bluuebunny/crossref_metadata_2025 huggingface dataset:
On some diophantine problems involving powers and factorials
Authors: Brindza B. , Erdös P.
Published: April 2009

In this paper the power values of the sum of factorials and a special diophantine problem related to the Ramanujan-Nagell equation are studied. The proofs are based on deep analytic results and Baker's method.
Generalised simultaneous approximation of functions
Authors: Van Der Poorten A. J.
Published: April 2009

We generalise the approximation theory described in Mahier's paper “Perfect Systems” to linked simultaneous approximations and prove the existence of nonsingular approximation and of transfer matrices by generalising Coates' normality zig-zag theorem. The theory sketched here may have application to constructions important in the theory of diophantine approximation.
Hereditary radicals and bands of associative rings
Authors: Kelarev A. V.
Published: April 2009

Bands of associative rings were introduced in 1973 by Weissglass. For the radicals playing most essential roles in the structure theory (in particular, for those of Jacobson, Baer, Levitsky, Koethe) it is shown how to find the radical of a band of rings. The technique of the general Kurosh-Amitsur radical theory is used to consider many radicals simultaneously.
Second order subexponential distributions
Authors: Geluk J. L. , Pakes A. G.
Published: April 2009

The class of subexponential distributionsSis characterized byF(0) = 0, 1 −F(2)(x) ~ 2(1 −F(x)) asx→ ∞. In this paper we consider a subclass ofSfor which the relation 1 −F(2)(x) − 2(1 −F(x)) + (1 −F(x))2=o(a(x)) asx→ ∞ holds, where α is a positive function satisfying α(X) = 0(1 −F(x)) (x→ ∞).
Semiprime near-rings
Authors: De Stefano Stefania , Sieno Simonetta Di
Published: April 2009

Some properties of v-semiprime (v = 0, 1, 2) near-rings are pointed out. In particular v semiprime near-rings which contain nil non-nilpotent ideals are studied.
An ordered suprabarrelled space
Authors: Ferrando J. C. , López-Pellicer M.
Published: April 2009

A locally convex space E is said to be ordered suprabarrelled if given any increasing sequence of subspaces of E covering E there is one of them which is suprabarrelled. In this paper we show that the space m0(X, Σ), where X is any set and Σ is a σ-algebra on X, is ordered suprabarrelled, given an affirmative answer to a previously raised question. We also include two applications of this result to the theory of vector measures.
A class of ideals of the centre of a group ring
Authors: O'Reilly Michael F.
Published: April 2009

Reynolds (1972), using character-theory, showed that the p-section sums span an ideal of the centre Z(kG) of the group algebra of a finite group G over a field k of characteristic dividing the order of G. In O'Reilly (1973) a character-free proof was given. Here we extend these techniques to show the existence of a wider class of ideals of Z(kG).
Positive values of inhomogeneous quinary quadratic forms of type (4,1)
Authors: Hans-Gill R. J. , Raka Madhu
Published: April 2009

Here it is proved that if Q(x, y, z, t, u) is a real indefinite quinary quadratic form of type (4,1) and determinant D, then given any real numbers x0, y0, z0, t0, u0 there exist integers x, y, z, t, u such that

All critical forms are also obtained.
Estimating |α – p / q|
Authors: Worley R. T.
Published: April 2009

An estimate for q2|α – p/;q| is obtained by considering the relation between the continued fractions for α and p / q. This leads to an extension of the standard result “q2|α – p/q| < 1 imples that for some n, p/q = (ipn + pn-1) / (iqn + qn-1) where i = 0, 1 or an+1 −1”.
Moment inequalities of the Liapunov type
Authors: MacGillivray H. L.
Published: April 2009

Characterisations of the distribution of a non-negative random variable are sought for which the Liapunov moment inequality is extended to give inequalities between inverse powers of moment ratios, which are known as mean sizes in considerations of particle size distributions. A solution is found for continuous distributions, and the conditions applied to a number of well-known distributions. A further class of distributions is considered for which the new inequalities hold but the inequality direction is reversed for some orders of the moments. The study involves examination of the signs of the third central moments of a family of distributions, obtained by a log transformation, from the weighted, or moment, distributions induced by the non-negative random variable.
Triple systems with a fixed number of repeated triples
Authors: Rodger C. A.
Published: April 2009

In this paper, linear embeddings of partial designs into designs are found where no repeated blocks are introduced in the embedding process. Triple systems, pure cyclic triple systems, cyclic and directed triple systems are considered. In particular, a partial triple system with no repeated triples is embedded linearly in a triple system with no repeated triples.
Quasi-regularity in Optimization
Authors: Ng Kung-Fu , Yost David
Published: April 2009

The notion of quasi-regularity, defined for optimization problems in Rn, is extended to the Banach space setting. Examples are given to show that our definition of quasi-regularity is more natural than several other possibilities in the general situation. An infinite dimensional version of the Lagrange multiplier rule is established.
Translation invariant functionals on Lp (G) when G is not amenable
Authors: Willis G. A.
Published: April 2009

It is shown that if G is a non-amenable group, then there are no non-zero translation invariant functionals on Lp(G) for 1 < p < ∞. Furthermore, if G contains a closed, non-abelian free subgroup, then there are no non-zero translation invariant functionals on C0(G). The latter is proved by showing that a certain non-invertible convolution operator on C0(G) is surjective.
Reflective subcategories, localizations and factorization systems: Corrigenda
Authors: Cassidy C. , Hébert M. , Kelly G. M.
Published: April 2009

