bluuebunny/crossref_metadata_2025 huggingface dataset:
A note on the circle actions on Einstein manifolds
Authors: Hwang Seungsu
Published: April 2009

A fundamental result in the theory of black holes due to Hawking asserts that the event horizon of a black hole in the stationary space-time is a 2-sphere topologically. In this article we prove the Riemannian analogue of Hawking's result. In other words, we prove that each bolt of a 4-dimensional complete noncompact Einstein manifold of zero scalar curvature admitting a semifree isometric circle action is a 2-sphere topologically. We also study the structure of the orbit space of an Einstein manifold admitting a free isometric circle action.
Restricted weak upper semicontinuous differentials of convex functions
Authors: Benítez Julio , Montesinos Vicente
Published: April 2009

We characterise restricted weak upper semicontinuity of the subdifferential of convex functions in terms of the Fenchel biconjugate mapping.
On (k, l)-sets in cyclic groups of odd prime order
Authors: Bier T. , Chin A. Y. M.
Published: April 2009

Let A be a finite Abelian group written additively. For two positive integers k, l with k ≠ l, we say that a subset S ⊂ A is of type (k, l) or is a (k, l) -set if the equation x1 + x2 + … + xk − xk+1−… − xk+1 = 0 has no solution in the set S. In this paper we determine the largest possible cardinality of a (k, l)-set of the cyclic group ℤP where p is an odd prime. We also determine the number of (k, l)-sets of ℤp which are in arithmetic progression and have maximum cardinality.
Relationships between widths of a convex body and of an inscribed parallelotope
Authors: Lassak Marek
Published: April 2009

Assume that a parallelotope P is inscribed in a three-dimensional convex body C A conjecture says that , where Wi is the ratio of the width of C to the width of P for the direction perpendicular to the i-th pair of parallel facets of P. We prove three weaker inequalities. One of them is , where a3 denotes the related axial diameter of C.
Dynamics for vortex curves of the Ginzburg-Landau equations
Authors: Zuhan Liu
Published: April 2009

We study the asymptotic behaviour of solutions to the evolutionary Ginzburg- Landau equations in three dimensions. We show that the motion of the Ginzburg-Landau vortex curves is the flow by curvature.
An extension of Jensen's form
Authors: Sofo A.
Published: April 2009

Arbitrary order forced difference-delay systems are considered, from which generated infinite sums of Binomial variation may be represented in closed form. It will be proved that the infinite sums may be expressed in a closed form which depends on dominant zeros of the polynomial characteristic functions. A connection between the infinite sum and generalised hypergeometric series will also be demonstrated.
An extension of the Grünwald–Marcinkiewicz interpolation theorem
Authors: Mills T. M. , Vértesi P.
Published: April 2009

Just over 60 years ago, G. Grünwald and J. Marcinkiewicz discovered a divergence phenomenon pertaining to Lagrange interpolation polynomials based on the Chebyshev nodes of the first kind. The main result of the present paper is an extension of their now classical theorem. In particular, we shall show that this divergence phenomenon occurs for odd higher order Hermite–Fejér interpolation polynomials of which Lagrange interpolation polynomials form one special case.
Classifying a family of symmetric graphs
Authors: Zhou Sanming
Published: April 2009

Let Γ be a G-symmetric graph admitting a nontrivial G-invariant partition ℬ of block size υ. For blocks B, C of ℬ adjacent in the quotient graph Γℬ, let k be the number of vertices in B adjacent to at least one vertex in C. In this paper we classify all possibilities for (Γ Γℬ, G) in the case where k = υ − 1 ≥ 2 and ℬ(α) = ℬ(β) for adjacent vertices α β of Γ where for a vertex of Γ, say γ ∈ B, ℬ(γ) denotes the set of blocks C such that γ is the only vertex in B not adjacent to any vertex in C.
Twisted Alexander polynomial for the Braid group
Authors: Morifuji Takayuki
Published: April 2009

In this paper, we study the twisted Alexander polynomial, due to Wada [11], for the Jones representations [6] of Artin's braid group.
A note on Kummer theory of division points over singular Drinfeld modules
Authors: Li Anly
Published: April 2009

In this paper, we shall establish a Kummer theory of division points over singular Drinfeld modules which is in complete analogy with the classical one in number fields.
On admissible distributions attached to convolutions of Hilbert modular forms
Authors: Dabrowski Andrzej
Published: April 2009

Dedicated to Jana

The aim of this note is to check the admissibility property of the distribution attached to convolution of Hilbert modular forms.
The space of p-summable sequences and its natural n-norm
Authors: Gunawan Hendra
Published: April 2009

We study the space lp, 1 ≤ p ≤ ∞, and its natural n-norm, which can viewed as a generalisation of its usual norm. Using a derived norm equivalent to its usual norm, we show that lp is complete with respect to its natural n-norm. In addition, we also prove a fixed point theorem for lp as an n-normed space.
On entire solutions of a certain type of nonlinear differential equation
Authors: Yang Chung-Chun
Published: April 2009

In this note, we shall study, via Nevanlinna's value distribution theory, the uniqueness of transcendental entire solutions of the following type of nonlinear differential equation:
(*) L (f (z)) – p (z) fn(z) = h (z),
where L (f) denotes a linear differential polynomial in f with polynomials as its co-efficients, p (z) a polynomial (≢ 0), h an entire function, and n an integer ≥ 3. We show that if the equation (*) has a finite order transcendental entire solution, then it must be unique, unless L (f) ≡ 0.
Hemivariational inequalities with the potential crossing the first eigenvalue
Authors: Th. Kyritsi Sophia , Papageorgiou Nikolaos S.
Published: April 2009

