bluuebunny/crossref_metadata_2025 huggingface dataset:
Algorithmes des fractions continues et de Jacobi-Perron
Authors: Adam Brigitte , Rhin Georges
Published: April 2009

We give an algorithm by which one can compute, using only rational numbers, the continued fraction and more generally the Jacobi-Perron algorithm expansion of real algebraic numbers.
Derivations on semiprime rings
Authors: Vukman Joso
Published: April 2009

The main result: Let R be a 2-torson free semiprime ring and let D: R → R be a derivation. Suppose that [[D(x), x], x] = 0 holds for all x ∈ R. In this case [D(x), x] = 0 holds for all x ∈ R.
On finite products of totally permutable groups
Authors: Ballester-Bolinches A. , Pedraza-Aguilera M.C. , Pérez-Ramos M.D.
Published: April 2009

In this paper the structure of finite groups which are the product of two totally permutable subgroups is studied. In fact we can obtain the -residual, where is a formation, -projectors and -normalisers, where is a saturated formation, of the group from the corresponding subgroups of the factor subgroups.
Conditions for the solvability of singular boundary value problems
Authors: Liu Xiyu
Published: April 2009

Consider the singular boundary value problem (r(x′))′ + f(t, x) = 0, 0 < t < 1. We give necessary and sufficient conditions for this problem to have solutions. In addition, a uniqueness result is obtained.
On the behaviour of the sup- and inf-convolutions of a function near the boundary
Authors: Cranny Timothy R.
Published: April 2009

The study of nonclassical solutions for elliptic and parabolic PDE's often involves the use of regularisation processes such as the sup- and inf-convolutions. In this note we study the behaviour of these regularised functions near the boundary of the domain, and derive constraints on the appropriate second-order sub- and superdifferentials on and near the boundary. Potential applications to regularity results are also noted.
Periodic solutions of a second order nonlinear differential equation
Authors: Mehri Bahman
Published: April 2009

We consider the following non-linear nonautonomous second order differential equation

where h(x) is continuous, f, p are continuous and periodic with respect to t of period w. Using the Leray-Schauder fixed point technique we prove that the above equation possesses at least one non-trivial periodic solution of period w.
Constructing lattice-ordered fields and division rings
Authors: Redfield R.H.
Published: April 2009

Neumann's totally ordered power series fields and division rings may be tipped over to form archimedean lattice-ordered fields and division rings. This process is described and then generalised to produce non-archimedean lattice-ordered fields and division rings in which 1 > 0 and, as well, ones in which 1 ≯ 0.
The reducibility theorem for linearised polynomials over finite fields
Authors: Cohen Stephen D.
Published: April 2009

A self-contained elementary account is given of the theorem of S. Agou that classifies all composite irreducible polynomials of the form over a finite field of characteristic p. Written to appeal to a wide readership, it is intended to complement the original rather technical proof and other contributions by the author and by Moreno.
A note on a paper of Bowcock and Yu
Authors: Stavroulakis I. P.
Published: April 2009

Consider the first order differential equation (1) , where pi, and τi, for i = 1,…,n, are positive constants. To find necessary and sufficient conditions, in terms of the coefficients and the delays only, under which all solutions of (1) oscillate, is a problem of great importence. In a recent paper, Bowcock and Yu claimed that is a necessary and sufficient condition for all solutions of (1) to be oscillatory. In this paper a counterexample shows that the above result is not valid and the error in this paper is indicated.
On the inversion of Fourier transforms
Authors: Asmar Nakhlé H. , Merryfield Kent G.
Published: April 2009

Let G be a locally compact abelian group, with character group Ĝ. Let ψ be an arbitrary continuous real-valued homomorphism defined on Ĝ. For f in LP(G), 1 < p ≤ 2, let

where 1[−ν, ν] is the indicator function of the interval [ − ν, ν ], and I is an unbounded increasing sequence of positive real numbers. Then there is a constant Mp, independent of f, such that ‖M#f‖p ≤ Mp ‖f‖p. Consequently, the pointwise limit of the function exists, almost everywhere on G, as ν tends to infinity. Using this result and a generalised version of Riesz's theorem on conjugate functions, we obtain a pointwise inversion for Fourier transforms of functions on Ra × Tb, where a and b are nonnegative integers, and on various other locally compact abelian groups.
A generalised quasi-variational inequality without upper semicontinuity
Authors: Cubiotti Paolo , Yuan Xian-Zhi
Published: April 2009

In this note we deal with the following problem: given a nonempty closed convex subset X of Rn and two multifunctions Γ : X → 2X and , to find ( such that

We prove a very general existence result where neither Γ nor Φ are assumed to be upper semicontinuous. In particular, our result give a positive answer to an open problem raised by the first author recently.
The Selmer groups and the ambiguous ideal class groups of cubic fields
Authors: Chen Yen-Mei J.
Published: April 2009

In this paper, we study a family of elliptic curves with CM bywhich also admits a ℚ-rational isogeny of degree 3. We find a relation between the Selmer groups of the elliptic curves and the ambiguous ideal class groups of certain cubic fields. We also find some bounds for the dimension of the 3-Selmer group over ℚ, whose upper bound is also an upper bound of the rank of the elliptic curve.
Testing on null sequences is enough for Bochner integrability
Authors: Mayoral Fernando , Paúl Pedro J.
Published: April 2009

Let E be a normed space, a Fréchet space or a complete (DF)-space satisfying the dual density condition. Let Ω be a Radon measure space. We prove that a function f: Ω → Eis Bochner p-integrable if (and only if) fis p-integrable with respect to the topology of uniform convergence on the norm-null sequences from E′.
On the range of the Y-transform
Authors: Tuan Vum Kim
Published: April 2009

