bluuebunny/crossref_metadata_2025 huggingface dataset:
Unit sum numbers of right self-injective rings
Authors: Khurana Dinesh , Srivastava Ashish K.
Published: April 2009

In a recent paper (which is to appear in J. Algebra Appl.) we proved that every element of a right self-injective ring R is a sum of two units if and only if R has no factor ring isomorphic to ℤ2 and hence the unit sum number of a nonzero right self-injective ring is 2, ω or ∞. In this paper we characterise right self-injective rings with unit sum numbers ω and ∞. We prove that the unit sum number of a right self-injective ring R is ω if and only if R has a factor ring isomorphic to ℤ2 but no factor ring isomorphic to ℤ2 × ℤ2, and also in this case every element of R is a sum of either two or three units. It follows that the unit sum number of a right self-injective ring R is ∞ precisely when R has a factor ring isomorphic to ℤ2 × ℤ2. We also answer a question of Henriksen (which appeared in J. Algebra, Question E, page 192), by giving a large class of regular right self-injective rings having the unit sum number ω in which not all non-invertible elements are the sum of two units.
Weak Type Estimates for Riesz-Laguerre Transforms
Authors: Sasso Emanuela
Published: April 2009

We prove that the first order Riesz transforms associated to the Laguerre semigroup are weak-type (1, 1). We also present a counterexample showing that for the Riesz transforms of order three or higher the weak type (1, 1) estimate fails.
On Bleimann-Butzer-Hahn operators for exponential functions
Authors: Abel Ulrich , Ivan Mircea
Published: April 2009

Some inequalities involving the binomial coefficients are obtained. They are used to determine the domain of convergence of the Bleimann, Butzer and Hahn approximation process for exponential type functions. An answer to Hermann's conjecture related to the Bleimann, Butzer and Hahn operators for monotone functions is given.
Integration Operator Acting on Hardy and Weighted Bergman Spaces
Authors: Rättyä Jouni
Published: April 2009

Questions related to the operator Jg(f)(z):= ∫xof (ζ)g′(ζ) dζ, induced by an analytic function g in the unit disc, are studied. It is shown that a function G is the derivative of a function in the Hardy space Hp if and only if it is of the form G = Fψ′ where F ∈ Hq, ψ ∈ H3 and 1/s = 1/p − 1/q. Moreover, a complete characterisation of when Jg is bounded or compact from one weighted Bergman space into another is established, and an asymptotic formula for the essential norm of Jg, the distance from compact operators in the operator norm, is given. As an immediate consequence it is obtained that if p < 2 + α and α > −1, then any primitive of belongs to where q = ((2 + α) p)/(2 + α − p). For α = −1 this is a sharp result by Hardy and Littlewood on primitives of functions in Hardy space , 0 < p < 1.
Some sufficient conditions for graphs to have (g, f)-factors
Authors: Zhou Sizhong
Published: April 2009

Suppose that G is a graph with vertex set V (G) and edge set E (G), and let g and f be two non-negative integer-valued functions defined on V (G) such that g (x) ≤ f (x) for each x ∈ V (G). A (g, f)-factor of G is a spanning subgraph F of G such that g (x) ≤ dF (x) ≤ f (x) for each x ∈ V (F). In this paper, some sufficient conditions for a graph to have a (g, f)-factor are given.
On the self-intersections of an immersed sphere
Authors: Borbély Albert
Published: April 2009

A closed curve f: S1 → ℝ2 in general position gives rise to a word whose letters are the self-intersection points, each of them appearing exactly twice. Such a word is called a Gauss code. The problem of determining whether a given Gauss code is realisable or not was first proposed by Gauss and it has been settled a long time ago. The analogous question for immersions f: S2 → ℝ3 in general position is settled only in a special case when the immersion has no triple points. We give a necessary condition for a system of curves to be realisable by a general immersion f: S2 → ℝ3.
Remarks on the semivariation of vector measures with respect to Banach spaces.
Authors: Blasco Oscar
Published: April 2009

Suppose that and . It is shown that any Lp(µ)-valued measure has finite L2(v)-semivariation with respect to the tensor norm for 1 ≤ p < ∞ and finite Lq(v)-semivariation with respect to the tensor norm whenever either q = 2 and 1 ≤ p ≤ 2 or q > max{p, 2}. However there exist measures with infinite Lq-semivariation with respect to the tensor norm for any 1 ≤ q < 2. It is also shown that the measure m (A) = χA has infinite Lq-semivariation with respect to the tensor norm if q < p.
A note on Nk configurations and theorems in projective space
Authors: Glynn David G.
Published: April 2009

A method of embedding nk configurations into projective space of k–1 dimensions is given. It breaks into the easy problem of finding a rooted spanning tree of the associated Levi graph. Also it is shown how to obtain a “complementary” “theorem” about projective space (over a field or skew-field F) from any nk theorem over F. Some elementary matroid theory is used, but with an explanation suitable for most people. Various examples are mentioned, including the planar configurations: Fano 73, Pappus 93, Desargues 103 (also in 3d-space), Möbius 84 (in 3d-space), and the resulting 74 in 3d-space, 96 in 5d-space, and 107 in 6d-space. (The Möbius configuration is self-complementary.) There are some nk configurations that are not embeddable in certain projective spaces, and these will be taken to similarly not embeddable configurations by complementation. Finally, there is a list of open questions.
A rank for right congruences on inverse semigroups
Authors: Gould Victoria
Published: April 2009

The S-rank (where ‘S’ abbreviates ‘sandwich’) of a right congruence ρ on a semigroup S is the Cantor-Bendixson rank of ρ in the lattice of right congruences ℛ of S with respect to a topology we call the finite type topology. If every ρ ϵ ℛ possesses S-rank, then S is ranked. It is known that every right Noetherian semigroup is ranked and every ranked inverse semigroup is weakly right Noetherian. Moreover, if S is ranked, then so is every maximal subgroup of S. We show that a Brandt semigroup 0(G, I) is ranked if and only if G is ranked and I is finite.

