bluuebunny/crossref_metadata_2025 huggingface dataset:
Convolution properties of a class of bounded analytic functions
Authors: Zhongzhu Zou , Owa Shigeyoshi
Published: April 2009

Let A be the class of functionsf(z) which are analytic in the unit disk U withf(0) =f′(0) - 1 = 0. A subclass S(λ,M) (λ > 0,M> 0) of A is introduced. The object of the present paper is to prove some interesting convolution properties of functionsf(z) belonging to the class S(λ,M). Also a certain integral operatorJforf(z) in the class A is considered.
A formula on the approximate subdifferential of the difference of convex functions
Authors: Martínez-legaz J.E. , Seeger A.
Published: April 2009

We give a formula on the ε−subdifferential of the difference of two convex functions. As a by-product of this formula, one recovers a recent result of Hiriart-Urruty, namely, a necessary and sufficient condition for global optimality in nonconvex optimisation.
Semiregular group divisible designs with dual properties
Authors: Rahilly Alan
Published: April 2009

A construction method for group divisible designs is employed to construct (i) infinitely many non-symmetric semiregular group divisible designs whose duals are semiregular group divisible designs, and (ii) infinitely many transversal designs whose duals are group divisible 3-associate designs. A construction method for affine α−resolvable balanced incomplete block designs is also given and illustrated.
Rings whose additive endomorphisms are ring endomorphisms
Authors: Dugas Manfred , Hausen Jutta , Johnson Johnny A.
Published: April 2009

A ring R is said to be an AE-ring if every endomorphism of its additive group R+ is a ring endomorphism. Clearly, the zero ring on any abelian group is an AE-ring. In a recent article, Birkenmeier and Heatherly characterised the so-called standard AE-lings, that is, the non-trivial AE-rings whose maximal 2-subgroup is a direct summand. The present article demonstrates the existence of non-standard AE-rings. Four questions posed by Birkenmeier and Heatherly are answered in the negative.
On the dynamics of a periodic delay logistic equation with diffusion
Authors: Gopalasamy K. , Weng Pei-Xuan
Published: April 2009

Sufficient conditions are obtained for the existence of a globally attractive positive periodic solution of the periodic diffusive delay logistic system

in whichτandKare positive periodic functions of periodτ, nis a positive integer and ö is a nonnegative number; sufficient conditions are also obtained for all positive solutions to be oscillatory about the periodic solution.
Dichotomies for systems with discontinuous coefficients
Authors: Naulin Raúl
Published: April 2009

In this work we are concerned with the problem of the existence of an exponential dichotomy for the linear singularly perturbed system εx′ = A(t)x, where the matrix A(t) is piecewise uniformly continuous, that is, A(t) admits points of discontinuity but is uniformly continuous in any interval where it is continuous. We shall prove that the classical result regarding the existence of an exponential dichotomy extends to this case, when there is a constant γ > 0 such that |Reλ(t)| ≥ γ > 0 for any eigenvalue λ(t) of A(t). The proofs are obtained by means of the quasidiagonalisation of a non-constant matrix: For A(t), a piecewise uniformly continuous matrix and σ > 0 there exists a bounded, piecewise constant function L(t): J → ℂn×n, and a bounded matrix Δ(t, σ) such that L-1(t)A(t)L(t) = Λ(t) + Δ(t, σ), |Δ(t, σ)| ≤ σ, where Λ(t) is the diagonal matrix consisting of eigenvalues of A(t).
The Weak* Karlovitz lemma for dual lattices
Authors: Sims Brailey
Published: April 2009

We establish the Karlovitz lemma for a nonexpansive self mapping of a nonempty weak* compact convex set in a weak* orthogonal dual Banach lattice.
Extreme points in spaces between Dirichlet and Vanishing Mean Oscillation
Authors: Wirths K. J. , Xiao J.
Published: April 2009

Forp∈ (0, ∞) defineQp0(∂Δ) as the space of all Lebesgue measurable complex-valued functionsf; on the unit circle ∂Δ for which ∫∂Δf;(z)|dz|/(2π) = 0 and

as the open subarcIof ∂Δ varies. Note that eachQp,0(∂Δ) lies between the Dirichlet space and Sarason's vanishing mean oscillation space. This paper determines the extreme points of the closed unit ball ofQp,0(∂Δ) equipped with an appropriate norm.
Weighted discrepancy of Faure-Niederreiter nets for a certain sequence of weights
Authors: Pillichshammer Friedrich
Published: April 2009

In this note we give a bound for the weighted star discrepancy of Faure-Niederreiter (0, m, s)-nets in prime-power base b ≥ s – 1 for the special sequence of weights given by γi = 1/i2, i ≥ 1.
Global existence and comparison theorem for a nonlinear parabolic equation
Authors: Hesaaraki Mahmoud , Moameni Abbas
Published: April 2009

In this paper we consider a nonlinear parabolic equation with gradient dependent nonlinearities of the form

0 < p, q and a, b ∈ ℝ, with homogeneous boundary condition in a bounded domain Ω ⊆ ℝ,N. In the case 0 < p, q ≤ 1 we prove the existence of solution for suitable initial data. A comparison theorem for the solutions with respect to supersoultions and subsolutions is proved. Using these result, uniqueness and boundedness of solutions is studied.
Determination of torsion Abelian groups by their automorphism groups
Authors: Schultz P. , Sebeldin A. , Sylla A. L.
Published: April 2009

An Abelian torsion group is determined by its automorphism group if and only if its locally cyclic component is determined by its automorphism group. We describe the locally cyclic groups that are determined by their automorphism groups.
A Riemann type theorem for series of operators on Banach spaces
Authors: Aizpuru A. , Gutiérrez-Dávila A. , Sala A.
Published: April 2009

