bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the number of subgroups in finite solvable groups
Authors: Herzog Marcel , Manz Olaf 
Published: April 2009

AbstractThe main result of this paper is an upper bound for the number of maximal subgroups in finite solvable groups. Our result improves an earlier one of Cook, Wiegold and Williamson [1]. At the end, we use our bound to deduce an estimation for the total number of subgroups in finite solvable groups.
Lp-Lq estimates off the line of duality
Authors: Bak J.-G. , McMichael D. , Oberlin D. 
Published: April 2009

AbstractTheorems 1 and 2 are known results concerning Lp–Lq estimates for certain operators wherein the point (1/p, 1/q) lies on the line of duality 1/p + 1/q = 1. In Theorems 1′ and 2′ we show that with mild additional hypotheses it is possible to prove Lp-Lq estimates for indices (1/p, 1/q) off the line of duality. Applications to Bochner-Riesz means of negative order and uniform Sobolev inequalities are given.
Balanced directed cycle designs based on cyclic groups
Authors: Nilrat Chaufah , Praeger Cheryl E. 
Published: April 2009

AbstractA balanced directed cycle design with parameters (υ, k, 1), sometimes called a (υ, k, 1)-design, is a decomposition of the complete directed graph into edge disjoint directed cycles of length k. A complete classification is given of (υ, k, 1)-designs admitting the holomorph {øa, b: x ↦ ax + b∣ a, b ∈ Zυ, (a, υ1) = 1} of the cyclic group Zυ as a group of automorphisms. In particular it is shown that such a design exists if and ony if one of (a) k = 2, (b) p ≡ 1 (mod k) for each prime p dividing υ, or (c) k is the least prime dividing υ, k2 does not divide υ, and p ≡ 1 (mod k) for each prime p < k dividing υ.
On elementary amenable groups of finite Hirsch number
Authors: Wehrfritz B. A. F. 
Published: April 2009

AbstractWe give an alternative short proof of a recent theorem of J. A. Hillman and P.A. Linnell that an elementary amenable group with finite Hirsch number has, modulo its locally finite radical, a soluble normal subgroup with index and derived length bounded only in terms of the Hirsch number of the group.
On the faithful representations, of degree 2n, of certain extensions of 2-groups by orthogonal and symplectic groups
Authors: Glasby S. P. 
Published: April 2009

AbstractIf R is a 2-group of symplectic type with exponent 4, then R is isomorphic to the extraspecial group , or to the central product 4 o 21+2n of a cyclic group of order 4 and an extraspecial group, with central subgroups of order 2 amalgamated. This paper gives an explicit description of a projective representation of the group A of automorphisms of R centralizing Z(R), obtained from a faithful representation of R of degree 2n. The 2-cocycle associated with this projective representation takes values which are powers of −1 if R is isomorphic to and powers of otherwise. This explicit description of a projective representation is useful for computing character values or computing with central extensions of A. Such central extensions arise naturally in Aschbacher's classification of the subgroups of classical groups.
Weakly-injective modules over hereditary noetherian prime rings
Authors: Jain S. K. , López-Permouth S. R. 
Published: April 2009

AbstractA module M is said to be wealdy-injective if and only if for every finitely generated submodule N of the injective hull E(M) of M there exists a submodule X of E(M), isomorphic to M such that N ⊂ X. In this paper we investigate weakly-injective modules over bounded hereditary noetherian prime rings. In particular we show that torsion-free modules over bounded hnp rings are always wealdy-injective, while torsion modules with finite Goldie dimension are weakly-injective only if they are injective.As an application, we show that weakly-injective modules over bounded Dedekind prime rings have a decomposition as a direct sum of an injective module B, and a module C satisfying that if a simple module S is embeddable in C then the (external) direct sum of all proper submodules of the injective hull of S is also embeddable in C. Indeed, we show that over a bounded hereditary noetherian prime ring every uniform module has periodicity one if and only if every weakly-injective module has such a decomposition.
On Schur's conjecture
Authors: Turnwald Gerhard 
Published: April 2009

