bluuebunny/crossref_metadata_2025 huggingface dataset:
Toral automorphisms and antiautomorphisms of rotation algebras
Authors: Yaohua Hu , Stacey P.J.
Published: April 2009

If U, V are the generators of a rational or irrational rotation C*-algebra then an automorphism φ of the algebra is determined by φ(U) = λUaVc and φ(V) = μUbVd where λ, μ are complex numbers of modulus 1 and a, b, c, d are integers with ad − bc = 1. If ad − bc = −1, then these formulae determine an antiautomorphsm of the algebra. The classification of such automorphisms and antiautomorphisms up to conjugacy by arbitrary automorphisms is studied and an almost complete classification is obtained.
Local rigidity and group cohomology I: Stowe's theorem for Banach manifolds
Authors: Brunsden Victor
Published: April 2009

Stowe's Theorem on the stability of the fixed points of a C2 action of a finitely generated group Γ is generalised to C1 actions of such groups on Banach manifolds. The result is then used to prove that if φ is a Cr action on a smooth, closed, manifold M satisfying H1(Γ, Dr−1(M)) = 0, then φ is locally rigid. Here, r ≥ 2 and Dk(M) is the space of Ck tangent vector fields on M. This generalises a local rigidity result of Weil for representations of a finitely generated group Γ in a Lie group.
On the soluble length of groups with prime-power order
Authors: Evans-Riley Susan , Newman M.F. , Schneider Csaba
Published: April 2009

We show that for every integer k ≥ 3 and every prime p ≤ 5 there is a group with soluble length k and order .
The fixed point property for some uniformly nonoctahedral Banach spaces
Authors: Jiménez-Melado A.
Published: April 2009

Roughly speaking, we show that a Banach space X has the fixed point property for nonexpansive mappings whenever X has the WORTH property and the unit sphere of X does not contain a triangle with sides of length larger than 2.
Polytopes of roots of type AN
Authors: Cho Soojin
Published: April 2009

Polytopes of roots of type An−1 are investigated, which we call Pn. The polytopes, , of positive roots and the origin have been considered in relation to other branches of mathematics [4]. We show that exactly n copies of forms a disjoint cover of Pn. Moreover, those n copies of can be obtained by letting the elements of a subgroup of the symmetric group Sn generated by an n-cycle act on . We also characterise the faces of Pn and some facets of , which we believe to be useful in some optimisation problems. As by-products, we obtain an interesting identity on the number of lattice paths and a triangulation of the product of two simplices.
Images of Hankel operators on the polydisk
Authors: Choe Boo Rim , Lee Young Joo
Published: April 2009

We study images of Hankel operators on the Bergman or Hardy space of the poly-disk. We give characterisations of pairs of antiholomorphic symbols inducing Hankel operators whose images are mutually orthogonal.
On copies of the null sequence Banach space in some vector measure spaces
Authors: Ferrando J.C. , Amigó J.M.
Published: April 2009

In this note we extend a result of Drewnowski concerning copies of C0 in the Banach space of all countably additive vector measures and study some properties of complemented copies of C0 in several Banach spaces of vector measures.
Quasiprimitivity and quasigroups
Authors: Phillips J.D. , Smith J.D.H.
Published: April 2009

It is well known that Q is a simple quasigroup if and only if Mlt Q acts primitively on Q. Here we show that Q is a simple quasigroup if and only if Mlt Q acts quasiprimitively on Q, and that Q is a simple right quasigroup if and only if RMlt Q acts quasiprimitively on Q.
Remarks on James's distortion theorems II
Authors: Dowling Patrick N. , Randrianantoanina Narcisse , Turett Barry
Published: April 2009

If a Banach space X contains a complemented subspace isomorphic to ℓ1 and if ε > 0, then there exists a subspace Y of X and a projection P from X onto Y such that Y is (1 + ε)-isometric to ℓ1 and ∥P∥ ≤ 1 + ε. A stronger result for c0 is proved for Banach spaces whose dual unit ball is weak sequentially compact.
Global existence of solutions to degenerate wave equations with dissipative terms
Authors: Aassila Mohammed
Published: April 2009

In this paper we prove the global existence and study the asymptotic behaviour of solutions to a degenerate wave equation with a nonlinear dissipative term.
Monochromatic arithmetic progressions with large differences
Authors: Brown Tom C. , Landman Bruce M.
Published: April 2009

A generalisation of the van der Waerden numbers w(k, r) is considered. For a function f: Z+ → R+ define w(f, k, r) to be the least positive integer (if it exists) such that for every r-coloring of [1, w(f, k, r)] there is a monochromatic arithmetic progression {a + id: 0 ≤ i ≤ k −1} such that d ≥ f(a). Upper and lower bounds are given for w(f, 3, 2). For k > 3 or r > 2, particular functions f are given such that w(f, k, r) does not exist. More results are obtained for the case in which f is a constant function.
Nonlinear multipoint boundary value problems for weakly coupled systems
Authors: Thompson H.B. , Tisdell C.C.
Published: April 2009

We establish existence results concerning solutions to multipoint boundary value problems for weakly coupled systems of second order ordinary differential equations with fully nonlinear boundary conditions.
Order preserving functions on ordered topological vector spaces
Authors: Candeal J.C. , Induráin E. , Mehta G.B.
Published: April 2009

In this paper we prove the existence of continuous order preserving functions on ordered topological vector spaces in an infinite-dimensional setting. In a certain class of topological vector spaces we prove the existence of topologies for which every continuous total preorder has a continuous order preserving representation and show that the Mackey topology is the finest topology with this property. We also prove similar representation theorems for reflexive Banach spaces and for Banach spaces that may not have a pre-dual.
On zero-dimensionality and fragmented rings
Authors: Coykendall Jim , Dobbs David E. , Mullins Bernadette
Published: April 2009

