bluuebunny/crossref_metadata_2025 huggingface dataset:
The Plancherel formula for the horocycle spaces and generalizations, II
Authors: Lipsman Ronald L.
Published: April 2009

The Plancherel formula for various semisimple homogeneous spaces with non-reductive stability group is derived within the framework of the Bonnet Plancherel formula for the direct integral decomposition of a quasi-regular representation. These formulas represent a continuation of the author's program to establish a new paradigm for concrete Plancherel analysis on homogeneous spaces wherein the distinction between finite and infinite multiplicity is de-emphasized. One interesting feature of the paper is the computation of the Bonnet nuclear operators corresponding to certain exponential representations (roughly those induced from infinite-dimensional representations of a subgroup). Another feature is a natural realization of the direct integral decomposition over a canonical set of concrete irreducible representations, rather than over the unitary dual.
Hardy's legacy to number theory
Authors: Vaughan R. C.
Published: April 2009

This is an expanded version of two lectures given at the conference held at Sydney University in December 1997 on the 50th anniversary of the death of G. H. Hardy.
The growth of certain amalgamated free products and HNN-extensions
Authors: Edjvet M. , Johnson D. L.
Published: April 2009

Here we mean growth in the sense of Milnor and Gromov. After a brief survey of known results, we compute the growth series of the groups, with respect to generators {x, y}. This is done using minimal normal forms obtained by informal use of judiciously chosen rewrite rules. In both of these examples the growth series is a rational function, and we suspect that this is not the case for the Baumslag-Solitar group

.
Quasi θ-spaces and pairwise θ-perfect irreducible mappings
Authors: Kandil A. , Kerre E. E. , El-Shafei M. E. , Nouh A. A.
Published: April 2009

In this paper we extend the notion of perfect, θ-continuous, irreducible and θ-perfect mappings to bitopological spaces. The main result is the following: the (small) image of an (i, j)-canonical open sets is an (i, j)-canonical open set under a pairwise θ-closed irreducible surjective mapping. Also we extend the notion of θ-proximity spaces to quasi θ-proximity spaces and point out the interrelation between it and separated quasi-proximity spaces by means of a pairwise θ-perfect irreducible mappings.
Bifurcation and stability of positive solutions of a two-point boundary value problem
Authors: Wang Shin-Hwa , Kazarinoff Nicholas D.
Published: April 2009

We consider the existence of multiple positive solutions of a nonlinear two-point boundary value problem by modifying a “time map” technique introduced by J. Smoller and A. Wasserman. We count the number of positive solutions and find their Conley indices and thus determine their stabilities.
Bifurcation of steady-state solutions of a scalar reaction-diffusion equation in one space variable
Authors: Wang Shin-Hwa , Kazarinoff Nicholas D.
Published: April 2009

We study the bifurcation of steady-state solutions of a scalar reaction-diffusion equation in one space variable by modifying a “time map” technique introduced by J. Smoller and A. Wasserman. We count the exact number of steady-state solutions which are totally ordered in an order interval. We are then able to find their Conley indices and thus determine their stabilities.
Isomorphisms of hypergroups
Authors: Bloom Walter R. , Walter Martin E.
Published: April 2009

Let K1, K2 be locally compact hypergroups. It is shown that every isometric isomorphism between their measure algebras restricts to an isometric isomorphism between their L1-algebras. This result is used to relate isometries of the measure algebras to homeomorphisms of the underlying locally compact spaces.
Euclidean linear invariance and uniform local convexity
Authors: Ma Wancang , Minda David
Published: April 2009

Let S(p) be the family of holomorphic functions f defined on the unit disk D, normalized by f(0) = f1(0) – 1 = 0 and univalent in every hyperbolic disk of radius p. Let C(p) be the subfamily consisting of those functions which are convex univalent in every hyperbolic disk of radius p. For p = ∞ these become the classical families S and C of normalized univalent and convex functions, respectively. These families are linearly invariant in the sense of Pommerenke; a natural problem is to calculate the order of these linearly invariant families. More precisely, we give a geometrie proof that C(p) is the universal linearly invariant family of all normalized locally schlicht functions of order at most coth(2p). This gives a purely geometric interpretation for the order of a linearly invariant family. In a related matter, we characterize those locally schlicht functions which map each hyperbolically k-convex subset of D onto a euclidean convex set. Finally, we give upper and lower bounds on the order of the linearly invariant family S(p) and prove that this class is not equal to the universal linearly invariant family of any order.
Classification of 4- and 5-arc-transitive cubic graphs of small girth: corrigendum
Authors: Morton Margaret J.
Published: April 2009

The purpose of this brief note is to point out an omission, at the top of page 145, in my paper [1]. Richard Weiss has kindly pointed out that there exist 5-arc-transitive graphs with no 4-arc regular group of automorphisms.
The associated order of a preorder
Authors: Miller John Boris
Published: April 2009

Any preorder P on a set X has an associated preorder P′, P″, P‴, … The proerties of this sequence are studied. When X is finite the sequence is eventually periodic with period P = 1 or p = 1, the eventual constant preorder is full p = 2 the possible forms which the eventual alternating order can take are examined: first, the possible combinations of components are enumerated; second, the notion of ramification at a caste is used to show that X may in a heuristic sense be of unbounded complexity. If X is orderdense the periodicity starts at P′.
Subdirect products of E–inversive semigroups
Authors: Mitsch H.
Published: April 2009