We establish a correspondence between the lattice of congruences on a chain E, and the lattice of right congruences contained within the least group congruence on any inverse semigroup S with semilattice of idempotents E(S) ≅ E. Consequently we argue that the (inverse) bicyclic monoid B is not ranked; moreover, a ranked semigroup cannot contain a bicyclic -class. On the other hand, B is weakly right Noetherian, and possesses trivial (hence ranked) subgroups.

Our notion of rank arose from considering stability properties of the theory Ts of existentially closed (right) S-sets over a right coherent monoid S. The property of right coherence guarantees that the existentially closed S-sets form an axiomatisable class. We argue that B is right coherent. As a consequence, it follows from known results that TB is a theory of B-sets that is superstable but not totally transcendental.
Constructions of general polynomial lattices for multivariate integration
Authors: Kritzer Peter , Pillichshammer Friedrich
Published: April 2009

We study a construction algorithm for certain polynomial lattice rules modulo arbitrary polynomials. The underlying polynomial lattices are special types of digital nets as introduced by Niederreiter. Dick, Kuo, Pillichshammer and Sloan recently introduced construction algorithms for polynomial lattice rules modulo irreducible polynomials which yield a small worst-case error for integration of functions in certain weighted Hilbert spaces. Here, we generalize these results to the case where the polynomial lattice rules are constructed moduloarbitrarypolynomials.
On the integers represented by x4 − y4
Authors: Dąbrowski Andrzej
Published: April 2009

Let p be a prime number ≥ 5, and n a positive integer > 1. This note is concerned with the diophantine equation x4 − y4 = nzp. We prove that, under certain conditions on n, this equation has no non-trivial solution in Z if p ≥ C(n), where C(n) is an effective constant.
Perturbation theory of multivalued atkinson operators in normed spaces
Authors: Álvarez Teresa , Wilcox Diane
Published: April 2009

We prove several stability results for Atkinson linear relations under additive perturbation by small norm, strictly singular and strictly cosingular multivalued linear operators satisfying some additional conditions.
Composition operators on Lorentz spaces
Authors: Arora S. C. , Datt Gopal , Verma Satish
Published: April 2009

Fredholm, injective, isometric and surjective composition operators on Lorentz spaces L(p, q) are characterised in this paper.
A note on the theorem of Baturov
Authors: Muñoz María
Published: April 2009

D.P. Baturov proved in ‘Subspaces of function spaces’ Vestnik Moskov University Series I (1987) that Lindelöf degree equals extent for subspaces of Cp(Χ) when Χ is a Lindelöf Σ-space. We prove that if the Lindelöf degree of the subspace is “big enough” the equality is true for a topological space Χ not necessarily Lindelöf Σ.
On generalised prime essential rings and special and nonspecial radicals
Authors: France-Jackson Halina
Published: April 2009

For a supernilpotent radical α and a special class σ of rings we call a ring R (α, σ)-essential if R is α-semisimple and for each ideal P of R with R/P ε σ, P ∩ I ≠ 0 whenever I is a nonzero two-sided ideal of R. (α, σ)-essential rings form a generalisation of prime essential rings introduced by L. H. Rowen in his study of semiprime rings and their subdirect decompositions and they have been a subject of investigations of many prominent authors since. We show that many important results concerning prime essential rings are also valid for (α, σ)-essential rings and demonstrate how (α, σ)-essential rings can be used to determine whether a supernilpotent radical is special. We construct infinitely many supernilpotent nonspecial radicals whose semisimple class of prime rings is zero and show that such radicals form a sublattice of the lattice of all supernilpotent radicals. This generalises Yu.M. Ryabukhin's example.
Partial regularity of stablep-harmonic maps into spheres
Authors: Hong Min-Chun
Published: April 2009

In this paper we prove partial regularity for a weakly stablep-harmonic map from Ω intoSkwhenk> 2p– 1.
Simple rings with injectivity conditions on one-sided ideals
Authors: Clark John , Van Huynh Dinh
Published: April 2009

This paper looks at simple rings which have right ideals satisfying various types of injectivity conditions. We characterise when a simple regular ring is right self-injective and show that if R is a simple ring in which every right ideal is the direct sum of quasi-continuous right ideals then R is either Artinian or a non-selfinjective right Goldie ring in which every right ideal is a direct sum of uniform right ideals.
Strong convergence theorems for fixed points of pseudo-contractive semigroup
Authors: Li Xue-Song , Huang Nan-Jing
Published: April 2009

We study some convergence of two kinds of implicit iteration processes for approximating common fixed points of a pseudo-contractive semigroup in uniformly convex Banach spaces with uniformly Gateaux differential norms. As special cases, we get some convergence of the implicit iteration processes for approximating common fixed points of a nonexpansive semigroup in uniformly smooth Banach spaces and give a positive answer to an open problem proposed by Xu in Bull. Austral. Math. Soc. (2005). The results presented in this paper generalise some corresponding results from Osilike in Panamer. Math. J. (2004), Suzuki in Proc. Amer. Math. Soc. (2002) and Xu in Bull. Austral. Math. Soc. (2005).
When do finite Blaschke products commute?
Authors: Chalendar Isabelle , Mortini Raymond
Published: April 2009