The ranges of the Y-integral transform in some spaces of functions are described.
Class two nilpotent capable groups
Authors: Heineken Hermann , Nikolova Daniela
Published: April 2009

We give a bound for the number of generators for groups of exponent p depending on the rank of the centre when centre and commutator subgroup coincide, provided that the group is isomorphic to the quotient group modulo the centre of some group.
Weakly continuous accretive operators in general Banach spaces
Authors: Fitzgibbon W.E.
Published: April 2009

Global wellposedness theorems are established for a class of abstract Cauchy initial value problems and a class of abstract Volterra equations which have a linear semigroup as a convolution kernel. These existence theorems are used to show that a class of nonlinear operators and a class of perturbed linear operators are m-accretive. The m-accretiveness results are used in turn to represent solutions to the differential and integral equations.
On commutativity of rings with some polynomial constraints
Authors: Ashraf Mohd , Quadri Murtaza A.
Published: April 2009

Let R be an associative ring with unity 1, N(R) the set of nilpotents, J(R) the Jacobson radical of R and n > 1 be a fixed integer. We prove that R is commutative if and only if it satisfies (xy)n = ynxn for all x, y ∈ R \ N(R) and commutators in R are n(n + 1)-torsion free. Moreover, we extend the same result in the case when x, y ∈ R\J(R).
Conserved quantities for axisymmetric cavities near boundaries
Authors: Paull R. , Blake J.R.
Published: April 2009

In axisymmetric irrotational flows of a perfect fluid under gravity there are three basic conserved quantities; axial momentum, energy and a circulation based, radial moment of momentum. This paper adapts these conservation principles to describe cavity collapse adjacent to a rigid boundary in a semi-infinite perfect fluid. They afford a global model accounting for volume change, migration and jet formation; physically the most significant features of bubble collapse close to a rigid boundary.
Almost nilpotent gamma rings
Authors: Booth G.L. , Groenewald N.J.
Published: April 2009

In this paper we introduce the concept of almost nilpotence for Γ-rings, similar to the corresponding concept for rings, as defined by Van Leeuwen and Heyman. An almost mlpotent radical property Α0 is introduced for Γ-rings, and shown to be supernilpotent. If M is a Γ-ring with left and right operator rings L and R respectively, then Α(L)+ = Α0(M) = Α(R)*, where Α(−) denotes the almost nilpotent radical of a ring. If M is a Γ-ring and m, n are positive integers, then Α0(Mm, n) is the almost nilpotent radical of the Γn, m-ring Mm, n.
Some inequalities for diophantine approximation by continued fractions
Authors: Tong Jingcheng
Published: April 2009

Let ξ be an irrational number with simple continued fraction expansion ξ = [a0;a1,a2,…,an,…], let pn/qn be its nth convergent and let θn = qn|qnξ − pn|. In this paper a general method is introduced to deduce a series of inequalities involving the triple (θn−1, θn, θn+1).
Properties of the trajectories of set-valued integrals in banach spaces
Authors: Papageorgiou Nikolaos S.
Published: April 2009

Let F: T → 2x \ {} be a closed-valued multifunction into a separable Banach space X. We define the sets and We prove various convergence theorems for those two sets using the Hausdorff metric and the Kuratowski-Mosco convergence of sets. Then we prove a density theorem of CF and a corresponding convexity theorem for F(·). Finally we study the “differentiability” properties of K(·). Our work extends and improves earlier ones by Artstein, Bridgland, Hermes and Papageorgiou.
Monotone clones, residual smallness and congruence distributivity
Authors: McKenzie Ralph
Published: April 2009

Corresponding to each ordered set there is a variety, determined up to equivalence, generated by an algebra whose term operations are all the monotone operations on the ordered set. We produce several characterisations of the finite bounded ordered sets for which the corresponding variety is congruence-distributive. In particular, we find that congruence-distributivity, congruence-modularity, and residual smallness are equivalent for these varieties.
On topologies in a topos
Authors: Tavakoli Javad
Published: April 2009

Johnstone and Paré have each given a way of constructing the largest topology allowing a given object to be a sheaf. In this paper we use the notion of a partial map to construct such a topology in a simple way.
Slices, RNP, strong regularity, and martingales
Authors: Girardi Maria , Uhl J.J.
Published: April 2009

The usual proof that dentability implies the Radon-Nikodým property involves a clever but rather baroque exhaustion argument. This note presents a very short and simple proof of this implication. The techniques in this new proof are then generalised to derive some direct proofs of recent results concerning strongly regular operators on L1.
On uniformly bounded sequences in Orlicz spaces
Authors: Balder Erik J.
Published: April 2009

A useful result for uniformly bounded sequences of functions in Orlicz spaces is generalised by means of a recent extension of Komlós' theorem. The same generalisation can also be proven differently, by means of Young measures.
Composition operators on some Möbius invariant Banach spaces
Authors: Makhmutov Shamil , Tjani Maria
Published: April 2009

We characterise the compact composition operators from any Mobius invariant Banach space to VMOA, the space of holomorphic functions on the unit disk U that have vanishing mean oscillation. We use this to obtain a characterisation of the compact composition operators from the Bloch space to VMOA. Finally, we study some properties of hyperbolic VMOA functions. We show that a function is hyperbolic VMOA if and only if it is the symbol of a compact composition operator from the Bloch space to VMOA.
The Julia set of a random iteration system
Authors: Zhou Ji
Published: April 2009

