We investigate the static and dynamic properties of a Tonks–Girardeau gas in a harmonic trap with an eccentric δ-perturbation of variable strength. For this, we first find the analytic eigensolution of the single particle problem and then use this solution to calculate the spatial density and energy profiles of the many-particle gas as a function of the strength and position of the perturbation...

A perturbation matrix A = A is considered, where A 2 IR and 0 2 IR. The matrix A is singular i A contains a real singular matrix. A problem is to decide if A is singular or nonsingular, a NP-hard problem. The decision can be made by the computation of the componentwise distance to the nearest singular matrix de ned on the basis of the real spectral radius, and by the solution of 4 eigenvalue pr...

Severe mode switching is often observed when the PK-method used in flutter analysis of complex aircraft configurations, particular nearly 100 vibrational modes are considered. In commonly commercial software NASTRAN, resulting eigenroots sorted an ascending order frequency. Therefore, appearance massive mode-switching instances cannot be avoided analyses, especially for engineering applications...

In this paper, the region in which the structural system is situated is divided into four subregions, namely upper, lower, left and right subregions. The stiffness matrix of the entire system is then formed and using the existing direct symmetry and reverse symmetry, the relationships between the entries of the matrix are established. Examples are included to illustrate the steps of the method.

We use refined isogeometric analysis (rIGA) to solve generalized Hermitian eigenproblems (Ku=λMu). rIGA conserves the desirable properties of maximum-continuity (IGA) while it reduces solution cost by adding zero-continuity basis functions, which decrease matrix connectivity. As a result, enriches approximation space and interconnection between degrees freedom. compare computational costs versu...

In fundamental theories of physics, the dynamical equations all have time inversion invariance. Except for the evolution of some simple system which has realistic inverse processes, but for a slightly more complicated system, the evolution processes are irreversible. This is the problem of arrow of time, which is always warmly debated. In different point of view, we find there may have some con...

Abstract In a separable Hilbert space X , we study the controlled evolution equation $$\begin{aligned} u'(t)+Au(t)+p(t)Bu(t)=0, \end{aligned}$$ u′(t)+</mml...

We prove a variant of Sch’nol’s theorem in a general setting: for generators of strongly local Dirichlet forms perturbed by measures. As an application, we discuss quantum graphs with δor Kirchhoff boundary conditions. Dedicated to Shmuel Agmon on the occasion of his 85th birthday Introduction The behavior of solutions to elliptic partial differential equations and its interplay with spectral p...