker Elling

数学物理学报(英文版) 2009, 29 (6): 1647-1656. DOI: 10.1016/S0252-9602(10)60007-0

摘要（808）

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Numerical approximations of multi-dimensional shock waves sometimes exhibit an instability called the carbuncle phenomenon.
Techniques for suppressing carbuncles are trial-and-error and lack in reliability and generality, partly because theoretical knowledge about carbuncles is equally unsatisfactory. It is not known which numerical schemes are affected in which circumstances, what causes carbuncles to appear and whether carbuncles are purely numerical artifacts or rather features of a continuum equation or model.

This article presents evidence towards the latter: we propose that carbuncles are a special class of entropy solutions which can be physically correct in some circumstances. Using "filaments'', we trigger a single carbuncle in a new and more reliable way, and compute the structure in detail in similarity coordinates. We argue that carbuncles can, in some circumstances, be valid vanishing viscosity limits.
Trying to suppress them is making a physical assumption that may be false.

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19. A CHARACTERIZATION OF LOCALLY COMPACT INNER AMENABLE GROUPS

Ali Ghaffari

数学物理学报(英文版) DOI: 10.1016/S0252-9602(08)60061-2

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20. MULTIPLE SOLUTIONS FOR THE p&q-LAPLACIAN PROBLEM WITH CRITICAL EXPONENT

李工宝, 张国

数学物理学报(英文版) 2009, 29 (4): 903-918. DOI: 10.1016/S0252-9602(09)60077-1

摘要（1027）

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In this paper, we study the existence of multiple solutions for the following nonlinear elliptic problem of p&q-Laplacian type involving the critical Sobolev exponent:

−△_pu − △_qu = |u|^p*−2u + μ|u|^r−2u in Ω,
u|∂Ω= 0,

where Ω ⊂ R^N is a bounded domain, N > p, p* = N_p /N−p is the critical Sobolev exponent and μ > 0. We prove that if 1 < r < q < p < N, then there is a μ₀ > 0, such that for any μ ∈ (0, μ₀), the above mentioned problem possesses infinitely many weak solutions. Our result generalizes a similar result in [8] for p-Laplacian type problem.

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