Parity features for classes of the infinite symmetric group

A conjugacy class in the infinite-symmetric group is said to have parity features if no finitary odd permutation is a product of two of its members. The conjugacy classes having parity features are determined. The role played by a property of this kind in determining products of conjugacy classes in any group in which every element is conjugate with its inverse is studied.     

Zu den dreigliedrigen Zwanglaufketten der quasihyperbolischen Kinematik

We present a calculus for those projective-kinematic-chains with three members, where every chain element possesses at each moment three linearly independent poles. As applications we discuss the generation problem for pairs of envelope curves as path-curves and give an extensive treatment of the quasi-hyperbolic chains.

Herrn Professor Dr. O. Giering zum 60. Geburtstag gewidmet     

Cycle Cover Ratio of Regular Matroids

A cycle in a matroid is a disjoint union of circuits. This paper proves that every regular matroidM without coloops has a set S of cycles whose union is E(M) such that every element is in at most three of the cycles in S. It follows immediately from this that, on average, each element of M is in at most three members of the cycle cover S. This improves on a 1989 result of Jamshy and Tarsi who proved that there is a cycle cover for which this average is at most 4, and conjectured that a cycle cover exists for which the average is at most 2.     

On Semitransitive Collections of Operators

A collection F of operators on a vector space V is said to be semitransitive if for every pair of nonzero vectors x and y in V there exists a member T of F such that either Tx = y or Ty = x (or both). We study semitransitive algebras and semigroups of operators. One of the main results is that if the underlying field is algebraically closed, then every semitransitive algebra of operators on a space of dimension n contains a nilpotent element of index n. Among other results on semitransitive semigroups, we show that if the rank of nonzero members of such a semigroup acting on an n-dimensional space is a constant k, then k divides n.     

Algebras in which non-scalar elements have small centralizers

We describe algebras in which the centralizer of every non-scalar element is equal to the subalgebra generated by this element, and finite-dimensional algebras (over perfect fields) in which the centralizer of every non-scalar element is commutative.     

Amenable and Locally Amenable Algebraic Frames

Order - We say a prime element of an algebraic frame is amenable if it comparable to every compact element. If every prime element of an algebraic frame L is amenable, we say L is an amenable...     

Varieties of Lattices with Geometric Descriptions

A lattice L is spatial if every element of L is a join of completely join-irreducible elements of L (points), and strongly spatial if it is spatial and the minimal coverings of completely join-irreducible elements are well-behaved. Herrmann et al. proved in 1994 that every modular lattice can be embedded, within its variety, into an algebraic and spatial lattice. We extend this result to n-distributive lattices, for fixed n. We deduce that the variety of all n-distributive lattices is generated by its finite members, thus it has a decidable word problem for free lattices. This solves two problems stated by Huhn in 1985. We prove that every modular (resp., n-distributive) lattice embeds within its variety into some strongly spatial lattice. Every lattice which is either algebraic modular spatial or bi-algebraic is strongly spatial. We also construct a lattice that cannot be embedded, within its variety, into any algebraic and spatial lattice. This lattice has a least and a largest element, and it generates a locally finite variety of join-semidistributive lattices.     

Regularity conditions on skew and symmetric elements in superalgebras with superinvolution

We study semiprime superalgebras with superinvolution, under certain additional regularity conditions. More precisely, we assume regularity conditions either on every nonzero homogeneous symmetric element, or on every nonzero homogeneous skewsymmetric element.     

Strongly q-Nil-Clean Rings

Siberian Mathematical Journal - Under study are the rings whose every element is a sum of a nilpotent and a q-potent that commute with one another. We describe the rings whose every element is a...     

Twisted conjugacy classes of the unit element

We study twisted conjugacy classes of the unit element in different groups. Fel’shtyn and Troitsky showed that the twisted conjugacy class of the unit element of an abelian group is a subgroup for every automorphism. The structure is investigated of a group whose twisted conjugacy class of the unit element is a subgroup for every automorphism (inner automorphism).     