We study Kalton's theorem on the unconditional convergence of series of compact operators and we use some matrix techniques to obtain sufficient conditions, weaker than previous ones, on the convergence and unconditional convergence of series of compact operators. Finally, we characterise weak unconditionally Cauchy series in Cℒ(X, Y) in the terms of certain spaces of vector sequences.
A local approach to a class of locally finite groups
Authors: Ballester-Bolinches A. , Pedraza Tatiana
Published: April 2009

This paper is devoted to the study of a class of generalised P-nilpotent groups in the universe cℒ̄ of all radical locally finite groups satisfying min-q for every prime q. Some results of finite groups are extended and a characterisation of the injectors associated with this class is given.
Products of three idempotent transformations
Authors: Sullivan R. P. , Thomas Rachel
Published: April 2009

In 1988 Howie, Robertson and Schein characterised the transformations of a finite set X that can be written as a product of two or of three idempotent transformations of X; and in 1989 Saito did the same for products of four idempotents. In 1998 Thomas extended the characterisation of two idempotents to arbitrary sets, and here we characterise products of three idempotents in general. We also define a notion of complexity for transformations of any set and use it to provide a different solution to the three-idempotent problem.
Sufficient conditions for invexity
Authors: Ha Nguyen Xuan , Van Luu Do
Published: April 2009

In this paper, we show that the Robinson, Nguyen–Strodiot–Mifflin and Jourani constraint qualifications are sufficient conditions for invexity of constrained functions with respect to the same scale function in Lipschitzian mathematical programmings. A Kuhn-Tucker necessary optimality condition is also given under the constraint qualification on the invexity property of constrained functions.
Tensor products of divisible effect algebras
Authors: Pulmannová Sylvia
Published: April 2009

Tensor products of divisible effect algebras and tensor products of the corresponding universal groups are studied. It is shown that the universal group of the tensor product of divisible effect algebras is (isomorphic to) the tensor product of the corresponding universal groups. Moreover, it is shown that the tensor product of two unit intervals [0, 1] of real numbers is not a lattice.
Dense orbits and compactness of groups
Authors: Previts W. H. , Wu T. S.
Published: April 2009

Using results from topological groups and topological dynamics for locally compact spaces, Aoki has shown that when a group automorphism of a locally compact totally disconnected group is ergodic under the Haar measure, the group is compact. We provide some remarks on Aoki's proof. Also we present a new proof of his result using the structure of locally compact totally disconnected groups established by Willis.
Compact composition operators on Block spaces
Authors: Xiong Chengji
Published: April 2009

The present paper proposes new criteria for compactness of a composition operator Cφf = f ∘ φ on the Bloch space and the little Bloch space. For the case when φ is univalent, a criterion given by K. Madigan and A. Matheson is generalised.
Local compactness in free topological groups
Authors: Nickolas Peter , Tkachenko Mikhail
Published: April 2009

We show that the subspace An(X) of the free Abelian topological group A(X) on a Tychonoff space X is locally compact for each n ∈ ω if and only if A2(X) is locally compact if an only if F2(X) is locally compact if and only if X is the topological sum of a compact space and a discrete space. It is also proved that the subspace Fn(X) of the free topological group F(X) is locally compact for each n ∈ ω if and only if F4(X) is locally compact if and only if Fn(X) has pointwise countable type for each n ∈ ω if and only if F4(X) has pointwise countable type if and only if X is either compact or discrete, thus refining a result by Pestov and Yamada. We further show that An(X) has pointwise countable type for each n ∈ ω if and only if A2(X) has pointwise countable type if and only if F2(X) has pointwise countable type if and only if there exists a compact set C of countable character in X such that the complement X \ C is discrete. Finally, we show that F2(X) is locally compact if and only if F3(X) is locally compact, and that F2(X) has pointwise countable type if and only if F3(X) has pointwise countable type.
Vector quasi-equilibrium problems
Authors: Khaliq Abdul , Krishan Sonam
Published: April 2009

In this paper we establish existence theorems for vector quasi-equilibrium problems in Hausdorff topological vector spaces both under compactness and noncompactness assumptions.
Connes-amenability and normal, virtual diagonals for measure algebras, II
Authors: Runde Volker
Published: April 2009

We prove that the following are equivalent for a locally compact groupG:

(i)Gis amenable;

(ii)M(G) is Connes-amenable;

(iii)M(G) has a normal, virtual diagonal.
On uniformly distributed sequences of integers and Poincaré recurrence III
Authors: Nair R.
Published: April 2009

Let S be a semigroup contained in a locally compact Abelian group G. Let Ĝ denote the Bohr compactification of G. We say that a sequence contained in S is Hartman uniform distributed on G if

for any character χ in Ĝ. Suppose that (Tg)g∈s is a semigroup of measurable measure preserving transformations of a probability space (X, β, μ) and B is an element of the σ-algebra β of positive μ measure. For a map T: X → X and a set A ⊆ X let T−1A denote {x ∈ X: Tx ∈ A}. In an earlier paper, the author showed that if k is Hartman uniform distributed then

In this paper we show that ≥ cannot be replaced by =. A more detailed discussion of this situation ensues.
Almost contractive retractions in Orlicz spaces
Authors: Lewicki Grzegorz , Trombetta Giulio
Published: April 2009