This paper presents two properties of the Julia set of a random iteration system of rational functions, which are similar to the well-known results in the classical case.
Relative continuity of direct sums of M-injective modules
Authors: Zhongkui Liu , Ahsan Javed
Published: April 2009

Let M be a left R-module and  be an M-natural class with some additional conditions. It is proved that every direct sum of M-injective left R-modules in  is  -continuous (-quasi-continuous) if and only if every direct sum of M- injective left R-modules in  is M-injective.
Regular polygons and transfinite diameter
Authors: Grandcolas Michel
Published: April 2009

We study the behaviour of the transfinite diameter of regular polygons of fixed diameter, as a function of the number of their vertices.
Bimodules for Cuntz-Krieger algebras of infinite matrices
Authors: Szymański Wojciech
Published: April 2009

We show that any Cuntz-Krieger algebra Aover an infinite 0–1 matrixAmay be realised as a Cuntz-Pimsner algebra Xfor a Hilbert bimoduleXover a suitable AbelianC*-algebra with totally disconnected spectrum. Using Pimsner's six-term exact sequence for theKK-groups we calculate theK-groups of A. We also give a description of the corresponding Toeplitz algebra Xin terms of generators and relations.
Hankel measures on Hardy space
Authors: Xiao Jie
Published: April 2009

We characterise the complex measures μ on the open unit disk D such that for all f in the Hardy space H2. The characterisation involves Carleson measures, the duality between H1 and BMOA, and Hankel operators.
Almost all extraspecialp-groups are swan groups
Authors: Green David John , Minh Pham Anh
Published: April 2009

LetPbe an extraspecialp-group which is neither dihedral of order 8, nor of odd orderp3and exponentp. LetGbe a finite group havingPas a Sylowp-subgroup. Then the mod-pcohomology ring ofGcoincides with that of the normaliserNG(P).
Inducing characters and nilpotent injectors
Authors: Sanus Lucía
Published: April 2009

Let G be a finite group and let N be a normal subgroup of G. If G/N is solvable and H/N is a nilpotent injector of G/N, then there exists a canonical basis of the complex space of the class functions of G which vanish off the G-conjugates of H.
A sharp lower bound for the Ricci curvature of bounded hypersurfaces in space forms
Authors: Veeravalli Alain R.
Published: April 2009

Dedicated to Lamiae and Lucas Zakaria with great affection.

We give a sharp lower bound for the Ricci curvature of bounded complete hypersurfaces of space forms. This leads to several applications.
A remark on the η-invariant for automorphisms of hyperelliptic Riemann surfaces
Authors: Morifuji Takayuki
Published: April 2009

We give a characterisation for the vanishing of the η-invariant of prime order automorphisms of hyperelliptic Riemann surfaces through the mapping torus construction. To this end, we introduce a notion of s-symmetry for finite order surface automorphisms.
A note on p-adic Carlitz's q-Bernoulli numbers
Authors: Kim Taekyun , Rim Seog-Hoon
Published: April 2009

In a recent paper I have shown that Carlitz's q-Bernoulli number can be represented as an integral by the q-analogue μq of the ordinary p-adic invariant measure. In the p-adic case, J. Satoh could not determine the generating function of q-Bernoulli numbers. In this paper, we give the generating function of q-Bernoulli numbers in the p-adic case.
A cone characterisation of reflexive locally convex spaces
Authors: Qiu Jinghui
Published: April 2009

In this paper, we find the dual relationship between solidness and the angle property of cones, which is characteristic of reflexivity for locally convex spaces.
On simple, primitive and prime rings relative to a torsion theory
Authors: Dauns John , Zhou Yiqiang
Published: April 2009

For a hereditary torsion theory τ, we show by examples that the concepts of τ-Artinian τ-simple, τ-Artinian τ-primitive, τ-Artinian τ-prime, τ-Artinian τ-semiprimitive, and τ-Artinian τ-semiprime rings are different from each other and thus answer a question raised by Bland in his book [Topics in Torsion Theory, (Mathematical Research, 103, Wiley-VCH, 1998]. The example of a τ-Artinian τ-primitive ring which is not τ-simple here appears to be a counter-example to a result of Bland in the same publication.
Hölder continuity of solutions of some degenerate elliptic differential equations
Authors: Mohammed Ahmed
Published: April 2009

Weak solutions of the degenerate elliptic differential equation Lu := −div(A (x)∇u)+b·∇u+Vu = f, with |b|2ω−1, V, f in some appropriate function spaces, will be shown to be Hölder continuous.
Analytic discs in the polynomial hull of a disc fibration over the sphere
Authors: Černe Miran
Published: April 2009

It is shown that for each pointPin the interior of the polynomial hull of a disc fibrationXover the unit sphere ∂nthere exists anH∞analytic disc with boundary inXand passing throughp.
A submatrix of the character table
Authors: Navarro Gabriel
Published: April 2009

Let G be a finite group and let p be a prime number. We consider the Submatrix of the character table of G whose rows are indexed by the characters in blocks of maximal defect, and whose columns are indexed by the conjugacy classes of P′-size. We prove that this matrix has maximum rank.
An existence theorem for nonlinear hemivariational inequalities at resonance
Authors: Gasiński Leszek , Papageorgiou Nikolaos S.
Published: April 2009

We consider a nonlinear hemivariational inequality with the p-Laplacian at resonance. Using an extension of the nonsmooth mountain pass theorem of Chang, which makes use of the Cerami compactness condition, we prove the existence of a nontrivial solution. Our existence results here extends a recent theorem on resonant hemivariational inequalities, by the authors in 1999.
A metrisation theorem for pseudocompact spaces
Authors: Good Chris , Mohamad A. M.
Published: April 2009

