bluuebunny/crossref_metadata_2025 huggingface dataset:
Lattice points in a convex Set of given width
Authors: Elkington G. B. , Hammer J.
Published: April 2009

Let S be a closed bounded convex set in d-dimensional Euclidean space Ed. The width w(S) of S is the minimum distance between supporting hyperplanes of S, and L(S) is the number of integral lattice points in the interior of S.
Dirichlet-finite outer functions
Authors: Yamashita Shinji
Published: April 2009

Given a measurable function k non-negative a.e. on the circle |z| = 1, when is the outer function Tk (see(1.3)) continuous on the disk |z| < 1 and further, Dirichlet-finite: We shall show, among other results, that the answer is in the positive if , with ess inf k > 0.
Imperfect bifurcation and Banach space singularity theory
Authors: Arkeryd Leif
Published: April 2009

This paper generalizes the theory of imperfect bifurcation via singularity theory as developed by M. Golubitsky and D. Schaeffer to a Banach space setting. Like the parameter-free potential catastrophe theory, where similar generalizations have been discussed in the literature, Banach control spaces allow useful uniform control of function parameters through the universal unfolding. Among the results are tests for various germ properties and discussion of their reducibility under a Liapunov—Schmidt type splitting, as well as a generalization of the finite dimensional unfolding and germ classification theory.
A congruence-free inverse semigroup associated with a pair of infinite cardinals
Authors: Howie J. M.
Published: April 2009

Let m, n be infinite cardinals such that m < n, and let X be a set of cardinality m. Within the symmetric inverse semigroup on X the elements whose domain and range have complements of cardinality m form an inverse semigroup T. The closure Eω of the semilattice E of idempotents of T is a fundamental bismple inverse semigroup. Its maximum congruence is described. The quotient of Eο by this maximum congruence is a bisimple, congruence is a bisimple, congruence-free inverse semigroup.
Some formulas related to dilogarithms, the zeta function and the Andrews-Gordon identities
Authors: Richmond Bruce , Szekeres George
Published: April 2009

It is shown that non-trivial relations between certain values of the dilogarithm function can be obtained through the asymptotic comparison of coefficients of the expressions which appear in the Rogers-Ramanujan and Andrews-Gordon identities.
The Boolean ring universal over a meet semilattice
Authors: Evans Elliot
Published: April 2009

The Boolean ring B{M} universal over a meet semilattice M is examined. It is the vector space over the two element field Z2 with base M\{0}. The Z2 linear independence of a meet subsemilattice of a Boolean ring is characterized in order theoretic terms and some ramifications of this on B[M] are considered. The space (ℱpM) of proper filters of M is shown homeomorphic to the Stone space S(B[M]) of B[M] if M has no least element, with ℱP(M) ∪ {M} and S(B[M]) homeomorphic otherwise. The congruence lattice θ(M) of M is compared to the ideal lattice ℱ(B [M]) of B [M] with best results coming if M is a tree with zero when θ (M) = ℐ (B [M]).
Dimension and finite closure
Authors: Gross W. F.
Published: April 2009

If is a model with dimension and finite closure, then T() is No-categorical. If is atomic, has dimension and finitely many algebraic elements, then has finite closure or a finite basis. If has finite closure, satisfies the Exchange Lemma, and one-one maps between independent subsets are elementary, then has dimension.
Random semigroup acts on a finite set
Authors: Högnäs Göran
Published: April 2009

LetXbe a finite set andSa semigroup of transformations ofX. We investigate the trace onXof a random walk onS. We relate the structure of the trace process, which turns out to be a Markov chain, to that of the random walk. We show, for example, that all periods of the trace process divide the period of the random walk.
On the existence of support maps with dense images
Authors: Sims Brailey
Published: April 2009

For a normed linear space X we investigate conditions for the existence of support maps under which the image of X is a dense subset of the dual. In the case of finite-dimensional spaces a complete answer is given. For more general spaces some sufficient conditions are obtained.
Submanifolds and the length of the second fundamental tensor
Authors: Hasanis Thomas
Published: April 2009

A sufficient condition, for a complete submanifold of a Riemannian manifold of positive constant curvature to be umbilical, is given. The condition will be given by an inequality which is established between the length of the second fundamental tensor and the mean curvature.
Projectives in some categories of Hausdorff spaces
Authors: Raha Asit Baran
Published: April 2009

An investigation on the existence of projective objects and projective resolutions has been carried out in some categories more general than the category of compact spaces and continuous maps.
Rearranging measures
Authors: Brown G. , Williamson J. H.
Published: April 2009

A churning transformation can be defined on probability measures by an infinite sequence of finite permutations of mass. Continuity and absolute continuity of measures are invariants for such transformations but it is shown that certain probability measures whose Fourier-Stieltjes transforms fail to vanish at infinity may be churned into measures whose transforms do vanish in this sense.
A simple proof of an identity of Ramanujan
Authors: Hirschhorn M. D.
Published: April 2009

One of Ramanujan's unpublished, unproven identities has excited considerable interest over the years. Indeed, no fewer than four proofs have appeared in the literature. The object of this note is to present yet another proof, simpler than the others, relying only on Jacobi's triple product identity.
Strictly positive and strongly positive semigroups
Authors: Majewski Adam , Robinson Derek W.
Published: April 2009