A semigroup S is called E-inversive if for every a ∈ S ther is an x ∈ S such that (ax)2 = ax. A construction of all E-inversive subdirect products of two E-inversive semigroups is given using the concept of subhomomorphism introduced by McAlister and Reilly for inverse semigroups. As an application, E-unitary covers for an E-inversive semigroup are found, in particular for those whose maximum group homomorphic image is a given group. For this purpose, the explicit form of the least group congruence on an arbitrary E-inversive semigroup is given. The special case of full subdirect products of a semilattice and a group (that is, containing all indempotents of the direct product) is investigated and, following an idea of Petrich, a construction of all these semigroups is provided. Finally, all periodic semigroups which are subdirect products of a semilattice or a band with a group are characterized.
A new approach to the distribution of the duration of the busy period for a G/G/l queueing system
Authors: Stadje Wolfgang
Published: April 2009

For a G/G/l queueing system let Xt be the number of customers present at time t and Yt(Zt) be the time elapsed since the last arrival of a customer (the last completion of a service) at time t. Let τl be the time until the number of customers in the sustem is reduced from j to j – l, given that X0 = j ≧ l, Y0 = y, Z0 = z. For the joint distribution of τl and Yτl and the Laplace transforms of the τl intergral equations are derived. Under slight conditions these integral equations have unique solutions which can be determined by standard methods. Our results offer a method for calculating the busy period distribution which is completely different from the usual fluctuatuion theoretic approach.
On the geometry of spheres in normed linear spaces
Authors: Gao Ji , Lau Ka-Sing
Published: April 2009

Some simplifications of Schäffer's girth and perimeter of the unit spheres are introduced. Their general properties are discussed, and they are used to study the lp, Lp spaces, uniformly nonsquare spaces, and their isomorphic classes.
Integral inequalities resembling Copson's inequality
Authors: Mohapatra R. N. , Vajavelu K.
Published: April 2009

The present paper deals with two inequalities which resemble Copson's integral inequalities. From our theorems, we obtain two interesting corollaries.
Minimal varieties and quasivarieties
Authors: Bergman Clifford , McKenzie Ralph
Published: April 2009

We prove that every locally finite, congruence modular, minimal variety is minimal as a quasivariety. We also construct all finite, strictly simple algebras generating a congruence distributive variety, such that the sett of unary term perations forms a group. Lastly, these results are applied to a problem in algebraic logic to give a sufficient condition for a deductive system to be structurally complete.
Collineation groups preserving an oval in a projective place of odd order
Authors: Biliotti Mauro , Korchmaros Gabor
Published: April 2009

In this paper we investigate the structure of a collineation group G of a finite projective plane Π of odd order, assuming that G leaves invariant an oval Ω of Π. We show that if G is nonabelian simple, then G ≅ PSL(2, q) for q odd. Several results about the structre and the action of G are also obtained under the assumptions that n ≡ 1 (4) and G is transitive on the points of Ω.
The AND/OR Theorem for Perceptrons
Authors: Bruce I. D. , Easdown D.
Published: April 2009

Minsky and Papert claim that, for any positive integer n, there exist predicates of order 1 whose conjunction and disjunction have order greater than n. Their proof is amended and a stronger result obtained of which their claim is a special case.
M-Cohyponormal powers of composition operators
Authors: Khurana Satish K. , Ram Babu
Published: April 2009

Let T1, i = 1, 2 be measurable transformations which define bounded composition operators C Ti on L2 of a σ-finite measure space. Let us denote the Radon-Nikodym derivative of with respect to m by hi, i = 1, 2. The main result of this paper is that if and are both M-hyponormal with h1 ≤ M2(h2 o T2) a.e. and h2 ≤ M2(h1 o T1) a.e., then for all positive integers m, n and p, []* is -hyponormal. As a consequence, we see that if is an M-hyponormal composition operator, then is -hyponormal for all positive integers n.
Self-complementary graph decompositions
Authors: Rodger C. A.
Published: April 2009

A complementary decomposition of λKn into a graph G is an edge-disjoint decomposition of λKn into copies of G such that if each copy H of G is replaced by its complement in V(H) then the result is an edge-disjoint decomposition of λKn into copies of GC it is a self- complementary decomposition if G = Gc. The spectrum for the last self-complementary graph on at most 7 vertices is found.
Uniform distribution and lattice point counting
Authors: Everest G. R.
Published: April 2009

A well-known theorem of Hardy and Littlewood gives a three-term asymptotic formula, counting the lattice points inside an expanding, right triangle. In this paper a generalisation of their theorem is presented. Also an analytic method is developed which enables one to interpret the coefficients in the formula. These methods are combined to give a generalisation of a “heightcounting” formula of Györy and Pethö which itself was a generalisation of a theorem of Lang.
An open mapping theorem on homogeneous spaces
Authors: Koshi Shozo , Takesaki Masamichi
Published: April 2009

We shall prove an open mapping theorem concerning a Polish group acting transitively on a complete metric space.
Metrical properties of best approximants
Authors: Blom Jos
Published: April 2009

A rational number is called a best approximant of the irrational number ζ if it lies closer to ζ than all rational numbers with a smaller denominator. Metrical properties of these best approximants are studied. The main tool is the two-dimensional ergodic system, underlying the continued fraction expansion.
Multiplication Operators and Dynamical Systems
Authors: Singh R. K. , Manhas Jasbir Singh
Published: April 2009