AbstractWe study polynomials over an integral domainRwhich, for infinitely many prime idealsP, induce a permutation ofR/P. In many cases, every polynomial with this property must be a composition of Dickson polynomials and of linear polynomials with coefficients in the quotient field ofR. In order to find out which of these compositions have the required property we investigate some number theoretic aspects of composition of polynomials. The paper includes a rather elementary proof of ‘Schur's Conjecture’ and contains a quantitative version for polynomials of prime degree.
Instability theorems for certain nth order differential equations
Authors: Wen-Jian Li , Kui-chen Duan 
Published: April 2009

AbstractIn this paper we study the instability of certain nth order differential equations by means of Liapunov's functions and obtain some sufficient conditions for the equations being unstable. A method of constructing Liapunov's function for instability is being perfected. In particular the problem Ezeio posed in 1982 has been resolved to some extent.
Classes of modules with many direct summands
Authors: Al-Khazzi I. , Smith P. F. 
Published: April 2009

AbstractLet R be any ring with identity, M a unital right R-module and α ≥ 0 an ordinal. Then M is a direct sum of a semisimple module and a module having Krull dimension at most α if and only if for every submodule N of M there exists a direct summand K of M such that K ⊆ N and N/K has Krull dimension at most α.
Constructions for arc-transitive digraphs
Authors: Conder Marston , Lorimer Peter , Praeger Cheryl 
Published: April 2009

AbstractA number of constructions are given for arc-transitive digraphs, based on modifications of permutation representations of finite groups. In particular, it is shown that for every positive integer s and for any transitive permutation group p of degree k, there are infinitely many examples of a finite k-regular digraph with a group of automorphisms acting transitively on s-arcs (but not on (s + 1)-arcs), such that the stabilizer of a vertex induces the action of P on the out-neighbour set.
Normal families of holomorphic functions
Authors: Chen Huai-Hui , Hua Xin-Hou 
Published: April 2009

AbstractLet a(z) be a meromorphic function with only simple poles, and let k∈ N. Suppose that f(z) is meromorphic. We first set up an inequality in which T(r, f) is bounded by the counting function of the zeros of f(k) + af2, and then we prove a corresponding normal criterion. An example shows that the restriction on the poles of a(z) is best possible.
Linear independence of translations
Authors: Rosenblatt Joseph 
Published: April 2009

AbstractIt was shown by Edgar and Rosenblatt that f ∈ Lp (ℝn), 1 ≤ p < 2n/ (n-1), and f ≠0, then f has linearly independent translates. Using a result of Hömander, it is shown here that the same theorem holds if p = 2n / (n−1). This gives a sharp result because for n ≥2, there exists f ∈C0 (ℝn), f ≠0, which is simultaneously in all Lp (ℝn), p > 2n/(n−1), that has a linear dependence relation among its translates. References and some discussion are included.
Centralizer near-rings that are rings
Authors: Hausen Jutta , Johnson Johnny A. 
Published: April 2009

AbstractGiven an R-module M, the centralizer near-ring ℳR (M) is the set of all functions f: M → M with f(xr)= f(x)r for all x ∈ M and r∈R endowed with point-wise addition and composition of functions as multiplication. In general, ℳR(M) is not a ring but is a near-ring containing the endomorphism ring ER(M) of M. Necessary and/or sufficient conditions are derived for ℳR(M) to be a ring. For the case that R is a Dedekind domain, the R-modules M are characterized for which (i) ℳR(M) is a ring; and (ii)ℳR(M) = ER(M). It is shown that over Dedekind domains with finite prime spectrum properties (i) and (ii) are equivalent.
On a class of radicals of rings
Authors: Mazurek R. 
Published: April 2009

AbstractLet λ be a property that a lattice of submodules of a module may possess and which is preserved under taking sublattices and isomorphic images of such lattices and is satisfied by the lattice of subgroups of the group of integer numbers. For a ring R the lower radical Λ generated by the class λ(R) of R-modules whose lattice of submodules possesses the property λ is considered. This radical determines the unique ideal Λ (R) of R, called the λ-radical of R. We show that Λ is a Hoehnke radical of rings. Although generally Λ is not a Kurosh-Amitsur radical, it has the ADS-property and the class of Λ-radical rings is closed under extensions. We prove that Λ (Mn (R)) ⊆ Mn (Λ(R)) and give some illustrative examples.
The Urysohn-Menger sum formula: an extension of the Dydak-Walsh theorem to dimension one
Authors: Dranišnikov Aleksander N. , Repovš Dušan 
Published: April 2009

