bluuebunny/crossref_metadata_2025 huggingface dataset:
Independence results concerning Dedekindfinite sets
Authors: Monro G. P.
Published: April 2009

A Dedekind-finite set is one not equinumerous with any of its proper subsets; it is well known that the axiom of choice implies that all such sets are finite. In this paper we show that in the absence of the axiom of choice it is possible to construct Dedekind-finite sets which are large, in the sense that they can be mapped onto large ordinals; we extend the result to proper classes. It is also shown that the axiom of choice for countable sets is not implied by the assumption that all Dedekind-finite sets are finite.
Cauchy completion of Abelian tight Riesz groups
Authors: Sherman B. F.
Published: April 2009

This paper concerns the completions of partially ordered groups introduced by Fuchs (1965a) and the author (to appear); the p.o. groups under consideration are, generally, abelian tight Riesz groups, and so, throughout, the word “group” will refer to an abelian group.

In section 3 we meet the cornerstone of the work, the central product theorem, by means of which we can interpret the Cauchy completion of a tight Riesz group in terms of the completion of any of its o-ideals; one particularly important case arises when the group has a minimal o-ideal. Such a minimal o-ideal is o-simple, and in section 6 the completion of an isolated o-simple tight Riesz group is shown to be a tight Riesz real vector space.
Contractors and secant methods for finding roots of non-linear functionals
Authors: Altman Mieczyslaw
Published: April 2009

A further development of the concept of contractors for non-linear functionals is presented by introducing two-point contractors. On this basis two-point secant methods are proposed for finding roots of non-linear functionals in Banach spaces.
Strong maximum principles for weakly coupled systems of quasilinear parabolic inequalities
Authors: Dow M. A.
Published: April 2009

Výborný and I (1972) proved maximum principles for a quasilinear elliptic operator where the boundary satisfied a smoothness condition weaker than the interior sphere property. In this paper I extend these to parabolic operators of a similar form and through a simple device to weakly coupled systems of such operators. Finally, I extend all of these results to an operator similar to the “parabolic” case of an operator introduced by Redheffer (1971). His conditions on the coefficients are replaced by conditions analogous to those Dow and Výborný (1972).
Reflective subcategories, localizations and factorizationa systems
Authors: Cassidy C. , Hébert M. , Kelly G. M.
Published: April 2009

This work is a detailed analysis of the relationship between reflective subcategories of a category and factorization systems supported by the category.
Varieties of completely regular semigroups
Authors: Reilly Norman R.
Published: April 2009

If CS(respectively, O) denotes the class of all completely simple semigroups (respectively, semigroups that are orthodox unions of groups) then CS(respectively, O) is a variety of algebras with respect to the operations of multiplication and inversion. The main result shows that the lattice of subvarieties of is a precisely determined subdirect product of the lattice of subvarieties of CSand the lattice of subvarieties of O. A basis of identities is obtained for any variety in terms of bases of identities for . Several operators on the lattice of subvarieties of are also introduced and studied.
Continuous trace C*-algebras with given Dixmer-Douady class
Authors: Raeburn Iain , Taylor Joseph L.
Published: April 2009

We give an explicit construction of a continuous trace C*algebra with prescribed Dixmier-Douady class, and with only finite-dimensional irreducible representations. These algebras often have non-trivial automorphisms, and we show how a recent description of the outer automorphism group of a stable continuous trace C*algebra follows easily from our main result. Since our motivation came from work on a new notion of central separable algebras, we explore the connections between this purely algebraic subject and C*a1gebras.
Some non-critical idempotents in the closure of the characters in the maximal ideal space of M(D2)
Authors: Lake Jane
Published: April 2009

This paper shows that the idempotent generalized characters associated with a Raikov System generated by a K2 set in is contained in the closure of the characters D2 in ΔM(D2).
A note on the index laws of fractional calculus
Authors: Mcbride Adam C.
Published: April 2009

Two index laws for fractional integrals and derivatives, which have been extensively studied by E. R. Love, are shown to be special cases of an index law for general powers of certain differential operators, by means of the theory developed in a previous paper. Discussion of the two index laws, which are rather different in appearance, can thus be unified.
Dualities for some De Morgan algebras with operators and Lukasiewicz algebras
Authors: Cignoli Roberto , De Gallego Marta S.
Published: April 2009

Algebras (A, ∧, ∨, ~, γ, 0, 1) of type (2,2,1,1,0,0) such that (A, ∧, ∨, ~, γ 0, 1) is a De Morgan algebra and γ is a lattice homomorphism from A into its center that satisfies one of the conditions (i) a ≤ γa or (ii) a ≤ ~ a ∧ γa are considered. The dual categories and the lattice of their subvarieties are determined, and applications to Lukasiewicz algebras are given.
On separable noncyclic extensions of rings
Authors: Szeto George , Wong Yuen-Fat
Published: April 2009

The separable cyclic extension of rings is generalized to a separable noncyclic extension of rings: a crossed product with a factor set over a ring (not necessarily commutative). A representation of separable idempotents for a separable crossed product is obtained, and simplifications for some special factor sets are also given.
An axially symmetric forced convection problem
Authors: Belward J. A.
Published: April 2009