Let X be a completely regular Hausdorff space, let V be a system of weights on X and let T be a locally convex Hausdorff topological vector space. Then CVb(X, T) is a locally convex space of vector-valued continuous functions with a topology generated by seminorms which are weighted analogues of the supremum norm. In the present paper we characterize multiplication operators on the space CVb(X, T) induced by operator-valued mappings and then obtain a (linear) dynamical system on this weighted function space.
Nilpotent-by-Černikov CC-groups
Authors: Otal Javier , Peña Juan Manuel
Published: April 2009

In this paper we study groups with Černikov conjugacy classes which are nilpotent-by-Černikov groups, giving full characterizations of them and applying the results obtained to some related areas.
Certain inequalities involving fractional powers
Authors: Kemp A. W.
Published: April 2009

The note re-examines Brown's new inequalities involving polynomials and fractional powers. Shorter proofs are provided, and greater attention is given to the conditions for the inequalities to hold.
On unilateral shift operators and C0-operators
Authors: Jung Il Bong , Kim Yong Chan
Published: April 2009

Let S(n) be a unilateral shift operator on a Hilbert space of multiplicity n. In this paper, we prove a generalization of the theorem that if S(1) is unitarily equivalent to an operator matrix form relative to a decomposition ℳ ⊕ N, then E is in a certain class C0 which will be defined below.
Lp-functions satisfying the mean value property on homogeneous spaces
Authors: Sitaram A. , Willis G. A.
Published: April 2009

It is proved that on certain kinds of homogeneous spaces, the only Lp function, 1≤ p < ∞, satisfying the mean value property is the zero function.
Constructing graphs which are ½-transitive
Authors: Alspach Brian , Marušič Dragan , Nowitz Lewis
Published: April 2009

An infinite family of vertex-and edge-transitive, but not arc-transitive, graphs of degree 4 is constructed.
Möbius covariance of iterated Dirac operators
Authors: Peetre Jaak , Qian Tao
Published: April 2009

Using Fourier transforms, we give a new proof of certain identites for the fundamental solutions of the iterated Dirac operators and Ḏl = (Σ/Σx0 + Ḏ)l. Based on the close relationship between the fundamental solutions and the conformal weights we then give a simple proof of B. Bojarski's results on the conformal covariance of Ḏl. We also prove a new conformal covatiance result of D.
When is the composition of two power series even?
Authors: Horwitz Alan L. , Rubel Lee A.
Published: April 2009

If h is the composition of two formal power series f and g, and if h is even, what can be said about f and g? Some partial answers are given here.
On finite ρ-groups with isomorphic maximal subgroups
Authors: Hermann Peter Z.
Published: April 2009

Finite ρ-groups with all of their maximal subgroups isomorphic are studied by means of the coclass. All such groups of coclass I and 2 are determined, while those of coclass 3 are shown to have order at most ρ13. A general bound for the order is given as a function of ρ and the coclass only.
The persistence of logconcavity for positive solutions of the one dimensional heat equation
Authors: Keady G.
Published: April 2009

Consider positive solutions of the one dimensional heat equation. The space variablexlies in (–a, a): the time variabletin (0,∞). When the solutionusatisfies (i)u (±a, t)= 0, and (ii)u(·, 0) is logconcave, we give a new proof based on the Maximum Principle, that, for any fixedt > 0, u(·, t)remains logconcave. The same proof techniques are used to establish several new results related to this, including results concerning joint concavity in (x, t) similar to those considered in Kennington [15].
Imbedded subgroups of abelian groups
Authors: Berlinghoff W. P. , Moore J. D. , Reid J. D.
Published: April 2009

A subgroupHof an abelianp–groupGis pure inGif the inclusion map ofHintoGis an isometry with respect to the (pseudo-) metrics onHandGassociated with theirp–adic topologies. In this paper, those subgroups (called here imbedded subgroups) of abelian groups for which the inclusion is a homeomorphism with respect to thep–adic topologies are studied, the aim being to compare the concepts of imbeddedness and purity. Perhaps the main results indicate that imbedded subgroups are considerably more abundant than pure subgroups. Groups for which this is not the case are characterized.
On presentation of PSL (2, pn)
Authors: Campbell C. M. , Robertson E. F. , Williams P. D.
Published: April 2009

We give presentations for the groups PSL(2, pn), p prime, which show that the deficiency of these groups is bounded below. In particular, for p = 2 where SL(2, 2n) = PSL(2, 2n), we show that these groups have deficiency greater than or equal to – 2. We give deficiency – 1 presentations for direct products of SL(2, 2n) for coprime ni. Certain new efficient presentations are given for certain cases of the groups considered.
Fixed point theorems in H-spaces and equilibrium points of abstract economies
Authors: Tarafdar E.
Published: April 2009

Some fixed point theorems on H-spaces are presented. These theorems are then applied to generalize a theorem of Fan concerning sets with convex sections to H-spaces and to prove the existence of equilibrium points of abstract economics in which the commodity space is an H-space.
The strong c-Symmetric distribution
Authors: Ranga A. Sri
Published: April 2009

In this paper, we consider a class of strong symmetric distributions, which we refer to as the strong c-symmetric distributions. We provide, as the main result of this paper, conditions satisfied by the recurrence relations of certain polynomials associated with these distributions.
Some finiteness conditions in lattices—using nonstandard proof methods
Authors: Insall Matt
Published: April 2009

We discuss the application of nonstandard methods to local versions of certain lattice notions. In a particular case, we find that imposition of certain local conditions imply a surprising global one, namely boundedness of the given lattice.
Uncertainty principles like Hardy's theorem on some Lie groups
Authors: Bagchi S. C. , Ray Swagato K.
Published: April 2009

