bluuebunny/crossref_metadata_2025 huggingface dataset:
The topology of the space of Denjoy integrable functions
Authors: Seng Chew Tuan , Yee Lee Peng
Published: April 2009

In this paper, the topology of the Denjoy space and characterisation of precompact sets in the Denjoy space are given.
Highly transitive representations of free groups and free products
Authors: Glass A.M.W. , McCleary Stephen H.
Published: April 2009

A permutation group is highly transitive if it is n–transitive for every positive integer n. A group G of order-preserving permutations of the rational line Q is highly order-transitive if for every α1 < … < αn and β1 < … < βn in Q there exists g ∈ G such that αig = βi, i = 1, …, n. The free group Fn(2 ≤ η ≤ אo) can be faithfully represented as a highly order-transitive group of order-preserving permutations of Q, and also (reproving a theorem of McDonough) as a highly transitive group on the natural numbers N. If G and H are nontrivial countable groups having faithful representations as groups of order-preserving permutations of Q, then their free product G * H has such a representation which in addition is highly order-transitive. If G and H are nontrivial finite or countable groups and if H has an element of infinite order, then G * H can be faithfully represented as a highly transitive group on N. Some of the representations of Fη on Q can be extended to faithful representations of the free lattice-ordered group Lη.
The topological configuration of a real algebraic curve
Authors: Sakkalis Takis
Published: April 2009

This paper presents an algorithm, motivated by Morse Theory, for the topological configuration of the components of a real algebraic curve {f(x, y) = 0}. The running time of the algorithm is O(n12 (d + log n)2 log n), where n, d are the degree and maximum coefficient size of f(x, y).
On time dependent multistep dynamic processes
Authors: Szidarovszky Ferenc , Argyros Ioannis K.
Published: April 2009

The discrete time scale Liapunov theory is extended to time dependent, higher order, nonlinear difference equations in a partially ordered topological space. The monotone convergence of the solution is examined and the speed of convergence is estimated.
Nonsingular retractable modules and their endomorphism rings
Authors: Khuri Soumaya Makdissi
Published: April 2009

A module RM is said to be retractable if HomR (M, U) ≠ 0 for each nonzero submodule U of M. M is said to be a CS module if every complement submodule of M is a direct summand in M. Retractable modules are compared to nondegenerate modules on the one hand and to e–retractable modules on the other (nondegenerate implies retractable implies e–retractable); and it is shown that if M is nonsingular and retractable, then EndRM is a left CS ring if and only if M is a CS module.
Rapidly decreasing behaviour of solutions in nonlinear 3-D-thermoelasticity
Authors: Jiang Song
Published: April 2009

In this paper we study the asymptotic behaviour, as |x| → ∞, of solutions to the initial value problem in nonlinear three-dimensional thermoelasticity in some weighted Sobolev spaces. We show that under some conditions, solutions decrease fast for each t as x tends to infinity. We also consider the possible extension of the method presented in this paper to the initial boundary value problem in exterior domains.
Left ideals in the near-ring of affine transformations
Authors: Mutter Wolfgang
Published: April 2009

In this paper we determine the left ideals in the near-ring Aff(V) of all affine transformations of a vector space V. It is shown that there is a Galois correspondence between the filters of affine subspaces of V and those left ideals of Aff(V) which are not left invariant. In particular, the not left invariant finitely generated left ideals of Aff(V) are precisely the annihilators of the affine subspaces of V. A similar correspondence exists between the filters of linear subspaces of V and the left invariant left ideals of Aff (V). If V is finite-dimensional, then all left ideals of Aff(V) are finitely generated.
The metrisability of precompact sets
Authors: Robertson Neill
Published: April 2009

A uniform space is trans-separable if every uniform cover has a countable subcover. We show that a uniform space is trans-separable if it contains a suitable family of precompact sets. Applying this result to locally convex spaces, we are able to deduce that the precompact subsets of a wide class of spaces are metrisable. The proof of our main Theorem is based on a cardinality argument, and is reminiscent of the classical Bolzano-Weierstrass Theorem.
Values of polynomials over finite fields
Authors: von zur Gathen Joachim
Published: April 2009

Let q be a prime power, Fq a field with q elements, f ∈ Fq[x] a polynomial of degree n ≥ 1, V(f) = #f(Fq) the number of different values f(α) of f, with α ∈ Fq, and p = q – V(f). It is shown that either ρ = 0 or 4n4 > q or 2pn > q. Hence, if q is “large” and f is not a permutation polynomial, then either n or ρ is “large”.
Existence of optimal controls for a class of nonlinear distributed parameter systems
Authors: Papageorgiou Nikolaos S.
Published: April 2009

In this paper we examine a Lagrange optimal control problem driven by a nonlinear evolution equation involving a nonmonotone, state dependent perturbation term. For this problem we establish the existence of optimal admissible pairs. For the same system we also examine a time optimal control problem involving a moving target set. Finally we work out in detail an example of a strongly nonlinear parabolic distributed parameter system.
On the p-norm of the truncated n-dimensional Hilbert transform
Authors: Pandey J.N. , Singh O.P.
Published: April 2009

It is shown that a bounded linear operator T from Lρ(Rn) to itself which commutes both with translations and dilatations is a finite linear combination of Hilbert-type transforms. Using this we show that the ρ-norm of the Hilbert transform is the same as the ρ-norm of its truncation to any Lebesgue measurable subset of Rn with non-zero measure.
Projective submersions
Authors: Podestà Fabio
Published: April 2009