Let Bk denote the Euclidean unit ball in ℝκ equipped with the k-dimensional Lebesgue measure and let φ: ℝ+ → ℝ+ be a convex function satisfying φ(0) = 0, φ(t) > 0 for some t > 0. Denote by Eφ = Eφ(Bk) the Orlicz space of finite elements (see (1.6)) generated by φ. The aim of this paper is to show that there exists a retraction of the closed unit ball in Eφ onto the unit sphere in Eφ being a (2 + ɛ)γφ;-set contraction (Theorem 3.6), which generalises [9, Corollary 6] proved for the case of Lp[−1, 1], 1 ≤ p < ∞. Here γφ, denote the Hausdorff measure of noncompactness. This theorem is proved both for the Amemiya and the Luxemburg norms. Also some related results concerning the case of s-convex (0 < s ≤ 1) functions are presented.
On the affine diameter of closed convex hypersurfaces
Authors: Sheng Weimin , Trudinger Neil S.
Published: April 2009

In this paper we prove that the affine diameter of any closed uniformly convex hypersurface in Euclidean space enclosing finite volume is bounded from above.
A question from the Kourovka notebook on formation products
Authors: Ballester-Bolinches A. , Calvo Clara , Esteban-Romero R.
Published: April 2009

It is shown in this paper that if  is a class of simple groups such that π() = char , the -saturated formation ℌ generated by a finite group cannot be expressed as the Gaschütz product  ∘  of two non--saturated formations if ℌ ≠ . It answers some open questions on products of formations. The relation between ω-saturated and -saturated formations is also discussed.
On basic embeddings of compacta into the plane
Authors: Mramor-Kosta Neža , Trenklerová Eva
Published: April 2009

A compactum K ⊂ ℝ2 is said to be basically embedded in ℝ2 if for each continuous function f: K → ℝ there exist continuous functions g, h: ℝ → ℝ such that f(x, y) = g(x) + h(y) for each point (x, y) ∈ K. Sternfeld gave a topological characterization of compacta K which are basically embedded in ℝ2 which can be formulated in terms of special sequences of points called arrays, using arguments from functional analysis. In this paper we give a simple topological proof of the implication: if there exists an array in K of length n for any n ∈ ℕ, then K is not basically embedded.
A superconvergence result for solutions of compact operator equations
Authors: Kulkarni Rekha P.
Published: April 2009

Over the last 20 years, since the publication of Sloan's paper on the improvement by the iteration technique, various approaches have been proposed for post-processing the Galerkin solution of multi-dimensional second kind Fredholm Integral equation. These methods include the iterated Galerkin method proposed by Sloan, the Kantorovich method and the iterated Kantorovich method. Recently, Lin, Zhang and Yan have proposed interpolation as an alternative to the iteration technique. For an integral operator, with a smooth kernel using the orthogonal projection onto a space of discontinuous piecewise polynomials of degree ≤r− 1, previous authors have established an orderrconvergence for the Galerkin solution and 2rfor the iterated Galerkin solution. Equivalent results have also been established for the interpolator projection at Gauss points and some interpolation post-processing technique. In this paper, a method is introduced and shown to have convergence of order 4r. The size of the system of equations that must be solved, in implementing this method, remains the same as for the Galerkin method.
Powerful numbers in short intervals
Authors: De Koninck Jean-Marie , Luca Florian , Shparlinski Igor E.
Published: April 2009

Let κ ≥ 2 be an integer. We show that there exist infinitely many positive integers N such that the number of κ-full integers in the interval (Nκ, (N + 1)κ) is at least (log N)1/3+ο(1). We also show that the ABC-conjecture implies that for any fixed δ > 0 and sufficiently large N, the interval (N, N + N1−(2+δ)/κ) contains at most one κ-full number.
On certain equations in rings
Authors: Vukman Joso , Kosi-Ulbl Irena , Eremita Daniel
Published: April 2009

In this paper we prove the following result: LetRbe a 2-torsion free semiprime ring. Suppose there exists an additive mappingT:R→Rsuch thatT(xyx)=T(x)yx−xT(y)x+xyT(x)holds for all pairsx, y∈R. ThenTis of the form2T(x)=qx+xq, whereqis a fixed element in the symmetric Martindale ring of quotients ofR.
A characterisation of Hilbert spaces via orthogonality and proximinality
Authors: Saidi Fathi B.
Published: April 2009

In this paper we adopt the notion of orthogonality in Banach spaces introduced by the author in [6]. There, the author showed that in any two-dimensional subspace F of E, every nonzero element admits at most one orthogonal direction. The problem of existence of such orthogonal direction was not addressed before. Our main purpose in this paper is the investigation of this problem in the case where E is a real Banach space. As a result we obtain a characterisation of Hilbert spaces stating that, if in every two-dimensional subspace F of E every nonzero element admits an orthogonal direction, then E is isometric to a Hilbert space. We conclude by presenting some open problems.
Poincaré inequality for abstract spaces
Authors: Ranjbar-Motlagh Alireza
Published: April 2009

The Poincaré inequality is generalised to metric-measure spaces which support a strong version of the doubling condition. This generalises the Poincaré inequality for manifolds whose Ricci curvature is bounded from below and metric-measure spaces which satisfy the measure contraction property.
Centralisers on rings and algebras
Authors: Vukman Joso , Kosi-Ulbl Irena
Published: April 2009

In this paper we investigate identities related to centralisers in rings and algebras. We prove, for example, the following result. LetAbe a semisimpleH*-algebra and letT:A→Abe an additive mapping satisfying the relationT(xm+n+1) =xmT(x)xnfor allx∈Aand some integersm≥ 1,n≥ 1. In this caseTis a left and a right centraliser.
Affine Baire-one functions on Choquet simplexes
Authors: Spurný Jiří
Published: April 2009

Metrisable Choquet simplexes with the set of extreme points being an Fσ-set are characterised by means of the behaviour of the space of affine Baire-one functions.
Carlson type inequalities for finite sums and integrals on bounded intervals
Authors: Larsson Leo , Páles Zsolt , Persson Lars-Erik
Published: April 2009

