bluuebunny/crossref_metadata_2025 huggingface dataset:
Stone's theorem and completeness of orthogonal systems
Authors: Craven B. D.
Published: April 2009

It is well known (e.g. Stone [1]) that the Stone-Weierstrass approximation theorem can be used to prove the completeness of various systems of orthogonal polynomials, e.g. Chebyshev polynomials. In this paper, Stone's theorem is used to prove a more general completeness theorem, which includes as special cases Plancherel's theorem, the corresponding theorem for Hankel transforms, the completeness of various polynomial systems, and certain expansions in Jacobian elliptic functions. The essential feature common to all these systems is a certain algebraic structure — if S is an appropriate vector space spanned by orthogonal functions, then the algebra A generated by S is contained in the closure of S in a suitable norm.
Non-negative values of quadratic forms
Authors: Worley R. T.
Published: April 2009

In a paper [1] of the same title Barnes considered the problem of finding an upper bound for the infimumm+(f) of the non-negative values1of an indefinite quadratic formfinnvariables, of given determinant det(f) ≠ 0 and of signatures. In particular it was announced (and later proved — see [2]) thatm+(f) ≦ (16/5)+for ternary quadratic forms of determinant 1 and signature — 1. A simple consequence of this result is thatm+(f) ≦ (256/135)+for quaternary quadratic forms of determinant — 1 and signature — 2.
Radius of univalence and starlikeness of a class of analytic functions
Authors: Gupta R. S.
Published: April 2009

Letp denote the family of functions regular in E{z:|z| < 1} and with positive real part there. We propose to study, in this article, the subclass p2a1 of p whose functions P(z) have pre-assigned second coefficient 2a1. In what follows we may assume, without loss in generality, that a1 is real and non-negative. This assumption will be made throughout. As is well known [2], 0 ≦ a1 ≦ 1. In Theorem 1 we derive a generalization of Zmorovic's theorem 1, [3]. determine the radius of univalence and starlikeness of the class of functions
On a class of near-rings
Authors: Szeto George
Published: April 2009

In [3], Ligh proved that every distributively generated Boolean near-ring is a ring, and he gave an example to which the above fact can not be extended. That is, let G be an additive group and let the multiplication on G be defined by xy = y for all x, y in G. Ligh called this Boolean near-ring G a general Boolean near-ring. near-ring. Then in [4], Ligh called Ra β-near-ring if for each x in R, x2 = x and xyz = yxz for all x, y, z in R, and he proved that the structure of a β-near-ring is “very close” to that of a usual Boolean ring. We note that general Boolean near-rings and Boolean semirings as defined in [5] are β-near-rings. The purpose of this paper is to generalize the structure theorem on β-near-rings given by Ligh in [4] to a broader class of near-rings.
The near center of an orthomodular lattice
Authors: Janowitz M. F.
Published: April 2009

The results described herein were obtained in connection with the development of some lattice theoretic machinery needed by Randall and Foulis in their treatment of the so-called “logic of empirical science” (See [3] for an introduction to this subject). The final product, however, turned out to be of sufficient interest to warrant its independent presentation.
Fractional integrals of generalised functions
Authors: Erdélyi A.
Published: April 2009

The concept of integrals of fractional order of a function f, defined by if Reα > 0, can be extended to generalised functions in the framework of the theory of convolution of distributions. The resulting theory [2, Chap. I §5.5] is very satisfactory for many purposes but there are circumstances in which it is not suitable. Such circumstances arise in particular if it is necessary to multiply, before or after integratrion, by non-integral powers of the variable. Pointwise multiplication by fractional powers of the independent variable does not make sense in the theory of distributions.
Quasi-homeomorphisms and lattice-equivalences of topological spaces
Authors: Kai-Wing Yip
Published: April 2009

In his paper [1], Thron introduced a concept of lattice-equivalence of topological spaces. Let C(X) denote the lattice of all closed sets of a topological space X. Two topological spaces X and Y are said to be lattice-equivalent if there exists a lattice-isomorphism between C(X) and C(Y). It is clear that for any continuous function f: X → Y, the induced map ψf: C(Y) → C(X), defined by ψ(F)=f−1(F), is a lattice-homomorphism. Furthermore, if h: X→ Y is a homeomorphism then ψh: C(Y) → C(X) is a lattice-isomorphism. Thron proved among others that for TD-spaces X and Y, any lattice-isomorphism: C(Y) → C(X) can be induced by a homeomorphism f: X → Y in the above way.
On Hewitt's τ-maximal spaces
Authors: Kirch Murray R.
Published: April 2009

Let τ be any cardinal number. Edwin Hewitt [3] has defined a topological space (X, J) to be τ-maximal if δ(J) ≥ τ and δ(J') < τ whenever J' is a topology for X which is strictly stronger that J (Δ denotes dispersion character, the least cardinality of a nonempty open set). The notion of an ℵ0-maximal space was introduced independently by Katětov [4].
A note on generalized unique extension of measures
Authors: Huang Deng-Yuan
Published: April 2009

In Theorem 1, we shall discuss some properties of semifinite measure, that is, the measure μ on a ring R of sets with the property that, for every E in R, μ(E) is equal to the least upper bound of μ(F) where F runs over sets such that F is in R (F ⊂ E) and μ(F) < ∞. Let σ(R) be the σ-ring generated by R. To prove Theorem 2 we shall use the uniqueness theorem in Luther's paper [2], which is stated as a lemma in this paper.
Duplication of Room squares
Authors: Wallis W. D.
Published: April 2009