A simple diffusion-convection heat transfer model is formulated which leads to an axially symmetric partial differential equation. The equation is shown to be closely related to a second one which is adjoint to the original equation in one variable can and be interpreted as a description of another diffusion-convection model. Fundamental solutions of the original equation are constructed and interpreted with reference to both models. Some boundary value problems are solved in series form and integral representations of the solutions are also given. The boundary value problems are shown to be equivalent to an integral equation and the correspondence between the two formulations is understood in terms of the two diffusion-convection problems. A Péclet number is defined in one of the boundary value problems and the behaviour of the solutions is studied for large and small values of this parameter.
Approximation with norms defined by derivations
Authors: Briggs J. M.
Published: April 2009

A linear mappingDof the algebra of polynomial functionsP[0, 1] into the algebra of all continuous complex-valued functionsC[0,1] is called aderivationprovidedD(fg)=fD(g)+gD(f)for all polynomialsfandg. The derivations ofP[0, 1] intoC[0,1] are easily seen to be all mappings of the formDwwherewis a continuous function on [0, 1] andDw(f) =wf' (f' denotes the ordinary derivative off). In fact,w=D(x) wherexis the coordinate function. LetDwbe such a derivation, and let ∥ · ∥ denote the supremum norm on C[0,1]. ThenDwgives rise to an algebra norm ∥ · ∥wonP[0,1] denned by.
On the set of finite subsets of a set
Authors: Hickman J. L
Published: April 2009

We sometimes think of medial (that is, infinite Dedekind-finite) sets as being “small” infinite sets. Medial cardinals can be defined as those cardinals that are incomparable to ℵℴ; hence we tend to think of them as being spread out on a plane “just above” the natural numbers, which seems to lend support to the view expressed above that medial sets are “small”.
On a class of analytic functions
Authors: Goel R. M.
Published: April 2009

LetS(α) denote the class of functionsregular and analytic in the unit discE= {z¦z¦< 1¦} and satisfying the condition,.
Rectifiably ambiguous points of planar sets
Authors: Bagemihl Frederick , Humke Paul D.
Published: April 2009

Denote by P the Euclidean plane with a rectangular Cartesian coordinate system where the x-axis is horizontal and the y-axis is vertical. An arc in P shall mean a simple continuous curve Λ:{t: 0 ≦ t < 1} P having the properties that limitt→1 Λ(t) exists and limitt→1Λ(t) ≠ Λ(t0) for 0 ≦t0 < 1. An arc at a pointζ in P shall be an arc Λ where limt→1 Λ(t) = ζ. If S is an arbitrary subset of the plane, ζ is termed an ambiguous point relative to S provided there are arcs Λ and Γ at ζ with Λ ⊆ S and Γ ⊆ P–S; such arcs are referred to as arcs of ambiguity at ζ. If A is a set of arcs we say a point ζ in P is accessible via A provided there is an arc at ζ which is an element of A. If B is also a collection of arcs, then A and B are said to be pointwise disjoint if whenever α∈A and β ∈ B, α ∩ β = Ø. The collections A and B are said to be terminally arcwise disjoint if whenever α ∈ A and β ∈ B and both α and β are arcs at a point ζ in P, then a ∩ β contains no arc at ζ. If S is a planar set, we let A(S) denote the set of all arcs contained in S. Note that if S ∩ T = Ø then A(S) and A(T) are pointwise disjoint collections of arcs.
Computation of the generalised factorial function
Authors: Doran H. E.
Published: April 2009

The generalised factorial function (z; K)! has been defined by Smith White and Buchwald [1] in terms of an infinite product which converges very slowly, about 105 terms being required for four figure accuracy if |z| = 10. A method is given for the computation of (z; k)! for 0 < |z|≦ 10 to four figure accuracy.
Stochastic non-linear programming
Authors: Hanson M. A.
Published: April 2009

Although many varied techniques have been proposed for handling deterministic non-linear programming problems there apperars to have been little success in solving the more realistic problem of stochastic non-linear programming, despite the many results that have been obtained for stochastic linear programming. In this paper the stochastic non-linear problem is treated by means of an adaptation of a method used by Berkovitz [1] in obtaining an exiatence theorem for a type of inequality constrained variational problem involving one independent variable. The stochastic programming problem of course involves many independent variables. Necessary conditions are obtained for the existence of a solution of a fairly general type of non-linear problem, and these conditions are shown to be also sufficient for the convex problem. A duality theorem is given for the latter problem.
Terminal path numbers for certain families of trees
Authors: Meir A. , Moon J. W.
Published: April 2009

We determine the limiting distribution of the distance from the root of a tree to any nearest endnode of the tree (other than the root) for certain families of rooted trees.
The spectrum of skew Room squares
Authors: Stinson D. R.
Published: April 2009

We give a short proof that skew Room squares exist for all odd sides s exceeding 5.
On characters of height zero
Authors: Basmaji B. G.
Published: April 2009

Every irreducible ordinary character in a p-block of a finite metabelian group is of height 0 if and only if the defect group of the p-block is abelian.
Construction principle and transfinite induction up to ε0
Authors: Yasugi Mariko
Published: April 2009