In this paper we study a nonlinear hemivariational inequality involving the p-Laplacian. Our approach is variational and uses a recent nonsmooth Linking Theorem, due to Kourogenis and Papageorgiou (2000). The use of the Linking Theorem instead of the Mountain Pass Theorem allows us to assume an asymptotic behaviour of the generalised potential function which goes beyond the principal eigenvalue of the negative p-Laplacian with Dirichlet boundary conditions.
On the group of automorphisms of an analytic group
Authors: Previts W. H. , Wu T. S.
Published: April 2009

Let G be an analytic group and let Aut G denote the group of all topological group automorphisms of G. We investigate when Aut G is almost algebraic. We provide various conditions, some of which are known, under which Aut G is almost algebraic. We also provide examples showing that there does not seem to be a clear and concise way to characterise G so that Aut G is almost algebraic in terms of the maximal central torus in G.
Functions invariant under the Bochner–Martinelli integral
Authors: Lee Jaesung
Published: April 2009

We give an elementary proof of the statement that a function f on the closed unit ball of Cn, integrable on the unit sphere, is holomorphic if it is invariant under the Bochner–Martinelli integral transform.
Linear maps on von Neumann algebras preserving zero products on tr-rank
Authors: Jianlian Cui , Jinchuan Hou
Published: April 2009

In this paper, we give some characterisations of homomorphisms on von Neumann algebras by linear preservers. We prove that a bounded linear surjective map from a von Neumann algebra onto another is zero-product preserving if and only if it is a homomorphism multiplied by an invertible element in the centre of the image algebra. By introducing the notion of tr-rank of the elements in finite von Neumann algebras, we show that a unital linear map from a linear subspace ℳ of a finite von Neumann algebra ℛ into ℛ can be extended to an algebraic homomorphism from the subalgebra generated by ℳ into ℛ; and a unital self-adjoint linear map from a finite von Neumann algebra onto itself is completely tr-rank preserving if and only if it is a spatial *-automorphism.
Characterisation of orthogonality in certain Banach spaces
Authors: Saidi Fathi B.
Published: April 2009

In this paper we adopt the notion of orthogonality introduced by the author in a previous article. We establish a characterisation for orthogonality in the spaces , where S is a set of positive integers and C is the field of complex numbers. Generalisations of the usual characterisation of orthogonality in the Hilbert spaces , via inner products, are obtained.
A note on the heat kernel on the Heisenberg group
Authors: Sikora Adam , Zienkiewicz Jacek
Published: April 2009

We describe the analytic continuation of the heat kernel on the Heisenberg group ℍn(ℝ). As a consequence, we show that the convolution kernel corresponding to the Schrödinger operatereisLis a smooth function on ℍn(ℝ) \Ss, whereSs= {(0, 0, ±sk) ∈ ℍn(ℝ) :k=n,n+ 2,n+ 4,…}. At every point ofSsthe convolution kernel ofeisLhas a singularity of Calderón–Zygmund type.
The Kunze–Stein phenomenon on the isometry group of a tree
Authors: Veca Alessandro
Published: April 2009

Let G be the group of isometries of a homogeneous tree . In the first part of this paper we decompose G in terms of certain subgroups N, ℤ, and K to obtain the related integral formula

Then, by using ideas of A. Ionescu and the formula above, we prove that

and that a related maximal operator on  is bounded from L2, 1() to L2,∞(). We finally show that Lp, 1(K\G/K) is a commutative Banach algebra of convolutors for Lp(G) and give an explicit description of its Gelfand spectrum.
Amenability and topological centres of the second duals of Banach algebras
Authors: Ghahramani F. , Laali J.
Published: April 2009

Let  be a Banach algebra and let ** be the second dual algebra of  endowed with the first or the second Arens product. We investigate relations between amenability of ** and Arens regularity of  and the rôle topological centres in amenability of **. We also find conditions under which weak amenability of ** implies weak amenability of .
Restriction of Siegel modular forms to modular curves
Authors: Poor Cris , Yuen David S.
Published: April 2009

We study homomorphisms form the ring of Siegel modular forms of a given degree to the ring of elliptic modular forms for a congruence subgroup. These homomorphisms essentially arise from the restriction of Siegel modular forms to modular curves. These homomorphisms give rise to linear relations among the Fourier coefficients of a Siegel modular form. We use this technique to prove that dim .
Deficiencies of lattices in connected Lie groups
Authors: Hillman Jonathan A.
Published: April 2009

We complete the determination of the groups of positive deficiency which occur as lattices in connected Lie groups. The torsion free groups among them are 3-mainfold groups. We show that any other torsion free 3-manifold group which is such a lattice is the group of an aspherical closed geometric 3-manifold.
On numbers which are differences of two conjugates of an algebraic integer
Authors: Dubickas Artūras
Published: April 2009

We investigate which numbers are expressible as differences of two conjugate algebraic integers. Our first main result shows that a cubic, whose minimal polynomial over the field of rational numbers has the form x3 + px + q, can be written in such a way if p is divisible by 9. We also prove that every root of an integer is a difference of two conjugate algebraic integers, and, more generally, so is every algebraic integer whose minimal polynomial is of the form f (xe) with an integer e ≥ 2.
Completely monotone fading memory relaxation modulii
Authors: Anderssen R. S. , Loy R. J.
Published: April 2009