We study the following questions. Which finite Blaschke products are eigenvectors of the composition operatorsTu:f↦f∘u, what are the possible eigenvalues, and which pairs (B,C) of finite Blaschke products commute (that is, satisfyB∘C=C∘B).
On the operators which are invertible modulo an operator ideal
Authors: Aiena Pietro , González Manuel , Martínez-Abejón Antonio
Published: April 2009

We study the semigroups l and r of left and right invertible operators modulo an operator ideal , respectively. We show that these semigroups allow us to obtain useful characterisations of the radical rad of  For example, rad; is the perturbation class for l and r.
A note on the ideals of groupoid C*-algebras from Smale spaces
Authors: Hou Chengjun , Chen Xiamoman
Published: April 2009

In this note, we characterise completely the ideals of the groupoid C*-algebra arising from the asymptotic equivalence relation on the points of a Smale space and show that the related Ruelle algebra is simple when the Smale space is topologically transitive.
Integrated solutions of stochastic evolution equations with additive noise
Authors: Filinkov A. , Maizurna I.
Published: April 2009

We investigate the existence of a solution to the abstract stochastic evolution equation with additive noise:

in the case when A is the generator of an n-times integrated semigroup.
On the set of Hilbert polynomials
Authors: Levin Alexander B.
Published: April 2009

We characterise the set of all Hilbert polynomials of standard graded algebras over a field and give solutions of some open problems on Hilbert polynomials. In particular, we prove that a chromatic polynomial of a graph is a Hilbert polynomial of some standard graded algebra.
On Helly's principle for metric semigroup valued BV mappings to two real variables
Authors: Balcerzak M. , Belov S. A. , Chistyakov V. V.
Published: April 2009

We introduce a concept of metric space valued mappings of two variables with finite total variation and define a counterpart of the Hardy space. Then we establish the following Helly type selection principle for mappings of two variables: Let X be a metric space and a commutative additive semigroup whose metric is translation invariant. Then an infinite pointwise precompact family of X-valued mappings on the closed rectangle of the plane, which is of uniformly bounded total variation, contains a pointwise convergent sequence whose limit is a mapping with finite total variation.
An estimate for the total mean curvature in negatively curved spaces
Authors: Borbély Albert
Published: April 2009

Let Mn be a nonpositively curved complete simply connected manifold and D ⊂ Mn be a convex compact subset with non-empty interior and smooth boundary. It is shown that the total mean curvature ∂D can be estimated in terms of volume and curvature bound.
Gramian analysis of multivariate frame multiresolution analyses
Authors: Lim Jae Kun
Published: April 2009

We perform a Gramian analysis of a frame multiresolution analysis to give a condition for it to admit a minimal wavelet set and to show that the frame bounds of the natural generator for the wavelet space of a degenerate frame multiresolution analysis shrink.
On meromorphic solutions of certain nonlinear differential equations
Authors: Heittokangas J. , Korhonen R. , Laine I.
Published: April 2009

In this paper, we consider the growth of meromorphic solutions of nonlinear differential equations of the form L (f) + P (z, f) = h (z), where L (f) denotes a linear differential polynomial in f, P (z, f) is a polynomial in f, both with small meromorphic coefficients, and h (z) is a meromorphic function. Specialising to L (f) − p (z) fn = h (z), where p (z) is a small meromorphic function, we consider the uniqueness of meromorphic solutions with few poles only. Our results complement earlier ones due to C.-C. Yang.
Smoothing spline in a convex closed set of Hilbert space
Authors: Dicheva Natasha
Published: April 2009

A characterisation of a smoothing spline is sought in a convex closed set C of Hilbert space: , T and A are linear operators. A representation of the solution is obtained in the terms of the kernels of the above operators, of the dual operators T*, A* and of the dual cone C0. A particular case is considered when T is the differential operator and A is the operator-trace of a function.
Asymptotical smoothness and its applications
Authors: Kaczor Wiesława , Prus Stanisław
Published: April 2009

In this paper we introduce the notion of asymptotical smoothness of a Banach space and show that it is strongly related to the Kadec-Klee property. This notion is then applied to obtain new theorems about weak convergence of almost orbits of three various types of semigroups of mappings.
Most finitely generated subgroups of infinite unitriangular matrices are free
Authors: Hołubowski Waldemar
Published: April 2009

In this note we prove that the groupGof infinite dimensional upper unitriangular matrices over a finite field contains an explicit countable subgroup ‘full’ of free subgroups. We deduce from this fact that, in a suitable sense, almost allk–generator subgroups ofGare free groups of rankk.
Local well posedness for strongly damped wave equations with critical nonlinearities
Authors: Carvalho Alexandre N. , Cholewa Jan W.
Published: April 2009

In this article the strongly damped wave equation is considered and a local well posedness result is obtained in the product space . The space of initial conditions is chosen according to the energy functional, whereas the approach used in this article is based on the theory of analytic semigroups as well as interpolation and extrapolation spaces. This functional analytic framework allows local existence results to be proved in the case of critically growing nonlinearities, which improves the existing results.
Asymptotical well behaviour for constrained minimisation problems
Authors: Aussel D. , Chou C. C.
Published: April 2009

