bluuebunny/crossref_metadata_2025 huggingface dataset:
Banach space operators with a boundedH∞ functional calculus
Authors: Cowling Michael , Doust Ian , Micintosh Alan , Yagi Atsushi
Published: April 2009

In this paper, we give a general definition forf(T)whenTis a linear operator acting in a Banach space, whose spectrum lies within some sector, and which satisfies certain resolvent bounds, and whenfis holomorphic on a larger sector.

We also examine how certain properties of this functional calculus, such as the existence of a boundedH∈functional calculus, bounds on the imaginary powers, and square function estimates are related. In particular we show that, ifTis acting in a reflexiveLpspace, thenThas a boundedH∈ functional calculus if and only if bothTand its dual satisfy square function estimates. Examples are given to show that some of the theorems that hold for operators in a Hilbert space do not extend to the general Banach space setting.
Commutative rings with comparable regular elements
Authors: Zanardo Paolo
Published: April 2009

Let ℜbe the class of commutative ringsRwith comparable regular elements, that is, given two non zero-divisors inR, one divides the other. Applying the notion ofV-valuation due to Harrison and Vitulli, we define the classV-val ofV-valuated rings, which is contained in ℜand contains the class of Manis valuation rings. We prove that these inclusions of classes are both proper. We investigate Prüfer rings inside ℜ, showing that there exist Prüfer rings which lie in ℜbut not inV-val; we prove that a ringRis a Prüfer valuation ring if and only if it is Prüfer andV-valuated, if and only if its lattice of regular ideals is a chain. Finally, we introduce and investigate the idealI∞of a ringR∈ ℜ, which corresponds to the counterimage of ∞, wheneverRisV-valuated.
Spectral synthesis and applications to C0-groups
Authors: Zarrabi M.
Published: April 2009

Let k ≥ 0 be an integer, T = (T(t))t ∈R a C0-group of bounded operators and A the infinitesimal generator of T. We prove that if, and , and if the spectrum of A is equal to {λ}, then A is bounded and (A – λ)k+1 = 0. Examples are given to show that these conditions are, essentially, the best possible.
A non-coprime Hall-Higman reduction theorem
Authors: Wang Yan-Ming
Published: April 2009

In a well-known paper, Hall and Higman proved the reduction theorem on a coprime order operator group acting on a finite group. This theorem plays an important role in local analysis of finite group theory. In this paper, we generalize the Hall-Higman reduction theorem by dropping the restrictive hypothesis (|G|, |H|) = 1 and determine the detailed structure of G completely.
Approximation and extension of continuous functions
Authors: Hernández-Muñoz Salvador
Published: April 2009

In this paper we study the approximation of vector valued continuous functions defined on a topological space and we apply this study to different problems. Thus we give a new proof of Machado's Theorem. Also we get a short proof of a Theorem of Katětov and we prove a generalization of Tietze's Extension Theorem for vector-valued continuous functions, thereby solving a question left open by Blair.
Partial regularity and everywhere continuity for a model problem from non-linear elasticity
Authors: Fusco Nicola , Hutchinson John E.
Published: April 2009

We prove a new energy or Caccioppoli type estimate for minimisers of the model functional ∫Ω|Du|2 + (det Du)2, where Ω ⊂ 2 and u: Ω → 2. We apply this to establish C∞ regularity for minimisers except on a closed set of measure zero. We also prove a maximum principle and use this to establish everywhere continuity of minimisers.
Modules with finite spanning dimension
Authors: Satyanarayana Bhavanari
Published: April 2009

It is well known that if M is a module with finite spanning dimension, then one can talk of Sd(K), the spanning dimension of K only when K is a supplement submodule in M. In this paper we extend this concept to general submodules and obtained some important results. We characterize the set of all supplement submodules of the module R/(x) over R where R is a Euclidean domain and x ∈ R. Moreover, it is proved that the number of distinct supplements in R/(x) is 2k and Sd(R/(x)) = k where k is the number of distinct nonassociate prime factors of x.
Subelliptic operators on Lie groups: regularity
Authors: Elst A. F. M. Ter , Robinson Derek W.
Published: April 2009

Let (ℋ,G, U) be a continuous representation of the Lie groupGby bounded operatorsg↦U(g)on the Banach space ℋ and let (ℋ,g, dU) denote the representation of the Lie algebragobtained by differentiation. Ifa1,…, ad′is a Lie algebra basis ofgandAi= dU(ai)then we examine elliptic regularity properties of the subelliptic operatorswhere (cij) is a real-valued strictly positive-definite matrix andc0, c1,…, cd′∈ C. We first introduce a family of Lipschitz subspaces ℋγ, γ > 0, of ℋ which interpolate between theCn-subspaces of the representation and for which the parameter γ is a continuous measure of differentiability. Secondly, we give a variety of characterizations of the spaces in terms of the semigroup generated by the closureofHand the group representation. Thirdly, for sufficiently large values of Rec0the fractional powers of the closure ofHare defined, and we prove that D()γ⊆γ′, for γ′ < 2γ/rwhereris the rank of the basis. Further we establish that 2γ/ris the optimal regularity value and it is attained for unitary representations or for the representations obtained by restrictingUto ℋγ. Many other regularity properties are obtained.
A note on the union-closed sets conjecture
Authors: Faro Giovanni Lo
Published: April 2009

It has been conjectured that for any union-closed set there exists some element which is contained in at least half the sets in . It is shown that this conjecture is true if the number of sets in is less than 25. Several conditions on a counterexample are also obtained.
Generalized theorem of Hartman-Grobman on measure chains
Authors: Hilger Stefan
Published: April 2009

We will prove the Theorem of Hartman-Grobman in a very general form. It states the topological equivalence of the flow of a nonlinear non-autonomous differential or difference equation with critical component to the flow of a partially linearized equation. The critical spectrum has not necessearily to be contained in the imaginary axis or the unit circle respectively. Further on we will employ the socalled calculus on measure chains within dynamical systems theory. Within this calculus the usual one dimensional time scales can be replaced by measure chains which are essentially closed subsets of R. The paper can be understood without knowledge of this calculus.