In linear viscoelasticity, the fundamental model is the Boltzmann caual integral equation

which defines how the stress σ(t) at time t depends on the earlier history of the shear rate via the relaxation modulus (kernel) G (t). Physical reality is achieved by requiring that the form of the relaxation modulus G (t) gives the Boltzmann equation fading memory, so that changes in the distant past have less effect now than the same changes in the more recent past. A popular choice, though others have previously been proposed and investigated, is the assumption that G (t) be a completely monotone function. This assumption has much deeper ramifications than have been identified, discussed or exploited in the rheological literature. The purpose of this paper is to review the key mathematical properties of completely monotone functions, and to illustrate how these properties impact on the theory and application of linear viscoelasticity and polymer dynamics. A more general representation of a completely monotone function, known in the mathematical literature, but not the rheological, is formulated and discussed. This representation is used to derive new rheological relationships. In particular, explicit inversion formulas are derived for the relationships that are obtained when the relaxation spectrum model and a mixing rule are linked through a common relaxation modulus.
On finite loops whose inner mapping groups are Abelian
Authors: Niemenmaa Markku
Published: April 2009

Loops are nonassociative algebras which can be investigated by using their multiplication groups and inner mapping groups If the inner mapping group of a loop is finite and Abelian, then the multiplication group is a solvable group. It is clear that not all finite Abelian groups can occur as inner mapping groups of loops. In this paper we show that certain finite Abelian groups with a special structure are not isomorphic to inner mapping groups of finite loops. We use our results and show how to construct solvable groups which are not isomorphic to multiplication groups of loops.
On tidy subgroups of locally compact totally disconnected groups
Authors: Previts W. H. , Wu T. S.
Published: April 2009

Willis has established a structure theory of locally compact totally disconnected groups. An important feature of this theory is the notion of a tidy subgroup. In this paper we provide several results regarding these subgroups.
The average distance property of classical Banach spaces II
Authors: Hinrichs Aicke , Wenzel Jörg
Published: April 2009

A Banach space X has the average distance property if there exists a unique real number r such that for each positive integer n and all x1,…,xn in the unit sphere of X there is some x in the unit sphere of X such that

We show that lp does not have the average distance property if p > 2. This completes the study of the average distance property for lp spaces.
Two hyperbolic Schwarz lemmas
Authors: Bernal-González L. , Calderón-Moreno M. C.
Published: April 2009

In this paper, a sharp version of the Schwarz–Pick Lemma for hyperbolic derivatives is provided for holomorphic selfmappings on the unit disk with fixed multiplicity for the zero at the origin. This extends a recent result due to Beardon. A property of preserving hyperbolic distances also studied by Beardon is here completely characterised.
A new minimax theorem and a perturbed James's theorem
Authors: Galán M. Ruiz , Simons S.
Published: April 2009

The main result of this paper is a sufficient condition for the minimax relation to hold for the canonical bilinear form on X × Y, where X is a nonempty convex subset of a real locally convex space and Y is a nonempty convex subset of its dual. Using the known “converse minimax theorem”, this result leads easily to a nonlinear generalisation of James's (“sup”) theorem. We give a brief discussion of the connections with the “sup-limsup theorem” and, in the appendix to the paper, we give a simple, direct proof (using Goldstine's theorem) of the converse minimax theorem referred to above, valid for the special case of a normed space.
Applications of the Gauge-invariant uniqueness theorem for graph algebras
Authors: Bates Teresa
Published: April 2009

We give applications of the gauge-invariant uniqueness theorem, which states that the Cuntz-Krieger algebras of directed graphs are characterised by the existence of a canonical action of . We classify theC*-algebras of higher order graphs, identify theC*-algebras of cartesian product graphs with a certain fixed point algebra and investigate a relation called elementary shift equivalence on graphs and its effect on the associated graphC*-algebras.
Order structure on certain classes of ideals in group algebras and amenability
Authors: Takahashi Yuji
Published: April 2009

LetGbe a separable, locally compact group and let d(G) be the set of all closed left ideals inL1(G) which have the formJμ= {f−f∗ μ:f∈L1(G)}−for some discrete probability measure μ. It is shown that if d(G) has a unique maximal element with respect to the order structure by set inclusion, thenGis amenable. This answers a problem of G.A. Willis. We also examine cardinal numbers of the sets of maximal elements in d(G) for nonamenable groups.
Weighted estimates for fractional maximal functions related to spherical means
Authors: Cowling Michael , García-Cuerva José , Gunawan Hendra
Published: April 2009

We prove weighted Lp-Lq estimates for the maximal operators ℳα, given by , where μt denotes the normalised surface measure on the sphere of centre 0 and radius t in Rd. The techniques used involve interpolation and the Mellin transform. To do this, we also prove weighted Lp-Lq estimates for the operators of convolution with the kernels |·|−α−iη.
Positive solutions of fourth-order superlinear singular boundary value problems
Authors: Shi Guoliang , Chen Shaozhu
Published: April 2009

This paper investigates fourth-order superlinear singular two-point boundary value problems and obtains necessary and sufficient conditions for existence ofC2orC3positive solutions on the closed interval.
H-joint numerical ranges
Authors: Li Chi-Kwong , Rodman Leiba
Published: April 2009