Reflective Subcategories, Localizations and Factorization Systems: Corrigenda C. Cassidy, M. Hébert and G. M. Kelly, 1980 Mathematics subject classification (Amer. Math. Soc.): 18 A 20.
On non-uniform and global descriptions of the rate of convergence of Asymptotic expansions in the central limit theorem
Authors: Hall Peter , Nakata T.
Published: April 2009

The leading term approach to rates of convergence is employed to derive non-uniform and global descriptions of the rate of convergence in the central limit theorem. Both upper and lower bounds are obtained, being of the same order of magnitude, modulo terms of order n-r. We are able to derive general results by considering only those expansions with an odd number of terms.
On the number of normal subgroups of an uncountable group
Authors: Burns R. G. , Lawrence John , Okoh Frank
Published: April 2009

In this paper two theorems are proved that give a partial answer to a question posed by G. Behrendt and P. Neumann. Firstly, the existence of a group of cardinality ℵ1 with exactly ℵ1 normal subgroups, yet having a subgroup of index 2 with 2ℵ1 normal subgroups, is consistent with ZFC (the Zermelo-Fraenkel axioms for set theory together with the Axiom of Choice). Secondly, the statement “Every metabelian-by-finite group of cardinality ℵ1 has 2ℵ1 normal subgroups” is consistent with ZFC.
Primitive ideals with bounded approximate units in L1-algebras of exponential lie groups
Authors: Bekka Mohammed El Bachir
Published: April 2009

Let G be an exponential Lie group. We study primitive ideals (i.e. kernels of irreducible *-representations of L1(G)), with bounded approximate units (b.a.u.). We prove a result relating the existence of b.a.u. in certain primitive ideals with the geometry of the corresponding Kirillov orbits. This yields for a solvable group of class 2, a characterization of the primitive ideals with b.a.u.
Duality properties of spaces of non-Archimedean valued functions
Authors: Govaerts W.
Published: April 2009

Let C(X, F) be the space of all continuous functions from the ultraregular compact Hausdorff space X into the separated locally K-convex space F; K is a complete, but not necessarily spherically complete, non-Archimedean valued field and C(X, F) is provided with the topology of uniform convergence on X We prove that C(X, F) is K-barrelled (respectively K-quasibarrelled) if and only if F is K-barrelled (respectively K-quasibarrelled) This is not true in the case of R or C-valued functions. No complete characterization of the K-bornological space C(X, F) is obtained, but our results are, nevertheless, slightly better than the Archimedean ones. Finally, we introduce a notion of K-ultrabornological spaces for K non-spherically complete and use it to study K-ultrabornological spaces C(X, F).
On the convexity and symmetry of solutions to an elliptic free boundary problem
Authors: Kawohl Bernhard
Published: April 2009

We study the existence, uniqueness and regularity of solutions to an exterior elliptic free boundary problem. The solutions model stationary solutions to nonlinear diffusion reaction problems, that is, they have compact support and satisfy both homogeneous Dirichlet and Neumann-type boundary conditions on the free boundary ∂{u > 0}. Then we prove convexity and symmetry properties of the free boundary and of the level sets {u > c} of the solutions. We also establish symmetry properties for the corresponding interior free boundary problem.
Semidirect product groups with Abelian automorphism groups
Authors: Curran M. J.
Published: April 2009

Miller's group of order 64 is a smallest example of a nonabelian group with an abelian automorphism group, and is the first in an infinite family of such groups formed by taking the semidirect product of a cyclic group of order 2m (m ≥ 3) with a dihedral group of order 8. This paper gives a method for constructing further examples of non abelian 2-groups which have abelian automorphism groups. Such a 2-group is the semidirect product of a cyclic group and a special 2-group (satisfying certain conditions). The automorphism group of this semidirect product is shown to be isomorphic to the central automorphism group of the corresponding direct product. The conditions satisfied by the special 2-group are determined by establishing when this direct product has an abelian central automorphism group.
Multipliers for Hardy spaces on locally compact Vilenkin groups
Authors: Onneweer C. W. , Quek T. S.
Published: April 2009

In a recent paper In a recent paper the authors proved a multiplier theorem for Hardy spaces Hp (G), 0 < p ≤ 1, defined on a locally compact Vilenkin group G. The assumptions on the multiplier were expressed in terms of the “norms” of certain Herz spaces K (1/p − 1/?r, r, p) with r restricted to 1 ≤ r < ∞ and p < r. In the present paper we show how this restriction on r may be weakened to p ≤ r ∞. Furthermore, we present two modifications of our main theorem and compare these with certain results for multipliers on LP (Rn)-spaces, 1 < p < ∞, due to Seeger and to Cowling, Fendler and Foumier. We also discuss the sharpness of some of our results.
On rings all of whose factor rings are integral domains
Authors: Hirano Yasuyuki
Published: April 2009

A ring R is called a (proper) quotient no-zero-divisor ring if every (proper) nonzero factor ring of R has no zero-divisors. A characterization of a quotient no-zero-divisor ring is given. Using it, the additive groups of quotient no-zero-divisor rings are determined. In addition, for an arbitrary positive integer n, a quotient no-zero-divisor ring with exactly n proper ideals is constructed. Finally, proper quotient no-zero-divisor rings and their additive groups are classified.
On the chromatic uniqueness of certain trees of polygons
Authors: Peng Y. H.
Published: April 2009

