Isospin symmetry breaking in ρ→πγ decay

In terms of effective field theory and mixed-propagator approach, we show that there is a larger hidden effect of isospin breaking in ρ→πγ decay due to a ω exchange, ρ→ω→πγ. The branching ratio is predicted as B(ρ→πγ) = (11.67±2.0)×10^-4, which is much larger than Particle Data Group's datum (6.8±1.7)×10^-4 and one of charged mode, B(ρ^±→π^±γ) = (4.5±0.5)×10^-4. Received: 7 January 2002 / Accepted: 2 April 2002     

Asymptotics of the parabolic Green function for an elliptic operator on a manifold with conical points

We construct the asymptotics ast→0 of the trace of the operator exp(−tP) for an elliptic operatorP on a manifold with conical points. Translated fromMatematicheskie Zametki, Vol. 63, No. 1, pp. 28–36, January, 1998. This research was supported by the Belarus Foundation for Basic Research under grant No. 96-01 00790.     

Index Reduction Formulas for Twisted Flag Varieties, II

This is a continuation of the determination begun in K-Theory 10 (1996), 517–596, of explicit index reduction formulas for function fields of twisted flag varieties of adjoint semisimple algebraic groups. We give index reduction formulas for the varieties associated to the classical simple groups of outer type A _n-1 and D _n, and the exceptional simple groups of type E ₆ and E ₇. We also give formulas for the varieties associated to transfers and direct products of algebraic groups. This allows one to compute recursively the index reduction formulas for the twisted flag varieties of any semi-simple algebraic group.     

A class of periodic groups

We deal with periodic groups saturated with dihedral groups. In particular, it is proved that periodic groups of bounded period, and also periodic Shunkov groups, saturated with dihedral groups, are locally finite.Supported by RFBR grant No. 03-01-00356 and by the Krasnoyarsk Science Foundation, project 11F0202C.Translated from Algebra i Logika, Vol. 44, No. 1, pp. 114–125, January–February, 2005.     

成批到达的有特殊服务时间的多重休假排队系统分析

本文利用嵌入马尔可夫链方法研究了多重休假M^X／Gn／1排队系统。首先，利用概率分析法得到了排队系统的嵌入马尔可夫链的一步转移概率矩阵，以此为依据得到系统的稳态队长和同批第一个接受服务顾客的稳态等待时间。     

Ginzburg-Landau minimizers with prescribed degrees. Capacity of the domain and emergence of vortices

Let Ω⊂R² be a simply connected domain, let ω be a simply connected subdomain of Ω, and set A=Ω?ω. Suppose that J is the class of complex-valued maps on the annular domain A with degree 1 both on ∂Ω and on ∂ω. We consider the variational problem for the Ginzburg-Landau energy Eλ among all maps in J. Because only the degree of the map is prescribed on the boundary, the set J is not necessarily closed under a weak H¹-convergence. We show that the attainability of the minimum of Eλ over J is determined by the value of cap(A)—the H¹-capacity of the domain A. In contrast, it is known, that the existence of minimizers of Eλ among the maps with a prescribed Dirichlet boundary data does not depend on this geometric characteristic. When cap(A)?π (A is either subcritical or critical), we show that the global minimizers of Eλ exist for each λ>0 and they are vortexless when λ is large. Assuming that λ→∞, we demonstrate that the minimizers of Eλ converge in H¹(A) to an S¹-valued harmonic map which we explicitly identify. When cap(A)<π (A is supercritical), we prove that either (i) there is a critical value λ₀ such that the global minimizers exist when λ<λ₀ and they do not exist when λ>λ₀, or (ii) the global minimizers exist for each λ>0. We conjecture that the second case never occurs. Further, for large λ, we establish that the minimizing sequences/minimizers in supercritical domains develop exactly two vortices—a vortex of degree 1 near ∂Ω and a vortex of degree −1 near ∂ω.     

Luminescence of porous silicon derived nanocrystals dispersed in water: dependence on initial porous silicon oxidation

Aqueous solutions of silicon nanocrystals have been obtained, by sonication, from porous Si (p-Si) aged in air for various times. The photoluminescence of these solutions changes with the aging time of p-Si. These changes correlate with nanocrystal core dimensions, i.e. with the oxidation of the nanocrystals. Infrared spectra show that the reaction with water depends on the age of the starting p-Si sample, since the native superficial oxide layer on p-Si inhibits these reactions.     

Mixed finite element methods for the Signorini problem with friction

In this article, we propose and study different mixed variational methods in order to approximate the Signorini problem with friction using finite elements. The discretized normal and tangential constraints at the contact interface are expressed by using either continuous piecewise linear or piecewise constant Lagrange multipliers in the saddle?point formulation. A priori error estimates are established and several numerical examples corresponding to the different choices of the discretized normal and tangential constraints are carried out. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006