We examine positive semigroups acting on Banach lattices and operator algebras. In the lattice framework we characterize strict positivity and strict ordering of holomorphic semigroups by irreducibility criteria. In the algebraic setting we derive ergodic criteria for irreducibility and discuss various aspects of strict positivity. Finally we examine invariant states of a C*-dynamical system in which the automorphism group is replaced by a strongly positive semigroup. We demonstrate that ergodic states are characterized by a cluster property despite the absence of a covariant implementation law for the semigroup.
Elementary abelian operator groups and admissible formations
Authors: Gross Fletcher
Published: April 2009

Suppose the elementary abelian group A acts on the group G where A and G have relatively prime orders. If CG(a) belongs to some formation F for all non-identity elements a in A, does it follow that G belongs to F? For many formations, the answer is shown to be yes provided that the rank of A is sufficiently large.
The distributive lattice free product as a sublattice of the abelianl-group free product
Authors: Powell Wayne B. , Tsinakis Constantine
Published: April 2009

This paper establishes an important link between the class of abelianl-groups and the class of distributive lattices with a distinguished element. This is accomplished by describing the distributive lattice free product of a family of abelianl-groups as a naturally generated sublattice of their abelianl-group free product.
Best Diophantine approximations to a set of linear forms
Authors: Lagarias J. C.
Published: April 2009

We define the notion of a best Diophantine approximation vector to a set of linear forms. This generalizes definitions of a best approximation vector to a single linear form and of a best simultaneous Diophantine approximation vector. We derive necessary and sufficient conditions for the existence of an infinite set of best Diophantine approximation vectors. Finally, we prove that such approximation vectors are spaced far apart in an appropriate sense.
On primitive abundant numbers
Authors: Cohen Graeme L.
Published: April 2009

Letnbe a natural with largest componentsd. We prove that ifxσ(n) =yn+z(x, y, zgiven positive integers),nis not primitive (y/x)-abundant andn/sis not (y/x)-perfect, thenn< 4(z+ ½)3/27y(ifz≥ 175). All solutions are tabled for the equationxσ(n) -ynwhenx= 1,y≥ 2, 1 ≤z≤ 210, andnis not primitivey-abundant. We also prove that ifnis primitive (y/x)-abundant, thens3d< (yn/2)2. A number of results are proved concerning the range of σ(n)/nwhennis primitive αabundant, for any real number α > 1. For example, then α(n/n< α + min {½ 3 αe-5a/9/2) and σ(n)/n< α /1.6α/logn. All primitive abundant numbersnwith α(n)/ ≥ 2.05 are listed.
The number of solutions to an equation arising from a problem on latin squares
Authors: Goulden I. P. , Vanstone S. A.
Published: April 2009

A recent article of G. Chang shows that an n × n partial latin square with prescribed diagonal can always be embedded in an n × n latin square except in one obvious case where it cannot be done. Chang's proof is to show that the symbols of the partial latin square can be assigned the elements of the additive abelian group Zn so that the diagonal elements of the square sum to zero. A theorem of M. Halls then shows this to be embeddable in the operation table of the group. In this paper, we show that when n is a prime one can determine exactly the number of distinct ways in which this assignment can be made. The proof uses some graph theoretic techniques.
Pseudo-idempotents in semigroups of functions
Authors: Cezus Frank A.
Published: April 2009

The aim of this paper is to generalize Theorem 2.10 (i) of [2]. As stated in [2] this theorem deals with the semigroup of all selfmaps on a discrete space and provides a characterization of H-classes which contain an idempotent. We will generalize this theorem to the case of other semigroups of functions on a discrete space, some semigroups of continuous functions on non-discrete topological spaces, and one semigroup of binary relations. The results in this paper form the main part of chapter 3 of [1]. Some results will be quoted from [1] without proof; the required proofs can easily be supplied by the reader.
On sets of integers not containing arithmetic progressions of prescribed length
Authors: Abbott H. L. , Liu A. C. , Riddell J.
Published: April 2009

Letm,nandlbe positive integers satisfyingm≦n≦l≦ 3. Denote byh(m, n, l) the largest integer with the property that from everyn-subset of {1,2, …,m} one can selecth(m, n, l) integers nolof which are in arithmetic progression. Letf(n, l) =h(n, n, l) and letg(n, l) = minmh(m, n, l). In what follows, by aP1-free set we shall mean a set of integers not containing an arithmetic progression of lengthl.
A classification of the commutator subgroup of the group of a boundary link
Authors: Chang Bai Ching
Published: April 2009

In Neuwirth's book “Knot Groups” ([2]), the structure of the commutator subgroup of a knot is studied and characterized. Later Brown and Crowell refined Neuwith's result ([1], and we thus know that ifGis the groups of a knotK, then [G, G] is either free of rank 2g, wheregis the genus ofK, or a nontrivial free product with amalgamation on a free group of rank 2g, and may be written in the form, whereFis free of rank 2g, and the amalgamations are all proper and identical.
Cauchy completion of partially ordered groups
Authors: Sherman B. F.
Published: April 2009

A number of completions have been applied to p.o.-groups — the Dede kind-Macneille completion of archimedean l.o. groups; the lateral completion of l.o. groups (Conrad [2]); and the orthocompletion of l.o. groups (Bernau [1]). Fuchs in [3] has considered a completion of p.o. groups having a non-trivial open interval topology — the only l.o. groups of this form being fully ordered. He applies an ordering, which arises from the original partial order, to the group of round Cauchy filters over this topology; Kowaisky in [6] has shown that group, imbued with a suitable topology, is in fact the topological completion of the original group under its open interval topology. In this paper a slightly different ordering, also arising from the original order, is proposed for the group of round Cauchy filters; Fuchs' ordering can be obtained from this one as the associated order.
Isomorphisms on countable vector spaces with recursive operations
Authors: Soare Robert I.
Published: April 2009