Free koszul homology and regular ideals in non-noetherian rings

It is shown that every element in a one-sided unit-regular ring is the sum of an idempotent and a one-sided unit. Also we prove that every element in a regular ring satisfying related comparability is the sum of an idempotent and the product of two one-sided units.     

J-clean环的推广

如果R中每个元素(对应地,可逆元)均可表示为一个幂等元与环R的Jacobson根中一个元素之和,则称环R是J-clean环(对应地,UJ环).所有的J-clean环都是UJ环.作为UJ环的真推广,本文引入GUJ环的概念,研究GUJ环的基本性质和应用.进一步地,研究每个元素均可表示为一个幂等元与一个方幂属于环的Jacobson根的元素之和的环.     

Social comparison,group composition,and incentive provision

This article analyzes the optimal composition of groups of arbitrary size according to the social preferences of group members in a situation of moral hazard. We focus on rivalry, pure self-interest and altruism to show that in a situation where every group member compares his or her remuneration to the average remuneration of all members in the same group, ideally there should be as many extreme altruists as there are extreme rivals. If, by contrast, every member of the group compares his or her own remuneration to that of a focal agent, ideally, this focal agent should be a strong altruist, while all other group members should be highly competitive. Our results show that it is important to foster heterogeneity in the social preferences of the members of a group in order to maximize the profitability of the firm.     

A Helly-Type Theorem for Intersections of Compact Connected Sets in the Plane

For a family C of nonempty compact sets in the plane, the following conditions are equivalent:(1) Every two (not necessarily distinct) members of C have a connected union and every three (not necessarily distinct) members of C have a simply connected union.(2) C is a family of simply connected sets such that every two (not necessarily distinct) members of C have a connected intersection and every three (not necessarily distinct) members of C have a nonempty intersection.If either set of conditions is satisfied, then { C : C in C } is nonempty, simply connected, and connected. Furthermore, if the collection C is finite, then it is also true that { C : C in C } is simply connected.     

Special tight frames

Special vector systems, in which every element is the preceding element multiplied by a unitary matrix U, are introduced. Necessary and sufficient conditions for such a system to be a tight frame are obtained (Theorem 1). Examples illustrating the necessity of every condition are given. The theorem is applied to the Mercedes-Benz frame. Let P denote the matrix composed of orthonormal eigenvectors of U. A new system of vectors in which every element equals the corresponding element of the initial system multiplied by P* is considered. It is proved that this system is a generalized harmonic frame if and only if the assumptions of Theorem 1 hold. This result is applied to show how to transform the Mercedes-Benz frame into a generalized harmonic frame.     

Exchange rings,units and idempotents

An associative ring R with identity is semiperfect if and only if every element of R is a sum of a unit and an idempotent, and R contains no infinite set of orthogonal idempotents. A ring which contains no infinite set of orthogonal idempotents is an exchange ring if and only if every element is a sum of a unit and an idempo-tent     

Elements in Regular QB-Rings

In this article, we prove that every element in a regular QB-ring is the sum of an idempotent and a quasi-invertible element.     

On local non‐compactness in recursive mathematics

A metric space is said to be locally non‐compact if every neighborhood contains a sequence that is eventually bounded away from every element of the space, hence contains no accumulation point. We show within recursive mathematics that a nonvoid complete metric space is locally non‐compact iff it is without isolated points. The result has an interesting consequence in computable analysis: If a complete metric space has a computable witness that it is without isolated points, then every neighborhood contains a computable sequence that is eventually computably bounded away from every computable element of the space. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Groups of exponent 24

It is proved that every group of exponent 24 containing an element of order 3 but not containing an element of order 6 is locally finite.     

A coupled finite element-optimization technique to determine critical microburst parameters for transmission towers

Most transmission line failures worldwide are attributed to high intensity wind events such as microburst. The velocity profile and loads associated with a microburst wind field vary significantly with the microburst configurations. An optimization technique is coupled with a finite element model in this study to identify the critical microburst parameters that lead to maximum forces in various members of a transmission tower structure. Moreover, the coupled genetic algorithms–finite element code is employed to determine the critical members that are likely to fail during a microburst event and the associated critical microburst configurations.