ARoom squareRof order 2nis a way of arranging 2nobjects (usually 1,2,…, 2n) in a square arrayRof side 2n– 1 so that:

(i) every cell of the array is empty or contains two objects;

(ii) each unordered pair of objects occurs once inR

(iii) every row and column ofRcontains one copy of each object.
Representation theorems for the weierstrass transform
Authors: Ditzian Z.
Published: April 2009

In this paper we shall be interested in the Weierstrass transform defined by (1.1.) converging (conditionally) for x in some interval, where (1.2) .
Projective bitopological spaces II.
Authors: Datta M. C.
Published: April 2009

Gleason [3] proved that in the category G of compact Hausdorff spaces and continuous maps, the projective objects are precisely the extremally disconnected spaces contained in the category. Strauss [7] generalised this and proved that in the category G of regular Hausdorif spaces and perfect maps the projective objects are again precisely the extremally disconnected ones. Observe that Gleason's category is a full subcategory of Strauss's category.
Identical relations in loops, I
Authors: Evans Trevor
Published: April 2009

The systematic study of identities in groups was begun by B. H. Neumann in 1937, [7]. Although many special loop identities have been extensively investigated, there is not, as yet, a general theory of identical relations in loops. We cannot hope that such a theory will be as rich in results as in the group case (except in the sense that loop theory includes group theory) but there are many interesting problems, including some which have no analogue in the associative case.
On Finite Groups With ‘Hidden’ Primes
Authors: Kovács L. G. , Neubüser Joachim , Neumann B. H.
Published: April 2009

The starting point of this investigation was a question put to us by Martin B. Powell: If the prime number p divides the order of the finite group G, must there be a minimal set of generators of G that contains an element whose order is divisible by p? A set of generators of G is minimal if no set with fewer elements generates G. A minimal set of generators is clearly irredundant, in the sense that no proper subset of it generates G; an irredundant set of generators, however, need not be minimal, as is easily seen from the example of a cyclic group of composite (or infinite) order. Powell's question can be asked for irredundant instead of minimal sets of generators; it turns out that the answer is not the same in these two cases. A different formulation, together with some notation, may make the situation clearer.
On Exposed and Farthest Points in Normed Linear Spaces
Authors: Edelstein M. , Lewis J. E.
Published: April 2009

Let S be a nonempty subset of a normed linear space E. A point s0 of S is called a farthest point if for some x ∈ E, . The set of all farthest points of S will be denoted far (S). If S is compact, the continuity of distance from a point x of E implies that far (S) is nonempty.
Simplexes Self-Polar for a Simplex
Authors: Konnully Augustine O.
Published: April 2009

In this paper we prove the existence of simplexes self-polar for a given simplex in projective space of dimensions higher than two. And noting the reciprocity of the relationship between a simplex and any simplex self-polar for it, further, we consider a configuration in projective space associated with a pair of mutually self-polar simplexes. Finally the results obtained are related to the simplexes determined by Hadamard matrices in space of special dimensions.
On the Unicellularity of Weighted Shifts
Authors: Harrison K. J.
Published: April 2009

An operator acting on a Banach space is said to be unicellular if its lattice of invariant subspaces is totally ordered by inclusion. Each weighted shift on a sequence space has a natural totally ordered set of invariant subspaces, and is unicellular if these are its only invariant subspaces.
Groups of Matrices With Integer Eigenvalues
Authors: Freislich M. R.
Published: April 2009

Let F be an algebraic number field, and S a subgroup of the general linear group GL(n, F). We shall call S a U-group if S satisfies the condition (U): Every x ∈ S is a matrix all of whose eigenvalues are algebraic integers. (This is equivalent to either of the following conditions: a) the eigenvalues of each matrix (x are all units as algebraic numbers; b) the characteristic polynomial for x has all its coefficients integers in F. In particular, then, every group of matrices with entries in the integers of F is a U-group.
On Finitely Generated Subgroups of Free Products
Authors: Burns R. G.
Published: April 2009

IfHis a subgroup of a groupGwe shall say thatGisH-residually finiteif for every elementginG, outsideH, there is a subgroup of finite index inG, containingHand still avoidingg. (Then, according to the usual definition,Gisresidually finiteif it isE-residually finite, whereEis the identity subgroup). Definitions of other terms used below may be found in § 2 or in [6].
Some Results on Configurations
Authors: Wallis Jennifer
Published: April 2009

A (v,k, λ) configurations is conjectured to exist for everyv,kand λ satisfying λ(v− 1) =k(k− 1) andk− λ is a square ifvis even,x2= (k − λ)y2+ (−1)(v−1)/2λz2has a solution in integersx,yandznot all zero forvodd.
One-regular cubic graphs of order a small number times a prime or a prime square
Authors: Feng Yan-Quan , Kwak Jin Ho
Published: April 2009

A graph is one-regular if its automorphism group acts regularly on the set of its arcs. In this paper we show that there exists a one-regular cubic graph of order 2p or 2p2 where p is a prime if and only if 3 is a divisor of p – 1 and the graph has order greater than 25. All of those one-regular cubic graphs are Cayley graphs on dihedral groups and there is only one such graph for each fixed order. Surprisingly, it can be shown that there is no one-regular cubic graph of order 4p or 4p2.
Posner's second theorem, multilinear polynomials and vanishing derivations
Authors: Filippis Vincenzo De , Vincenzo Onofrio Mario Di
Published: April 2009

