具有广义边界条件的迁移方程的性质

研究迁移理论中一类具有广义周期边界条件,非均匀介质板几何的定态迁移方程,证明了迁移算子是预解正算子,得到了微分算子的共轭算子及共轭算子的定义域.证明了迁移算子的共轭算子定义域的正锥在共轭空间的正锥中共尾.最后证明了迁移算子的增长界等于其谱界.     

具积分边值条件的迁移方程的性质

在L~1空间上研究了一类增生的细菌群体中具积分边界条件的迁移方程.得出迁移算子是预解正算子,微分算子的共轭算子及共轭算子的定义域.证明了迁移算子的共轭算子定义域的正锥在共轭空间的正锥中共尾.最后证明了迁移算子的增长界等于其谱界.     

L~1空间中具有周期边界条件的迁移方程的性质

在L~1空间研究板几何中具有周期边界条件的迁移方程.证明了迁移算子是预解正算子,得到了微分算子的共轭算子及共轭算子的定义域.证明了迁移算子的共轭算子定义域的正锥在共轭空间的正锥中共尾.最后证明了迁移算子的增长界等于其谱界.     

Rotenberg模型中迁移算子的谱分布

在L_p(1p+∞)空间中讨论了种群细胞增生中Rotenberg模型迁移算子的谱,采用线性算子理论,半群理论和比较算子等方法,证明了迁移算子B_H生成的C_0半群U_H(t)的渐近展开式是紧的,得到了迁移算子A_H的谱在整个复平面仅由可数个具有限代数重数的离散本征值组成,而且一∞是唯一可能的聚点.     

一般迁移方程相应余项的弱紧性及其应用

在L¹空间,研究了板几何中一类具周期边界条件的各向异性、连续能量、均匀介质的迁移方程.通过构造算子,利用比较算子方法,证明了该迁移算子A相应的迁移半群V(t)(t≥0)的Dyson-Phillips展开式的伽阶余项R_n(t)(n≥1)的弱紧性,得到了半群V(t)与U(t)(streaming算子B产生)本质谱相同,本质谱型一致;迁移算子A的谱在区域Γ中由有限个具有限代数重数的离散本征值组成;迁移方程解的渐近稳定性.     

板模型中一类具抽象边界条件的迁移方程解的渐近稳定性

运用线性算子理论,研究了板模型中一类具抽象边界条件的各向异性、连续能量、非均匀介质的迁移方程.采用半群理论、比较算子和豫解算子等方法证明了相应的迁移算子产生的C_0半群的Dyson-phillips展开式的第九阶余项的弱紧性,得到了这类迁移算子的谱在区域Γ_0中仅由有限个具有限代数重数的离散本征值组成.最后讨论了该迁移方程解的渐近稳定性.     

L~1空间中L-R型迁移方程的解对边界参数的连续依赖性

在L~1空间研究种群细胞增生中一类具扰动项的积分边界条件的迁移方程.证明了迁移算子是预解正算子,得到了微分算子的共轭算子,并证明其定义域的正锥在共轭空间的正锥中共尾,得到迁移算子的增长界等于其谱界.最后利用主算子对边界参数的连续依赖证明了迁移方程的解对边界参数连续依赖.     

平板几何中迁移方程的谱界和增长界的一个注记

本文在L~1空间研究平板几何中具有零边界的迁移方程,通过证明具有反射边界条件的迁移算子的预解式的范数对反射系数连续依赖,得到了反射边界迁移算子的预解式一致收敛于零边界迁移算子的预解式,进而得到零边界下谱界和增长界相等.     

板几何中奇异迁移方程解的渐近稳定性

在L~p(1p+∞)空间,研究了板几何中一类具反射边界条件的各向异性、连续能量、均匀介质的奇异迁移方程,通过构造算子,利用比较算子方法,证明了奇异迁移算子A相应的奇异迁移半群V(t)(t≥0)的Dyson-Phillips展开式的一阶余项R_1(t)的紧性,得到了半群V(t)与U(t)(streaming算子B产生)本质谱相同,本质谱型一致;迁移算子A的谱在区域T中由有限个具有限代数重数的离散本征值组成;迁移方程解的渐近稳定性.     

一类增生扩散型种群细胞中迁移方程的谱问题

在Lp(1≤p＜+∞)空间上,研究了一类具年龄结构的增生扩散型种群细胞中具无限周长的迁移方程,讨论了这类方程相应的迁移算子的谱,证明了在某个半平面该迁移算子的谱仅由可数个具有限代数重数的离散本征值组成等结果.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

正~~     

Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].