So our main theorem will be valid even for equations defined on very strange time scales such as sequences of closed intervals. This is especially interesting for applications within the theory of differential-difference equations or within numerical analysis of qualitative phenomena of dynamical systems.
Discrete C*-coactions and C*-algebraic bundles
Authors: Quigg John C.
Published: April 2009

Discrete C*-coactions are shown to be equivalent to discrete C* -algebraic bundles. Simplicity, primeness, liminality, postliminality, and nuclearity are related to the fixed point algebra and the cocrossed product. Ergodic, and more generally homogeneous, C*-coactions are characterized.
Locally graded groups with all subgroups normal-by-finite
Authors: Smith Howard , Wiegold James
Published: April 2009

In a paper published in this journal [1], J. T. Buckely, J. C. Lennox, B. H. Neumann and the authors considered the class of CF-groups, that G such that |H: CoreG (H)| is finite for all subgroups H. It is shown that locally finite CF-groups are abelian-by-finite and BCF, that is, there is an integer n such that |H: CoreG(H)| ≤ n for all subgroups H. The present paper studies these properties in the class of locally graded groups, the main result being that locally graded BCF-groups are abelian-by-finite. Whether locally graded CF-groups are BFC remains an open question. In this direction, the following problems is posed. Does there exist a finitely generated infinite periodic residually finite group in which all subgroups are finite or of finite index? Such groups are locally graded and CF but not BCF.
On irregularities of distribution III
Authors: Chen W. W. L.
Published: April 2009

We study the Lw-norm (2 ≤ W < ∞) of the discrepancy of a sequence of points in the unit cube relative to similar copies of a given convex polygon. In particular, we prove the rather surprising result that the estimates obtained have the same order of magnitude as the analogous question when the sequence of points is replaced by a set of points.
Coefficients of an analytic function subordination class determined by rotations
Authors: Kim Seok Chan
Published: April 2009

Let A denote the set of all functions analytic in U = {z: |;z| < 1} equipped with the topology of unifrom convergence on compact subsets of U. For F ∈ A define Let s(F) and s(F) denote the closed convex hull of s(F) and the set of extreme points of , respectively. Let R denote the class of all F ∈ A such that = {Fx}: |x| = 1} where Fx = F(xz).

We prove that |An| ≤ |AMN| for all positive integers M and N, and for . We also prove that if , then F is a univelaent halfplane mapping.
On the eigenvalues of Redheffer's matrix, II
Authors: Vaughan R. C.
Published: April 2009

The Redheffer matrix An = (aij)n×n defined by aij = 1 when i|j or j = 1 and aij = 0 otherwise has many interesting number theoretic properties. In this paper we give fairly precise estimates for its eigenvalues in punctured discs of small radius centred at 1.
Some examples related to Kato's conjecture
Authors: Hughes Rhonda J. , Chernoff Paul R.
Published: April 2009

We show that the Kato conjecture is true for m-accretive operators with highly singular coefficients. For operators of the form A = *F, where formally corresponds to d/dx + zδ on L2 (R), we prove that Dom (A1/2) = Dom() = e-zHH1(R) where H is the Heavysied function. By adapting recent methods of Auscher and Tchamitchian, we characterize Dom (A) in terms of an unconditional wavelet basis for L2(R).
The behaviour of the fourth type of Lauricella's hypergeometric series in n variables near the boundaries of its convergence region
Authors: Saigo Megumi , Srivastava H. M.
Published: April 2009

For Lauricella's hypergeometric function F(n)D of n variables, we prove two formulas exhibiting its behaviour near the boundaries of the n-dimensional region of convergence of the multiple series defining it. Each of these results can be applied to deduce the corresponding properties of several simpler hypergeometric functions of one, two, and more variables.
Insertion of a measurable function
Authors: Kotzé Wesley , Kubiak Tomasz
Published: April 2009

Some theorems on the existence of continuous real-valued functions on a topological space (for example, insertion, extension, and separation theorems) can be proved without involving uncountable unions of open sets. In particular, it is shown that well-known characterizations of normality (for example the Katětov-Tong insertion theorem, the Tietze extension theorem, Urysohn's lemma) are characterizations of normal σ-rings. Likewise, similar theorems about extremally disconnected spaces are true for σ-rings of a certain type. This σ-ring approach leads to general results on the existence of functions of class α.
The difference of consecutive eigenvalues
Authors: Ku Hsu-Tung , Ku Mei-Chin
Published: April 2009

Let M be a smooth bounded domain in Rn with smooth boundary, n ≥ 2, and . We prove an inequality involving the first k + 1 eigenvalues of the eigenvalue problem: where am−1 ≥ 0 are constants and at−1 = 1. We also obtain a uniform estimate of the upper bound of the ratios of consecutive eigenvalues.
Convergence of the backfitting algorithm for additive models
Authors: Ansley Craig F. , Kohn Robert
Published: April 2009