We establish a characterization of certain trees of polygons similar to that of n-gon-trees given by Chao and Li.
A note of the union-closed sets conjecture
Authors: Norton R. M. , Sarvate D. G.
Published: April 2009

Let = {A1, …, An} be a union-closed set. This note establishes a property which must be possessed by any smallest counterexample to the Union-Closed Sets Conjecture. Specifically, a counterexample to the conjecture with minimal n has at least three distinct elements, each of which appears in exactly (n − 1)/2 of the .
On maximal abelian groups of maps
Authors: Winkler Reinhard
Published: April 2009

The paper gives a rather simple description of all maximal abelian subgroups H of the symmetric group SM acting on an arbitrary set M. In the case of finite M this result is used to determine the maximal cardinality of such an H and the maximal number of permutations without fixed points contained in an abelian subgroup of SM.
Local uniqueness of solutions of the characteristic Cauchy problem
Authors: Petronilho Gerson
Published: April 2009

Local uniqueness of solutions of the characteristic Cauchy problem is shown for operators which are perturbations of operators which already have such a uniqueness.
The (CO)homology of groups given by presentations in which each defining relator involves at most two types of generators
Authors: Pride Stephen J.
Published: April 2009

Our set-up will consist of the following: (i) a graph with vertex set V and edge set E; (ii) for each vertex ∈ V a non-trivial group Gv given by a presentation (xν; rν); (iii) for each edge e = {u, ν} ∈ E a group Ge given by a presentation (xu, xv; re) where re consists of the elements of ru ∪ rv, together with some further words on xu ∪ xv. We let G = (x; r) where x = ∪v∈v xv, r = ∪e∈E re. Ouraim is to try to describe the structure of G in terms of the groups Gv, (v ∈ V), Ge (e ∈ E). Under suitable conditions the natural homomorphisms Gv, → G (ν ∈ V), Ge → Ge (e ε E) are injective; and there is a short exact sequence (where, for any group H, IH is the augmentation ideal). Some (co)homological consequences of these resultsare derived.
On strongly stable approximations
Authors: Nair M. Thamban
Published: April 2009

Ahues (1987) and Bouldin (1990) have given sufficient conditions for the strong stability of a sequence (Tn) of operators at an isolated eigenvalue of an operator T. This paper provides a unified treatment of their results and also generalizes so as to facilitate their application to a broad class of operators.
Maximal right ideals of transformation near-rings
Authors: Johnson Marjory J.
Published: April 2009

The purpose of this note is to characterize maximal right ideals of T0(G), the (left) mear-ring of transformations from a group (G, +) into itself which leave zero fixed. Using this characterization, we answer some questions raised by Heatherly (1972).
A class of modules over a locally finite group II
Authors: Hartley B.
Published: April 2009

Our main purpose in this paper is to obtain more precise information about two problems which we investigated in Hartley (1971a). They are as follows: Problem 1. Let G be a countable locally finite group and π be a set of primes. Suppose that G = HK, H◃G, H∩K = 1, where H is a normal π′-subgroup of G, K is a π-group and Ck(H) = 1. If we assume that the Sylow (that is, maximal) π-subgroups of G are conjugate, what can we say about the structure of K?
Totally commutative semigroups
Authors: Dudek Józef , Kisielewicz Andrzej
Published: April 2009

A semigroup is totally commutative if each of its essentially binary polynomials is commutative, or equivalently, if in every polynomial (word) every two essential variables commute. In the present paper we describe all varieties (equational classes) of totally commutative semigroups, lattices of subvarieties for any variety, and their free spectra.
Polynomials for hyperovals of Desarguesian planes
Authors: O'keefe Christine M. , Penttila Tim
Published: April 2009

This paper studies o-polynomials, that is, polynomials which represent hyperovals in Desarguesian projective planes of even order. We present theoretical restrictions on the form that O-polynomials can have, and we determine the number of o-polynomials corresponding to each of the known classes of hyperovals (other than Cherowitzo's). We use this to give the number of known o-polynomials for the fields of orders 4, 8, 16 and 32. Exploratory computer searches for o-polynomials for fields of small orders greater than 16 are reported.
Fitting classes based on groups of nilpotent length three with operator-isomorphic minimal normal subgroups
Authors: McCann Brendan
Published: April 2009

In this paper a technique for constructing Fitting Classes is applied to certain groups of nilpotent length three which have non-unique minimal normal subgroups. A characterisation of the minimal Fitting Class of some of these groups is also given.
Knot projections and Coxeter groups
Authors: Brunner A. M. , Lee Y. W.
Published: April 2009

Every knot admits a special projection with the property that under the projection discs in the canonical Seifert surface project disjointly. Under an isotopy, such a projection can be turned into a connected sum of what we call inseparable projections. The main result is that if there is no band in an inseparable projection with half-twisting number +1 or −1, then the projection is not a projection of the trivial knot. To prove this a non-cyclic Coxeter group is constructed as a quotient of the knot group. The construction is possibly of interest in itself. The techniques developed are applied to give a criterion to decide when an inseparable projection with 3 discs comes from the trivial knot.
The weak drop property on closed convex sets
Authors: Lin Pei-Kee , Yu Xintai
Published: April 2009

Recall a closed convex set C is said to have the weak drop property if for every weakly sequentially closed set A disjoint from C there exists x ∈ A such that co({x} ∩ C) ∪ A = {x}. Giles and Kutzarova proved that every bounded closed convex set with the weak drop property is weakly compact. In this article, we show that if C is an unbounded closed convex set of X with the weak drop property, then C has nonempty interior and X is a reflexive space.
How to obtain an asymptotic expansion of a sequence from an analytic identity satisfied by its generating function
Authors: Plotkin J. M. , Rosenthal John W.
Published: April 2009