AbstractLet X be a finite-dimensional separable metric space, presented as a disjoint union of subsets, X = A∪B. We prove the following theorem: For every prime p, c-dimZpX≦c-dimZpA + c–dimZpB + 1. This improves upon some of the earlier work by Dydak and Walsh.
On lacunary sets for nonabelian groups
Authors: Dooley A. H. 
Published: April 2009

AbstractResults concerning a class of lacunary sets are generalized from compact abelian to compact nonabelian groups. This class was introduced for compact abelian groups by Bozejko and Pytlik; it includes the p-Sidon sets of Edwards and Ross. A notion of test family is introduced and is used to give necessary conditions for a set to be lacunary. Using this, it is shown that (2) has no infinite p-Sidon sets for 1 ≤p<2.
Semigroups over generalized trees
Authors: Hays T. E. 
Published: April 2009

AbstractA semigroup over a generalized tree, denoted by the term ℳL-semigroup, is a compact semigroup S such that Green's relation H is a congruence on S and S/H is an abelian generalized tree with idempotent endpoints and E(S/H) a Lawson semilattice. Each such semigroup is characterized as being constructible from cylindrical subsemigroups of S and the generalized tree S/H in a manner similar to the construction of semigroups over trees and of the hormos. Indeed, semigroups over trees are shown to be particular examples of the construction given herein.
Covering Theorems for FINASIGS VIII—almost all conjugacy classes in An have exponent ≤4
Authors: Brenner J. L. 
Published: April 2009

AbstractThe product of two subsets C, D of a group is defined as . The power Ce is defined inductively by C0 = {1}, Ce = CCe−1 = Ce−1C. It is known that in the alternating group An, n > 4, there is a conjugacy class C such that CC covers An. On the other hand, there is a conjugacy class D such that not only DD≠An, but even De≠An for e<[n/2]. It may be conjectured that as n ← ∞, almost all classes C satisfy C3 = An. In this article, it is shown that as n ← ∞, almost all classes C satisfy C4 = An.
On the rate of convergence of moments in the central limit theorem
Authors: Hall Peter 
Published: April 2009

AbstractAn early extension of Lindeberg's central limit theorem was Bernstein's (1939) discovery of necessary and sufficient conditions for the convergence of moments in the central limit theorem. Von Bahr (1965) made a study of some asymptotic expansions in the central limit theorem, and obtained rates of convergence for moments. However, his results do not in general imply that the moments converge. Some better rates have been obtained by Bhattacharya and Rao for moments between the second and third. In this paper we give improved rates of convergence for absolute moments between the third and fourth.
Existence of nonatomic charges
Authors: Bhaskara Rao K. P. S. , Rao M. Bhaskara 
Published: April 2009

AbstractA complete characterization of Boolean algebras which admit nonatomic charges (i.e. finitely additive measures) is obtained. This also gives rise to a characterization of superatomic Boolean algebras. We also consider the problem of denseness of the set of all nonatomic charges in the space of all charges on a given Boolean algebra, equipped with a suitable topology.
On generalized Borel sets
Authors: Pfeffer W. F. 
Published: April 2009

AbstractA certain natural extension B of the Borel σ-algebra is studied in generalized weakly θ-refinable spaces. It is shown that a set belongs to B whenever it belongs to B locally. From this it is derived that if ℵωα is more complicated than aunion of less than ℵα weakly θ-refinable subspaces.
Green's relations for regular elements of sandwich semigroups, II; semigroups of continuous functions
Authors: Magill K. D. , Subbiah S. 
Published: April 2009

AbstractA sandwich semigroup of continuous functions consists of continuous functions with domains all in some space X and ranges all in some space Y with multiplication defined by fg = foαog where α is a fixed continuous function from a subspace of Y into X. These semigroups include, as special cases, a number of semigroups previously studied by various people. In this paper, we characterize the regular elements of such semigroups and we completely determine Green's relations for the regular elements. We also determine the maximal subgroups and, finally, we apply some of these results to semigroups of Boolean ring homomorphisms.
Powers of p–valent functions
Authors: Noonan J. W. 
Published: April 2009

