bluuebunny/crossref_metadata_2025 huggingface dataset:
Lagrangean conditions and quasiduality
Authors: Craven B.D.
Published: April 2009

For a constrained minimization problem with cone constraints, lagrangean necessary conditions for a minimum are well known, but are subject to certain hypotheses concerning cones. These hypotheses are now substantially weakened, but a counter example shows that they cannot be omitted altogether. The theorem extends to minimization in a partially ordered vector space, and to a weaker kind of critical point (a quasimin) than a local minimum. Such critical points are related to Kuhn-Tucker conditions, assuming a constraint qualification; in certain circumstances, relevant to optimal control, such a critical point must be a minimum. Using these generalized critical points, a theorem analogous to duality is proved, but neither assuming convexity, nor implying weak duality.
On circulant codes with prescribed distances
Authors: Deza M. , Eades Peter
Published: April 2009

Necessary and sufficient conditions are given for a square matrix to te the matrix of distances of a circulant code. These conditions are used to obtain some inequalities for cyclic difference sets, and a necessary condition for the existence of circulant weighing matrices.
On vector spaces of certain modular forms of given weights
Authors: Aggarwal A.R. , Agrawal M.K.
Published: April 2009

Let p be a rational prime and Qp be the field of p–adic numbers. Jean-Pierre Serre [Lecture Notes in Mathematics, 350, 191–268 (1973)] had defined p–adic modular forms as the limits of sequences of modular forms over the modular group SL2(Z). He proved that with each non-zero p–adic modular form there is associated a unique element called its weight k. The p–adic modular forms having the same weight form a Qp–vector space.

The object of this paper is to obtain a basis of p–adic modular forms and thus to know precisely all p–adic modular forms of a given weight k. The dimension of such modular forms as a Qp–vector space is countably infinite.
Coefficient estimates for starlike functions
Authors: Mogra M.L. , Juneja O.P.
Published: April 2009

Let (α β) denote the class of functions

analytic in the unit disc Δ ≡{z: |z| < 1} and satisfying

for some α, β (0 ≤ α < 1, 0 < β ≤ 1) and for all z ∈ Δ. In the present paper, sharp coefficient estimates for functions in (α, β) have been obtained. The results thus obtained not only generalize the corresponding results of Thomas H. MacGregor (Michigan Math. J. 10 (1963), 277–281), A.V. Boyd (Proc. Amer. Math. Soc. 17 (1966), 1016–1018) and others, but also give rise to analogous results for various other subclasses of starlike functions.
Density presentations of functors
Authors: Day B.J.
Published: April 2009

The article contains the basic theory resulting from the presentation of a dense functor N: A → C by means of an expansion K(k, C) ० NJk ≅ C the term dense functor being used instead of the equivalent term left-adequate functor. Results by various authors on the density type of a functor are formulated in the V-context for V symmetric monoidal closed, and elementary proofs are given. In particular a characterisation theorem containing the well-known results of Beck and Ulmer is established.
Construction of Fourier multipliers
Authors: Brown Gavin
Published: April 2009

The classical Wiener-Pitt phenomenon for measures may be formulated as an existence theorem for Fourier multipliers with irregular, spectral properties and the result has been refined in various ways over the years. The most recent development is due to Zafran, who exhibits abnormal spectral behaviour in multipliers whose transforms vanish at infinity and which operate onLpwhere 1 <p< ∞, p ≠ 2. Zafran's methods use Littlewood-Paley theory, interpolation, and the construction of a certain class of measures. We show here how the constructive element of his proof may be considerably simplified and sharpened.
Planetary waves in a rotating global ocean
Authors: Rickard J.A.
Published: April 2009

A theoretical study is made of the free periods of oscillation of a global layer of inviscid, incompressible fluid under the action of gravitational and Coriolis forces. The leading approximations to the eigenvalues are found to be sensitive to variations in the Froude number and also to the shape of the globe. It is shown that for oceanic and atmospheric motions displaying essentially the same features as the model, it is not sufficient to consider the motion as horizontally non-divergent.
Pareto optimum by independent trials
Authors: Gates D.J. , Rickard J.A.
Published: April 2009

We consider a method by which players in a continuous N-person game can arrive at a Pareto optimal solution by a trial process. The process has a number of novel features. Firstly, it is assumed that the players do not know the payoff functions. Secondly, the players are assumed to act quite independently. In spite of this lack of information and lack of cooperation, the players eventually arrive at what is usually regarded as a cooperative solution. The process is a model of the accounting procedures used by firms, and the results predict approach to an equilibrium state of a market model. Proofs are given only in outline here.
Fredholm theory for arbitrary measure spaces
Authors: Withers C.S.
Published: April 2009

The classical formulae for Fredholm integral equations, including expansions in terms of eigenfunctions such as Mercer's Theorem are extended to square-integrable kernels on an arbitrary measure space.
A primitive group ring
Authors: Brisley Warren , Groenhout R.
Published: April 2009

An explicit construction is given for a primitive group ring, together with an explicit construction of a faithful irreducible module for it.
Martin's Axiom and some classical constructions
Authors: McLaughlin T.G.
Published: April 2009

We display the relevance of Martin's Axiom to suitable forms of some long-known results in classical measure and category theory (for example, outer-measure-preserving partitions of sets of positive outer measure). While our theorems are at best fragmentarily new, the proofs are very simple, and, we think, instructive as regards the force of the axiom.
On semisubtractive halfrings
Authors: Dover R.E. , Stone H.E.
Published: April 2009

