bluuebunny/crossref_metadata_2025 huggingface dataset:
The semidirect product of an inverse semigroup and a group
Authors: Preston G. B.
Published: April 2009

It is shown that a semidirect product of an inverse semigroup and a group, in that order, contains an inverse subsemigroup that is a retract and that, together with the retraction mapping, forms free inverse morphic image of the semidirect product. The congruence determined by the retraction mapping is shown to be determined by the semigroup of idempotents of the semidirect product.
A note on compact subgroups of topological groups
Authors: Bagley R. W. , Peyrovian M. R.
Published: April 2009

Our main concern is the existence of maximal compact subgroups in a locally compact topological group. If G is a locally compact group such that P(G/G o), the set of periodic points of G/Go, is a compact subgroup of G/Go, than G has maximal compact subgroups K such that G/N is a Lie group where N = ∩K, the intersection of the collection K of all maximal compact subgroups of G. Also every compact subgroup of G is contained in a maximal compact subgroup. We given an example of a discrete group which has maximal finite subgroup and has finite subgroups not contained in maximal finite subgroups. We note that the above result on P(G/Go) is an extension of the well-known corresponding result for almost connected groups.
On a property of ideals of differentiable functions
Authors: Bruno Oscar P.
Published: April 2009

Let J ⊆ C∞ (Rn) be any ideal. Since a function of the variables t̄ = (t1,…,tn) is a function of the variables which does not depend on x̄, we have J ⊆ C∞ (IRn+P). Of course, J is not an ideal of C∞ (IRn+P), but it generates an ideal that we call . Consider the following statement (1) on J: “Given any if and only if for every fixed .

In this paper we show that statement (1) holds for a large class of finitely generated ideals although not for all of them. We say that ideals satisfying statement (1) have line determined extensions. We characterize these ideals to be closed ideals J(t̄) (in the sense of Whitney) such that for all p ∈ ℕ, the ideal is also closed. Finally, some non-trivial examples are developed.
On convergence of the conjugate Fourier series of a function of Wiener's class
Authors: Siddiqi Rafat N.
Published: April 2009

The main object of this paper is to extend the theorem of W.H. Young on convergence of the conjugate Fourier series to Wiener's class. We prove that the conjugate Fourier series of a function of Wiener's class converges to for every x for which exists.
Morita duality and artinian left duo rings
Authors: Xue Weimin
Published: April 2009

We characterise artinian left duo rings via Morita duality, and show that there is a large class of such rings that possess a duality.
Deformations of rings
Authors: Yanik Joe
Published: April 2009

Let A and A0 be rings with a surjective homomorphism A → A0. Given a flat extension B0 of A0, a deformation of B0/A0 over A is a flat extension B of A such that B ⊗AA0 is isomorphic to B0. We show that such a deformation will exist if A0 is an Artin local ring, A is noetherian, and the homological dimension of B0 over A0 is ≤ 2. We also show that a deformation will exist if the kernel of A is nilpotent and if A0 is a finitely generted A0-algebra whose defining ideal is a local complete intersection.
Besov-type characterisations for the Bloch space
Authors: Stroethoff Karel
Published: April 2009

We will prove local and global Besov-type characterisations for the Bloch space and the little Bloch space. As a special case we obtain that the Bloch space consists of those analytic functions on the unit disc whose restrictions to pseudo-hyperbolic discs (of fixed pseudo-hyperbolic radius) uniformly belong to the Besov space. We also generalise the results to Bloch functions and little Bloch functions on the unit ball in . Finally we discuss the related spaces BMOA and VMOA.
On the area growth of a hyperbolic surface
Authors: Leung Pui-Fai
Published: April 2009

We conjecture that if the rate of area growth of a geodesic disc of radius r on a smooth simply-connected complete surface with non-positive Gaussian curvature is faster than r2(logr)1+e for some ε ≥ 0, then the surface is hyperbolic. We prove this under an additional assumption that the surface is rotationally symmetric.
Inequalities and semigroups
Authors: Ralph W.J.
Published: April 2009

We define the notion of a convex function between semigroups and show that for such functions one obtains not only Jensen's Inequality but a new and powerful companion inequality. Taken together, these two inequalities can be easily applied to give trivial derivations of many of the classical inequalities as well as many new inequalities.
On the superpostition of functions in carleman classes
Authors: Ider Mostefa
Published: April 2009

In this paper we deal with classes of infinitely differentiable functions known in the literature as Carleman classes. Our main result is a characterisation of those Carleman classes that are closed under superposition. This result enables us to give a complete solution to a problem that has been considered by Gevrey, Cartan and Bang.
Data types in distributive categories
Authors: Walters R.F.C.
Published: April 2009

The purpose of this note is to describe some of the standard data types of computer science in the language of distributive categories. We believe that in this way we have achieved a simplification and a formal clarification of the specification of these data types.
An example on composite differentiable functions in infinite dimensions
Authors: Jaramillo J.A.
Published: April 2009

We present an example showing that a classical result due to Glaeser about the closedness of composition subalgebras of infinitely differentiable functions cannot be extended to the case of weakiy uniformly differentiable functions on Banach spaces.
On nilpotent and polycyclic groups
Authors: Hursey Robert J.
Published: April 2009