This paper is devoted to the study of the links between stationary sequence and minimising sequence for constrained minimisation problems. The constraint set is not supposed to be convex and no differentiability assumption is made on the objective function. New tools are developed in this general framework and we prove a necessary and a sufficient condition for such problems to have a “constrained asymptotical well behaviour” (that is, each stationary sequence is a minimising sequence). Our work extend that of Auslender, Cominetti and Crouzeix.
Existence conditions for a class of modular subgroups of genus zero
Authors: Hempel Joachim A.
Published: April 2009

Every subgroup of finite index of the modular groupPSL(2, ℤ) has asignatureconsisting of conjugacy-invariant integer parameters satisfying certain conditions. In the case of genus zero, these parameters also constitute a prescription for the degree and the orders of the poles of a rational functionFwith the property:

Functions correspond to subgroups, and we use this to establish necessary and sufficient conditions for existence of subgroups with a certain subclass of allowable signatures.
Duality and Lagrange multipliers for nonsmooth multiobjective programming
Authors: Zhou Houchun , Sun Wenyu
Published: April 2009

Without any constraint qualification, the necessary and sufficient optimality conditions are established in this paper for nonsmooth multiobjective programming involving generalised convex functions. With these optimality conditions, a mixed dual model is constructed which unifies two dual models. Several theorems on mixed duality and Lagrange multipliers are established in this paper.
On approximation properties of the parabolic potentials
Authors: Uyhan Simten B. , Gadjiev A.D. , Aliev Ilham A.
Published: April 2009

In this paper the approximation properties of parabolic potentials Hαf and ℋαf generated by the heat operators and , where

are studied as α → 0+.
Decomposition of complete graphs into stars
Authors: Cain Pauline
Published: April 2009

A star is a connected graph in which every vertex but one has valency 1. This paper concerns the question of when complete graphs can be decomposed into stars, all of the same order, which have pairwise disjoint edge-sets. It is shown that the complete graphs on rm and rm + 1 vertices, r > 1, can be decomposed into stars with m edges, if and only if r is even or m is odd.
Nonlinear differential equations in reflexive Banach spaces
Authors: Fitzgibbon W.E.
Published: April 2009

Let X be a reflexive Banach space and be a family of weakly continuous operators which map X to X. Conditions are provided which guarantee the existence and the uniqueness to the Cauchy initial value problem
Recurrent tensors and holonomy group
Authors: Datta D.K.
Published: April 2009

Let M be a connected C∞. A method is being introduced here to study the action of the holonomy group and the restricted holonomy group of Γ on a recurrent tensor. The main result of this paper is that if the recurrence covector W of a recurrent tensor S on M is an exact form then the tensor S is invariant under the holonomy group of Γ and if W is a closed form then S is invariant under the restricted holonomy group of Γ. In the last section, this result is applied to some particular cases including the case of a riemannian manifold with recurrent curvature.
Proof of a conformal mapping relationship
Authors: Brown A.
Published: April 2009

A proof is given of a result deduced from numerical work on the conformal mapping of the region exterior to a quadrilateral possessing an axis of symmetry. It is shown that the result follows from known relationships between hypergeometric functions.
Families of weighing matrices
Authors: Geramita Anthony V. , Pullman Norman J. , Wallis Jennifer S.
Published: April 2009

A weighing matrix is an n × n matrix W = W(n, k) with entries from {0, 1, −1}, satisfying = WWt = KIn. We shall call k the degree of W. It has been conjectured that if n ≡ 0 (mod 4) then there exist n × n weighing matrices of every degree k ≤ n.

We prove the conjecture when n is a power of 2. If n is not a power of two we find an integer t < n for which there are weighing matrices of every degree ≤ t.
Maximal Fitting classes of finite soluble groups
Authors: Bryce R.A. , Cossey John
Published: April 2009

From recent results of Lausch, it is easy to establish necessary and sufficient conditions for a Fitting class to be maximal in the class of all finite soluble groups. We use Lausch's methods to show that there are normal Fitting classes not contained in any Fitting class maximal in the class of all finite soluble groups. We also find conditions on Fitting classes and for to be maximal in .
A note on the summation of an infinite series involving a hypergeometric function
Authors: Williamson A.G.
Published: April 2009

The sum of an infinite series involving the 4F3 function is found by considering an infinite series whose terms involve the product of two Bessel functions of the first kind. Furthermore the infinite series involving the 4F3 function can be utilized to find an approximation to the 4F3 function of unit argument, for particular values of the parameters.
Schunk classes are nilpotent product closed
Authors: Wiegold James
Published: April 2009

The following result is proved. LetXbe a Schunk class andka positive integer. Then thek–th nilpotent product of any two groups inX¯ is inX¯.
Adjunction semigroups
Authors: Borrego J. T.
Published: April 2009

Let S and T be compact (topological) semigroups, A be a closed subsemigroup of S, and f be a continuous homomorphism of A onto T. It is a natural question to ask is there a compact semigroup Z containing T and a continuous homomorphism φ of S onto Z such that φ restricted to A is f?