Analogues of Artin-Wedderburn and Goldie structure theorems are obtained for a class of halfrings which includes the semisubtractive ones. In the semisubtractive case, precise results are obtained which show that non-ring examples of these structures are relatively limited.
On a nonlinear elliptic boundary-value problem
Authors: Dancer E.N.
Published: April 2009

We announce a number of results on the existence of solutions of nonlinear elliptic boundary value problems in the case where the dominating linear part is not invertible. Our theorems improve recent results of Landesman and Lazer, and Williams.
On the problem of non-smoothness of non-reflexive second conjugate spaces
Authors: Singer Ivan
Published: April 2009

We prove that if E is a Banach space which has a subspace G such that the conjugate space G* contains a proper norm closed linear subspace V of characteristic 1, then E** is not smooth and there exist in πE(E) points of non-smoothness for E**, where πE: E → E** is the canonical embedding. We show that the spaces E having such a subspace G constitute a large proper subfamily of the family of all non-reflexive Banach spaces.
On the boundedness operator
Authors: Lambrinos Panayotis Th.
Published: April 2009

This paper is a continuation of the study of the boundedness operator δ. By determination of the congruences (that is, collapsings) of the smallest lattice containing δ and closed under application of δ, a nev classification of all topological spaces is obtained according to boundedness criteria.
Some results on weighing matrices
Authors: Wallis Jennifer Seberry , Whiteman Albert Leon
Published: April 2009

It is shown that if q is a prime power then there exists a circulant weighing matrix of order q2 + q + 1 with q2 nonzero elements per row and column.

This result allows the bound N to be lowered in the theorem of Geramita and Wallis that “given a square integer k there exists an integer N dependent on k such that weighing matrices of weight k and order n and orthogonal designs (1, k) of order 2n exist for every n > N”.
On homologies in finite combinatorial geometries
Authors: Kirkpatrick P.B.
Published: April 2009

Any subset π* of the set of all planes through a line in a finite projective space PG(m, q) determines a subgeometry G(π*) of the combinatorial geometry associated with PG(m, q). In this paper the geometries G(π*) of rank greater than three in which every line contains at least four points, are characterized in terms of the existence of a certain set of automorphism groups Γ(C, X); where X is a copoint and C a point not in X, and each non-trivial element of Γ(C, X) fixes X and every copoint through C and fixes C and every point in X, but no other point; and where Γ(C, X) acts transitively on the points distinct from C and not in X of some line through C. As a corollary of the main theorem we obtain a characterization of the finite projective spaces PG(m, q) with m ≥ 3 and q ≥ 3.
A note on Hausdorff groups
Authors: Fay Temple H.
Published: April 2009

It is well known that in the category of Hausdorff groups continuous homomorphisms having dense image are epic. That these homomorphisms are precisely the epics is a conjecture. If one could prove that proper closed subgroups (endowed with the subspace topology) cannot have epic inclusions, then the conjecture would be shown to be true. Closed subgroups fall into two classifications:

(a) open (and hence closed) subgroups and

(b) nowhere dense closed subgroups.

In this note it is shown that proper open subgroups cannot have epic inclusion. To do so an algebraic construction of Peter J. Hilton is topologized. The nowhere dense case remains open.
Oscillatory behaviour of an equation arising from an industrial problem
Authors: Tomaras Alexander
Published: April 2009

The oscillatory character of the solutions of a differential equation with retarded arguments, relevant to an industrial problem, is investigated. It is also proved that one can maintain the oscillatory properties of this equation under proper conditions, if a forcing term is added to it. The results obtained extend already known results on the subject.
Nonexistence of certain supplementary difference sets
Authors: Wormald Nicholas
Published: April 2009

This paper finds restrictions on the parameters of supplementary difference sets in any group G with a subgroup of index 2, which therefore includes all cyclic groups of even orders. As a corollary to the main theorem, we have that if S1, …, Sr are r − {2v, k1, …, kr; 2λ} supplementary difference sets in such a group, then not all of v, k1, …, kr, λ are odd; also is the sum of r squares.
Sufficient Fritz John optimality conditions
Authors: Craven B.D.
Published: April 2009

The sufficient optimality conditions, of Fritz John type, given by Gulati for finite-dimensional nonlinear programming problems involving polyhedral cones, are extended to problems with arbitrary cones and spaces of arbitrary dimension, whether real or complex. Convexity restrictions on the function giving the equality constraint can be avoided by applying a modified notion of convexity to the other functions in the problem. This approach regards the problem as optimizing on a differentiable manifold, and transforms the problem to a locally equivalent one where the optimization is on a linear subspace.
On converse duality in complex nonlinear programming
Authors: Parida J.
Published: April 2009

In this note a converse duality theorem is proved for a class of nonlinear programming problems over polyhedral cones in finite dimensional complex space by a direct use of a Kuhn-Tucker type necessary and sufficient condition for constrained optimization in complex space.
On a system of Feferman
Authors: de Alcantara Luiz Paulo
Published: April 2009

A system of set theory which appears as an extension of Ackermann set theory is introduced. In this sytem we construct a syntactic model for a theory proposed by Feferman for the development of category theory.
Nonstandard topological extensions: Addendum
Authors: Herrmann Robert A.
Published: April 2009

It has recently come to my attention that, independent from my investigations in [1], Professor K.D. Stroyan [2] obtains for a Tychonoff space X and a normal base β a quotient space on *X which is homeomorphic to the Wallman-Frink Hausdorff compactification w(X, β). Consequently, if X is Tychonoff, then Corollary 4.1 in [1] implies that Stroyan's space is homeomorphic to the space w(X, β)S which is constructed in Theorem 4.1 in [1]. Stroyan's result is obtained by use of a monadic closure operator.