A commutative ring R is said to be fragmented if each nonunit of R is divisible by all positive integral powers of some corresponding nonunit of R. It is shown that each fragmented ring which contains a nonunit non-zero-divisor has (Krull) dimension ∞. We consider the interplay between fragmented rings and both the atomic and the antimatter rings. After developing some results concerning idempotents and nilpotents in fragmented rings, along with some relevant examples, we use the “fragmented” and “locally fragmented” concepts to obtain new characterisations of zero-dimensional rings, von Neumann regular rings, finite products of fields, and fields.
On the norm of symmetrised two-sided multiplications
Authors: Magajna Bojan , Turnšek Aleksej
Published: April 2009

The authors provide precise lower bounds for the completely bounded norm of the operatorTa,b: ß(H) → ß(H) defined byTa,b(x) =axb+bxaand the injective norm of the corresponding tensor. Further, they compute the norm of the operatorx↦a*xb+b*xaacting on the space of all conjugate-linear operators onH.
Coboundary equations of eventually expanding transformations
Authors: Ahn Young-Ho
Published: April 2009

Let T be an eventually expansive transformation on the unit interval satisfying the Markov condition. The T is an ergodic transformation on (X, ß, μ) where X = [0, 1), ß is the Borel σ-algebra on the unit interval and μ is the T invariant absolutely continuous measure. Let G be a finite subgroup of the circle group or the whole circle group and φ: X → G be a measurable function with finite discontinuity points. We investigate ergodicity of skew product transformations Tφ on X × G by showing the solvability of the coboundary equation φ(x) g (Tx) = λg (x), |λ| = 1. Its relation with the uniform distribution mod M is also shown.
On D-KKM theorem and its applications
Authors: Pathak H. K. , Khan M. S.
Published: April 2009

In this paper, we introduce a new class of set-valued mappings in a non-convex setting called D-KKM mappings and prove a general D-KKM theorem. This extends and improves the KKM theorem for several families of set-valued mappings, such as (X, Y), C(X, Y), C (X, Y), C (X, Y) and C (X, Y). In the sequel, we apply our theorem to get some existence results for maximal elements, generalised variational inequalities, and price equilibria.
Dominated extensions of functionals andV-convex functions of cancellative cones
Authors: Romaguera S. , Pérez E. A. Sánchez , Valero O.
Published: April 2009

LetCbe a cancellative cone and consider a subconeC0ofC. We study the natural problem of obtaining conditions on a non negative homogeneous function φ:C→R+so that for each linear functionalfdefined inC0which is bounded by φ, there exists a linear extension toC. In order to do this we assume several geometric conditions for cones related to the existence of special algebraic basis of the linear span of these cones.
Submanifolds satisfying some curvature conditions imposed on the Weyl tensor
Authors: Özgür Cihan
Published: April 2009

In this paper we define Weyl semiparallel ( ·h= 0) and Weyl 2-semiparallel ( ·∇̅h= 0) submanifolds. We considern-dimensional normally flat submanifolds satisfying these curvature conditions in (n+d)-dimensional Euclidean space n+d. We also consider normally flat submanifolds in (n+d)-dimensional Euclidean space n+dsatisfying the condition  ·h=LQ(g,h) and  ·∇̅h=LQ(g,∇̅h).
Certain locally nilpotent varieties of groups
Authors: Abdollahi Alireza
Published: April 2009

Let c ≥ 0, d ≥ 2 be integers and be the variety of groups in which every d-generator subgroup is nilpotent of class at most c. N.D. Gupta asked for what values of c and d is it true that is locally nilpotent? We prove that if c ≤ 2d + 2d−1 − 3 then the variety is locally nilpotent and we reduce the question of Gupta about the periodic groups in to the prime power exponent groups in this variety.
Optimality and duality without a constraint qualification for minimax programming
Authors: Zhou Houchun , Sun Wenyu
Published: April 2009

Without the need of a constraint qualification, we establish the optimality necessary and sufficient conditions for generalised minimax programming. Using these optimality conditions, we construct a parametric dual model and a parameter-free mixed dual model. Several duality theorems are established.
Relative approximations and Maschke functors
Authors: Zhu Bin
Published: April 2009

The notion of approximations relative to a functor is introduced and several characterisations of relative (dual) Maschke functors are given by using them. As an application, the injective objects in the category of comodules over a coring are described.
Improvement on the bounds of permutation groups with bounded movement
Authors: Alaeiyan Mehdi
Published: April 2009

Let G be a permutation group on a set Ω with no fixed points in Ω and let m be a positive integer. Then we define the movement of G as, m := move(G) := supΓ{|Γg \ Γ| │ g ∈ G}. Let p be a prime, p ≥ 5. If G is not a 2-group and p is the least odd prime dividing |G|, then we show that n := |Ω| ≤ 4m – p + 3.