The notion of the joint numerical range of several linear operators with respect to a sesquilinear form is introduced. Geometrical properties of the joint numerical range are studied, in particular, convexity and angle points, in connection with the algebraic properties of the operators. The main focus is on the finite dimensional case.
Maximum average distance in complex finite dimensional normed spaces
Authors: García-Vázquez Juan C. , Villa Rafael
Published: April 2009

A number r > 0 is called a rendezvous number for a metric space (M, d) if for any n ∈ ℕ and any x1,…xn ∈ M, there exists x ∈ M such that . A rendezvous number for a normed space X is a rendezvous number for its unit sphere. A surprising theorem due to O. Gross states that every finite dimensional normed space has one and only one average number, denoted by r (X). In a recent paper, A. Hinrichs solves a conjecture raised by R. Wolf. He proves that for any n-dimensional real normed space. In this paper, we prove the analogous inequality in the complex case for n ≥ 3.
Hardy's uncertainty principle on hyperbolic spaces
Authors: Andersen Nils Byrial
Published: April 2009

Hardy's uncertainty principle states that it is impossible for a function and its Fourier transform to be simultaneously very rapidly decreasing. In this paper we prove versions of this principle for the Jacobi transform and for the Fourier transform on real hyperbolic spaces.
Closed structures on the category of topological spaces determined by systems of filters
Authors: Pedicchio Maria Cristina
Published: April 2009

We give a characterization of monoidal closed structures, “determined by systems of filters” on the category of topological spaces and continuous maps. The method we use to introduce suitable topologies on the product set X × Y of spaces X and Y, and on the set of all continuous maps from X to Y, is essentially that of Wilker.
On Banach spaces of vector valued continuous functions
Authors: Cembranos Pilar
Published: April 2009

LetKbe a compact Hausdorff space and letEbe a Banach space. We denote byC(K, E) the Banach space of allE-valued continuous functions defined onK, endowed with the supremum norm.

Recently, Talagrand [Israel J. Math.44(1983), 317–321] constructed a Banach spaceEhaving the Dunford-Pettis property such thatC([0, 1],E) fails to have the Dunford-Pettis property. So he answered negatively a question which was posed some years ago.

We prove in this paper that for a large class of compactsK(the scattered compacts),C(K, E) has either the Dunford-Pettis property, or the reciprocal Dunford-Pettis property, or the Dieudonné property, or propertyVif and only ifEhas the same property.

Also some properties of the operators defined onC(K, E) are studied.
Set mappings of unrestricted order
Authors: Gibbon Greg G.
Published: April 2009

A set mapping on a set S is a function f mapping S into the powerset of S such that x ∉ f(x) for each x in S. The set map f has order θ if θ is the least cardinal such that |f(x)| < θ for each x in S. A subset H of S is free for f if x ∉ f(y) for all x, y in H. In this paper we use classical results about set mappings of large order to investigate conditions which ensure a large free set for set mappings of unrestricted order.
The Dirichlet problem for the equation of prescribed Gauss curvature
Authors: Trudinger Neil S. , Urbas John I.E.
Published: April 2009

We treat necessary and sufficient conditions for the classical solvability of the Dirichlet problem for the equation of prescribed Gauss curvature in uniformly convex domains in Euclidean n space. Our methods simultaneously embrace more general equations of Monge-Ampère type and we establish conditions which ensure that solutions have globally bounded second derivatives.
Varieties with modular subalgebra lattices
Authors: Evans Trevor , Ganter Bernhard
Published: April 2009

A classification is begun of varieties of algebras with the property that each algebra in the variety has a modular lattice of subalgebras. This turns out to be a very restrictive condition. Such a variety is hamiltonian. If the algebras in it are idempotent, then it is a variety of sets. A variety is subalgebra-modular if and only if it is hamiltonian and satisfies certain conditions on the terms in its three generator free algebras.
Twills with bounded float length
Authors: Hoskins Janet A. , Praeger Cheryl E. , Street Anne Penfold
Published: April 2009

The simple twills on n harnesses can be classified according to their maximum float length. The number of n-harness twills with specified maximum float length is determined both by Burnside enumeration and, for n ≤ 20 , by an adaptation of a sieve algorithm for twills.
A note on complete hypersurfaces of non-positive Ricci curvature
Authors: Smith G.H.
Published: April 2009

In this note we point out that a recent result of Leung concerning hypersurfaces of a Euclidean space has a simple generalisation to hypersurfaces of complete simply-connected Riemannian manifolds of non-positive constant sectional curvature.
Finite simple groups and finite primitive permutation groups
Authors: Praeger Cheryl E.
Published: April 2009

The classification of the finite simple groups has had far-reaching consequences for many branches of algebra. This paper is a discussion of several problems about primitive permutation groups which have been solved using the simple group classification.
Existence of solutions of Oseen type integral equations
Authors: Belward J.A.
Published: April 2009

Integral equations of Oseen type are first kind Fredholm equations whose kernels have a logarithmic singularity. They arise in exterior boundary value problems in fluid flow and heat transfer. Subject to the assumption of uniqueness of solutions of the parent exterior boundary value problem, solutions of the Oseen type integral equations are shown to exist.
Stability of functional differential equations of Volterra type
Authors: Rao M. Rama Mohana , Srinivas P.
Published: April 2009

The Liapunov-Razumikhin technique has been employed to study Lp stability properties of solutions of functional differential equations of delay type where the delay becomes unbounded as t ↠ +∞. These results have been applied to investigate sufficient conditions for L2-stability of Volterra integro-differentlal equations.
Coloring island maps
Authors: Jackson Brad , Ringel Gerhard
Published: April 2009

An empire map is a map where the set of countries is divided into disjoint subsets which we call empires. If one empire consists of a single country then the remaining map is called an empire island map, the single country being referred to as the ocean. If every empire consists of at most M countries then it is called an M-pire map.