I regret not mentioning Professor Stroyan's result in my paper [1].
Duality for generalized problems in complex programming
Authors: Mahajan D.G. , Vartak M.N.
Published: April 2009

Weak duality and direct duality theorems are proved, under appropriate assumptions, for the following pair of programming problems in complex space:

The objective function may be nondifferentiable and the constraints are of a more general nature than those considered earlier by various authors. Several well-known results are shown to be special cases of the results proved here.
A note on locally finite varieties
Authors: Wilson John S.
Published: April 2009

Evidence is presented which suggests that the following assertions about a variety ⊻ of groups may be equivalent:

(a) ⊻ is locally finite,

(b) all ⊻-groups satisfying the maximal condition for normal subgroups are finite, and

(c) all ⊻-groups satisfying the minimal condition for normal subgroups are finite.
A case of boundedness in Littlewood's problem on oscillatory differential equations
Authors: Morris G.R.
Published: April 2009

It is shown that all solutions of ẍ + 2x3 = p(t) are bounded, the notation indicating that p is periodic. It is not necessary to have a small parameter multiplying p.

The essential step is to show by appeal to Moser's theorem that, under the mapping (of the initial-value plane) which corresponds to the equation, there are invariant simple closed curves. This implies also that there is an uncountable infinity of almost-periodic solutions and, for each positive integer m, an infinity of periodic solutions of least period 2mπ (2π being taken as the least period of p ).

It is suggested that for a large class of equations the same attack would show all solutions of ẍ + g(x) = p(t) bounded. However, in order to show the method clearly, no generalisation is attempted here.
Fibrations and Grothendieck topologies
Authors: Hiller Howard Lyn
Published: April 2009

Given a site T, that is, a category equipped with a fixed Grothendieck topology, we provide a definition of fibration for morphisms of the presheaves on T. We verify that the notion is well-behaved with respect to composition, base change, and exponentiation, and is trivial on the topos of sheaves. We compare our definition to that of Kan fibration in the semi-simplicial setting. Also we show how we can obtain a notion of fibration on our ground site T and investigate the resulting notion in certain ring-theoretic situations.
Amicable orthogonal designs
Authors: Robinson Peter J.
Published: April 2009

A powerful tool in the construction of orthogonal designs has been amicable orthogonal designs. Recent results in the construction of Hadamard matrices has led to the need to find amicable orthogonal designs A, B in order n and of types (u1, U2, …, u6) and (ν1, ν2, …, νr) respectively satisfying At = -A, Bt = B, and ABt = BAt with

For simplicity, we say A, B are amicable orthogonal designs of type (u1, u2, …, us; v1, v2, …, vr).

We completely answer the question in order 8 by showing (1, 2, 2, 2; 8), (1, 2, 4; 2, 2, 4), (2, 2, 3; 2, 6), (7, 1, 7) and those designs derived from the above are the only possible.

We use our results to obtain new orthogonal designs in order 32.
On a problem of Hahn
Authors: Coppel W.A.
Published: April 2009

It is shown that for any almost periodic linear differential system asymptotic stability and uniform stability together imply uniform asymptotic stability.
Doubly transitive permutation groups involving the one-dimensional projective special linear groups
Authors: Praeger Cheryl E.
Published: April 2009

Let G be a doubly transitive permutation group on a finite set Ω, and for α in Ω suppose that Gα has a set Σ of non-trivial blocks of imprimitivity in Ω - {α}. If Gα is 2-transitive but not faithful on Σ, when is it true that the stabiliser in Gα of a block of Σ does not act faithfully on that block (that is, there is a nontrivial element in Gα which fixes every point of the block)? In a previous paper this question was answered when is the alternating or symmetric group, or a Mathieu group in its usual representation. In this paper we answer the question when , permuting the q + 1 points of the projective line, for some prime power q. We show that the only groups which arise satisfy either

(i) PSL(3, q) ≤ G ≤ PΓL(3, q) in its natural representation, or

(ii) G is a group of collineations of an affine translation plane of order q, and contains the translation group.
Error bounds for the modified Newton's method
Authors: Andrew A.L.
Published: April 2009

A strengthened form of the Kantorovich convergence theorem for the modified Newton's method is proved. The result is compared with previously known results.
On the transcendency of the solutions of a special class of functional equations: Corrigendum
Authors: Mahler Kurt
Published: April 2009

Mr V.E. Hoggatt, Jr, has pointed out an error in the examples of my paper [2], IfFmdenotes themth Fibonacci number, these examples asserted that

is transcendental. This is in fact false, for by a theorem of Good [1],

for it happens that

is a rational and not a transcendental function ofz, so that Theorem 1 of my paper cannot be applied. The value ofsfollows from (1) on putting.

Hence the following changes have to be made in [2].