Let K be a commutative ring with unity, R a prime K-algebra of characteristic different from 2, d and δ non-zero derivations of R, f (x1,…, xn) a multilinear polynomial over K.If

then f(x1,…,xnis central-valued on R.
C2 building and projective space
Authors: Lai K. F.
Published: April 2009

We study the stability map from the rigid analytic space of semistable points in P3 to convex sets in the building of Sp2 over a local field and construct a pure affinoid covering of the space of stable points.
Normality and exceptional functions of derivatives
Authors: Xu Yan
Published: April 2009

In this paper, we obtain some normality criteria for families of meromorphic functions that concern the exceptional functions of derivatives, which improve and generalize related results of Gu, Yang, Schwick, Wang-Fang, and Pang-Zalcman. Some examples are given to show the sharpness of our results.
A note on the theta characteristics of a compact Riemann surface
Authors: Biswas Indranil
Published: April 2009

Let X be a compact connected Riemann surface and ξ a square root of the holomorphic contangent bundle of X. Sending any line bundle L over X of order two to the image of dim H0(X, ξ ⊗ L) − dim H0(X, ξ) in Z/2Z defines a quadratic form on the space of all order two line bundles. We give a topological interpretation of this quadratic form in terms of index of vector fields on X.
On varieties of metabelian groups of prime-power exponent
Authors: Brooks M. S.
Published: April 2009

Let Un denote the variety of abelian groups of exponent dividing n, and let p be an arbitrary prime. In this paper all non-nilpotent, join-ireducible subvarieties of the product variety UpUp2 are determined. The proper subvarieties of this kind in fact form an infinite ascending chain …, and an arbitrary proper subvariety B of UpUp2 is either nilpotent or a join , where L is nilpotent and k is uniquely determined by B.
Congruences on simple regular ω-semigroups
Authors: Baird G. R.
Published: April 2009

The set E of idempotents of a semigroup S can be partially ordered by defining e ≦ f if and only if . If E = {ei: i = 0,1, …} and under this ordering e0 > e1 > e2, …, then we call S an ω-semigroup. Munn [7] has given a complete classification of simple regular ω-semigroups in terms of groups and group homomorphisms.
Embedding problems in semiring theory
Authors: Grillet Mireille P.
Published: April 2009

The main object of this paper is to give various constructions of the universal semiring of a partial semiring and apply them to find conditions for the embedding of partial semirings into semirings.
Convolution, fixed point, and approximation in Stieltjes-Volterra integral equations
Authors: Bitzer Carl W.
Published: April 2009

This paper focuses primarily on two aspects of Stieltjes-Volterra integral equation theory. One is a theory for convolution integrals — that is, integrals of the form — and the other is a fixed point theorem for a mapping which is induced by an integral equation. Throughout the paper I will denote the identity function whose range of definition should be clear from the context and all integrals will be left integrals, written , whose simplest approximating sum is [f(b) – f(a)]·g(a) and whose value is the limit of approximating sums with respect to successive refinements of the interval. Also, N will denote the set of elements of a complete normed ring with unity 1 and S will denote a set linearly ordered by ≦.
Isometries between matrix algebras
Authors: Cheung Wai-Shun , Li Chi-Kwong , Poon Yiu-Tung
Published: April 2009

As an attempt to understand linear isometries between C*-algebras without the surjectivity assumption, we study linear isometries between matrix algebras. Denote by Mm the algebra of m × m complex matrices. If k ≥ n and φ: Mn → Mk has the form X ↦ U[X ⊕ f(X)] V or X ↦ U[X1 ⊕ f(X)]V for some unitary U, V ∈ Mk and contractive linear map f: Mn → Mk, then ║φ(X)║ = ║X║ for all X ∈ Mn. We prove that the converse is true if k ≤ 2n - 1, and the converse may fail if k ≥ 2n. Related results and questions involving positive linear maps and the numerical range are discussed.
Wavelet decomposition of Calderón-Zygmund operators on function spaces
Authors: Lau Ka-Sing , Yan Lixin
Published: April 2009

We make use of the Beylkin-Coifman-Rokhlin wavelet decomposition algorithm on the Calderón-Zygmund kernel to obtain some fine estimates on the operator and prove theT(l) theorem on Besov and Triebel-Lizorkin spaces. This extends previous results of Frazieret al., and Han and Hofmann.
Transitive simple subgroups of wreath products in product action
Authors: Baddeley Robert W. , Praeger Cheryl E. , Schneider Csaba
Published: April 2009

A transitive simple subgroup of a finite symmetric group is very rarely contained in a full wreath product in product action. All such simple permutation groups are determined in this paper. This remarkable conclusion is reached after a definition and detailed examination of ‘Cartesian decompositions’ of the permuted set, relating them to certain ‘Cartesian systems of subgroups’. These concepts, and the bijective connections between them, are explored in greater generality, with specific future applications in mind.
Relatively compact-like perturbations, essential spectra and application
Authors: Latrach Khalid , Paoli J. Martin
Published: April 2009

The purpose of this paper is to provide a detailed treatment of the behaviour of essential spectra of closed densely defined linear operators subjected to additive perturbations not necessarily belonging to any ideal of the algebra of bounded linear operators. IfAdenotes a closed densely defined linear operator on a Banach spaceX, our approach consists principally in considering the class ofA-closable operators which, regarded as operators in ℒ(XA,X) (whereXAdenotes the domain ofAequipped with the graph norm), are contained in the set ofA-Fredholm perturbations (see Definition 1.2). Our results are used to describe the essential spectra of singular neutron transport equations in bounded geometries.
You can see the arrows in a quiver operator algebra
Authors: Solel Baruch
Published: April 2009