What we cail here the “construction principle” is a principle on the ground of which some functionals can be defined; the domain and the range of such a functional consist of some “computable” functionals of various finite types. The principle above is considered here as the basis of the functional interpretation of transfinite induction up to ε0. It is concretely repesented as the “term-forms”, where every term-form is shown to be “computable” in some sense.
On the commutativity of semi-prime rings
Authors: Al-Moajil Abdullah H.
Published: April 2009

It is shown that ifRis a 2-torsion-free semi-prime ring such that [xy, [xy, yx]] = 0 for allx, y∈R, thenRis commutative.
A simple proof of Jacobi's four-square theorem
Authors: Hirschhorn M. D.
Published: April 2009

A celebrated result, due to Jacobi, says that the number of representations of the positive integer n as a sum of four squares is equal to eight times the sum of the divisors of n which are not divisible by 4. We give a new and simple proof of this result which depends only on Jacobi's triple product identity.
Idempotent-separating extensions of regular semigroups with Abelian kernel
Authors: Loganathan M.
Published: April 2009

Let S be a regular semigroup and D(S) its associated category as defined in Loganathan (1981). We introduce in this paper the notion of an extension of a D(S)-module A by S and show that the set Ext(S, A) of equivalence classes of extensions of A by S forms an abelian group under a Baer sum. We also study the functorial properties of Ext(S, A).
On the characterisation of Asplund spaces
Authors: Giles J. R.
Published: April 2009

A Banach space is an Asplund space if every continuous convex function on an open convex subset is Fréchet differentiable on a dense G8 subset of its domain. The recent research on the Radon-Nikodým property in Banach spaces has revealed that a Banach space is an Asplund space if and only if every separable subspace has separable dual. It would appear that there is a case for providing a more direct proof of this characterisation.
A Characterization of semiprime ideals in near-rings
Authors: Rao V. Sambasiva
Published: April 2009

It is well known that in any near-ring, any intersection of prime ideals is a semiprime ideal. The aim of this paper is to prove that any semiprime ideal I in a near-ring N is the intersection of all minimal prime ideals of I in N. As a consequence of this we have any seimprime ideal I is the intersectionof all prime ideals containing I.
A note on the Harris-Sevast'yanov transformation for supercritical branching processes
Authors: Schuh H.-J.
Published: April 2009

We show that the Harris-Sevast'yanov transformation for supercritical Galton-Watson processes with positive extinction probability q can be modified in such a way that the extinction probability of the new process takes any value between 0 and q. We give a probabilistic interpretation for the new process. This note is closely related to Athreya and Ney (1972), Chapter 1.12.
Some comparison criteria in oscillation theory
Authors: Philos Ch. G.
Published: April 2009

The purpose of this paper is to establish comparison criteria, by which the oscillatory and asymptotic behavior of linear retarded differential equations of arbitrary order is inherited from the oscillation of an associated second order linear ordinary differential equation. These criteria are new even in the case of ordinary differential equations.
Fourier transforms and harmonic functions
Authors: Ormerod N.
Published: April 2009

The purpose of this paper is to present a novel proof of a well-known relationship between functions in harmonic subspaces of L2(Rn) ∪ L1 (Rn) and their Fourier transforms. The proof uses a characterisation of spherical harmonics given by Hecke and a method developed by the author in a previous paper.
The von Neumann kernel of a locally compact group
Authors: Rothman Sheldon , Strassberg Helen
Published: April 2009

For a locally compact group G, the von Neumann kernel, n(G), is the intersection of the kernels of the finite dimensional (continuous) unitary representations of G. In this paper we calculate n(G) explicitly for a general connected locally compact group and for certain classes of non-connected groups.
Nowhere simplicity in matroids
Authors: Downey R.
Published: April 2009

We examine the concepts of nowhere simplicity in a wide class of abstract dependence systems. Initially we examine how many of the existing results valid for L(ω), the lattice of r.e. sets, have analogues valid for more general lattices. For example, we show that any r. e. subspace of V∞ can be decomposed into a pair of nowhere simple subspaces.
Varieties of nilpotent groups of class four (II)
Authors: Fitzpatrick Patrick
Published: April 2009

The first paper (written jointly with L. G. Kovács) of this three-part series reduced the problem of determining all varieties of the title to the study of the varieties of nilpotent groups of class (at most) four whose free groups have no nontrivial elements of odd order. The present paper deals with these under the additional assumption that the variety contains all nilpotent groups of class three. We label each such variety by a vector of eleven parameters, each parameter a nonnegative integer or ∞, subject to numerous but simple conditions. Each vector satisfying these conditions is in fact used, and matches directly a (finite) defining set of laws for the variety it labels. Moreover, one can readily recognize from the parameters whether one variety is contained in another. The third paper will complete the determination of all varieties of nilpotent groups of class four.
Constructions of the maximal strongly character invariant segal algebras and their applications
Authors: Chen Chang-Pao
Published: April 2009