Let fn be a sequence of nonnegative integers and let f(x): = Σn≥0 fn xn be its generating function. Assume f(x) has the following properties: it has radius of convergence r, 0 < r < 1, with its only singualarity on the circle of convergence at x = r and f(r) = s; y = f(x) satisfies an analytic identity F(x, y) = 0 near (r, s); for some k ≥ 2 F0.j = 0, 0 ≤ j < k, F0.k ≠ 0 where Fi is the value at (r, s) of the ith partial derivative with respect to x and the jth partial derivative with respect to y of F. These assumptions form the basis of what we call the typical and general cases. In both cases we show how to obtain an asymptotic expansion of fn. We apply our technique to produce several terms in the asymptotic expansion of combinatorial sequences for which previously only the first term was known.
Metabelian Lie powers of group representations
Authors: Bryant R. M. , Stöhr R. , Zerck R.
Published: April 2009

Any representation of a group G on a vector space V extends uniquely to a representation of G on the free metabelian Lie algebra on V. In this paper we study such representations and make some group-theoretic applications.
On lattice-perfect measures
Authors: Stratigos P. D.
Published: April 2009

The general properties of lattice-perfect measures are discussed. The relationship between countable compactness and measure perfectness, and the relationship between lattice-measure tightness and lattice-measure perfectness are investigated and several applications in topological measure theory are given.
Equivariant KK-theory for inverse limits of G-C*-algebras
Authors: Schochet Claude
Published: April 2009

The Kasparov groups are extended to the setting of inverse limits of G-C*-algebras, where G is assumed to be a locally compact group. The K K-product and other important features of the theory are generalized to this setting.
On free products of completely regular semigroups
Authors: Jones Peter R.
Published: April 2009

The free product*CRSiof an arbitrary family of disjoint completely simple semigroups {Si}i∈i, within the variety CR of completely regular semigroups, is described by means of a theorem generalizing that of Kaďourek and Polák for free completely regular semigroups. A notable consequence of the description is that all maximal subgroups of*CRSiare free, except for those in the factorsSithemselves. The general theorem simplifies in the case of free CR-products of groups and, in particular, free idempotent-generated completely regular semigroups.
Central idempotents in p-adic group rings
Authors: Külshammer Burkhard
Published: April 2009

We provide character-free proofs of some results on idempotents in p-adic group rings, centering around Brauer's Second Main Theorem on Blocks.
Operators and the space of integrable scalar functions with respect to a Fréchet-valued measure
Authors: Fernández Antonio , Naranjo Francisco
Published: April 2009

We consider the spaceL1(ν,X) of all real functions that are integrable with respect to a measurevwith values in a real Fréchet spaceX. We study L-weak compactness in this space. We consider the problem of the relationship between the existence of copies ofl∞in the space of all linear continuous operators from a complete DF-spaceYto a Fréchet latticeEwith the Lebesgue property and the coincidence of this space with some ideal of compact operators. We give sufficient conditions on the measure ν and the spaceXthat imply thatL1(ν,X) has the Dunford-Pettis property. Applications of these results to Fréchet AL-spaces and Köthe sequence spaces are also given.
A note on uniform bounds of primeness in matrix rings
Authors: Van den Berg John E.
Published: April 2009

A nonzero ring R is said to be uniformly strongly prime (of bound n) if n is the smallest positive integer such that for some n-element subset X of R we have xXy ≠ 0 whenever 0 ≠ x, y ∈ R. The study of uniformly strongly prime rings reduces to that of orders in matrix rings over division rings, except in the case n = 1. This paper is devoted primarily to an investigation of uniform bounds of primeness in matrix rings over fields. It is shown that the existence of certain n-dimensional nonassociative algebras over a field F decides the uniform bound of the n × n matrix ring over F.
On the numerical range map
Authors: Joswig M. , Straub B.
Published: April 2009

Let A ∈ ℒ(Cn) and A1, A2 be the unique Hermitian operators such that A = A1 + i A2. The paper is concerned with the differential structure of the numerical range map nA: x ↦ ((A1x, x), (A1x, x)) and its connection with certain natural subsets of the numerical range W(A) of A. We completely characterize the various sets of critical and regular points of the map nA as well as their respective images within W(A). In particular, we show that the plane algebraic curves introduced by R. Kippenhahn appear naturally in this context. They basically coincide with the image of the critical points of nA.
A note on special involutions
Authors: Munn W. D.
Published: April 2009

The algebra consisting of those linear transformations of a complex inner product space that have a formal adjoint is shown to possess a special involution. Two earlier results concerning special involutions are then generalized.
Special radicals and matrix near-rings
Authors: Veldsman Stefan
Published: April 2009

Special radical classes of near-rings are defined and investigated. It is shown that our approach, which differs from previous ones, does cater for all the well-known radicals of near-rings. Moreover, most of the desirable properties from their ring theory counterpart are retained. The relationship between the special radical of a near-ring and the corresponding matrix near-ring is given.
Epicompletetion of archimedean l–groups and vector lattices with weak unit
Authors: Ball Richard N. , Hager Anthony W.
Published: April 2009