A group G is torsion-free, finitely generated, and nilpotent if and only if G is a supersolvable R-group. An ordered polycylic group G is nilpotent if and only if there exists an order on G with respect to which the number of convex subgroups is one more than the length of G. If the factors of the upper central series of a torsion-free nilpotent group G are locally cyclic, then consecutive terms of the series are jumps, and the terms are absolutely convex subgroups.
A generalisation of Mackey's theorem and the uniform boundedness principle
Authors: Swartz Charles
Published: April 2009

We construct a locally convex topology which is stronger than the Mackey topology but still has the same bounded sets as the Mackey topology. We use this topology to give a locally convex version of the Uniform Bouudedness Principle which is valid without any completeness or barrelledness assumptions.
Chen's problem on mixed foliate CR-submanifolds
Authors: Bashir Mohammed Ali
Published: April 2009

We prove that the simply connected compact mixed foliate CR-submanifold in a hyperbolic complex space form is either a complex submanifold or a totally real submanifold. This is the problem posed by Chen.
The Nevanlinna-Pick theorem and a non-positive definite matrix
Authors: Nakazi Takahiko
Published: April 2009

Let {zj} be an interpolation sequence in the open unit disc and {wj} a bounded sequence. In this note, it is shown that there is a function F in H∞ + C satisfying ‖F‖ ≤ 1 and as j → ∞ if and only if there exists a compact matrix [tij] such that on where .
Each weakly countably determined Asplund space admits a Fréchet differentiable norm
Authors: Fabian M.
Published: April 2009

If au Asplund space is weakly countably determined, then it admits an equivalent Fréchet differentiable norm and is weakly compactly generated. If on an Asplund space there exists an equivalent Gâteaux differentiable norm, then its dual has a projectional resolution of identity.
An extension of Müntz's theorems in multivariables
Authors: Ogawa Shirô , Kitahara Kazuaki
Published: April 2009

Müntz's theorems give necessary and sufficient conditions for a sequence of powers in one variable to be complete in the spaces of all real-valued continuous functions or square integrable functions with the usual norms.
Estimates for solutions of elliptic equations in a limit case
Authors: Giarrusso Ester , Trombetti Guido
Published: April 2009

Let u be a week solution of homogeneous Dirichlet problem for a second order elliptic equation of divergence form, in a bounded open subset of ℝn. We prove, that if the right hand side of the equation is an element of H−1, n(Ω), then u belongs to the Orlicz space LΦ where Φ(t) = exp(|t|n/(n−1)) − 1. We employ the properties of the Schwartz symmetrization thus obtaining the “best” constant of the estimate.
On composite polynomials whose zeros are in a half-plane
Authors: Aziz Abdul
Published: April 2009

Let P(z) and Q(z) be two polynomials of the same degree n. If P(z) and Q(z) are apolar and if one of then has all its zeros in a circular region C, then according to a famous result known as Grace's Apolarity Theorem, the other will have at least one zero in C. In this paper we relax the condition that P(z) and Q(z) are of the same degree and present some generalizations of Grace's Apolarity theorem for the case when the circular region C is a closed half-plane. As an application of these results, we also generalize some results of Walsh and Szegö.
Examples of expanding maps with some special properties
Authors: Du Bau-Sen
Published: April 2009

Let I be the unit interval [0, 1] of the real line. For integers k ≥ 1 and n ≥ 2, we construct simple piecewise monotonic expanding maps Fk, n in C0 (I, I) with the following three properties: (1) The positive integer n is an expanding constant for Fk, n for all k; (2) The topological entropy of Fk, n is greater than or equal to log n for all k; (3) Fk, n has periodic points of least period 2k · 3, but no periodic point of least period 2k−1 (2m+1) for any positive integer m. This is in contrast to the fact that there are expanding (but not piecewise monotonic) maps in C0(I, I) with very large expanding constants which have exactly one fixed point, say, at x = 1, but no other periodic point.
A modified projection method for equations of the second kind
Authors: Nair M. Thamban
Published: April 2009

A modified projection method is suggested for the approximate solution of second kind equations and it is compared with other methods.
Bounded and relatively bounded sets
Authors: Shell Niel
Published: April 2009

All subsets of a field that are intersections of almost-orders of the field are characterised, and all ring topologies on a field which are not finer than any nontrivial locally bounded ring are characterised.
Going-down underrings
Authors: Dobbs David E.
Published: April 2009

Let R be an integral domain with quotient field K. Ten conditions equivalent to “Either R is algebraic over ℤ or t.d.(R/Fp) ≤ 1 for some p” are given. One of these conditions, referred to in the title, is “Each extension of subrings of R having quotient field K satisfies the going-down property.” As consequences, other classes of rings are also characterised.
A commutativity result for rings
Authors: Klein A. A. , Nada I.
Published: April 2009

It is proved that a ring satisfying the variable indentity [[xn, y], y] = 0, n = n (x,y) ≥ 1, has nil commutator ideal.
Real hypersurfaces of a complex projective space
Authors: Kimura M.
Published: April 2009

We study real hypersurfaces M of a complex projective space and show that a condition on the derivative of the Ricci Tensor of M implies M is locally homogeneous with two or three principal curvatures.
Weak solutions of differential equations in Banach spaces
Authors: Papageorgiou Nikolaos S.
Published: April 2009

We consider the Cauchy problem x (t) = f (t,x (t)), x (0) = x0 in a nonreflexive Banach space X and for f: T × X → X a weakly continuous vector field. Using a compactness hypothesis involving a weak measure of noncompactness we prove an existence result that generalizes earlier theorems by Chow-Shur, Kato and Cramer-Lakshmikantham-Mitchell.
Orthogonality in normed spaces
Authors: Partington J. R.
Published: April 2009