It is proved that an M-pire map is colorable by 6M – 2 colors. Further there exists such a map which has 6M – 2 mutually adjacent empires.

If an M-pire island map has every country adjacent to the ocean, then it is colorable in 4M colors. Such a map exists with 4M mutually adjacent empires where every country is adjacent to the ocean.
HNN-extensions of algebras and applications
Authors: Mez Hans-Christian
Published: April 2009

The classic HNN-embedding theorem for groups does not transfer to associative rings or algebras. In its first part this paper presents constructions which provide such a theorem if an additional condition is put on the isomorphic subalgebras or if one restricts to algebras over fields and drops the associativity. The main part of the paper deals with applications of these results. For example, it is known that every existentially closed group is ω-homogeneous. It is shown that the corresponding is false for existentially closed associative Δ-algebras but true for existentially universal nonassociative K-algebras. Further-more, orthogonal sequences of idempotents in existentially closed associative Δ-algebras over a regular ring Δ are investigated. It is shown that the conjugacy class of such a sequence depends only on a corresponding order sequence. In particular, in every existentially closed K-algebra all idempotents different from 0 and 1 are conjugated.
Monotone method and periodic solution of non linear parabolic boundary value problem for systems
Authors: Devasahayam M. Paul
Published: April 2009

A system of parabolic equations is considered: Lui = uit − uix = fi (x, t, u, uix) on Q, Biui(j, t) = ωij(t), t ∈ (−∞, ∞), j = 0, 1, i = 1, 2, …, n, where Bi is one of the boundary operators Biui = ui or Biui = ∂ui/∂v + βi(x, t)ui, x = 0, 1, Ω = (0, 1), Q = Ω × R, u(=(u1, …, un)): Q → Rn, v(x) is the outward normal to the boundary ∂Ω, f, u, ω0, ω1 are n-valued functions and f, ω0, ω1 are periodic in t with period T and Bi is a positive function.

The paper is classified into two parts. The first part deals with the existence and uniqueness of periodic solutions of the above system of parabolic equations. The second part deals with a monotone iterative method which develops a monotone iterative scheme for the solution of the above system of equations. In this paper we establish the existence of coupled quasi-solutions of the above equation. Also we give a monotone iterative scheme for the construction of such a solution.
Locally uniformly rotund renorming and decompositions of Banach spaces
Authors: Zizler V.
Published: April 2009

A norm |·| of a Banach space x is called locally uniformly rotund if lim|xn−x| = 0 whenever xn, x ∈ X, and . It is shown that such an equivalent norm exists on every Banach space x which possesses a projectional resolution {pα} of the identify operator, for which all (pα+1−pα)X admit such norms. This applies, for example, for the dual space of a space with Fréchet differentiable norm.
The finite difference versus the finite element method for the solution of boundary value problems
Authors: Thomée Vidar
Published: April 2009

In this lecture we describe, discuss and compare the two classes of methods most commonly used for the numerical solution of boundary value problems for partial differential equations, namely, the finite difference method and the finite element method. For both of these methods an extensive development of mathematical error analysis has taken place but individual numerical analysts often express strong prejudices in favor of one of them. Our purpose is to try to convey our conviction that this attitude is both historically unjustified and inhibiting, and that familiarity with both methods provides a wider range of techniques for constructing and analyzing discretization schemes.
Free products of locally indicable groups with a single relator
Authors: Baumslag Benjamin
Published: April 2009

The method of proof of Magnus introduced in 1930 is adapted to prove the following theorem of Howie. If A and B are groups for which every finitely generated subgroup has an infinite cyclic image, and if one adds an additional relation (with obvious exceptions), then in the resultant group both A and B appear isomorphically.
Decompositions of graphs of modules over semisimple rings
Authors: Orzech Grace
Published: April 2009

In this paper we show that an R-module graph over a semisimple ring R can be written as a direct sum of graphic submodules that are uniquely determined up to isomorphism type. Moreover, this decomposition enables us to describe the R-module graph in graphic terms as a disjoint union of connected components, each of which consists of a complete directed graph on its vertices together with a set of loops at each vertex, determined by the loops at 0. We also give a graphic version of Maschke's Theorem.
Complex blow-up in Burgers' equation: an iterative approach
Authors: Joshi Nalini , Petersen Johannes A.
Published: April 2009

We show that for a given holomorphic noncharacteristic surface S ∈ ℂ2, and a given holomorphic function on S1 there exists a unique meromorphic solution of Burgers' equation which blows up on S. This proves the convergence of the formal Laurent series expansion found by the Painlevé test. The method used is an adaptation of Nirenberg's iterative proof of the abstract Cauchy-Kowalevski theorem.
Polygonal products of polycyclic by finite groups
Authors: Allenby R.B.J.T.
Published: April 2009