Moreover, if we suppose that the permutation group induced by G on each orbit is not a 2-group then we improve the last bound of n and for an infinite family of groups the bound is attained.
Autoconjugate functions and representations of monotone operators
Authors: Penot Jean-Paul
Published: April 2009

We show the existence of a convex representation of a maximal monotone operator by a convex function which is invariant with respect to the Fenchel conjugacy (up to an interchange of variables). We use the framework of generalized convexity.
Local analysis of frame multiresolution analysis with a general dilation matrix
Authors: Kim Hong Oh , Kim Rae Young , Lim Jae Kun
Published: April 2009

A multivariate semi-orthogonal frame multiresolution analysis with a general integer dilation matrix and multiple scaling functions is considered. We first derive the formulas of the lengths of the inital (central) shift-invariant space V0 and the next dilation space V1, and, using these formulas, we then address the problem of the number of the elements of a wavelet set, that is, the length of the shift-invariant space W0 := V1 ⊖ V0. Finally, we show that there does not exist a ‘genuine’ frame multiresolution analysis for which V0 and V1 are quasi-stable spaces satisfying the usual length condition.
Harmonic characteristic vector fields on contact metric three-manifolds
Authors: Perrone Domenico
Published: April 2009

In this paper we show that a contact metric three-manifold is a generalised (k, μ)-space on an everywhere dense open subset if and only if its characteristic vector field ξ determines a harmonic map from the manifold into its unit tangent sphere bundle equipped with the Sasaki metric. Moreover, we classify the contact metric three-manifolds whose characteristic vector field ξ is strongly normal (or equivalently, is harmonic and minimal).
On linear almost periodic systems with bounded solutions
Authors: Tkachenko V. I.
Published: April 2009

It is proved that in every neighbourhood of a system of linear differential equations with almost periodic skew-adjoint matrix with frequency module ℱ there exists a system with frequency module contained in the rational hull of ℱ possessing all almost periodic solutions.
Two theorems on generalised metric spaces
Authors: Svetlichny Sergey
Published: April 2009

We prove that any compact space, and even any countably compact space having the weak topology with respect to a sequence of symmetrisable subspaces, is metrisable. This generalises results of Arhangel'skii and Nedev on metrisability of symmetrisable compact spaces. Also we define and study contraction functions on generalised metric spaces whose topology can be described in terms of a ‘distance function’ which is not quite a metric. In particular we present necessary and sufficient conditions for a space of countable pseudo-character to be submetrisable in terms of real-valued contraction functions on this space.
Complete endomorphisms of the lattice of pseudovarieties of finite semigroups
Authors: Reilly Norman R. , Zhang Shuhua
Published: April 2009

The main result established that the mapping V → V ∩ W (V ∈ ℒ(F)) is a complete endomorphism of the lattice ℒ(F) of pseudovarieties of finite semigroups for certain particular pseudovarieties W, including the pseudovariety of bands.
Instability of the Dirichlet problem for Hamilton-Jacobi equation
Authors: Zhang Kewei
Published: April 2009

We show the instability of solutions of the Dirichlet problem for Hamilton-Jacobi equations under quite general conditions.
The Weyl functional calculus and two-by-two selfadjoint matrices
Authors: Ricker Werner J.
Published: April 2009

Let D be a (2 × 2) matrix with distinct eigenvalues λ1 and λ2. There is a basic and well known functional equation which provides a formula for constructing the matrix g (D), for any ℂ-valued function g defined on a subset of ℂ containing {λ1,λ2}, namely .

This equation is used to give a direct and transparent proof of the following fact due to Anderson: A pair of (2 × 2) selfadjoint matrices A1 and A2 commute if and only if the Weyl functional calculus of the pair (A1,A2), which is a matrix-valued distribution, has order zero (that is, is a measure).
Uncolouring of Lie colour algebras
Authors: McAnally D. S. , Brakcen A. J.
Published: April 2009

The link between a Lie colour algebra and a corresponding Lie superalgebra is clarified in the case of the general linear algebras. The Lie superalgebra inherits from the colour cocommutative coproduct of the corresponding Lie colour algebra, a super coproduct which differs from the usual one, and is not supercocommutative. It is associated with a new R-matrix satisfying the super Yang-Baxter equation.
Common fixed points of two nonexpansive mappings in Banach spaces
Authors: Suzuki Tomonari
Published: April 2009

In this paper, we discuss a necessary and sufficient condition for common fixed points of two nonexpansive mappings. We then prove a convergence theorem to a common fixed point. Finally, we discuss the existence of a nonexpansive retraction onto the set of common fixed points of nonexpansive mappings. In these theorems, we do not assume the strict (uniform) convexity of the norm of the Banach space.
A fourth-order parabolic equation with a logarithmic nonlinearlity
Authors: Bonfoh Ahmed
Published: April 2009

We consider some generalisations of the Cahn—Hilliard equation based on constitutive equations derived by M. Gurtin in (1996) with a logarithmic free energy. Compared to the classical Cahn—Hilliard equation (see [4, 5]), these models take into account the work of internal microforces and the anisotropy of the material. We obtain the existence and uniqueness of solutions results and then prove the existence of finite dimensional attractors.
Quantitative approach to weak noncompactness in the polygon interpolation method
Authors: Kryczka Andrzej
Published: April 2009

We study a quantitative approach to weak noncompactness of operators under the Cobos-Peetre polygon interpolation method for Banach N-tuples. In the case of operators acting between two J-spaces or two K-spaces obtained by this method we prove logarithmically convex-type inequalities for certain operator seminorm vanishing on the subspace of weakly compact operators. Geometrically speaking, in these estimates only some triangles inscribed in the polygon are involved. For operators acting from a J-space to a K-space we prove logarithmically convex-type estimates where all polygon vertices are included. In particular, the estimates obtained here give the new proofs of the results showing the relation between distribution of weakly compact operators among polygon vertices and weak compactness of operators under interpolation.
A construction of simple Lie subalgebras of certain types from triple systems
Authors: Kamiya Noriaki , Okubo Susumu
Published: April 2009