Let G denote any locally compact abelian group with the dual group Γ. We construct a new kind of subalgebra L1(G) ⊗ΓS of L1(G) from given Banach ideal S of L1(G). We show that L1(G) ⊗гS is the larger amoung all strongly character invariant homogeneous Banach algebras in S. when S contains a strongly character invariant Segal algebra on G, it is show that L1(G) ⊗гS is also the largest among all strongly character invariant Segal algebras in S. We give applications to characterizations of two kinds of subalgebras of L1(G)-strongly character invariant Segal algebras on G and Banach ideal in L1(G) which contain a strongly character invariant Segal algebra on G.
A result on iterated clique graphs
Authors: Chong-Keang Lim
Published: April 2009

S. T. Hedetniemi and P. J. Slater have shown that if G is a triangle-free connected graph with at least three vertices, then

where K(G) is the clique graph of G and K2(G) = K(K(G)) is the first iterated clique graph. In this paper, we generalize the above result to a wider class of graphs.
On cyclic maps
Authors: Lim K. L.
Published: April 2009

The definition of cyclic maps is recalled and their existence discussed. Among other things, it is shown that cyclicity of maps is closed under product and that if f is cyclic then Ωf is central.Some results of Gottlieb (1972) on homology are applied to investigate the relationship between cyclicity of maps and maps of finite order.
Doubly regular tournaments of Szekeres type
Authors: Ito Noboru
Published: April 2009

The purpose of this note is to determine the automorphism group of the doubly regular tournament of Szekeres type, and to use it to show that the corresponding skew Hadamard matrix H of order 2(q + 1), where q ≡5(mod 8) and q > 5, is not equivalent to the skew Hadamard matrix H(2q + 1) of quadratic residue type when 2q + 1 is a prime power.
The minimum determinant of Minkowski-reduced quinary quadratic forms
Authors: Barnes E. S. , Trenerry D. W.
Published: April 2009

Minkowski established a lower bound for the determinant D of a Minkowski-reduced quadratic form in terms of the product of its diagonal coefficients aii (i = 1, …n). Oppenheim and Barnes found, for n = 3 and n = 4 respectively, the precise minimum of D in terms of the aii; in each case the minimum is a polynomial in the aii. Here it is shown that no such result exists when n = 5; however a polynomial in all,…, a55 is determined which gives the minimum of D when a55 is sufficiently large.
A limit theorem for the tails of discrete infinitely divisible laws with applications to fluctuation theory
Authors: Embrechts Paul , Hawkes John
Published: April 2009

Suppose that (pn) is an infinitely divisible distribution on the non-negative integers having Lévy measure (vn). In this paper we derive a necessary and sufficient condition for the existence of the limit limn→∞ pn/vn. We also derive some other results on the asymptotic behaviour of the sequence (Pn) and apply some of our results to the theory of fluctuations of random walks. We obtain a necessary and sufficient condition for the first positive ladder epoch to belong to the domain of attraction of a spectrally positive stable law with index α, α ∈ (1,2).
The generation by two operators of the symplectic group over GF(2)
Authors: Room T. G.
Published: April 2009

The main result obtained in this paper is Theorem 1. The symplectic group on the skew matrix T of 2m rows and columns over GF (2)** can be generated by the two matrices Q, R, whereTi,j being the substitution matrix which interchanges the elements numbered i and j,.
Recurrence of extreme observations
Authors: Wilks S. S.
Published: April 2009

Suppose a preliminary set of m independent observations are drawn from a population in which a random variable x has a continuous but unknown cumulative distribution function F(x). Let y be the largest observation in this preliminary sample. Now suppose further observations are drawn one at a time from this population until an observation exceeding y is obtained. Let n be the number of further drawings required to achieve this objective. The problem is to determine the distribution function of the random variable n. More generally, suppose y is the r-th from the largest observation in the preliminary sample and let n denote the number of further trials required in order to obtain k observations which exceed y. What is the distribution function of n?
Transcendental numbers
Authors: Mahler Kurt
Published: April 2009

If K is a field and L an extension field, α ∈ L is said to be algebraic over K if it satisfies an equation with coefficients in K. If α does not satisfy any such on, it is called transcendental over K.
An integral equation from phytology
Authors: Miller J. B.
Published: April 2009

We examine the equation where with .
Translates of L∞ functions and of bounded measures
Authors: Edwards R. E.
Published: April 2009

D. A. Edwards has shown [1] that if X is a locally compact Abelian group and f ∈ L∞, then the translate fa of f varies continuously with α if and only if f is (equal l.a.e. to) a bounded, uniformly continuous function. He remarks that this is a sort of dual to part of a result due to Plessner and Raikov which asserts that an element μ of the space Mb of bounded Radon measures on X belongs to L1 (i.e., is absolutely continuous relative to Haar measure) if and only its translates vary continuously with the group element, the relevant topology on Mb being that defined by the natural norm of Mb as the dual of the space of continuous functions vanishing at infinity. The proof he uses (ascribed to Reiter) applies equally well in both cases, and also to the case in which X is non-Abelian. A brief examination shows that in the latter case it is ultimately immaterial whether left- or right-translates are considered; since the extra complexities of this case are principally terminological, we shall direct no further attention to it.
On a type of Riemannian space
Authors: Gupta Bandana
Published: April 2009