Some properties which different definitions or orthogonality in a normed space can possess are considered. It is shown that orthogonality can be defined on any separable space with many of the properties possessed by the usual orthogonality in an inner-product space, but that the possession of a further property forces the space to be isomorphic to a Euclidean space.
Uniform asymptotic smoothness of norms
Authors: Lewis T. , Whitfield J. , Zizler V.
Published: April 2009

We study a notion of smoothness of a norm on a Banach space X which generalizes the notion of uniform differentiability and is formulated in terms of unicity of Hahn Banach extensions of functionals on block subspaces of a fixed Schauder basis S in X. Variants of this notion have already been used in estimating moduli of convexity in some spaces or in fixed point theory. We show that the notion can also be used in studying the convergence of expansions coefficient of elements of X* along the dual basis S*.
Asymmetric invariant sets for completely positive maps on C*-algebras
Authors: Robertson A. Guyan
Published: April 2009

Let A be a noncommutative C*-algebra other than M2(I). We show that there exists a completely positive map φ of norm one on A and an element a ɛ A such that φ(a) = a, φ(a*a) = a*a, but φ(aa*) ≠ aa*.
On quadratic functionals
Authors: Šemrl Peter
Published: April 2009

In this note a general solution of the problem of the characterisation of quadratic functionals posed by Vukman is given.
Fixed point of sum for concave and convex operators with applications
Authors: Bingyou Li
Published: April 2009

In this paper we study fixed points of sums of α-concave and (−α)-convex operators in γ-complete partially ordered linear spaces. As an application we obtain existence and uniqueness theorems for solutions of a certain type of nonlinear integral equation.
Continuous chaotic functions of an interval have generically small scrambled sets
Authors: Mizera Ivan
Published: April 2009

It is shown that continuous self-mappings of a compact interval, chaotic in the sense of Li and Yorke, have generically, in the uniform topology, only scrambled sets which are nowhere dense and of zero Lebesgue measure.
On Chung's strong law of large numbers in general Banach spaces
Authors: Choi Bong Dae , Sung Soo Hak
Published: April 2009

Let { Xn, n ≥ 1 } be a sequence of independent Banach valued random variables and { an, n, ≥ 1 } a sequence of real numbers such that 0 < an ↑ ∞. It is shown that, under the assumption with some restrictions on φ, Sn/an → 0 a.s. if and only if Sn/an → 0 in probability if and only if Sn/an → 0 in L1. From this result several known strong laws of large numbers in Banach spaces are easily derived.
Nonexpansive projections onto two-dimensional subspaces of Banach spaces
Authors: Calvert Bruce , Fitzpatrick Simon
Published: April 2009

We show that if a three dimensional normed space X has two linearly independent smooth points e and f such that every two-dimensional subspace containing e or f is the range of a nonexpansive projection then X is isometrically isomorphic to ℓp(3) for some p, 1 < p ≤ ∞. This leads to a characterisation of the Banach spaces c0 and ℓp, 1 < p ≤ ∞, and a characterisation of real Hilbert spaces.
Groups whose three-generator subgroups are free
Authors: Baumslag Gilbert , Shalen Peter B.
Published: April 2009

We define a certain class of groups, Ck, which we show to contain the class of all k-free groups. Our main theorem shows that certain amalgamated free products of groups in C3, are again in C3. In the appendix we show that many 3-manifold groups belong to Ck for suitable k.
Generators for the bounded automorphisms of infinite-rank free nilpotent groups
Authors: Burns R.G. , Pi Lian
Published: April 2009

It is shown that the natural generalisations of the elementary Nielsen transformations of a free group to the infinite-rank case, furnish generators for the subgroup of “bounded” automorphisms of any relatively free nilpotent group of infinite rank. This settles the nilpotent analogue of a question of D. Solitar concerning the “bounded” automorphisms of absolutely free groups of infinite rank.
The heredity measure of an algebra
Authors: Dlab Vlastimil
Published: April 2009

The concept of the heredity measure of a semiprimary ring (or finite-dimensional algebra) is introduced and some of its elementary properties are studied.
Automorphisms of nilpotent-by-abelian groups
Authors: Gupta C.K. , Levin Frank
Published: April 2009

For F free of rank 4, a generating set for Aut (F/[F′, F′, F′]) exhibiting countably many wild automorphisms is obtained. Also included are examples of wild automorphisms in Aut (F/Vk+1) which are tame in Aut (F/Vk) for k ≥ 1, where Vk = [F″, F,…, F] (F repeats k times).
Permutable word products in groups
Authors: Kim P.S. , Rhemtulla A.H.
Published: April 2009

Let u(x1,…,xn) = x11 … x1m be a word in the alphabet x1, …,xn such that x1i ≠ x1i for all i = 1,…, m − 1. If (H1, …, Hn) is an n-tuple of subgroups of a group G then denote by u(H1, …, Hn) the set {u(h1,…,hn) | hi ∈ Hi}. If σ ∈ Sn then denote by uσ(H1,…,Hn) the set u(Hσ(1),…,Hσ(n)). We study groups G with the property that for each n-tuple (H1,…,Hn) of subgroups of G, there is some σ ∈ Sn σ ≠ 1 such that u(H1,…,Hn) = uσ(H1,…,Hn). If G is a finitely generated soluble group then G has this property for some word u if and only if G is nilpotent-by-finite. In the paper we also look at some specific words u and study the properties of the associated groups.
On bilinear forms represented by trees
Authors: Neumann Walter D.
Published: April 2009