We investigate Carlson type inequalities for finite sums, that is, inequalities of the form

to hold for some constant C independent of the finite, non-zero set a1,…,am of non-negative numbers. We find constants C which are strictly smaller than the sharp constants in the corresponding infinite series case. Moreover, corresponding results for integrals over bounded intervals are given and a case with any finite number of factors on the right-hand side is proved.
Uniformly perfect Julia sets of meromorphic functions
Authors: Wang Sheng , Liao Liang-Wen
Published: April 2009

Julia sets of meromorphic functions are uniformly perfect under some suitable conditions. So are Julia sets of the skew product associated with finitely generated semigroup of rational functions.
Chaos on function spaces
Authors: Aron Richard M. , Seoane-Sepúlveda Juan B. , Weber Andreas
Published: April 2009

We give a sufficient condition for an operator to be chaotic and we use this condition to show that, in the Banach space C0[0, ∞) the operator (τλ, cf)(t) = λf(t + c) (with λ > 1 and c > 0) is chaotic, with every n ∈ ℕ being a period for this operator. We also describe a technique to construct, explicitly, hypercyclic functions for this operator.
Carter subgroups in the group of units of an associative algebra
Authors: Bauer Thorsten , Siciliano Salvatore
Published: April 2009

In this paper we examine some properties of the Carter subgroups in the group of units of certain associative algebras. A description of the Carter subgroups in the case of a solvable associative algebra is obtained. Moreover, given an associative algebra A, we study relationships between the Cartan subalgebras of the Lie algebra associated with A and the Carter subgroups of the group of units of A.
On additive properties of general sequences
Authors: Tang Min , Chen Yong-Gao
Published: April 2009

LetA= {a1,a2,…} (a1<a2< …) be an infinite sequence of positive integers. LetA(n) be the number of elements ofAnot exceedingn, and denote byR2(n) the number of solutions ofai+aj=n, i≤j. In 1986, Erdős, Sárközy and Sós proved that if (n−A(n))/logn→ ∞(n→ ∞), then. In this paper, we generalise this theorem and give its quantitative form. For example, one of our conclusions implies that if limsup(n−A(n))/logn= ∞, thenfor infinitely many positive integersN.
On finite loops whose inner mapping groups are Abelian II
Authors: Niemenmaa Markku
Published: April 2009

If the inner mapping group of a loop is a finite Abelian group, then the loop is centrally nilpotent. We first investigate the structure of those finite Abelian groups which are not isomorphic to inner mapping groups of loops and after this we show that if the inner mapping group of a loop is isomorphic to the direct product of two cyclic groups of the same odd prime power order pn, then our loop is centrally nilpotent of class at most n + 1.
Some Schwarz type inequalities for sequences of operators in Hilbert spaces
Authors: Dragomir Sever S.
Published: April 2009

We give some inequalities of Cauchy-Bunyakovsky-Schwarz type for sequences of bounded linear operators in Hilbert spaces with applications.
On a type of Matrix ring
Authors: Tunapan Maliwan , Somsup Chitlada , Chairat Sarapee
Published: April 2009

In this note we discuss a type of matrix ring that has nice properties concerning the injectivity and quasi-injectivity of one-sided ideals.
Analogues of the Liouville theorem for linear fractional relations in Banach spaces
Authors: Khatskevich V.A. , Ostrovskii M.I. , Shulman V.S.
Published: April 2009

Consider a bounded linear operatorTbetween Banach spaces ℬ, ℬ′ which can be decomposed into direct sums ℬ = ℬ1⌖ ℬ2, ℬ′ = ℬ1′ ⌖ ℬ2′. Such linear operator can be represented by a 2 × 2 operator matrix of the formwhereTij∈ ℒ(ℬj, ℒi′)i, j= 1, 2. (By ℒ(ℬj, ℒi′) we denote the space of bounded linear operators acting from ℬjto ℬi′ (i, j= 1, 2).) The mapGTfromL(B1,B2) into the set of closed affine subspaces of ℒ(ℬ1′ ℬ2′), defined byis called alinear fractional relationassociated withT.

Such relations can be considered as a generalisation of linear fractional transformations which were studied by many authors and found many applications. Many traditional and recently discovered areas of application of linear fractional transformations would benefit from a better understanding of the behaviour of linear fractional relations. The present paper is devoted to analogues of the Liouville theorem “a bounded entire function is constant” for linear fractional relations.
The topological degree of A-proper mapping in the Menger PN-space (I)
Authors: Xiaoqin Huang , Miansen Wang , Chuanxi Zhu
Published: April 2009

In this paper, we introduce the concept of A-proper topological degree in Menger PN-space and study some of its properties. Utilising its properties, we obtain a new fixed point theorem.
The topological degree of A-proper mapping in the Menger PN-space (II)
Authors: Chuanxi Zhu , Xiaoqin Huang
Published: April 2009

In the paper “The topological degree of A-proper mapping in the Menger PN-space (I)”, the new concept of A-proper topological degree has been given. Now, utilising the new concept, we give the corresponding definitions of convex A-proper, P*-compact and Pγ-compact in Menger PN-space. As an application of these new concepts, we prove the existence of solution for some equations.
The joint distribution of the Riemann zeta - function
Authors: Laurinčikas A.
Published: April 2009

In the paper the asymptotic distribution of (|ζ(s)|,ζ(s)), where ζ(s) is the Riemann zeta - function, in the sense of weak convergence of probability measures is considered. For this, the continuity theorems for probability measures on ℝ × ℂ are used. Some aspects of the dependence of |ζ(s)| and ζ(s) are also discussed.
On the number of conjugacy classes of normalisers in a finite p-group
Authors: Gavioli Norberto , Legarreta Leire , Sica Carmela , Tota Maria
Published: April 2009