The backfitting algorithm is an iterative procedure for fitting additive models in which, at each step, one component is estimated keeping the other components fixed, the algorithm proceeding component by component and iterating until convergence. Convergence of the algorithm has been studied by Buja, Hastie, and Tibshirani (1989). We give a simple, but more general, geometric proof of the convergence of the backfitting algorithm when the additive components are estimated by penalized least squares. Our treatment covers spline smoothers and structural time series models, and we give a full discussion of the degenerate case. Our proof is based on Halperin's (1962) generalization of von Neumann's alternating projection theorem.
Approximations of positive operators and continuity of the spectral radius III
Authors: Aràndiga F. , Caselles V.
Published: April 2009

We prove estimates on the speed of convergence of the ‘peripheral eigenvalues’ (and principal eigenvectors) of a sequence Tn of positive operators on a Banach lattice E to the peripheral eigenvalues of its limit operator T on E which is positive, irreducible and such that the spectral radius r(T) of T is a Riesz point of the spectrum of T (that is, a pole of the resolvent of T with a residuum of finite rank) under some conditions on the kind of approximation of Tn to T. These results sharpen results of convergence obtained by the authors in previous papers.
On recursive solutions of a unit fraction equation
Authors: Brenton Lawrence , Bruner Robert R.
Published: April 2009

We consider the Egyptian fraction equation and discuss techniques for generating solutions. By examining a quadratic recurrence relation modulo a family of primes we have found some 500 new infinite sequences of solutions. We also initiate an investigation of the randomness of the distribution of solutions, and show that there are infinitely many solutions not generated by the aforementioned technique.
A particular class of supersoluble groups
Authors: Dirscherl W. , Heineken H.
Published: April 2009

We consider (finite) groups in which every two-generator subgroup has cyclic commutator subgroup. Among other things, these groups are metabelian modulo their hypercentres, and in the corresponding quotient group all subgroups of the commutator subgroup are normal.
On convex and starlike functions in a sector
Authors: Nunokawa M. , Thomas D. K.
Published: April 2009

Let f be analytic in D = {z: |z| < 1} with f(0) = f′(0)−1=0. For γ > 0, the largest α (γ) and β(γ) are found such that . The results solve the inclusion problem for convex and starlike functions defined in a sector.
Minimal annuli in R3 bounded by non-compact complete convex curves in parallel planes
Authors: Fang Yi
Published: April 2009

In this paper we consider the Plateau problem for surfaces of annular type bounded by a pair of convex, non-compact curves in parallel planes. We prove that for certain symmetric boundaries there are solutions to the non-compact Plateau problems (Theorem B). Except for boundaries consisting of a pair of parallel straight lines, these are the first known examples.
Extrapolation of the functional calculus of generalized Dirac operators and related embedding and Littlewood-Paley-type theorems. I
Authors: Ajiev Sergey S.
Published: April 2009

Several rather general sufficient conditions for the extrapolation of the calculus of generalized Dirac operators from L2 to Lp are established. As consequences, we obtain some embedding theorems, quadratic estimates and Littlewood–Paley theorems in terms of this calculus in Lebesgue spaces. Some further generalizations, utilised in Part II devoted to applications, which include the Kato square root model, are discussed. We use resolvent approach and show the irrelevance of the semigroup one. Auxiliary results include a high order counterpart of the Hilbert identity, the derivation of new forms of ‘off-diagonal’ estimates, and the study of the structure of the model in Lebesgue spaces and its interpolation properties. In particular, some coercivity conditions for forms in Banach spaces are used as a substitution of the ellipticity ones. Attention is devoted to the relations between the properties of perturbed and unperturbed generalized Dirac operators. We do not use any stability results.
Periodic Solution of the Caughy Problem
Authors: Dinh Tran Trung
Published: April 2009

We derive necessary and sufficient conditions for the existence of a time-periodic solution to the abstract Cauchy problem.
The Generalized Inverse A(2)T, Sof a Matrix Over an Associative Ring
Authors: Yu Yaoming , Wang Guorong
Published: April 2009

In this paper we establish the definition of the generalized inverse A(2)T, Swhich is a {2} inverse of a matrixAwith prescribed imageTand kernelsover an associative ring, and give necessary and sufficient conditions for the existence of the generalized inverseand some explicit expressions forof a matrix A over an associative ring, which reduce to the group inverse or {1} inverses. In addition, we show that for an arbitrary matrixAover an associative ring, the Drazin inverse Ad, the group inverse Agand the Moore-Penrose inverse. if they exist, are all the generalized inverse A(2)T, S.
Markoff type inequalities for curved majorants
Authors: Varma A. K. , Mills T. M. , Smith Simon J.
Published: April 2009

Let pn(x) be a real algebraic polynomial of degree n, and consider the Lp norms on I = [−1, 1]. A classical result of A. A. Markoff states that if ‖pn‖. ∞ ≤ 1, then ‖P′n‖∞ ≤ n2. A generalization of Markoff's problem, first suggested by P. Turán, is to find upper bounds for ‖pn(J)‖p if ∣pn(x)∣≤ ψ(x)x ∈ I. Here ψ(x) is a given function, a curved majorant. In this paper we study extremal properties of ‖p′n‖2 and ‖p″n‖2 if pn(x) has the parabolic majorant ∣p(x)∣≤ 1 − x2, x ∈ I. We also consider the problem, motivated by a well-known result of S. Bernstein, of maximising ‖(1 − x2)
Inequalities and representation formulas for functions of exponential type
Authors: Frappier C. , Olivier P.
Published: April 2009

