A Hardy inequality in a twisted Dirichlet–Neumann waveguide

We consider the Laplacian in a straight strip, subject to a combination of Dirichlet and Neumann boundary conditions. We show that a switch of the respective boundary conditions leads to a Hardy inequality for the Laplacian. As a byproduct of our method, we obtain a simple proof of a theorem of Dittrich and Kříž [5]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Maximally causal quantum mechanics

We present a new causal quantum mechanics in one and two dimensions developed recently at TIFR by this author and V Singh. In this theory both position and momentum for a system point have Hamiltonian evolution in such a way that the ensemble of system points leads to position and momentum probability densities agreeing exactly with ordinary quantum mechanics     

Asymptotic behaviour of certain zero-balanced hypergeometric series

In this paper an attempt has been made to give a very simple method of extending certain results of Ramanujan, Evans and Stanton on obtaining the asymptotic behaviour of a class of zero-balanced hypergeometric series. A more recent result of Saigo and Srivastava has also been used to obtain a Ramanujan type of result for a partial sum of a zero-balanced₄F₃ (1) and similar other partial series of higher order.     

On Spectral Integral Variations of Graphs

Let G be a general graph. The spectrum S ( G ) of G is defined to be the spectrum of its Laplacian matrix. Let G + e be the graph obtained from G by adding an edge or a loop e . We study in this paper when the spectral variation between G and G + e is integral and obtain some equivalent conditions, through which a new Laplacian integral graph can be constructed from a known Laplacian integral graph by adding an edge.     

On the Laplacian Eigenvalues and Metric Parameters of Hypergraphs

The aim of this paper is to generalize some concepts and recent results of the algebraic graph theory in order to investigate and describe, by algebraic methods, the properties of some combinatorial structures. Here we introduce a version of "Laplacian matrix" of a hypergraph and we obtain several spectral-like results on its metric parameters, such as the diameter, mean distance, excess, bandwidth and cutsets.     

The largest two Laplacian eigenvalues of a graph

In this article, we present lower bounds for the largest eigenvalue, the second largest eigenvalue and the sum of the two largest eigenvalues of the Laplacian matrix of a graph.     

Partial regularity for two dimensional Landau-Lifshitz equations

It is proved that any weak solution to the initial value problem of two dimensional Landau-Lifshitz equation is unique and is smooth with the exception of at most finitely many points, provided that the weak solution has finite energy.     

A-调和方程障碍问题的很弱解

本文给出A-调和方程障碍问题很弱解的定义.使用Hodge分解等工具,得到其局部与整体高阶可积性.     

Gravitational field of a tachyon in a de Sitter universe

An exact solution of Einstein’s equations is interpreted as describing the gravitational field of a tachyon in a de Sitter universe. Switching off the cosmological constant yields the gravitational field of a tachyon in flat spacetime background.