On p. 390, lines 7 and 10, the casek= 1 must each time be excluded, and in Theorem 2 the two numbersrandsmay not be both be 0.
The class of a nilpotent wreath product
Authors: Shield David
Published: April 2009

Let G be a group with a normal subgroup H whose index is a power of a prime p, and which is nilpotent with exponent a power of p. Gilbert Baumslag (Proc. Cambridge Philos. Soc. 55 (1959), 224–231) has shown that such a group is nilpotent; the main result of this paper is an upper bound on its nilpotency class in terms of parameters of H and G/H. It is shown that this bound is attained whenever G is a wreath product and H its base group.

A descending central series, here called the cpp-series, is involved in these calculations more closely than is the lower central series, and the class of the wreath product in terms of this series is also found.

Two tools used to obtain the main result, namely a useful basis for a finite p-group and a result about the augmentation ideal of the integer group ring of a finite p-group, may have some independent interest. The main result is applied to the construction of some two-generator groups of large nilpotency class with exponents 8, 9, and 25.
Irreducible homomorphisms for lattices over orders
Authors: Schmidt Joachim W.
Published: April 2009

Let Λ be a complete R-order in the semi-simple K-algebra A. Then it has been shown that for each indecomposable Λ-lattice M which is not projective, there exists a unique almost split sequence 0 → N → E → M → 0. Here we study the middle term E and characterize those almost split sequences where E has a projective direct summand. In the case where Λ is the group-ring RG for a finite group G, we get information about the almost split sequences for the syzygies and apply our results in an example.
Near-rings that reduce to rings
Authors: Scott S.D.
Published: April 2009

It is shown that a near-ring is a ring if it is generated by a group of automorphisms of its additive group that contains all inner automorphisms.
Computing the effectively computable bound in Baker's inequality for linear forms in logarithms, and: Multiplicative relations in number fields: Corrigenda and addenda
Authors: van der Poorten A. J. , Loxton J.H.
Published: April 2009

We indicate a number of qualifications and amendments that are necessary so as to correct the statements and proofs of the theorems in our papers “Computing the effectively computable bound in Baker's inequality for linear forms in logarithms”, 15 (1976), 33–57, and its sequel “Multiplicative relations in number fields”, 16 (1977), 83–98, and remark on recent observations that would yield yet sharper results.
Generalized convexity in mathematical programming
Authors: Mond B.
Published: April 2009

The role of convexity in the development of mathematical programming is reviewed. Many recent generalizations of convexity and their applications to optimization theory are discussed.
A generalisation to several dimensions of the Neuberg-Pedoe inequality, with applications
Authors: Lu Yang , Jing-Zhong Zhang , Neumann B.H.
Published: April 2009

A well-known inequality relating the areas and squares of the sides of two triangles is generalised to higher-dimensional euclidean spaces. Extension of the results to non-euclidean spaces is also considered.
A commutativity theorem for semiprime rings
Authors: Abu-Khuzam Hazar
Published: April 2009

Let R be a semiprime ring in which for each x in R there exists a positive integer n = n(x) < 1 such that (xy)n = xnyn for all y in R. Then R is commutative.
A generalisation of a recent characterisation of planar graphs
Authors: Little C.H.C.
Published: April 2009

Planar graphs have recently been characterised as those which have no strict elegant odd ring of circuits. Here we generalise that result by showing that its dual yields a theorem that is valid for all graphs.
Transformation groups of strong characteristic 0
Authors: Elaydi Saber
Published: April 2009

It is shown that a transformation group (X, T, Π) is of strong characteristic 0 if and only if it is of P-strong characteristic 0 for some replete semigroup P in the phase group, provided that all orbit closures are compact. It is shown also that, under certain conditions, (X, T, Π) is of P-strong characteristic 0 if and only if (X × X, T, Π × Π) is Liapunov stable.
On linear operators on ordered banach spaces
Authors: Yamamuro Sadayuki
Published: April 2009

The order structure of the space of all continuous linear operators on an ordered Banach space is studied. The main topic is the Robinson property, that is, the norm of a positive linear operator is attained on the positive unit cone.
The spherical building and regular semisimple elements
Authors: Lehrer G.I.
Published: April 2009

Let G be a connected reductive algebraic group defined over a finite field k. The finite group G(k) of k-rational points of G acts on the spherical building B(G), a polyhedron which is functorially associated with G. We identify the subspace of points of B(G) fixed by a regular semisimple element s of G(k) topologically as a subspace of a sphere (apartment) in B(G) which depends on an element of the Weyl group which is determined by s. Applications include the derivation of the values of certain characters of G(k) at s by means of Lefschetz theory. The characters considered arise from the action of G(k) on the cohomology of equivariant sheaves over B(G).
An extension of the essential supremum concept with applications to normal integrands and multifunctions
Authors: Balder E.J.
Published: April 2009

Let (T, T, μ) be a σ-finite measure space and X a Suslin space. Let A be a class of normal integrands on T × X. We discuss the existence of an essential supremum of A, namely, a normal integrand l with

where A0 is a countable subclass of A, and, for each α ∈ A,

In this way we obtain an extension of the classical essential supremum concept. The applications include a result on measurable selectors of nonmeasurable multifunctions.
Surjectivity of multifunctions under generalized differentiability assumptions
Authors: Gautier Serge , Isac George , Penot Jean-Paul
Published: April 2009

The aim of the present paper is to give some general surjectivity theorems for multifunctions using tangent cones and generalized differentiability assumptions.
On Hermite-Fejér type interpolation
Authors: Knoop H.-B. , Stockenberg B.
Published: April 2009