We extend an uncertainty principle due to Cowling and Price to Euclidean spaces, Heisenberg groups and the Euclidean motion group of the plane. This uncertainty principle is a generalisation of a classical result due to Hardy. We also show that on the real line this uncertainty principle is almost equivalent to Hardy's theorem.
Strong summability for the Marcinkiewicz means in the integral metric and related questions
Authors: Belinsky E. S.
Published: April 2009

The inequality of strong summability for the Marcinkiewicz means of multiply Fourier series is proved. The inequalities of strong summability with gaps for the different classes of integrable functions are established. The Bernstein inequality for the fractional derivative of analytic polynomials is proved.
Directed graphs and nilpotent rings
Authors: Kelarev A. V.
Published: April 2009

Suppose that a ring is a sum of its nilpotent subrings. We use directed graphs to give new conditions sufficient for the whole ring to be nilpotent.
An algebraic approach to Wigner's unitary-antiunitary theorem
Authors: Molnár Lajos
Published: April 2009

We present an operator algebraic approach to Wigner's unitary-antiunitary theorem using some classical results from ring theory. To show how effective this approach is, we prove a generalization of this celebrated theorem for Hilbert modules over matrix algebras. We also present a Wigner-type result for maps on primeC*-algebras.
Hilbert transform associated with finite maximal subdiagonal algebras
Authors: Randrianantoanina Narcisse
Published: April 2009

Let ℳ be a von Neumann algebra with a faithful normal trace τ, and let H∞ be a finite, maximal. subdiagonal algebra of ℳ. We prove that the Hilbert transform associated with H∞ is a linear continuous map from L1 (ℳ, τ) into L1.∞ (ℳ, τ). This provides a non-commutative version of a classical theorem of Kolmogorov on weak type boundedness of the Hilbert transform. We also show that if a positive measurable operator b is such that b log+b ∈ L1 (ℳ, τ) then its conjugate b, relative to H∞ belongs to L1 (ℳ, τ). These results generalize classical facts from function algebra theory to a non-commutative setting.
Sporadic group geometries and the action of involutions
Authors: Rowley Peter
Published: April 2009

This paper is an expository introduction to recent and current work on geometries associated with minimal parabolic subgroups and maximal 2-local subgroups of finite sporadic, based on lectures given by the authors at the Canberra Group Workshop, held at the Australian National University in June 1993.
Character degrees and nilpotence class in p-groups
Authors: Slattery Michael C.
Published: April 2009

Work of Isaacs and Passman shows that for some sets X of integers, p-groups whose set of irreducible character degrees is precisely X have bounded nilpotence class, while for other choices of X, the nilpotence class is unbounded. This paper presents a theoren which shows some additional sets of character degrees which bound nilpotence class within the family of metabelian p-groups. In particular, it is shown that is the non-linear irreducible character degrees of G lie between pa and pb, where a ≤ b ≤ 2a − 2, then the nilpotence class of G is bounded by a function of p and b − a.
The π-character theory of solvable groups
Authors: Isaacs I. M.
Published: April 2009

There is a deeper structure to the ordinary character theory of finite solvable groups than might at first be apparent. Mauch of this structure, which has no analog for general finite gruops, becomes visible onyl when the character of solvable groups are viewes from the persepective of a particular set π of prime numbers. This purely expository paper discusses the foundations of this πtheory and a few of its applications. Included are the definitions and essential properties of Gajendragadkar's π-special characters and their connections with the irreducible πpartial characters and their associated Fong characters. Included among the consequences of the theory discussed here are applications to questions about the field generated by the values of a character, about extensions of characters of subgroups and about M-groups.
Regular maps with small parameters
Authors: Conder Marston
Published: April 2009

Regular maps of type {p, q}r and the associated groups Gp,q,r are considered for small values for p, q and r. In particular, it is shown that the groups G4,6,6 and G5,5,6 are Abelian-by-infinite, and there are infinitely many regular maps of each of the types {4, 6}6, {5, 5}6, {5, 6}6 and {6, 6}6.
Vertex-primitive half-transitive graphs
Authors: Taylor D. E. , Xu Ming-Yao
Published: April 2009

Given an infinite family of finite primitive groups, conditions are found which ensure that almost all the orbitals are not self-paired. If p is a prime number congruent to ±1(mod 10), these conditions apply to the groups P S L (2, p) acting on the cosets of a subgroup isomorphic to A5. In this way, infinitely many vertex-primitive ½-transitive graphs which are not metacirculants are obtained.
Coverings and coverings
Authors: Alperin J. L. , Glauberman George
Published: April 2009

Coverings of certain simplical complexes constructed from subgroups of group G are related to covering groups of G.
Extending abelian groups to rings
Authors: Batten Lynn M. , Coulter Robert S. , Henderson Marie
Published: April 2009

For any abelian group G and any function f: G → G we define a commutative binary operation or ‘multiplication’ on G in terms of f. We give necessary and sufficient conditions on f for G to extend to a commutative ring with the new multiplication. In the case where G is an elementary abelian p–group of odd order, we classify those functions which extend G to a ring and show, under an equivalence relation we call weak isomorphism, that there are precisely six distinct classes of rings constructed using this method with additive group the elementary abelian p–group of odd order p2.
Monothetic algebraic groups
Authors: Falcone Giovanni , Plaumann Peter , Strambach Karl
Published: April 2009