We generalise the classical Bernstein's inequality: . Moreover we obtain a new representation formula for entire functions of exponential type.
The least number of coincidence points on surfaces
Authors: Jezierski Jerzy
Published: April 2009

Bo Ju Jiang introduced an invariant lying in the braid group which is the best lower bound of the number of fixed points in a homotopy class of a given pair of self maps of a surface. Here we modify this construction to get a lower bound of the number of coincidence points of a pair of maps between two closed surfaces.
Level crossings of a random trigonometric polynomial with dependent coefficients
Authors: Farahmand K.
Published: April 2009

This paper provides an asymptotic estimate for the expected number of K-level crossings of the random trigonometric polynomial g1 cos x + g2 cos 2x+ … + gn cos nx where gj (j = 1, 2, …, n) are dependent normally distributed random variables with mean zero and variance one. The two cases of ρjr, the correlation coeffiecient between the j-th and r-th coefficients, being either (i) constant, or (ii) ρ∣j−r∣ρ, j ≠ r, 0 < ρ < 1, are considered. It is shown that the previous result for ρjr = 0 still remains valid for both cases.
Some remarks on modularity of the congruence lattice of regular ω-semigroups
Authors: Bonzini C. , Cherubini A.
Published: April 2009

In this paper conditions of M-symmetry, strong, semimodularity and θ-modularity for the congruence lattice L (S) of a regular ω-semigroup S are studied. They are proved to be equivalent to modularity. Moreover it is proved that the kernel relation is a congruence on L(S) if and only if L(S) is modular, generalizing an analogous result stated by Petrich for bisimple ω-semigroups.
Artinian band sums of rings
Authors: Kelarev A. V.
Published: April 2009

Band sums of associative rings were introduced by Weissglass in 1973. The main theorem claims that the support of every Artinian band sum of rings is finite. This result is analogous to the well-known theorem on Artinian semigroup rings.
Concentration-cancellation and Hardy spaces
Authors: Vecchi Italo
Published: April 2009

Let υ∈ be a sequence of DiPema-Majda approximate solutions to the 2-d incompressible Euler equations. We prove that if the vorticity sequence is weakly compact in the Hardy space H1 (R2) then a subsequence of υ∈ converges strongly in the energy norm to a solution of the Euler equations.
On existence varieties of orthodox semigroups
Authors: Doyle J.
Published: April 2009

An existence variety of regular semigroups is a class of regular semigroups which is closed under the operations of forming all homomorphic images, all regular subsemigroups and all direct products. In this paper we generalize results on varieties of inverse semigroups to existence varieties of orthodox semigroups.
On the number of subgroups in finite solvable groups
Authors: Herzog Marcel , Manz Olaf
Published: April 2009

The main result of this paper is an upper bound for the number of maximal subgroups in finite solvable groups. Our result improves an earlier one of Cook, Wiegold and Williamson [1]. At the end, we use our bound to deduce an estimation for the total number of subgroups in finite solvable groups.
Corrigendum to Multiplication operators and dynamical systems
Authors: Singh R. K. , Manhas J. S.
Published: April 2009

Throughout Section 2 of [1], X should be taken as a completely regular Hausdorff KR-space. The lines 1 through 26 in the proof of Theorem 2.1 of the paper should be replaced by the following lines.
Lp-Lq estimates off the line of duality
Authors: Bak J.-G. , McMichael D. , Oberlin D.
Published: April 2009

Theorems 1 and 2 are known results concerning Lp–Lq estimates for certain operators wherein the point (1/p, 1/q) lies on the line of duality 1/p + 1/q = 1. In Theorems 1′ and 2′ we show that with mild additional hypotheses it is possible to prove Lp-Lq estimates for indices (1/p, 1/q) off the line of duality. Applications to Bochner-Riesz means of negative order and uniform Sobolev inequalities are given.
Balanced directed cycle designs based on cyclic groups
Authors: Nilrat Chaufah , Praeger Cheryl E.
Published: April 2009

A balanced directed cycle design with parameters (υ, k, 1), sometimes called a (υ, k, 1)-design, is a decomposition of the complete directed graph into edge disjoint directed cycles of length k. A complete classification is given of (υ, k, 1)-designs admitting the holomorph {øa, b: x ↦ ax + b∣ a, b ∈ Zυ, (a, υ1) = 1} of the cyclic group Zυ as a group of automorphisms. In particular it is shown that such a design exists if and ony if one of (a) k = 2, (b) p ≡ 1 (mod k) for each prime p dividing υ, or (c) k is the least prime dividing υ, k2 does not divide υ, and p ≡ 1 (mod k) for each prime p < k dividing υ.
On elementary amenable groups of finite Hirsch number
Authors: Wehrfritz B. A. F.
Published: April 2009

We give an alternative short proof of a recent theorem of J. A. Hillman and P.A. Linnell that an elementary amenable group with finite Hirsch number has, modulo its locally finite radical, a soluble normal subgroup with index and derived length bounded only in terms of the Hirsch number of the group.
On the faithful representations, of degree 2n, of certain extensions of 2-groups by orthogonal and symplectic groups
Authors: Glasby S. P.
Published: April 2009