For the Hermite-Fejér interpolation operator of higher order constructed on the roots , 1 ≤ k ≤ m, of the Jacobi-polynomial it is shown that is positive for all m ∈ N, if (α, β) ∈ [−¾, −¼]2. Further there is given an bound, which implies for arbitrary f ∈ C(I) and (α, β) ∈ [−¾, −¼]2.
Subordination theorems for p-valent functions with initial gaps
Authors: Singh Prem , Satyanarayana A.V.V.
Published: April 2009

In the present note we prove some results for p-valent functions with initial gaps by means of N-subordination.
Presentations for some direct products of groups
Authors: Kenne P.E.
Published: April 2009

We give efficient presentations for the direct product of two copies of the alternating group of degree five and the direct product of the alternating group of degree five and the binary icosahedral group.
Variational formulation of higher order elliptic boundary value problems
Authors: Pryde A.J.
Published: April 2009

Let A be an elliptic (partial) differential operator of order 2m on a compact manifold with boundary Г. Let B be a normal system of m differential boundary operators on Г. Assume all manifolds and coefficients are arbitrarily smooth. We construct sesquilinear forms J in terms of which there are equivalent variational formulations of the natural boundary value problems determined by A and B with solutions in Sobolev spaces HS (M), 0 < s < 2m. Such forms are also constructed for problems with mixed boundary conditions. The variational formulation permits localization of a priori estimates and the interchange of existence and uniqueness questions between the boundary value problem and an associated adjoint problem.
Stability of a constant mean curvature surface in R3
Authors: Koh Sung Eun
Published: April 2009

We solve the question raised by Barbosa and do Carmo as to whether there exists a complete, noncompact stably immersed surface in R3 with nonzero constant mean curvature. We show that such a surface is necessarily minimal, that is, its mean curvature is zero.
On the total torsion of certain nonclosed sphere curves
Authors: Zemyan Stephen M.
Published: April 2009

In this note, we establish some results concerning the total torsion and the total absolute torsion of certain non-closed stereographically projected analytic curves. The method of proof involves only elementary techniques of integration, a periodicity argument and Liouville's Theorem.
A commutativity criterion for prespectral operators
Authors: Ricker Werner
Published: April 2009

It is shown that if a bounded linear operator A commutes with a prespectral operator T of class Γ, then A commutes with the resolution of the identity of class Γ for T, say P (·), if and only if A*(Γ) ⊆ [PC*Γ. Here A* is the dual operator of A and [Pc]*Γ is the linear span of the set {U*ξ U ε P (·) c, ξ ε Γ} where P (·) c denotes the commutant of the range of P (·).
On the logarithmic derivatives of subordinate functions
Authors: Elhosh M. M.
Published: April 2009

Coefficient and integral mean bounds are obtained for functions subordinate to close-to-convex functions.
Adjoint-triangle theorems for conservative functors
Authors: Im G. B. , Kelly G. M.
Published: April 2009

An adjoint-triangle theorem contemplates functors P: C → A and T: A → B where T and TP have left adjoints, and gives sufficient conditions for P also to have a left adjoint. We are concerned with the case where T is conservative - that is, isomorphism-reflecting; then P has a left adjoint under various combinations of completeness or cocompleteness conditions on C and A, with no explicit condition on P itself. We list systematically the strongest results we know of in this direction, augmenting those in the literature by some new ones.
Conformally natural Ahlfors-Weill sections and Bers' reproducing formulas
Authors: Nag Subhashis
Published: April 2009

We differentiate certain refined Ahlfors-Weill local sections of the Bers projections. This yields reproducing formulas for holomorphic functions – which are then shown to be naturally related to Bers' important and well-known reproducing formulas.
Approximation by smooth embedded hypersurfaces with positive mean curvature
Authors: Lin Fang Hua
Published: April 2009

Here we initiate the study of the following problem. Let Ω be a compact domain in a Riemannian manifold such that ∂Ω is of minimum area for the contained volume. Can ∂Ω be approximated by smooth hypersurfaces of positive mean curvature? It reduces to the question of whether or not a stable (or minimizing) hypercone in a Euclidian space can be approximated by smooth hypersurfaces of positive mean curvature. The positive solution to the problem may be useful for studying the curvature and topology of Ω.

We show in this paper that such approximation is possible provided that the given minimal cone satisfies some additional hypothesis.
A characterisation of the absolute quasi-retracts in a class of acyclic continua
Authors: Akis V.N. , Curtis D.W.
Published: April 2009

The class of quasi-retracts of AR's (AQR's) was first considered by Stallings, who observed that every AQR has the fixed point property. More recently, it has been shown that the class of AQR's is closed with respect to the operations of taking cones, suspensions, or products with AR's, and that no AQR separates a Euclidean space. In this paper we show that every AQR is acyclic, and we obtain a simple, direct characterization of the AQR's in a certain class of acyclic continua.
Solving singular integral equations via (0,2,3) lacunary interpolation
Authors: Venturino Ezio
Published: April 2009

A modified product rule method for solving Cauchy-type singular integral equations is proposed. It is based on interpolating the unknown and some of its higher derivatives at any prespecified points. At these nodes the value of the unknown can be calculated directly by solving the discretized linear system. No need of further interpolatory formulae arises, as is the case with other quadrature methods.
The dimension of graphs with respect to the direct powers of a two-element graph
Authors: Kriegel Klaus , Pöschel Reinhard , Wessel Walter
Published: April 2009