We have constructed all simple Lie superalgebras from some triple systems. In particular, we shall discuss simple Lie superalgebras of P(n), Q(n) and Cartan types W(n), S(n), H(n) in this article.
Approximation by functions with bounded derivative on Banach spaces
Authors: Fry R.
Published: April 2009

Let X be a separable Banach space which admits a C1-smooth norm, and let G ⊂ X be an open subset. Then any real-valued, bounded and uniformly continuous map on G can be uniformly approximated on G by C1-smooth functions with bounded derivative.
Characteristic polynomials of graph coverings
Authors: Feng Rongquan , Kwak Jin Ho , Lee Jaeun
Published: April 2009

In this note, a formula for the characteristic polynomial of any (regular or irregular) graph covering is described.
On some sub-Riemannian objects in hypersurfaces of sub-Riemannian manifolds
Authors: Tan Kang-Hai , Yang Xiao-Ping
Published: April 2009

We study some sub-Riemannian objects (such as horizontal connectivity, horizontal connection, horizontal tangent plane, horizontal mean curvature) in hypersurfaces of sub-Riemannian manifolds. We prove that if a connected hypersurface in a contact manifold of dimension more than three is noncharacteristic or with isolated characteristic points, then there exists at least a piecewise smooth horizontal curve in this hypersurface connecting any two given points in it. In any sub-Riemannian manifold, we obtain the sub-Riemannian version of the fundamental theorem of Riemannian geometry: there exists a unique nonholonomic connection which is completely determined by the sub-Riemannian structure and is “symmetric” and compatible with the sub-Riemannian metric. We use this nonholonomic connection to study horizontal mean curvature of hypersurfaces.
On evaluation formulas for double L-values
Authors: Tsumura Hirofumi
Published: April 2009

In this paper, we give some evaluation formulas for the values of double L-series of Tornheim's type, in terms of the Dirichlet L-values and the Riemann zeta values at positive integers. As special cases, these give the formulas for double L-values given by Terhune.
Fixed point property for general topologies in some Banach spaces
Authors: Pineda Maria A. Japón , Prus Stanislaw
Published: April 2009

We study the fixed point property with respect to general vector topologies in L-embedded Banach spaces. Considering a class of topologies in l1 such that the standard basis is convergent, we characterise those of them for which the fixed point property holds. We show that in c0-sums of some Banach spaces the weak topology is in a sense the coarsest topology for which the fixed point property holds.
Non-minimal tree actions and the existence of non-uniform tree lattices
Authors: Carbone Lisa
Published: April 2009

A uniform tree is a tree that covers a finite connected graph. Let X be any locally finite tree. Then G = Aut(X) is a locally compact group. We show that if X is uniform, and if the restriction of G to the unique minimal G-invariant subtree X0 ⊆ X is not discrete then G contains non-uniform lattices; that is, discrete subgroups Γ for which Γ/G is not compact, yet carries a finite G-invariant measure. This proves a conjecture of Bass and Lubotzky for the existence of non-uniform lattices on uniform trees.
The class groups of the imaginary Abelian number fields with Galois group (ℤ/2ℤ)n
Authors: Ahn Jeoung-Hwan , Kwon Soun-Hi
Published: April 2009

Assuming the Generalised Riemann Hypothesis we determine all imaginary Abelian number fieldsNwhose Galois groupG(N/ℚ) is isomorphic to (ℤ/2ℤ)nfor some integersn≥ 1 and the square of every ideal ofNis principal.
On two open problems about strongly clean rings
Authors: Wang Zhou , Chen Jianlong
Published: April 2009

A ring is called strongly clean if every element is the sum of an idempotent and a unit which commute. In 1999 Nicholson asked whether every semiperfect ring is strongly clean and whether the matrix ring of a strongly clean ring is strongly clean. In this paper, we prove that if R = {m/n ∈ ℚ: n is odd}, then M2(R) is a semiperfect ring but not strongly clean. Thus, we give negative answers to both questions. It is also proved that every upper triangular matrix ring over the ring R is strongly clean.
Norm of composition operators on the Bloch space
Authors: Xiong Chengji
Published: April 2009

The author estimates the semi-norm and norm of composition operators on the Block space; and obtains several necessary conditions for a composition operator to be isometric.
Distance to the intersection of two sets
Authors: Martinón Antonio
Published: April 2009

We give sufficient conditions so that the distance of a point to the intersection of two sets agrees with the maximum of the distances to each of them. The results are established in several settings: complete metric spaces, Banach spaces and spaces of subsets of Banach spaces.
Maximal averages along curves over the p-adic numbers
Authors: Rogers Keith M.
Published: April 2009

Let ℚp denote the p-adic numbers. We consider curves in defined by p-adic polynomials of one p-adic variable. We show that maximal averages along these curves are bounded, where 1 < q < ∞.
The similarity problem for tensor products of certain C*-algebras
Authors: Pop Florin
Published: April 2009

We prove that every bounded representation of the tensor product of two C*-algebras, one of which is nuclear and contains matrices of any order, is similar to a *-representation.
A remark on preinvex functions
Authors: Peng Jianwen , Long Xianjun
Published: April 2009

In this paper, we show that the ratio of preinvex functions is invex. Hence, we give a positive answer to the open question which was proposed in a paper of Yang, Yang and Teo in (2003).
Existence and L∞ estimates for a class of singular ordinary differential equations
Authors: Gomes J. M.
Published: April 2009

We prove the existence of a positive solution to an equation of the form (1/Φ(t)) (Φ(t)u′(t))′ = f(u(t)) with Dirichlet conditions where the friction term Φ′/Φ is increasing. Our method combines variational and topological arguments and provides an L∞ estimate of the solution.
Diametrically contractive mappings
Authors: Xu Hong-Kun
Published: April 2009

