bluuebunny/crossref_metadata_2025 huggingface dataset:
Some topological properties of vector measures and their integral maps
Authors: Anantharaman R. , Garg K. M.
Published: April 2009

In the present paper we prove that every finite dimensional non-atomic measure ν is open and monotone (viz. ν–1 preserves connected sets) relative to the usual Fréchet-Nikodým topology on its domain and the relative topology on its range. An arbitrary finite dimensional measure is found on the other hand to be biquotient.

Given a vector measure ν, we further investigate the properties of its integral map Tν: φ → ∫ φdν defined on the set of functions φ in L1(|ν|) for which φ(s) ∈ [0,1] |ν|-almost everywhere. When ν is finite dimensional, Tν is found to be always open. In general, when Tν is open, the set of extreme points of the closed convex hull of the range of ν is proved to be closed, and when ν and Tν are both open, the range of ν in itself is closed.
Non-tall compact groups admit infinite Sidon sets
Authors: Hutchinson M. F.
Published: April 2009

Riesz polynomials are employed to give a sufficient condition for a non-abelian compact group G to have an infinite uniformly approximable Sidon set. This condition is satisfied if G admits infinitely many pairwise inequivalent continuous irreducible unitary representations of the same degree. Consequently a compact Lie group admits an infinite Sidon set if and only if it is not semi-simple.
Groups which are an infinite cyclic extension of a unique base group
Authors: Brunner A. M. , McCool James , Pietrowski Alfred
Published: April 2009

Let G be a group which has exactly one normal subgroup N with G/N infinite cyclic; clearly such a group is an HNN group with base N and stable letter t, where t induces an automorphism θ, of N under conjugation. We call such a group G a unique base group with automorphism θ, and base N.
Some new Orthogonal diagonal latin squares
Authors: Wallis W. D. , Zhu L.
Published: April 2009

A recursive construction for orthogonal diagonal latin squares, using group divisible designs, is presented. In consequence the numbers of orders for which the existence of such squares is in question is reduced to 72.
Invariant measures for piecewise linear fractional maps
Authors: Schweiger F.
Published: April 2009

Let T: [0,1] → [0,1] be a map which is given piecewise as a linear fractional map such that T0 = T] = 0 and T'0 < 1. Then T is ergodic and admits an invariant measure which can be calculated explicitly.
Generalized Semi-Fredholm transformations
Authors: Tacon D. G.
Published: April 2009

The class ϕ+(X, Y) of semi-Fredholm transformations consists of those transformationsT:X→Yfor which α(T) = dim kerT< ∞ and for whichT(X) is closed. It forms an open subset of B (X, Y) closed under perturbation by compact transformations and is a particularly important class of transformation sinceTis Fredholm if and only ifT∈ ϕ+(X, Y) andT′ ∈ ϕ+(Y′.X′). The realization that elements of ϕ+(X, Y) have very simple nonstandard characterizations lead the author to consider the possibility of finding an analogous open class of transformation which is closed under perturbation by weakly compact transformations. Consequently this paper investigates two related classes which contain ϕ+(X, Y). The first such class coincides with the class of Tauberian transformations whilst the second consists of those transformations which have Tauberian extensions on the nonstandard hulls. The Tauberian transformations are closed under perturbation by weakly compact transformations but in general are not open. The “super” Tauberian transformations are closed under perturbation by super weakly compact transformations and in fact form an open subset of B(X, Y).
Compactness and connectedness as composable properties
Authors: Muenzenberger T. B. , Smithson R. E.
Published: April 2009

In [5] Magill showed that compactness is a composable property of Hausdorff spaces. (That is, if α,β are compact subsets of X × X, then α ○ β is also compact when X is T2.) Also Magill gave an example to show that the composition of connected relations need not be connected. Subsequently, he characterized Hausdorff k-spaces in terms of the semigroup of compact relations in X.
Finite near-rings with trivial annihilators
Authors: Szeto George
Published: April 2009

In [3] and [4], the near-rings R with no zero divisors are studied. In particular, a near-ring R is a near-field if it has a non-zero right distributive element ([4], Theorem 1.2.). Also, (R, +) is a nilpotent group if not all non-zero elements of R are left identities of R ([3], Theorem 2). The purpose of the present paper is to extend the above results to a class of near-rings with zero divisors; that is, the set of annihilators of an element x in R, T(x) = {g/xg = 0} is either {0} or R. The examples of such near-rings are those R with (R, +) simple groups and those R with no zero divisors as given in [1], [2], [3] and [4]. For this r, we can easily see that R = A∪S where A = {x/T(x) = R} and S = {x/T(x) = {0}}. Then the second part of this paper will give a structural theorem on the semi-group (S, · ), and more properties on R can be derived.
Amenability and invariant subspaces
Authors: Lau Anthony To-Ming
Published: April 2009

Let E be a topological vector space (over the real or complex field). A well-known geometric form of the Hahn-Banach theorem asserts that if U is an open convex subset of E and M is a subspace of E which does not meet U, then there exists a closed hyperplane H containing M and not meeting U. In this paper we prove, among other things, that if S is a left amenable semigroup (which is the case, for example, when S is abelian or when S is a solvable group, see [3, p.11]), then for any right linear action of S on E, if U is an invariant open convex subset of E containing an invariant element and M is an invariant subspace not meeting U, then there exists a closed invariant hyperplane H of E containing M and not meeting U. Furthermore, this geometric property characterizes the class of left amenable semigroups.
On the almost periodic solution of an abstract diffferential equation
Authors: Rao Aribindi Satyanarayan
Published: April 2009