AbstractIf f is areally mean p–valent in the unit disc, if λ>0 and if fλ is defined as a single-valued analytic function on the unit disc with finitely many arcs removed, several results in the recent literature suggest that fλ might be areally mean pλ–valent. The purpose of this note is to determine the valence of fλ when f is areally mean p–valent, and also to characterize those functions for which fλ is pλ–valent for all λ>0. Analogous results are obtained for functions which are either s–dimensionally mean p–valent or logarithmically mean p–valent.
The structure sheaf of an incidence algebra
Authors: Barnwell Beth Goldston , Mewborn A. C. 
Published: April 2009

AbstractLet R be the incidence algebra of a finite partially ordered set T over a commutative noetherian ring A. Then the spectrum of R is homeomorphic to the product (Spec A) x T, where Spec A has the usual Zariski topology and T has the order topology. An explicit construction is given for the structure sheaf of R over its spectrum.
A remark on C-compact spaces
Authors: Nayar Bhamini M. P. 
Published: April 2009

AbstractIt has been observed by a number of researches that although it is well-known that all continuous functions defined on C-compact spaces are closed functions, this property does not characterize C-compact spaces. In this note we employ the notion of strongly subclosed relations to prove that a space is C-compact if and only if all functions on it with strongly subclosed inverses are closed functions.
Application of the Bruhat-Tits tree of SU3(h) to some Ã2 groups
Authors: Cartwright Donald I. , Steger Tim 
Published: April 2009

AbstractLet K be a nonarchimedean local field, let L be a separable quadratic extension of K, and let h denote a nondegenerate sesquilinear formk on L3. The Bruhat-Tits building associated with SU3(h) is a tree. This is applied to the study of certain groups acting simply transitively on vertices of the building associated with SL(3, F), F = Q3 or F3((X)).
Subordination in the sense of Bochner and a related functional calculus
Authors: Schilling René L. 
Published: April 2009

AbstractWe prove a new representation of the generator of a subordinate semigroup as limit of bounded operators. Our construction yields, in particular, a characterization of the domain of the generator. The generator of a subordinate semigroup can be viewed as a function of the generator of the original semigroup. For a large class these functions we show that operations at the level of functions has its counterpart at the level of operators.
On groups in which every subgroup is subnormal of defect at most three
Authors: Traustason Gunnar 
Published: April 2009

AbstractIn this paper we study groups in which every subgroup is subnormal of defect at most 3. LetGbe a group which is either torsion-free or of prime exponent different from 7. We show that every subgroup inGis subnormal of defect at most 3 if and only ifGis nilpotent of class at most 3. WhenGis of exponent 7 the situation is different. While every group of exponent 7, in which every subgroup is subnormal of defect at most 3, is nilpotent of class at most 4, there are examples of such groups with class exactly 4. We also investigate the structure of these groups.
Functions of bounded expansion: normal and Bloch functions
Authors: Gauthier P. M. , Xiao J. 
Published: April 2009

AbstractNormal functions and Bloch functions are respectively functions of bounded spherical expansion and bounded Euclidean expansion. In this paper we discuss the behaviour of normal functions and of Bloch functions in terms of the maximal ideal space of H∞, the Bergman projection and the Ahlfors-Shimizu characteristic.
A Global algorithm for geodesics
Authors: Noakes Lyle 
Published: April 2009

AbstractThe problem of finding a george joinning given points x0, x1in a connected complete Riemannian manifold requires much more effort than determining a geodesic from initial data. Boundary value problems of this type are sometimes solved using shooting methods, which work best when good initial guesses are available expectually when x0, x1are nearby. Galerkin methods have their drawbacks too. The situation is much more difficult with general variational problems, which is why we focus on the Riemannian case.Our global algorithm is very simple to implement, and works well in practice, with no need for an initial guess. The proof of convergence to elementary and very carefully stated. with a view to possible generalizations latter on we have in mind the much larger class of interesting problems arising in optimal control especially from mechanical engineering.
Regular cyclic actions on complex projective space with codimension-two fixed points
Authors: Little Robert D. 
Published: April 2009

AbstractIfM2nis a cohomologyCPnandPis an odd prime, letGpbe the cyclic group of orderp. A TypeI I0Gpaction onM2nis an action with fixed point set a codimension-2 submanifold and an isolated point. A TypeI I0Gpaction is standard if it is regular and the degree of the fixed codimension-2 submanifold is one. If n is odd and M2nadmits a standardGpaction of TypeI I0, then every TypeI I0GpactionM2nis standard and so, if n is odd,CPnadmits aGpaction of TypeI I0if and only if the action is standard.
The Vanishing problem of the string class with degree 3
Authors: Kuribayashi Katsuhiko , Yamaguchi Toshihiro 
Published: April 2009