If R is a 2-group of symplectic type with exponent 4, then R is isomorphic to the extraspecial group , or to the central product 4 o 21+2n of a cyclic group of order 4 and an extraspecial group, with central subgroups of order 2 amalgamated. This paper gives an explicit description of a projective representation of the group A of automorphisms of R centralizing Z(R), obtained from a faithful representation of R of degree 2n. The 2-cocycle associated with this projective representation takes values which are powers of −1 if R is isomorphic to and powers of otherwise. This explicit description of a projective representation is useful for computing character values or computing with central extensions of A. Such central extensions arise naturally in Aschbacher's classification of the subgroups of classical groups.
Weakly-injective modules over hereditary noetherian prime rings
Authors: Jain S. K. , López-Permouth S. R.
Published: April 2009

A module M is said to be wealdy-injective if and only if for every finitely generated submodule N of the injective hull E(M) of M there exists a submodule X of E(M), isomorphic to M such that N ⊂ X. In this paper we investigate weakly-injective modules over bounded hereditary noetherian prime rings. In particular we show that torsion-free modules over bounded hnp rings are always wealdy-injective, while torsion modules with finite Goldie dimension are weakly-injective only if they are injective.

As an application, we show that weakly-injective modules over bounded Dedekind prime rings have a decomposition as a direct sum of an injective module B, and a module C satisfying that if a simple module S is embeddable in C then the (external) direct sum of all proper submodules of the injective hull of S is also embeddable in C. Indeed, we show that over a bounded hereditary noetherian prime ring every uniform module has periodicity one if and only if every weakly-injective module has such a decomposition.
On Schur's conjecture
Authors: Turnwald Gerhard
Published: April 2009

We study polynomials over an integral domainRwhich, for infinitely many prime idealsP, induce a permutation ofR/P. In many cases, every polynomial with this property must be a composition of Dickson polynomials and of linear polynomials with coefficients in the quotient field ofR. In order to find out which of these compositions have the required property we investigate some number theoretic aspects of composition of polynomials. The paper includes a rather elementary proof of ‘Schur's Conjecture’ and contains a quantitative version for polynomials of prime degree.
Legendre transforms and Apéry's sequences
Authors: Schmidt Asmus L.
Published: April 2009

This article studies particular sequences satisfying polynomial recurrences, among those Apéry's sequence which is shown to be the Legendre transform of the sequence. This results in the construction of simultaneous approximations of π 2/8 and ζ(3).
Two gradient properties of explicitly convex functions
Authors: Yang Xinmin
Published: April 2009

In this paper, two gradient properties of explicit convex functions are given.
Instability theorems for certain nth order differential equations
Authors: Wen-Jian Li , Kui-chen Duan
Published: April 2009

In this paper we study the instability of certain nth order differential equations by means of Liapunov's functions and obtain some sufficient conditions for the equations being unstable. A method of constructing Liapunov's function for instability is being perfected. In particular the problem Ezeio posed in 1982 has been resolved to some extent.
Classes of modules with many direct summands
Authors: Al-Khazzi I. , Smith P. F.
Published: April 2009

Let R be any ring with identity, M a unital right R-module and α ≥ 0 an ordinal. Then M is a direct sum of a semisimple module and a module having Krull dimension at most α if and only if for every submodule N of M there exists a direct summand K of M such that K ⊆ N and N/K has Krull dimension at most α.
Constructions for arc-transitive digraphs
Authors: Conder Marston , Lorimer Peter , Praeger Cheryl
Published: April 2009

A number of constructions are given for arc-transitive digraphs, based on modifications of permutation representations of finite groups. In particular, it is shown that for every positive integer s and for any transitive permutation group p of degree k, there are infinitely many examples of a finite k-regular digraph with a group of automorphisms acting transitively on s-arcs (but not on (s + 1)-arcs), such that the stabilizer of a vertex induces the action of P on the out-neighbour set.
Morita equivalence for semigroups
Authors: Talwar S.
Published: April 2009

In this paper we shall extend the classical theory of Morita equivalence to semigroups with local units. We shall use the concept of a Morita context to rediscover the Rees theorem and to characterise completely 0-simple and regular bisimple semigroups.
Normal families of holomorphic functions
Authors: Chen Huai-Hui , Hua Xin-Hou
Published: April 2009

Let a(z) be a meromorphic function with only simple poles, and let k∈ N. Suppose that f(z) is meromorphic. We first set up an inequality in which T(r, f) is bounded by the counting function of the zeros of f(k) + af2, and then we prove a corresponding normal criterion. An example shows that the restriction on the poles of a(z) is best possible.
Linear independence of translations
Authors: Rosenblatt Joseph
Published: April 2009

It was shown by Edgar and Rosenblatt that f ∈ Lp (ℝn), 1 ≤ p < 2n/ (n-1), and f ≠0, then f has linearly independent translates. Using a result of Hömander, it is shown here that the same theorem holds if p = 2n / (n−1). This gives a sharp result because for n ≥2, there exists f ∈C0 (ℝn), f ≠0, which is simultaneously in all Lp (ℝn), p > 2n/(n−1), that has a linear dependence relation among its translates. References and some discussion are included.
Centralizer near-rings that are rings
Authors: Hausen Jutta , Johnson Johnny A.
Published: April 2009

Given an R-module M, the centralizer near-ring ℳR (M) is the set of all functions f: M → M with f(xr)= f(x)r for all x ∈ M and r∈R endowed with point-wise addition and composition of functions as multiplication. In general, ℳR(M) is not a ring but is a near-ring containing the endomorphism ring ER(M) of M. Necessary and/or sufficient conditions are derived for ℳR(M) to be a ring. For the case that R is a Dedekind domain, the R-modules M are characterized for which (i) ℳR(M) is a ring; and (ii)ℳR(M) = ER(M). It is shown that over Dedekind domains with finite prime spectrum properties (i) and (ii) are equivalent.
On a class of radicals of rings
Authors: Mazurek R.
Published: April 2009