In connection with Relativity, Kottler [2] introduced the space V4 whose metric tensor is given by xi being space coordinates and Ф being a function of x1 only, and showed that if Where a and b are arbitrary constants, then the V4 is an Einstein space.
Inequalities for ideal bases in algebraic number fields
Authors: Mahler K.
Published: April 2009

In a paper of nearly thirty years ago (Mahler 1937) I first studied approximation properties of algebraic number fields relative to their full system of inequivalent valuations. I now return to these questions with a slightly improved method and establish a number of existence theorems for such fields.
Single-server queueing systems with uniformly limited queueing time
Authors: Daley D. J.
Published: April 2009

The paper considers the queueing systemGI/G/1 with a type of customer impatience, namely, that the total queueing-time is uniformly limited. Using Lindiley's approach [10], an integral equation for the limiting waiting- time distribution is derived, and this is solved explicitly forM/G/1 using an expansion of the Pollaczek-Khintchine formula. It is also solved, in principle for Ej/G/l, and explicitly for Ej/Ek/l. A duality noted between GIA(x)/GB(x)/l and GIB(x)/GA(x)/l relates solutions for GI/Ek/l to Ek/G/l. Finally the equation for the busy period in GI/G/l is derived and related to the no-customer-loss distribution and dual distributions.
Generalized Minkowski formulae for compact submanifolds of a Riemannian manifold
Authors: Smith Geoffrey Howard
Published: April 2009

In 1903 H. Minkowski obtained two integral formulae for closed convex surfaces in three dimensional Euclidean space. In this paper we obtain generalised Minkowski formulae on compact orientable immersed submanifolds of an arbitrary Riemannian manifold. By successive specialisation we indicate how known integral theorems can be obtained as particular cases of our result.
On random interpolation
Authors: Erdös P.
Published: April 2009

In a recent paper Salem and Zygmund [1] proved the following result: Put and denote the φv(t) Rademacher function. Denote by Ln(t,θ) the unique trigonometric polynominal (in θ) of degree not exceeding n
Continuously infinite matrices and the algebraic theory of Fredholm's equation
Authors: Smith–White W. B.
Published: April 2009

In this note the theory of the integral equation is reduced to elementary matrix algebra. The Fredholm theorems are proved without the introduction of the usual parameter λ and without using the properties of the resolvent considered as an analytic function of the complex variable λ. There is an exact correspondence between the properties of the equation (1) and the properties of a finite linear system. Here the proofs of these properties are also in extact correspondence with the same for the elementary case.
Über die Normalstruktur von mehrfach faktorisierten Gruppen
Authors: Wielandt Helmut
Published: April 2009

Ein Teil von Philip Halls bekannter Theorie der auflösbaren Gruppen läßt sich, wie im folgenden gezeigt wird, auf beliebige endiliche Gruppen G ausdehnen. Wir fragen: Was kann man über die Normalstruktur (Hauptreihen, Kompositionsfaktoren) von G aussagen, wenn man mehrere Zer legungen von G in Produkte von Untergruppen mit gegebener Normalstruktur kennt? Eine Antwort gibt der folgende Satz, das Hauptergebnis dieser Note:
On the spaces of certain classes of entire functions
Authors: Krishnamurthy V.
Published: April 2009

Let ρ and d be two positive numbers. We shall be concerned in this paper with two classes of entire functions, namely: (i) the class C (ρ, d) of all entire functions of order ρ and type not exceeding d — we note that this class includes all entire functions of order less than ρ;
An n-dimensional analogue of Cauchy's integral theorem
Authors: Michael J. H.
Published: April 2009

As in [5] a parametric n-surface in Rk (where k ≧ n) will be a pair (f, Mn), consisting of a continuous mapping f of an oriented topological manifold Mn into the euclidean k-space Rk. (f, Mn) is said to be closed if Mn is compact. The main purpose of this paper is to use the method of [4] to prove a general form of Cauchy's Integral Theorem (Theorem 5.3) for those closed parametric n-surfaces (f, Mn) in Rn+1, which have bounded variation in the sense of [5] and for which f(Mn) has a finite Hausdorff n-measure. As in [4], the proof is carried out by approximating the surface with a simpler type of surface. However, when n > 1, a difficulty arises in that there are entities, which occur in a natural way, but are not parametric surfaces. We therefore introduce a concept which we call an S-system and which forms a generalisation (see 2.2) of the type of closed parametric n-surface that was studied in [5] II, 3 in connection with a proof of a Gauss-Green Theorem. The surfaces of [5] II, 3 include those that are studied in this paper.
On representing integers as products of integers of a prescribed type
Authors: Elliott P. D. T. A.
Published: April 2009

A general group-theoretic procedure is indicated for representing rational integers as products of other integers. A detailed example is given.
Derived functors of the torsion functor and local cohomology of noncommutative rings
Authors: Golan Jonathan S. , Raynaud Jacques
Published: April 2009