We prove that a polygonal product of polycyclic by finite groups amalgamating normal subgroups, with trivial mutual intersections, is cyclic subgroup separable. Because of a recent example (stated below) of the author this substantial improvement on a recent theorem of Kim is essentially best possible.
On the coercivity of elliptic systems in two dimensional spaces
Authors: Zhang Kewei
Published: April 2009

We establish necessary conditions for quadratic forms corresponding to strongly elliptic systems in divergence form to have various coercivity properties in a smooth domain in ℝ2. We prove that if the quadratic form has some coercivity property, then certain types of BMO seminorms of the coefficients of the system cannot be very large. We use the connection between Jacobians and Hardy spaces and the special structures of elliptic quadratic forms defined on 2 X 2 matrices.
Existence theorems for vector variational inequalities
Authors: Daniilidis Aris , Hadjisavvas Nicolas
Published: April 2009

Given two real Banach spaces X and Y, a closed convex subset K in X, a cone with nonempty interior C in Y and a multivalued operator from K to 2L(x, y), we prove theorems concerning the existence of solutions for the corresponding vector variational inequality problem, that is the existence of some x0 ∈ K such that for every x ∈ K we have A(x − x0) ∉ − int C for some A ∈ Tx0. These results correct previously published ones.
On the growth of fundamental groups of nonpositive curvature manifolds
Authors: Yang Yi-Hu
Published: April 2009

Milnor's classic result that the fundamental group of a compact Riemannian manifold of negative sectional curvature has exponential growth is generalised to the case of negative Ricci curvature and non-positive sectional curvature.
On the ring of locally bounded Nash meromorphic functions
Authors: Kucharz Wojciech , Rusek Kamil
Published: April 2009

We show that the ring of locally bounded Nash meromorphic functions on a connected d-dimensional Nash submanifold of ℝn is a Prüfer domain and every finitely generated ideal in this ring can be generated by d + 1 elements.

Moreover, every finitely generated ideal can be generated by d elements if and only if the Nash manifold is noncompact.
An invariant subspace theorem on subdecomposable operators
Authors: Liu Mingxue
Published: April 2009

H. Mohebi and M. Radjabalipour raised a conjecture on the invariant subspace problem in 1994. In this paper, we prove the conjecture under an additional condition, and obtain an invariant subspace theorem on subdecomposable operators.
Quasi-Baer ring extensions and biregrular rings
Authors: Birkenmeier Gary F. , Kim Jin Yong , Park Jae Keol
Published: April 2009

A ringRwith unity is called a (quasi-) Baer ring if the left annihilator of every (left ideal) nonempty subset ofRis generated (as a left ideal) by an idempotent. Armendariz has shown that ifRis a reduced PI-ring whose centre is Baer, thenRis Baer. We generalise his result by considering the broader question: when does the (quasi-) Baer condition extend to a ring from a subring? Also it is well known that a regular ring is Baer if and only if its lattice of principal right ideals is complete. Analogously, we prove that a biregular ring is quasi-Baer if and only if its lattice of principal ideals is complete.
Marcinkiewicz multipliers on the Heisenberg group
Authors: Veneruso Alessandro
Published: April 2009

Let Hn be the Heisenberg group of dimension 2n + 1. Let ℒ1,…,ℒn be the partial sub-Laplacians on Hn and T the central element of the Lie algebra of Hn. We prove that the operator m (ℒ1,…,ℒn,−iT) is bounded on Lp (Hn), 1 < p < +∞, if the function m satisfies a Marcinkiewicz-type condition in Rn+1.
Decomposition of the Steinberg group over local rings into involutions
Authors: Nan Ji Zhu
Published: April 2009

We consider the stable Steinberg group St (R) over local rings. An element x is called an involution if x2 = 1. We prove that every element δ in St (R) is the product of at most 5 involutions.
Sequential completeness of quotient groups
Authors: Dikranjan Dikran , Tkačenko Michael
Published: April 2009

We discuss various generalisations of countable compactness for topological groups that are related to completeness. The sequentially complete groups form a class closed with respect to taking direct products and closed subgroups. Surprisingly, the stronger version of sequential completeness calledsequential h-completeness(all continuous homomorphic images are sequentially complete) implies pseudocompactness in the presence of good algebraic properties such as nilpotency. We also study quotients of sequentially complete groups and find several classes ofsequentially q-completegroups (all quotients are sequentially complete). Finally, we show that the pseudocompact sequentially complete groups are far from being sequentiallyq-complete in the following sense: every pseudocompact Abelian group is a quotient of a pseudocompact Abelian sequentially complete group.
Formations, bihomorphisms and natural transformations
Authors: Ensor Andrew
Published: April 2009

Given a variety ν and ν-algebras A and B, an algebraic formationF: A ⇉ B is a ν-homomorphism FL R × A → B, for some ν-algebra R, and the resulting functions F (r,-): A → B for r ∈ R are termed formable. Firstly, as motivation for the study of algebraic formations, categorical formations and their relationship with natural transformations are explained. Then, formations and formable functions are described for some common varieties of algebras, including semilattices, lattices, groups, and implication algebras. Some of their general properties are investigated for congruence modular varieties, including the description of a uniform congruence which provides information on the structure of B.
On an diophantine equation
Authors: Luca Florian
Published: April 2009

In this note, we find all solutions of the diophatine equation x2 + 3m = yn, where (x, y, m, n) are non-negative integers with x ≠ 0 and n ≥ 3.
Verifying the independence of partitions of a probability space
Authors: Mulay S. B. , Wagner C. G.
Published: April 2009

Let {E1, … Er} and {F1, … Fs} be partitions of a probability space. We exhibit a natural bijection from the set of efficient ways of verifying the independence of such partitions to the set of spanning trees of the complete bipartite graph Kr, s.
A degree one Borsuk-Ulam theorem
Authors: Calegari Danny
Published: April 2009

We generalise the Borsuk-Ulam theorem for maps Mn → ℝn.