A contractive mapping on a complete metric space may fail to have a fixed point. Diametrically contractive mappings are introduced and it is shown that a diametrically contractive self-mapping of a weakly compact subset of a Banach space always has a fixed point.
A counterexample using 4-linear forms
Authors: Pérez-García David
Published: April 2009

We prove that, for n ≥ 4 and arbitrary infinite dimensional Banach spaces X1,…Xn, there exists an extendible n-linear form T: X1 x…x Xn →  that is not integral.
Stability of Dhombres' equation
Authors: Batko Bogdan
Published: April 2009

One of the most important examples of conditional Cauchy equations with the condition dependent on the unknown function is Dhombres' equation

This paper is devoted to the stability of the above equation.
A strong excision theorem for generalised Tate cohomology
Authors: Kosta N. Mramor
Published: April 2009

We consider the analogue of the fixed point theorem of A. Borel in the context of Tate cohomology. We show that for general compact Lie groups G the Tate cohomology of a G-CW complex X with coefficients in a field of characteristic 0 is in general not isomorphic to the cohomology of the fixed point set, and thus the fixed point theorem does not apply. Instead, the following excision theorem is valid: if X′ is the subcomplex of all G-cells of orbit type G/H where dim H > 0, and V is a ring such that for every finite isotropy group H the order |H| is invertible in V, then . In the special cases G = 𝕋, the circle group, and G = 𝕌, the group of unit quaternions, a more elementary geometric proof, using a cellular model of is given.
A new variational method for thep(x)-Laplacian equation
Authors: Galewski Marek
Published: April 2009

Using a dual variational method we shall show the existence of solutions to the Dirichlet problemwithout assuming Palais-Smale condition.
On the Ky Fan inequality and related inequalities II
Authors: Neuman Edward , Sándor József
Published: April 2009

Ky Fan type inequalities for means of two or more variables are obtained. Refinements and improvements of known inequalities are derived. Applications to symmetric elliptic integrals of the first and second kind are also included.
Height estimates on cubic twists of the Fermat elliptic curve
Authors: Jedrzejak Tomasz
Published: April 2009

We give bounds for the canonical height of rational and integral points on cubic twists of the Fermat elliptic curve. As a corollary we prove that there is no integral arithmetic progression on certain curves in this family.
On second-order converse duality for a nondifferentiable programming problem
Authors: Yang Xin Min , Zhang Ping
Published: April 2009

Certain shortcomings are described in the second order converse duality results in the recent work of (J. Zhang and B. Mond, Bull. Austral. Math. Soc. 55(1997) 29–44). Appropriate modifications are suggested.
Existence of positive solutions for nonlocal and nonvariational elliptic systems
Authors: Chen Yujuan , Gao Hongjun
Published: April 2009

In the paper we prove a result on the existence of positive solutions for a class of nonvariational elliptic system with nonlocal source by Galerkin methods and a fixed point theorem in finite dimensions. We establish another existence result by the super and subsolution method and a monotone iteration.
Bounded vector measures on effect algebras
Authors: Hwang Hong Taek , Li Longlu , Kim Hunnam
Published: April 2009

Let (L, ⊥, ⊕,0,1) be an effect algebra and X a locally convex space with dual X′. A function μ: L → X is called a measure if μ(a ⊕ b) = μ(a) + μ(b) whenever a⊥b in L and it is bounded if is bounded for each orthogonal sequence {an} in L. We establish five useful conditions that are equivalent to boundedness for vector measures on effect algebras.
Proper 1-ball contractive retractions in Banach spaces of measurable functions
Authors: Caponetti D. , Trombetta A. , Trombetta G.
Published: April 2009

In this paper we consider the Wośko problem of evaluating, in an infinite-dimensional Banach space X, the infimum of all k ≤ 1 for which there exists a k-ball contractive retraction of the unit ball onto its boundary. We prove that in some classical Banach spaces the best possible value 1 is attained. Moreover we give estimates of the lower H-measure of noncompactness of the retractions we construct.
Riemann-Siegel sums via stationary phase
Authors: Tuck E. O.
Published: April 2009

A new representation is obtained for the Riemannξfunction, in the form of a series of integrals, multiplied by an exponential factor capturing the correct decay rate for large imaginary argument. Each term in this series then has a simple stationary-phase asymptote, the total agreeing with the Riemann-Siegel sum.
Rings having zero-divisor graphs of small diameter or large girth
Authors: Mulay S. B.
Published: April 2009

Let R be a commutative ring possessing (non-zero) zero-divisors. There is a natural graph associated to the set of zero-divisors of R. In this article we present a characterisation of two types of R. Those for which the associated zero-divisor graph has diameter different from 3 and those R for which the associated zero-divisor graph has girth other than 3. Thus, in a sense, for a generic non-domain R the associated zero-divisor graph has diameter 3 as well as girth 3.
Lipschitz functions with maximal Clarke subdifferentials are staunch
Authors: Borwein Jonathan M. , Wang Xianfu
Published: April 2009

In a recent paper we have shown that most non-expansive Lipschitz functions (in the sense of Baire's category) have a maximal Clarke subdifferential. In the present paper, we show that in a separable Banach space the set of non-expansive Lipschitz functions with a maximal Clarke subdifferential is not only generic, but also staunch in the space of non-expansive functions.
On the exponents modulo 3 in the standard factorisation of n!
Authors: Liu Wei , Chen Yong-Gao
Published: April 2009