The adjacency matrix of a weighted graph determines an integral bilinear form. The trees with unimodular adjacency matrices are described with special emphasis on the definite and semidefinite cases, since they arise as configuration graphs of good divisors in compact complex surfaces.
Growth sequences of finitely generated groups II
Authors: Stewart A.G.R. , Wiegold James
Published: April 2009

A study is made of the minimum number of generators of the n-th direct power of certain finitely generated groups.
Homomorphisms on an orthogonally decomposable Hilbert space V
Authors: Yamamuro Sadayuki
Published: April 2009

For a triple (M, H,ξ0) of a von Neumann algebra M on a Hilbert space H with a cyclic and separating vector ξ0, every order isormorphism ø, of H such that øξ0 = ξ0 is an orthogonal decomposition isomorphism if and only if ξ0 is a trace vector.
Polynomial rings over rings integral over their centres
Authors: Wangneo C. L.
Published: April 2009

We prove in this paper that every finitely generated critical module over A[X] is compressible where A is a Noetherian ring integral over a subring of its centre. Here A[X] denotes the polynomial ring over A in a commuting indeterminate X.
Remarks on completeness in spaces of linear operators
Authors: Ricker W.
Published: April 2009

Whereas a locally convex Hausdorff space X inherits any completeness properties that the space of continuous linear operators, L (X), in X, may have (for the topology of pointwise convergence in X), this is not so in the converse situation and is the problem discussed here. The barrelledness of X in its Mackey topology plays an important role: if L (X) is quasicomplete, then X is barrelled for its Mackey topology. Consequently, for Mackey spaces X is turns out that L (X) is quasicomplete if and only if X is quasicomplete and barrelled: this is false if sequential completeness is substituted for quasicompleteness. Furthermore, there exist non-barrelled spaces X for which X and L (X) are quasicomplete (sequentially complete). Hence, although barrelledness is a sufficient condition for completeness of L (X) in various senses, it is certainly not necessary.
On balanced one-sided ideals
Authors: Schultz T. G.
Published: April 2009

The relation between the subclass X of balanced one-sided ideals, which contains all two-sided ideals, and weakly prime one-sided ideals is considered. If a member P of X is prime, then it is prime in its idealizer I (P). Furthermore, if the ring is left and right noetherain, then I (P) modulo P is a prime Goldie ring.
Closed derivation on the unit square
Authors: Jean Maw-Ding
Published: April 2009

In this paper we extend Kurose's structure theorem to characterize a closed derivation in the algebra of continuous functions on the unit square, under the conditions that the range is the whole algebra and the kernel is the set of all functions depend only on the second variable, as a partial derivative with respect to signed measures on the unit square.
Extensions of the Fuglede-Putnam-type theorems to subnormal operators
Authors: Furuta Takayuki
Published: April 2009

At first we investigate the similarity between the Kleinecke-Shirokov theorem for subnormal operators and the Fuglede-Putnam theorem and also we show an asymptotic version of this similarity. These results generalize results of Ackermans, van Eijndhoven and Martens. Also we show two theorems on degree of approximation on subnormal derivation ranges. These results generalize results of Stampfli on degree of approximation on normal derivation ranges. The purpose of this paper is to show that the Fuglede-Putnam-type theorem on normal operators can certainly be generalized to subnormal operators.
On the Fourier transforms
Authors: Wang Hwai-chiuan
Published: April 2009

In this article we give a new proof of the theorem that a positive even convex function on the real line, which vanishes at infinity, is the Fourier transform of an integrable function. Related results in several variables are also proved. As an application of our results we solve the factorization problem of Sobolev algebras.
The power concavity of solutions of some semilinear elliptic boundary-value problems
Authors: Keady Grant
Published: April 2009

Let Ω be a bounded convex domain in R2 with a smooth boundary. Let 0 < γ < 1. Let be a solution, positive in Ω, of

Then the function uα is concave for α = (l–γ)/2.
Periodic solutions of quasilinear non-autonomous systems with impulses
Authors: Hristova S.G. , Bainov D.D.
Published: April 2009

The paper considers a system of differential equations with impulse perturbations at fixed moments in time of the form

where x ∈ Rn, ε is a small parameter,

Sufficient conditions are found for the existence of the periodic solution of the given system in the critical and non-critical cases.
Lebesgue constants for double Hausdorff means
Authors: Ustina F.
Published: April 2009

As is well known, the divergence of the set of constants known as the Lebesgue constants corresponding to a particular method of summability implies the existence of a continuous, periodic function whose Fourier series, summed by the method, diverges at a point, and of another such function the sums of whose Fourier series converge everywhere but not uniformly in the neighborhood of some point.

In 1961, Lorch and Newman established that if L(n; g) is the nth Lebesgue constant for the Hausdorff summability method corresponding to the weight function g(u), then

where

where the summation is taken over the jump discontinuities {εk} of g(u) and M{f(u)} denotes the mean value of the almost periodic function f(u).