Let R be an associative ring which is not necessarily commutative. For any torsion theory τ on the category of left R-modules and for any nonnegative integer n we define and study the notion of the nth local cohomology functor with respect to τ. For suitably nice rings a bound for the nonvanishing of these functors is given in terms of the τ-dimension of the modules.
A conjecture of Lennox and Wiegold concerning supersoluble groups
Authors: Groves J. R. J.
Published: April 2009

We prove a conjecture of Lennox and Wiegold that a finitely generated soluble group, in which every infinite subset contains two elements generating a supersoluble group, is finite-by-supersoluble.
On the lattice of varieties of completely regular semigroups
Authors: Jones P. R.
Published: April 2009

Several morphisms of this lattice V(CR) are found, leading to decompostions of it, and various sublattices, into subdirect products of interval sublattices. For example the map V → V ∪ G (where G is the variety of groups) is shown to be a retraction of V(CR); from modularity of the lattice V(BG) of varieties of bands of groups it follows that the map V → (V ∪ V V G) is an isomorphism of V(BG).
Geometry in quotient reflexive spaces
Authors: Yorke A. C.
Published: April 2009

The structure and geometry of Banach spaces with the property that E(4) = Ê** + E⊥ ⊥ are investigated: such spaces are called quotient reflexive spaces here. For these spaces, if E is very smooth, Ê is also very smooth, and if E* is weakly locally uniformly rotund (WLUR), E(4) is smooth on a certain (relatively) norm dense subset of Ê**. Consequently, for quotient reflexive spaces, WLUR and very-WLUR are equivalent in E*.
On the stability of a second-order differential equation
Authors: Daykin D. E. , Chang K. W.
Published: April 2009

In this note we discuss the stability at the origin of the solutions of the differential equation where a dot indicates a differentiation with respect to time, and α, β are real-valued functions of any arguments. We tacitly assume that α, β are such that solutions to (1) do in fact exist. Under the transformation equation (1) takes the equivalent familiar form .
Sur l'unicité des solutions de l'équation d'abel-schröder et l'itération continue
Authors: Coifman R.
Published: April 2009

Soit f(x) continue strictement croissante pour x ∈ [0, a0] et telle que 0 < f(x) < x pour x ∈ 0, a0]. Il est connu que l'équation fonctionnelle d'Abel ainsi que l'équation de Schröder possèdent une infinité de solutions continues strictement croissantes.
Series Solution of a Functional Equation
Authors: Pranger W.
Published: April 2009

In this we will study analytic solutions to the linear functional equationwherefandhare given functions, x is a given complex number and the function g is to be found. This is a generalization of Schröder's functional equation. The results obtained are global in nature and the solutions holomorphic. The equation will be viewed from the standpoint of linear operator theory. When studied in this manner one arrives at a general operator inversion formula.
Self-polar double configurations in projective geometry: I. A general condition for self-polarity
Authors: Room T. G.
Published: April 2009

Let be a p×q matrix of linear forms in the n+1 coordinates in a projective space Πn. Then points which satisfy the q equations in general span a space Πn-q, but will span a space Πn-q+1 if a set μ,={μβ of multipliers can be found such that Such a set μ can be found if and only if the equations have solutions.
A second look at a queueing system with moving average input process
Authors: Finch P. D. , Pearce C.
Published: April 2009

We consider a single-server queueing system with first-come first-served queue discipline in which (i) customers arrive at the instants 0 = A0 < A1 < A2 < …, with time interval between the mth and (m+1)th arrivals
Polynomial solutions of binomial congruences
Authors: Lindgren H.
Published: April 2009

Polynomial solutions of a few binomial congruences have been known for a long time. For instance Legendre showed that the congruence has a solution this being the expansion of as far as the term of degree m — 3. [1] It seems that only restricted types, e.g. (1), have been investigated.
Permutational products of groups
Authors: Neumann B. H.
Published: April 2009

We deal with questions about the possible embeddings of two given groupsAandBin a groupPsuch that the intersection ofAandBis a given subgroupH. The data, consisting of the “constituents”AandBwith the “amalgamated” subgroupH, form anamalgam.1According to a classical theorem of Otto Schreier [5], every amalgam of two groups can be embedded in a groupF, the “free product ofAandBwith amalgamated subgroupH” or the “generalized free product” of the amalgam. This has the property that every groupPin which the amalgam is embedded and which is generated by the amalgam, is a homomorphic image of it. Hence theorems on the existence of certain embedding groupsPcan be interpreted also as theorems on the existence of certain normal subgroups ofF.
The numerical solution of integral equations using Chebyshev polynomials
Authors: Elliott David
Published: April 2009

An investigation has been made into the numerical solution of non-singular linear integral equations by the direct expansion of the unknown function f(x) into a series of Chebyshev polynomials of the first kind. The use of polynomial expansions is not new, and was first described by Crout [1]. He writes f(x) as a Lagrangian-type polynomial over the range in x, and determines the unknown coefficients in this expansion by evaluating the functions and integral arising in the equation at chosen points xi. A similar method (known as collocation) is used here for cases where the kernel is not separable. From the properties of expansion of functions in Chebyshev series (see, for example, [2]), one expects greater accuracy in this case when compared with other polynomial expansions of the same order. This is well borne out in comparison with one of Crout's examples.
Quasi-dual-continuous modules
Authors: Mohamed Saad , Müller Bruno J. , Singh Surjeet
Published: April 2009