In the category W of archimedean l–groups with distinguished weak order unit, with unitpreserving l–homorphism, let B be the class of W-objects of the form D(X), with X basically disconnected, or, what is the same thing (we show), the W-objects of the M/N, where M is a vector lattice of measurable functions and N is an abstract ideal of null functions. In earlier work, we have characterized the epimorphisms in W, and shown that an object G is epicomplete (that is, has no proper epic extension) if and only if G ∈ B. This describes the epicompletetions of a give G (that is, epicomplete objects epically containing G). First, we note that an epicompletion of G is just a “B-completion”, that is, a minimal extension of G by a B–object, that is, by a vector lattice of measurable functions modulo null functions. (C[0, 1] has 2c non-eqivalent such extensions.) Then (we show) the B–completions, or epicompletions, of G are exactly the quotients of the l–group B(Y(G)) of real-valued Baire functions on the Yosida space Y(G) of G, by σ-ideals I for which G embeds naturally in B(Y(G))/I. There is a smallest I, called N(G), and over the embedding G ≦ B(Y(G))/N(G) lifts any homorphism from G to a B–object. (The existence, though not the nature, of such a “reflective” epicompletion was first shown by Madden and Vermeer, using locales, then verified by us using properties of the class B.) There is a unique maximal (not maximum) such I, called M(Y(G)), and B(Y(G))/M(Y(G)) is the unique essentialBcompletion. There is an intermediate σ -ideal, called Z(Y(G)), and the embedding G ≦ B(y(G))/Z(Y(G)) is a σ-embedding, and functorial for σ -homomorphisms. The sistuation stands in strong analogy to the theory in Boolean algebras of free σ -algebras and σ -extensions, though there are crucial differences.
A note on Riesz sets and lacunary sets
Authors: Brummelhuis R. G. M.
Published: April 2009

W. Rudin has proved that the union of the Riesz set N ⊆ R with a Λ(l)-subset of Z is again a Riesz set. In this note we generalize his result to compact groups whose contains a circle group, thereby extending an earlier F. and M. Riesz theorem for such groups by the author. We also investigate the possibility of constructing Λ(p)-sets for these groups, departing from Λ(p)-sets for the circle group in center.
Growth sequence of globally idemportent semigroups
Authors: Pollák György
Published: April 2009

The n–th member of the growth sequence of a globally idempotent finite semigroup without identity element is at least 2n. (This had been conjectured by J. Wiegold.)
H∞ functional calculus of elliptic operators with C∞ coefficients on Lp spaces of smooth domains
Authors: Duong Xuan Thinh
Published: April 2009

The purpose of this paper is to show that higher order elliptic partial differential operators on smooth domains have an H∞ functional calculus and satisfy quadratic estimates in Lp spaces on these domains.
On the product Πn≧1 (1 + qn x + q2n x2)
Authors: Yang Kung-Wei
Published: April 2009

We study the coefficients An in the expansion of the infinite product We first derive a recurrence relation for An and from it we obtain an explicit expression of An. We then prove a convolution identity involving An.
Some quantitative results related to Roth's theorem: Corrigenda
Authors: Bombieri E. , Poorten A. J. Van Der
Published: April 2009

Theorem 1 of the paper [1] is stated in an unnecessarily weak form. What is actually proved is much stronger.
Fixed points of mappings satisfying semicontractivity conditions
Authors: Schu Jürgen
Published: April 2009

Let A be a subset of a Banach space E. A mapping T: A →A is called asymptoically semicontractive if there exists a mapping S: A×A→A and a sequence (kn) in [1, ∞] such that Tx=S(x, x) for all x ∈A while for each fixed x ∈A, S(., x) is asymptotically nonexpansive with sequence (kn) and S(x,.) is strongly compact. Among other things, it is proved that each asymptotically semicontractive self-mpping T of a closed bounded and convex subset A of a uniformly convex Banach space E which satisfies Opial's condition has a fixed point in A, provided s has a certain asymptoticregurity property.
On prime one-sided ideals, bi-ideals and quasi-ideals of a gamma ring
Authors: Booth G. L. , Groenewald N. J.
Published: April 2009

Let M be a Γ-ring with right operator ring R. We define one-sided ideals of M and show that there is a one-to-one correspondence between the prime left ideals of M and R and hence that the prime radical of M is the intersection of its prime left ideals. It is shown that if M has left and right unities, then M is left Noetherian if and only if every prime left ideal of M is finitely generated, thus extending a result of Michler for rings to Γ-rings.

Bi-ideals and quasi-ideals of M are defined, and their relationships with corresponding structures in R are established. Analogies of various results for rings are obtained for Γ-rings. In particular we show that M is regular if and only if every bi-ideal of M is semi-prime.
Periodic groups with many permutable subgroups
Authors: Longobardi Patrizia , Maj Mercede , Rhemtulla Akbar , Smith Howard
Published: April 2009

Groups in which every infinite set of subgroups contains a pair that permute were studied by M. Curzio, J. Lennox, A. Rhemtulla and J. Wiegold. The question whether periodic groups in this class were locally finite was left open. Here we show that if the generators of such a group G are periodic then G is locally finite. This enables us to get the following characterisation. A finitely generated group G is centre-by-finite if and only if every infinite set of subgroups of G contains a pair that permute.
Some generalizations in H-modular spaces of Fan's best approximation theorem
Authors: Bardaro Carlo , Ceppitelli Rita
Published: April 2009

We state best approximation and fixed point theorems in modular spaces endowed with an H-space structure given by the modular topology. We consider both the cases of single valued functions and multifunctions. These theorems extend some previous results due to Ky Fan.
On questions of B. J. Gardner and A. D. Sands
Authors: Beidar K. I.
Published: April 2009