Abstract: Under certain suitable conditions, the Stepanov-bounded solution of an abstract differential equation corresponding to a Stepanov almost periodic function is strongly (weakly) almost periodic.
Boundedness and completeness in locally convex spaces and algerbras
Authors: Joseph Gerard A.
Published: April 2009

The set of bounded elements of a unital l.m.c. algebra is characterised as the union of certain naturally defined normed subalgebras, and an analogous characterisation is given for algebras of quotient-bounded operators on a locally convex space. Pseudocomplete l.m.c. algebras are characterised in terms of the completeness of these subalgebras, and the equivalence of this condition with the pseudocompleteness of the quotient-bounded operator algebras established. The scalar multiples of the identity in a unital l.m.c. algebra are characterised in terms of certain boundedness conditions.
A further characterization of a projective special linear group
Authors: Adnan Saad
Published: April 2009

In this paper we present a characterization of PSL(2,7) by a condition different from that given in our previous paper.
Concise survey of mathematical logic
Authors: Stillwell John
Published: April 2009

This paper contains proofs of the compactness, completeness and Löwenheim-Skolem theorems for predicate logic, together with their application to nonstandard numbers; proofs of undecidability in predicate logic and number theory, and the Gödel incompleteness theorem.
On the concept of length in the sense of Lausch-Nöbauer and its generalizations
Authors: Eigenthaler Günther , Wiesenbauer Johann
Published: April 2009

In this paper the concept of length as defined for groups by Lausch–Nöbauer in their book Algebra of Polynomials (North Holland, Amsterdam, 1973) is generalized in several ways. It turns out that the main results of Lausch-Nöbauer concerning it remain valid for this generalization.
An infinite family of Williamson matrices
Authors: Spence Edward
Published: April 2009

In this paper the following result is proved. Suppose there exists a C-matrix of order n + 1. Then if n≡1 (mod 4) there exists a Hadamard matrix of order 2nr(n + 1), while if n≡3 (mod 4) there exists a Hadamard matrix of order nr(n + 1) for all r ≧0. If n≡1 (mod 4) is a prime power, the method is adapted to prove the existence of a Hadamard matrix of the Williamson type, of order 2nr(n + 1), for all r ≧0.
On the enumeration of homeomorphism classes of finite topologies
Authors: Krishnamurthy V.
Published: April 2009

An algorithm called UNLABEL is devised to uniquely label an unlabelled transitive digraph. This is used to construct a one-one correspondence between homeomorphism classes of finite nondiscrete To-topologies and certain generalised Young tableaux of shape-type α. For sets of cardinality 2, 3, 4 and 5 these classes are enumerated and classified in several ways. The notion of a generalised descriptor graph is then introduced to enumerate the homeomorphism classes of all topologies on these sets.
Subgroups with centre in HNN groups
Authors: Karrass A. , Solitar D.
Published: April 2009

A subgroup with non-trivial centre in a one-relator group is shown to be a treed HNN group (graph product) with infinite cyclic vertices. Moreover, subgroups with non-trivial centre in HNN groups are also examined.
Starter-adder methods in the construction of Howell designs
Authors: Anderson B. A. , Gross K. B.
Published: April 2009

The powerful starter-adder theorems for constructing Howell Designs are improved and consequently many types of Howell Designs that previously could only be constructed by multiplicative techniques are shown amenable to a modified starter-adder method. The existence question for Howell Designs of many new types H(s, 2n) is settled affirmatively. For prime powers pn, p ≧ 7, we reduce the entire existence question for designs of type H*(pn, 2r), pn + 1 ≦ 2r ≦ 2pn to the corresponding question for designs of type H*(p, 2m), p + 1 ≦ 2m≦2p. If these designs exist, s has no prime divisors ≤ 7 and t odd is “close” to 1, a design H * (s, s + t) is shown to exist.
Left invariant measure in topological semigroups
Authors: Chew James
Published: April 2009

We consider the problem of the existence of a left invariant measure in a class of topological semigroups. Several authors have considered this and related problems on semigroups satisfying similar conditions, but the invariance they considered is right invariance. This paper is different in that it deals with left invariance.
A multifunction generalization of Gale's Ascoli theorem
Authors: Fox Geoffrey , Morales Pedro
Published: April 2009

Our purpose is to improve the Gale-type multifunction Ascoli theorem of Mancuso (1971; page 470). This latter supposes the range space to be normal and Hausdorff, and therefore does not contain Gale's theorem (1950; page 304). To obtain a multifunction theorem containing Gale's theorem (also Mancuso's theorem), we return to Gale's essential hypotheses. Thus, we assume the regularity of the range space in the sufficiency direction, and, in the necessity direction, weassume the domain to be a k-space and the range to be a regular Hausdorff space. We dispense with the “point-like” condition imposed by Mancuso. Unexplained terminology and notation is that of Mancusopos;s paper.
Semigroups in rings
Authors: Cresp J. , Sullivan R. P.
Published: April 2009

A subsetSof a ringRis a left semigroup ideal ofRifRS⊈ R, and a left ring ideal ofRif in additionSis a subring ofR. Gluskin (1960) investigated those rings with 1 which possess the property: (λ) every left semigroup ideal is a left ring ideal.
Notes on differential calculus in topological linear spaces, II
Authors: Yamamuro S.
Published: April 2009

Throughout this note, let E and F be locally convex Hausdorff spaces over the real number field R. We denote real numbers by Greek letters. The sets of all continuous semi-norms on E and F will be denoted by P(E) and P(F) respectively, and A will always stand for an open subset of E.
Groups with an automorphism cubing many elements
Authors: MacHale Desmond
Published: April 2009