We consider C∞ manifolds endowed with torsionfree affine connections and C∞ projective submersions between them which, by definition, map geodesics into geodesics up to parametrisation. After giving a differential characterisation of these mappings, we deal with the case when one of the given connections is projectively flat or satisfies certain conditions concerning its Ricci tensor; under these hypotheses we prove that the projective submersion is actually a covering.
A characterisation result for matrix rings
Authors: Fuchs P.R.
Published: April 2009

For a ring R with identity we show that the existence of certain nilpotent elements forces R to be a matrix ring of size ≥ 2.
A theorem of Archimedes about spheres and cylinders and two-point homogeneous spaces
Authors: Djorić M. , Vanhecke L.
Published: April 2009

Starting from the well-known classical theorem of Archimedes about the volumes of spheres and circumscribing cylinders in three-dimensional Euclidean space, one considers circumscribing tubes of small geodesic spheres in general Riemannian manifolds and one derives new characterisations of two-point homogeneous spaces from it.
Approximation in function modules
Authors: Sejeeni Fowzi Ahmed
Published: April 2009

We investigate the existence of best approximation of an element α in a function module from a subfunction module whose fibers satisfy the intersection property of balls. Also we investigate the lower semicontinuity of the metric projection associated with such a subfunction module.
Open images of compactifications of the ray
Authors: Awartani Marwan M.
Published: April 2009

Let X be a compactification of the ray with the arc as remainder. The following characterisation of the open images of X is obtained: Let h: X → Y be an open onto map. If Y is not homeomorphic to [0, 1] or the one-point space, then h is a homeomorphism. In 1977 open images of the usual sin (1/x) continuum were characterised by Professor Sam B. Nadler.
Topological dimensions of global attractors for semilinear PDE's with delays
Authors: So Joseph W.-H. , Wu Jianhong
Published: April 2009

An estimate is obtained on the Hausdorff and fractal dimensions of global attractors of semilinear partial differential equations with delay: ẋ(t) = Ax(t) + f(xt). The method employed is to associate such an equation with a nonlinear semigroup on a product space and then appeal to the upper estimate due to Constantin, Foias and Teman on topological dimensions of global attractors for general nonlinear dynamical systems.
On n-flat modules over a commutative ring
Authors: Dobbs David E.
Published: April 2009

Let R be a commutative ring with unit, T an R-module, and n a positive integer. It is proved that T is n-flat over R if B⊗RT is B-torsionfree for each n–generated commutative R-algebra B. The converse holds if T is n–generated, in which case T is actually flat over R. Several other instances of the converse are established, but it is shown that the converse fails in general, even for R an integral domain, T an ideal of R, and n = 1.
Recurrence in persistent dynamical systems
Authors: Choi Sung Kyu , Chu Chin-Ku , Lee Keon-Hee
Published: April 2009

The purpose of this paper is to study the chain recurrent sets under persistent dynamical systems, and give a necessary condition for a persistent dynamical system to be topologically stable. Moreover we show that the various recurrent sets depend continuously on persistent dynamical systems.
On a reflected Ornstein-Uhlenbeck process with an application
Authors: Attia F.A.
Published: April 2009

The resolvent operator and the moment generating function of a reflected Ornstein-Uhlenbeck process are obtained. These results are then applied to determine the long-run average cost and the total expected discounted cost of operating a finite storage system with content-dependent release rate.
Covariance function and ergodicity of asymptotically stationary random fields
Authors: Anh V.V. , Lunney K.E.
Published: April 2009

A class of second-order asymptotically stationary random fields is shown to contain the class of almost harmonisable random fields. A continuity theorem which leads to the spectral representation for the covariance function of asymptotically stationary random fields is established. A mean ergodic theorem for the fields is also given. When stationarity is assumed, the results reduce to the well-known corresponding theorems for stationary random fields.
On the l-adic representations attached to simple abelian varieties of type IV
Authors: Chi Wenchen
Published: April 2009

The l-adic representations associated to prime dimensional type IV absolutely simple abelian varieties over number fields are studied. The image of such a representation was computed. The results coincide with the well-known conjectures of Mumford and Tate.
On spectral decomposition of immersions of finite type
Authors: Chen Bang-Yen , Petrovic Mira
Published: April 2009

Let x: M → Em be an immersion of finite type. In this paper we study the following two problems: (1) When is the spectral decomposition ofthe immersion x linearly independent? (2) When is the spectral decomposition orthogonal? Several results in this respect were obtained.
Rate of approximation of functions of bounded variation by modified Lupas operators
Authors: Yuankwei Wang , Shunsheng Guo
Published: April 2009

This paper discusses the rate of approximation of functions of bounded variation using the Modified Lupas operator. We obtain an approximation theorem and our estimate is essentially the best possible.
On the topological entropy of transitive maps of the interval
Authors: Coven Ethan M. , Hidalgo Melissa C.
Published: April 2009

The topological entropy of a continuous map of the interval is the supremum of the topological entropies of the piecewise linear maps associated to its finite invariant sets. We show that for transitive maps, this supremum is attained at some finite invariant set if and only if the map is piecewise monotone and the set contains the endpoints of the interval and the turning points of the map.
Zeros of recurrence sequences
Authors: van der Poorten A.J. , Schlickewei H.P.
Published: April 2009

We give an upper bound for the number of zeros of recurrence sequences defined over an algebraic number field in terms of their order, the degree of their field of definition and the number of prime ideal divisors of the characteristic roots of the sequence.
On the growth of compositions of linear and meromorphic functions
Authors: Qiao Jianyong
Published: April 2009