In this paper, a partial extension of this result to the two dimensional analogue is obtained. This extension is summarized in Theorem 1.3.
On the zeros of a polynomial and its derivative
Authors: Aziz Abdul
Published: April 2009

Let P(z) be a polynomial of degree n and P′(z) be its derivative. Given a zero of P′(z), we shall determine regions which contains at least one zero of P(z). In particular, it will be shown that if all the zeros of P(z) lie in |z| < 1 and W1, W2, …, Wn−1 are the zeros of P′(z), then each of the disks |(z/2)–wj| < ½ and |z–Wj| < 1, j = 1, 2, …, n−1 contains at least one zero of P(z). We shall also determine regions which contain at least one zero of the polynomials mP(z) + zP′(z) and P′(z) under some appropriate assumptions. Finally some other results of similar nature will be obtained.
On the radical theory of Andrunakievich varieties
Authors: Ánh P.N. , Loi N.V. , Wiegandt R.
Published: April 2009

In 1978 Anderson and Gardner investigated semisimple classes and recently Buys and Gerber developed the theory of special radicals in Andrunakievich varieties. In this note we continue the study of radical theory in Andrunakievich varieties. Sharpening some of the results of Anderson and Gardner we prove versions of Sands' Theorem characterizing semisimple classes by regularity, coinductivity and being closed under extensions. In the proof we follow a new method which avoids calculations with defining identities of the variety. We generalize van Leeuwen's Theorem characterizing semisimple classes of hereditary radicals as classes being regular and closed under essential extensions and subdirect sums.
Bilateral approximations and periodic solutions of systems of differential equations with impulses
Authors: Hristova S.G. , Bainov D.D.
Published: April 2009

The paper justifies a method of bilateral approximations for finding the periodic solution of a non-linear system of differential equations with impulsive perturbations at fixed moments of time.
On the absolute summability factor of Fourier series
Authors: Okuyama Yasuo
Published: April 2009

The purpose of this paper is to give a general theorem on the absolute Riesz summability factor of Fourier series which implies Matsumoto's Theorem [Tôhoku Math. J. 8 (1956), 114–124] and to deduce some results from the theorem.
Finite Prandtl number convection with nearly insulating boundaries
Authors: Riahi N.
Published: April 2009

Arbitrary Prandtl number convection in a layer with nearly insulating boundaries is investigated. For B1/3 > 3.95P (P is the Prandtl number and B being the ratio between the thermal conductivities of the boundary and of the fluid) two-dimensional rolls are stable. The heat transported by the stable rolls reaches its peak at a critical P = B1/3/5.77 beyond which the heat flux decreases with increasing P. For B1/3 = 3.95P rolls become unstable to disturbances in the form of rolls oriented at a right angle to the original rolls. For B1/3 > 3.95P square pattern convection represents the preferred stable convection. The stable square pattern transports the maximum amount of heat at a critical P = B1/3/3.7.
Invex functions and constrained local minima
Authors: Craven B.D.
Published: April 2009

If a certain weakening of convexity holds for the objective and all constraint functions in a nonconvex constrained minimization problem, Hanson showed that the Kuhn-Tucker necessary conditions are sufficient for a minimum. This property is now generalized to a property, called K-invex, of a vector function in relation to a convex cone K. Necessary conditions and sufficient conditions are obtained for a function f to be K-invex. This leads to a new second order sufficient condition for a constrained minimum.
Stability criteria for contractive semigroups via maximality procedures
Authors: Turinici Mihai
Published: April 2009

An abstract metrical version of the well-known Ekeland and Brøndsted maximality principle is used to derive a number of stability criteria for a class of (function) contractive semigroups on (complete) metric spaces, extending a number of classical contributions due to Bre'zis and Browder.
On orbits of algebraic groups and Lie groups
Authors: Richardson R.W.
Published: April 2009

In this paper we will be concerned with orbits of a closed subgroup Z of an algebraic group (respectively Lie group) G on a homogeneous space X for G. More precisely, let D be a closed subgroup of G and let X denote the coset space G/D. Let S be a subgroup of G and let Z denote (GS)0 the identity component of GS, the centralizer of S in G. We consider the orbits of Z on XS, the set of fixed points of S on X. We also treat the more general situation in which S is an algebraic group (respectively Lie group) which acts on G by automorphisms and acts on X compatibly with the action of G; again we consider the orbits of (GS)0 on XS.
Handlebody decompositions for G-manifolds
Authors: Field M.J.
Published: April 2009

We construct handle-bundle decompositions of compact G-manifolds, G a compact Lie group, that are particularly well adapted to the orbit structure of the group action.
On explicit estimates for linear forms in the values of a class of E-functions
Authors: Guangshan Xu , Lianxiang Wang
Published: April 2009

We apply methods of Mahler to obtain explicit lower bounds for certain combinations of E-functions satisfying systems of linear differential equations as studied by Makarov. Our results sharpen and generalise earlier results of Mahler, Shidlovskii, and Väänänen.
Certain integrals for classes of p-valent meromorphic functions
Authors: Kumar Vinod , Shukla S.L.
Published: April 2009

In this paper we introduce two classes, namely Γp(m, M) and Σp(m, M), of functions

regular and p-valent in D − {0} where D = {z : |z| < 1}. We show that, for suitable choices of real constants α, β and γ, the integral operators of the form

map into , where is the class of p-valent meromorphically starlike functions of order ρ, 0 ≤ ρ < 1. For the classes Γp(m, M) and Σp(m, M), we obtain class preserving integral operators of the form

with suitable restrictions on real constants α and γ.