An example of two disjoint special classes whose upper radicals coincide is presented. It is shown that the left hereditary subradical of the hereditary idempotent radical is right hereditary. An example of a hereditary and principally left hereditary radical which is not left hereditary is constructed.
Radicals and subdirect decompositions of Ω-groups
Authors: Mlitz R. , Veldsman S.
Published: April 2009

Starting with a class ℳ of Ω-groups, necessary and sufficient conditions on ℳ are given to ensure that the corresponding Hoehnke radical ρ (determined by the subdirect closure of ℳ as semisimple class) is a radical in the sense of Kurosh and Amitsur; has a hereditary semisimple class; satisfies the ADS-property; has a hereditary radical class or satisfies ρN ∩ I ⊆ ρI and lastly, have both a hereditary radical and semisimple class or satisfies ρN ∩ I = ρI.
Pairwise complete regularity as a separation axiom
Authors: Aarts J. M. , Mršević M.
Published: April 2009

Focussing on complete regularity, we discuss the separation properties of bitopological spaces. The unifying concept is that of separation by a pair of bases (B1, B2) for the closed sets of a bitopological space (S, J1, J2). For various separation properties a characterization is presented in terms of separation by a pair of closed bases. This is extended to results concerning pairs of subbases. Here the notion of screening by pairs of subbases plays a central role and the characterization of complete regularity in a natural way fits in between those of regularity and normality. In the key lemma the relation with quasi-proximities is exhibited.
Monomial representations and generalizations
Authors: Bessenrodt Christine
Published: April 2009

We study the characteristic p analogue of M-groups, the so-called Mp-group Generalizing this notion, we also consider the condition that the modular irreducible representations are induced from representations of dimension < p, or even weaker, of dimension not divisible by p.
Functional least squares estimators in an additive effects outliers model
Authors: Dhar Sunil K.
Published: April 2009

Consider the additive effects outliers (A.O.) model where one observes , with The sequence of r.v.s is independent of and , are i.i.d. with d.f. , where the d.f.s Ln, n ≦ 0, are not necessarily known and εj's are i.i.d.. This paper discusses the asymptotic behavior of functional least squares estimators under the above model. Uniform consistency and uniform strong consistency of these estimators are proven. The weak convergence of these estimators to a Gaussian process and their asymptotic biases are also discussed under the above A.O. model.
Constructions of balanced ternary designs
Authors: Sarvate D. G.
Published: April 2009

A construction for balanced ternary designs is given. Based on the designs so obtained, a construction of partially balanced ternary designs is given, which gives balanced ternary designs and series of symmetric balanced ternary designs in special cases.
Fonctions propres de l'opérateur de Laplace-Beltrami associé au bi-disque
Authors: Tahani Taoufiq
Published: April 2009

Soit D I'opérateur de Laplace-Beltrami sur le bi-disque. On démontre que les fonctions ζ → Plgr; (ζ, u) provenant du noyau de Poisson associé au bi-disque sont les seules solutions réelles normalisées du système. qui satisfont une certaine hypothèse.
Characterization of two-distance sequences
Authors: Lunnon W. F. , Pleasants P. A. B.
Published: April 2009

Three differently defined classes of two-symbol sequences, which we call the two-distance sequences, the linear sequences and the characteristic sequences, have been discussed by a number of authors and some equivalences between them are known. We present a self-contained proof that the three classes are the same (when ambiguous cases of linear sequences are suitably in terpreted). Associated with each sequence is a real invariant (having a different appropriate definition for each of the three classes). We give results on the relation between sequences with the same invariant and on the symmetry of the sequences. The sequences are closely related to Beatty sequences and occur as digitized straight lines and quasicrystals. They also provide examples of minimal word proliferation in formal languages.
Covering in the lattice of subuniverses of a finite distributive lattice
Authors: Lengvárszky Zsolt , McNulty George F.
Published: April 2009

The covering relation in the lattice of subuniverses of a finite distributive lattices is characterized in terms of how new elements in a covering sublattice fit with the sublattice covered. In general, although the lattice of subuniverses of a finite distributive lattice will not be modular, nevertheless we are able to show that certain instances of Dedekind's Transposition Principle still hold. Weakly independent maps play a key role in our arguments.
Lp-multipliers of mixed-norm type on locally compact Vilenkin groups
Authors: Onneweer C. W. , Quek T. S.
Published: April 2009

Let G be a locally compact Vilenkin group with dual group Γ. We prove Littlewood-Paley type inequalities corresponding to arbitrary coset decompositions of Γ. These inequalities are then applied to obtain new Lp(G) multiplier theorems. The sharpness of some of these results is also discussed.
Testing modules for irreducibility
Authors: Holt Derek F. , Rees Sarah
Published: April 2009

A practical method is described for deciding whether or not a finite-dimensional module for a group over a finite field is reducible or not. In the reducible case, an explicit submodule is found. The method is a generalistaion of the Parker-Norton ‘Meataxe’ algorithm, but it does not depend for its efficiency on the field being small. The principal tools involved are the calculation of the nullspace and the characteristic polynomial of a matrix over a finite field, and the factorisation of the latter. Related algorithms to determine absolute irreducibility and module isomorphism for irreducibles are also described. Details of an implementation in the GAP system, together with some performance analyses are included.
Kronecker classes of fields and covering subgroups of finite groups
Authors: Praeger Cheryl E.
Published: April 2009