Let p be a prime and m be a positive integer. For a positive integer n, let ep(n) be the nonnegative integer with pep(n) | n and pep(n)+1 ∤ n. As a corollary of our main result we derive an asymptotic formula for the counting function with regard to the condition ep(n!) ≡ ɛ (mod 3), where ɛ ∈ Z3. In 2001, Sander proved the result with modulus 2.
Multiple solutions for some Neumann problems in exterior domains
Authors: Hsu Tsing-San , Lin Huei-Li
Published: April 2009

In this paper, we show that if q(x) satisfies suitable conditions, then the Neumann problem -Δu+u = q(x)ⅠuⅠp−2u in Ω has at least two solutions of which one is positive and the other changes sign.
Weak L- Spaces
Authors: Gao Yin-Zhu
Published: April 2009

In this paper, semi-weak L-spaces and weak L-spaces (which are generalisations of Lindelöf spaces) are introduced and studied.
Semilinear elliptic Neumann problems with rapid growth in the nonlinearity
Authors: Looker Jason R.
Published: April 2009

The existence and regularity of solutions to semilinear elliptic Neumann problems are investigated. Motivated by the Poisson–Boltzmann equation of biophysics and semiconductor modeling, the nonlinearity is assumed to be a continuous, strictly monotone increasing function that passes through the origin with asymptotically superlinear and unbounded growth. Pseudomonotone operator theory is utilised to establish the existence and uniqueness of a weak solution in the Sobolev space W1,2. With an additional assumption on the nonlinearity, we show that this weak solution belongs to .
Characterisations of Ω-stability and structural stability via inverse shadowing
Authors: Choi Taeyoung , Lee Keonhee , Zhang Yong
Published: April 2009

We give characterisations of Ω-stable diffeomorphisms and structurally stable diffeomorphisms via the notions of weak inverse shadowing and orbital inverse shadowing, respectively. More precisely, it is proved that the C1 interior of the set of diffeomorphisms with the weak inverse shadowing property coincides with the set of Ω-stable diffeomorphisms and the C1 interior of the set of diffeomorphisms with the orbital inverse shadowing property coincides with the set of structurally stable diffeomorphisms.
Approximate convexity in vector optimisation
Authors: Gupta Anjana , Mehra Aparna , Bhatia Davinder
Published: April 2009

Approximate convex functions are characterised in terms of Clarke generalised gradient. We apply this characterisation to derive optimality conditions for quasi efficient solutions of nonsmooth vector optimisation problems. Two new classes of generalised approximate convex functions are defined and mixed duality results are obtained.
On isometric actions
Authors: Mulay S. B.
Published: April 2009

To a cardinal k ≥ 2, we associate a simply-connected polyhedral surface Σk endowed with a bounded metric dk such that every group of cardinality k has an isometric, properly discontinuous action on (Σk, dk). If ℵ0 ≤ k ≤ 2ℵ0 and G is a group of cardinality k, then we extend (Σk, dk) to a simply-connected bounded metric space (MG, dG) such that the action of G extends to an isometric, properly discontinuous action on (MG, dG) and G is the full isometry-group of (MG, dG).
On an elliptic equation ofp-Kirchhoff type via variational methods
Authors: Júlio Francisco , Corrêa S. A. , Figueiredo Giovany M.
Published: April 2009

This paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of thep-Kirchhoff typeandwhere Ω is a bounded smooth domain of ℝN, 1 <p<N,s≥p* = (pN)/(N–p) andMandfare continuous functions.
On generalised mixed co-quasi-variational inequalities with noncompact valued mappings
Authors: Ahmad Rais , Ansari Qamrul Hasan , Irfan Syed Shakaib
Published: April 2009

In this paper, we consider generalised mixed co-quasi-variational inequalities with noncompact valued mappings and propose an iterative algorithm for computing their approximate solutions. We prove that the approximate solutions obtained by the proposed algorithm converge to the exact solution of our co-quasi-variational inequality. Some special cases are also discussed.
ABS-type methods for solving full row rank linear systems using a new rank two update
Authors: Amini K. , Mahdavi-Amiri N. , Peyghami M. R.
Published: April 2009

ABS mthods are direct iteration methods for solving linear systems where the i-th iterate satisfies the first i equations, and therefore a system on m equations is solved in at most m ABS steps. In this paper, using a new rank two update of the Abaffian matrix, we introduce a class of ABS-type methods for solving full row rank linear equations, where the i-th iterate solves the first 2i equations. So, termination is achieved in at most ⌊(m + 1)/2⌋ steps. We also show how to decrease the dimension of the Abaffian matrix by choosing appropriate parameters.
On hypercyclicity and supercyclicity criteria
Authors: Bermúdez Teresa , Bonilla Antonio , Peris Alfredo
Published: April 2009

We show that the Hypercyclicity Criterion coincides with other existing hypercyclicity criteria and prove that a wide class of hypercyclic operators satisfy the Criterion. The results obtained extend or improve earlier work of several authors. We also unify the different versions of the Supercyclicity Criterion and show that operators with dense generalised kernel and dense range are supercyclic.
Pseudo-differential equations connected with p-adic forms and local zeta functions
Authors: Zuniga-Galindo W. A.
Published: April 2009

We study the asymptotics of fundamental solutions of p-adic pseudo-differential equations of type

where f(∂,β) is a pseudo-differential operator with symbol , f is a form of arbitrary degree with coefficients in a p-adic field, λ ≥ 0, and g is a Schwartz-Bruhat function.
Polynomials on banach spaces whose duals are isomorphic to ℓ1 (Γ)
Authors: Cilia Raffaella , D'Anna Maria , Gutiérrez Joaquín M.
Published: April 2009