Our results generalize almost all known results obtained so far in this direction.
Cardinality of discrete subsets of a topological space
Authors: Gauld David B. , Vamanamurthy M.K.
Published: April 2009

In this paper we prove two results relating the cardinalities of discrete subsets to those of dense subsets of a topological space. In particular, we show that

(1) closed discrete subsets of separable normal spaces are countable, and

(2) discrete subsets of separable regular spaces have cardinalities at most that of the continuum.
Bounds for solutions of systems of linear equations
Authors: Vaaler Jeffrey D. , van der Poorten A.J.
Published: April 2009

We apply recent results of Vaaler that simultaneously bound linear forms so as to obtain a ‘Siegel lemma’, sharper than those that have appeared in the literature, and in a shape convenient for application in transcendence theory.
Continued fraction solutions of the Riccati equation
Authors: Stokes A.N.
Published: April 2009

It is shown that for a solution of a Riccati equation with polynomial coefficients an expansion can be constructed as a Stieltjes continued fraction, with coefficients given by a recurrence relation, which is in general non-linear. Particular expansions associated with hypergeometric and confluent hypergeometric equations are given, and are shown to have a uniquely simple form.
On some Banach space sequences
Authors: Khalil Roshdi
Published: April 2009

We introduce the Banach space of vector valued sequences lp, q(E), 1 ≤ p, q ≤ ∞, where E is a Banach space. Then we study the relation between lp, q(E) and the Schur multipliers of lpE, where E is taken to be some lr.
Time lags and density dependence in age dependent two species competition
Authors: Gopalsamy K.
Published: April 2009

Sufficient conditions are obtained for the existence and linear stability of time independent age distributions in two species competition with age and time lagged density dependent mortality and fertility functions.
Weak ideal invariance and orders in artinian rings: Corrigendum
Authors: Beachy John A.
Published: April 2009

Let R be an associative ring with identity element which has Krull dimension on the left (see [3] for the relevant definitions). For any ordinal α, and any module RX, let τα(X) denote the sum in. X of all cyclic submodules of Krull dimension less than α. (The Krull dimension of a module X will be denoted by |x|.) It is clear that if X' is a submodule of X, then τα(X) = X' ∩ τα(X) and that f[τα(X)] ⊆ τα(Y) for any R-homomorphism f: X→Y. Thus τα defines a torsion preradical.
Some results concerning symmetric distributions
Authors: Csörgoö Sándor , Heathcote C.R.
Published: April 2009

The purpose of this note is to establish results of a technical nature concerning a stochastic process that appears to be useful in the study of certain problems in statistical inference. These problems concern a test for symmetry, a method for obtaining an adaptive estimator of the centre of symmetry, and the detection of outliers with respect to the normal distribution. Details of the applications will be presented elsewhere.
Differential forms with values in groups
Authors: Kock Anders
Published: April 2009

In the context of synthetic differential geometry, we present a notion of differential form with values in a group object, typically a Lie group or the group of all diffeomorphisms of a manifold. Natural geometric examples of such forms and the role of their exterior differentiation is given. The main result is a comparison with the classical theory of Lie algebra valued forms.
Line-rank 3 affine planes
Authors: Kallaher Michael J. , Kelly Graham
Published: April 2009

We consider finite affine planes having a collineation group acting as a rank 3 permutation group on the affine lines. By a classical result of A. Wagner, such affine planes are translation planes. We show that if, in addition, the plane has odd dimension or dimension 2 over its kernel, then the plane is Desarguesian.
Generators of simple algebras
Authors: Choate David
Published: April 2009

It is shovn that simple algebras of characteristic not equal to 2, which contain non-trivial elements that satisfy xn = x for some fixed, minimal integer n > 1, are generated by these elements.
Isomorphisms of some Segal algebras and their multiplier algebras
Authors: Tewari U.B. , Parthasarathy K.
Published: April 2009

Let G1, G2, be locally compact groups and let S1, S2, be Segal algebras on G1, G2, respectively. Under certain conditions on G1, G2, and S1, S2, we prove that if there is a bipositive or isometric isomorphism between S1, S2, or between their multiplier algebras then G1, and G2, are topologically isomorphic.
Radii of univalence, starlikeness, and convexity
Authors: Yamashita Shinji
Published: April 2009

Let a function be regular in the disk |z| < 1. The radius of univalence 0.164 … of the family of f with |an| ≤ n (n ≥ 2) is, actually, the radius of star-likeness. The radius of univalence 1 - [k/(l+K)]½ of the family of f with |an| ≤ k (n ≥ 2), where K > 0 is a constant, is, actually, the radius of starlikeness. The radii of convexity of the two families are estimated from below.
Abstract Bochner-Weil-Raikov theorem in topological algebras
Authors: Fragoulopoulou Maria
Published: April 2009

Each continuous positive linear form on a commutative locally m-convex *-algebra E with a bounded approximate identity, accepts an integral representation on the hermitian spectrum (hermitian characters) of E. An alternative form of the latter is also obtained. The presented results constitute an abstract form of the Bochner-Weil-Raikov theorem within the frame of topological *-algebras.
Hyperbolic manifolds admitting holomorphic fiberings
Authors: Nag Subhashis
Published: April 2009