In this paper we prove that a completely regular pseudocompact space with a quasi-regular-Gδ-diagonal is metrisable.
Some new generalisations of inequalities of Hardy and Levin–Cochran–Lee
Authors: C˘iz˘mes˘ija Aleksandra , Pec˘arić Josip
Published: April 2009

In this paper finite versions of Hardy's discrete, Hardy's integral and the Levin–Cochran–Lee inequalities will be considered and some new generalisations of these inequalities will be derived. Moreover, it will be shown that the constant factors involved in the right-hand sides of the integral results obtained are the best possible.
Nonuniqueness and wellposedness of abstract Cauchy problems in a Fréchet space
Authors: Kunstmann Peer Christian
Published: April 2009

Suppose that A is a closed linear operator in a Fréchet space X. We show that there always is a maximal subspace Z containing all x ∈ X for which the abstract Cauchy problem has a mild solution, which is a Fréchet space for a stronger topology. The space Z is isomorphic to a quotient of a Fréchet space F, and the part Az of A in Z is similar to the quotient of a closed linear operator B on F for which the abstract Cauchy problem is well-posed. If mild solutions of the Cauchy problem for A in X are unique it is not necessary to pass to a quotient, and we reobtain a result due to R. deLaubenfels.

Moreover, we obtain a continuous selection operator for mild solutions of the inhomogeneous equation.
Dimension invariance of subdivisions
Authors: Lee Jeh Gwon , Liu Wei-Ping , Nowakowski Richard , Rival Ivan
Published: April 2009

The dimension of an ordered set is invariant with respect to any subdivision of its completion. This may be applied to support the conjecture (still open) that the problem to determine the (order) dimension of an N-free ordered set is NP-complete.
Large deviation results for a U-statistical sum with product kernel
Authors: Borovskikh Y. V. , weber N. C.
Published: April 2009

Large deviation theorems are proved for non-degenerate U-statistical sums of degree m with kernel h (x1, …, xm) = x1 … xm under the Cramér condition and under the Linnik condition. The method of proof uses truncation and the contraction technique.
The Perimeter of optimal convex lattice polygons in the sense of different metrics
Authors: Stojaković Miloš
Published: April 2009

Classes of convex lattice polygons which have minimal lp-perimeter with respect to the number of their vertices are said to be optimal in the sense of the lp-metric.

It is proved that if p and q are arbitrary integers or ∞, the asymptotic expression for the lq-perimeter of these optimal convex lattice polygons Qp(n) as a function of the number of their vertices n is
. for arbitrary ɛ > 0,
where
.
and Ap is equal to the area of the planar shape |x|p + |y|p ≤ 1.
Alternative quasialgebras
Authors: Albuquerque Helena , Elduque Alberto , Pérez-Izquierdo José María
Published: April 2009

Alternative division quasialgebras which are not associative, are characterized. Their grading groups are shown to be always Abelian and they are built from some specific graded associative algebras by means of a graded Cayley-Dickson process.
A useful lemma concerning subseries convergence
Authors: Matheron E.
Published: April 2009

We give simple and almost identical proofs of several classical results in Functional Analysis by means of a single lemma concerning subseries convergence.
Some New Poincaré-type inequalities
Authors: Cheung Wing-Sum
Published: April 2009

New and improved Poincaré-type integral inequalities involving many functions of many variables are established. These in turn can serve as generators and can generate numerous Poincaré-type integral inequalities by choosing different parameters.
Finding common fixed points of nonexpansive mappings by iteration: Corrigendum
Authors: Rhoades B. E.
Published: April 2009

In [3] the following theorem was stated.
Brauer points on Fermat curves
Authors: McCallum William G.
Published: April 2009

In honour of George Szekeres on his 90th birthday

If X is a variety over a number field K, the set of K-rational points on X is contained in the subset of the adelic points cut out by the Brauer group; we call this set the set of Brauer points on the variety. If S is a set of valuations of K, we also define S-Brauer points in a natural way. It is natural to ask how good a bound on the rational points is provided by the Brauer (or S-Brauer) points.

Let p > 3 be a prime number, and let X be the Fermat curve of degree p, xp + yp = 1. Let K be the field of p-th roots of unity, and let r be the p-rank of the class group of K. In this paper we show that if r < (p + 3)/8, then the set of p-Brauer points on X has cardinality at most p. We construct elements of the Brauer group of X by relating it to the Weil-Chatelet group of the jacobian of X, then use the method of Coleman and Chabauty to bound the points cut out by these elements.
The pseudoidentity problem and reducibility for completely regular semigroups
Authors: Almedia Jorge , Trotter Peter G.
Published: April 2009

Dedicated to George Szekeres on the occasion of his 90th birthday

Necessary and sufficient conditions for equality over the pseudovariety CR of all finite completely regular semigroups are obtained. They are inspired by the solution of the word problem for free completely regular semigroups and clarify the role played by groups in the structure of such semigroups. A strengthened version of Ash's inevitability theorem (κ-reducibility of the pseudovariety G of all finite groups) is proposed as an open problem and it is shown that, if this stronger version holds, then CR is also κ-reducible and, therefore, hyperdecidable.
Graphs without cycles of even length
Authors: Lam Thomas
Published: April 2009

Dedicated to George Szekeres on his ninetieth birthday

In this paper we prove that a bipartite graph with parts of sizes M and N, having no cycles of even length less that or equal to 2(2k + 1), where k is a positive integer, has at most (NM)(k+1)/(2k+1) + Dk(N + M) edges, where Dk only depends on k.