Let f(z) be a meromorphic function; we shall investigate the asymptotic behaviour of the ratio T(r, f(z + α))/T(r, f(z)) and T(r, f(αz))/T(r, f(z)), and discuss the growth of the meromorphic solutions of some functional equations.
Uniform partition and the best least-squares piecewise polynomial approximation
Authors: Dubeau François
Published: April 2009

It is shown that the best least-squares piecewise n degree polynomial approximation of xn+1 over [a, b] is obtained for a uniform partition. Moreover the approximation is continuous for n odd and discontinuous, with equal stepsizes at the nodes, for n even.
On operator ideals determined by sequences
Authors: González Manuel , Martinón Antonio
Published: April 2009

We associate with an operator ideal 𝒜 (in the sense of Pietsch) a class of bounded sequences S𝒜 by using the 𝒜-variation of Astala. If 𝒜 and B are operator ideals, and we define (𝒜, B) as the class of operators which map a sequence of S𝒜 into a sequence of SB, we obtain the following:

Theorem. If Tn: X → Y is a sequence of operators and for every sequence (xn) ⊂ X in S𝒜 there exists p such that (Tpxn) belongs to SB, then Tm ∈ (𝒜, B) for some m.

The compact operators, weakly compact operators and some other operator ideals can be represented as (𝒜, B). Hence several results of Tacon and other authors are a consequence of this theorem.
Representations of Weyl groups of type B induced from centralisers of involutions
Authors: Ryan Philip D.
Published: April 2009

Let G be a Weyl group of type B, and T a set of representatives of the conjugacy classes of self-inverse elements of G. For each t in T, we construct a (complex) linear character πt of the centraliser of t in G, such that the sum of the characters of G induced from the πt contains each irreducible complex character of G with multiplicity precisely 1. For Weyl groups of type A (that is, for the symmetric groups), a similar result was published recently by Inglis, Richardson and Saxl.
The centraliser of the injective tensor product
Authors: Werner Wend
Published: April 2009

The aim of this note is to obtain an intrinsic product formula for the centraliser of the injective tensor product of a couple of Banach spaces, Z(). More precisely, we are going to prove that

Here, the spaces and depend only on X and Y, respectively, and Xk denotes the topological k-product.

A Counterexaple used to demonstrate that the k-product cannot beavoided serves as an answer to a question posed by W. Rueß and D. Werner concerning the behaviour of M-ideals on Y.
On direct bifurcations into chaos and order for a simple family of interval maps
Authors: Du Bau-Sen
Published: April 2009

We present a simple one-parameter family of interval maps which has a direct bifurcation from order to chaos and then a direct (reverse) bifurcation from chaos back to order.
The sup metric on infinite products
Authors: Borges Carlos R.
Published: April 2009

We study the properties of the sup metric on infinite products Z = X.(If d is a bounded metric on X then ρ, defined by ρ((xα), (yα)) = , is the sup metric on Z.) In particular, we prove that if X is an AR(metric) or a topological group then so is Z.
Existence of solutions of nonlinear differential equations with deviating arguments
Authors: Balachandran K. , Ilamaran S.
Published: April 2009

We prove an existence theorem for nonlinear differential equations with deviating arguments and with implicit derivatives. The proof is based on the notion of measure of noncompactness and the Darbo fixed point theorem.
Quadratic systems with a weak focus
Authors: Pingguang Zhang , Suilin Cai
Published: April 2009

In this paper we study the number and the relative position of the limit cycles of a plane quadratic system with a weak focus. In particular, we prove the limit cycles of such a system can never have (2, 2)-distribution, and that there is at most one limit cycle not surrounding this weak focus under any one of the following conditions:

(i) the system has at least 2 saddles in the finite plane,

(ii) the system has more than 2 finite singular points and more than 1 singular point at infinity,

(iii) the system has exactly 2 finite singular points, more than 1 singular point at infinity, and the weak focus is itself surrounded by at least one limit cycle.
A remark on boundedness of Bloch functions
Authors: Samotij Krzysztof
Published: April 2009

Two consequences of a theorem of Dahlberg are derived. Let f be a holomorphic function in the unit disk D of the complex plane, and let E be an Fσ subset of the unit circle T. Suppose that |f(rw)| ≤ M, ω ∈ T/E, for some constant M.

Then f is bounded in either of the two cases:

(i) if f is in the Bloch space and E is of zero measure with respect to the Hausdorff measure associated with the function ψ(t) = t log log (2πee/t),

(ii) if f is integrable with respect to the planar Lebesgue measure on D and E is of zero measure with respect to the Hausdorff measure associated with the function ψ(t) = t log(2πee/t).
Topological essentiality and differential inclusions
Authors: Gorniewicz Lech , Slosarski Miroslaw
Published: April 2009

In the present paper a concept of topological essentiality for a large class of multivalued mappings is introduced. This concept is strictly related to the Leray-Schauder topological degree theory but is simpler and also more general. Applying the above concept to boundary value problems for differential inclusion with both upper semi-continuous and lower semi-continuous right hand sides, several new results are obtained.
Lattice isomorphisms of orthodox semigroups
Authors: Johnston Katherine G. , Cleary F.D.
Published: April 2009

It is shown that the set of all orthodox subsemigroups of an orthodox semigroup forms a lattice. This lattice is a join-sublattice of the lattice of all semigroups, but is not in general a meet-sublattice. We obtain results concerning lattice isomorphisms between orthodox semigroups, several of which include known results for inverse semigroups as special cases.
On approximation by trigonometric Lagrange interpolating polynomials II
Authors: Borwein P.B. , Xie T.F. , Zhou S.P.
Published: April 2009