Let λ be a property that a lattice of submodules of a module may possess and which is preserved under taking sublattices and isomorphic images of such lattices and is satisfied by the lattice of subgroups of the group of integer numbers. For a ring R the lower radical Λ generated by the class λ(R) of R-modules whose lattice of submodules possesses the property λ is considered. This radical determines the unique ideal Λ (R) of R, called the λ-radical of R. We show that Λ is a Hoehnke radical of rings. Although generally Λ is not a Kurosh-Amitsur radical, it has the ADS-property and the class of Λ-radical rings is closed under extensions. We prove that Λ (Mn (R)) ⊆ Mn (Λ(R)) and give some illustrative examples.
A Hall-type closure property for certain Fitting classes
Authors: Brison Owen J.
Published: April 2009

A closure operation connected with Hall subgroups is introduced for classes of finite soluble groups, and it is shown that this operation can be used to give a criterion for membership of certain special Fitting classes, including the so-called ‘central-socle’ classes.
Still more generalizations of Hardy's inequality
Authors: Pečarić J. E. , Love E. R.
Published: April 2009

These generalizations of Hardy's Integral Inequality are generalizations of some inequalities of B. G. Pachpatte.
Two commutative amenable non-symmetric Banach algebras
Authors: Johnson B. E.
Published: April 2009

We show that a commutative amenable Banach algebra need not be symmetric by constructing suitable examples.
Unique factorisation in P.I. group-rings
Authors: Chatters A. W.
Published: April 2009

We shall give necessary and sufficient conditions on the ring R and the group G for the group-ring RG to be a prime P. I. ring with the unique factorisation property as defined in [5].
Some local properties of the solutions of second-order differential equations
Authors: Cheng Jiuyi , Rossi John
Published: April 2009

We investigate the asymptotics and zero distribution of solutions of ω″ + Aω = 0 where A is an entire function of very slow growth. The results parallel the classical case when A is assumed to be a polynomial.
When can one domain enclose another in 3?
Authors: zhou Jiazu
Published: April 2009

In this paper, we give a sufficient condition (Theorem) in order that one domain D1 bounded by a C2-smooth boundary can be enclosed in, or enclose, another domain D0 bounded by the same kind of boundary. A same kind of sufficient condition for convex bodies (Corollary) is also obtained.
The Urysohn-Menger sum formula: an extension of the Dydak-Walsh theorem to dimension one
Authors: Dranišnikov Aleksander N. , Repovš Dušan
Published: April 2009

Let X be a finite-dimensional separable metric space, presented as a disjoint union of subsets, X = A∪B. We prove the following theorem: For every prime p, c-dimZpX≦c-dimZpA + c–dimZpB + 1. This improves upon some of the earlier work by Dydak and Walsh.
Growth sequences of finite groups III
Authors: Wiegold James
Published: April 2009

Let G be a finite group with d(G) = α, d(G/G′) = β≥1. If G has non-abelian simple images, let s denote the order of a smallest such image. Then d(Gn) = βn provided that βn≥α + 1 + log8n. If all simple images of G are abelian, then d(Gn) = βn provided that βn≥α. If G is non-trivial and perfect, with s again denoting the order of a smallest non-abelian simple image, then d(Gsn)≼d(G) + n for all n≥0. These results improve on results in previous papers with similar titles.
On the normal structure of a one-point stabilizer in a doubly transitive permutation group
Authors: Atkinson M. D. , Praeger Cheryl E.
Published: April 2009

Let G be a doubly transitive permutation group on a finite set Ω, and let Kα be a normal subgroup of the stabilizer Gα of a point α in Ω. If the action of Gα on the set of orbits of Kα in Ω − {α} is 2-primitive with kernel Kα it is shown that either G is a normal extension of PSL(3, q) or Kα ∩ Gγ is a strongly closed subgroup of Gαγ in Gα, where γ ∈ Ω − {α}. If in addition the action of Gα on the set of orbits of Kα is assumed to be 3-transitive, extra information is obtained using permutation theoretic and centralizer ring methods. In the case where Kα has three orbits in Ω − {α} strong restrictions are obtained on either the structure of G or the degrees of certain irreducible characters of G. Subject classification (Amer. Math. Soc. (MOS) 1970: 20 B 20, 20 B 25.
On lacunary sets for nonabelian groups
Authors: Dooley A. H.
Published: April 2009

Results concerning a class of lacunary sets are generalized from compact abelian to compact nonabelian groups. This class was introduced for compact abelian groups by Bozejko and Pytlik; it includes the p-Sidon sets of Edwards and Ross. A notion of test family is introduced and is used to give necessary conditions for a set to be lacunary. Using this, it is shown that (2) has no infinite p-Sidon sets for 1 ≤p<2.
Semigroups over generalized trees
Authors: Hays T. E.
Published: April 2009

A semigroup over a generalized tree, denoted by the term ℳL-semigroup, is a compact semigroup S such that Green's relation H is a congruence on S and S/H is an abelian generalized tree with idempotent endpoints and E(S/H) a Lawson semilattice. Each such semigroup is characterized as being constructible from cylindrical subsemigroups of S and the generalized tree S/H in a manner similar to the construction of semigroups over trees and of the hormos. Indeed, semigroups over trees are shown to be particular examples of the construction given herein.
Covering Theorems for FINASIGS VIII—almost all conjugacy classes in An have exponent ≤4
Authors: Brenner J. L.
Published: April 2009