Let G be a group and αn the mapping which takes every element of G to its nth power, where n is an integer. It is well known that if αn is an automorphism then G is Abelian in the cases n = -1,2, and 3. For any other integer n(≠ 0) there exists a non-Abelian group which admits αn as the identity automorphism. Indeed Miller (1929) has shown that if n ≠ 0, ±1, 2, 3 then there exist non-Abelian groups which admit αn as a non-trivial automorphism.
On tensor product graphs
Authors: Sampathkumar E.
Published: April 2009

The tensor product G ⊕ H of graphs G and H is the graph with point set V(G) × V(H) where (υ1, ν1) adj (υ2, ν2) if, and only if, u1 adj υ2 and ν1 adj ν2. We obtain a characterization of graphs of the form G ⊕ H where G or H is K2.
Generalized discrete l-groups
Authors: Mott Joe L.
Published: April 2009

Let G be an abelian lattice ordered group (an l-group). If G is, in fact, totally ordered, we say that G is an 0–group. A subgroup and a sublattice of G is an l-subgroup. A subgroup C of G is called convex if 0 ≦ g ≦ c ∈ C and g ∈ G imply g ∈ C, C is an l-ideal if C is a convex l-subgroup of G. If C is an l-ideal of G, then G/C is also an l-group under the canonical ordering inherited from G. If, in fact, G/C is an 0–group, then C is said to be a prime subgroup of G.
A note on prime radicals of certain group rings
Authors: Tan Keng-Teh
Published: April 2009

Let R be a ring (with identity) and P(R) denote its prime radical. R is called semi-prime when P(R) = (0). If G is a group, the group ring of G over R will be denoted by RG.
Representations of ordered groups with compatible tight Riesz orders
Authors: Reilly N. R.
Published: April 2009

A tight Riesz group G is a partially ordered group G that satisfies a strengthened form of the Riesz interpolation property. The term “tight” was introduced by Miller in (1970) and the tight interpolation property has been considered by Fuchs (1965), Miller (1973), (to appear), (preprint), Loy and Miller (1972) and Wirth (1973). If G is free of elements called pseudozeros then G is a non-discrete Hausdorff topological group with respect to the open interval topology U. Moreover the closure P of the cone P of the given order is the cone of an associated order on G. This allows an interesting interplay between the associated order, the tight Riesz order and the topology U. Loy and Miller found of particular interest the case in which the associated partial order is a lattice order. This situation was considered in reverse by Reilly (1973) and Wirth (1973), who investigated the circumstances under which a lattice ordered group, and indeed a partially ordered group, permits the existence of a tight Riesz order for which the initial order is the associated order. These tight Riesz orders were then called compatible tight Riesz orders. In Section one we relate these ideas to the topologies denned on partially ordered groups by means of topological identities, as described by Banaschewski (1957), and show that the topologies obtained from topological identities are precisely the open interval topologies from compatible tight Riesz orders.
General rings of functions
Authors: Sultan A.
Published: April 2009

Several authors have studied various types of rings of continuous functions on Tychonoff spaces and have used them to study various types of compactifications (See for example Hager (1969), Isbell (1958), Mrowka (1973), Steiner and Steiner (1970)). However many important results and properties pertaining the Stone-Čech compactification and the Hewitt realcompactification can be extended to a more general setting by considering appropriate lattices of sets, generalizing that of the lattice of zero sets in a Tychonoff space. This program was first considered by Wallman (1938) and Alexandroff (1940) and has more recently appeared in Alo and Shapiro (1970), Banachewski (1962), Brooks (1967), Frolik (1972), Sultan (to appear) and others.
Closed subalgebras of homogeneous Banach algebras
Authors: Tseng Ching-Nan , Wang Hawi-Chiuan
Published: April 2009

Rudin's synthesis method for investigating closed subalgebras of L1(G), where G is an infinite compact abelian group, is extended to the study of closed subalgebras in homogeneous Banach algebras and Segal algebras. Necessary and sufficient conditions are given for the synthesis to hold in certain classes of homogeneous Banach algebras and it is proved that in the Ap(G) algebras the synthesis holds for 1 ≦ p 2 but fails for Ap(T), 2 < p < ∞.
Embedding the affine complement of three intersecting lines in a finite projective plane
Authors: Mullin R. C. , Singhi N. M. , Vanstone S. A.
Published: April 2009

An (r, 1)–design is a pair (V, F) where V is a v–set and F is a family of non-null subsets of V (b in number) which satisfy the following. (1) Every pair of distinct members of V is contained in precisely one member of F. (2) Every member of V occurs in precisely r members of F. A pseudo parallel complement PPC(n,α) is an (n + 1, 1)–design with v = n2 – αn and b ≦ n2 + n − α in which there are at least n – α a blocks of size n. A pseudo intersecting complement PIC(n, α) is an (n + 1, 1)–design with v = n2 − αn + α − 1 and b ≦ n2 + n – α in which there are at least n − α + 1 blocks of size n − 1. It has previously been shown that for α ≧ 4, every PIC(n, α) can be embedded in a PPC(n, α − 1) and that for n > (α4 − 2α3 + 2α2 + α − 2)/2, every PPC(n, α) can be embedded in a finite projective plane of order n. In this paper we investigate the case of α = 3 and show that any PIC(n, 3) is embeddable in a PPC(n,2) provided n ≥ 14.
Semilattices with a transitive automorphism group
Authors: Pastijn F.
Published: April 2009

If L is any semilattice, let TL denote the Munn semigroup of L, and Aut (L) the automorphism group of L.

