Regularity conditions for semigroups of isotone transformations of countable chains

Let Γ be a linearly ordered set (a chain), O(Γ) be the semigroup of all isotone transformations of Γ (i.e., order-preserving transformations). We find some necessary and some sufficient conditions on the chain Γ for the semigroup O(Γ) to be regular. For example, if Γ is a complete chain with a maximal element and a minimal one, then O(Γ) is regular. In particular, O(Γ) is regular if Γ is finite. We find necessary and sufficient conditions for the regularity of O(Γ) in the case where Γ is countable. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 8, pp. 97–104, 2006.     

The first return time properties of an irrational rotation

If an ergodic system has positive entropy, then the Shannon-McMillan-Breiman theorem provides a relationship between the entropy and the size of an atom of the iterated partition. The system also has Ornstein-Weiss' first return time property, which offers a method of computing the entropy via an orbit. We consider irrational rotations which are the simplest model of zero entropy. We prove that almost every irrational rotation has the analogous properties if properly normalized. However there are some irrational rotations that exhibit different behavior.

     

On a stochastic wave equation with unilateral boundary conditions

We prove the existence and uniqueness of solutions to the initial boundary value problem for a one-dimensional wave equation with unilateral boundary conditions and random noise. We also establish the existence of an invariant measure.

     

Energy Estimate for the Type-Ⅱ Superconducting Film

We study the minimizers of the Ginzburg-Landau model for variable thickness, superconducting, thin films with high k, placed in an applied magnetic field hex, when hex is of the order of the ＂first critical field＂, i.e. of the order of ｜lnε｜. We obtain the asymptotic estimates of minimal energy and describe the possible locations of the vortices.     

On exchange rings with primitive factor rings artinian

Abstract

In this paper we introduce generalized ideal-stable regular rings. It is shown that if a regular ring R is a generalized I-stable ring, then every square matrix over I is the product of an idempotent matrix and an generalized invertible matrix and admits a diagonal reduction by some generalized invertible matrices.     

On convertible nonnegative matrices * †

An n× nmatrix Ais called convertible if there is an n× n(1, -1)-matrix Hsuch that per A= det(H°A) where H ° Adenotes the Hadamard product of Hand A. A convertible (0,l)-matrix is called extremal if replacing any zero entry with a 1 breaks the convertibility. In this paper some properties of

nonnegative convertible matrices are investigated and some classes of extremal convertible (0,1)-matrices are obtained.     

Determination of Spectra of Functions

Boundaries of convex and compact spectra of functions on plane are fully described without passing to the complexification and the Fourier transform.     

Compactly supported multiwindow dual Gabor frames of rational sampling density

We consider multiwindow Gabor systems (G _N ; a, b) with N compactly supported windows and rational sampling density N/ab. We give another set of necessary and sufficient conditions for two multiwindow Gabor systems to form a pair of dual frames in addition to the Zibulski–Zeevi and Janssen conditions. Our conditions come from the back transform of Zibulski–Zeevi condition to the time domain but are more informative to construct window functions. For example, the masks satisfying unitary extension principle (UEP) condition generate a tight Gabor system when restricted on [0, 2] with a?=?1 and b?=?1. As another application, we show that a multiwindow Gabor system (G _N ; 1, 1) forms an orthonormal basis if and only if it has only one window (N?=?1) which is a sum of characteristic functions whose supports ‘essentially’ form a Lebesgue measurable partition of the unit interval. Our criteria also provide a rich family of multiwindow dual Gabor frames and multiwindow tight Gabor frames for the particular choices of lattice parameters, number and support of the windows. (Section 4)