In 1996 Poland and Rhemtulla proved that the number v (G) of conjugacy classes of non-normal subgroups of a non-Hamiltonian nilpotent group G is at least c − 1, where c is the nilpotency class of G. In this paper we consider the map that associates to every conjugacy class of subgroups of a finite p-group the conjugacy class of the normaliser of any of its representatives. In spite of the fact that this map need not be injective, we prove that, for p odd, the number of conjugacy classes of normalisers in a finite p-group is at least c (taking into account the normaliser of the normal subgroups). In the case of p-groups of maximal class we can find a better lower bound that depends also on the prime p.
Groups acting on a set whose orbits are all singleton
Authors: Pournaki M. R.
Published: April 2009

In this article using techniques which appeared in Witt's proof of Wedderburn's theorem, an arithmetical characterisation of groups acting on a set whose orbits are all singleton is given. This can then be used to obtain a new proof of Wedderburn's theorem.
On some generalisations of the Erdős distance problem over finite fields
Authors: Shparlinski Igor E.
Published: April 2009

We use exponential sums to obtain new lower bounds on the number of distinct distances defined by all pairs of points (a, b) ∈ A × B for two given sets where is a finite field of q elements and n ≥ 1 is an integer.
Upper semi continuity of attractors of delay differential equations in the delay
Authors: Kloeden Peter E.
Published: April 2009

It is shown that if a retarded delay differential equation has a global attractor in the space C ([—τ0, ], ℝd) for a given nonzero constant delay τ0, then the equation has an attractor Aτ in the space C ([—τ, 0], ℝd) for nearby constant delays τ. Moreover the attractors Aτ converge upper semi continuously to in C ([—τ0, 0], ℝd) in the sense that they are identified through corresponding segments of entire trajectories in ℝd with nonempty compact subsets of C ([—τ0, 0], ℝd) which converge upper semi continuously to in C ([—τ0, 0], ℝd).
Real hypersurfaces with η-parallel shape operator in complex two-plane Grassmannians
Authors: Choi Young Suk , Suh Young Jin
Published: April 2009

In this paper we give a characterisation of -invariant real hypersurfaces of type A; that is, a tube over a totally geodesic G2(ℂm+1) in complex two-plane Grassmannians G2(ℂm+2) or a ruled real hypersurface foliated by complex hypersurfaces which includes a maximal totally geodesic submanifold G2(ℂm+1) in G2(ℂm+2) in terms of η-parallel shape operator.
The n-insertive subgroups of units
Authors: Dolžn David
Published: April 2009

Let R be a finite ring. Let us denote its group of units by G = G(R) and its Jacobson radical by J = J(R). Let n be an arbitrary integer. We prove that R is an n-insertive ring if and only if G is an n-insertive group and show that every n-insertive finite ring is a direct sum of local rings. We prove that if n is a unit, then the local ring R is n-insertive if and only if its Jacobson group 1 + J is n-insertive and find an example to show that this is not true if n is a non-unit.
Semilocal E-convexity and semilocal E-convex programming
Authors: Hu Qing-Jie , Jian Jin-Bao , Zheng Hai-Yan , Tang Chun-Ming
Published: April 2009

In this paper, a new type of generalised convexity—semilocal E-convexity is introduced by combining the concepts of the semi-E-convexity in X.S. Chen [J. Math. Anal. Appl. 275(2002), 251–262] and semilocal convexity in G.M. Ewing [SIAM. Rev. 19(1977), 202–220], and some of its basic characters are discussed. By utilising the new concepts, we derive some optimality conditions and establish some duality results for the inequality constrained optimisation problem.
Change of ring and torsion-theoretic injectivity
Authors: Crivei Iuliu , Crivei Septimiu , Purdea Ioan
Published: April 2009

Let τ be a hereditary torsion theory in R-Mod. Then any ring homomorphism γ: R → S induces in S-Mod a torsion theory σ given by the condition that a left S-module is σ-torsion if and only if it is τ-torsion as a left R-module. We show that if γ: R → S is a ring epimorphism and A is a τ-injective left R-module, then AnnA Ker(γ) is σ-injective as a left S-module. As a consequence, we relate τ-injectivity and σ-injectivity, and we give some applications.
Schur property and lP isomorphic copies in Musielak–Orlicz sequence spaces
Authors: Zlatanov B.
Published: April 2009

The author shows that if the dual of a Musielak–Orlicz sequence space lΦ is a stabilized asymptotic l∞, space with respect to the unit vector basis, then lΦ is saturated with complemented copies of l1 and has the Schur property. A sufficient condition is found for the isomorphic embedding of lp spaces into Musielak–Orlicz sequence spaces.
Extension problems and non-Abelian duality for C*-algebras
Authors: an Huef Astrid , Kaliszewski S. , Raeburn Iain
Published: April 2009

Suppose that H is a closed subgroup of a locally compact group G. We show that a unitary representation U of H is the restriction of a unitary representation of G if and only if a dual representation Û of a crossed product C*(G) ⋊ (G/H) is regular in an appropriate sense. We then discuss the problem of deciding whether a given representation is regular; we believe that this problem will prove to be an interesting test question in non-Abelian duality for crossed products of C*-algebras.
An infinite class of identities
Authors: Alaca Ayşe , Alaca Şaban , Williams Kenneth S.
Published: April 2009

An infinite class of identities relating infinite products is proved. It is shown that this class contains a famous identity of Jacobi.
Weighted composition operators with closed range
Authors: Palmberg N.
Published: April 2009

We study the closed range property of weighted composition operators on weighted Bergman spaces of infinite order (including the Hardy space of infinite order). We give some necessary and sufficient conditions and find a complete characterisation for weighted composition operators associated with conformal mappings. We also give the corresponding results for composition operators on the Bloch-type spaces. Therefore, the results obtained in this paper also improve and generalise the results of Ghatage, Yan, Zheng and Zorboska.
The Strictly Efficient Subgradient of Set-Valued Optimisation
Authors: Li Taiyong , Xu Yihong
Published: April 2009