We call an algebraic group monothetic if it possesses a dense cyclic subgroup. For an arbitrary field k we describe the structure of all, not necessarily affine, monothetic k-groups G and determine in which cases G has a k-rational generator.
A note on the boundedness of Bergman-type operators on mixed norm spaces
Authors: Lou Zengjian
Published: April 2009

We prove the boundedness of Bergman-type operators on mixed norm spaces Lp·q (φ) for 0 < q < 1 and 0 < p ≤ ∞ of functions on the unit ball of ” with an application to Gleason's problem.
Extinction and explosion of nonlinear Markov branching processes
Authors: Pakes Anthony G.
Published: April 2009

This paper concerns a generalization of the Markov branching process that preserves the random walk jump chain, but admits arbitrary positive jump rates. Necessary and sufficient conditions are found for regularity, including a generalization of the Harris-Dynkin integral condition when the jump rates are reciprocals of a Hausdorff moment sequence. Behaviour of the expected time to extinction is found, and some asymptotic properties of the explosion time are given for the case where extinction cannot occur. Existence of a unique invariant measure is shown, and conditions found for unique solution of the Forward equations. The ergodicity of a resurrected version is investigated.
The exact order of generalized diaphony and multidimensional numerical integration
Authors: Lev Vsevolod F.
Published: April 2009

For a point set in the multidimensional unit torus we introduce an Lk-measure of uniformity of distribution, which for k=2 reduces to diaphony (and thus in this case essentially coincides with Weyl L2-discrepancy). For k ∈ [1, 2] we establish a sharp asymptotic for this new measure as the number of points of the set tends to infinity. Upper and lower-bound estimates are given also for k >2.
On the value distribution of iterated entire functions
Authors: Jian-Hua Zheng
Published: April 2009

Let f be a transcendental entire function and denote the n-th iterate fn. For n ≥ 2, we give an explict estimate of the number of periodic points of f with period n, that is, fix-points of fn which are not fix-points of fk for 1 ≤ k <n.
Non-embeddings of the real flag manifolds RF (1, 1,n– 2)
Authors: Ajayi Deborah O. , Ilori Samuel A.
Published: April 2009

This paper gives non-embeddings and non-immersions for the real flag manifolds RF(1, 1,n–2), n > 3 and shows that Lam's immersions forn= 4 and 5 and Stong's result forn= 6 are the best possible.
The domain space of an analytic composition operator
Authors: Domenig Thomas , Jarchow Hans , Riedl Reinhard
Published: April 2009

In this paper we show that, for analytic composition operators between weighted Bergman spaces (including Hardy spaces) and as far as boundedness, compactness, order boundedness and certain summing properties of the adjoint are concerned, it is possible to modify domain spaces in a systematic fashion: there is a space of analytic functions which embeds continuously into each of the spaces under consideration and on which the above properties of the operator are decided.

A remarkable consequence is that, in the setting of composition operators between weighted Bergman spaces, the properties in question can be identified as properties of the operator as a map between appropriately chosen Hilbert spaces.
Radon transform on affine buildings of rank three
Authors: Atanasi Laura
Published: April 2009

We define the Radon transform for functions on the set of chambers of affine, locally finite, rank three buildings. We investigate the problem of the inversion of this transform. Explicit inversion formulas are exhibited for functions which fulfill required summability conditions.
Direct and converse inequalities for positive linear operators on the positive semi-axis
Authors: Adell José A. , Sangüesa Carmen
Published: April 2009

We consider positive linear operators of probabilistic typeL1facting on real functionsfdefined on the positive semi-axis. We deal with the problem of uniform convergence ofL1ftof, both in the usual sup-norm and in a uniformLptype of norm. In both cases, we obtain direct and converse inequalities in terms of a suitable weighted first modulus of smoothness off. These results are applied to the Baskakov operator and to a gamma operator connected with real Laplace transforms, Poisson mixtures and Weyl fractional derivatives of Laplace transforms.
Partial characters with respect to a normal subgroup
Authors: Navarro Gabriel , Sanus Lucia
Published: April 2009

Suppose that G is a π-separable group. Let N be a normal π1-subgroup of G and let H be a Hall π-subgroup of G. In this paper, we prove that there is a canonical basis of the complex space of the class functions of G which vanish of G-conjugates ofHN. When N = 1 and π is the complement of a prime p, these bases are the projective indecomposable characters and set of irreduciblt Brauer charcters of G.
An extension of the principle of spatial averaging for inertial manifolds
Authors: Kwean Hyukjin
Published: April 2009

In this paper we extend a theorem of Mallet-Paret and Sell for the existence of an inertial manifold for a scalar-valued reaction diffusion equation to new physical domains ωn ⊂ Rn, n = 2,3. For their result the Principle of Spatial Averaging (PSA), which certain domains may possess, plays a key role for the existence of an inertial manifold. Instead of the PSA, we define a weaker PSA and prove that the domains φn with appropriate boundary conditions for the Laplace operator, δ, satisfy a weaker PSA. This weaker PSA is enough to ensure the existence of an inertial manifold for a specific class of scalar-valued reaction diffusion equations on each domain ωn under suitable conditions.
On two pairs of non-self hybrid mappings
Authors: Ćirić Ljubomir B. , Sheok Ume Jeong , Nikolić Nebqjša T.
Published: April 2009