AbstractLet ξbe anSO(n)-bundle over a simple connected manifoldMwith a spin structureQ → M. The string class is an obstruction to h1 the structure groupLSpin(n)of the loop group bundleLQ → LMto the universal central extension ofLSpain(n)by the circle. We prove that the string class vanishes if and only if 1/2 the first Pontrjagin clsss of values whenMis a compact simply connected homogeneous space of rank one, a simpiy connected 4 dimensional manifold or a finite product space of those manifolds. This result is deduced by using the Eclesberg spectral sequence converging to the modpcohomology ofLMwhoseE2-term to the Hochschild homology of the modpcohomology algebra ofM. The key to the consideration is existence of a morphism of algebras, which is injective below degree 3, from an important graded commutator algebra into the Hochschild homology of a certain graded commutative algebra.
Continuous nilpotents on topological spaces
Authors: Sullivan R. P. , Rubinstein J. H. 
Published: April 2009

AbstractK. D. Magill has investigated the semigroup generated by the idempotent continuous mappings of a topological space into itself and examined whether this semigroup determines the space to within homeomorphism. By analogy with this (and related work of Bridget Bos Baird) we now consider the semigroup generated by nilpotent continuous partial mappings of a space into itself.
Democrat, Republican, or None of the Above? The Role of Religiosity in Muslim American Party Identification
Authors: Barreto Matt A. , Bozonelos Dino N. 
Published: April 2009

AbstractThe role of religiosity as an important predictor of partisan identification has been well researched over the years, with most of our understanding of religion focused on Christianity. However, it is not clear that religiosity operates equally for the partisan identification of non-Christian religious groups. One of the most discussed religious minority groups in the United States today is Muslim-Americans. Numbering between 2.3 million and 7 million, Muslim-Americans have been the focus of considerable debate regarding religion and American political inclusion. We argue that religiosity does influence Muslim-American party identification, however not in the same manner as with other groups. While the two major political parties encourage religiosity among Protestants, Jews, and Catholics, they are either silent or opposed to religiosity among Muslims within their parties. Thus, religiosity among Muslim-Americans may not necessarily lead to partisan identification with either Republicans or Democrats. Rather, high levels of religiosity, coupled with perceptions of discrimination against Muslims, may lead many to oppose both major political parties and instead identify with “none of the above.” This is not to say that Muslim-Americans reject civic engagement or political participation in the United States, but rather the two political parties have not carved out a space to welcome Islam, as they have for Christianity and Judaism. We examine new data from the 2007 Muslim-American Public Opinion Survey to assess the predictors of partisan identification among Muslims in the United States.
The Congressional Representation of Muslim-American Constituents
Authors: Martin Shane 
Published: April 2009

AbstractLegislators' responsiveness to constituency preferences is an accepted cornerstone of American representative democracy. Focusing on key domestic anti-terrorism votes during the 109th Congress, this study explores whether or not the presence of Muslim-Americans in a district influenced House members' roll-call behavior. We apply and test two competing theories of representation: the congruence theory and the minority backlash hypothesis. Using original data on Muslim-American constituency size, our analysis indicates little evidence of a representational backlash and some evidence that both Democratic and Republican members are positively responsive in their roll-call behavior to the presence of Muslim voters in their districts.
Americans' Views of Muslims and Mormons: A Social Identity Theory Approach
Authors: Penning James M. 
Published: April 2009

AbstractAlthough American society is religiously pluralistic, not all religious groups enjoy equal levels of public approval and support. Indeed, America has a history of viewing members of nontraditional religious groups with considerable distrust and suspicion. Two religious groups in particular — Muslims and Mormons — have come under fire in recent years, though not necessarily for the same reasons. Muslims and Mormons have frequently been viewed as outside the mainstream of American culture and, perhaps for that reason, have suffered from discrimination, threats, and violence. This article examines Americans' views of these two important and rapidly growing groups, using social identity theory as the primary vehicle of analysis. The theory proves useful in helping us explain variance in Americans' views of these two groups. While a variety of social, political and religious variables help to explain Americans' views of Muslims and Mormons, religious variables have the greatest impact.