The subgradient, under strict efficiency, of a set-valued mapping is developed, and the existence of the subgradient is proved. Optimality conditions in terms of Lagrange multipliers for a strictly efficient point are established in the general case and in the case with ic-cone-convexlike data.
On inequalities of Hilbert's type
Authors: Li Yongjin , He Bing
Published: April 2009

By introducing the function 1/(min{x, y}), we establish several new inequalities similar to Hilbert's type inequality. Moreover, some further unification of Hardy-Hilbert's and Hardy-Hilbert's type integral inequality and its equivalent form with the best constant factor are proved, which contain the classic Hilbert's inequality as special case.
Characterisation of Embeddings in Lorentz Spaces
Authors: Gogatishvili A. , Johansson M. , Okpoti C. A. , Persson L.-E.
Published: April 2009

Some new integral conditions characterising the embedding ∧p(v) ↪ Γq(w), 0 < p, q ≤ ∞ are presented, including proofs also for the cases (i) p = ∞, 0 < q < ∞, (ii) q = ∞, I < p < ∞ and (iii) p = q = ∞. Only one condition is necessary for each case which means that our conditions are different from and simpler than other corresponding conditions in the literature. We even prove our results in a more general frame namely when the space Γq(w) is replaced by the more general space . In our proof we use a technique of discretisation and anti-discretisation developed by A. Gogatishvili and L. Pick, where they considered the opposite embedding.
Équations de Fermat de type (5, 5,p)
Authors: Billerey Nicolas
Published: April 2009

Soient p un nombre premier ≥ 7 et d un entier naturel sans puissances cinquièmes. Nous mettons en œuvre les différentes méthodes modulaires connues pour l'étude de l'équation diophantienne x5+y5 = dzp. Nous montrons en particulier qu'elle n'admet aucune solution propre et non triviale pour p ≥ 7 ou pour une infinité de nombres premiers, dans certains cas où d est de la forme 2α.3β.5γ. Pour d = 3, on énonce un critère permettant de vérifier, notamment, que tel est le cas lorsque p est ≤ 106.

Let p be a prime number ≥ 7 and d be a positive integer fifth power free. We use the known modular methods for the study of the diophantine equation x5+y5 = dzp. We prove that this equation has no non trivial proper solution for p ≥ 7 or for infinitely many prime numbers, in some cases where d is of the form 2α.3β.5γ. For d = 3, we give a criterion which allows us to verify that this holds if p is less than 106.
Generalised symmetries of partial differential equations via complex transformations
Authors: Ferraioli D. Catalano , Manno G. , Pugliese F.
Published: April 2009

We consider two systems of real analytic partial differential equations, related by a holomorphic contact map H. We study how the generalised symmetries of the first equation are mapped into those of the second one, and determine under which conditions on H such a map is invertible. As an application of these results, an example of physical interest is discussed.
Notes on the binding numbers for (a, b, k)-critical graphs
Authors: Zhou Sizhong , Jiang Jiashang
Published: April 2009

Let G be a graph of order n, and let a, b, k be nonnegative integers with 1 ≤ a < b. An [a, b]-factor of graph G is defined as a spanning subgraph F of G such that a ≤ dF(x) ≤ b for each x ϵ V (F). Then a graph G is called an (a, b, k)-critical graph if after deleting any k vertices of G the remaining graph of G has an [a, b]-factor. In this paper, it is proved that G is an (a, b, k)-critical graph if the binding number

and

Furthermore, it is showed that the result in this paper is best possible in some sense.
A periodic wavelet method for the second kind of the logarithmic integral equation
Authors: Gao Jing , Jiang Yao-Lin
Published: April 2009

A periodic wavelet Galerkin method is presented in this paper to solve a weakly singular integral equations with emphasis on the second kind of Fredholm integral equations. The kernel function, which includes of a smooth part and a log weakly singular part, is discretised by the periodic Daubechies wavelets. The wavelet compression strategy and the hyperbolic cross approximation technique are used to approximate the weakly singular and smooth kernel functions. Meanwhile, the sparse matrix of systems can be correspondingly obtained. The bi-conjugate gradient iterative method is used to solve the resulting algebraic equation systems. Especially, the analytical computational formulae are presented for the log weakly singular kernel. The computational error for the representative matrix is also evaluated. The convergence rate of this algorithm is O (N-p log(N)), where p is the vanishing moment of the periodic Daubechies wavelets. Numerical experiments are provided to illustrate the correctness of the theory presented here.
The Symplecticity of the Magnus Representation for Homology Cobordisms of Surfaces
Authors: Sakasai Takuya
Published: April 2009

The Magnus matrix is an algebraic invariant assigned to each homology cobordism of a surface. We show that this matrix satisfies an equality which can be regarded as a non-commutative symplectic relation.
An Analogue of Beurling's Theorem for the Heisenberg Group
Authors: Huang Jizheng , Liu Heping
Published: April 2009

In this paper, we prove an analogue of Beurling's theorem on the Heisenberg group. Then we derive some other versions of the uncertainty principle.
Enumeration of groups of prime-power order
Authors: Witty Brett E.
Published: April 2009

Finite group theorists have been interested in counting groups of prime-power order, as a preliminary step to counting groups of any finite order and to assist in explicitly listing such groups. In 1960, G. Higman considered when the functions giving the number of groups of prime-power order pn, for fixed n and varying p, is of a particular form, called polynomial on residue classes (PORC). The suggestion that such counting functions are PORC is known as Higman's PORC conjecture. In his 1960 paper [4] he proved that a certain class of groups of prime-power order, now called exponent-p class two groups, have counting functions that are PORC, but did not furnish explicit PORC functions.
Convergence theorems for topological group valued measures on effect algebras
Authors: Mazarío Francisco García
Published: April 2009