We give a simple proof of the result that if the total space of a holomorphic fiber bundle is (complete) hyperbolic then both the fiber and the base manifold must be (complete) hyperbolic. Shoshichi Kobayashi tried to set up examples where the total space is hyperbolic but the base is not; our theorem shows that any such example is bound to fail.
Standard elements in a nearlattice
Authors: Cornish William H. , Noor A.S.A.
Published: April 2009

Nearlattices, or lower semllattices in which any two elements have a supremum whenever they are bounded above, provide an interesting generalization of lattices. In this context, we study standard, neutral, and central elements, as well as standard ideals. A new perspective is obtained in the well established case of lattices.
Average distances in compact connected spaces
Authors: Yost David
Published: April 2009

We give a simple proof of the fact that compact, connected topological spaces have the “average distance property”. For a metric space (X, d), this asserts the existence of a unique number a = a(X) such that, given finitely many points x1, …, xn ∈ X, then there is some y ∈ X with

We examine the possible values of a(X) , for subsets of finite dimensional normed spaces. For example, if diam(X) denotes the diameter of some compact, convex set in a euclidean space, then a(X) ≤ diam(X)/√2 . On the other hand, a(X)/diam(X) can be arbitrarily close to 1 , for non-convex sets in euclidean spaces of sufficiently large dimension.
Laws in groupoids derived from semigroups
Authors: Kim Ann Chi
Published: April 2009

A simple change of the operation in a commutative semigroup leads to a groupoid. It is shown that it has no finite basis for its laws.
Note on total categories
Authors: Tholen Walter
Published: April 2009

It is shown that, for a semi-topological functor T: A → X, the category A is total, that is, the Yoneda embedding of A has a left adjoint, if X is total. In particular, monadic categories over Set (possibly without rank) are total, and full reflective subcategories of total categories are total.
Stability in the gaming equation
Authors: Gait Jason
Published: April 2009

We discuss a computationally stable numerical method for the solution of linear programs and games. The method is useful in obtaining approximate solutions to large numerically unstable linear programs.
Criteria for functions to be Bloch
Authors: Yamashita Shinji
Published: April 2009

Criteria for a holomorphic function f defined in |z| < 1 to be Bloch, namely, , are obtained in terms of the area and the length of the images of non-Euclidean disks and non-Euclidean circles, respectively.
Ideals generated by singular inner functions
Authors: von Renteln Michael
Published: April 2009

Singular inner functions are in many respects the most important and difficult type of functions in the Banach algebra H∞ of bounded analytic functions in the unit disc. This paper is concerned with ideals generated by singular inner functions. In particular, conditions on the associated measures are given so that the ideal spans the whole algebra H∞. To this end the local boundary behavior of a singular inner function is studied and the results obtained there may be of independent interest.
A note on Baire spaces and continuous lattices
Authors: Hofmann Karl H.
Published: April 2009

We prove a Baire category theorem for continuous lattices and derive category theorems for non-Hausdorff spaces which imply a category theorem of Isbell's and have applications to the spectral theory of C*-algebras. The same lattice theoretical methods yield a proof of de Groot's category theorem for regular subcompact spaces.
On a certain kind of reducible rational fractions
Authors: Lewin Mordechai
Published: April 2009

The rational fraction

a, c, p, q positive integers, reduces to a polynomial under conditions specified in a result of Grosswald who also stated necessary and sufficient conditions for all the coefficients to tie nonnegative.

This last result is given a different proof using lemmas interesting in themselves.

The method of proof is used in order to give necessary and sufficient conditions for the positive coefficients to be equal to one. For a < 2pq, a = αp + βq, α, β nonnegative integers, c > 1, the exact positions of the nonzero coefficients are established. Also a necessary and sufficient condition for the number of vanishing coefficients to be minimal is given.
The completion of a topological group
Authors: Nummela Eric C.
Published: April 2009

During the 1920's and 30's, two distinct theories of “completions” for topological spaces were being developed: the French school of mathematics was describing the familiar notion of “complete relative to a uniformity”, and the Russian school the less well-known idea of “absolutely closed”. The two agree precisely for compact spaces.

The first part of this article describes these two notions of completeness; the remainder is a presentation of the interesting, but apparently unrecorded, fact that the two ideas coincide when put in the context of topological groups.
A unified treatment of transfinite constructions for free algebras, free monoids, colimits, associated sheaves, and so on
Authors: Kelly G.M.
Published: April 2009

Many problems lead to the consideration of “algebras”, given by an object A of a category A together with “actions” TkA → A on A of one or more endofunctors of A, subjected to equational axioms. Such problems include those of free monads and free monoids, of cocompleteness in categories of monads and of monoids, of orthogonal subcategories (= generalized sheaf-categories), of categories of continuous functors, and so on; apart from problems involving the algebras for their own sake.

Desirable properties of the category of algebras - existence of free ones, cocompleteness, existence of adjoints to algebraic functors - all follow if this category can be proved reflective in some well-behaved category: for which we choose a certain comma-category T/A

We show that the reflexion exists and is given as the colimit of a simple transfinite sequence, if A is cocomplete and the Tk preserve either colimits or unions of suitably-long chains of subobjects.