Everyone knows the Borsuk-Ulam theorem as a simple application of some of the first ideas one encounters in algebraic topology.
A formula for the Euler characteristic of line singularities on singular spaces
Authors: Jiang Guangfeng
Published: April 2009

We prove an algebraic formula for the Euler characteristic of the Milnor fibres of functions with critical locus a smooth curve on a space which is a weighted homogeneous complete intersection with isolated singularity.
Poisson transforms and mixed automorphic forms on semisimple Lie groups
Authors: Lee Min Ho , Myung Hyo Chul
Published: April 2009

We discuss Poisson transforms which carry sections of certain vector bundles to mixed automorphic forms, and identify vector bundles whose sections are liftings of holomorphic forms on families of Abelian varieties via Poisson transforms.
Smoothing the domain out for positive solutions
Authors: Liu Yaping
Published: April 2009

For a given nonlinear partial differential equation defined on a bounded domain with irregular boundary, the available analytical tools are very limited in relation to the study of positive solutions. In this paper wer first use weak convergence methods to show that for an elliptic equation of a certain type, classical positive solutions on nearby smooth domains approach a generalised positive solution on the given domain. The idea is then applied to sublinear elliptic problems to obtain existence and uniqueness results.
On zeta functions associated with polynomials
Authors: Dąbrowski Andrzej
Published: April 2009

We give direct proofs of meromorphic continuality on the whole complex plane of certain zeta functions ZP, Q (s) and Z (P/Q, s) associated with a pair of polynomials P, Q. We calculate ZP, Q (−q) (q a non-negative integer) and give explicit formulas for the residues of Z (P/Q, s) at poles.
On ω–limit sets of autonomous systems in infinite dimensional Banach spaces
Authors: Herzog Gerd
Published: April 2009

We prove that each Polish space is homeomorphic to the ω–limit set of a bounded solution of an autonomous equationx′ =f(x) inl2×c0, in whichfis Lipschitz continuous on bounded sets.
On some theorems of Tarafdar
Authors: Husain S.A. , Sehgal V.M.
Published: April 2009

In a recent paper (Bull. Austral. Math. Soc. 13 (1975), 241–245), Tarafdar has considered nonexpansive self mappings on a subset X of a locally convex vector space E and proved an extension to E of a theorem of Göhde. The purpose of this paper is to show that the condition f: X → X, in Göhde-Tarafdar's Theorem in the above paper, may be weakened to f: X → E with f(∂X) ⊆ X. As a consequence, it is further shown that an extension to E of a well-known common fixed point theorem of Belluce and Kirk due to Tarafdar remains true on domains that are not necessarily bounded or quasi-complete.
Solid convergence structure equals pseudotopology
Authors: Wyler Oswald
Published: April 2009

A new brief proof of the fact stated in the title is presented.
A note on Fritz John sufficiency
Authors: Borwein J.M.
Published: April 2009

An elementary proof is given of a sufficient optimality condition recently proven by B.D. Craven. This proof avoids the use of a transposition theorem and this allows for a strengthening of Craven's result.
Boundary-value problems for weakly nonlinear ordinary differential equations
Authors: Dancer E.N.
Published: April 2009

In this paper, we announce results on the Dirichlet and periodic boundary-value problems for the equation-x″(t) =g(x(t)) –f(t) on [0, π]. We consider degenerate cases not covered by the author's earlier work.
On the condition number of certain Rayleigh-Ritz-Galerkin matrices
Authors: Omodei Bernard J.
Published: April 2009

Martin H. Schultz [Bull. Amer. Math. Soc. 76 (1970), 840–844] has investigated the spectral condition number of the Rayleigh-Ritz-Galerkin matrices that arise when normalized B-spline coordinate functions are used to approximate the solution of a class of linear, self-adjoint, elliptic boundary value problems in one dimension. This paper shows how results analogous to those of Schultz [op. cit.] can be established under weaker assumptions. We also extend the results to boundary value problems in higher dimensions.
Some functors arising from the consideration of torsion theories over noncommutative rings
Authors: Golan Jonathan S.
Published: April 2009

To each associative (but not necessarily commutative) ringRwe assign the complete distributive latticeR-tors of (hereditary) torsion theories overR-mod. We consider two ways of making this process functorial – once contravariantly and once covariantly – by selecting appropriate subcategories of the category of associative rings. Combined with a functor due to Rota, this gives us functors from these subcategories to the category of commutative rings.
The category of uniform convergence spaces is cartesian closed
Authors: Lee R.S.
Published: April 2009

This paper first assigns specific uniform convergence structures to the products and function spaces of pairs of uniform convergence spaces, and then establishes a bijection between corresponding sets of morphisms which yields cartesian closedness.
Certain classes of univalent functions with negative coefficients II
Authors: Gupta V.P. , Jain P.K.
Published: April 2009

Let P*(α, β) denote the class of functions

analytic and univalent in |z| < 1 for which

where α є [0, 1), β є (0, 1].