The product of two subsets C, D of a group is defined as . The power Ce is defined inductively by C0 = {1}, Ce = CCe−1 = Ce−1C. It is known that in the alternating group An, n > 4, there is a conjugacy class C such that CC covers An. On the other hand, there is a conjugacy class D such that not only DD≠An, but even De≠An for e<[n/2]. It may be conjectured that as n ← ∞, almost all classes C satisfy C3 = An. In this article, it is shown that as n ← ∞, almost all classes C satisfy C4 = An.
On the rate of convergence of moments in the central limit theorem
Authors: Hall Peter
Published: April 2009

An early extension of Lindeberg's central limit theorem was Bernstein's (1939) discovery of necessary and sufficient conditions for the convergence of moments in the central limit theorem. Von Bahr (1965) made a study of some asymptotic expansions in the central limit theorem, and obtained rates of convergence for moments. However, his results do not in general imply that the moments converge. Some better rates have been obtained by Bhattacharya and Rao for moments between the second and third. In this paper we give improved rates of convergence for absolute moments between the third and fourth.
Existence of nonatomic charges
Authors: Bhaskara Rao K. P. S. , Rao M. Bhaskara
Published: April 2009

A complete characterization of Boolean algebras which admit nonatomic charges (i.e. finitely additive measures) is obtained. This also gives rise to a characterization of superatomic Boolean algebras. We also consider the problem of denseness of the set of all nonatomic charges in the space of all charges on a given Boolean algebra, equipped with a suitable topology.
Three-groups with cyclic centre and central quotient of maximal class
Authors: Conlon S. B.
Published: April 2009

All three-groups with cyclic centre and such that the quotient by the centre has maximal class are listed and a presentation with generators and relations for each is given.
On generalized Borel sets
Authors: Pfeffer W. F.
Published: April 2009

A certain natural extension B of the Borel σ-algebra is studied in generalized weakly θ-refinable spaces. It is shown that a set belongs to B whenever it belongs to B locally. From this it is derived that if ℵωα is more complicated than aunion of less than ℵα weakly θ-refinable subspaces.
Green's relations for regular elements of sandwich semigroups, II; semigroups of continuous functions
Authors: Magill K. D. , Subbiah S.
Published: April 2009

A sandwich semigroup of continuous functions consists of continuous functions with domains all in some space X and ranges all in some space Y with multiplication defined by fg = foαog where α is a fixed continuous function from a subspace of Y into X. These semigroups include, as special cases, a number of semigroups previously studied by various people. In this paper, we characterize the regular elements of such semigroups and we completely determine Green's relations for the regular elements. We also determine the maximal subgroups and, finally, we apply some of these results to semigroups of Boolean ring homomorphisms.
Powers of p–valent functions
Authors: Noonan J. W.
Published: April 2009

If f is areally mean p–valent in the unit disc, if λ>0 and if fλ is defined as a single-valued analytic function on the unit disc with finitely many arcs removed, several results in the recent literature suggest that fλ might be areally mean pλ–valent. The purpose of this note is to determine the valence of fλ when f is areally mean p–valent, and also to characterize those functions for which fλ is pλ–valent for all λ>0. Analogous results are obtained for functions which are either s–dimensionally mean p–valent or logarithmically mean p–valent.
The structure sheaf of an incidence algebra
Authors: Barnwell Beth Goldston , Mewborn A. C.
Published: April 2009

Let R be the incidence algebra of a finite partially ordered set T over a commutative noetherian ring A. Then the spectrum of R is homeomorphic to the product (Spec A) x T, where Spec A has the usual Zariski topology and T has the order topology. An explicit construction is given for the structure sheaf of R over its spectrum.
Mal'cev conditions, spectra and kronecker product
Authors: Neumann Walter D.
Published: April 2009

It is shown that every possible spectrum of a Mal'cev definable class of varieties which should occur does occur. It follows that there are continuum many Mal'cev definable classes, a result also obtained by Taylor (1975) and Baldwin and Berman (1976).
A fixed point theorem with applications to convolution equations
Authors: Edwards R. E.
Published: April 2009

The well-known Banach Contraction Principle asserts that any self-map F of a complete metric space M with the property that, for some number k < 1, for all x, y,∈M, possesses a unique fixed point in M. some extensions and analogues have recently been given by Edelstein [1]. For the reader's convenlience we state here the result of Edelstein which we shall employ. It asserts that if F is a self-map of a metric space M having the property that for any two distinct points x and y of M, and if x0 is a point of M such that the sequence of iterates xn = Fn (x0) contains a subsequence which converges in M, then the limit of this subsequence is the unique fixed point of F.
Functions of three variables which satisfy both the heat equation and Laplace's equation in two variables
Authors: Widder D. V.
Published: April 2009

In a recent paper on statistical fluid mechanics Professor J. Kampé de Fériet [1] employed several integrals of which the following is a typical exampleThe functionu(x, y, t), which it defines, formally satisfies the following three classical differential equations
A theorem on partitions
Authors: Graham R. L.
Published: April 2009

Certain integers have the property that they can be partitioned into distinct positive integers whose reciprocals sum to 1, e.g., and In this paper we prove that all integers exceeding 77 possess this property. This result can then be used to establish the more general theorem that for any positive rational numbers α and β there exists an integer r(α, β) such that any integer exceeding r(α, β) can be partitioned into distinct positive integers exceeding β whose reciprocals sum to α.
On H. Simpson's six-conic theorem
Authors: Denniston R. H. F.
Published: April 2009