We prove that two quiver operator algebras can be isometrically isomorphic only if the quivers (=directed graphs) are isomorphic. We also show how the graph can be recovered from certain representations of the algebra.
Real rank of C*-algebras associated with graphs
Authors: Jeong Ja A
Published: April 2009

For a locally finite directed graph E, it is known that the graph C*-algebra C*(E) has real rank zero if and only if the graph E satisfies the loop condition (K). In this paper we extend this to an arbitrary directed graph case using the desingularization of a graph due to Drinen and Tomforde
On the Mathieu group M23
Authors: Bryce N.
Published: April 2009

Until 1965, when Janko [7] established the existence of his finite simple group J1, the five Mathieu groups were the only known examples of isolated finite simple groups. In 1951, R. G. Stanton [10] showed that M12 and M24 were determined uniquely by their order. Recent characterizations of M22 and M23 by Janko [8], M22 by D. Held [6], and M11 by W. J. Wong [12], have facilitated the unique determination of the three remaining Mathieu groups by their orders. D. Parrott [9] has so characterized M22 and M11, while this paper is an outline of the characterization of M23 in terms of its order.
Sequential Tests for Normal Markov Sequence
Authors: Phatarfod R. M.
Published: April 2009

This is a sequel to the author's (Phatarfod [9]) paper in which an analogue of Wald's Fundamental Identity (F.I.) for random variables defined on a Markov chain with a finite number of states was derived. From it the sampling properties of sequential tests of simple hypotheses about the parameters occurring in the transition probabilities were obtained. In this paper we consider the case of continuous Markovian variables. We restrict our attention to the practically important case of a Normal Markov sequenceX0,X1,X2,… such thattheYrbeing independent normal variables with mean zero and variance σ2.
The order of certain Dirichlet series
Authors: An Chung-Ming
Published: April 2009

This paper is a continuation of [1]1 We shall use the same notations as those in [1]. Let F(X) ∈ R[X], X = (X1, …, Xn), be a polynomial of degree d > 0 and h(x) ∈ SP(Rn), i.e. h(x) is the sum of a polynomial and a Schwartz funtion. We shall consider Dirichlet series of the type where NF = {x∈Rn: F(x) = 0}. We proved, in [1], that Z(h, F, s) is regular for σ > (n+p)/d and possesses the analytic continuation to the whole s-plane when Fd(x) (the highest homogeneous part of F(X)) ≠ 0 for x ≠ 0. In this paper, we shall say the following.
An ascoli theorem for multi-valued functions
Authors: Mancuso Vincent J.
Published: April 2009

The concept of simultaneous or collective continuity of a family of single valued functions was introduced by Gale [3] for regular spaces to replace equicontinuiry in metric spaces. Smithson [6] extended the standard point-open and compact-open function space topologies to include multi-valued functions. The aim of this paper is to use these topologies and extend the notion of collective continuity in order to obtain an Ascoli type theorem for multi-valued functions analogous to Theorem 1 in [3, p. 304]. We have the following theorem in mind:
On the times of births in a linear birthprocess
Authors: Neuts Marcel F. , Resnick Sidney I.
Published: April 2009

If S1, S2,… are the times of successive births in a pure birth-process with linear birthrate and i > 0 individuals initially, then given that there are k > 0 births in (0, t), the random variables eλS1—1, eλS2−1,λS1−1 are distributed (conditionally) like the order statistics of k independent random variables, all uniformly distributed on the interval (0, eλt–1), regardless of the initial population size. A similar property holds for the pure death process.
On the critical Galton-Watson process with immigration
Authors: Pakes A. G.
Published: April 2009

Consider a Galton-Watson process in which each individual reproduces independently of all others and has probabilityaj(j= 0, l, …) of giving rise tojprogeny in the following generation and in which there is an independent immigration component wherebj(j= 0, l, …) is the probability thatjindividuals enter the population at each generation. Then lettingXn(n= 0, l, …) be the population size of the n-th generation, it is known (Heathcote [4], [51]) that {Xn} defines a Markov chain on the non-negative integers. Unless otherwise stated, we shall consider only those offspring and immigration distributions that make the Markov chain {Xn} irreducible and aperiodic.
Amenable transformation semigroups
Authors: Wilde Carroll , Jayachandran Toke
Published: April 2009

For any set X denote by m(X) the Banach space of all bounded real-valued functions on X, equipped with the supremum norm, and denote by (X) the semigroup (under functional composition) of all transformations of X, i.e. mappings with domain X and range contained in X. A pair (X, S), where S is a subsernigroup of (X), will be called a transformation semigroup. Important examples are obtained by letting X be the underlying set in an abstract semigroup and considering the pairs (X, S1) and (X, S2), where S1 [Sn] denotes the set of left [right] multiplication mappings of X. We shall call transformation semigroups in these classes of examples l-[r-] semigroups.
Local hardy and BMO spaces on non-homogeneous spaces
Authors: Yang Dachun
Published: April 2009

Let µ be Radon measure on Rd which may be non doubling. The only condition that µ must satisfy is the size condition µ(B(x, r)) ≤ Crn for some fixed n є (0, d). Recently, Tolsa introduced the spaces RBMO(µ) and Hatb1.∞ (µ), which, in some ways, play the role of the classical spaces BMO and H1 in case u is a doubling measure. In this paper, the author considers the local versions of the spaces RBMO(µ) and Hatb1.∞ (µ) in the sense of Goldberg and establishes the connections between the spaces RBMO(µ) and Hatb1.∞ (µ) with their local versions. An interpolation result of linear operators is also given.
Some new permutability properties of hypercentrally embedded subgroups of finite groups
Authors: Ezquerro L. M. , Soler-Escrivà X.
Published: April 2009