Every finite loopless undirected graph G is isomorphic to an induced subgraph of a suitable finite direct power of the undirected graph G0 with two adjacent vertices 0,1 and one loop at vertex 1. The least natural number m such that G can be represented in this way is called its G0-dimension. We give some upper and lower bounds of this dimension depending on certain other graph invariants and determine its exact values for some special classes of graphs. Some methods to determine a concrete G0-representation, that is an embedding of G into , are presented. Moreover we show that the problem of determining the G0-dimension of a graph is NP-complete.
Bifurcations of second order problems with jumping nonlinearities
Authors: Drábek Pavel , Kučera Milan
Published: April 2009

In this paper we deal with nonlinear second order boundary value problems for ordinary differential equations including the case of jumping nonlinearities. The set of generalised eigenvalues in the case of nonconstant coefficients is described. It is proved that these generalised eigenvalues are simultaneously bifurcation points of the problem with coefficients also depending on the solution u = u(x).
Quadratic eigenvalue problems
Authors: Jones A.S.
Published: April 2009

A class of problems in forced convection give rise to quadratic eigenvalue problems. In this paper it is shown that the eigenvalues are necessarily real. The extension of this result to a wider class of problems is also discussed.
Near-ring-semigroups of continuous selfmaps
Authors: Magill K.D.
Published: April 2009

We find necessary and sufficient conditions on a topological space X so that S(X), the semigroup of all continuous selfmaps of X, is isomorphic to the multiplicative semigroup of a near-ring. The analogous problem is also considered for the semigroup of all continuous selfmaps which fix some point of X.
On the weak*-Radon Nikodym property
Authors: Saab Elias
Published: April 2009

We say that a certain property in a Banach space E is stable by subspaces if every closed subspace of E enjoys the same property. It is well known that the Radon-Nikodym property is stable by subspaces while the Weak Radon-Nikodym property is not. In his recent memoir, Talagrand investigated the stability of the Weak*Radon-Nikodym property which is a generalization of the Weak Radon-Nikodym property and showed that under Axiom L, the Weak*Radon-Nikodym property is stable by subspaces. It is still an open problem whether or not this result holds without this extra set theoretical hypothesis. In this paper we show that in a dual Banach space, the Weak*Radon-Nikodym property is stable by subspaces without assuming Axiom L. Other related results are discussed.
Singleton arrays in coding theory
Authors: Maruta Tatsuya , Kikumasa Isao , Kaneta Hitoshi
Published: April 2009

We construct all Singleton arrays for the field GF(q) when q is odd. There exist φ(q − 1) arrays in this case.
Multiobjective fractional duality
Authors: Egudo Richard R.
Published: April 2009

The concept of efficiency (Pareto optimum) is used to formulate duality for multiobjective fractional programming problems. We consider programs where the components of the objective function have non-negative and convex numerators while the denominators are concave and positive. For this case the Mond-Weir extension of Bector dual analogy is given. We also give the Schaible type vector dual. The case where functions are ρ-convex (weakly or strongly convex) is also considered.
On certain sequences of least squares approximants
Authors: Bokhari M.A.
Published: April 2009

A sequence of certain rational functions is determined where each member solves an ℓ2-minimisation problem on a “large” set of roots of unity. The sequence is compared with another sequence of L2-rational approximants. Our main result extends a result of Rivlin on Walsh type equiconvergence.
Sharp conditions for oscillations caused by retarded and advanced perturbations
Authors: Bowcock J.E. , Yu Y.H.
Published: April 2009

In this paper we study the oscillatory behaviour of solutions of equations of the forms , where pi, and τi, for i = 1, 2,…, n, are positive constants and p is an arbitary constant. Three necessary and sufficient conditions for all solutions of (A) and (B) respectively to be oscillatory are established. These results extend and generalise previous results in a new approach.
Quasi–additive solutions of nonlinear differential equations II
Authors: Jones A.S.
Published: April 2009

In a previous paper, the author sought to classify those solutions of second order nonlinear ordinary differential equations which can be expressed as sums of solutions of related equations. In that paper one sub-class of solutions was overlooked. This paper is to remedy that defect.
The limiting behaviour of certain sequences of continued fractions
Authors: Angell David
Published: April 2009

We investigate the set of limit points of the continued fractions

where x1, x2, … is a given sequence of positive integers. We show that this set is closed, and that it may include any given countable subset of [0, 1] if the integers xk are chosen appropriately. Our main result, which has applications in transcendence theory, is that the sequence of continued fractions has no rational limit point when the sequence {xk} of partial quotients is bounded.
A convergence property of Dubins' representation of distributions
Authors: Sheu Shey Shiung
Published: April 2009

Let (Xn)n≥1 be a sequence of random variables with zero means and uniformly bounded variences. Let τn be the stopping time defined on a given Brownian motion (Bt)t≥0, B0 = 0, by Dubins' method such that B(τn) has the same distribution as Xn. We prove that Xn converging to 0 in distribution implies that τn converges to 0 in probability. Examples are presented to illustrate the result is the best possible.
Topologies on locally compact groups
Authors: Cleary Joan , Morris Sidney A.
Published: April 2009