In this paper we study the validity of several convergence theorems for measures defined on an effect algebra and taking values in a Hausdorff commutative topological group. We establish the Brooks-Jewett theorem and the Nikodým convergence theorem, giving as a corollary a result, due to Aarnes, about the convergence of a sequence of normal linear functionals on a von Neumann algebra. We prove two new convergence theorems concerning completely additive and τ-smooth measures, and we obtain also a convergence theorem for regular measures.
A question of Paul Erdös and nilpotent-by-finite groups
Authors: Taeri Bijan
Published: April 2009

Let n be a positive integer or infinity (denoted ∞), k a positive integer. We denote by Ωk(n) the class of groups G such that, for every subset X of G of cardinality n + 1, there exist distinct elements x, y ∈ X and integers t0, t1…, tk such that , where xi, ∈ {x, y}, i = 0, 1,…,k, x0 ≠ x1. If the integers t0, t1,…,tk are the same for any subset X of G, we say that G is in the class Ω̅k(n). The class k (n) is defined exactly as Ωk(n) with the additional conditions . Let t2, t3,…,tk be fixed integers. We denote by the class of all groups G such that for any infinite subsets X and Y there exist x ∈ X, y ∈ Y such that , where xi ∈ {x, y}, x0 ≠ x1, i = 2, 3, …, k. Here we prove that (1) If G ∈ k(2) is a finitely generated soluble group, then G is nilpotent.

(2) If G ∈ Ωk(∞) is a finitely generated soluble group, then G is nilpotentby-finite.

(3) If G ∈ Ω̅k(n), n a positive integer, is a finitely generated residually finite group, then G is nilpotent-by-finite.

(4) If G is an infinite -group in which every nontrivial finitely generated subgroup has a nontrivial finite quotient, then G is nilpotent-by-finite.
A duality proof of sampling localisation in relaxation spectrum recovery
Authors: Loy R. J. , Newbury C. , Anderssen R. S. , Davies A. R.
Published: April 2009

In a recent paper, Davies and Anderssen (1997) examined the range of relaxation times, on which the linear viscoelasticity relaxation spectrum could be reconstructed, when the oscillatory shear data were only known on a fixed finite interval of frequencies. In particular, they showed that, for such oscillatory shear data, knowledge about the relaxation spectrum could only be recovered on a specific finite interval of relaxation times. They referred to this phenomenon as sampling localisation. The purpose of this note is show how their result can be proved using a duality argument, and, thereby, establish the fundamental nature of sampling localisation in relaxation spectrum recovery.
Convolution of Riemannian manifolds and its applications
Authors: Chen Bang-Yen
Published: April 2009

It is well-known that warped products play some important roles in differential geometry as well as in physics. In this article we extend the notion of warped product to the notion of convolution of Riemannian manifolds. We study the basic properties of convolutions of Riemannian manifolds. We also apply the notion of convolution to establish and characterise the Euclidean version of Segre embedding.
Hitting probabilities of conditional Brownian motion and polarisation
Authors: Betsakos Dimitrios
Published: April 2009

We study the behaviour of the hitting probabilities of conditional Brownian motion in a domain D in Euclidean space when we apply polarization to D. We also study how polarization affects the probability that conditional Brownian motion meets a subset of D.
Chapman-Jouguet detonation profile for a qualitative model
Authors: Razani Abdolrahman
Published: April 2009

In this article, the existence of traveling wave fronts for a one step chemical reaction with a natural discontinuous reaction rate function is studied. This discontinuity occurs because of the cold boundary difficulty and implies a discontinuous system of ordinary differential equations. By some general topological arguments in ordinary differential equations, the Chapman-Jouguet detonation for exothermic reactions is shown to exist. In addition, the uniqueness of this wave is considered.
On totally paranormal operators
Authors: Schmoeger Christoph
Published: April 2009

A continuous linear operator on a complex Banach space is said to be paranormal if ‖Tx‖2 ≤ ‖T2x‖ ‖x‖ for all x ∈ X. T is called totally paranormal if T–λ is paranormal for every λ ∈ C. In this paper we investigate the class of totally paranormal operators. We shall see that Weyl's theorem holds for operators in this class. We also show that for totally paranormal operators the Weyl spectrum satisfies the spectral mapping theorem. In Section 5 of this paper we investigate the operator equations eT = eS and eTeS = eSeT for totally paranormal operators T and S.
From surfaces in the 5-sphere to 3-manifolds in complex projective 3-space
Authors: Bolton J. , Scharlach C. , Vrancken L.
Published: April 2009

In a previous paper it was shown how to associate with a Lagrangian submanifold satisfying Chen's equality in 3-dimensional complex projective space, a minimal surface in the 5-sphere with ellipse of curvature a circle. In this paper we focus on the reverse construction.
Derivations, local derivations and atomic boolean subspace lattices
Authors: Li Pengtong , Ma Jipu
Published: April 2009

Let ℒ be an atomic Boolean subspace lattice on a Banach space X. In this paper, we prove that if ℳ is an ideal of Alg ℒ then every derivation δ from Alg ℒ into ℳ is necessarily quasi-spatial, that is, there exists a densely defined closed linear operator T: 𝒟(T) ⊆ X → X with its domain 𝒟(T) invariant under every element of Alg ℒ, such that δ(A) x = (TA – AT) x for every A ∈ Alg ℒ and every x ∈ 𝒟(T). Also, if ℳ ⊆ ℬ(X) is an Alg ℒ-module then it is shown that every local derivation from Alg ℒ into ℳ is necessary a derivation. In particular, every local derivation from Alg ℒ into ℬ(X) is a derivation and every local derivation from Alg ℒ into itself is a quasi-spatial derivation.
C*-algebras of infinite real rank
Authors: Chigogidze A. , Valov V.
Published: April 2009