Terminology and notation may be found in Dekker [1] and [2]. Briefly, we fix arecursively enumerable(r.e.) fieldFwith recursive structure, and let Ū be the vector space overFconsisting of ultimately vanishing countable sequences of elements ofFwith the usual definitions of vector addition and multiplication by a scalar. A subspaceVof Ū is called anα-spaceifVhas a basisBwhich is contained in some r.e. linearly independent setS.
Ordinary differential equations
Authors: Coppel W. A.
Published: April 2009

This is the text and invited lecture given at the 20th Annual Meeting of the Australian Mathematical Society in Perth, May 1976.

In this talk I want to give a survey of some of the areas of research in ordinary differential equations. In view of the vastness of the field, the limited thime available and may own inadequacies I will restrict attention to problems in which I have been involved in some way, although I won't be speaking about my own work. Even with this restriction it will be necessary to be somewhat superficial. However, in spite of all these drawbacks, I thought it would assist communication among mathematicians simply to have an idea of what other people are doing. Since this is my purpose I will not mention the quite mild smoothness hypotheses in the statements of some results.
Group inverses and Drazin inverses of bidiagonal and triangular Toeqlitz matrices
Authors: Hartwig R. E. , Shoaf J.
Published: April 2009

Necessary and sufficient sonditions are given for the existence of the group and Drazin inverses of bidiagonal and triangular Toeplitz matrices over an arbitrary ring.
Some criteria for the regularity of a direct product of regular p-groups
Authors: Groves J. R. J.
Published: April 2009

A sufficient condition, which may also be necessary, for the regularity of the direct product of two finite regular p-groups is obtained. In an attempt to decide the necessity of the condition, we look at two related questions. Firstly, does the regularity of the direct square of a regular p-group imply the regularity of all the finite direct powers; secondly, is the join of two regular varieties regular? Fainally, the results obtained are used to give some precise answers in special cases.
The exceptional case in a theorem of Bose and Shrikhande
Authors: de Witte Paul , Wallis Jennifer Seberry
Published: April 2009

It is shown that (n being an integer) any non-trivial finite linear space with n2- 1 points, all of degree at most n+1, is embeddable in a finite projective plane of order n. This generalizes a theorem of Bose and Shrikhande and settles the unsolved case n = 6.
Commutators and abelian groups
Authors: Rodney D. M.
Published: April 2009

If G is a group, then K(G) is the set of commutators of elements of G. C is the class of groups such that G′ = K(G) is the minimal cardinality of any generating set of dG. We prove: Theorem A. Let G be a nilpotent group of class two such that G' is finite and d(G′) < 4.Then G < G.

Theorm B. Let G be a finite group such that G′ is elementary abelian of order p3. Then G ∈ C.

Theorem C. Let G be a finite group with an elementary abelian Sylow p-subgroup S, of order p2, such that S ⊆ K(G). Then S ⊆K(G).
Inverse semigroups of homeomorphisms between open subsets
Authors: Baird Bridget Bos
Published: April 2009

The symbolIG(X) denotes the inverse semigroup, under composition of functions, of all homeomorphisms between open subsets of aT1topological spaceX. The first result is that two such semigroupsIG(X) andIG(Y) are isomorphic if and only if the spacesXandYare homeomorphic. Ideals ofIG(X) are next examined and it is shown that for many spacesXthe semigroupIG(X) is 0-simple. We also look at congruences onIG(X); one result is that we determine a congruence which in many instances is the largest proper congruence onIG(X).
Congruence-free right simple semigroups
Authors: Trotter P. G.
Published: April 2009

Congruence-free right simple semigroups with idempotents are simple groups or have order 2. It is shown in this paper that there exist congruence-free simple semigroups without idempotents. Some properties of congruences on right simple semigroups, expressed mainly in terms of their unitary and left unitary subsemigroups, are determined. These are used to provide characterizations of congruence-free right simple semigroups.
Some properties of endomorphisms in residually finite groups
Authors: Hirshon Ronald
Published: April 2009

If ε is an endomorphism of a finitely generated residually finite group onto a subgroup Fε of finite index in F, then there exists a positive integer k such that ε is an isomorphism of Fεk. If K is the kernel of ε, then K is a finite group so that if F is a non trivial free product or if F is torsion free, then ε is an isomorphism on F. If ε is an endomorphism of a finitely generated resedually finite group onto a subgroup Fε (not necessatily of ginite index in F) and if the kernel of ε obeys the minimal condition for subgroups then there exists a positive integer k such that ε is an isomorphism on Fεk.
On uniqueness and continuability of the Emden–Fowler equation
Authors: Kwong Man Kam
Published: April 2009

The Emden-Fowler equation x″(t) + a(t)|x|γ sgn x = 0, t ≧ 0, is said to be in the sublinear or superlinear case according to whether γ < 1 or γ > 1. Conditions on a(t) are given to ensure local uniqueness of solutions in the sublinear case and continuability of solutions in the superlinear case. Boundedness of solutions is also studied.
Classes of operators on vector valued integration spaces
Authors: Fleming R. J. , Jamison J. E.
Published: April 2009

