广义随机Solow经济增长模型

本文在文[1]的基础上进一步拓广了随机Solow经济增长模型．利用白噪声分析理论建立的广义随机Solow经济增长模型，将随机Solow模型推广到包含广义白噪声泛函及具有非可料扩散系数的情形，并且借助U—泛函方法表明了Picard迭代法在此仍十分有效．     

Epitaxial Cu(In,Ga)S2 thin film solar cells

Epitaxial layers of the quaternary compound Cu(In,Ga)S₂ and the ternary compound CuInS₂ were grown on Si(111) substrates via Molecular Beam Epitaxy. The layers were investigated for their morphological and structural properties using Rutherford backscattering spectroscopy, atomic force microscopy, reflection high-energy electron diffraction and X-Ray diffraction. Furthermore, complete solar cell devices were processed from these layers and their photovoltaic properties were investigated by means of I(U)-curves under illumination. Thus, efficiencies up to η=3.2% were achieved. The comparatively low performance of the solar cell devices is attributed to certain heterogeneities of the samples as a result of the growth process.     

Global Existence for a Parabolic-hyperbolic Free Boundary Problem Modelling Tumor Growth

In this paper we study a free boundary problem modelling tumor growth, proposed by A. Friedman in 2004. This free boundary problem involves a nonlinear second-order parabolic equation describing the diffusion of nutrient in the tumor, and three nonlinear first-order hyperbolic equations describing the evolution of proliferative cells, quiescent cells and dead cells, respectively. By applying Lp theory of parabolic equations, the characteristic theory of hyperbolic equations, and the Banach fixed point theorem, we prove that this problem has a unique global classical solution.     

Geometric constrains for global regularity of 2D quasi-geostrophic flows

We study the two-dimensional quasi-geostrophic equations (2D QG) in Sobolev spaces. We first prove a new analytic condition for global regularity which is both sufficient and necessary. We then prove several new results on the geometric constraints on the 2D QG active scalar which suppress the development of singularity from the nonlinear stretching mechanism. We focus mainly on the case with critical dissipation. Our results are also relevant to the inviscid case.     

Boundary Area Growth and the Spectrum of Discrete Laplacian

We introduce the boundary area growth as a new quantity for an infinite graph. Using this, we give some upper bounds for the bottom of the spectrum of the discrete Laplacian which relates closely to the transition operator. We also give some applications and examples.     

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.     

A fourth-order parabolic equation modeling epitaxial thin film growth

We study the continuum model for epitaxial thin film growth from Phys. D 132 (1999) 520-542, which is known to simulate experimentally observed dynamics very well. We show existence, uniqueness and regularity of solutions in an appropriate function space, and we characterize the existence of nontrivial equilibria in terms of the size of the underlying domain. In an investigation of asymptotical behavior, we give a weak assumption under which the ω-limit set of the dynamical system consists only of steady states. In the one-dimensional setting we can characterize the set of steady states and determine its unique asymptotically stable element. The article closes with some illustrative numerical examples.     

Finite-size scaling in the theory above the upper critical dimension

We derive exact results for several thermodynamic quantities of the O ( n ) symmetric field theory in the limit in a finite d-dimensional hypercubic geometry with periodic boundary conditions. Corresponding results are derived for an O ( n ) symmetric model on a finite d-dimensional lattice with a finite-range interaction. The leading finite-size effects near T_c of the field-theoretic model are compared with those of the lattice model. For 2 < d < 4, the finite-size scaling functions are verified to be universal. For d > 4, significant lattice effects are found. Finite-size scaling in its usual simple form does not hold for d > 4 but remains valid in a generalized form with two reference lengths. The finite-size scaling functions of the field theory turn out to be nonuniversal whereas those of the lattice model are independent of the nonuniversal model parameters. In particular, the field-theoretic model exhibits finite-size effects whose leading exponents differ from those of the lattice model. The widely accepted lowest-mode approach is shown to fail for both the field-theoretic and the lattice model above four dimensions. Received: 20 October 1997 / Accepted: 5 March 1998     

Some results related to the toughness of 3-domination critical graphs

A graph G is said to be k-γ-critical if the size of any minimum dominating set of vertices is k, but if any edge is added to G the resulting graph can be dominated with k−1 vertices. The structure of k-γ-critical graphs remains far from completely understood, even in the special case when the domination number γ=3. In a 1983 paper, Sumner and Blitch proved a theorem which may regarded as a result related to the toughness of 3-γ-critical graphs which says that if S is any vertex cutset of such a graph, then G−S has at most |S|+1 components. In the present paper, we improve and extend this result considerably.     

Electrodeposition of epitaxial nickel films on GaAs

The structural and magnetic properties of Ni films grown by electrodeposition from simple sulfate solutions directly onto the (0 0 1) and (0 1 1) surfaces of n-GaAs have been studied. In-plane X-ray diffraction has been used to show that Ni grows on (0 0 1) GaAs with two different preferred epitaxial relationships: (1) perpendicular to plane (0 0 1)_Ni(0 0 1)_GaAs and preferred orientation in-plane [1 0 0]_Ni[1 1 0]_GaAs and (2) perpendicular to plane (0 1 1)_Ni(0 0 1)_GaAs and preferred orientation in-plane [1 1 1]_Ni[1 1 0]_GaAs. Nickel films grown on (0 1 1) n-GaAs show only a single preferred growth relationship: perpendicular to plane (1 1 1)_Ni(0 1 1)_GaAs and in-plane [1 1 0]_Ni[1 1 0]_GaAs. The magnetic properties were strongly dependent on the substrate orientation. The films grown on GaAs (0 0 1) showed a small but definite four-fold magnetic anisotropy in plane with the highest remanence being found along the GaAs [1 0 0] direction. In contrast, the Ni films grown on the (0 1 1) GaAs showed a pronounced uniaxial anisotropy with an anisotropy field of approximately 500 Oe.