We introduce the notion of weakly (strongly) infinite real rank for unital C*-algebras. It is shown that a compact space X is weakly (strongly) infine-dimensional if and only if C (X) has weakly (strongly) infinite real rank. Some other properties of this concept are also investigated. In particular, we show that the group C*-algebra C* (∞) of the free group on countable number of generators has strongly infinite real rank.
There are no denting points in the unit ball of 𝒫(2H)
Authors: Kim Sung Guen
Published: April 2009

For any infinite dimensional real Hilbert space H we show that the unit ball of the space of continuous 2-homogeneous polynomials on H, 𝒫(2H), has no denting points. Thus the unit ball of 𝒫(2H) has no strongly exposed points.
New interpolation theorems related to the space BMOA on spaces of homogeneous type
Authors: Zhang Qi-Hui , Ni Da-Ping
Published: April 2009

Let (χ, d, μ) be a space of homogeneous type in the sense of Coifman and Weiss, and BMOA(χ) be the space of BMO type associated with an “approximation to the identity” {At}t>0 and introduced by Duong and Yan. In this paper, we establish new interpolation theorems of operators related to the space BMOA(χ).
Extended Cesàro operator between some holomorphic function spaces
Authors: Lv Xiaofen
Published: April 2009

We characterize the boundedness and compactness of the extended Cesàro operator Tg from H∞ to the mixed norm space and Bloch-type space (or little Bloch-type space), where g is a given holomorphic function in the unit ball of Cn and Tg is defined by .
Congruences on semigroups generated by injective nilpotent transformations
Authors: Marques-Smith M. Paula O. , Sullivan R.P.
Published: April 2009

In 1987, Sullivan characterised the elements of the semigroupNI(X) generated by the nilpotents inI(X), the symmetric inverse semigroup on an infinite setX; and, in the same year, Gomes and Howie did the same for finiteX. In 1999, Marques-Smith and Sullivan determined all the ideals ofNI(X) for arbitraryX. In this paper, we use that work to describe all the congruences onNI(X).
A generalised Lucasian primality test
Authors: Zhang Zhenxiang , Zhou Weiping , Liu Xianbei
Published: April 2009

We present a primality test for numbers of the form Mh, n = h·2n ±1 (in particular with h divisible by 15), which generalises Berrizbeitia and Berry's test for such numbers with h ≢ 0 mod 5. With our generalised test, the primality of such a number Mh, n can be proved by means of a Lucas sequence with a seed determined by h and πq — primary irreducible divisor of a prime q ≡ 1 mod 4. We call the prime q a judge of the number Mh, n. We prescribe a sequence S of 48 primes ≡ 1 mod 4 in the interval [13, 2593] such that, for all odd h = 15t < 108 and for all n < 7.3 1011, each number Mh, n has a judge q in . Comparisons with Bosma's explicit primality criteria in “a well-defined finite sense” for the case h = 3t < 105 are given.
Packing dimension and measure of homogeneous Cantor sets
Authors: Baek H.K.
Published: April 2009

For a class of homogeneous Cantor sets, we find an explicit formula for their packing dimensions. We then turn our attention to the value of packing measures. The exact value of packing measure for homogeneous Cantor sets has not yet been calculated even though that of Hausdorff measures was evaluated by Qu, Rao and Su in (2001). We give a reasonable lower bound for the packing measures of homogeneous Cantor sets. Our results indicate that duality does not hold between Hausdorff and packing measures.
Bounds for the normalised Jensen functional
Authors: Dragomir Sever S.
Published: April 2009

New inequalities for the general case of convex functions defined on linear spaces which improve the famous Jensen's inequality are established. Particular instances in the case of normed spaces and for complex and real n-tuples are given. Refinements of Shannon's inequality and the positivity of Kullback-Leibler divergence are obtained.
A class of majorant functions for contractors and equations
Authors: Altman Mieczyslaw
Published: April 2009

Majorant functions for contractors can be defined in a natural war. Such a case is considered here in order to find iterative solutions of general equations in Banach spaces by means of contractors. A class of majorant functions is defined which contains in particular the linear majorant ones. Local and global existence and convergence theorems are proved.
Entire functions mapping countable dense subsets of the reals onto each other monotonically
Authors: Sato Daihachiro , Rankin Stuart
Published: April 2009

It is shown that for arbitrary countable dense ssets A and B of the real line, there exists a transcendental entire function whose restriction to the real line is a real-valued strictly monotone increasing surjection taking A onto B The technique used is a modification of the procedure Maurer used to show that for countable dense subsets A and B of the plane, there exists a transcendental entire function whose restriction to A is a bijection from A to B.
On the edge-reconstruction of graphs
Authors: Dörfler W.
Published: April 2009

A graph X is edge-reconstructible if it is uniquely determined up to isomorphism by the set of graphs X – e obtained by deleting one, edge e. The graphs of a comparatively rich class are shown to be edge-reconstructible. This class contains all non-trivial strong products and certain lexicographic products.
Two-variable laws for a class of finite simple groups
Authors: Southcott Bruce
Published: April 2009

This paper presents a two-variable basis for the variety generated by the finite simple group PSL(2, 2n).
Divergence of Fourier series: Corrigenda. II
Authors: Izumi Masako , Izumi Shin-ichi
Published: April 2009

The proof of divergence of Fourier series which was constructed in the authors' earlier paper [Bull. Austral. Math. Soc. 8 (1973), 289–304] is not complete. The object of this paper is to show that the unestimated terms do not disturb the divergence.