Using the Iwasawa structure theorem for connected locally compact Hausdorff groups we show that every locally compact Hausdorff group G is homeomorphic to Rn × K × D, where n is a non-negative integer, K is a compact group and D is a discrete group. This makes recent results on cardinal numbers associated with the topology of locally compact groups more transparent. For abelian G, we note that the dual group, Ĝ, is homeomorphic to This leads us to the relationship card G = ω0(Ĝ) + 2ω0(G), where ω (respectively, ω0) denotes the weight (respectively local weight) of the topological group. From this classical results such as card G = 2 card Ĝ for compact Hausdorff abelian groups, and ω(G) = ω(Ĝ) for general locally compact Hausdorff abelian groups are easily derived.
Asymptotic stability of systems with impulses by the direct method of Lyapunov
Authors: Kulev G.K. , Bainov D.D.
Published: April 2009

In the present paper the asymptotic and globally asymptotic stability of the zero solution of systems with impulses are investigated. For this purpose piecewise continuous auxiliary functions are used which are analogous to Lyapunov's functions. The theorem of Marachkov on the asymptotic stability of systems without impulses is generalised. The results obtained are formulated in four theorems.
Isotropic varieties in the singular symplectic geometry
Authors: Janeczko Stanisław , Kowalczyk Adam
Published: April 2009

Maximal isotropic varieties of the singular symplectic structure on R2n are characterised in terms of generating families. The normal forms of the simplest singularities (of codimension 1) are obtained with the help of the theory of boundary singularities.
A class of nonconvex functions and mathematical programming
Authors: Weir T. , Jeyakumar V.
Published: April 2009

A class of functions, called pre-invex, is defined. These functions are more general than convex functions and when differentiable are invex. Optimality conditions and duality theorems are given for both scalar-valued and vector-valued programs involving pre-invex functions.
On minimal faithful permutation representations of finite groups
Authors: Easdown David , Praeger Cheryl E.
Published: April 2009

The minimal (faithful) degree μ(G) of a finite group G is the least positive integer n such that G ≲ Sn. Clearly if H ≤ G then μ(H) ≤ μ(G). However if N ◃ G then it is possible for μ(G/N) to be greater than μ(G); such groups G are here called exceptional. Properties of exceptional groups are investigated and several families of exceptional groups are given. For example it is shown that the smallest exceptional groups have order 32.
Fubini's theorem for Radon polymeasures
Authors: Jefferies Brian
Published: April 2009

A theorem is given on the interchange of integrals for the product of a Radon polymeasure and a measure. Examples show that if the conditions of the theorem are not satisfied, then the conclusions may not hold.
Almost periodic solutions of nonlinear parabolic equations
Authors: Yang Yisong
Published: April 2009

In this note the recent result of Corduneanu on almost periodicity of L2(G)-bounded solutions of nonlinear parabolic equations is extended to the case when the nonlinear growth rate is beyond the first eigenvalue of the associated elliptic boundary value problem.
On Mosco convergence of convex sets
Authors: Beer Gerald
Published: April 2009

We present a natural topology compatible with the Mosco convergence of sequences of closed convex sets in a reflexive space, and characterise the topology in terms of the continuity of the distance between convex sets and fixed weakly compact ones. When the space is separable, the topology is Polish. As an application, we show that in this context, most closed convex sets are almost Chebyshev, a result that fails for the stronger Hausdorff metric topology.
Oscillatory properties of the solutions of linear equations of neutral type
Authors: Bainov D.D. , Myshkis A.D. , Zahariev A.I.
Published: April 2009

In this paper the oscillatory and asymptotic properties of solutions of the equation

are investigated where δ = ±1, τ > 0, σ > 0, the functionsr(s) andare non- decreasing and.
New characterisations of pseudocompact spaces
Authors: Yan-Min Wang
Published: April 2009

In this paper, we give a new characterisation of pseudo-compact spaces, namely a space X is pseudocompact if and only if each σ-point finite open cover of X has a finite subfamily whose union is dense. As a corollary, we show that every pseudocompact σ-metacompact (or screenable) space is compact, which sharpens some known results.
Complex vector bundles on real algebraic varieties of small dimension
Authors: Kucharz Wojciech
Published: April 2009

LetXbe an affine real algebraic variety. In this paper, assuming that dimX≤ 7 and thatXsatisfies some other reasonable conditions, we give a characterisation of those continuous complex vector bundles onXwhich are topologically isomorphic to algebraic complex vector bundles onX.
A Class of functional equations which have entire solutions
Authors: Walker Peter L.
Published: April 2009

We consider the Abelian functional equation

where φ is a given entire function and g is to be found. The inverse function f = g−1 (if one exists) must satisfy

We show that for a wide class of entire functions, which includes φ(z) = ez − 1, the latter equation has a non-constant entire solution.
Fractional integration and the hyperbolic derivative
Authors: Kwon E.G.
Published: April 2009

We improve S. Yamashita's hyperbolic version of the well-known Hardy-Littlewood theorem. Let f be holomorphic and bounded by one in the unit disc D. If (f#)p has a harmonic mojorant in D for some p, p > 0, then so does σ(f)q for all q, 0 < q < ∞. Here
On two theorems concerning sets with convex sections
Authors: Tarafdar E.
Published: April 2009

In this note two theorems of Ma and Fan concerning sets with convex sections are generalised.
A topological approach to a conjecture of Rhodes
Authors: Pin J.E.
Published: April 2009