Abstrac In this paper we obtain some results on coincidence and common fixed points for two pairs of multi-valued and single-valued non-self mappings in complete convex metric spaces. We improve on previously used methods of proof and obtain results for mappings which are not necessarily compatible and not necessarily continuous, generalizing some known results. In particular, a theorem by Rhoades [19] and a theorem by Ahmed and Rhoades [2] are generalized and improved.
Rate of escape of random walks on free products
Authors: Gilch Lorenz A.
Published: April 2009

Suppose we are given the free product V of a finite family of finite or countable sets (Vi)i∈∮and probability measures on each Vi, which govern random walks on it. We consider a transient random walk on the free product arising naturally from the random walks on the Vi. We prove the existence of the rate of escape with respect to the block length, that is, the speed at which the random walk escapes to infinity, and furthermore we compute formulae for it. For this purpose, we present three different techniques providing three different, equivalent formulae.
An Open Mapping Theorem For Pro-Lie Groups
Authors: Hofmann Karl H. , Morris Sidney A.
Published: April 2009

A pro-Lie group is a projective limit of finite dimensional Lie groups. It is proved that a surjective continuous group homomorphism between connected pro-Lie groups is open. In fact this remains true for almost connected pro-Lie groups where a topological group is called almost connected if the factor group modulo the identity component is compact. As consequences we get a Closed Graph Theorem and the validity of the Second Isomorphism Theorem for pro-Lie groups in the almost connected context.
Canonical Varieties of Completely Regular Semigroups
Authors: Petrich Mario
Published: April 2009

Completely regular semigroups CR are regarded here as algebras with multiplication and the unary operation of inversion. Their lattice of varieties is denoted by L(CR). Let B denote the variety of bands and L(B) the lattice of its subvarieties. The mapping V → V ∩ B is a complete homomorphism of L(CR) onto L(B). The congruence induced by it has classes that are intervals, say VB = [VB, VB] for V ∈ L(CR). Here VB = V ∩ B. We characterize VB in several ways, the principal one being an inductive way of constructing bases for v-irreducible band varieties. We term the latter canonical. We perform a similar analysis for the intersection of these varieties with the varieties BG, OBG and B.
Unique factorization in the ring R[x]
Authors: Beauregard Raymond A.
Published: April 2009

If R is a commutative unique factorization domain (UFD) then so is the ring R[x]. If R is not commutative then no such result is possible. An example is given of a bounded principal right and left ideal domain R, hence a similarity-UFD, for which the polynomial ring R[x] in a central indeterminate x is not a UFD in any reasonable sense. On the other hand, it is shown that if R is an invariant UFD then R[x] is a UFD in an appropriate sense.
Conjugacy classes of subgroups in p-groups
Authors: Brandl Rolf
Published: April 2009

The set C(G) of conjugacy classes of subgroups of a group G has a natural partial order. We study p-groups G for which C(G) has antichains of prescribed lengths.
Some fixed point theorems
Authors: Subrahmanyam P. V. , Reilly I. L.
Published: April 2009

Banach's contraction principle guarantees the existence of a unique fixed point for any contractive selfmapping of a complete metric space. This paper considers generalizations of the completeness of the space and of the contractiveness of the mapping and shows that some recent extensions of Banach's theorem carry over to spaces whose topologies are generated by families of quasi-pseudometrics.
Fixed points of asymptotically regular multivalued mappings
Authors: Beg Ismat , Azam Akbar
Published: April 2009

Some results on fixed point of asymptotically regular multivalued mapping are obtained in metric spaces. The structure of common fixed points and coincidence points of a pair of compatible multivalued mappings is also discussed. Our work generalizes known results of Aubin and Siegel, Dube, Dube and Singh, Hardy and Rogers, Hu, Iseki, Jungck, Kaneko, Nadler, Ray and Shiau, Tan and Wong.
A computer-aided analysis of some finitely presented groups
Authors: Newman M. F. , O'Brien E. A.
Published: April 2009

We answer some questions which arise from a recent paper of Campbell, Heggie, Robertson and Thomas on one-relator free products of two cyclic groups. In the process we show how publicly accessible computer programs can be used to help answer questions about finite group presentations.
Hypersurfaces of En+1 Satisfying Δx = Ax + B
Authors: Hasanis Th. , Vlachos Th.
Published: April 2009

We consider hypersurfaces of En+1 whose position vector x satisfies Δx = Ax + B, where Δ is the induced Laplacian, and prove that these are open parts of minimal hypersurfaces, hyperspheres or generalized circular cylinders.
On zero-sum turan problems of Bialostocki and Dierker
Authors: Caro Y. , Roditty Y.
Published: April 2009

Assume G is a graph with m edges. By T(n, G) we denote the classical Turan number, namely, the maximum possible number of edges in a graph H on n vertices without a copy of G. Similarly if G is a family of graphs then H does not have a copy of any member of the family. A Zk-colouring of a graph G is a colouring of the edges of G by Zk, the additive group of integers modulo k, avoiding a copy of a given graph H, for which the sum of the values on its edges is 0 (mod k). By the Zero-Sum Turan number, denoted T(n, G, Zk), k¦m, we mean the maximum number of edges in a Zk-colouring of a graph on n vertices that contains no zero-sum (mod k) copy of G. Here we mainly solve two problems of Bialostocki and Dierker [6].

Problem 1. Determine T(n, tK2, Zk) for ¦|t. In particular, is it true that T(n, tK2, Zk) = T(n, (t+k-1)K2)?