The article draws heavily on the work of earlier authors, unifies and simplifies this, and extends it to new problems. Moreover the reflectivity in T/A is stronger than any earlier result, and will be applied in forthcoming articles, in an enriched version, to the study of categories with structure.
Quasi-similarity orbit of a subclass of compact operators on a Hilbert space
Authors: Chourasia N.N.
Published: April 2009

In this note we study certain properties of quasi-similarity orbit of a subclass of compact operators defined on a separable Hilbert space. This class and its quasi-similarity orbit were introduced and studied by Fialkow in Pacific J. Math. 70 (1977), 151–161.
On the stability of barrelled topologies, III
Authors: Robertson W.J. , Tweddle I. , Yeomans F.E.
Published: April 2009

Let E be a barrelled space with dual F ≠ E*. It is shown that F has uncountable codimension in E*. If M is a vector subspace of E* of countable dimension with M ∩ F = {o}, the topology τ(E, F+M) is called a countable enlargement of τ(E, F). The results of the two previous papers are extended: it is proved that a non-barrelled countable enlargement always exists, and sufficient conditions for the existence of a barrelled countable enlargement are established, to include cases where the bounded sets may all be finite dimensional. An example of this case is given, derived from Amemiya and Kōmura; some specific and general classes of spaces containing a dense barrelled vector subspace of codimension greater than or equal to c are discussed.
Distribution of iterates of first order difference equations
Authors: McGuire James B. , Thompson Colin J.
Published: April 2009

An invariant measure which is absolutely continuous with respect to Lebesgue measure is constructed for a particular first order difference equation that has an extensive biological pedigree. In a biological context this invariant measure gives the density of the population whose growth is governed by the difference equation. Further asymptotically universal results are obtained for a class of difference equations.
A duality theorem for nondifferentiable convex programming with operatorial constraints
Authors: Kanniappan P. , Sastry Sundaram M.A.
Published: April 2009

A duality theorem of Wolfe for non-linear differentiable programming is now extended to minimization of a non-differentiable, convex, objective function defined on a general locally convex topological linear space with a non-differentiable operatorial constraint, which is regularly subdifferentiable. The gradients are replaced by subgradients. This extended duality theorem is then applied to a programming problem where the objective function is the sum of a positively homogeneous, lower semi continuous, convex function and a subdifferentiable, convex function. We obtain another duality theorem which generalizes a result of Schechter.
Murskii's algebra does not satisfy min
Authors: Oates-Williams Sheila
Published: April 2009

This note shows that the variety generated by Murskii's 3-element algebra contains an infinite descending chain of subvarieties, thus falsifying a conjecture made previously by the author and M.R. Vaughan-Lee.
A note on the concept of multiset
Authors: Hickman J.L.
Published: April 2009

In various papers on some of the theoretical aspects of computing, the reader is confronted with a mathematical entity called a “multiset”, and is told that a multiset is “an unordered collection of elements that may have repeated occurrences of identical elements” (see, for example, Nachum Dershowitz and Zohar Manna, “Proving termination with multiset orderings”, Lecture Notes in Computer Science, 71). These entities are then manipulated in accordance with the classical laws of set algebra. The purpose of this note is to present a formal foundation for this concept of multiset, and to show by means of examples that if this foundation is adopted then, although certain sections of classical set algebra can be applied to multisets, it certainly cannot be applied in total.
Generalized absolute continuity of a function of Wiener's class
Authors: Siddiqi Rafat Nabi
Published: April 2009

In the present paper we give a criterion for a function of Wiener's class to belong to the class of generalized absolute continuity, in terms of Fourier-Young coefficients {Ck}. More precisely, we prove the following theorem.

THEOREM. Let Λ = (λn,k) be a normal almost periodic matrix of real numbers such that λn,k ≥ λn,k+1 for all n and k. Then for any function f of Wiener's class Vν (1 < ν < 2) to be of class of generalized absolute continuity Ap (1 < p < ∞) it is necessary and sufficient that {|Ck|2} is summable Λ to zero.
Minimal requirements for Minkowski's theorem in the plane I
Authors: Arkinstall J.R.
Published: April 2009

Let K be a closed convex set in the Euclidean plane, with area A(K), which contains in its interior only one point 0 of the integer lattice. If K has other than one or three chords bisected by 0, it is shown that A(K) ≤ 4. Also, if K has three such chords, A(K) ≤ 4.5. The results are generalised to any lattice in the plane.
Conjugacy classes in projective and special linear groups
Authors: Wall G.E.
Published: April 2009

The conjugacy classes in the finite-dimensional projective full linear, special linear and projective special linear groups over an arbitrary commutative field are determined. The results over a finite field are applied to certain enumerative problems.
Oscillating properties of the solutions of a class of neutral type functional differential equations
Authors: Zahariev A.I. , Bainov D.D.
Published: April 2009

The present paper deals with some oscillating and asymptotic properties of the functional differential equations of the form

where λ is an arbitrary positive constant and τ > 0 is a constant delay.
Limitation theorems for some methods of summability
Authors: Tanaka Minoru
Published: April 2009

The object of this paper is to establish limitation theorems for the ordinary and also absolute generalized Nörlund methods which include some known results as special cases. We shall give a different proof of the recent result of S. Narang (Proc. Indian Acad. Sci. Sect. A 88 (1979), 115–123), and we get a generalization of the result of G. Das (J. London Math. Soc. 41 (1966), 685–692) which states the summability factors of the absolute Nörlund methods.
Operator semistable probability measures on a Hilbert space
Authors: Laha R.G. , Rohatgi V.K.
Published: April 2009

A characterization of the class of operator semistable probability measures on a real separable Hilbert space is given.