We show that every semilattice L can be isomorphically embedded as a convex subsemilattice in a semilattice L' which has a transitive automorphism group in such a way that (i) every partial isomorphism α of L can be extended to an automorphism of L', (ii) every partial isomorphism: α: eL → fL of L can be extended to a partial isomorphism αL′: eL′ → fL′ of L′ such that TL → TL′, α → αL′ embeds TL' isomorphically in TL′, (iii) every automorphism γ of L can be extended to an automorphism γL′ of L′ such that Aut (L) → Aut (L′), γ → γL embeds Aut (L) isomorphically in Aut (L′).
A continued fraction of Ramanujan
Authors: Hirschhorn M. D.
Published: April 2009

In a manuscript discovered in 1976 by George E. Andrews, Ramanujan states a formula for a certain continued fraction, without proof. In this paper we establish formulae for the convergents to the continued fraction, from which Ramanujan's result is easily deduced.
An inequality from applied probability
Authors: Henderson W.
Published: April 2009

J. F. C. Kingman (1967) proved that if {φn}, n = 1, 2, …, N is any set of Radon-Nikodym derivatives of λn w.r.t. μn, when λn, μn are the restrictions of λ, μ respectively to a sub σ-algebra Gn of G then where bn ≧ 0 ∀n and .
Extensions of filters and fields of sets (I)
Authors: Grzegorek E. , Weglorz B.
Published: April 2009

We investigate the problem of the existence of filters with some properties. This leads to a solution of two problems of Ulam concerning σ-fields on the real line.
Linear operators generated by Sonnenschein matrices
Authors: Wood B.
Published: April 2009

An approximation method based on a certain Sonnenschein matrix is studied. Results are obtained for approximation in an interval and in the complex plane. A connection between convergence of the approximation process and regularity of the matrix is also discussed.
Some infinite classes of Hadamard matrices
Authors: Seberry Jennifer
Published: April 2009

A recursive method of A. C. Mukhopadhay is used to obtain several new infinite classes of Hadamard matrices. Unfortunately none of these constructions give previously unknown Hadamard matrices of order <40,000.
Monodromy in local groups
Authors: Atkin C. J.
Published: April 2009

A monodromy theorem for homomorphisms of local groups into groups is proved. It follows that under suitable conditions the universal group of the local group depends only on the germ of the local group (up to natural isomorphism).

1980 Mathematics subject classification (Amer. Math. Soc.): 22 E 05.
Local and global extrema for functions of several variables
Authors: Calvert Bruce , Vamanamurthy M. K.
Published: April 2009

Let p: R2 → R be a polynomial with a local minimum at its only critical point. This must give a global minimum if the degree of p is < 5, but not necessarily if the degree is ≥ 5. It is an open question what the result is for cubics and quartics in more variables, except cubics in three variables. Other sufficient conditions for a global minimum of a general function are given.

1980 Mathematics subject classification (Amer. Math. Soc.): 26 B 99, 26 C 99.
Thue's equation over function fields
Authors: Schmidt Wolfgang M.
Published: April 2009

Suppose we are given a “Thue equation” f(x, y) = 1, where f is a binary form with coefficients in a function field K of characteristic zero. A typical result is that if f is of degree at least 5 and has no multiple factors, then every solution x = (x, y) of the equation with components in K has H(x)≤90H(f) + 250g. Here g is the genus of K and H(x), H(f) are suitably defined heights. No assumption is made that x be “integral” in some sense. As an application, bounds are derived for “integral” solutions of hyperelliptic equations over K.
Transcendence theory and its applications
Authors: Baker A.
Published: April 2009

This is the text of an invited address given at the Summer Research Institute of the Australian National University in January 1978. It provides a survey of the subject matter of the title.
Simultaneous approximation of numbers connected with the exponential function
Authors: Waldschmidt Michel
Published: April 2009

We give several results concerning the simultaneous approximation of certain complex numbers. For instance, we give lower bounds for |a–ξo|+ |ea– ξ1|, whereais any non-zero complex number, and ξ are two algebraic numbers. We also improve the estimate of the so-called Franklin Schneider theorem concerning |b– ξ | + |a– ξ | + |ab– ξ. We deduce these results from an estimate for linear forms in logarithms.
Rational approximations toe
Authors: Davis C. S.
Published: April 2009

The greatest lower bound (in fact, ½) is found of constants k such thatfor an infinity of rationalsp/q.
Weak compactness of Fréchet-derivatives: application to composition operators
Authors: Dierolf Peter , Voigt Jürgen
Published: April 2009

We prove a result on compactness properties of Fréchet-derivatives which implies that the Fréchet-derivative of a weakly compact map between Banach spaces is weakly compact. This result is applied to characterize certain weakly compact composition operators on Sobolev spaces which have application in the theory of nonlinear integral equations and in the calculus of variations.
An extremal problem in graph theory II
Authors: Abbott H. L. , Katchalski M. , Liu A. C.
Published: April 2009

We contine our study of the following combinatorial problem: What is the largest integer N = N (t, m, p) for which there exists a set of N people satisfying the following conditions: (a) each person speaks t languages, (b) among any m people there are two who speak a common language and (c) at most p speak a common language. We obtain bounds for N(t, m, p) and evaluate N(3, m, p) for all m and infintely many values of p.
Adams completion for cohomology theories arising from Kan extensions
Authors: Nanda Sribatsa
Published: April 2009

It is shown that a cohomology theory over an admissible category, which is obtained from an additive cohomology theory over a smaller admissible category, through the Kan extension process, always admits global Adams completion.
Positive values of inhomogeneous 5-ary quadratic forms of type (3, 2)
Authors: Hans-Gill R. J. , Raka Madhu
Published: April 2009

