Lattices of interpretability types of varieties

Let be the set of all primes, the field of all algebraic numbers, and Z the set of square-free natural numbers. We consider partially ordered sets of interpretability types such as , and , where AD is a variety of -divisible Abelian groups with unique taking of the pth root _p(x) for every p , is a variety of -modules over a normal field , contained in , and G_n is a variety of n-groupoids defined by a cyclic permutation (12 ...n). We prove that , and are distributive lattices, with and where ub and ub_f are lattices (w.r.t. inclusion) of all subsets of the set and of finite subsets of , respectively.Deceased.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 198–210, March–April, 2005.     

A Delocalization Property for Assembly Maps and an Application in Algebraic K-Theory of Group Rings

Let be a group, F the free -module on the set of finite order elements in , with acting by conjugation, and the ring extension of by % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeaacaGaaiaabeqaamaabaabaaGcbaWaaiWaaeaada% WcaaqaaiaaigdaaeaatCvAUfKttLearyGqLXgBG0evaGqbciab-5ga% UbaaieaacaGFLbGaaGOmaiaabc8acqWFPbqAcaqGVaGae8NBa42aaq% qaaeaacqGHdicjcqaHZoWzcqGHiiIZcqqHtoWrcaqGGaGaae4Baiaa% bAgacaqGGaGaae4BaiaabkhacaqGKbGaaeyzaiaabkhacaqGGaGae8% NBa4gacaGLhWoaaiaawUhacaGL9baaaaa!563E!\[\left\{ {\frac{1}{n}e2{\text{\pi }}i{\text{/}}n\left| {\exists \gamma \in \Gamma {\text{ of order }}n} \right.} \right\}\]. For a ring R with , we build an injective assembly map , detected by the Dennis trace map. This is proved by establishing a delocalization property for the assembly map in Hochschild homology, namely providing a gluing of simpler assembly maps (i.e. localized at the identity of ) to build , and by delocalizing a known assembly map in K-theory to define . We also prove the delocalization property in cyclic homology and in related theories.     

Repleteness and regular lattice measures

Let X be an abstract set and L a lattice of subsets of X. To each lattice regular measure µ, we associate two induced measures and on suitable lattices of the Wallman space IR(L) and another measure µ on the spaceIR(L). We will investigate the reflection of smoothness properties of p onto , and µ; and try to set some new criterion for repleteness and measure repleteness.     

The Kreîn-Langer problem for Hilbert space operator valued functions on the band

We deal with the Kreîn-Langer problem for -valued functions on the band (–2a, 2a)×, where is the algebra of continuous linear operators on a Hilbert space ,a a finite positive number and a topological Abelian group. We show that every weakly continuous -indefinite function admits a strongly continuous -indefinite continuation to × with the same indefiniteness index . We give a parametrization of the extensions in terms of operator-valued Schur functions.     

On Locally Projective Graphs of Girth 5

Let be a graph and G be a 2-arc transitive automorphism group of . For a vertex x let G(x)^(x) denote the permutation group induced by the stabilizer G(x) of x in G on the set (x) of vertices adjacent to x in . Then is said to be a locally projective graph of type (n,q) if G(x)^(x) contains PSL_n(q) as a normal subgroup in its natural doubly transitive action. Suppose that is a locally projective graph of type (n,q), for some n 3, whose girth (that is, the length of a shortest cycle) is 5 and suppose that G(x) acts faithfully on (x). (The case of unfaithful action was completely settled earlier.) We show that under these conditions either n=4, q=2, has 506 vertices and , and contains the Wells graph on 32 vertices as a subgraph. In the latter case if, for a given n, at least one graph satisfying the conditions exists then there is a universal graph W(n) of which all other graphs for this n are quotients. The graph W(3) satisfies the conditions and has 2²⁰ vertices.     

Study of Noetherian Γ-Semirings via Operator Semirings

In this paper we study Noetherian -semirings and obtain Cohens theorem for a special class of -semirings. Weak primary decomposition theorem for a particular type of -semirings is also obtained.Presently Lecturer in Mathematics, University of Burdwan, GOLAPBAG, W.B. INDIA.     

On the Movement of Transitive Permutation p-Groups

Let G be a transitive permutation group on a set and m a positive integer. If | – | m for every subset of and all g G, then || 2mp/(p – 1) where p is the least odd prime dividing |G|. It was shown by Mann and Praeger [13] that, for p = 3, the 3-groups G which attain this bound have exponent p. In this paper we will show a generalization of this result for any odd primes.AMS Subject Classification (2000), 20BXX     

On the Operator Semirings of a Γ-Semiring

In this paper we introduce the notion of operator semirings of a -semiring to study -semirings. It is shown that the lattices of all left (right) ideals (two-sided ideals) of a -semiring and its right (respectively left) operator semiring are isomorphic. This has many applications to characterize various -semirings.AMS Subject Classification (2000): 16Y60, 16Y99     

Cohomology of solvable lie algebras and solvmanifolds

The cohomology H^* (G/,) of the de Rham complex *(G/) of a compact solvmanifold G/ with deformed differential d = d + , where is a closed 1 -form, is studied. Such cohomologies naturally arise in Morse-Novikov theory. It is shown that, for any completely solvable Lie group G containing a cocompact lattice G, the cohomology H^*(G/, ) is isomorphic to the cohomology H^*( ) of the tangent Lie algebra of the group G with coefficients in the one-dimensional representation : defined by () = (). Moreover, the cohomology H ^*(G/,) is nontrivial if and only if -[] belongs to a finite subset of H ¹(G/,) defined in terms of the Lie algebra .Translated from Matematicheskie Zametki, vol. 77, no. 1, 2005, pp. 67–79.Original Russian Text Copyright © 2005 by D. V. Millionshchikov.This revised version was published online in April 2005 with a corrected issue number.     