Problem 2. Does there exist a constant c(t, k) such that T(n, Ft, Zk) ≦ c(t, k)n, where Ft is the family of cycles of length at least t?
The residual finiteness of HNN-extensions and generalized free products of nilpotent groups: a characterization
Authors: Raptis E. , Varsos D.
Published: April 2009

We study the residual finiteness of free products with amalgamations and HNN-extensions of finitely generated nilpotent groups. We give a characterization in terms of certain conditions satisfied by the associated subgroups. In particular the residual finiteness of these groups implies the possibility of extending the isomorphism of the associated subgroups to an isomorphism of their isolated closures in suitable overgroups of the factors (or the base group in case of HNN-extensions).
On the geometry of multisymplectic manifolds
Authors: Cantrijn F. , Ibort A. , De León M.
Published: April 2009

A multisymplectic structure on a manifold is defined by a closed differential form with zero characteristic distribution. Starting from the linear case, some of the basic properties of multisymplectic structures are described. Various examples of multisymplectic manifolds are considered, and special attention is paid to the canonical multisymplectic structure living on a bundle of exterior k-forms on a manifold. For a class of multisymplectic manifolds admitting a ‘Lagrangian’ fibration, a general structure theorem is given which, in particular, leads to a classification of these manifolds in terms of a prescribed family of cohomology classes.
On the Stone-Čech bicompactification of a bispace
Authors: Garcia-Ferreira S. , Romaguera S. , Sanchis M.
Published: April 2009

In this paper we study the Stone-Čech bicompactification () of the bispace (X, P, Q). We show that the ring of all continuous real-valued functions on () may be identified with the uniform closure of a suitable subring ofC(). Using this result, we give a characterization of the Wallman-Sanin compactifications of the pairwise Tychonoff bitopological spaces.
Fractal n-hedral tilings of ℝd
Authors: Xu You
Published: April 2009

An n-hedral tiling of ℝd is a tiling with each tile congruent to one of the n distinct sets. In this paper, we use the iterated function systems (IFS) to generate n-hedral tilings of ℝd. Each tile in the tiling is similar to the attractor of the IFS. These tiles are fractals and their boundaries have the Hausdorff dimension less than d. Our results generalize a result of Bandt.
Landau-Lifshitz equation of ferromagnetism with external magnetic field
Authors: Pang P. Y. H. , Xiao J. , Zhou F.
Published: April 2009

In this article, we prove the existence and uniqueness of solution for the Cauchy problem of the Landau-Lifshitz equation of ferromagnetism with external magnetic field. We also show that the solution is globally regular with the exception of at most finitely many blow-up points. An energy identity at blow-up points is presented.
Pseudo MV-algebras are intervals in ℓ-groups
Authors: Dvurečenskij Anatolij
Published: April 2009

We show that any pseudo MV-algebra is isomorphic with an interval Γ(G, u), where G is an ℓ-group not necessarily Abelian with a strong unit u. In addition, we prove that the category of unital ℓ-groups is categorically equivalent with the category of pseudo MV-algebras. Since pseudo MV-algebras are a non-commutative generalization of MV-algebras, our assertions generalize a famous result of Mundici for a representation of MV-algebras by Abelian unital ℓ-groups. Our methods are completely different from those of Mundici. In addition, we show that any Archimedean pseudo MV-algebra is an MV-algebra.
Transcendental meromorphic solutions of some algebraic differential equations
Authors: Ishizaki Katsuya , Toda Nobushige
Published: April 2009

In this paper we treat transcendental meromorphic solutions of some algebraic differential equations. We consider the number of distinct transcendental meromorphic solutions. Algebraic relations between meromorphic solutions and comparisons of the growth of transcendental meromorphic solutions are also discussed.
Baer and quasi-Baer properties of group rings
Authors: Yi Zhong , Zhou Yiqiang
Published: April 2009

A ring R is said to be a Baer (respectively, quasi-Baer) ring if the left annihilator of any nonempty subset (respectively, any ideal) of R is generated by an idempotent. It is first proved that for a ring R and a group G, if a group ring RG is (quasi-) Baer then so is R; if in addition G is finite then |G|–1 € R. Counter examples are then given to answer Hirano's question which asks whether the group ring RG is (quasi-) Baer if R is (quasi-) Baer and G is a finite group with |G|–1 € R. Further, efforts have been made towards answering the question of when the group ring RG of a finite group G is (quasi-) Baer, and various (quasi-) Baer group rings are identified. For the case where G is a group acting on R as automorphisms, some sufficient conditions are given for the fixed ring RG to be Baer.
On five well-known commutator identities
Authors: Ellis Graham J.
Published: April 2009

We conjecture that five well-known identities universally satisfied by commutators in a group generate all such universal commutator identies. We use homological techniques to partially prove the conjecture.
On Cm-bounding sets
Authors: Biström Peter , Bjon Sten , Lindström Mikael
Published: April 2009

Let E be a quasi-complete locally convex space and A a subset of E. It is shown that if every real-valued C∞-function in the weak topology of E is bounded on A, then A is relatively weakly compact. Furthermore, if all real-valued C∞-functions on E are bounded on A, then A is relatively compact in the associated semi-weak topology of E.
On certain pairs of automorphisms of rings
Authors: Brešar Matej
Published: April 2009