Kronecker classes of algebraci number fields were introduced by W. Jehne in an attempt to understand the extent to which the structure of an extension K: k of algebraic number fields was influenced by the decomposition of primes of k over K. He found an important link between Kronecker equivalent field extensions and a certain covering property of their Galois groups. This surveys recent contributions of Group Theory to the understanding of Kronecker equivalence of algebraic number fields. In particular some group theoretic conjectures related to the Kronecker class of an extension of bounded degree are explored.
The nuclear length of a character
Authors: Wheeler Wayne W.
Published: April 2009

If G is a π-separable group and χ is an irreducible character of G, then Issacs gas defined an associated pair (W, γ), called a nucleus of χ. The nucleus is the last term in a certain chain of pairs (I, Ω), where I is a subgroup of G and Ω is an irreducible character of I. The length of this chain is an invariant of χ that we call the nuclear length. In this paper we study bounds on the nuclear length of χ as a function of the π-length of G and as a function of the character degree χ(1).
A Class of Limit Algebras Associated with Directed Graphs
Authors: Kribs David W. , Solel Baruch
Published: April 2009

Every directed graph defines a Hilbert space and a family of weighted shifts that act on the space. We identify a natural notion of periodicity for such shifts and study their C* -algebras. We prove the algebras generated by all shifts of a fixed period are of Cuntz-Krieger and Toeplitz-Cuntz-Krieger type. The limit C* -algebras determined by an increasing sequence of positive integers, each dividing the next, are proved to be isomorphic to Cuntz-Pimsner algebras and the linking maps are shown to arise as factor maps. We derive a characterization of simplicity and compute the K-groups for these algebras. We prove a classification theorem for the class of algebras generated by simple loop graphs.
Generalized hypergroups and orthogonal polynomials
Authors: Lasser Rupert , Obermaier Josef , Rauhut Holger
Published: April 2009

The concept of semi-bounded generalized hypergroups (SBG hypergroups) is developed. These hypergroups are more special than generalized hypergroups introduced by Obata and Wildberger and more general than discrete hypergroups or even discrete signed hypergroups. The convolution of measures and functions is studied. In the case of commutativity we define the dual objects and prove some basic theorems of Fourier analysis. Furthermore, we investigate the relationship between orthogonal polynomials and generalized hypergroups. We discuss the Jacobi polynomials as an example.
Moduli space of branched superminimal immersions of a compact Riemann surface into S4
Authors: Loo Bonaventure
Published: April 2009

In this paper we describe the moduli spaces of degree d branched superminimal immersions of a compact Riemann surface of genus g into S4. We prove that when d ≥ max {2g, g + 2}, such spaces have the structure of projectivzed fibre products and are path-connected quasi projective varieties of dimension 2d − g + 4. This generalizes known results for spaces of harmonic 2-spheres in S4.
Maximal convergence groups and rank one symmetric spaces
Authors: Basmajian Ara , Zeinalian Mahmoud
Published: April 2009

abstract

We show that the group of conformal homeomorphisms of the boundary of a rank one symmetric space (except the hyperbolic plane) of noncompact type acts as a maximal convergence group. Moreover, we show that any family of uniformly quasiconformal homeomorphisms has the convergence property. Our theorems generalize results of Gehring and Martin in the real hyperbolic case for Möbius groups. As a consequence, this shows that the maximal convergence subgroups of the group of self homeomorphisms of the d–sphere are not unique up to conjugacy. Finally, we discuss some implications of maximality.
The Monge-Ampère equation and warped products of higher rank
Authors: Bechtluft-Sachs Stefan , Samiou Evangelia
Published: April 2009

abstract

We show that a warped product Mf = nf has higher rank and nonpositive curvature if and only if f is a convex solution of the Monge-Ampère equation. In this case we show that M contains a Euclidean factor.
Multidimensional Hausdorff operators on the real Hardy space
Authors: Lerner A. K. , Liflyand E.
Published: April 2009

For a wide family of multivariate Hausdorff operators, the boundedness of an operator from this family i s proved on the real Hardy space. By this we extend and strengthen previous results due to Andersen and Móricz.
Elastica in SO(3)
Authors: Popiel Tomasz , Noakes Lyle
Published: April 2009

In a Riemannian manifold M, elastica are solutions of the Euler-Lagrange equation of the following second order constrained variational problem: find a unit-speed curve in M, interpolating two given points with given initial and final (unit) velocities, of minimal average squared geodesic curvature. We study elastica in Lie groups G equipped with bi-invariant Riemannian metrics, focusing, with a view to applications in engineering and computer graphics, on the group SO(3) of rotations of Euclidean 3-space. For compact G, we show that elastica extend to the whole real line. For G = SO(3), we solve the Euler-Lagrange equation by quadratures.
A generalization of the matrix form of the Brunn-Minkowski inequality
Authors: Yuan Jun , Lenga Gangsong
Published: April 2009

In this paper, we establish an extension of the matrix form of the Brunn-Minkowski inequality. As applications, we give generalizations on the metric addition inequality of Alexander.