Hypercentrally embedded subgroups of finite groups can be characterized in terms of permutability as those subgroups which permute with all pronormal subgroups of the group. Despite that, in general, hypercentrally embedded subgroups do not permute with the intersection of pronormal subgroups, in this paper we prove that they permute with certain relevant types of subgroups which can be described as intersections of pronormal subgroups. We prove that hypercentrally embedded subgroups permute with subgroups of prefrattini type, which are intersections of maximal subgroups, and with F-normalizers, for a saturated formation F. In the soluble universe, F-normalizers can be described as intersection of some pronormal subgroups of the group.
A note on commutative Baer rings
Authors: Speed T. P. , Evans M. W.
Published: April 2009

The class of commutative rings known as Baer rings was first discussed by J. Kist [4], where many interesting properties of these rings were established. Not necessarily commutative Baer rings had previously been studied by I. Kaplansky [3], and by R. Baer himself [1]. In this note we show that commutative Baer rings, which generalize Boolean rings and p-rings, satisfy the Birkhoff conditions for a variety. Next we give a set of equations characterising this variety involving + and * as binary operations, – and as unary operations, and 0 as nullary operation. Finally we describe Baer-subdirectly irreducible commutative Baer rings and state the appropriate representation theorem.
Absolute summability of some series related to a fourier series
Authors: Dikshit H. P.
Published: April 2009

Let {Pn} be a given sequence of constants, real or complx, such that then , defines the sequence {tn} of (N, pn) means of Σnan. The series Σnan is said to be summable I|N, pn|, if {tn} ∈ BV, −|−tn−1| ∞.
Uniqueness of complementing pairs in partially ordered abelian groups
Authors: Hansen Rodney T.
Published: April 2009

Let A and B denote subsets of an abelian group (G, +). The pair (A, B) is called a complementing pair for A + B provided each element of the sum is uniquely represented. A complementing pair (A, B) for C is denoted (A, B) ~ C.
Decomposition theorems for the generalized metaharmonic equation in several independent variables
Authors: Colton David
Published: April 2009

In this paper solutions of the generalized metaharmonic equation in several independent variables where λ > 0 are uniquely decomposed into the sum of a solution regular in the entire space and one satisfying a generalized Sommerfeld radiation condition. Due to the singular nature of the partial differential equation under investigation it is shown that the radiation condition in general must hold uniformly in a domain lying in the space of several complex variables. This result indicates that function theoretic methods are not only the correct and natural avenue of approach in the study of singular ordinary differential equations, but are basic in the investigation of singular partial differential equations as well.
Annihilator and complemented banach*-algebras
Authors: Tomiuk B. J. , Wong Pak-Ken
Published: April 2009

The study of complemented Banach*-algebras taken up in [1] was confined mainly toB*-algebras. In the present paper we extend this study to (right) complemented Banach*-algebras in whichx*x= 0 impliesx= 0. We show that ifAis such an algebra then every closed two-sided ideal ofAis a *-ideal. Using this fact we obtain a structure theorem forAwhich states that ifAis semi-simple thenAcan be expressed as a topological direct sum of minimal closed two sided ideals each of which is a complemented Banach*-algebra. It follows thatAis an A*-algebra and is a dense subalgebra of a dual B*-algebraU, which is determined uniquely up to *-isomorphism.
Formulae for absolute moments
Authors: Brown B. M.
Published: April 2009

The purpose of this note is to derive an alternative expression to that given in Lemma 1 below (due to Hsu, and to von Bahr) for the absolute moments of a random variable, in terms of the characteristic function.
Soluble Semigroups
Authors: Trotter Peter G.
Published: April 2009

The cancellation law is a necessary condition for a semigroup to be embedded in a group. In general, this condition is not sufficient; necessary and sufficient conditions are rather complicated (see [1]). It is, therefore, of interest to find large classes of semigroups for which the cancellation law is sufficient to ensure embeddability in a group.
Note on the combinatorial formula for nHr
Authors: Nath G. Baikunth , Iyer P. V. Krishna
Published: April 2009

nHr denotes the number of n × n matrices with non-negative integral entries, with row-sums and column-sums all equal to r. Kenji Mano [3] investigated the number nHr in which n distinct objects each replicated r times can be distributed in equal numbers among n cells. He gives an intricate formula for the case r = 2. Recently, Anand et al. [1], making use of partitions, extended it to 3Hr and stated a plausible formula for nHr.
Convergence of iterates and differentiability
Authors: Papp Francis J. , Nielsen Robert M.
Published: April 2009

Given a function T mapping a Hausdorff locally convex topological vector space Φ into Φ and a point φ0 of Φ, convergence of the elementary filter associated with the sequence of iterates determined by T and φ0 is investigated. Sufficient conditions that the limit φ if it exists, be a fixed point of T are given and in the case Φ is the space of real valued functions of a real variable differentiability of the limit function φ is investigated.
Invariant linear functionals
Authors: Woodward W. Randolph , Chivukula R. R.
Published: April 2009