Let Q(x, y, z, t, u) be a real indefinite 5-ary quadratic form of type (3,2) and determinant D(> 0). Then given any real numbers x0, y0, z0, t0, u0 there exist integers x, y, z, t, u such that 0 < Q(x+x0,y+y0,z+z0,t+t0,u+u0)≦(16D)1/5. All the critical forms are also determined.
Maximal subfields of algebraically closed fields
Authors: Guralnick Robert M. , Miller Michael D.
Published: April 2009

Let K be an algebraically closed field of characteristic zero, and S a nonempty subset of K such that S Q = Ø and card S < card K, where Q is the field of rational numbers. By Zorn's Lemma, there exist subfields F of K which are maximal with respect to the property of being disjoint from S. This paper examines such subfields and investigates the Galois group Gal K/F along with the lattice of intermediate subfields.
Regular semigroups, fundamental semigroups and groups
Authors: McAlister D. B.
Published: April 2009

In this paper we obtain necessary and sufficient conditions on a regular semigroup in order that it should be an idempotent separating homomorphic image of a full subsemigroup of the direct product of a group and a fundamental or combinatorial regular semigroup. The main tool used is the concept of a prehomomrphism θ:S→Tbetween regular semigroups. This is a mapping such that (ab)θ ≦ aθ bθin the natural partial order onT.
Random Fourier series on compact abelian hypergroups
Authors: Fournier John J. F. , Ross Kenneth A.
Published: April 2009

Random Fourier series are studied for a class of compact abelian hypergroups. The randomizing factors are assumed to be independent and uniformly subgaussian. In the presence of a natural teachnical hypothesis, an entropy condition of Dudley is shown to be sufficient for almost sure continuity. The classical results on almost sure membership in Lp, where p < ∞, are generalized to this setting. As an application, it is shown that a simple condition on the dual object implies that the de Leeuw-Kahane-Katznelson phenomenon occurs. Another application is the analogue of a classical sufficient condition for almost sure continuity. Examples illustrating the general theory are given for the hypergroup of conjugacy classes of SU(2) and for a class of compact countable hypergroups.
The Lindelöf degree of scattered spaces and their products
Authors: Gewand Marlene E.
Published: April 2009

Different methods are used to show that a finite or countable product of Lindelöf scattered spaces is Lindelöf. Also, a technique of Kunen is modified to yield results concerning the Lindelöf degree of the Gδ and Gα-topologies on the countable product of compact scattered spaces.
Maps on D1 and D2 spaces
Authors: Potoczny H. B.
Published: April 2009

A space X is said to be D1 provided each closed set has a countable basis for the open sets containing it. It is said to be D2 provided there is a countable base {Un} such that each closed set has a countable base for the open sets containing it, which is a subfamily of {Un}. In this paper, we give a separation theorem for D1 spaces, and provide a characterization of D1 and D2 spaces in terms of maps.
On an inversion theorem of Möbius
Authors: Loxton J. H. , Sanders J. W.
Published: April 2009

The theme of the paper is a Möbius inversion principle for infinite sums. We deal with the origins and unprincipled use of this idea in the nineteenth century, its rigorous justification under minimal hypotheses and some applications to a problem in numerical integration.
A Commutativity theorem for semiprime rings
Authors: Gupta Vishnu
Published: April 2009

It is shown that if R is a semiprime ring with 1 satisfying the property that, for each x, y ∈ R, there exists a positive integer n depending on x and y such that (xy)k − xkyk is central for k = n,n+1, n+2, then R is commutative, thus generalizing a result of Kaya.
Orthodox semirings and rings
Authors: Zeleznikow John
Published: April 2009

We show that in a regular ring (R, +, ·), with idempotent setE, the following conditions are equivalent: (i)(ii) (R, ·) is orthodox. (iii) (R, ·) is a semilattice of groups. These and other conditions are also considered for regular semigroups, and for semirings (S, +, · ), in which (S, +) is an inverse semigroup. Examples are given to show that they are not equivalent in these cases.
Coextensions of pseudo-Inverse semigroups by rectangular bands
Authors: Meakin John
Published: April 2009

We say that a regulär semigroup S is a coetension of a (regular) semigroup T by rectangular bands if there is a homomorphism ϕ: S → T from S onto T such that, for each e = e2 ∈ S, e(ϕ ϕ-1) is a rectangular band. Regular semigroups which are coextesions of pseudo-inverse semigroups by rectangular bands may be characterized as those regular semigroups S with the property that, for each e = e2 ∈ S, ω(e) = {f = f2 ∈ S: ef = f} and ωl(e) = {f = f2 ∈ S: fe = f} are bands: this paper is concerned with a study of such semigroups.
Orthomorphisms of a commutative W*-algebra
Authors: Dodds P. G.
Published: April 2009

If M is a commutative W*-algebra of operators and if ReM is the Dedekind complete Riesz space of self-adjoint elements of M, then it is shown that the set of densely defined self-adjoint transformations affiliated with ReM is a Dedekind complete, laterally complete Riesz algebra containing ReM as an order dense ideal. The Riesz algebra of densely defined orthomorphisms on ReM is shown to coincide with , and via the vector lattice Randon-Nikodym theorem of Luxemburg and Schep, it is shown that the lateral completion of ReM may be identified with the extended order dual of ReM.
Biordered sets are biordered subsets of idempotents of semigroups
Authors: Easdown David
Published: April 2009