In particular, we show that when k = 1, D1 = 1 is possible.
A Bryce and Cossey type theorem in a class of locally finite groups
Authors: Ballester-Bolinches A. , Camp-Mora S.
Published: April 2009

In this paper the subgroup-closed saturated Fitting formations of radical locally finite groups with min-p for all p are fully characterised. Moreover the study of a class of generalised nilpotent groups introduced by Ballester-Bolinches and Pedraza is continued.
Polynomial representations of the Diffie-Hellman mapping
Authors: Mahassni Edwin El , Shparlinski Igor
Published: April 2009

We obtain lower bounds on the degrees of polynomials representing the Diffie-Hellman mapping (gx, gy) → gxy, where g is a primitive root of a finite field q of q elements. These bounds are exponential in terms of log q. In particular, these results can be used to obtain lower bounds on the parallel arithmetic complexity of breaking the Diffie-Hellman cryptosystem. The method is based on bounds of numbers of solutions of some polynomial equations.
Isometries of spaces of unbounded continuous functions
Authors: Araujo Jesús , Jarosz Krzysztof
Published: April 2009

By the classical Banach-Stone Theorem any surjective isometry between Banach spaces of bounded continuous functions defined on compact sets is given by a homeomorphism of the domains. We prove that the same description applies to isometries of metric spaces of unbounded continuous functions defined on non compact topological spaces.
On the existence of Chapman-Jouguet detonation waves
Authors: Hesaaraki Mahmoud , Razani Abdolrahman
Published: April 2009

The existence of travelling wave solutions to equations of a viscous, heat-conducting combustible fluid is proved. The reactions are assumed to be one step exothermic reactions with a natural discontinuous reaction rate function. The problem is studied for a general gas. Instead of assuming the ideal gas conditions we consider a general thermodynamics which is described by a fairly mild set of hypotheses. The existence proof of travelling waves for Chapman-Jouguet detonation reduces to finding specific heteroclinic orbits of a discontinuous system of ordinary differential equations: these heteroclinic orbits connect a rest point corresponding to unburnt state to that of the burnt state. The existence proof for heteroclinic orbits corresponding to Chapman-Jouguet detonation waves is carried out by some general topological arguments in ordinary differential equations theory.
Semi-Baer modules over domains
Authors: Lee Sang Bum
Published: April 2009

For a commutative domain R with 1, R-module M is called a semi-Baer module if for all divisible R-modules D. We show that finitely generated modules of projective dimension at most 1 are semi-Baer modules and if R is Prüfer or Matlis, then all modules of projective dimension at most 1 are semi-Baer modules.
A permutability problem in infinite groups and Ramsey's theorem
Authors: Abdollahi Alireza , Hassanabadi Aliakbar Mohammadi
Published: April 2009

We use Ramsey's theorem to generalise a result of L. Babai and T.S. Sós on Sidon subsets and then use this to prove that for an integer n > 1 the class of groups in which every infinite subset contains a rewritable n-subset coincides with the class of groups in which ever infinite subset contains n mutually disjoint non-empty subsets X1,…,Xn such that X1…Xn∩Xσ(1) …xσ(n) ≠ θ for some non-identity permutation σ on the set {1,…,n}.
A 3-space problem related to the fixed point property
Authors: Fetter Helga , de Buen Berta Gamboa
Published: April 2009

We study some properties which imply weak normal structure and thus the fixed point property. We investigate whether the latter two properties are inherited by spaces obtained by direct sum with a finite dimensional space. We exhibit a space X which satisfies Opial's condition, X ⊕ ℝ does not have weak normal structure but X ⊕ ℝ has the fixed point property.
Blocks of homogeneous effect algebras
Authors: Jenča Gejza
Published: April 2009

Effect algebras, introduced by Foulis and Bennett in 1994, are partial algebras which generalise some well known classes of algebraic structures (for example orthomodular lattices, MV algebras, orthoalgebras et cetera). In the present paper, we introduce a new class of effect algebras, calledhomogeneous effect algebras. This class includes orthoalgebras, lattice ordered effect algebras and effect algebras satisfying the Riesz decomposition property. We prove that every homogeneous effect algebra is a union of its blocks, which we define as maximal sub-effect algebras satisfying the Riesz decomposition property. This generalizes a recent result by Riec˘anová, in which lattice ordered effect algebras were considered. Moreover, the notion of a block of a homogeneous effect algebra is a generalisation of the notion of a block of an orthoalgebra. We prove that the set of all sharp elements in a homogeneous effect algebraEforms an orthoalgebraEs. Every block ofEsis the centre of a block ofE. The set of all sharp elements in the compatibility centre ofEcoincides with the centre ofE. Finally, we present some examples of homogeneous effect algebras and we prove that for a Hilbert space ℍ with dim (ℍ) > 1, the standard effect algebra ℰ(ℍ) of all effects in ℰ is not homogeneous.
An exponential diophantine equation
Authors: Le Maohua
Published: April 2009

Let p be an odd prime with p > 3. In this paper we give all positive integer solutions (x, y, m, n) of the equation x2 + p2m = yn, gcd (x, y) = 1, n > 2 satisfying 2 | n of 2 ∤ n and p ≢ (−1)(p−1)/2(mod 4n.
Inverse semigroup homomorphisms via partial group actions
Authors: Steinberg Benjamin
Published: April 2009

This papar constructs all homomorphisms of inverse semigroups which factor through anE-unitary inverse semigroup; the construction is in terms of a semilattice component and a group component. It is shown that such homomorphisms have a unique factorisation βα with α preserving the maximal group image, β idempotent separating, and the domainIof βE-unitary; moreover, theP-representation ofIis explicitly constructed. This theory, in particular, applies whenever the domain or codomain of a homomorphism isE-unitary. Stronger results are obtained for the case ofF-inverse monoids.