H. Simpson [1] has proved a theorem about six points P1,…,P6 (no three in line, not all on a conic) of the real projective plane. He calls P1 an “in-point” or an “out-point”, according as it lies inside or outside the conic (denoted by a Roman figure I) through the other five points; and so on. The theorem is that there are either two, three, or six in-points.
On continuous time models in the theory of dams
Authors: Kingman J. F. C.
Published: April 2009

The problem of storage in an infinite dam with a continuous release has been studied by a number of authors ([5], [3], [2]), who have formulated it in probabilistic terms by supposing the input to be a continuous time stochastic process. These authors have encountered difficulties which they have overcome by regarding the continuous time problem as a limit of discrete time analogues. analogues. The purpose of this paper is to suggest that these difficulties are the result of an unfortunate specification of the problem, and to show that the adoption of a slightly different (and more realistic) formulation avoids the difficulties and allows a treatment which does not have recourse to discrete time analogues.
Asymptotic transient behaviour of the bulk service queue
Authors: Craven B. D.
Published: April 2009

Various authors have studied the transient behaviour of single-server queues. Notably, Takacs [13], [14] has analysed a queue with recurrent input and exponential service time distributions, Keilson and Kooharian [9], [10] and Finch [5] have considered a queue with general independent input and service times, Finch [6] has analysed a queue with non-recurrent input and Erlang service, and Jaiswal [8] has considered the bulk-service queue with Poisson input and Erlang service.
A remark on C-compact spaces
Authors: Nayar Bhamini M. P.
Published: April 2009

It has been observed by a number of researches that although it is well-known that all continuous functions defined on C-compact spaces are closed functions, this property does not characterize C-compact spaces. In this note we employ the notion of strongly subclosed relations to prove that a space is C-compact if and only if all functions on it with strongly subclosed inverses are closed functions.
Application of the Bruhat-Tits tree of SU3(h) to some Ã2 groups
Authors: Cartwright Donald I. , Steger Tim
Published: April 2009

Let K be a nonarchimedean local field, let L be a separable quadratic extension of K, and let h denote a nondegenerate sesquilinear formk on L3. The Bruhat-Tits building associated with SU3(h) is a tree. This is applied to the study of certain groups acting simply transitively on vertices of the building associated with SL(3, F), F = Q3 or F3((X)).
Subordination in the sense of Bochner and a related functional calculus
Authors: Schilling René L.
Published: April 2009

We prove a new representation of the generator of a subordinate semigroup as limit of bounded operators. Our construction yields, in particular, a characterization of the domain of the generator. The generator of a subordinate semigroup can be viewed as a function of the generator of the original semigroup. For a large class these functions we show that operations at the level of functions has its counterpart at the level of operators.
On groups in which every subgroup is subnormal of defect at most three
Authors: Traustason Gunnar
Published: April 2009

In this paper we study groups in which every subgroup is subnormal of defect at most 3. LetGbe a group which is either torsion-free or of prime exponent different from 7. We show that every subgroup inGis subnormal of defect at most 3 if and only ifGis nilpotent of class at most 3. WhenGis of exponent 7 the situation is different. While every group of exponent 7, in which every subgroup is subnormal of defect at most 3, is nilpotent of class at most 4, there are examples of such groups with class exactly 4. We also investigate the structure of these groups.
Functions of bounded expansion: normal and Bloch functions
Authors: Gauthier P. M. , Xiao J.
Published: April 2009

Normal functions and Bloch functions are respectively functions of bounded spherical expansion and bounded Euclidean expansion. In this paper we discuss the behaviour of normal functions and of Bloch functions in terms of the maximal ideal space of H∞, the Bergman projection and the Ahlfors-Shimizu characteristic.
A Radon-Nikodým theorem for vector polymeasures
Authors: Fernández F. J. , Guerra P. Jiménez , Ulecia M. T.
Published: April 2009

A Radon-Nikodým theorem for Banach valued polymeasures is proved.
A Global algorithm for geodesics
Authors: Noakes Lyle
Published: April 2009

The problem of finding a george joinning given points x0, x1in a connected complete Riemannian manifold requires much more effort than determining a geodesic from initial data. Boundary value problems of this type are sometimes solved using shooting methods, which work best when good initial guesses are available expectually when x0, x1are nearby. Galerkin methods have their drawbacks too. The situation is much more difficult with general variational problems, which is why we focus on the Riemannian case.

Our global algorithm is very simple to implement, and works well in practice, with no need for an initial guess. The proof of convergence to elementary and very carefully stated. with a view to possible generalizations latter on we have in mind the much larger class of interesting problems arising in optimal control especially from mechanical engineering.
Regular cyclic actions on complex projective space with codimension-two fixed points
Authors: Little Robert D.
Published: April 2009

IfM2nis a cohomologyCPnandPis an odd prime, letGpbe the cyclic group of orderp. A TypeI I0Gpaction onM2nis an action with fixed point set a codimension-2 submanifold and an isolated point. A TypeI I0Gpaction is standard if it is regular and the degree of the fixed codimension-2 submanifold is one. If n is odd and M2nadmits a standardGpaction of TypeI I0, then every TypeI I0GpactionM2nis standard and so, if n is odd,CPnadmits aGpaction of TypeI I0if and only if the action is standard.