具有功能反应的两斑块扩散时滞竞争系统正周期解的存在性

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＦｏｒｍａｎｙｓｐｅｃｉｅｓｔｈｅｓｐａｔｉａｌｆａｃｔｏｒｓａｒｅｉｍｐｏｒｔａｎｔｉｎｐｏｐｕｌａｔｉｏｎｄｙｎａｍｉｃｓ .Ｔｈｅｔｈｅｏｒｅｔｉｃａｌｓｔｕｄｙｏｆｓｐａｔｉａｌｄｉｓｔｒｉｂｕｔｉｏｎｈａｓｂｅｅｎｅｘｔｅｎｓｉｖｅｌｙｓｔｕｄｉｅｄｉｎｍａｎｙｐａｐｅｒｓ .Ｍｏｓｔｏｆｔｈｅｐｒｅｖｉｏｕｓｐａｐｅｒｓｆｏｃｕｓｅｄｏｎｔｈｅｃｏｅｘｉｓｔｅｎｃｅｏｆｐｏｐｕｌａｔｉｏｎｓｍｏｄｅｌｌｅｄｂｙｓｔｓｔｅｍｓｏｆｏｒｄｉｎａｒｙｄｉｆｆｅｒｅ…     

ON A SET OF h-HARMONIC HOMOGENEOUS POLYNOMIALS

1　IntroductionLet Sd- 1 bethe unitsphere of Rd,Πdthe space of allpolynomialsofd variables,and x(i)= (x1 ,… ,xi) (i=1 ,… ,d) .In this paper,we are concerned with the homogeneous polyno-mials orthogonal with the weightfunction h(x(d) ) =x2 k11 …x2 kdd on Sd- 1 ,where ki≥ 0 (i=1 ,… ,d) .Connected with the weightfunction h(x(d) ) are the following differential-differenceoperators introduced by Charles F. Dunkl in [3 ] ,Dip(x(d) ) = p(x(d) ) xi+ di=1kip(x(d) ) -p(x1 ,… ,-xi,… ,xd)xi,Δ…     

Maximum norm stability of difference schemes for parabolic equations on overset nonmatching space-time grids

In this paper, theoretical results are described on the maximum norm stability and accuracy of finite difference discretizations of parabolic equations on overset nonmatching space-time grids. We consider parabolic equations containing a linear reaction term on a space-time domain which is decomposed into an overlapping collection of cylindrical subregions of the form , for . Each of the space-time domains are assumed to be independently grided (in parallel) according to the local geometry and space-time regularity of the solution, yielding space-time grids with mesh parameters and . In particular, the different space-time grids need not match on the regions of overlap, and the time steps can differ from one grid to the next. We discretize the parabolic equation on each local grid by employing an explicit or implicit -scheme in time and a finite difference scheme in space satisfying a discrete maximum principle. The local discretizations are coupled together, without the use of Lagrange multipliers, by requiring the boundary values on each space-time grid to match a suitable interpolation of the solution on adjacent grids. The resulting global discretization yields a large system of coupled equations which can be solved by a parallel Schwarz iterative procedure requiring some communication between adjacent subregions. Our analysis employs a contraction mapping argument.

Applications of the results are briefly indicated for reaction-diffusion equations with contractive terms and heterogeneous hyperbolic-parabolic approximations of parabolic equations.

     

Epi-Convergence and Lower and Epi-Upper Semicontinuous Approximations in Distribution

The paper introduces an extension of the epi-convergence, the lower semicontinuous approximation and the epi-upper semicontinuous approximation of random real functions in distribution. The new notions could be helpful tools for sensitivity analyzes of stochastic optimization problems. The research is evoked by S. Vogel and continues the research started by Vogel and the author.     

Integral transformations by the index of Lommel's function

In this paper we study a class of integral transformations with kernels consisting of Lommel's functions of a certain index. Boundedness properties, Parseval type formula, inversion theorem are proved in Lebesgue spaces of integrable functions. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Spectrum of the Two-Dimensional Periodic Schrödinger Operator

The absence of eigenvalues (of infinite multiplicity) for the two-dimensional periodic Schrödinger operator with a variable metric is proved. The method of proof does not use the change of variables reducing the metric to a scalar form.     

Existence of an Angular Density of Roots of Entire Functions of Order Zero

We obtain sufficient conditions for the set of roots of an entire function of order zero of strongly regular growth to possess an angular density.     

Modularity and Total Ellipticity of Some Multiple Series of Hypergeometric Type

We collect some new evidence for the validity of the conjecture that every totally elliptic hypergeometric series is modular invariant and briefly discuss a generalization of such series to Riemann surfaces of arbitrary genus.     

Rational Approximation of Analytic Functions Having Generalized Orders of Rate of Growth

Let f be holomorphic on a domain G C¯ and _n be the error in best approximation of f in the supremum norm on a compact set E G by rational functions of order n. We obtain results characterizing the degree of decrease of the best approximation _n in terms connected with the condenser (E,F), F=C¯ \ G¯, and the rate of growth of the maximum modulus of f(z). In particular, if f has a generalized order (, , f) in the domain G, thenlim sup_n (n)/ (log (1/log⁺((_{0 1} ....... _n)^1/n(n+1) ))) (, , f),where = exp (1/C(E,F)), C(E,F) is the capacity of the condenser (E,F).     

On Duality for a Class of Quasiconcave Multiplicative Programs

Multiplicative programs are a difficult class of nonconvex programs that have received increasing attention because of their many applications. However, given their nonconvex nature, few theoretical results are available. In this paper, we study a particular case of these programs which involves the maximization of a quasiconcave function over a linear constraint set. Using results from conjugate function theory and generalized geometric programming, we derive a complete duality theory. The results are further specialized to linear multiplicative programming.