We prove that the dual of a Banach space E is isomorphic to an ℓ1(Γ) space if and only if, for a fixed integer m, every m-homogeneous 1-dominated polynomial on E is nuclear. This extends a result for linear operators due to Lewis and Stegall. The same techniques used for this result allow us to prove that, if every m-homogeneous integral polynomial between two Banach spaces is nuclear, then every integral (linear) operator between the same spaces is nuclear.
Iterative processes with errors for nonlinear equations
Authors: Ćirić Łjubomir , Ume Jeong Sheok
Published: April 2009

In this paper we introduce and consider a class of multi-valued and single-valued operators of generalised monotone type. We proved a new general lemma on the convergence of real sequences and some new convergence theorems for the Ishikawa and Mann iteration processes with errors to the unique fixed point of such operators, which are not necessarily Lipschitz operators. Our results generalise, improve, and extend several recent results.
Isomorphism classes of authentication codes
Authors: Feng Rongquan , Kwak Jin Ho , Lloyd E. Keith
Published: April 2009

In this paper, we give several kinds of characterisations of isomorphic authentication codes by examining a correspondence between optimal authentication codes and some combinatorial designs. The isomorphism classes of some kinds of authentication codes are also enumerated.
Every AF-algebra is Morita equivalent to a graph algebra
Authors: Tyler Jason
Published: April 2009

We show how to modify any Bratteli diagram E for an AF-algebra A to obtain a Bratteli diagram KE for A whose graph algebra C*(KE) contains both A and C*(E) as full corners.
Spectral multipliers of Laplace transform type for the Laguerre operator
Authors: Sasso Emanuela
Published: April 2009

We shall work with the Laguerre measure on and the associated Laplacian ℒα, by means of which the Laguerre semigroup is defined. Our main result is a multiplier theorem, saying that a functions of ℒα which is of Laplace transform type defines an operator of weak type (1, 1) for the Laguerre measure. Our starting point is the well-known relationship between the Laguerre and Ornstein-Uhlenbeck semigroups.
On a new singular direction of meromorphic functions
Authors: Hui Guo , Hua Zheng Jian , Ng Tuen Wai
Published: April 2009

In this paper, by using Ahlfors' theory of covering surfaces, we establish the existence of a new singular direction for a meromorphic functions f, namely a T direction for f, for which the Nevanlinna characteristic function T(r, f) is used as a comparison function.
a-T-menability of groups acting on trees
Authors: Gal Światoslaw R.
Published: April 2009

We present some partial results concerning a-T-menability of groups acting on trees. Various known results are given uniform proofs.
Prime powers as conjugacy class lengths of π-elements
Authors: Beltrán Antonio , Felipe María José
Published: April 2009

Let G be a finite group and π an arbitrary set of primes. We investigate the structure of G when the lengths of the conjugacy classes of its π-elements are prime powers. Under this condition, we show that such lengths are either powers of just one prime or exactly {1,qa, rb}, with q and r two distinct primes lying in π and a, b > 0. In the first case, we obtain certain properties of the normal structure of G, and in the second one, we provide a characterisation of the structure of G.
Inverse shadowing of circle maps
Authors: Park Jong-Jin , Lee Keonhee
Published: April 2009

We show that the concepts of shadowing and (c, h−) inverse shadowing of circle homeomorphisms are equivalent.
A noncommutative half-angle formula
Authors: Willis George
Published: April 2009

The half-angle formulæ, familiar from trigonometry, can be used to compute the polar decomposition of the operator on l2(ℤ) of convolution by δ0 + δ1. This calculation is extended here to a non-commutative setting by computing the polar decomposition of certain convolution operators on the spaces of square integrable functions of free groups.
Inverse semigroups all of whose proper homomorphic images are groups
Authors: Tucci Ralph P.
Published: April 2009

We characterise those inverse semigroups whose proper(non-isomorphic) homomorphic images are all groups. We also show that the bicyclic semigroup is the only such semigroup in certain cases.
Centre and norm
Authors: Beidleman J.C. , Heineken H. , Newell M.
Published: April 2009

We establish a correlation between the structures of a group of power automorphisms of some group and their mutual commutator subgroup and consider the consequences for the norm of a group, and for its capability.
Proficient presentations and direct products of finite groups
Authors: Gruenberg K.W. , Kovács L.G.
Published: April 2009

LetGbe a finite group,Fa free group of finite rank,Rthe kernel of a homomorphism φ ofFontoG, and let [R, F], [R, R] denote mutual commutator subgroups. Conjugation inFyields aG-module structure onR/[R, R] letdg(R/[R, R]) be the number of elements required to generate this module. Defined(R/[R, F]) similarly. By an earlier result of the first author, for a fixedG, the differencedG(R/[R, R]) −d(R/[R, F]) is independent of the choice ofFand φ; here it is called the proficiency gap ofG.If this gap is 0, thenGis said to be proficient. It has been more usual to considerdF(R), the number of elements required to generateRas normal subgroup ofF:the groupGhas been called efficient ifFand φ can be chosen so thatdF(R) =dG(R/[R, F]). An efficient group is necessarily proficient; but (though usually expressed in different terms) the converse has been an open question for some time.
On groups’ with small orders of elements
Authors: Gupta Narain D. , Mazurov Victor D.
Published: April 2009

For a periodic group G, denote by ω(G) the set of orders of elements in G. We prove that if ω(G) is a proper subset of the set {1, 2, 3, 4, 5} then either G is locally finite or G contains a nilpotent normal subgroup N such that G/N is a 5-group.
Finitely presented centre-by-metabelian Lie algebras
Authors: Bryant R.M. , Groves J.R.J.
Published: April 2009