On the essential norm of the Cauchy singular integral operator in weighted rearrangement-invariant spaces

In this paper we extend necessary conditions for Fredholmness of singular integral operators with piecewise continuous coefficients in rearrangement-invariant spaces [19] to the weighted caseX(,w). These conditions are formulated in terms of indices (Q _t w) and (Q _t w) of a submultiplicative functionQ _t w, which is associated with local properties of the space, of the curve, and of the weight at the pointt. Using these results we obtain a lower estimate for the essential norm |S| of the Cauchy singular integral operatorS in reflexive weighted rearrangement-invariant spacesX(,w) over arbitrary Carleson curves :

An existence theorem for generalized quasi-variational inequalities

In this paper, we deal with the following generalized quasi-variational inequality problem: given a closed convex subsetX ⁿ , a multifunction :X 2 ⁿ and a multifunction :X 2 ^X , find a point ( ) X × ⁿ such that We prove an existence theorem in which, in particular, the multifunction is not supposed to be upper semicontinuous.     

Linear Versus Nonlinear Rules for Mixture Normal Priors

The problem under consideration is the -minimax estimation, under L₂loss, of a multivariate normal mean when the covariance matrix is known. The family of priors is induced by mixing zero mean multivariate normals with covariance matrix I by nonnegative random variables , whose distributions belong to a suitable family G. For a fixed family G, the linear (affine) -minimax rule is compared with the usual -minimax rule in terms of corresponding -minimax risks. It is shown that the linear rule is "good", i.e., the ratio of the risks is close to 1, irrespective of the dimension of the model. We also generalize the above model to the case of nonidentity covariance matrices and show that independence of the dimensionality is lost in this case. Several examples illustrate the behavior of the linear -minimax rule.     

A quasi-variational problem in nonlinear elasticity

Summary R³ and R² are bounded, connected, Lipschitz open sets. v: R is the vertical displacement of an elastic membrane stretched on and fixed at the boundary. The condition is imposed on the admissible deformations :R³ of a hyperelastic body whose reference configuration is . The additional constraint ³(x)v(^1,2(x)), forcing the body to stay above the membrane, is relaxed in order to show the existence of a minimizer of total energy of the mechanical sistem.     

The lower algebraicK-theory of virtually infinite cyclic groups

This paper gives a proof of a conjecture of W.-C. Hsiang for the negativeK-theory of integral grouprings , when the group is a subgroup of a uniform lattice in a Lie group. The authors' earlier paper reduced this result to the very special cases where either is finite or is virtually infinite cyclic. The finite case was done much earlier by Carter extending results of Bass and Murthy. The major work of the present paper consists of proving the conjecture when is virtually infinite cyclic.Both authors were supported in part by the National Science Foundation.     

Octagonality conditions in projective and affine planes

A projective confined configuration with axis and centre will be introduced in terms of a non-degenerate octagon satisfying some hypotheses on the position of its diagonal points (i.e. intersections of edges having distance 8 in the flag graph ( )) and its first minor diagonal lines (i.e. diagonal lines joining vertices of distance 6 in ( )). That confined configuration gives rise to a certain configurational condition whose affine specialization (i.e. the axis coincides with the line at infinity) is equivalent to the affine Pappos condition, whereas its little specialization (i.e. the centre lies on the axis) turns out to be equivalent to the little Desargues condition. In Pappian projective planes can be completed to a configuration of type (12₄, 16₃).     

On the stochastic independence properties of hard-core distributions

A probability measurep on the set of matchings in a graph (or, more generally 2-bounded hypergraph) ishard-core if for some : [0,), the probabilityp(M) ofM is proportional to . We show that such distributions enjoy substantial approximate stochastic independence properties. This is based on showing that, withM chosen according to the hard-core distributionp, MP () the matching polytope of , and >0, if the vector ofmarginals, (Pr(AM):A an edge of ), is in (1–) MP (), then the weights (A) are bounded by someA(). This eventually implies, for example, that under the same assumption, with fixed, as the distance betweenA, B tends to infinity.Thought to be of independent interest, our results have already been applied in the resolutions of several questions involving asymptotic behaviour of graphs and hypergraphs (see [14, 16], [11]–[13]).Supported in part by NSFThis work forms part of the author's doctoral dissertation [16]; see also [17]. The author gratefully acknowledges NSERC for partial support in the form of a 1967 Science and Engineering Scholarship.     

Inzidenzräume mit Süss'scher Kollineationsgruppe

The following theorem will be proved: THEOREM. Let (P,) be a linear space with dimension dim(P,) 2, such that each line contains at least three points. Let further Aut(P,) be a two — transitive group of collineations on the point set P, such that every automorphism fixing one flag (p,L), fixes all lines through p. Then (P,) is a desarguesian affine space and contains the whole group of dilatations of (P,). Moreover one can define an addition and a multiplication on the point set, such that (P,+,-) is a nearfield, the line joining the neutral elements is a normal subfield and consists of the affine transformations x a + mx, m 0 and= (K).

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Herrn Professor Dr. Helmut Karzel zum 60. Geburtstag     

Classifying Arc-Transitive Circulants of Square-Free Order

A circulant is a Cayley graph of a cyclic group. Arc-transitive circulants of square-free order are classified. It is shown that an arc-transitive circulant of square-free order n is one of the following: the lexicographic product , or the deleted lexicographic , where n = bm and is an arc-transitive circulant, or is a normal circulant, that is, Aut has a normal regular cyclic subgroup.