A new arrow notation is used to describe biordered sets. Biordered sets are characterized as biordered subsets of the partial algebras formed by the idempotents of semigroups. Thus it can be shown that in the free semigroup on a biordered set factored out by the equations of the biordered set there is no collapse of idempotents and no new arrows.
Athwart immersions in Euclidean space
Authors: Robertson S. A. , de Carvalho F. J. Craveiro
Published: April 2009

Let f and g denote immersions of the n-manifolds M and N, respectively, in Rn+1. We say that f is athwart to g if f(M) and g(N)m have no tangent hyperplane in common. In this paper necessary conditions for athwartness are obtained.
Subspaces associated with boundary points of the numerical range
Authors: Majumdar S. , Sims Brailey
Published: April 2009

Stampfli and Embry characterized points in the numerical range which are extreme in terms of the linearity of corresponding sets of vectors. Das and Craven generalized this to include the case of unattained boundary points. We give an alternative proof of this result using a technique of Berberian. This approach appears to be more conceptual in that it enables us to deduce the result from that of Stampfli and Embry. We also illustrate how the same technique may be used to generalize other results of Embry.
Extension of Riesz homomorphisms.I
Authors: Buskes G. J. H. M.
Published: April 2009

In this paper we characterize boundedly laterally complete Riesz spaces, boundedly laterally complete Riesz spaces with the lateral boundedness property and Riesz spaces in which every principal ideal is finite dimensional. The characterizations are given in terms of extension properties of certain Riesz homomorphisms.
On certain varieties of groups which are central extensions
Authors: Bryce R. A.
Published: April 2009

Connexions are sought between the subvarieties of a variety U of groups and the subvarieties of the variety of all groups which are central extensions by groups in U, in the case when U has the form . Here , is the variety of abelian groups of exponent dividing r and Bis a variety of soluble groups of finite exponent.
On large cohomological dimension and tautness
Authors: Deo Satya , Muttepawar Subhash , Singh Mohan
Published: April 2009

We prove that for a non-discrete spaceX, the inequality DimL(X) ≥ dimL(X) + 1 always holds if (i)Xis paracompact and each point isGδ, or (ii)Xis a completely paracompact Moritak-space. Consequently, ifXis a non-discrete completely paracompact space in which each point is aGδ-set or it is also a Moritak-space then, the equality DimL(X) = dimL(X) + 1 always holds. We apply this equality to show that for such a spaceXthere exists a pointx ∈ Xand a family ϕ of supports onXsuch that {x} is not ϕ-taut with respect to sheaf cohomology. This generalizes a corresponding known result forRn. We also discuss the usual sum theorems for this large cohomological dimension; the finite sum theorem for closed sets is proved, and for all others, counter examples are given. Subject to a small modification, however, all of the sum theorems hold for a large class of spaces.
A fundamental group topology
Authors: Houghton C. H.
Published: April 2009

The topology of the Čech fundamental group of the one-point compactification of an appropriate space Y induces a topology on the fundamental group of Y. We describe this topology in terms of a topological group introduced by Higman.
Notes on congruences on regular semigroups.I
Authors: Koch R. J. , Madison B. L.
Published: April 2009

Four properties of congruences on a regular semigroup S are studied and compared. Let R, L and D denote Green's relations and let V = {(a, b) ∈ S × S|a and b are mutually inverse}. A congruence ρ on S is (1) rectangular provided ρ ∩ D = (ρ ∩ L) ° (ρ ∩ R), (2) V-commuting provided ρ ° V = V ° ρ, (3) (L, R)-commuting provided L ° ρ = ρ ° L, and R ° ρ = ρ ° R, and (4) idempotent-regular provided each idempotent ρ-class is a regular subsemigroup of S.

A rectangular congruence is (L, R)-commuting and a V-commuting congruence is idempotent-regular. If ρ is idempotent-regular and (L, R)-commuting then ρ is V-commuting. Examples and conditions are given to show what other implications among the four properties hold. In addition to characterizations of the properties, these are studied in the presence of other conditions on S. For example, if S is a stable regular semigroup, then each congruence under D is rectangular.
A posteriori error estimates for elliptic boundary-value problems
Authors: Chan W. L.
Published: April 2009

A posteriori error estimates for a class of elliptic unilateral boundary value problems are obtained for functions satisfying only part of the boundary conditions. Next, we give an alternative approach to the a posteriori error estimates for self-adjoint boundary value problems developed by Aubin and Burchard. Further, we are able to construct an alternative estimate with mild additional assumptions. An example of a linear differential operator of order 2k is given.
Some inequalities for trigonometric polynomials
Authors: Frappier Clément
Published: April 2009

We obtain various refinements and generalizations of a classical inequality of S. N. Bernstein on trigonometric polynomials. Some of the results take into account the size of one or more of the coefficients of the trigonometric polynomial in question. The results are obtained using interpolation formulas.
Counting 2-circulant graphs
Authors: Chia Gek-Ling , Lim Chong-Keang
Published: April 2009

Alspach and Sutcliffe call a graph X(S, q, F) 2-circulant if it consists of two isomorphic copies of circulant graphs X(p, S) and X(p, qS) on p vertices with “cross-edges” joining one another in a prescribed manner. In this paper, we enumerate the nonisomorphic classes of 2-circulant graphs X(S, q, F) such that |S| = m and |F| = k. We also determine a necessary and sufficient condition for a 2-circulant graph to be a GRR. The nonisomorphic classes of GRR on 2p vertices are also enumerated.
Some groups with T1 primitive ideal spaces
Authors: Carey A. L. , Moran W.
Published: April 2009