Let B be a Banach space and let ℒ(B) denote the space of all bounded inear operators from B to B, which is a Banach algebra under composition of operators as multiplication. By a semigroup of operators G on B, we mean a norm bounded subser G of ℒ (B) which is a subsemigroup in the multiplicative structure of ℒ(B). The purpose of this paper is to study the existence of nonzero continuous linear functionals on B invariant under G, that is given B and G, does there exist μ∈B*, with μ ≠ 0, such that μ(Sx) = μ(x) for all x∈B and S∈G. This question is an attempt to generalize the familiar concepts of invariant means and amenability of semigroups. If H is any semigroup and m(H) is the Banach space of all bounded real valued functions on H with supremum norm, then a mean is a positive normalized continuous linear functional on m(H). A mean is called (left) [right] invariant if it is invariant under (left) [right] translations and H is called (left)[right] amenable if there exists such a mean; e.g., F is a left invariant mean if F∈m(H)* is such that (i) ‖F‖ = 1, (ii) F(x)≧0 if x(g)≧0 for all g∈H, (iii) F(xg) = F(x) for all x∈m(H) and g∈G where xg(h) = x(gh) for all h∈H. Amenability of semigroups has been studied extensively in recent years, for example see Day [2] or Hewitt and Ross [6] for an introduction, and Day [3] for a comprehensive survey.
Constructible lattices
Authors: Janowitz M. F.
Published: April 2009

This paper is a continuation of [2] and will use the terminology and notation introduced therein. Basically, we seek to investigate the structure of indexed lattices in which the set of lengths of the minimal indexing chains is bounded.
On classes of null sets
Authors: Lloyd John
Published: April 2009

Results concerning classes of null sets have been obtained by various authors. See, for example, [3], [4], [6], [7]. This paper contains results concerning classes of null sets and the notion of a ‘small system’. The motivation for considering ‘small systems’ comes from a paper by Riečan (c.f. [2]).
On further properties of improjective operators
Authors: Tarafdar E.
Published: April 2009

This is a continuation of our work [4]. The purpose of this paper is to find the relation of the class of improjective operators on some Banach space, with the classes of strictly singular, strictly cosingular and φ-admissible perturbations on X and to investigate those pairs of Banach spaces for which all bounded linear operators having either of the pair as domain and the other as range are improjective, or strictly singular. The beginning of Section 1 is intended to familiarize the reader with the concepts and notations used in this paper.
On the laws of the variety se
Authors: Bryant Roger M.
Published: April 2009

A group is called an s-group if it is locally finite and all its Sylow subgroups are abelian. Kovács [4] has shown that, for any positive integer e, the class se of all s-groups of exponent dividing e is a (locally finite) variety. The proof of this relies on the fact that, for any e, there are only finitely many (isomorphism classes of) non-abelian finite simple groups in se; and this is a consequence of deep results of Walter and others (see [6]). In [2], Christensen raised the finite basis question for the laws of the varieties se. It is easy to establish the finite basis property for an se which contains no non-abelian finite simple group; and Christensen gave a finite basis for the laws of the variety s30, whose only non-abelian finite simple group is PSL(2,5). Here we prove Theorem For any positive integer e, the varietysehas a finite basis for its laws.
Further generalizations of Neumann's integral
Authors: Pye W.
Published: April 2009

A generalization of Neumann's integral connecting the two kinds of Legendre function is obtained. It contains an extra parameter which is not a function of the parameters of the Legendre functions, unlike all previous extensions of the original formula. These extensions are shown to be particular cases of the new generalization and some further particular cases are also indicated.
About directed unions of Artinian subrings of a Von Neumann regular ring
Authors: Karim Driss
Published: April 2009

This work is concerned with the question of when a von Neumann regular ring is expressible as a directed union of Artinian subrings.
Certain functional relations for the double harmonic series related to the double Euler numbers
Authors: Tsumura Hirofumi
Published: April 2009

In this paper, we give certain analytic functional relations for the double harmonic series related to the double Euler numbers. These can be regarded as continuous generalizations of the known discrete relations obtained by the author recently.
Modules which are invariant under monomorphisms of their injective hulls
Authors: Alahmadi A. , Er N. , Jain S. K.
Published: April 2009

In this paper certain injectivity conditions in terms of extensions of monomorphisms are considered. In particular, it is proved that a ring R is a quasi-Frobenius ring if and only if every monomorphism from any essential right ideal of R into R(N)R can be extended to RR. Also, known results on pseudo-injective modules are extended. Dinh raised the question if a pseudo-injective CS module is quasi-injective. The following results are obtained: M is quasi-injective if and only if M is pseudo-injective and M2 is CS. Furthermore, if M is a direct sum of uniform modules, then M is quasi-injective if and only if M is pseudo-injective. As a consequence of this it is shown that over a right Noetherian ring R, quasi-injective modules are precisely pseudo-injective CS modules.
Cohomological characterization of the Hilbert symbol over Q*p
Authors: Romo Fernando Pablos
Published: April 2009

The aim of this work is to offer a new characterization of the Hilbert symbol Q*p from the commutator of a certain central extension of groups. We obtain a characterization for Q*p (p≠2) and a different one for Q*2.
The distribution of the irreducibles in an algebraic number field
Authors: Bradley David M. , Özlük Ali E. , Rozario Rebecca A. , Snyder C.
Published: April 2009

We study the distribution of principal ideals generated by irreducible elements in an algebraic number field.
Partial automorphisms of stable C*-algebras and Hilbert C*-bimodules
Authors: Kodaka Kazunori
Published: April 2009