Sharp results concerning coefficients, distortion theorem and radius of convexity for the class P*(α, β) are determined. A comparable theorem for the classes C*(α, β) and P*(α, β) is also obtained. Furthermore, it is shown that the class P*(α, ß) is closed under ‘arithmetic mean’ and ‘convex linear combinations’.
A computer aided study of a group defined by fourth powers: Addendum
Authors: Newman M.F.
Published: April 2009

The fact that the group studied in the original paper, M.F. Newman, Bull. Austral. Math. Soc. 14 (1976), 293–297, is infinite follows immediately from a result in a 1940 paper of Coxeter. The computer aided methods give more detailed information about the group and some related groups.
Arithmetic properties of certain functions in several variables III
Authors: Loxton J.H. , van der Poorten A.J.
Published: April 2009

We obtain a general transcendence theorem for the solutions of a certain type of functional equation. A particular and striking consequence of the general result is that, for any irrational number w, the function

takes transcendental values at all algebraic points α with 0 < |α| < 1.
A classification of groups with a centralizer condition II
Authors: Arad Zvi , Herzog Marcel
Published: April 2009

Let G be a finite group. A nontrivial proper subgroup M of G is called a CC-subgpoup if M contains the centralizer in G of each of its nonidentity elements. In this paper groups containing a CC-subgroup of order divisible by 3 are completely determined.
On the optimal control of a manufacturing firm
Authors: Teo K.L. , Lin G.C.I. , Yeo L.T.
Published: April 2009

Various existing models of the optimal control of production rates of manufacturing firms are discussed. A new model is derived by considering the combined effects of: the inventory level of the firm, the shipment sent from the firm, the shipment rate, the Orders received by the firm, the demand rate, the rate of change of the demand rate, the production rate, the advertising expenditure, and the level of unfilled Orders. Further, a new version of shortage cost is introduced. The well-known Pontryagin maximum principle and transversality condition are used to obtain the optimal production rate and the optimal advertising expenditure. A numerical example is given for Illustration.
On a conjecture of Mahler
Authors: Dumir V.C. , Hans-Gill R.J.
Published: April 2009

Let R be the field of real numbers. For α in R, let ‖α‖ be the distance of α from the nearest integer. The following conjecture of Kurt Mahler [Bull. Austral. Math. Soc. 14 (1976), 463–465] is proved.

Let m, n be two positive integers n ≥ 2m. Let S be a finite or infinite set of positive integers with the following properties:

(Q1) S contains the integers m, m+1, …, n−m;

(Q2) every element of S satisfies

Then
On the largest Hausdorff compactification of a Hausdorff convergence space
Authors: Vinod-Kumar
Published: April 2009

For a Hausdorff convergence space, necessary and sufficient conditions for its Richardson compactification to be the largest Hausdorff compactification are found and by modifying the convergence structure of the Richardson compactification, it is shown that the largest Hausdorff compactification, whenever it exists, is given by that modified Richardson compactification.
Invariant means and fixed point properties on completely regular spaces
Authors: Grossman Marvin W.
Published: April 2009

Two theorems are presented which characterize the existence of multiplicative left invariant means on a given algebra of unbounded continuous functions on a topological semigroup S in terms of certain common fixed point properties of actions of S on completely regular spaces. Also a lattice formulation of a related result of Theodore Mitchell for the case of bounded functions is shown to be equivalent to a certain common fixed point property on Bauer simplexes.
A remark on elementary abelian groups
Authors: Hickman J.L.
Published: April 2009

Dr M.F. Newman has asked whether in the absence of the Axiom of Choice it is possible to have two non-isomorphic elementary abelian groups of the same (finite) exponent and of the same (infinite) cardinality. By means of an example, I show that this is in fact possible, if the exponent is at least five; I do not know the answer in the remaining two cases. The example given requires the construction of a Fraenkel-Mostowski model of set theory, and for this purpose I draw upon the terminology, constructions, and results contained in the first two sections of a previous paper, “The construction of groups in models of set theory that fail the Axiom of Choice” (Bull. Austral. Math. Soc. 14 (1976), 199–232), with which I assume familiarity.
A non-homology boundary link with zero Alexander polynomial
Authors: Hillman Jonathan A.
Published: April 2009

This paper presents a necessary condition for a ribbon link to be an homology boundary link and gives a consequent simple counterexample to the conjecture of Smythe that the vanishing of the first Alexander polynomial characterizes homology boundary links among all 2-component links.
Multiplication operators and composition operators with closed ranges
Authors: Singh R.K. , Kumar Ashok
Published: April 2009

The characterizations of the closed ranges of the multiplication operators and the composition operators on L2 (λ) are reported in this paper.
The intersection of a continuum of open dense sets
Authors: Broughan Kevin A.
Published: April 2009

It is proved that every metrizable topological space without isolated points is the union of a continuum or fewer nowhere dense subsets.
A result on tournaments with an application to counting
Authors: Eplett W.J.R.
Published: April 2009

A generating function is derived for the number of transitions to the first passage through a particular vertex of a random walk on a doubly regular tournament. As an application of this result, we obtain a generating function for the number of solutions (q1, …,qk) ofqi≡r(modp), wherepis a prime of the form 4l+ 3 and theqiare quadratic residues modulop.