In the category of compact Hausdorff spaces, the answer to the analogous question may be given by the following construction due to Borsuk. Let X and Y be compact Hausdorff spaces, A be a closed subspace of X and f a continuous function of A onto Y. Then R(f, X) = {(x, y)|f(x) = f(y) or x = y} is a closed equivalence relation on X. The adjunction space Z(f, x) is X/R(f, X). The purpose of this note is to investigate this construction in semigroups.
A theorem on homeomorphism groups and products of spaces
Authors: Vobach A. R.
Published: April 2009

Let H(C) be the group of homeomorphisms of the Cantor set, C, onto itself. Let p: C → M be a map of C onto a compact metric space M, and let G(p, M) be is a group.

The map p: C → M is standard, if for each (x, y) ∈ C × C such that p(x) = p(y), there is a sequence and a sequence such that xn → x and hn (xn) → y Standard maps and their associated groups characterize compact metric spaces in the sense that: Two such spaces, M and N, are homeomorphic if and only if, given p standard from C onto M, there is a standard q from C onto N for which G(p, M) = h−1G(q, N)h, for some h ∈ H(C) The present paper exhibits a structure theorem connecting these characterizing subgroups of H(C) and products of spaces: Let M1 and M2 be compact metric spaces. Then there are standard maps p: C → M1 × M2 and pi: C → Mi, i = 1, 2, such that G(p, M1 × M2) = G(p1, M1) ∩ G(p2, M2).
Varieties of topological groups
Authors: Morris Sidney A.
Published: April 2009

We introduce the concept of a variety of topological groups and of a free topological group F(X, ) of on a topological space X as generalizations of the analogous concepts in the theory of varieties of groups. Necessary and sufficient conditions for F(X, ) to exist are given and uniqueness is proved. We say the topological group FM,(X) is moderately free on X if its topology is maximal and it is algebraically free with X as a free basis. We show that FM(X) is a free topological group of the variety it generates and that if FM(X) is in then it is topologically isomorphic to a quotient group of F(X, ). It is also shown how well known results on free (free abelian) topological groups can be deduced. In the algebraic theory there are various equivalents of a free group of a variety. We examine the relationships between the topological analogues of these. In the appendix a result similar to the Stone-Čech compactification is proved.
Comments on bases in dependence structures
Authors: Brualdi Richard A.
Published: April 2009

Dependence structures (in the finite case, matroids) arise when one tries to abstract the properties of linear dependence of vectors in a vector space. With the help of a theorem due to P. Hall and M. Hall, Jr concerning systems of distinct representatives of families of finite sets, it is proved that if B1 and B2 are bases of a dependence structure, then there is an injection σ: B1 → B2 such that (B2 / {σ(e)}) ∩ {e} is a basis for all e in B1. A corollary is the theorem of R. Rado that all bases have the same cardinal number. In particular, it applies to bases of a vector space. Also proved is the fact that if B1 and B2 are bases of a dependence structure then given e in B1 there is an f in B2 such that both (B1 / {e}) ∩ {f} and (B2 / {f}) ∩ {e} are bases. This is a symmetrical kind of replacement theorem.
A generalized Banach-Mazur theorem
Authors: Kleiber Martin , Pervin W. J.
Published: April 2009

For every infinite cardinal a we letCa, be the set of all real-valued continuous functions on a product of a closed unit intervals with the supmetric. It is shown thatCahas separability degreea. Further, the classical theorem of Banach and Mazur is generalized by showing that every metric space of separability degreeais isometric to a subspace ofca
The connectivity of total graphs
Authors: Behzad Mehdi
Published: April 2009

We associate with a graph (finite, undirected, without loops and multiple lines) a graph T(G), called the total graph of G. This new graph has the property that a one-to-one correspondence can be established between its points and the elements (points and lines) of G such that two points of T(G) are adjacent if and only if the corresponding elements of G are adjacent or incident. The object of this article is to prove the following theorem: If K(G1) = n, n ≥ 1, and λ(G2) = m, m ≥ 1, then K(T(G1)) ≥ n + 2 + [(n - 2)/3], λ(T(G1)) ≥ 2n, K(T(G2)) ≥ m + 1, and λ(T(G2)) ≥ 2m, where k(G) and λ(G) denote the connectivity and line-connectivity of the graph G.
Analytic iterations on Riemann surfaces
Authors: Lavie Meira
Published: April 2009

A complex analytic family of mappings P → M(α, P) from an abstract Riemann surface (analytic manifold) into itself is studied. The mapping M(α, P) is assumed to satisfy in local coordinates the autonomous differential equation = L(w), and the condition M(O, P) = P. Under certain assumptions of regularity of the reciprocal differential L in a domain D ⊂ S, we prove that for every fixed α, ∣a∣ < α, the mapping M(α, P) is conformal and one to one in D. Moreover, it is shown that the family of mappings M(α, P) satisfies the iteration equation M[a, M(b, P)] = M(a + b, P) and hence is an analytic group (analytic iteration).
On regular semigroups whose idempotents form a subsemigroup
Authors: Hall T. E.
Published: April 2009

For brevity the semigroups in the title are called orthodox semigroups. The finest inverse semigroup congruence on an orthodox semigroup is shown to have a simple form and conversely, regular semigroups whose finest inverse congruence has this simple form are shown to be orthodox. Next ideal extensions of orthodox semigroups by orthodox semigroups are shown to be also orthodox, whence a finite semigroup is orthodox if and only if each principal factor is orthodox and completely O-simple or simple. Finally it is determined which completely O-simple semigroups are orthodox.
Interior preserving maps
Authors: Memp T.
Published: April 2009