Quasi-dual-continuous modules, which generalize the concept of dual-continuous modules, are studied Mohamed, Müller and Singh had obtained some decomposition theorems and their partial converses for dual-continuous modules. It is shown that these results can be extended to quasi-dual-continuous modules. Further, a short proof of a decomposition theorem for quasi-dual-continuous modules established recently by Oshiro is given. Some more structure theorems for such modules are established. Finally, quasi-dual-continuous covers are studied, and duals for results of Müller and Rizvi are derived.
On continuation of quasi-analytic solutions of partial differential equations to compact convex sets
Authors: Abramczuk Wojciech
Published: April 2009

In the early 70s A. Kaneko studied the problem of continuation of regular solutions of systems of linear partial differential equations with constant coefficients to compact convex sets. We show here that the conditions be obtained for real analytic solutions also hold in the quasi-analytic case. In particular we show that every quasi-analytic solution of the system p(D)u = 0 defined outside a compact convex subset K or Rn can be continued as a quasi-analytic solution to K if and only if the system is determined and the -module Ext1(Coker p′, ) has no elliptic component; here is the ring of polynomials in n variables, p is a matrix with elements from and p′ is the transposed matrix. In the scalar case, i.e. when p is a single polynomial, these conditions mean that p has no elliptic factor.
Completeness of normed linear spaces admitting centers
Authors: Astaneh Ali Ansari
Published: April 2009

It is shown that a normed linear space admitting (Chebyshev) centers is complete. Then the ideas in the proof of this fact are used to show that every incomplete CLUR (compactly locally uniformly rotund) normed linear space contains a closed bounded convex subset B with the following properties: (a)Bdoes not contain any farthest point; (b)Bdoes not contain any nearest point (to the elements of its complement).
The standard summation operator, the Euler-Maclaurin sum formula, and the Laplace transformation
Authors: Miller John Boris
Published: April 2009

A proof is given of the Euler-Maclaurin sum formula, on a Banach space of differentiable vector-valued functions of bounded exponential growth, using the Laplace transformation. Some related summation formulae are proved by the same methods. Properties of the standard summation operator are proved, namely spectral properties and boundedness, continuity and differentiability results.
Mahler's matrices
Authors: Lehmer D. H.
Published: April 2009

Recently K. Mahler [1] introduced a set of φ(2n) matrices of n rows and columns which form under multiplication the abelian group of the residue classes prime to 2n modulo 2n. These remarkable matrices whose elements 0, 1 and −1, have latent roots and determinants which can be given explicitly. Thus we have new examples of matrices with given elements whose powers, roots, inverses and determinants can be written down precisely. Such matrices are often useful in testing the efficacy of methods for finding these functions for a general matrix.
Asymptotic formulae for solutions of linear second-order differential equations with a large parameter
Authors: Thorne R. C.
Published: April 2009

Uniform asymptotic formulae are obtained for solutions of the differential equation for large positive values of the parameter u. Here p is a positive integer, θ an arbitrary parameter and z a complex variable whose domain of variation may be unbounded. The function ƒ (u, θ, z) is a regular function of ζ having an asymptotic expansion of the form for large u.

The results obtained include and extend those of earlier writers which are applicable to this equation.
On the Clifford collineation, transform and similarity groups. I.
Authors: Bolt Beverley , Room T. G. , Wall G. E.
Published: April 2009

Papers I, II of this projected series lay the algebraic foundations of the theory of the Clifford groups; I deals with the casep> 2, II with the casep= 2. The present introduction refers to both papers. Our theory has applications in group theory, geometry and number theory.
Pulse diffraction by an imperfectly reflecting wedge
Authors: Papadopoulos V. M.
Published: April 2009

A similarity method is used to develop a solution of the wave equation within a sector with mixed boundary conditions. In this manner the field which results from the diffraction of an incident pulse of step function time dependence is found.
Subsets characterizing the closure of the numerical range
Authors: Das K. C. , Majumdar S. , Sims Brailey
Published: April 2009

For an operator on a Hilbert space, points in the closure of its numerical range are characterized as either extreme, non-extreme boundary, or interior in terms of various associated sets of bounded sequences of vectors. These generalize similar results due to Embry, for points in the numerical range.
Unique solvability of the strong Hamburger moment problem
Authors: Njåstad Olav , Thron W. J.
Published: April 2009

Methods from the theory of orthogonal polynomials are extended to L-polynomials . By this means the authors and W. B. Jones (J. Math. Anal. Appl. 98 (1984), 528–554) solved the strong Hamburger moment problem, that is, given a double sequence , to find a distribution function ψ(t), non-decreasing, with an infinitenumber of points of increase and bounded on −∞ < t < ∞, such that for all integers . In this article further menthods such as analogues of the Lioville-Ostrogradski formula and of the Christoffel-Darboux formula are developed to investigated When the moment porblem has a unique solution. This will be the case if and only if a sequence of nested disks associated with the sequence has only a point as its intersection (the so called limit point case).
Torsion theories over semihereditary rings
Authors: Evans M. W.
Published: April 2009