Let Lp(Ω, K) denote the Banach space of weakly measurable functions F defined on a finite measure space and taking values in a separable Hilbert space K for which ∥ F ∥p = ( ∫ | F(ω) |p)1/p < + ∞. The bounded Hermitian operators on Lp(Ω, K) (in the sense of Lumer) are shown to be of the form , where B(ω) is a uniformly bounded Hermitian operator valued function on K. This extends the result known for classical Lp spaces. Further, this characterization is utilized to obtain a new proof of Cambern's theorem describing the surjective isometries of Lp(Ω, K). In addition, it is shown that every adjoint abelian operator on Lp(Ω, K) is scalar.
The stability index of a cactus
Authors: Grant Douglas D. , Holton D. A.
Published: April 2009

We show that ifGis a connected graph of ordernsuch that no line lies in more than one cycle (in other words,Gis a cactus of ordern), then the stability index ofGis one of the integers 0, 1,n−7,n−6,n−5,n−4 orn.
Rigidity in order-types
Authors: Hickman J. L.
Published: April 2009

A totally ordered set (and corresponding order-type) is said to be rigid if it is not similar to any proper initial segment of itself. The class of rigid ordertypes is closed under addition and multiplication, satisfies both cancellation laws from the left, and admits a partial ordering that is an extension of the ordering of the ordinals. Under this ordering, limits of increasing sequences of rigid order-types are well defined, rigid and satisfy the usual limit laws concerning addition and multiplication. A decomposition theorem is obtained, and is used to prove a characterization theorem on rigid order-types that are additively prime. Wherever possible, use of the Axiom of Choice is eschewed, and theorems whose proofs depend upon Choice are marked.
Weak rotundity in Banach spaces
Authors: Yorke A. C.
Published: April 2009

Weak rotundity is defined. One version characterizes the duals of very smooth spaces, another characterizes the duals of extremely smooth spaces. Weak rotundity methods are used to investigate the differentiability of the norm in E**, and to obtain information about quotient spaces, when E** is smooth.
Analysis of the effect of certain forcings on the nonoscillatory solutions of even order equations
Authors: Kartsatos Athanassios G.
Published: April 2009

Properties of solutions of, are studied in the causeuH(t, u)>0 foru≠0. It is shown that two inequalities may always be associated with (I) in such a way that if one of these inequalities has a small positive solution and the other inequality has a small negative solution, then (I) is oscillatory. Further asymptotic properties of (I) are studied under assumptions involving intermediate antiderivativesP(i)(t), withP(n)=Q. Several results of this type ensure the non-existence of positive solutions of (I).
On majorizing and cone-absolutely summing mappings
Authors: Wong Yau-Chuen
Published: April 2009

The notions of majorizing mappings and cone-absolutely summing mappings are studied in the locally convex Riesz space setting. It is shown that a locally convex Riesz space Y is an M-space in the sense of Jameson (1970) if and only if, for any locally convex space E, every continuous linear map from E into Y is majorizing. Another purpose of this note is to study the lattice properties of the vector space ℒl(X, Y) of cone-absolutely summing mappings from one locally convex Riesz space into another Y. It is shown that if Y is both locally and boundedly order complete, then ℒl(X, Y) is an l-ideal in Lb(X, Y). This improves a result of Krengel.
Groups with large conjugacy classes
Authors: Balogun Bola O.
Published: April 2009

A finite group is called repetition-free if its conjugacy classes have distinct sizes. It is known that a supersolvable repetition-free group is necessarily isomorphie to Sym(3). the symmetric group on three symbols. Thus the question arises as to whether Sym (3) is the only repetition-free group. In this paper it is proved that if mk denotes the minimum of the orders of the centralizers of elements of a repetition-free group G and mk ≦ 4 then G is isomorphie to Sym (3).
Simultaneous Diophantine approximation
Authors: Mack J. M.
Published: April 2009

Using a method suggested by E. S. Barnes, it is shown that the simultaneous inequalities r(p — αr)2 < c, r(q — βr)2 < c have an infinity of integral solutions p, q, r (with r > 0), for arbitrary irrationals α and β, provided that c > 1/2.6394. This improves an earlier result of Davenport, who shows that the same conclusion holds if c > 1/46¼ = 1/2.6043 ….
The Diophantine equationy2= x(x2+ 21Dx+ 112D2)and the conjectures of Birch and Swinnerton-Dyer
Authors: Rajwade A. R.
Published: April 2009

Some of the conjectures of Birch and Swinnerton-Dyer have been verified for curves with complex multiplication by √ — 7. TheL-functionLD(1) of such curves at the points= 1 is written as a finite sum of division values ofp-functions and the integer property ofLD(1) is proved.
Characterization of a family of simple groups by their character table
Authors: Herzog Marcel , Wright David
Published: April 2009

The paper establishes a method for bounding the 2-rank of a simple group with one conjugacy class of involutions, by means of its character table. For many groups of 2-rank ≦ 4, this bound is shown to be exact. The main result is that the simple groups G2(q),(q,6) = 1, are characterized bv their character table.
A note on semigroups in rings
Authors: Ligh Steve
Published: April 2009

Recently J. Cresp and R. P. Sullivan (1975) investigated those rings R with the following properties: (*) every multiplicative subsemigroup of R is a subring. (**) every multiplicative subsemigroup of R containing 0 is a subring. For rings with (*) they obtained the following characterization.
Note on compact closed categories
Authors: Day B. J.
Published: April 2009

