Constructing Solutions of an Ill-Posed Nonlinear Singularly Perturbed Problem for an Equation of Elliptic Type

Mathematical Notes -     

Determination of the electric field gradient asymmetry from Berry’s phase in NQR of powder samples

An effect of Berry’s phase on the NQR spectrum of the rotating powder sample is described and applied for the determination of the electric field gradient asymmetry. The proposed method involves the analysis of the frequency singularities in the NQR powder patterns of the rotating samples. The Berry’s phases for the eigenstates, associated with an adiabatically changing quadrupole hamiltonian, are calculated for nuclei with a spin I = 3/2 and I = 1 as a function of the asymmetry parameter.     

Idealization of a decomposition theorem

In 1986, Tong [13] proved that a function f : (X,τ)→(Y,φ) is continuous if and only if it is α-continuous and A-continuous. We extend this decomposition of continuity in terms of ideals. First, we introduce the notions of regular-I-closed sets, A _I-sets and A _I -continuous functions in ideal topological spaces and investigate their properties. Then, we show that a function f : (X,τ,I)→(Y, φ) is continuous if and only if it is α-I-continuous and A _I-continuous. This revised version was published online in June 2006 with corrections to the Cover Date.     

A note on strongly π-regular rings

Let R be an associative ring with unit and let N(R) denote the set of nilpotent elements of R. R is said to be stronglyπ-regular if for each x∈R, there exist a positive integer n and an element y∈R such that x ⁿ=x ^{n +1} y and xy=yx. R is said to be periodic if for each x∈R there are integers m,n≥ 1 such that m≠n and x ^m=x ⁿ. Assume that the idempotents in R are central. It is shown in this paper that R is a strongly π-regular ring if and only if N(R) coincides with the Jacobson radical of R and R/N(R) is regular. Some similar conditions for periodic rings are also obtained. This revised version was published online in June 2006 with corrections to the Cover Date.     

D∞-APPROXIMATION OF PRODUCT VARIATIONS OF TWO PARAMETER SMOOTH SEMIMARTINGALES

Let X be a two parameter smooth semimartingale and (~X) be its process of the product variation. It is proved that (~X) can be approximated as D∞-limit of sums of its discrete product variations as the mesh of division tends to zero. Moreover, this result can be strengthen to yield the quasi sure convergence of sums by estimating the speed of the convergence.     

应用参数假设检验分析特异功能是否存在

本文应用参数假设检验知识分析“特异功能”者是否有特异功能。     

关于奇ATm核1/2+[411]转动带的系统分析

壳模型计算表明,1/2⁺[411]出现于¹⁵⁷Tm核的基态可能是由非轴对称形变造成的.但是新近从¹⁵⁷Yb衰变纲图给出的¹⁵⁷Tm低激发谱中,指认了一个建立在1/2⁺[411]带头上的基态转动带,并认为该带的性质是轴对称的,提取了该带的惯性参数与脱耦合参数.通过对奇ATm核1/2⁺[411]转动带的系统分析,强调了在¹⁵⁷Tm核中非轴对称γ自由度效应的重要性.     

析氢反应动力学的交流阻抗法研究

利用交流阻抗法测定析氢电化学动力学参数，得到与极化曲线法一致的结果，为确定复杂析氢过程速率的决定步骤提供了判据。     

Regularization of singular systems of linear algebraic equations by shifts

Regularization of singular systems of linear algebraic equations by shifts is examined. New equivalent conditions for the shift regularizability of such systems are derived.     

The completion of the classification of the regular near octagons with thick quads

Brouwer and Wilbrink [3] showed the nonexistence of regular near octagons whose parameters s, t₂, t₃ and t satisfy s ≥ 2, t₂ ≥ 2 and t₃ ≠ t₂(t₂+1). Later an arithmetical error was discovered in the proof. Because of this error, the existence problem was still open for the near octagons corresponding with certain values of s, t₂ and t₃. In the present paper, we will also show the nonexistence of these remaining regular near octagons. MSC2000 05B25, 05E30, 51E12 Postdoctoral Fellow of the Research Foundation - Flanders