We show that trigonometric Lagrange interpolating approximation with arbitrary real distinct nodes in Lp space for 1 ≤ p < ∞, as that with equally spaced nodes in Lp space for 1 < p < ∞ in an earlier paper by T.F. Xie and S.P. Zhou, may also be arbitrarily “bad”. This paper is a continuation of this earlier work by Xie and Zhou, but uses a different method.
Existence theorems for a multivalued boundary value problem
Authors: Marano Salvatore A.
Published: April 2009

Let F be a multifunction from [a, b] × ℝn × ℝn into ℝn, with non-empty closed convex values. In this paper we prove that, under suitable assumptions, the multivalued boundary value problem

has at least one solution u ∈ W2, p([a, b], ℝn). Next we point out some particular cases.
Smoothness and the asymptotic-norming properties of Banach spaces
Authors: Hu Zhibao , Lin Bor-Luh
Published: April 2009

We study some smoothness properties of a Banach space X that are related to the weak* asymptotic-norming properties of the dual space X*. These properties imply that X is an Asplund space and are related to the duality mapping of X.
Necessary conditions of optimal impulse controls for distributed parameter systems
Authors: Yong Jiongmin , Zhang Pingjian
Published: April 2009

Optimal control problem of semilinear evolutionary distributed parameter systems with impulse controls is considered. Necessary conditions of optimal controls are derived. The result generalises the usual Pontryagin's maximum principle.
Balls intersection properties of Banach spaces
Authors: Chen Dongjian , Hu Zhibao , Lin Bor-Luh
Published: April 2009

Necessary and sufficient conditions for a Banach space with the Mazur intersection property to be an Asplund space are given. It is proved that Mazur intersection property is determined by the separable subspaces of the space. Corresponding problems for a space to have the ball-generated property are considered. Some comments on possible renorming so that a space having the Mazur intersection property are given.
The expected dimension of a sum of vector subspaces
Authors: Dobbs David E. , Lancaster Mark J.
Published: April 2009

Let W be an n−dimensional vector space over a field F. It is shown that the expected dimension of a vector subspace of W is n/2. If F is infinite, the expected dimension of a sum of a pair of subspaces of W is (n + 1)/2 if n > 1; and 3/4 if n = 1. If F is finite, with q elements, the expected dimension of a sum of subspaces of W depends on q and n. For fixed n, the limiting value of this expectation as q → ∞ is n if n is even; and n − 1/4 if n is odd. Moreover, if F is finite and n > 1, the expected dimension of a sum of three (not necessarily distinct) subspaces of W has limit n as q → ∞.
On the rate of convergence in the strong law of large numbers for arrays
Authors: Hu Tien-Chung , Weber N.C.
Published: April 2009

For sequences of independent and identically distributed random variables it is well known that the existence of the second moment implies the law of the iterated logarithm. We show that the law of the iterated logarithm does not extend to arrays of independent and identically distributed random variables and we develop an analogous rate result for such arrays under finite fourth moments.
Lattice of idempotent separating congruences in a ℙ-regular semigroup
Authors: Sen M.K. , Seth A.
Published: April 2009

In this paper we introduce the concept of ℙ-regular, normal subset of a ℙ-regular semigroup, give an alternate characterisation of the maximum idempotent separating congruence in a ℙ-regular semigroup and finally describe the lattice of the idempotent separating congruences in a ℙ-regular semigroup.
A note on Lie nilpotent group rings
Authors: Sharma R.K. , Bist Vikas
Published: April 2009

Let KG be the group algebra of a group G over a field K of characteristic p > 0. It is proved that the following statements are equivalent: KG is Lie nilpotent of class ≤ p, KG is strongly Lie nilpotent of class ≤ p and G′ is a central subgroup of order p. Also, if G is nilpotent and G′ is of order pn then KG is strongly Lie nilpotent of class ≤ pn and both U(KG)/ζ(U(KG)) and U(KG)′ are of exponent pn. Here U(KG) is the group of units of KG. As an application it is shown that for all n ≤ p+ 1, γn(L(KG)) = 0 if and only if γn(KG) = 0.
A remark on the loxodromic mapping conjecture
Authors: Harrison Jenny , Pugh Charles
Published: April 2009

The loxodromic mapping conjecture of J. Harrison is affirmed for diffeomorphisms of the 2-sphere that embed in flows.
Note on a theorem of Gromoll-Grove
Authors: Cairns Grant , Escobales Richard H.
Published: April 2009

D. Gromoll and K. Grove showed that metric flows on constant curvature spaces are either flat or locally spanned by Killing vector fields. We generalise this result to certain flows on manifolds of variable curvature.
Duality for a non-differentiable programming problem
Authors: Zhang J. , Mond B.
Published: April 2009

A generalised dual to a non-differentiable programming problem is given and duality established under general convexity and invexity conditions. A second order dual is also given and duality theorems proved under generalised second order invexity condition.
The fixed point problem for generalised nonexpansive maps
Authors: Smyth Michael A.
Published: April 2009

This paper is concerned with extending the theory of the existence of fixed points for generalised nonexpansive maps as far as possible. This can be seen as a continuation of the work of Maurey on the extension of the fixed point theory for nonexpansive maps beyond the requirement of normal structure type conditions.
Chain recurrence and discretisation
Authors: Garay Barnabas M. , Hofbauer Josef
Published: April 2009