Several categorical aspects of localisation to compact closed categories and free compact closed categories are discussed.
Weak and unbounded order convergence in Banach lattices
Authors: Wickstead A. W.
Published: April 2009

A net (xy) in a vector lattice is unbounded order convergent (uo-convergent) to 0 if u ∧ |xv| order converges to 0 for all u ≧ 0. We consider, in a Banach lattice, the relationship between weak and uo-convergence. We characterise those Banach lattices in which weak convergence implies uo-convergence and those in which uo-convergence of a bounded net implies weak convergence. Finally we combine the results to characterise those Banach lattices in which weak and uo-convergence coincide for bounded nets.
Ideals in autometrized algebras
Authors: Swamy K. L. N. , Rao N. P.
Published: April 2009

A notion of a normal autometrized algebra is introduced which generalises the concepts of Boolean geometry. Brouwerian geometry, autometrized lattice ordered groups, semi-Brouwerian geometry, etc. The notions of ideals and congruence relations are introduced in normal autometrized algebras and a one to one correspondence between ideals and congruence relations is established. Some other common properties of the above geometries are also obtained for normal autometrized algebras.
Distribution of unitarily k-free integers
Authors: Suryanarayana D. , Rao R. Sita Rama Chandra
Published: April 2009

Let k be a fixed integer ≧2. A positive integer n is called unitarily k-free, if the multiplicity of each prime divisor of n is not a multiple of k; or equivalently, if n is not divisible unitarily by the kth power of any integer > 1. By a unitary divisor, we mean as usual a divisor d > 0 of n such that (d,(n/d)) = 1. The integer 1 is also considered to be unitarily k-free. These integers were first defined by Cohen (1961; § 1). Let Q*k denote the set of unitarily k-free integers. When k = 2, the set Q*2 coincides with the set Q* of exponentially odd integers (that is, integers in whose canonical representation each exponent is odd) discussed by Cohen himself in an earlier paper (1961; § 1 and § 6). Let x denote a real variable 1 and let Q*k denote the number of unitarily k-free integers ≦ x. Cohen (1961; Theorem 3.2) established by purely elementary methods that , where , the product being extended over all primes p and ζ(k) denotes the Riemann Zeta function. In the same paper Cohen (1961; Theorem 4.2) improved the order estimate of the error term in (1.1) to O(x1/k), by making use of the properties of real Dirichiet series. Later, he (Cohen; 1964) proved the same result by purely elementary methods eliminating the use of Dirichlet series.
Recursive density types and Nerode extensions of arithmetic
Authors: Aczel P.
Published: April 2009

The notion of a recursive density type (R.D.T.) was introduced by Medvedev and developed by Pavlova (1961). More recently the algebra of R.D.T.'s was initiated by Gonshor and Rice (1969). The R.D.T.'s are equivalence classes of sets of integers, similar in many respects to the R.E.T.'s. They may both be thought of as effective analogues of the cardinal numbers. While the equivalence relationfor R.E.T.'s is defined in terms of partial recursive functions, that for R.D.T.'s may be characterized in terms of recursively bounded partial functions (see 4.22a).
Generators of reflexive algebras
Authors: Longstaff W. E.
Published: April 2009

For any collection of closed subspaces of a complex Hilbert space the set of bounded operators that leave invariant all the members of the collection is a weakly-closed algebra. The class of such algebras is precisely the class of reflexive algebras as defined for example in Radjavi and Rosenthal (1969) and contains the class of von Neumann algebras.In this paper we consider the problem of when such algebras are finitely generated as weakly-closed algebras. It is to be hoped that analysis of this problem may shed some light on the famous unsolved problem of whether every von Neumann algebra on a separable Hilbert space is finitely generated. The case where the underlying space is separable and the collection of subspaces is totally ordered is dealt with in Longstaff (1974). In the present paper the result of Longstaff (1974) is generalized to the case of a direct product of countably many totally ordered collections each on a separable space. Also a method of obtaining non-finitely generated reflexive algebras is given.
On p-groups with a cyclic commutator subgroup
Authors: Miech R. J.
Published: April 2009

This paper contains the complete classification of the finite p-groups G where p is an odd prime, G is generated by two elements, and the commutator subgroup of G is cyclic. These groups are a special kind of two-generator metabelian group, a class that has been studied by Szekeres (1965). He determined the defining relations of such groups but, as he noted, a “residual isomorphism problem” remains. The cyclic commutator groups are simple when considered from this first point of view; they have a short, easily derived set of defining relations. However, the isomorphism problem is a bit complicated for the defining relations contain nine parameters and each of these parameters might and can be an invariant of the group.
Some groups of Fibonacci type
Authors: Johnson D. L. , Mawdesley H.
Published: April 2009

The recent resurgence of interest in the groups introduced in Conway (1967), together with their analogues, is recorded in Johnson, Wamsley and Wright(to appear).
Note on operations generating the group operations in nilpotent groups of class 3
Authors: Plonka Ernest
Published: April 2009

Let K be a class of groups and let ω(K) denote the set of all such words w(x, y) that the group operations 1, x-1, xy in every group G ∈ K can be expressed as a superposition of w and the projections e1(x, y) = x, e2(x, y) = y.
Growth sequences of finite groups II
Authors: Wiegold James
Published: April 2009

The aim of this paper is to give solutions of some of the problems raised in Wiegold (1974). The main content is the proof of Theorems A and B following, which are improvements of Theorems 4.5 and 3.4 respectively of Wiegold (1974). All unexplained notation will be as in that paper, which would perhaps best be viewed as a preliminary to this one.
Estimation of Partial derivatives of the average of densities belonging to a family of densities
Authors: Susarla V. , Kumar S.
Published: April 2009