In this paper we prove algebraic generalizations of some results of C. J. K. Batty and A. B. Thaheem, concerned with the identity α + α−1 = β + β−1 where α and β are automorphisms of a C*-algebra. The main result asserts that if automorphisms α, β of a semiprime ring R satisfy α + α-1 = β + β−1 then there exist invariant ideals U1, U2 and U3 of R such that Ui ∩ Uj = 0, i ≠ j, U1 ⊕ U2 ⊕ U3 is an essential ideal, α = β on U1, α = β−1 on U2, and α2 = β2 = α−2 on U3. Furthermore, if the annihilator of any ideal in R is a direct summand (in particular, if R is a von Neumann algebra), then U1 ⊕ U2 ⊕ U3 = R.
Biduals of weighted banach spaces of analytic functions
Authors: Bierstedt K. D. , Summers W. H.
Published: April 2009

For a positive continuous weight function ν on an open subset G of CN, let Hv(G) and Hv0(G) denote the Banach spaces (under the weighted supremum norm) of all holomorphic functions f on G such that ν f is bounded and ν f vanishes at infinity, respectively. We address the biduality problem as to when Hν(G) is naturally isometrically isomorphic to Hν0(G)**, and show in particular that this is the case whenever the closed unit ball in Hν0(G) in compact-open dense in the closed unit ball of Hν(G).
Commutative absolute subretracts
Authors: Jespers E. , Parmenter M. M.
Published: April 2009

Directly indecomposable absolute subretracts that are commutative Noetherian rings are described. This is an application of our main result characterizing unital directly indecomposable absolute subretracts which contain a maximal ideal with nonzero annihilator.
On certain subrings of prime rings with derivations
Authors: Brešar M. , Vukman J.
Published: April 2009

Let D be a nonzero derivation of a noncommutative prime ring R, and let U be the subring of R generated by all [D(x), x], x ∞ R. A classical theorem of Posner asserts that U is not contained in the center of R. Under the additional assumption that the characteristic of R is not 2, we prove a more general result stating that U contains a nonzero left ideal of R as well as a nonzero right ideal of R.
Regulating hulls of almost completely decomposable groups
Authors: Mader A. , Vinsonhaler C.
Published: April 2009

This note investigates torsion-free abelian groups G of finite rank which embed, as subgroups of finite index, in a finite direct sum C of subgroups of the additive group of rational numbers. Specifically, we examine the relationship between G and C when the index of G in C is minimal. Some properties of Warfield duality are developed and used (in the case that G is locally free) to relate our results to earlier ones by Burkhardt and Lady.
Twistor diagrams and the algebraic de Rham theorem
Authors: Jozsa Richard , Rice John
Published: April 2009

A method for computing the number of contours for a twistor diagram, using Grothendieck's algebraic de Rham theorem, is described and some examples are given.
Congruences on free monoids and submonoids of polycyclic monoids
Authors: Meakin John , Sapir Mark
Published: April 2009

We establish a one-to-one “group-like” correspondence between congruences on a free monoid X* and so-called positively self-conjugate inverse submonoids of the polycyclic monoid P(X). This enables us to translate many concepts in semigroup theory into the language of inverse semigroups.
Finite Generation of the Extension Algebra Ext(M, M)
Authors: Schulz Rainer
Published: April 2009

For a module M Over an Artin algebra R, we discuss the question of whether the Yoneda extension algebra Ext(M, M) is finitely generated as an algebra. We give an answer for bounded modules M. (These are modules whose syzygies have direct summands of bounded lengths.)
The number of exceptional approximations in Roth's theorem
Authors: Schmidt Wolfgang M.
Published: April 2009

Roth's Theorem says that given ρ < 2 and an algebraic number α, all but finitely many rational numbers x/y satisfy |α - (x/y)|< |y|-ρ. We give upper bounds for the number of these exceptional rationals when 3 ≤ ρ ≤ d, where d is the degree of α. Our result suplements bounds given by Bombieri and Van der Poorten when 2 > ρ ≤ 3; naturally the bounds become smaller as ρ increases.
Groups with all subgroups normal-by-finite
Authors: Buckley J. T. , Lennox John C. , Neumann B. H. , Smith Howard , Wiegold James
Published: April 2009

A groupGhas all of its subgroups normal-by-finite ifH/ coreG(H) is finite for all subgroupsHofG. These groups can be quite complicated in general, as is seen from the so-called Tarski groups. However, the locally finite groups of this type are shown to be abelian-by-finite; and they are then boundedly core-finite, that is to say, there is a bound depending onGonly for the indices |H: coreG(H)|.
On the logarithmic coefficients of close-to-convex functions
Authors: Elhosh M. M.
Published: April 2009

Logarithmic coefficient bounds for some univalent functions are given in this paper.
Growth of linear semigroups
Authors: Okniński Jan
Published: April 2009

We show that the growth function of a finitely generated linear semigroup S ⊆ Mn(K) is controlled by its behaviour on finitely many cancellative subsemigroups of S. If the growth of S is polynomially bounded, then every cancellative subsemigroup T of S has a group of fractions G ⊆ Mn (K) which is nilpotent-by-finite and of finite rank. We prove that the latter condition, strengthened by the hypothesis that every such G has a finite unipotent radical, is sufficient for S to have a polynomial growth. Moreover, the degree of growth of S is then bounded by a polynomial f(n, r) in n and the maximal degree r of growth of finitely generated cancellative T ⊆ S.
Hall's ray in inhomogeneous diophantine approximation
Authors: Cusick T. W. , Moran W. , Pollington A. D.
Published: April 2009

The aim of the paper is to show the existence of a ‘Hall's ray’ for the particular case of the one-sided inhomogeneous diophantine approximation problem, where the irrational is the golden ratio. The proof uses a sum-set method similar to that used by Marshall Hall for the original result of this kind.