Upper and lower semicontinuity results for the chain recurrent set are shown to remain valid in numerical dynamics with constant stepsizes. It is also pointed out that the chain recurrent set contains numerical ω–limit sets for discretisations with a variable stepsize sequence approaching zero.
A family of Chebyshev-Halley type methods in Banach spaces
Authors: Gutiérrez J.M. , Hernández M.A.
Published: April 2009

A family of third-order iterative processes (that includes Chebyshev and Halley's methods) is studied in Banach spaces. Results on convergence and uniqueness of solution are given, as well as error estimates. This study allows us to compare the most famous third-order iterative processes.
Totally disconnected, nilpotent, locally compact groups
Authors: Willis G.
Published: April 2009

It is shown that, if G is a totally disconnected, compactly generated and nilpotent locally compact group, then it has a base of neighbourhoods of the identity consisting of compact, open, normal subgroups. An example is given showing that the hypothesis that G be compactly generated is necessary.
Hopfian and co-Hopfian groups
Authors: Deo Satya , Varadarajan K.
Published: April 2009

The main results proved in this note are the following:

(i) Any finitely generated group can be expressed as a quotient of a finitely presented, centreless group which is simultaneously Hopfian and co-Hopfian.

(ii) There is no functorial imbedding of groups (respectively finitely generated groups) into Hopfian groups.

(iii) We prove a result which implies in particular that if the double orientable coverNof a closed non-orientable aspherical manifoldMhas a co-Hopfian fundamental group then π1(M) itself is co-Hopfian.
Multiobjective symmetric duality with invexity
Authors: Gulati T.R. , Husain I. , Ahmed A.
Published: April 2009

Usual duality results are proved for Wolfe and Mond-Weir type multiobjective symmetric dual problems without nonnegativity constraints under invexity/generalised invexity assumptions. Moreover, assuming the kernel function to be skew symmetric, the multiobjective problems are exhibited to be self duals.
Banach algebras of topologically bounded index
Authors: Green J.J.
Published: April 2009

We consider normed and Banach algebras satisfying a condition topologically analogous to bounded index for rings. We investigate stability properties, prove a topological version of a theorem of Jacobson, and find in many cases co-incidence with well-known finiteness properties.
Rational interpolation to |x| at the Chebyshev nodes
Authors: Brutman Lev , Passow Eli
Published: April 2009

Recently the authors considered Newman-type rational interpolation to |x| induced by arbitrary sets of interpolation nodes and showed that under mild restrictions on the location of the interpolation nodes, the corresponding sequence of rational interpolants converges to |x|. In the present paper we consider the special case of the Chebyshev nodes which are known to be very efficient for polynomial interpolation. It is shown that, in contrast to the polynomial case, the approximation of |x| induced by rational interpolation at the Chebyshev nodes has the same order as rational interpolation at equidistant points.
Computing the topological degree of polynomial maps
Authors: Sakkalis Takis , Ligatsikas Zenon
Published: April 2009

Let C be a cube in Rn+1 and let F = (f1, …, fn+1) be a polynomial vector field. In this note we propose a recursive algorithm for the computation of the degree of F on C. The main idea of the algorithm is that the degree of F is equal to the algebraic sum of the degrees of the map (f1, f2, …, fi−1, fi, fi+1, …, fn+1) over all sides of C, thereby reducing an (n + 1)–dimensional problem to an n–dimensional one.
Periodic-recurrent property of some continua
Authors: Charatonik Janusz J. , Charatonik Wlodzimierz J.
Published: April 2009

The equality between the closures of the sets of periodic and of recurrent points (called the periodic-recurrent property) is extended from mappings of a tree to mappings defined on a λ-dendroid obtained as a compactification of the complement of a finite subset of a tree provided that the components of the remainder have the same finite depth and each has the periodic-recurrent property.
On a Banach space without a weak mid-point locally uniformly rotund norm
Authors: Hu Zhibao , Moors Warren B. , Smith Mark A.
Published: April 2009

In this paper we show that (i) l∞ does not admit an equivalent weak mid-point locally uniformly rotund norm and (ii) l∞ / c0 does not admit an equivalent rotund norm.
Systems of differential equations with fully nonlinear boundary conditions
Authors: Thompson H.B.
Published: April 2009

We give sufficient conditions involving f, g and ω in order that systems of differential equations of the form y″ = f(x, y, y′), x in [0, 1] with fully nonlinear boundary conditions of the form g((y(0), y(1)), (y′(0), y′(1))) = 0 have solutions y with (x, y) in . We use Schauder degree theory in a novel space. Well known existence results for the Picard, the periodic and the Neumann boundary conditions follow as special cases of our results.
On conjecture of Resnikoff and Saldaña
Authors: Kohnen Winfried
Published: April 2009

In 1974 Resnikoff and Saldaña made a remarkable conjecture about the growth of the Fourier coefficients of a Siegel cusp form F of arbitrary genus g ≥ 1. In the present note, we point out that this conjecture is at least true on average.
Quotient de Hadamard en plusieurs variables
Authors: Necer Abdelkader
Published: April 2009

We obtain some results about a conjecture of Hadamard's quotient of rational series in the case of several variables.
Subdifferential Rolle's and mean value inequality theorems
Authors: Azagra D. , Deville R.
Published: April 2009