Recently, attention has been drawn to the problem of estimation of a k-variate probability density and its partial derivatives of various orders. Specifically, let X1, …, Xn be i.i.d. k-variate random variables with common density f wrt Lebesgue measure μ on the k-dimensional σ-field Bk. Parzen (1962) in the k = 1 case and Cacoullos (1966) in the k ≧ 1 case gave the asymptotic properties of a class of kernel estimates fn(x), x ∈ Rk, of f(x) based on X1, …, Xn. The asymptotic properties given in the above two papers concern consistency, asymp-totic unbiasedness, bounds for the mean squared error and asymptotic normality of fn. Also in the context of an empirical Bayes two-action problem, Johns and Van Ryzin (1972) introduced kernel estimates for f(x) and the derivative f'(x)for x∈R1 when f is a mixture of univariate exponential densities wrt Lebesgue measure on B1. They also investigated the asymptotic unbiasedness and themean squared error convergence properties of these estimates. Lin (1968) statedsome generalizations of the results of Johns and Van Ryzin, with applicationsto empirical Bayes decision problems.
A note on linear recursive sequences
Authors: Mignotte M.
Published: April 2009

We consider linear recursive sequences of integers not all zero such that , where the aj are rational integers.
Semirings with a completely simple additive semigroup
Authors: Grillet Mireille P.
Published: April 2009

We construct all semirings with a given completely simple additive semiroup ℳ(G, I, ∧, P) by means of an associative and distributive multiplication on G, and associative multiplications on I and ∧ satisfying certain conditions.
Generalized mean value theorems of the differential calculus
Authors: Diaz J. B. , Výborný R.
Published: April 2009

Two generalized mean value theorems, for functions with values in a linear locally convex topological space, are proved, as consequences of two theorems for real valued functions of real variable.
A class of harmonically convergent sets
Authors: Kløve Torleiv
Published: April 2009

Following Craven (1965) we say that a set M of natural numbers is harmonically convergent if converges, and we call μ(M) the harmonic sum of M. (Craven defined these concepts for sequences rather than sets, but we found it convenient to work with sets.) Throughout this paper, lower case italics denote non-negative integers.
Second-order Ehrenfeucht games and the deciability of the second-order theory of an equivalence relation
Authors: Tenney Richard L.
Published: April 2009

In this paper we extend a method of Ehrenfeucht and Fraissé to second-order theories and use this extension to prove the decidability of the second-order theory of an equivalence relation.
Changing the scalar multiplication on a vector lattice
Authors: Conard Paul
Published: April 2009

Throughout this paper only abelian l-groups will be considered and G will denote an abelian l-group. G is large in the l-group H or H is an essential extension of G if G is an l-subgroup of H and for each l-ideal L ≠ 0 of H we have L ∩ G ≠ 0. A ν-hull of G is a minimal vector lattice that contains G and is an essential extension of G. Each G admits a ν-hull (Conrad (1970)).We shall be interested in the following properties of G.
On a subgroup of the group of multiplicative arithmetic functions
Authors: Carroll T. B. , Gioia A. A.
Published: April 2009

An arithmetic function f is said to be multiplicative if f(1) = 1 and f(mn) = f(m)f(n) whenever (m, n) = 1, where (m, n) denotes as usual the greatest common divisor of m and n. Furthermore an arithmetic function is said to be linear (or completely multiplicative) if f(1) = 1 and f(mn) = f(m)f(n) for all positive integers m and n.The Dirichlet convolution of two arithmetic functions f and g is defined by for all n∈Z+. Recall that the set of all multiplicative functions, denoted by M, with this operation is an abelian group.
The Moore-Penrose inverse of a sum of matrices
Authors: Hung Ching-Hsiang , Markham Thomas L.
Published: April 2009

Suppose U and V are to m × n matrices over the complex field. We obtain a representation for the Moore–Penrose inverse of the sum U + V. A well-known result of Cline is then derived as a special case of a corollary of this representation.
A note on Karamata's generalised regular variation
Authors: Maller R. A.
Published: April 2009

In this note, a one sided aspect of regular variation is considered, and some different results which can be obtained by bounding the ratio f(xλ)/f(x) above or below are given.
Restricted diophantine approximation
Authors: Worley R. T.
Published: April 2009

The problem considered is that of approximating irrationals α by rationals p/q where p and q avoid certain congruence classes mod 2k for certain integers k. Results are obtained which give close bounds on a number c such that |α - p/q| < c/q2 has infinitely many solutions where p and q can be expressed as the sum of three squares.
Proper colourings of K15
Authors: Heinrich Katherine
Published: April 2009

We denote the complete graph on n vertices by Kn. A proper k–colouring of Kn is a way of assigning colours from a set of k colours to the edges of Kn in such a way that no monochromatic triangles are formed. It is known that there are precisely two proper 3-colourings of K16 each of which has exactly one proper 3-colouring of K15 embedded in it. We show that these two are the only proper 3-colourings of K15.
Generalizations of decomposition theorems known over perfect rings
Authors: Mohamed Saad , Singh Surjeet
Published: April 2009

In this paper we introduce and study the notion of dual continuous (d–continuous) modules. A decomposition theorem for a d–continuous module is proved; this generalizes all known decomposition theorems for quasi-projective modules. Besides we study the structure of d–continuous modules over some special types of rings.
Second order elliptic boundary value problems in spaces with homogeneous norms
Authors: Pryde A. J.
Published: April 2009

