Extremal maximal sectorial extensions of sectorial relations

The extremal maximal sectorial extensions of a not necessarily densely defined sectorial relation (multivalued linear operator) in a Hilbert space are characterized in terms of a construction which goes back to Sebestyén and Stochel. In particular the two extreme maximal sectorial extensions, namely the Friedrichs extension and the Kreĭn extension, are characterized. For this purpose a survey is given of the connection between closed sectorial forms and maximal sectorial relations.     

On the development of a triple‐preserving Maxwell's equations solver in non‐staggered grids

We present in this paper a finite difference solver for Maxwell's equations in non‐staggered grids. The scheme formulated in time domain theoretically preserves the properties of zero‐divergence, symplecticity, and dispersion relation. The mathematically inherent Hamiltonian can be also retained all the time. Moreover, both spatial and temporal terms are approximated to yield the equal fourth‐order spatial and temporal accuracies. Through the computational exercises, modified equation analysis and Fourier analysis, it can be clearly demonstrated that the proposed triple‐preserving solver is computationally accurate and efficient for use to predict the Maxwell's solutions. Copyright © 2009 John Wiley & Sons, Ltd.     

基于可拓变换的二维随机变量分布律的研究

建立了随机事元之间的关系事元,研究随机事件之间的关系.利用关系元刻画了两个随机事件之间的关系.运用可拓变换初步研究了二维离散型随机变量的分布律和边缘分布律的传导分布.     

Wavelets with differential relation

Divergence-free wavelets are successfully applied to numerical solutions of Navier-Stokes equation and to analysis of incompressible flows. They closely depend on a pair of one-dimensional wavelets with some differential relations. In this paper, we point out some restrictions of those wavelets and study scaling functions with the differential relation; Wavelets and their duals are discussed; In addition to the differential relation, we are particularly interested in a class of examples with the interpolatory property; It turns out there is a connection between our examples and Micchelli’s work.     

自然数幂方和用二项系数表示的系数公式

得到了自然数幂方和由二项系数表示的系数a_i~(k)的公式,和由排列数表示的系数b_i~(k)的公式,证明了系数存在唯一性及系数间的若干重要性质,给出了计算系数的C-语言程序.     

Entanglement conditions for four-mode states via the uncertainty relations in conjunction with partial transposition

From the Heisenberg uncertainty relation in conjunction with partial transposition, we derive a class of inequalities for detecting entanglements in four-mode states. The sufficient conditions for bipartite entangled states are presented. We also discuss the generalization of the entanglement conditions via the Schrödinger-Robertson indeterminacy relation, which are in general stronger than those based on the Heisenberg uncertainty relation.     

Correlations between electronic energy bands spin splitting and magnetic profile symmetry of magnetic superlattice

We have theoretically investigated the energy band structures of two typical magnetic superlattices formed by perpendicular or parallel magnetization ferromagnetic stripes periodically deposited on a two-dimensional electron gas (2DEG), where the magnetic profile in the perpendicular magnetization is of inversion anti-symmetry, but of inversion symmetry in parallel magnetization, respectively. We have shown that the energy bands of perpendicular magnetization display the spin-splitting and transverse wave-vector symmetry, while the energy bands of the parallel magnetization exhibit spin degeneration and transverse wave-vector asymmetry. These distinguishing spin-dependent and transverse wave-vector asymmetry features are essential for future spintronics devices applications.     

A relation for general and inverse semigroups

The relation in the title is S defined by

Diffusive-Dispersive Traveling Waves and Kinetic Relations: Part I: Nonconvex Hyperbolic Conservation Laws

Motivated by the theory of phase transition dynamics, we consider one-dimensional, nonlinear hyperbolic conservation laws with nonconvex flux-function containing vanishing nonlinear diffusive-dispersive terms. Searching for traveling wave solutions, we establish general results of existence, uniqueness, monotonicity, and asymptotic behavior. In particular, we investigate the properties of the traveling waves in the limits of dominant diffusion, dominant dispersion, and asymptotically small or large shock strength. As the diffusion and dispersion parameters tend to 0, the traveling waves converge to shock wave solutions of the conservation law, which either satisfy the classical Oleinik entropy criterion or are nonclassical undercompressive shocks violating it.     

Exchange Relation Planar Algebras

An inclusion of II ₁ factors NM of finite index has as an invariant, a double sequence of finite-dimensional algebras known as the standard invariant. Planar algebras were introduced by V. Jones as a geometric tool for computing standard invariants of existing subfactors as well as generating standard invariants for new subfactors. In this paper we define a class of planar algebras, termed exchange relation planar algebras, that provides a general framework for understanding several classes of known subfactor inclusions: the Fuss–Catalan algebras (i.e. those coming from the presence of intermediate subfactors) and all depth 2 subfactors. In addition, we present a new class of planar algebras (and thus a new class of subfactors) coming from automorphism subgroups of finite groups.