In this note we give a subdifferential mean value inequality for every continuous Gâteaux subdiferentiable function f in a Banach space which only requires a bound for one but not necessarily all of the subgradients of f at every point of its domain. We also give a subdifferential approximate Rolle's theorem satating that if a subdifferentiable function oscilllates between −ɛ and ɛ on the boundary of the unit ball then there exists a subgradient of the function at an interior point of the ball which has norm less than or equal to 2ɛ.
Fundamental theorem of prehomogeneous vector spaces of characteristic p
Authors: Kimura Tatsuo , Kogiso Takeyoshi , Fujinaga Makiko
Published: April 2009

For a local field of characteristic 0, the functional equations of zeta distributions of prehomogeneous vector spaces have been obtained by M. Sato, Shintani, Igusa, F. Sato and Gyoja. In this paper, we shall consider the case of local fields of characteristic p > 0.
Finite dimensional H-invariant spaces
Authors: Hare K.E. , Ward J.A.
Published: April 2009

A subset V of M(G) is left H-invariant if it is invariant under left translation by the elements of H, a subset of a locally compact group G. We establish necessary and sufficient conditions on H which ensure that finite dimensional subspaces of M(G) when G is compact, or of L∞(G) when G is locally compact Abelian, which are invariant in this weaker sense, contain only trigonometric polynomials. This generalises known results for finite dimensional G-invariant subspaces. We show that if H is a subgroup of finite index in a compact group G, and the span of the H-translates of μ is a weak*-closed subspace of L∞(G) or M(G) (or is closed in Lp(G)for 1 ≤ p < ∞), then μ is a trigonometric polynomial.

We also obtain some results concerning functions that possess the analogous weaker almost periodic condition relative to H.
Semi-invex functions and their subdifferentials
Authors: Dutta J. , Vetrivel V. , Nanda S.
Published: April 2009

We introduce the notion of semi-invex function (non-smooth) and the associated subdifferential. We study their properties and establish the conditions for optimality in constrained and unconstrained minimisation problems.
Metrisation of Moore spaces and abstract topological manifolds
Authors: Fearnley David L.
Published: April 2009

The problem of metrising abstract topological spaces constitutes one of the major themes of topology. Since, for each new significant class of topological spaces this question arises, the problem is always current. One of the famous metrisation problems is the Normal Moore Space Conjecture. It is known from relatively recent work that one must add special conditions in order to be able to get affirmative results for this problem. In this paper we establish such special conditions. Since these conditions are characterised by local simplicity and global coherence they are referred to in this paper generically as “abstract topological manifolds.” In particular we establish a generalisation of a classical development of Bing, giving a proof which is complete in itself, not depending on the result or arguments of Bing. In addition we show that the spaces recently developed by Collins designated as “W satisfying open G(N)” are metrisable if they are locally separable and locally connected and regular. Finally, we establish a new necessary and sufficient condition for spaces to be metrisable.
Categorical equivalence of finite groups
Authors: Zádori László
Published: April 2009

We determine the minimal relational sets related to finite groups. With the help of this result we prove that two categorically equivalent finite groups are weakly isomorphic.
Inequalities for symmetric means, symmetric harmonic means, and their applications
Authors: Ku Hsu-Tung , Ku Mei-Chin , Zhang Xin-Min
Published: April 2009

In this paper, we establish a number of inequalities involving symmetric means and symmetric harmonic means. We then apply these new inequalities to obtain many geometric inequalities of isoperimetric type for plane polygons.
Generic Gateaux differentiability via smooth perturbations
Authors: Georgiev Pando Gr , Zlateva Nadia P.
Published: April 2009

We prove that in a Banach space with a Lipschitz uniformly Gateaux smooth bump function, every continuous function which is directionally differentiable on a dense Gδ subset of the space, is Gateaux differentiable on a dense Gδ subset of the space. Applications of this result are given.
A note on bump functions that locally depend on finitely many coordinates
Authors: Fabian M. , Zizler V.
Published: April 2009

We show that if a continuous bump function on a Banach space X locally depends on finitely many elements of a set F in X*, then the norm closed linear span of F equals to X*. Some corollaries for Markuševič bases and Asplund spaces are derived.
Stirring our way to Sharkovsky's theorem
Authors: Patinkin Seth
Published: April 2009

The periodic-point or cycle structure of a continuous map of a topological space has been a subject of great interest since A.N. Sharkovsky completely explained the hierarchy of periodic orders of a continuous map f: R → R, where R is the real line. In this paper the topological idea of “stirring” is invoked in an effort to obtain a transparent proof of a generalisation of Sharkovsky's Theorem to continuous functions f: I → I where I is any interval. The stirring approach avoids all graph-theoretical and symbolic abstraction of the problem in favour of a more concrete intermediate-value-theorem-oriented analysis of cycles inside an interval.
Tree maps with non divisible periodic orbits
Authors: Ye Xiangdong
Published: April 2009

Let End (T) be the number of ends of a treeTandf:T→Tbe continuous. We show thatfhas a non divisible periodic orbit if and only if there are somex∈Tandn> 1 with (n, m) = 1 for each 2 ≤m≤ End(T) such thatx∈ (f(x),fn(x)). Consequently the property of a tree map with a non divisible periodic orbit is preserved under small perturbation.
On the index of Dirac operators on arithmetic quotients
Authors: Deitmar Anton
Published: April 2009

The aim of this note is to show how the trace formula of Arthur-Selberg can be used to derive index theorems for noncompact arithmetic manifolds. Of special interest is the question, under which circumstances there is an index formula without error term, that is, of the same shape as in the compact case. We shall thus present evidence for the hypothesis that the error term for the Euler operator vanishes in the case that the rational rank is smaller than the real rank.
Closed linear maps from a barrelled normed space into itself need not be continuous
Authors: Bonet José
Published: April 2009