It is a curious fact that, while the functions which preserve closures are exactly the closed continuous functions, the interior-preserving functions form a much smaller class than the open continuous functions. In fact, the interior-preserving maps are essentially homeomorphisms, surjections between discrete spaces, and “sums” of these.
Zero-free fortifying homomorphisms and semigroups of relations
Authors: Magill Kenneth D.
Published: April 2009

In this paper, the concept of a fitted semigroup of binary relations is introduced. The binary operation for these semigroups is ordinary composition of relations. A particular type of homomorphism is investigated which maps a certain kind of subsemigroup of one fitted semigroup into another. The main result states that these homomorphisms are injective and gives a representation for them. This and several related results are then applied to the semigroup of all binary relations on a topological space which have a certain prescribed type of topological property. Compactness is one of these properties and the semigroup SK[X] of all compact binary relations on a Hausdorff k–space X is given special attention. It is shown that X and Y are homeomorphic if and only if a number of statements are true which relate the semigroups SK[x] and SK[y].For example, in order that X and y be homeomorphic it is both necessary and sufficient that some nonzero ideal of SK[X] be isomorphic to some nonzero ideal of SK[y].
On the group ring of a finite abelian group
Authors: Ayoub Raymond G. , Ayoub Christine
Published: April 2009

The group ring of a finite abelian group G over the field of rational numbers Q and over the rational integers Z is studied. A new proof of the fact that the group ring QG is a direct sum of cyclotomic fields is given – without use of the Maschke and Wedderburn theorems; it is shown that the projections of QG onto these fields are determined by the inequivalent characters of G. It is proved that the group of units of ZG is a direct product of a finite group and a free abelian group F and the rank of F is determined. A formula for the orthogonal idempotents of QG is found.
On the equivalence of invariant integrals and minimal ideals in semigroups
Authors: Tserpes N. A. , Kartsatos A. G.
Published: April 2009

Let S be a Hausdorff topological semigroup and Cb,(S), Cc (S), the spaces of real valued continuous functions on S which are respectively bounded and have compact support. A regular measure m on S is r*-invarient if m(B) = for every Borel B ⊂ S and every x ∈ S, where tx: s → sx is the right translation by x. The following theorem is proved: Let S be locally compact metric with the tx's closed. Then the following statements are equivalent: (i) S admits a right invariant integral on Cc (S). (ii) S admits an r*–invariant measure, (iii) S has a unique minimal left ideal. The above equivalence is considered also for normal semigroups and analogous results are obtained for finitely additive r*–invariant measures. Also in the case when S is a complete separable metric semigroup with the tx's closed, the following statements are equivalent: (i) S admits a right invariant integral I on Cb(S) such that I(1) = 1 and satisfying Daniel's condition. (ii) S admits an r*–invariant probability measure. (iii) S has a right ideal which is a compact group and which is contained in a unique minimal left ideal. Finally, in order that a locally compact S admit a right invariant measure, it suffices that S contain a right ideal F which is a left group such that (B ∩ F)x = BX ∩ Fx for all Borel B ⊂ S.
Generalisations of Turán's main theorems on lower bounds for sums of powers
Authors: van der Poorten A.J.
Published: April 2009

In his book,Eine neue Methode in der Analysis und deren Andwendungen, P. Turán proved a number of new theorems given lower bounds for sums of powers. Since it was only his intention to demonstrate a new type of result, his bounds are by no means best possible nor are his proofs easily susceptible of improvement.

We generalise Turán's so-called Main Theorems to exponential sums with polynomial coefficients by a simple method involving only the evaluation and estimation of certain determinants. This approach gives in each case a result known to be asymptotically correct in the various exponents, and when specialised to the case of constant coefficients it provides in each case best-known results.

Our method moreover applies in more general circumstances and provided only that the determinants which arise can be conveniently estimated serves to provide lower bounds for other than exponential sums.
A commutativity theorem for rings
Authors: Outcalt D.L. , Yaqub Adil
Published: April 2009

Let R be an associative ring with identity in which every element is either nilpotent or a unit. The following results are established. The set N of nilpotent elements in R is an ideal. If R/N is finite and if x ≡ y (mod N) implies x2 = y2 or both x and y commute with all elements of N, then R is commutative. Examples are given to show that R need not be commutative if “X2 = y2” is replaced by “xk = yK” for any integer k > 2. The case N = (0) yields Wedderburn's Theorem.
On commutativity in certain rings
Authors: Moore H.G.
Published: April 2009

I.N. Herstein has shown that an associative ring in which the nilpotent elements are “well-behaved”, and such that every element satisfies a certain polynomial identity, is commutative. This result is generalized here. Specifically, it is shown that an alternative ring R which satisfies the following three properties is commutative:

(i) for x ∈ R, there exists an integer n(x) and a polynomial px (t) with integer coefficients such that xn+1p(x) = xn;

(ii) for a fixed positive integer m, a a nilpotent and b an arbitrary element of R, a - am commutes with b - bm;

(iii) for the same m, a and b, (ab+b)m = (ba+b)m and (ab)m = ambm.