Let A be a C*-algebra and K the C*-algebra of all compact operators on a countably infinite dimensional Hilbert space. In this note, we shall show that there is an isomorphism of a semigroup of equivalence classes of certain partial automorphisms of A ⊗ K onto a semigroup of equivalence classes of certain countably generated A-A-Hilbert bimodules.
Gradings of non-graded Hamiltonian Lie algebras
Authors: Caranti A. , Mattarei S.
Published: April 2009

A thin Lie algebra is a Lie algebra graded over the positive integers satisfying a certain narrowness condition. We describe several cyclic grading of the modular Hamiltonian Lie algebrasH(2: n; ω2)(of dimension one less than a power ofp) from which we construct infinite-dimensional thin Lie algebras. In the process we provide an explicit identification ofH(2: n; ω2)with a Block algebra. We also compute its second cohomology group and its derivation algebra (in arbitrary prime characteristic).
Some properties of mean periodic functions
Authors: Laird P. G.
Published: April 2009

This paper presents some properties of continuous complex-valued mean periodic functions of a single real variable. The theory of these functions is due mainly to Schwartz [7] and they have also been considered by Kahane [4, 5]. Most of the properties outlined here are also shared by the continuous meanperiodic functions on a half line introduced by Koosis [6].
Transient heat flow from a thin circular disk — small-time solution
Authors: Blackwell J. H.
Published: April 2009

Summary

In a previous paper [1] an approximate analytical solution, useful for large times, was obtained for the transient heat flow from a thin circular disk held at constant temperature and immersed in an infinite medium. In the present work a first approximation has been found for the complementary “small-time” solution and the details of this solution examined. Some numerical calculations are included.
Absolute summability of a fourier series and its derived series by a product method
Authors: Dikshit H. P.
Published: April 2009

Let Σan be a given infinite series with the sequence of partial sums {Sn}. Let {Pn} be a sequence of constants, real or complex, and let us write Pn = p0 + p1 + … + pn; P-1 = P-1 = 0.
The Euler-Lagrange expression and degenerate lagrange densities
Authors: Lovelock D.
Published: April 2009

It is well known that many of the field equations from theoretical physics (e.g. Einstein field equations, Maxwell's equations, Klein-Gordon equation) can be obtained from a variational principle with a suitably chosen Lagrange density. In the case of the Einstein equations the corresponding Lagrangian is degenerate (i.e., the associated Euler-Lagrange equations are of second order whereas in general these would be of fourth order), while in the cases of the Maxwell and Klein-Gordon equations the Lagrangian usually used is not degenerate.
Some generalizations of normal series in infinite groups
Authors: Phillips Richard E.
Published: April 2009

In this paper, we are concerned with certain generalizations of subnormal and ascendent (transfinitely subnormal) subgroups of a group. A subgroup A of a group G is called f-ascendent in G if there is a well ordered ascending complete series of subgroups of G, where for all α < λ, either Gα ⊲ Gα+1 or [Gα+1: Gα] < ∞. If such a series has finite length, A is called F-subnormal in G.
The structure of a special class of near-rings
Authors: Ligh Steve
Published: April 2009

It is well known that a Boolean ring is isomorphic to a subdirect sum of two-element fields. In [3] a near-ring (B, +, ·) is said to be Boolean if there exists a Boolean ring (B, +, Λ, 1) with identity such that · is defined in terms of +, Λ, and 1 and, for any b ∈ B, b · b = b. A Boolean near-ring B is called special if a · b = (a ν x) Λ b, where x is a fixed element of B. It was pointed out that a special Boolean near-ring is a ring if and only if x = 0. Furthermore, a special Boolean near-ring does not have a right identity unless x = 0. It is natural to ask then whether any Boolean near-ring (which is not a ring) can have a right identity. Also, how are the subdirect structures of a special Boolean near-ring compared to those of a Boolean ring. It is the purpose of this paper to give a negative answer to the first question and to show that the subdirect structures of a special Boolean near- ring are very ‘close’ to those of a Boolean ring. In fact, we will investigate a class of near-rings that include the special Boolean near-rings and the Boolean semi- rings as defined in [8].
Asymptotic results for the solutions of a certain differential equation
Authors: Mahony J. J.
Published: April 2009

The asymptotic behaviour, for large real positive values of the independent variable t, of solutions of the ordinary differential equation is considered. (The dots denote differentiation with respect to t.) It is shown that this asymptotic behaviour can be obtained by comparison with the differential equation For both equations when a2 < 2 the solutions are unbounded oscillatory functions but when a2 > 2 the solutions are essentially monotone. The critical case a2 = 2 has not been investigated here although the present results suggest that the solutions are probably monotone. The asymptotic estimates of the solutions of equation (1) are first obtained by heuristic means commonly used by Applied Mathematicians working on singular perturbation problems. A basis for a formal expansion is obtained in terms of a recurrence relation and the first few terms are displayed explicitly. These formal expansion estimates are used to guide a rigorous analysis which is essentially an extension of the techniques used in validating solutions obtained by the Langer related equation technique. For the oscillatory case, a pair of Volterra integral equations is used to justify the asymptotic representations for an arbitrary large interval for t but not including the point at infinity.
Fixed points of quasi-nonexpansive mappings
Authors: Dotson W. G.
Published: April 2009