Special cases of our results include theP-theorem and the factorisation theorem for homomorphisms fromE-unitary inverse semigroups (via idempotent pure followed by idempotent separating). We also deduce a criterion of McAlister–Reilly for the existence ofE-unitary covers over a group, as well as a generalisation toF-inverse covers, allowing a quick proof that every inverse monoid has anF-inverse cover.
Convolution kernels of (n + 1)-fold Marcinkiewicz multipliers on the Heisenberg group
Authors: Fraser A. J.
Published: April 2009

We prove a characterisation, in terms of regularity and cancellation conditions, of the convolution kernels of Marcinkiewicz multiplier operators m (𝔏1,…,𝔏n, iT) on the Heisenberg group ℍn, where 𝔏1,…,𝔏n are the n partial sub-Laplacians. The necessity of these regularity and cancellation conditions was established by Fraser (2001); here, we prove their sufficiency.
On adequate links and homogeneous links
Authors: Lee Sang Youl , Park Chan-Young , Seo Myoungsoo
Published: April 2009

In this paper, we give several inequalities concerning the genus and the degree of the Jones Polynomial of an adequate link and of a homogeneous link and their applications.
Maximal compact subgroups and the centre in an analytic group
Authors: Previts W. H. , Wu T. S.
Published: April 2009

In this paper we study the centre of a simply connected analytic group. We present two structure theorems on the centres of such groups. We also study maximal tori and maximal compact subgroups of an analytic group, and as a result, we extend a theorem by Goto.
Towards the fixed point property for superreflexive spaces
Authors: Wiśnicki Andrzej
Published: April 2009

A Banach space X is said to have property (Sm) if every metrically convex set A ⊂ X which lies on the unit sphere and has diameter not greater than one can be (weakly) separated from zero by a functional. We show that this geometrical condition is closely connected with the fixed point property for nonexpansive mappings in superreflexive spaces.
Sylow permutable subnormal subgroups of finite groups II
Authors: Ballester-Bolinches A. , Esteban-Romero R.
Published: April 2009

In this paper a local version of Agrawal's theorem about the structure of finite groups in which Sylow permutability is transitive is given. The result is used to obtain new characterisations of this class of finite groups.
On a multidimensional Volkenborn integral and higher order Bernoulli numbers
Authors: Kim Min-Soo , Son Jin-Woo
Published: April 2009

In this paper, using a multidimensional Volkenborn integral, we give ap-adic expression of the higher order Bernoulli numbers. This shows immediately the relation to the sums of products of the ordinary Bernoulli numbers of Dilcher in 1996. We also consider the Mahler expansion of severalp-adic variables function, and give some examples.
Vanishing of the integral of the Hurwitz zeta Function
Authors: Broughan Kevin A.
Published: April 2009

A proof is given that the improper Riemann integral of ζ(s, a) with respect to the real parameter a, taken over the interval (0, 1], vanishes for all complex s with ℜ(s) < 1. The integral does not exist (as a finite real number) when ℜ(s) ≥ 1.
Some weighted estimates for imaginary powers of Laplace operators
Authors: Gunawan Hendra
Published: April 2009

We study the boundedness of singular integral operators that are imaginary powers of the Laplace operator in Rn, especially from weighted Hardy spaces to weighted Lebesgue spaces where 0 < p ≤ 1. In particular, we prove some estimates for these operators when 0 < p ≤ 1 and w is in the Muckenhoupt's class Aq, for some q > 1.
Maximal (k, l)-free sets in ℤ/pℤ are arithmetic progressions
Authors: Plagne Alain
Published: April 2009

Given two different positive integers k and l, a (k, l)-free set of some group (G, +) is defined as a set  ⊂ G such that k∩l = ∅. This paper is devoted to the complete determination of the structure of (k, l)-free sets of ℤ/pℤ (p an odd prime) with maximal cardinality. Except in the case where k = 2 and l = 1 (the so-called sum-free sets), these maximal sets are shown to be arithmetic progressions. This answers affirmatively a conjecture by Bier and Chin which appeared in a recent issue of this Bulletin.
A characterisation of simple groupsPSL(5,q)
Authors: Iranmanesh A. , Alavi S. H.
Published: April 2009

Order components of a finite group are introduced in [4]. We prove that, for everyq,PSL(5,q) can be uniquely determined by its order componets. A main consequence of our result is the validity of Thompson's conjecture for the groups under consideration.
Weakly compact sets and smooth norms in Banach spaces
Authors: Fabian Marián , Montesinos Vicente , Zizler Václav
Published: April 2009

Two smoothness characterisations of weakly compact sets in Banach spaces are given. One that involves pointwise lower semicontinuous norms and one that involves projectional resolutions of identity.
Hausdorff dimension of random fractals with overlaps
Authors: Yu Z. G. , Anh V. V. , Lau K. S.
Published: April 2009

This paper considers random fractals generated by contractive transformations which satisfy a separation condition weaker than the open set condition. This condition allows overlaps in the iterations. Estimates of the Hausdorff dimension of this kind of random fractals are obtained.
Multipliers on weighted function spaces over locally compact vilenkin groups
Authors: Zhu Yueping
Published: April 2009

