Actions of Compact Groups on Compact (4,m)-Quadrangles

We establish sharp upper bounds for the dimensions of compact groups which act effectively on finite-dimensional compact generalized quadrangles with four-dimensional point rows. These bounds are attained, or indeed approached, only for explicitly known actions of Lie groups on Moufang quadrangles.     

Bootstrap current fraction scaling for spherical torus plasmas

Dependence of the bootstrap current fraction of spherical torus plasma on the aspect ratio and the triangular deformation is studied by using a simple equilibrium model, the Solov‘ev-type equilibrium. Two bootstrap current models are used: one is the single-ion collisionless regime model, the other is the recently developed arbitrary collisional regime model. It is found that besides the well known favourable effect of the small aspect ratio on the enhancement of the bootstrap current fraction, the triangularity is beneficial for raising the total bootstrap current though it does not change its fraction much.     

Knotted pictures of the Bell bases on the surface of a trivial torus

By means of the method of torus knot theory, this paper gives the complete processes of obtaining the knotted pictures of four Bell bases from the knotted pictures of four basic two qubit states.     

A Class of Compact Kählerian Solvmanifolds and a General Conjecture

We give some explicit examples of compact Kählerian solvmanifolds and, by extending them naturally, we find a class of compact Kählerian solvmanifolds; namely, a finite quotient of a complex torus that is a holomorphic fiber bundle over a complex torus with fiber a complex torus. Then we see that under some restriction a compact solvmanifold is Kählerian if and only if it belongs to this class. We are thus led to a conjecture that this result would hold without any restriction.     

准周期驱动圆映射的环面分岔机制及标度关系

研究了准周期驱动圆映射的倍环面分岔数p与驱动强度ε之间的标度关系,并详细讨论了系统参数对环面分岔的影响,获得了准周期驱动圆映射的倍环面分岔机制。     

The automorphism group of a rigid affine variety

An irreducible algebraic variety X is rigid if it admits no nontrivial action of the additive group of the ground field. We prove that the automorphism group of a rigid affine variety contains a unique maximal torus . If the grading on the algebra of regular functions defined by the action of  is pointed, the group  is a finite extension of . As an application, we describe the automorphism group of a rigid trinomial affine hypersurface and find all isomorphisms between such hypersurfaces.     

Automorphism Group of q-Quantum Torus Lie Algebra with q a Root of Unity*

Let α be an automorphism of a ring R. We study the skew Armendariz of Laurent series type rings (α-LA rings), as a generalization of the standard Armendariz condition from polynomials to skew Laurent series. We study on the relationship between the Baerness and p.p. property of a ring R and these of the skew Laurent series ring R[[x, x ^?1; α]], in case R is an α-LA ring. Moreover, we prove that for an α-weakly rigid ring R, R[[x, x ^?1; α]] is a left p.q.-Baer ring if and only if R is left p.q.-Baer and every countable subset of S _?(R) has a generalized countable join in R. Various types of examples of α-LA rings are provided.     

Width of parametric resonance regions for equations on a torus

We present new proofs of the theorem on the width of the forbidden regions for the Hill equation with a small potential and the theorem on the width of the parametric resonance regions for a first-order differential equation on a torus. These results are special cases of the theorem proved in this paper by the normal form method.Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 129–135, July, 1998.The author wishes to thank M. F. Kondrat'eva, V. V. Sidorenko, and the referee for useful remarks.This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-01411.     

The asymptotic eigenfunctions of the operator ?D(x, y)? corresponding to Liouville metrics and waves on water captured by bottom irregularities

We construct a set of examples of bottom reliefs for which there exist captured waves corresponding to quasimodes of the wave operator ∇D(x, y)∇. Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 414–422, September, 1998. The author thanks S. Yu. Dobrokhotov for stating the problem and numerous helpful discussions.