2000 Mathematics subject classification: primary 52A40.
Local Homomorphisms of Topological Groups
Authors: Zelenyuk Yevhen
Published: April 2009

A mapping f : G → s from a left topological group G into a semigroup S is a local homomorphism if for every x є G \ {e}, there is a neighborhood Ux of e such that f (xy) = f (x)f (y) for all y є Ux \ {e}. A local homomorphism f : G → S is onto if for every neighborhood U of e, f(U \ {e}) = S. We show that

(1) every countable regular left topological group containing a discrete subset with exactly one accumulation point admits a local homomorphism onto N,

(2) it is consistent that every countable topological group containing a discrete subset with exactly one accumulation point admits a local homomorphism onto any countable semigroup,

(3) it is consistent that every countable nondiscrete maximally almost periodic topological group admits a local homomorphism onto the countably infinite right zero semigroup.
Strongly zero-dimensional bispaces
Authors: Künzi Hans-Peter A.
Published: April 2009

Let Cb be the admissible functorial quasi-uniformity on the completely regular bispaces which is spanned by the upper quasi-uniformity on the real line. Answering a question posed by B. Banaschewski and G. C. L. Brümmer in the affirmative we show that CbX is transitive for every strongly zero-dimensional bispace X.
Maximal subgroups of infinite dimensional general linear groups
Authors: Macpherson Dugald
Published: April 2009

Let k be an infinite cardinal, F a field, and let GL(k, F) be the group of all non-singular linear transformations on a ki-dimensional vector space V over F. Various examples are given of maximal subgroups of GL(k, F). These include (i) stabilizers of families of subspaces of V which are like filters or ideals on a set, (ii) almost stabilizers of certain subspaces of V, (iii) almost stabilizers of a direct decomposition of V into two k-dimensional subspaces.

It is also noted that GL(k, F) is not the union of any chain of length k of proper subgroups.
Finite one-relator products of two cyclic groups with the relator of arbitrary length
Authors: Campbell C. M. , Heggie P. M. , Robertson E. F. , Thomas R. M.
Published: April 2009

In this paper we consider the groupsG = G(α, n)defined by the presentations. We derive a formula for [G′:″] and determine the order ofGwhenevern≦ 7. We show thatGis a finite soluble group ifnis odd, but thatGcan be infinite whennis even,n≧ 8. We also show thatG(6, 10) is a finite insoluble group involvingPSU(3, 4), and that the groupHwith presentationis a finite group of deficiency zero of order at least 114,967,210,176,000.
Generalised harmonic analysis of a class of nonstationary random fields
Authors: Anh V. V. , Lunney K. E.
Published: April 2009

The paper gives a spectral representation for a class of random fields which are bounded in mean square almost surely. A characterisation of the corresponding spectral measure in the representation is obtained based on Beurling's duality theory and generalised Fourier transforms. A representation for the covariance function of asymptotically stationary random fields is also derived.
Finite group actions on 4-manifolds
Authors: Cho Yong Seung
Published: April 2009

Let X be a closed, oriented, smooth 4-manifold with a finite fundamental group and with a non-vanishing Seiberg-Witten invariant. Let G be a finite group. If G acts smoothly and freely on X, then the quotient X/G cannot be decomposed as X1#X2 with (Xi) > 0, i = 1, 2. In addition let X be symplectic and c1(X)2 > 0 and b+2(X) > 3. If σ is a free anti-symplectic involution on X then the Seiberg-Witten invariants on X/σ vanish for all spinc structures on X/σ, and if η is a free symplectic involution on X then the quotients X/σ and X/η are not diffeomorphic to each other.
Moore-Penrose inversion in complex contracted inverse semigroup algebras
Authors: Munn W. D.
Published: April 2009

It is shown that every element of the complex contracted semigroup algebra of an inverse semigroup S = S0 has a Moore-Penrose inverse, with respect to the natural involution, if and only if S is locally finite. In particular, every element of a complex group algebra has such an inverse if and only if the group is locally finite.
The Möbius boundedness of the space Qp
Authors: Pengyan Hu , Jihuai Shi , Wenjun Zhang
Published: April 2009

In this note, a characterization of the Möbius invariant space Qp for the range 1 - 1/n lt; p ≤ 1 is given. As a special case p = 1, we get the Möbius boundedness of BMOA in the space H2. This extends the corresponding result for 1-dimension.
On 4-dimensional generalized complex space forms
Authors: Kim Un Kyu
Published: April 2009

We characterize four-dimensional generalized complex forms and construct an Einstein and weakly *-Einstein Hermitian manifold with pointwise constant holomorphic sectional curvature which is not globally constant.
Developable surfaces in Euclidean space
Authors: Ushakov Vitaly
Published: April 2009

The classical notion of a two-dimensional develpable surface in Euclidean three-space is extended to the case of arbitrary dimension and codimension. A collection of characteristic properties is presented. The theorems are stated with the minimal possible integer smoothness. The main tool of the investigation is Cartan's moving frame method.
β-transformation, invariant measure and uniform distribution
Authors: Brown Gavin , Yin Qinghe
Published: April 2009

Let Tβ be the β-transformation on [0, 1). When β is an integer Tβ is ergodic with respect to Lebesgue measure and almost all orbits {} are uniformly distributed. Here we consider the non-integer case, determine when Tα, Tβ have the same invariant measure and when (appropriately normalised) orbits are uniformly distributed.
The module structure of Solomon's descent algebra
Authors: Blessenohl Dieter , Laue Hartmut
Published: April 2009

A close connection is uncovered between the lower central series of the free associative algebra of countable rank and the descending Loewy series of the direct sum of all Solomon descent algebras Δn, n ∈ ℕ0. Each irreducible Δn-module is shown to occur in at most one Loewy section of any principal indecomposable Δn-module.A precise condition for his occurence and formulae for the Cartan numbers are obtained.