The “type II conjecture”, proposed by J. Rhodes, gives an algorithm to compute the kernel of a given finite semigroup. We show that this conjecture is a consequence of another conjecture, of a topological nature. This new conjecture gives a simple and effective characterisation of the recognisable subsets of a free monoid that are closed in the finite group topology for the free monoid.
Farthest points in W*-compact sets
Authors: Deville R. , Zizler V.E.
Published: April 2009

We show that while farthest points always exist in w* -compact sets in duals to Radon-Nikodym spaces, this is generally not the case in dual Radon-Nikodym spaces. We also show how to characterise weak compactness in terms of farthest points.
Une caractérisation du fibré cotangent
Authors: van Duc Tong
Published: April 2009

We prove that the Lie algebra of infinitesimal automorphisms of the cotangent structure on the total space of the cotangent bundle of a manifold is isomorphic to the semi-direct product of the Lie algebra of the vector fields on the manifold by the space of closed 1-forms, the vector fields operating on the forms by Lie derivation. The derivations of this algebra Lie are completely determined and we prove that it characterises the cotangent bundle.
Another approach to extensions of continuous mappings
Authors: Sun Shu-Hao
Published: April 2009

First, we give a more general extension theorem about continuous mappings. It is shown that the Taimanov-Eilenberg-Steenrod extension theorem and the Engelking extension theorem are special cases and that this theorem implies the Dugunji extension theorem. The localic version of this theorem also generalises Joyal's extension theorem for locales. Then, using the same technique, we obtain another more interesting extension theorem and its applications. In particular, we sharpen a well-known result due to Wallman.
Rings whose additive endomorphisms are N-multiplicative
Authors: Feigelstock Shalom
Published: April 2009

Sullivan's problem of describing rings, all of whose additive endomorphisms are multiplicative, is generalised to the study of rings R satisfying ϕ(a1 … an) = ϕ(a1)…ϕ(an) for every additive endomorphism ϕ of R, and all a1,…,an ∈ R, with n > 1 a fixed positive integer. It is shown that such rings possess a bounded (finite) ideal A such that [R/A]n = 0 ([R/A]2n−1 = 0). More generally, if f(X1, …, Xt) is a homogeneous polynomial with integer coefficients, of degree > 1, and if a ring R satisfies ϕ[f(a1, …, at)] = f[ϕ(a1), …, ϕ(at)] for all additive endomorphisms ϕ, and all a1, …, at ∈ R, then R possesses a bounded ideal A such that R/A satisfies the polynomial identity f.
Normalising elements and radicals, I.
Authors: Whelan E.A.
Published: April 2009

In this paper we study rings and bimodules with no known one-sided chain conditions, but whose (two-sided) ideals and subbimodules are ‘nicely’ generated. We define bi-noetherian polycentral (BPC) and bi-noetherian polynormal (BPN) rings and bimodules, large classes of (almost always) non-noetherian objects, and put on record the basic facts about them. Any BPC ring is a BPN ring. In the case of rings we reduce their properties to properties of the prime ideals, and study the d.c.c. on (two-sided) ideals. We define both the artinian and bi-artinian radicals of a BPN ring, and use them to show that for BPN rings the intersections of the powers of both the Brown-McCoy and the Jacobson radicals are zero.
The endomorphism ring of a finite-length module
Authors: Schulz Rainer
Published: April 2009

Let M be an R-module of finite length. For a simple R-module A, let ℓA denote the nuber of times the isomorphism type of A appears in a composition chain of M, and let σ denote the maxinium of the ℓA, A ranging over all simple submodules of M. Let S be the endomorphism ring of M. We show that the Loewy length of S is bounded by σ.
Iterative solution of nonlinear equations of the monotone type in Banach spaces
Authors: Chidume C.E.
Published: April 2009

Let E be a real Banach space with a uniformly convex dual, and let K be a nonempty closed convex and bounded subset of E. Suppose T: K → K is a continuous monotone map. Define S: K → K by Sx = f – Tx for each x in K and define the sequence iteratively by x0 ∈ K, xn+1 = (1 – Cn)xn + CnSxn, n ≥ 0, where is a real sequence satisfying appropriate conditions. Then, for any given f in K, the sequence converges strongly to a solution of x + Tx = f in K. Explicit error estimates are also computed. A related result deals with iterative solution of nonlinear equations of the dissipative type.
On equational theories of semilattices with operators
Authors: Ježek J. , PudláK P. , Tůma J.
Published: April 2009

In 1986, Lampe presented a counterexample to the conjecture that every algebraic lattice with a compact greatest element is isomorphic to the lattice of extensions of an equational theory. In this paper we investigate equational theories of semi-lattices with operators. We construct a class of lattices containing all infinitely distributive algebraic lattices with a compact greatest element and closed under the operation of taking the parallel join, such that every element of the class is isomorphic to the lattice of equational theories, extending the theory of a semilattice with operators.
On Lagrange interpolation with equidistant nodes
Authors: Byrne Graeme J. , Mills T.M. , Smith Simon J.
Published: April 2009

A quantitative version of a classical result of S.N. Bernstein concerning the divergence of Lagrange interpolation polynomials based on equidistant nodes is presented. The proof is motivated by the results of numerical computations.
Equipartition of convex bodies
Authors: Scott Paul R.
Published: April 2009

We show that a compact convex body in En cannot be partitioned by n + 1 hyperplanes into 2n+l – 1 subsets of equal measure, thus generalising a result in the plane due to R.C. and E.F. Buck.