Let G be a second countable locally compact group possessing a normal subgroup N with G/N abelian. We prove that if G/N is discrete then G has T1 primitive ideal space if and only if the G-quasiorbits in Prim N are closed. This condition on G-quasiorbits arose in Pukanzky's work on connected and simply connected solvable Lie groups where it is equivalent to the condition of Auslander and Moore that G be type R on N (-nilradical). Using an abstract version of Pukanzky's arguments due to Green and Pedersen we establish that if G is a connected and simply connected Lie group then Prim G is T1 whenever G-quasiorbits in [G, G] are closed.
On the lower central factors of free centre-by-metabelian groups
Authors: Gupta N. D. , Hurley T. C. , Levin F.
Published: April 2009

We describe the structure of the lower central factors of free centre-by-metabelian groups.
Invariance of infinite-dimensional classes of spaces
Authors: Wenner B. R.
Published: April 2009

The central area of investigation is in the isolation of conditions on mappings which leave invariant the classes of locally finite-dimensional metric spaces and strongly countable-dimensional metric spaces. Examples of such properties are open and closed with discrete point-inverses, open and finite-to-one, or open, closed, and countable-to-one.
On subsequential limit points of a sequence of iterates. II
Authors: Maiti M. , Babu A. C.
Published: April 2009

J. B. Diaz and F. T. Metcalf established some results concerning the structure of the set of cluster points of a sequence of iterates of a continuous self-map of a metric space. In this paper it is shown that their conclusions remain valid if the distance function in their inequality is replaced by a continuous function on the product space. Then this idea is extended to some other mappings and to uniform and general topological spaces.
One-point extensions of locally para-H-closed spaces
Authors: Zahid M. I. , Heath R. W.
Published: April 2009

A space X is para-H-closed if every open cover of X has a locally-finite open refinement (not necessarily covering the space) whose union is dense in X. In this paper, we study one-point para-H-closed extensions of locally para-H-closed spaces.
Symmetrisable operators :Part III Hilbert space operators Symmetrisable by bounded operators
Authors: Silberstein J. P. O.
Published: April 2009

The fact that the most general symmetrisable operators in Hilbert Space do not possess a number of the desirable properties of such operators in unitary spaces makes it necessary to look for a more restricted class of operators. There are two reasons for our particular choice. In the first place many of the conditions introduced in the course of Part II concerned reltionships between the domain of the symmetrising operatorHand the domain and range of the symmetrisable operatorA. These conditions are now all automatically satisfied. The other reason is that the construction used in section 4 to relate symmetrisable operators to certain symmetric operators clearly required that eitherHorH−1was bounded. The case ofH−1bounded has already been dealt with in section 9 and shown to be fairly simple. The case in which H is bounded is clearly of considerable complexity, since we have already seen (example in proof of Theorem 10.6.) that the con |H| the bound ofHby
The limit theorem for aperiodic discrete renewal processes
Authors: Finch P. D.
Published: April 2009

A discrete renewal process is a sequence {X4} of independently and inentically distributed random variables which can take on only those values which are positive integral multiples of a positive real number δ. For notational convenience we take δ = 1 and write where .
Some Krein-Milman theorems for order-convexity
Authors: Wirth Andrew
Published: April 2009

Analogues of the Krein-Milman theorem for order-convexity have been studied by several authors. Franklin [2] has proved a set-theoretic result, while Baker [1] has proved the theorem for posets with the Frink interval topology. We prove two Krein-Milman results on a large class of posets, with the open-interval topology, one for the original order and one for the associated preorder. This class of posets includes all pogroups. Cellular-internity defined in Rn by Miller [3] leads to another notion of convexity, cell-convexity. We generalize the definition of cell-convexity to abelian l-groups and prove a Krein-Milman theorem in terms of it for divisible abelian l-groups.
Normal complements in finite solvable groups
Authors: Friesen Donald K.
Published: April 2009

A well known theorem ([1] page 432) in the study of finite groups states that if P is a Sylow p-subgroup of the finite group G, and if P0 is a normal subgroup of P such that whenever two elements, σ and τ, of P are conjugate in G, the cosets σP0 and τP0 are conjugate in P/P0, then there is a normal subgroup K of G such that G = KP and K ∩ P = P0. In this note we will extend this result to allow P to be any Hall subgroup if G is solvable. More precisely, following theorem will be the proved.
On the existence of rigid arcs
Authors: Pearson B. J.
Published: April 2009

By an arc we mean a nondegenerate simply ordered set which is compact and connected in its order topology. A space X is rigid if the only homeomorphism of X onto itself is the identity map. Examples of rigid totally disconnected compact ordered spaces may be found in [1], [2], and [3]. It is the purpose of this note to prove the existence of an arc such that no two of its subarcs are homeomorphic. The proof makes use of arcs of large cardinality and the technique of inverse limit spaces.
Some torsion-free group rings with nilpotent prime radicals
Authors: Tan Keng-Teh
Published: April 2009

LetRbe a ring with identity. We will useJ(R) andP(R) to denote the Jacobson and prime radicals ofR, respectively. IfGis a group, the group ring ofGoverRwill be denoted byRG.
Recursive equivalence types of vector spaces
Authors: Hamilton Alan G.
Published: April 2009

We consider subspaces of a vector spaceUF, which is countably infinite dimensional over a recursively enumerable fieldFwith recursive operations, where the operations inUFare also recursive, and where, of course,FandUFare sets of natural numbers. It is the object of this paper to investigate recursive equivalence types of such vector spaces and the ways in which their properties are analogous to and depend on properties of recursive equivalence types of sets.
Rotundity redux
Authors: Yorke A. C.
Published: April 2009