It is shown that finitely presented centre-by-metabelian Lie algebras are Abelian-by-finite-dimensional.
Subgroup coverings of some linear groups
Authors: Bryce R.A. , Fedri V. , Serena L.
Published: April 2009

Acoverfor a group is a collection of proper subgroups whose union is the whole group. A cover isminimalif no other cover contains fewer members. We termminimiseda minimal cover with the property that substituting for a member of the cover by a proper subgroup of that member produces a collection which is no longer a cover. We here describe the minimised covers for the groups GL2(q), SL2(q), PSL2(q) and PGL2(q).
Recalcitrance in groups
Authors: Burns R.G. , Herfort W.N. , Kam S.-M. , Macedońska O. , Zalesskii P.A.
Published: April 2009

Motivated by a well-known conjecture of Andrews and Curtis, we consider the question as to how in a given n-generator group G, a given set of n “annihilators” of G, that is, with normal closure all of G, can be transformed by standard moves into a generating n-tuple. The recalcitrance of G is defined to be the least number of elementary standard moves (”elementary M-transformations”) by means of which every annihilating n-tuple of G can be transformed into a generating n-tuple. We show that in the classes of finite and soluble groups, having zero recalcitrance is equivalent to nilpotence, and that a large class of 2-generator soluble groups has recalcitrance at most 3. Some examples and remarks are included.
What groups were: A study of the development of the axiomatics of group theory
Authors: Neumann Peter M.
Published: April 2009

This paper is devoted to a historical study of axioms for group theory. It begins with the emergence of groups in the work of Galois and Cauchy, treats two lines of development discernible in the latter half of the nineteenth century, and concludes with a note about some twentieth century ideas. One of those nineteenth century lines involved Cayley, Dyck and Burnside; the other involved Kronecker, Weber (very strongly), Hölder and Frobenius.
Monoid kernels and profinite topologies on the free Abelian group
Authors: Steinberg Benjamin
Published: April 2009

To each pseudovariety of Abelian groups residually containing the integers, there is naturally associated a profinite topology on any finite rank free Abelian group. We show in this paper that if the pseudovariety in question has a decidable membership problem, then one can effectively compute membership in the closure of a subgroup and, more generally, in the closure of a rational subset of such a free Abelian group. Several applications to monoid kernels and finite monoid theory are discussed.
A note on the 2 k-th mean value of the Hurwitz zeta function
Authors: Kumchev A.
Published: April 2009

Consider the error term in the asymptotic formula

In this note we obtain δ(k) ≍ 1/(k6 log2k) which, for large values of k, presents a substantial improvement over the previously known result .
Counterexamples concerning powers of sectorial operators on a Hilbert space
Authors: Simard Arnaud
Published: April 2009

We give explicit constructions of semigroups and operators with particular properties. First we build a bounded C0-semigroup which is invertible and which is not similar to a semigroup of contractions. Afterwards we exhibit operators which admit bounded imaginary powers of angle ω > 0 on a Hilbert space but which do not admit a bounded functional calculus on the sector of angle ω. (This gives the limit of McIntosh's fundamental result.) Finally we build, in the 2-dimensional Hilbert space, an operator which is not the negative generator of a semigroup of contractions, although its imaginary powers are bounded by eπ|s|/2.
On isocompactness of function spaces
Authors: Cao Jiling
Published: April 2009

Let Cp(X) be the space of all continuous real-valued functions on a Tychonoff space X with the pointwise topology. In this note, we show that if X is a space, then Cp(X) is isocompact. This gives an answer to a recent question of Arkhangel'skii in the class of spaces.
Square-integrable representations of non-unimodular groups
Authors: Carey A.L.
Published: April 2009

In the last three years a number of people have investigated the orthogonality relations for square integrable representations of non-unimodular groups, extending the known results for the unimodular case. The results are stated in the language of left (or generalized) Hilbert algebras. This paper is devoted to proving the orthogonality relations without recourse to left Hilbert algebra techniques. Our main technical tool is to realise the square integrable representation in question in a reproducing kernel Hilbert space.
A fixed point theorem for a family of nonexpansive mappings
Authors: Sehgal V.M.
Published: April 2009

Let E be a separated, locally convex topological vector space and F a commutative family of nonexpansive mappings defined on a quasi-complete convex (not necessarily bounded) subset X of E. In this paper, it is proved that if one of the mappings in F is condensing with a bounded range then the family F has a common fixed point in X. This result improves several well-known results and supplements a recent result of E. Tarafdar (Bull. Austral. Math. Soc. 13 (1975), 241–254) for such mappings.
Free products amalgamating unitary subsemigroups
Authors: Preston G.B.
Published: April 2009

Let Si, i ∈ I, be a set of semigroups such that Si ∩ Sj = U, if i ≠ j, and such that U is a unitary subsemi-group of Si for each i in I. The semigroup amalgam [{Si | i ∈ I}; U] determined by this system is the partial groupoid G = USi in which a product of two elements is defined if and only if they both belong to the same Si and their product is then taken as their product in Si. In 1962, J.M. Howie showed that the amalgam G is embeddable in the free product of the Si, amalgamating U. To prove this result it suffices to find any semigroup in which G can be embedded. In this paper, by taking convenient representations of the Si, adapting a method recently (1975) used by T.E. Hall for inverse semigroups, we provide a short method of constructing such a semigroup.
On sequences of lattice packings
Authors: Hammer Joseph , Dwyer Denis
Published: April 2009

In this note we establish theorems on compactness of lattice packings.