In this note, we consider multipliers on weighted function spaces over totally disconnected locally compact Abelian groups (Vilenkin groups). First we present an multiplier result. Then we give an multiplier result under a similar condition of Lu-Yang type. In Section 3, we obtain a result about the boundedness of multipliers on weighted Besov spaces.
Parts formulas involving conditional Feynman integrals
Authors: Chang Seung Jun , Skoug David
Published: April 2009

In this paper we first obtain a basic formula for the conditional analytic Feynman integral of the first variation of a functional on Wiener space. We then apply this basic result to obtain several integration by parts formulas for conditional analytic Feynman integrals and conditional Fourier-Feynman transforms.
Fréchet algebras with a Laurent series generator and the annulus algebras
Authors: Bhatt S. J. , Dedania H. V. , Patel S. R.
Published: April 2009

Banach and Fréchet algebras with a Laurent series generator are investigated leading, via the discrete Beurling algebras, to functional analytic characterisations of the holomorphic function algebras on the annulus as well as the C∞-algebra on the unit circle.
On continuity and selections of multifunctions
Authors: Dodos Pandelis
Published: April 2009

The notions of a Baire-1 and a weak Baire-1 multifunction are defined and a striking analogy between Baire-1 multifunctions and classical Baire-1 functions is established. A selection theorem is presented which asserts that if X is a metrisable space, Y a Polish space and F: X → 2Y/{∅} a closed-valued, weak Baire-1 multifunction, then F admits a Baire-1 selection. Using the machinery developed we prove that if X is a Banach space with separable dual, then every weak* usco, defined on a completely metrisable space Z, which values are weakly* compact subsets of the dual, is norm lower semicontinuous on a dense Gδ set.
Extensions of uniformly smooth norms on Banach spaces
Authors: Fry R.
Published: April 2009

We give a characterisation for the extension of uniformly smooth norms from subspaces Y of superreflexive spaces X to uniformly smooth norms on all of X. This characterisation is applied to obtain results in various contexts.
Some remarks on CS modules and SI rings
Authors: Van Huynh Dinh
Published: April 2009

We discuss some results on CS modules, SI rings, and SC rings. Then we consider the question of when, over a right SC ring R, every right R-module is CS. In Theorem 3.1 we show that this is the case if and only if R is a right countably Σ-CS ring. In light of this, we give an example showing that a result proved by Chen (2000) is incorrect. Furthermore, Theorem 4.1 shows that the assumptions of Chen (2000) can be weakened considerably.
Formulae associated with 5, 7, 9 and 11 squares
Authors: Barrucand Pierre , Hirschhorn Michael D.
Published: April 2009

Let rk (n) denote the number of representations of n as the sum of k squares. We give elementary proofs of relations between rk (n) and rk (m) where n = 4λm and 4 ∤ m, when k = 5, 7, 9 and 11. The relations, which were first stated without proof by Stieltjes, are of the form rk (n) = Crk (m) where C depends on λ and on the residue of m modulo 8. They have recently been include by S. Cooper in a more complete description of the relations between rk (n) and rk (n′) where n′ is the squarefree part of n, when k = 5, 7, 9 and 11.
The compositional inverse of a class of permutation polynomials over a finite field
Authors: Coulter Robert S. , Henderson Marie
Published: April 2009

A new class of bilinear permutation polynomials was recently identified. In this note we determine the class of permutation polynomials which represents the functional inverse of the bilinear class.
Some properties of Fatou and Julia sets of transcendental meromorphic functions
Authors: Jian-Hua Zheng , Sheng Wang , Zhi-Gang Huang
Published: April 2009

The radial distribution of Julia sets and non-existence of unbounded Fatou components of transcendental meromorphic functions are investigated in this paper.
Construction of sunny nonexpansive retractions in Banach spaces
Authors: Benavides Tomas Dominguez , Acedo Genaro López , Xu Hong-Kun
Published: April 2009

Let  be a commutative family of nonexpansive self-mappings of a closed convex subset C of a uniformly smooth Banach space X such that the set of common fixed points is nonempty. It is shown that if a certain regularity condition is satisfied, then the sunny nonexpansive retraction from C to F can be constructed in an iterative way.
A note on tensor products of reflexive algebras
Authors: Dong Zhe
Published: April 2009

In this short note, we obtain a concrete description of rank-one operators in Alg(ℒ1 ⊗…⊗ ℒn). Based on this characterisation, we give a simple proof of the tensor product formula:

if Alg(ℒ1 ⊗…⊗ ℒn) is weakly generated by rank-one operators in itself and ℒi(i = 1,…,n) are subspace lattices.
Relation between the Shapley value and null group cohomology
Authors: Madrecki Andrzej
Published: April 2009

The purpose of this paper is to give an application of homological methods to game theory. The main theorems give conditions of a homological nature for the existence and uniqueness of the Shapley value for games with continuum players.
On analytic functions with reference to an integral operator
Authors: Parvatham R. , Shanmugam T.N.
Published: April 2009

Let E = {z: |z| < 1} and let H = {w : regular in E, w(0) = 0, |w(z)| < l, z ∈ E}.