Examples are given to show that all three properties are essential, and it is shown that for associative rings certain modified versions of these properties are individually enough to assure that the commutator ideal of the ring is nil.
Diffusion and convection in viscous flow
Authors: Pillow A. F.
Published: April 2009

A survey is made of the way in which a variety of physical scalar and vector quantities are diffused, and convected out of fixed regions in moving fluids. In particular, viscous flow itself is viewed as the diffusion and convection of circulation which is generated at the boundaries of the fluid by the no-slip condition. The non-linearity of the problem arises from the fact that the convection field is in part self-generated by the diffused circulation. Ways of overcoming these difficulties are reviewed in the light of the above point of view. New kinematic interpretations are given for the equations governing axisymmetric viscous flow and these are used to determine the flow vector for ring circulation, angular momentum and other relevant physical quantities.
Totally unordered subsets of a partially well ordered set
Authors: Ward Martin
Published: April 2009

An order on the collection of totally unordered subsets of a partially well ordered set is defined, shown to satisfy the descending chain condition but not to be necessarily a partial well order itself.
A note on flasque sheaves
Authors: Campbell J. M. , Kovács L. G.
Published: April 2009

We give an elementary and self-contained proof of the result that the sheaf M~ determined by an injective module M over a commutative noetherian ring is flasque.
A Stone-Weierstrass theorem for random functions
Authors: Mukherjea A.
Published: April 2009

It is shown in this note that if Q is an algebra of uniformly bounded mean-square continuous real-valued random functions indexed in a compact set T, containing all bounded random variables and separating points of T (i.e., given t1 and t2 in T, there is a random function Xt in Q such that , then given any mean square continuous random function, there is a sequence in Q converging in mean square to the given random function uniformly on T.
The Dirichlet boundary value problem for two non-overlapping spheres
Authors: Ross Dieter K.
Published: April 2009

A new method is found for solving the general Dirichlet problem for two non-overlapping spheres of different radius. The expression for the external potential involves hypergeometric functions and is obtained from an infinite set of linear equations. In essence the method makes use of the fact that (I–A)–1 = I + A + A2 + A3 + …, where A belongs to a certain class of infinite matrices and I is the unit matrix.
Identities in tensor products of Banach algebras
Authors: Loy R. J.
Published: April 2009

Let A1, A2 be Banach algebras, A1 ⊗ A2 their algebraic tensor product over the complex field. If ‖ · ‖α is an algebra norm on A1 ⊗ A2 we write A1 ⊗αA2 for the ‖ · ‖α-completion of A1 ⊗ A2. In this note we study the existence of identities and approximate identities in A1 ⊗αA2 versus their existence in A1 and A2. Some of the results obtained are already known, but our method of proof appears new, though it is quite elementary.
Spaces having no large dyadic subspace
Authors: Gait Jason
Published: April 2009

Gillman-Henriksen have defined a class of spaces, containing the discrete spaces and their Stone-Čech compactifications, called F'-spaces. The dyadic spaces are the continuous images of products of finite discrete spaces – a class which contains the compact metric spaces and all compact topological groups. In this paper it is shown that F'-spaces have no infinite dyadic sutspaces and, almost always, no dyadic compactifications. An interesting corollary is that if βX \ X is dyadic, then X is pseudocompact.
A note on types
Authors: Gardner B. J.
Published: April 2009

A characterization is obtained of the types τ for which [G/G(τ)](τ) = 0 for all torsion-free abelian groups G.
Maximal sum-free sets in finite abelian groups
Authors: Rhemtulla A. H. , Street Anne Penfold
Published: April 2009

A subset S of an additive group G is called a maximal sum-free set in G if (S+S) ∩ S = ø and ∣S∣ ≥ ∣T∣ for every sum-free set T in G. It is shown that if G is an elementary abelian p–group of order pn, where p = 3k ± 1, then a maximal sum-free set in G has kpn-1 elements. The maximal sum-free sets in Zp are characterized to within automorphism.
Some problems on idempotent measures on semigroups
Authors: Tserpes N. A. , Mukherjea A.
Published: April 2009

Essentially this paper does the following: In Section 2 it gives necessary and sufficient conditions in order that the support of an idempotent measure on a locally compact semigroup S, be completely simple. In Section 3 it proves that if I is an ideal of S of positive measure μ (= any probability measure), then μn (I) strictly increases to the limit 1. If in addition μ is idempotent, then μ (N-1N) and μ(NN-1) are positive for any open set N. In Section 4 certain compactness conditions are proven equivalent to joint weak*–continuity of the convolution of bounded measures and a limit theorem concerning the convolution powers (Cesarò sums) of μ is proven.
Fundamental singularities in the theory of water waves with surface tension
Authors: Rhodes-Robinson P. F.
Published: April 2009

In this paper the forms are obtained for the harmonic potential functions describing the fundamental wave-source and multipole singularities which pertain to the study of infinitesimal time-harmonic waves on the free surface of water when the effect of surface tension is included. Line and point singularities are considered for both the cases of infinite and finite constant depth of water. The method used is an extension of that which has been used to obtain these potentials in the absence of surface tension.
Averaging and integral manifolds (II)
Authors: Palmer K. J.
Published: April 2009

In the first part of this paper (written jointly with W.A. Coppel) the existence and properties of an integral manifold were established for the system

x′ =f(t, x, y)

y′ =A(t)y + g(t, x, y)

where f and g are “integrally small”. In this second part of the paper the stability properties of the integral manifold are investigated. Solutions are found which are bounded on the positive half of the real line and it is shown that these solutions approach the manifold exponentially and, moreover, that they are asymptotic to particular solutions on the manifold.
The conjugate of a smooth Banach space
Authors: Tacon D. G.
Published: April 2009

A Banach space X is smooth if at every point of the unit sphere there is only one supporting hyperplane of the unit ball; and strictly convex, or rotund, if the unit sphere contains no line segment.