We consider the interior and Dirichiet problems and problems with first order boundary conditions, for a second order homogeneous elliptic partial differential operator with constant coefficients. Under natural conditions on the operators, these problems give rise to isomorphisms between the appropriate spaces with homogeneous norms. From there we obtain a priori estimates and regularity results for boundary value problems in Sobolev spaces.
Growth sequences of finite groups IV
Authors: Wiegold James
Published: April 2009

The main result is that d(Ssm) = n+2 for every finite non-abelian two-generator simple group S of order s and every integer n > 0. This is applied to give a very close estimate on d(Gn) for any finite group G whose simple images are two-generator. The article is based on the author's previous papers with similar titles.
Separating conjugates in amalgamated free products and HNN extensions
Authors: Dyer Joan L.
Published: April 2009

A group G is termed conjugacy separable (c.s.) if any pair of distinct conjugacy classes may be mapped to distinct conjugacy classes in some finite epimorph of G. The free product of A and B with cyclic amalgamated subgroup H is shown to be c.s. if A and B are both free, or are both finitely generated nilpotent groups. Further, one-relator groups with nontrivial center and HNN extensions with c.s. base group and finite associated subgroups are also c.s.
Near-rings of polynomials and polynomial functions
Authors: Pilz Günter , so Yong-Sian
Published: April 2009

In this paper we investigate near-rings of polynomials and polynomial functions. After some results which belong to universal algebra we turn our attention to the familiar case of polynomials and polynomial functions over a commutative ring with identity. We study the relation between ring- and near-ring homomorphisms, and the behaviour of polynomial near-rings when the ring splits into a direct sum. A discussion of the structure of these polynomial near-rings (radical, semisimplicity) finishes this paper. These investigations are motivated by Clay and Doi (1973).
Characterizations of functionally compact spaces
Authors: Herrington L. L.
Published: April 2009

This paper gives characterizations of functionally compact spaces in terms of filterbases and nets. Also, a topological property that is weaker than countable compactness but stronger than first countable minimality is investigated.
Extensions of orthomorphisms
Authors: Wickstead A. W.
Published: April 2009

We consider, on an Archimedean Riesz space, the spaces of all linear operators lying between two multiples of the identity (for the order), those leaving all ideals invariant and the order bounded orthomorphisms. We find, if E is uniformly complete, necessary and sufficient conditions for all such operators defined on sublattices of E to extend to the whole of E. Examples are given to show the role of uniform completeness. For the space of all orthomorphisms we give a sufficient condition on E for such an extension to exist.
Uniform spaces, spanier quasitopologies, and a duality for locally convex algebras
Authors: Dubuc Eduardo J. , Porta Horacio
Published: April 2009

Gelfand-type duality results can be obtained for locally convex algebras using a quasitopological structure on the spectrum of an algebra (as opposed to the topologies traditionally considered). In this way, the duality between (commutative, with identity) C*-algebras and compact spaces can be extended to pro-C*-algebras and separated quasitopologies. The extension is provided by a functional representation of an algebra A as the algebra of all continuous numerical functions on a quasitopological space. The first half of the paper deals with uniform spaces and quasitopologies, and has independent interest.
On characters in the principal 2-block
Authors: Berger Thomas R. , Herzog Marcel
Published: April 2009

Let k be a complex number and let u be an element of a finite group G. Suppose that u does not belong to O(G), the maximal normal subgroup of G of odd order. It is shown that G satisfies X(1) – X(u) = k for every complex nonprincipal irreducible character X in the principal 2-block of G if and only if G/O(G) is isomorphic either to C2, a cyclic group of order 2, or to PSL (2, 2n), n ≧ 2.
Isomorphisms between skew polynomial rings
Authors: Rimmer M.
Published: April 2009

Let R be any ring and α any automorphism of R. We determine here all the automorphisms of the skew polynomial ring R[x, α] which fix R elementwise. We then deal with isomorphisms between different skew polynomial rings whose underlying rings are isomorphic.
Ideals in simple rings
Authors: Davenport W. Harold
Published: April 2009

In this article, we define the concept of a Malcev ideal in an alternative ring in a manner analogous to Lie ideals in associative rings. By using a result of Kleinfield's we show that a nonassociative alternative ring of characteristic not 2 or 3 is a ring sum of Malcev ideals Z and [R, R] where Z is the center of R and [R, R] is a simple non-Lie Malcev ideal of R. If R is a Cayley algebra over a field F of characteristic 3 then [R, R] is a simple 7 dimensional Lie algebra. A similar result is obtained if R is a simple associative ring.
Projective limit of infinite Radon measures
Authors: Okada Susumu , Okazaki Yoshiaki
Published: April 2009

We show that for any self-consistent sequentially maximal system {μα} of infinite (perhaps non-σ-finite) Radon measures, the projective limit of {μα} exists.
Higher order derivatives in topological linear spaces
Authors: Lloyd J. W.
Published: April 2009

The higher order chain rule for Fréchet and Hadamard differentiable mappings on topological linear spaces is proved and various formulae for (g°f)(n) (x) are given. Leibniz' theorem (in a very general form) is also proved.
Sharply two-transitive families of permutations on an immune set
Authors: Dekker J. C. E.
Published: April 2009

It is known that there is a finite affine (or projective) plane of order n if and only if there is a sharply two-transitive set of permutations of degree n. This paper deals with a generalization of this theorem, in which finite sets are replaced by isolated sets, cardinalities by isols and certain effectiveness conditions are imposed on the two systems involved which are trivially satisfied in the finite case.