Let P(A, B) denote the class of functions in E which can be put in the form (1 + Aw(z))/(1 + Bw(z)), −1 ≤ A < B ≤ 1, w(z) ∈ H. Let S*(A, B) denote the class of functions f(z) of the form such that zf′(z)/f(z) ∈ P(A, B). If f(z) ∈ S*(A, B) and g(z) ∈ S*(C, D) then, in this paper the radius of starlikeness of order β (β ∈ [0, 1]) of the following integral operator

is determined. Conversely, a sharp estimate is obtained for the radius of starlikeness of the class of functions

where g(z) and F(z) belong to the class S*(A, B).
On two new classes of locally convex spaces
Authors: Kitahara Kazuaki
Published: April 2009

The purpose of this paper is to introduce two new classes of locally convex spaces which contain the classes of semi-Montel and Montel spaces. Further we give some examples and study some properties of these classes. As to permanence properties, these classes have similar properties to semi-Montel and Montel spaces except strict inductive limits and these classes are not always preserved under their completions. We shall call these two classes as β–semi–Montel and β–Montel spaces. A β–semi–Montel space is obtained by replacing the word “bounded” by “strongly bounded” in the definition of a semi–Montel space. If a β–semi–Montel space is infra-barrelled, we call the space β–Montel.
On convex and starlike univalent functions
Authors: Pandey R.K. , Bhargava G.P.
Published: April 2009

In this paper we obtain some classical results by using the general integral operators which transform Jakubowski's class K(m, M) into itself and K(μ) × S(m, M) into K(μ). Our results generalize some recent known results due to Causey and Reade, Patil and Thakare.
On complete reducibility of module bundles
Authors: Prema G. , Kiranagi B.S.
Published: April 2009

We prove the local triviality of module bundles over semisimple Lie algebra bundles and using this result we establish the complete reducibility of module bundles over semisimple Lie algebra bundles.
On approximation in spaces of continuous functions
Authors: Gonska Heinz H.
Published: April 2009

This paper deals with approximation of certain operators defined on the space C(X) of real-valued continuous functions on an arbitrary compact metric space (X, d). In particular the problem of giving quantitative Korovkin type theorems for approximation by positive linear operators is solved. This is achieved by using a smoothing approach and the least concave majorant of the modulus of continuity of a function f in C(X). Several new estimates are given as applications, including such for Shepard's method of metric interpolation.
A translation plane of order 81 and its full collineation group
Authors: Abatangelo Vito
Published: April 2009

In this paper a new translation plane of order 81 is constructed. Its collineation group is solvable and acts on the line at infinity as a permutation group K which is the product of a group of order 5 belonging to the center of K with a group of order 48. A 2-Sylow subgroup of K is the direct product of a dihedral group of order 8 with a group of order 2. K admits six orbits. They have lengths 4, 6, 12, 12, 24, 24.
P-groups with non-abelian automorphism groups and all automorphisms central
Authors: Malone J. J.
Published: April 2009

For each odd prime p this paper gives an example of a non-abelian p-group with a non-abelian automorphism group in which each automorphism is central.
On the Möbius function of Hom(P, Q)
Authors: Speed T.P.
Published: April 2009

A formula is given for the Möbius function of the poset Hom(P, Q) of all order-preserving maps between two finite posets P and Q. Two applications of the formula are presented.
Small subharmonic functions
Authors: Fenton P.C.
Published: April 2009

Some time ago Barry [Proc. London Math. Soc. 12 (1962), 445–495] established the right connection between the smallest and largest values of small subharmonic functions on certain circles about the origin. The behaviour of functions extremal for this connection is investigated.
Analytic mappings with negative coefficients in the unit disc
Authors: Mogra M.L.
Published: April 2009

Let be analytic in the unit disc U(|z| <1) and let F(z) = (l-λ)f (Z) + λ(f(z)*h(z)) where with cn 's are known and are nonnegative, λ ≥ 0 In the present paper, using convolution methods we investigate the mapping properties of F(z) when f(z) belongs respectively to several subclasses of analytic functions with negative coefficients.
The density of subsequences
Authors: Choate David B.
Published: April 2009

Let A = {a1, a2, …} be an increasing sequence of positive integers whose upper density, θ, is less than 1, Then the counting function of the subsequence

does not exceed .
Comparaison resultats pour la stabilité pratique
Authors: Kiventidis Thomas
Published: April 2009

We develop some comparison theorems that connect the solutions of a differential system and its perturbation in a manner useful in the practical stability.
Perfect McLain groups are superperfect
Authors: Berrick A. J. , Downey R. G.
Published: April 2009

It is shown that if a McLain group is perfect, then it is super-perfect. The proof involves demonstrating that any dense linearly ordered set has the apparently stronger property of being superdense.
Universally Incomparable Ring-Homomorphisms
Authors: Dobbs David E. , Fontana Marco
Published: April 2009

A homomorphism f: R → T of (commutative) rings is said to be universally incomparable in case each base change R → S induces an incomparable map S → S⊗RT. The most natural examples of universally incomparable homomorphisms are the integral maps and radiciel maps. It is proved that a homomorphism f: R → T is universally incomparable if and only if f is an incomparable map which induces algebraic field extensions of fibres, k(f-1(Q))→k(Q), for each prime ideal Q of T. In several cases (f algebra-finite, T generated as R-algebra by primitive elements, T an overring of a one-dimensional Noetherian domain R), each universally incomparable map is shown to factor as a composite of an integral map and a special kind of radiciel.
Algebras generated by symmetric idempotents
Authors: Choate David
Published: April 2009

Let F be a field. If A is an F-algebra with involution that is generated (as a space) by symmetric idempotents, then A is a subdirect product of copies of F if and only if every idempotent in A is symmetric.
Automorphism groups of orthomodular lattices
Authors: Kalmbach Gudrun
Published: April 2009

Every group is the automorphism group of an orthomodular lattice.
A Density problem for Hardy spaces of almost periodic functions
Authors: Owens Robyn
Published: April 2009

We construct a counterexample, for p = 1, to the conjecture posed by Milaszevitch in 1970: is the space of functions which are analytic in the upper half plane and uniformly almost periodic in its closure dense in the Hardy space Hp (0 < p ∞) of analytic almost periodic functions?