Although there is a strong duality between these notions, Klee has produced a smooth space whose conjugate is not rotund. However there is no known example of a smooth space with conjugate not isomorphic to a rotund space.

The main purpose of this note is to show that if X is a smooth space with a certain property, X* is isomorphic to a rotund space. This will follow from a mapping theorem which implies the existence of a set Γ and a continuous one-to-one linear map T of X* into co(Γ).
The topological structure of 𝒟–classes
Authors: Stralka A.R.
Published: April 2009

Let S be a compact, topological semigroup with identity. Suppose D, L and R are the D, L and R classes of some x ∈ S. Let (L, α., L/H), (R, β, R/H), (D, γ, D/H) and (D, δ, D/R) by the fibre spaces gotten where α, β γ an δ are the natural maps. It is shown that (D, γ, D/H) has topologically the same structure as the fibre space associated with (L, α, L/H) by R. Also if (L, α, L/H) is locally trivial (locally a cartesian product) then so is (D, δ, D/R) and if both (L, α, L/H) and (R, β, R/H) are locally trivial then so is (D, γ, D/H).
Continuity of derivations on topological algebras of power series
Authors: Loy R.J.
Published: April 2009

Let A be an algebra of formal power series in one indeterminate over the complex field, D a derivation on A. It is shown that if A has a Fréchet space topology under which it is a topological algebra, then D is necessarily continuous provided the coordinate projections satisfy a certain equicontinuity condition. This condition is always satisfied if A is a Banach algebra and the projections are continuous. A second result is given, with weaker hypothesis on the projections and correspondingly weaker conclusion.
On the relationship between graphs and partially balanced incomplete block designs
Authors: Wallis W.D.
Published: April 2009

Certain theorems which are already known show that if a partially balanced incomplete block design with suitable parameters exists then there is a (V, K, Λ)-graph. We prove that the existence of such a graph is in fact equivalent to the existence of a certain partially balanced design. The known necessary conditions for (V, K, Λ)-graphs then follow from well-known necessary conditions for designs.
A generalization of a theorem of Wedderburn
Authors: Ligh Steve
Published: April 2009

Outcalt and Yaqub have extended the Wedderburn Theorem which states that a finite division ring is a field to the case where R is a ring with identity in which every element is either nilpotent or a unit. In this paper we generalize their result to the case where R has a left identity and the set of nilpotent elements is an ideal. We also construct a class of non-commutative rings showing that our generalization of Outcalt and Yaqub's result is real.
Torsion theories and coherent rings
Authors: Campbell J.M.
Published: April 2009

Chase has given several characterizations of a right coherent ring, among which are: every direct product of copies of the ring is left-flat; and every finitely generated submodule of a free right module is finitely related. We extend his results to obtain conditions for the ring of quotients of a ring with respect to a torsion theory to be coherent.
Spectral approximation theorems for bounded linear operators
Authors: Lo W.S.
Published: April 2009

In this paper we present some approximation theorems for the eigenvalue problem of a compact linear operator defined on a Banach space. In particular we examine: criteria for the existence and convergence of approximate eigenvectors and generalized eigenvectors; relations between the dimensions of the eigenmanifolds and generalized eigenmanifolds of the operator and those of the approximate operators.
Divergence of Fourier series
Authors: Izuml Masako , Izumi Shin-Ichi
Published: April 2009

Carleson has proved that the Fourier series of functions belonging to the class L2 converge almost everywhere.

Improving his method, Hunt proved that the Fourier series of functions belonging to the class Lp (p > 1) converge almost everywhere. On the other hand, Kolmogoroff proved that there is an integrable function whose Fourier series diverges almost everywhere. We shall generalise Kolmogoroff's Theorem as follows: There is a function belonging to the class L(logL)p (p > 0) whose Fourier series diverges almost everywhere. The following problem is still open: whether “almost everywhere” in the last theorem can be replaced by “everywhere” or not. This problem is affirmatively answered for the class L by Kolmogoroff and for the class L(log logL)p (0 < p < 1) by Tandori.
Corrigendum: On the relation of a distributive lattice to its lattice of ideals
Authors: Gaskill Herbert S.
Published: April 2009

There are errors in my paper [1], Lemma 1 and from the end of Lemma 4 to the end of the paper.

LEMMA 1. If L is any finite lattice and L has a point which is both join and meet reducible then L is not weakly transferable.

We replace Lemma 5 by the following sequence.
The limits of time stepping when used to solve the long wave equations numerically
Authors: Tronson K.
Published: April 2009

The two approaches (the hydrodynnmical-numerical and the harmonic methods) to the solution of the long wave equations are compared, enabling an analysis of the limits imposed by time stepping. The minimum time scale of motions, which may be modelled by the time stepping scheme, is determined from the stability condition derived for the harmonic method.
A note on quasi-uniform continuity
Authors: Lambrinos Panayotis Th.
Published: April 2009

It is shown that:

(i) a continuous function from a compact quasi-uniform space into a quasi-uniform space is not necessarily quasiuniformly continuous;

(ii) if the range of the function is a uniform space, the function will be necessarily quasi-uniformly continuous.

(This contradicts an example in the literature and generalizes a classical result.) Finally, a generalization of (ii) is given by means of a suitable boundedness notion.
Some inequalities in trigonometric approximation
Authors: Ching Chin-Hung , Chui Charles K.
Published: April 2009

For a nonconstant L2 (−π, π) function f, we prove that and that the inequalities are sharp.