Examples of normed barrelled spacesEor quasicomplete barrelled spacesEare given such that there is a non-continuous linear map from the spaceEinto itself with closed graph.
On a diophantine equation
Authors: Muriefah Fadwa S. Abu , Arif S. Akhtar
Published: April 2009

In this paper the equation x2 + 32k = yn where n ≥ 3 is studied. For n = 3, it is proved that it has a solution only if k = 3K + 2 and then there is a unique solution x = 46 × 33K and y = 13 × 32K. For n > 3 theorems are proved which determine a large number of values of k and n for which this equation has no solution. It is proved that if this equation has a solution for n > 3, then n is odd and k = 2δ.k′ where δ ≥ 1, (2, δ) = 1, k′ ≡ 15 (mod 20) and all the primes divisors p of n are congruent to 11 (mod 12).
Convergence of a quadrature formula for variable-signed weight functions
Authors: Jung H.S. , Kwon K.H.
Published: April 2009

A quadrature formula for a variable-signed weight function w(x) is constructed using Hermite interpolating polynomials. We show its mean and quadratic mean convergence. We also discuss the rate of convergence in terms of the modulus of continuity for higher order derivatives with respect to the sup norm.
Spherical submanifolds with special quadric representations
Authors: Lu Jitan
Published: April 2009

In this paper, we study submanifolds in the unit hypersphere satisfying where is the quadric representation of the submanifold, and B and C are two constant matrices. We prove that the totally geodesic submanifolds are the only submanifolds in the unit hypersphere whose quadric representations satisfy
The exponential stability of the problem of transmission of the wave equation
Authors: Liu Weijiu , Williams Graham
Published: April 2009

The problem of exponential stability of the problem of transmission of the wave equation with lower-order terms is considered. Making use of the classical energy method and multiplier technique, we prove that this problem of transmission is exponentially stable.
Centralisers of Galois group actions
Authors: Kisin Mark
Published: April 2009

If f is a polynomial over a field E, and σ a permutation of the roots of f, we show that σ is given by a polynomial p with coefficients in E (that is, p(a) = σ(a) for each root a of f) if and only if σ commutes with all the Galois automorphisms.
Perfect codes on the towers of Hanoi graph
Authors: Li Chi-Kwong , Nelson Ingrid
Published: April 2009

We characterise all the perfect k-error correcting codes that can be defined on the graph associated with the Towers of Hanoi puzzle. In particular, a short proof for the existence of 1-error correcting code on such a graph is given.
Semigroup rings in semisimple varieties
Authors: Kelarev A.V.
Published: April 2009

We describe semigroup rings which belong to self-dual varieties generated by a finite number of finite fields.
PF-rings of generalised power series
Authors: Liu Zhongkui
Published: April 2009

Let R be a commutative ring and (S, ≤) a strictly ordered monoid which satisfies the condition that 0 ≤ s for every s ∈ S. We show that the generalised power series ring [[RS ≤]] is a PF-ring if and only if R is a PF-ring.
Iteration processes for approximating fixed points of operators of monotone type
Authors: Chang Shih-Sen , Tan Kok-Keong
Published: April 2009

In this paper, the unique fixed points of multi-valued and single-valued operators of monotone type are approximated by Ishikawa iteration processes or Mann and Ishikawa iteration processes with errors in uniformly smooth Banach spaces. The operators may not satisfy the Lipschitzian conditions and the domain or the range of the operators may not be bounded. The results presented improve and extend some recent results.
The modular counterparts of Cayley's hyperdeterminants
Authors: Glynn David G.
Published: April 2009

LetHbe a hypersurface of degreeminPG(n, q),q=ph,pprime.

(1) Ifm<n+ 1,Hhas 1 (modp) points.

(2) Ifm=n+ 1,Hhas 1 (modp) points ⇔Hp−1has no term

We show some applications, including the generalised Hasse invariant for hypersurfaces of degreen+ 1 inPG(n, F), various porperties of finite projective spaces, and in particular ap-modular invariant detpof any (n+ 1)r+2= (n+ 1)×…×(n+ 1) array on hypercubeAover a field characteristicp. This invariant is multiplicative in that detp(AB) = detp(B), whenever the product (or convolution of the two arraysAandBis defined, and both arrays are not 1-dimensional vectors. (IfAis (n+ 1)r+2andBis (n+ 1)s+2, thenABis (n+ 1)r+s+2.) The geometrical meaning of the invariant is that over finite fields of characteristicpthe number of projections ofAfromr+ 1 points in any givenr+ 1 directions of the array to a non-zero point in the final direction is 0 (modp). Equivalently, the number of projections ofAfromrpoints in any givenrdirections to a non-singular (n+ 1)2matrix is 0 (modp). Historical aspects of invariant theory and connections with Cayley's hyperdeterminant Det for characteristic 0 fields are mentioned.
Quotients of permutation groups
Authors: Cossey John
Published: April 2009

If G is a finite permutation group of degree d and N is a normal subgroup of G, Derek Holt has given conditions which show that in some important special cases the least degree of a faithful permutation representation of the quotient G/N will be no larger than d. His conditions do not apply in all cases of interest and he remarks that it would be interesting to know if G/F(G) has a faithful representation of degree no larger than d (where F(G) is the Fitting subgroup of G). We prove in this note that this is the case.
Exponential actions, orbits and their kernels
Authors: Ludwig J. , Molitor-Braun C.
Published: April 2009