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 02F40, secondary 05B25.
Lie and Jordan structure in operator algebras
Authors: Robinson Derek W. , Størmer Erling
Published: April 2009

Let υ be a C*-algebra, α a *-anti-automorphism of order 2, and υα(±1) = {A; A ∈ υ, α(A) = ± A} the spectral subspaces of α. It follows that υα(+ 1) is a Jordan algebra and υα(− 1) is a Lie algebra. We begin the classification of pairs of Jordan and Lie algebras which can occur in this manner by examining υ = ℒ(ℋ), the algebra of bounded operators on a Hilbert space ℋ.
Congruences contained in an equivalence on a semigroup
Authors: Jones P. R.
Published: April 2009

The main theorem of this paper shows that the lattice of congruences contained is some equivalence π on a semigroup S can be decomposed into a subdirect product of sublattices of the congruence lattices on the ‘prinipal π-facotrsρ of S—the semigroups formed by adjoining zeroes to the π-classes—whenever these are well-defined. The theorem is then applied to various equavalences and classes of semigroups to give some new results and alternative proofs of known ones.
Mean Value theorems for multiplicative functions bounded in mean α-power, α >1
Authors: Elliott P. D. T. A.
Published: April 2009

On analogy with functions if Lebesuge class Lα on the real line the author considers those multiplicative arthmetic functions which are bounded in mean α>1. Necessary and sufficient conditions are obtained in order that they should have a mean-value, zero or non-zero. An application is made to Ramanujan's τ-function.
Uniform boundedness principles for regular Borel vector measures
Authors: Kupka Joseph
Published: April 2009

The setting is a compact Hausfroff space ω. The notion of a Walls class of subsets of Ω is defined via strange axioms—axioms whose justification rests with examples such as the collection of regular open sets or the range of a strong lifting. Avarient of Rosenthal' famous lwmma which applies directly to Banach space-valued measures is esablished, and it is used to obtain, in elementary fashion, the following two uniform boundedness principles: (1)The Nikodym Boundedness Theorem. If K is a family of regular Borel vector measures on Ω which is point-wise bounded on every set of a fixed Wells class, then K is uniformly bounded. (2)The Nikodym Covergence Theorem. If {μn} is a sequence of regular Borel vector measures on Ω which is converguent on every set of a fixed Wells class, then the μn are uniformly countably additive, the sequence {μn} is convergent on every Borel subset of Ω and the pointwise limit constitutes a regular Borel measure.
On the continuous linear image of a Banach space
Authors: Cross R. W.
Published: April 2009

A subspace of a Banach space is called anoperator rangeif it is the continuous linear image of a Banach space. Operator ranges and operator ideals with fixed range space are investigated. Properties of strictly singular, strictly cosingular, weakly sequentially precompact, and other classes of operators are derived. Perturbation theory and closed semi-Fredholm operators are discussed in the final section.
On closure and factorization properties of subexponential and related distributions
Authors: Embrechts Paul , Goldie Charles M.
Published: April 2009

For a distribution function F on [0, ∞] we say F ∈ if {1 – F(2)(x)}/{1 – F(x)}→2 as x→∞, and F∈, if for some fixed γ > 0, and for each real , limx→∞ {1 – F(x + y)}/{1 – F(x)} ═ e– n. Sufficient conditions are given for the statement F ∈ F * G ∈ and when both F and G are in y it is proved that F*G∈pF + 1(1 – p) G ∈ for some (all) p ∈(0,1). The related classes ℒt are proved closed under convolutions, which implies the closure of the class of positive random variables with regularly varying tails under multiplication (of random variables). An example is given that shows to be a proper subclass of ℒ 0.
Coverings of products of linear topological spaces
Authors: Todd Aaron R.
Published: April 2009

An extension of the Banach-Mackey theorem is used to prove a theorem about countable families of closed balanced convex sets that cover a product of linear topological spaces. This theorem clarifies proofs that certain Baire-type properties, including the unordered Baire-like property, are preserved under products. A modification of the theorem is used to show that a property involving the bounded-absorbing sequences of DeWilde and Houet is also productive. Finally, a question is posed about balanced absorbing sets relating to products of linear Baire spaces.

1980 Mathematics subject classification (Amer. Math. Soc.): 46 A 99.
Norm and order properties of Banach lattices
Authors: Bedingfield Susan E. , Wirth Andrew
Published: April 2009

The interrelationships between norm convergence and two forms of convergence defined in terms of order, namely order and relative uniform convergence are considered. The implications between conditions such as uniform convexity, uniform strictness, uniform monotonicity and others are proved. In particular it is shown that a σ-order continuous, σ-order complete Banach lattice is order continuous.

1980 Mathematics subject classification (Amer. Math. Soc.): 46 A 40.
Subexponential distribution functions
Authors: Pitman E. J. G.
Published: April 2009

A distribution function (F on [0,∞) belongs to the subexponential class if and only if 1−F(2) (x) ~ 2(1−F(x)), as x→ ∞. For an important class of distribution functions, a simple, necessary and sufficient condition for membership of is given. A comparison theorem for membership of and also some closure properties of are obtained.

1980 Mathematics subject classification (Amer. Math. Soe.): primary 60 E 05; secondary 60 J 80.