A self-mapping T of a subset C of a normed linear space is said to be non-expansive provided ║Tx — Ty║ ≦ ║x – y║ holds for all x, y ∈ C. There has been a number of recent results on common fixed points of commutative families of nonexpansive mappings in Banach spaces, for example see DeMarr [6], Browder [3], and Belluce and Kirk [1], [2]. There have also been several recent results concerning common fixed points of two commuting mappings, one of which satisfies some condition like nonexpansiveness while the other is only continuous, for example see DeMarr [5], Jungck [8], Singh [11], [12], and Cano [4]. These results, with the exception of Cano's, have been confined to mappings from the reals to the reals. Some recent results on common fixed points of commuting analytic mappings in the complex plane have also been obtained, for example see Singh [13] and Shields [10].
On a common abstraction of Boolean rings and lattice ordered groups II
Authors: Rao V. V. Rama
Published: April 2009

In an earlier paper, the author has obtained a solution [8] to Birkhoff's problem No. 105 [1]: Is there a common abstraction which includes Boolean algebras (Rings) and lattice ordered groups as special cases? The solution actually turns out to be the direct product of a Boolean ring and a lattice ordered group. Birkhoff's problem has also been solved by Swamy, Wyler, and Nakano by presenting respectively i) Dually Residuated Lattice Ordered Semigroups (D.R.1. semigroups) [2, 3, 4, 5], ii) Clans [6], and iii) Multirings [7].
Polarities and ovals in the Hughes plane
Authors: Room T. G.
Published: April 2009

In 1946 Baer (Polarities infinite projective planes, Bull. Am. Math. Soc. 52, 77–93) showed that the absolute points of a polarity in a finite projective plane of odd non-square order always form an oval, that is, in a plane of order n there are exactly n+ 1 absolute points and no three are collinear. It is well known that the absolute points of polarities in planes of odd square order form ovals in some cases.

If the oval is a subset of the set of absolute points, then the oval itself determines the polarity, and this makes it appear unlikely that the oval could be a proper subset. Among other results in the paper it is to be proved that in the regular Hughes plane there is a polarity which is determined by an oval which is a relatively small subset of the set of absolute points. Explicitly, if Ω is the Hughes plane of order q2 and A is the central subplane of order q, then every conic in Δ can be extended to an oval in Ω, and this oval determines a polarity in which there are ½(q3–q) additional absolute points.
On the radii of starlikeness and convexity of certain classes of regular functions
Authors: Chichra Pran Nath
Published: April 2009

Let Rn denote the class of functions f(z) = z+anzn+ … (n ≧ 2) which are regular in the open disc|z| < 1 (hereafter called E) and satisfy for all z in E. Rnis a subclass of the class of close-to-star function in E [9, p. 61]. MacGregor showed that the radius of univalence and starlikeness of Rn is , see [4,5]. The radius of convexity of R = R2 is r0 = 0.179 …, where r0 is the smallest positive root of the equation 1−5r−3r2−r3 = 0, see [8].
On Fourier transform multipliers in Lp
Authors: Okikiolu G. O.
Published: April 2009

We denote by R the set of real numbers, and by Rn, n ≧ 2, the Euclidean space of dimension n. Given any subset E of Rn, n ≧ 1, we denote the characteristic function of E by xE, so that XE(x) = 0 if x ∈ E; and XE(X) = 0 if x ∈ Rn/E.The space L(Rn) Lp consists of those measurable functions f on Rn such that is finite. Also, L∞ represents the space of essentially bounded measurable functions with ║f║>0; m({x: |f(x)| > x}) = O}, where m represents the Lebesgue measure on Rn The numbers p and p′ will be connected by l/p+ l/p′= 1.
Tight Riesz groups
Authors: Loy R. J. , Miller J. B.
Published: April 2009

The theory of partially ordered topological groups has received little attention in the literature, despite the accessibility and importance in analysis of the group Rm. One obstacle in the way of a general theory seems to be, that a convenient association between the ordering and the topology suggests that the cone of all strictly positive elements be open, i.e. that the topology be at least as strong as the open-interval topology U; but if the ordering is a lattice ordering and not a full ordering then U itself is already discrete. So to obtain in this context something more interesting topologically than the discrete topology and orderwise than the full order, one must forego orderings which make lattice-ordered groups: in fact, the partially ordered group must be an antilattice, that is, must admit no nontrivial meets or joins (see § 2, 10°).
Some nonoscillation criteria for inclusions
Authors: Agarwal Ravi P. , Grace Said R. , O'Regan Donal
Published: April 2009

New nonoscillatory criteria are presented for second order differential inclusions. The theory relies on Ky Fan's fixed point theorem for upper semicontinuous multifunctions.
Partitions into large unequal parts from a general sequence
Authors: Fergusson Kevin John
Published: April 2009

An asymptotic estimate is obtained for the number of partitions of the positive integer n into unequal parts coming from a sequence u, with each part greater than m, under suitable conditions on the sequence u. The estimate holds uniformly with respect to integers m such that 0 ≤ m ≤ n1−δ, as n → ∞, where δ is a given real number, such that 0 < δ < 1.
Seminormal and subnormal subgroup lattices for transitive permutation groups
Authors: Praeger Cheryl E.
Published: April 2009

Various lattices of subgroups of a finite transitive permutation group G can be used to define a set of ‘basic’ permutation groups associated with G that are analogues of composition factors for abstract finite groups. In particular G can be embedded in an iterated wreath product of a chain of its associated basic permutation groups. The basic permutation groups corresponding to the lattice L of all subgroups of G containing a given point stabiliser are a set of primitive permutation groups. We introduce two new subgroup lattices contained in L, called the seminormal subgroup lattice and the subnormal subgroup lattice. For these lattices the basic permutation groups are quasiprimitive and innately transitive groups, respectively.