Let be a nilpotent Lie algebra which is an exponential -module, being an exponential algebra of derivations of . Put = exp and = exp . If Ω is a closed orbit of * under the action of , then Ker is dense in Ker Ω for the topology of L1 () and the algebra Ker is nilpotent, where denotes the minimal closed ideal of L1() whose hull is Ω. Moreover, the -prime ideals of Ll() coincide with the kernels Ker Ω, where Ω denotes an arbitrary orbit (not necessarily closed) in *.
The n-th derivative characterisation of Möbius invariant Dirichlet space
Authors: Aulaskari Rauno , Nowak Maria , Zhao Ruhan
Published: April 2009

In this paper we give the n-th derivative criterion for functions belonging to recently defined function spaces Qp and Qp, 0. For a special parameter value p = 1 this criterion is applied to BMOA and VMOA, and for p > 1 it is applied to the Bloch space and the little Bloch space . Further, a Carleson measure characterisation is given to Qp, and in the last section the multiplier space from Hq into Qp is considered.
Quotient supermanifolds
Authors: Bartocci Claudio , Bruzzo Ugo , Ruipérez Daniel Hernández , Pestov Vladimir
Published: April 2009

A necessary and sufficient condition for the existence of a supermanifold structure on a quotient defined by an equivalence relation is established. Furthermore, we show that an equivalence relation R on a Berezin-Leĭtes-Kostant supermanifold X determines a quotient supermanifold X/R if and only if the restriction R0 of R to the underlying smooth manifold X0 of X determines a quotient smooth manifold X0/R0.
Comparable characterisations of two classes of Banach spaces by subdifferentials
Authors: Giles J.R.
Published: April 2009

We characterise Banach spaces not containing ℓ1 and Banach spaces which are Asplund spaces by continuity properties of the subdifferential mappings of their equivalent norms.
Some inequalities for planar convex sets containing one lattice point
Authors: Cifre M. A. Hernández , Gomis S. Segura
Published: April 2009

We obtain two inequalities relating the diameter and the (minimal) width with the area of a planar convex set containing exactly one point of the integer lattice in its interior. They are best possible. We then use these results to obtain some related inequalities.
Remarks on square functions in the Littlewood-Paley theory
Authors: Sato Shuichi
Published: April 2009

We prove that certain square function operators in the Littlewood-Paley theory defined by the kernels without any regularity are bounded on , 1 < p < ∞, w ∈ Ap (the weights of Muckenhoupt). Then, we give some applications to the Carleson measures on the upper half space.
Pseudo-monotonicity and degenerated or singular elliptic operators
Authors: Drábek P. , Kufner A. , Mustonen V.
Published: April 2009

Using the compactness of an imbedding for weighted Sobolev spaces (that is, a Hardy-type inequality), it is shown how the assumption of monotonicity can be weakened still guaranteeing the pseudo-monotonicity of certain nonlinear degenerated or singular elliptic differential operators. The result extends analogous assertions for elliptic operators.
Tail probabilities for weighted sums of products of normal random variables
Authors: Ivanoff B. Gail , Weber N.C.
Published: April 2009

Weighted sums of products of independent normal random variables arise naturally as distributional limits for various statistics. This note investigates the rate at which the tail probability of these sums approaches zero.
Jones polynomials of periodic knots
Authors: Bae Yongju , Kim Young Kon , Park Chan-Young
Published: April 2009

We calculate the Zulli's matrix of a periodic knot and give some necessary conditions for the Jones polynomial of a periodic knot, which are slightly different from Yokota's result.
Holomorphic functional calculi and sums of commuting opertors
Authors: Albrecht David , Franks Edwin , McIntosh Alan
Published: April 2009

Let S and T be commuting operators of type ω and type ϖ in a Banach space X. Then the pair has a joint holomorphic functional calculus in the sense that it is possible to define operators f(S, T) in a consistent manner, when f is a suitable holomorphic function defined on a product of sectors. In particular, this gives a way to define the sum S + T when ω + ϖ < π. We show that this operator is always of type μ where μ = max{ω, ϖ}. We explore when bounds on the individual functional calculi of S and T imply bounds on the functional calculus of the pair (S, T), and some implications for the regularity problem of when ∥(S + T)u∥ is equivalent to ∥Su∥ + ∥Tu∥.
Stability of discrete orthogonal projections for continuous splines
Authors: Grigorieff R.D. , Sloan I.H.
Published: April 2009

In this paper Lp stability and convergence properties of discrete orthogonal projections on the finite element space Sh of continuous polynomial splines of order r are proved. The discrete inner products are defined by composite quadrature rules with positive weights on a sequence of nonuniform grids. It is assumed that the basic quadrature rule Q has at least r quadrature points in order to resolve Sh, but no accuracy is required. The main results are derived under minimal further assumptions, for example the rule Q is allowed to be non-symmetric, and no quasi-uniformity of the mesh is required. The corresponding stability of the orthogonal L2-projections has been studied by de Boor [1] and by Crouzeix and Thomee [2]. Stability of the first derivative of the projection is also proved, under an assumption (unless p = 1) of local quasi-uniformity of the mesh.
Fréchet AL-spaces have the Dunford-Pettis property
Authors: Díaz J.C. , Fernández A. , Naranjo F.
Published: April 2009

A Fréchet lattice E is an AL-space if its topology can be defined by a family of lattice seminorms that are additive in the positive cone of E. Grothendieck proved that AL-Banach spaces have the Dunford-Pettis property. This result was recently extended by Fernández and Naranjo to AL-Fréchet spaces with a continuous norm and weak order unit. In this note we show how to remove both hypotheses.