Recently the concept of uniform rotundity was generalized for real Banach spaces by using a type of “area” devised for these spaces. This paper modifies the methods used for uniform rotundity and applies them to weak rotundity in real and complex spaces. This leads to the definition of k-smoothness, k-very smoothness and k-strong smoothness. As an application, several sufficient conditions for reflexivity are obtained.
The positive part of a Fourier transform
Authors: Logli Augusto
Published: April 2009

We consider the function u whose Fourier transform is the positive part of the Fourier transform of a function f on Rn. If n ≤ 2 and f satisfies simple regularity conditions (in particular if f is in the Schwartz space Y(Rn), then u lies in L1(Rn). If n ≥ 3, then simple counterexamples exist; for example, if f(x) = |x|2 exp(-|x|2), then u does not lie in L1(Rn).
Some examples of finiteness conditions in centre-by-metabelian groups
Authors: Groves J. R. J.
Published: April 2009

Centre-by-metabelian groups with the maximal condition for normal subgroups are exhibited which (a) are residually finite but have quotient groups which are not residually finite; and (b) have all quotients residually finite but are not abelian-by-polycyclic.
On saturated permutative varieties and consequences of permutation identities
Authors: Khan N. M.
Published: April 2009

We determine which permutative varieties are saturated and classify all nontrivial permutation identities for the class of all globally idempotent semigroups.
Families of partial representing sets
Authors: Balanda Kevin P.
Published: April 2009

Assume GCH. Let κ, μ, Σ be cardinals, with κ infinite. Let be a family consisting of λ pairwise almost disjoint subsets of Σ each of size κ, whose union is Σ. In this note it is shown that for each μ with 1 ≤ μ ≤min(λ, Σ), there is a “large” almost disjoint family of μ-sized subsets of Σ, each member of having non-empty intersection with at least μ members of the family .
Conformally flat hypersurfaces of symmetric spaces
Authors: Matsuyama Yoshio
Published: April 2009

In this paper we consider how much we can say about an irreducible symmetric space M which admits a single hypersurface with at most two distinct principal curvatures. Then we prove that if N is conformally flat, then N is quasiumbilical and M must be a sphere, a real projective space or the noncompact dual of a sphere or a real projective space.
Saturation on locally compact abelian groups
Authors: Bloom Walter R. , Sussich Joseph F.
Published: April 2009

Let G be a locally compact abeian group, (μρ) a net of bounded Radon measures on G. In this paper we consider conditions under which (μρ) is saturated in Lp (G) and apply these results to the Fejér and Picard approximation processes.
On the order scale of a uniform space
Authors: Kent D. C.
Published: April 2009

The order topology is compact and T2 in both the scale and retracted scale of any uniform space (S, U). if (S, U) is T2 and totally bounded, the Samuel compactification associated with (S, U) can be obtained by uniformly embedding (S, U) in its order retracted scale (that is, the retracted scale with its order topology). This implies that every compact T2 space is both a closed subspace of a complete, infinitely distributive lattice in its order topology, and also a continuous, closed image of a closed subspace of a complete atomic Boolean algebra in its order topology.
Recursive properties of isomorphism types
Authors: Moses Michael
Published: April 2009

For Γ a revursively enumerable set of formulae, a structure U on a recursive universe is said to be “Γ-recursively enumerable” if the satisfaction predicate restricted to Γ is recursively enumerable (equivalently, if the formulae of Γ uniformulae of Γ uniformly denote recursively enumerable relations on U).

For recursively enumerable sets Γ1 ⊆ Γ2 of formulae we shall, under certain conditions, characterize structures U with the following properties.

1) Every isomorphism form U to a Γ1-recursively enumerable structure is a recursive isomorphism.

2) Every Γ1-recursively enumerable structure isomorphic to U is recursively isomorphic to U.

3) Every Γ1-recursively enumerable structure isomorphic to U is Γ2-recursively enumerable.
A lemma on maximal sets and the theorem of Denjoy-Vitali
Authors: Finch P. D.
Published: April 2009

By an ∮-related family ∮ we mean a non-empty family ∮ of elements such that to each element F ∈ ∮ is associated a set R(F) of elements of ∮, called the R-class of F, which contains F. An element G ∈ R(F) is said to be R-related to F. By an R-section S of ∮ we mean a set of elements of ∮ such that for any elements F1, F2 of S either F1 ∈ R(F2) or F2 ∈R(F1). If R(F) = {F} for each F ∈ ∮ then the only R-Sections are the sets {F}. The interesting applications of the lemma proved below are to those cases when there exist R-sections which do not contain a finite number of elements.
On the characteristic functional for a replacement model
Authors: Davis A. W.
Published: April 2009

J. Gani and G. F. Yeo ([2] and [3]) have recently investigated certain age-distributions associated with a replacement model which serves, in particular, as a model for phage reproduction. In this paper, the characteristic functional for this model will be obtained explicitly.
Felix Adalbert Behrend
Authors: Cherry T. M. , Neumann B. H.
Published: April 2009

Felix Behrend was born at Berlin-Charlottenburg, Germany, on 23 April, 1911, the eldest of four children of Dr. Felix W. Behrend and his wife Maria, nee Zöllner. Felix Behrend senior was a mathematics and physics master at the Herderschule, a noted “Reform-Realgymnasium” in one of the western suburbs of Berlin; he was a widely known educationalist, and later headmaster of an important school elsewhere in Berlin, until demoted and finally dismissed by the Nazis, partly because of some Jewish ancestry, partly because of his liberal political views.