In this paper the class of rings for which the right flat modules form the torsion-free class of a hereditary torsion theory (G, ℱ) are characterized and their structure investigated. These rings are called extended semihereditary rings. It is shown that the class of regular rings with ring homomorphism is a full co-reflective subcategory of the class of extended semihereditary rings with “flat” homomorphisms. A class of prime torsion theories is introduced which determines the torsion theory (G, ℱG). The torsion theory (JG, ℱG) is used to find a suitable generalisation of Dedekind Domain.
Homogeneous bundles and the trace of the heat kernel
Authors: Fegan H. D.
Published: April 2009

We study the heat equation on a homogeneous bundle over a compact Lie group. The trace of the heat kernel is explicitly calculated. By comparing this with the formula constructed form the eigenvalues (with multiplicities) of the Laplacian we obtain and unusual formula involving the Clebsch-Gordan numbers. The main method is to use invariance under conjugation to pass from the group to its maximal torus, where a direct calculation can be carried out.
Planarity and minimal path algorithms
Authors: Manaster Alfred B. , Remmel Jeffrey B. , Schmerl James H.
Published: April 2009

In 1981 two notions of effective presentation of countable connected graphs were formulated by J. C. E. Dekker—namely, edge recognition algorithm graphs and minimal path algorithm graphs. In this paper we show that every planar graph has a minimal path algorithm presentation but that some graphs have no minimal path algorithm presentations. We introduce the notion of a shortest distance algorithm graph, show that it lies strictly between the two notions of Dekker, and show that every graph has a shortest distance algorithm presentation. Finally, in contrast to Dekker's result about minimal path algorithm graphs, we produce a shortest distance algorithm graph which has no spanning tree which is an edge recognition algorithm graph.
The positive values of inhomogeneous ternary quadratic forms
Authors: Barnes E. S.
Published: April 2009

Let f(x, y, z) be an indefinite ternary quadratic form of signature (2, 1) and determinant d ≠ 0. Davenport [3] has shown that there exist integral x, y, z with, the equality sign being necessary if and only if f is a positive multiple of f1(x, y, z) = x2 + yz.
On paracompact regular spaces
Authors: Yuan Shuen
Published: April 2009

A topological space is paracompact if and only if each open cover of the space has an open locally finite refinement. It is well-known that an unusual normality condition is satisfied by each paracompact regular space X [p. 158, 5]: Let α be a locally finite (discrete) family of subsets of X, then there is a neighborhood V of the diagonal Δ(X) (in X × X), such that V[x] intersects at most a finite number of members (respectively at most one member) of {V[A]: A ∈ α} for each x ∈ X. In this not we will show that a variant of this condition actually characterizes paracompactness. Among other results, an improvement to a recent result of H. H.Corson [2] is given so as to accord with a conjecture of J. L. Kelley [p. 208, 5] more prettily, and we connect paracompactness to metacompactness [1]
Evaluation of determinant of 11th order in the theory of partitions
Authors: Hussain S. Manzur
Published: April 2009

Determinants [1] of 5th and 7th orders have already been discussed in connection with the Theorems 4 and 5 of Atkin and Swinnerton-Dyer [2]. The determinant under consideration occurs in the investigation of Dyson's rank function for q = 11 given by Atkin and Hussain [3]. As regards the notation it may be mentioned that the author has adopted the same as that of Atkin and Hussain [3].
The practical use of variation principles in the determination of the stability of non linear systems
Authors: Lyness J. N. , Blatt J. M.
Published: April 2009

We are interested in the motion of non linear systems. In this paper we use a variation principle and an iteration procedure in order to treat the stability of free oscillations against small disturbances of the initial conditions. It is found that approximations to the low lying stability lines can be obtained using the Rayleigh-Ritz variation principle and that these approximations can be consistently improved using an iteration procedure. These approximations are compared with the tabulated values in the special case of the Mathieu Equation. The results are in general a considerable improvement on those obtained using the usual Perturbation Theory, and have a much wider range of validity.
A property of an iteration process
Authors: Lyness J. N.
Published: April 2009

The familiar variation-iteration method for solving the eigenvalue equation Cψ = λBψ (C and B are Hermitean operators), is applied to a case in which the operator C, and hence also the eigenvalues λ, depend on a continuous parameter a. It is shown that certain exact properties of the functions λ = λ(a) can be deduced from low-order results in the variation-iteration scheme.
A characterisation of the moebius and similarity groups
Authors: Lorimer P. J.
Published: April 2009

Let PGL(2, F) denote the group of all Moebius transformations over a field F. In a recent paper [2], the author has given a characterisation of the groups PGL(2, F), F finite, char F ≠ 2. It is the purpose of this paper to give a similar characterisation of the group PGL (2, F), char F = 2, F finite or infinite.
Permutable power series and regular iteration
Authors: Baker I. N.
Published: April 2009

If f(z) is a power series convergent for |z| < ρ, where ρ > 0, then f(z) is said to have a fixpoint of multiplir a1 at z = 0. In the (local) iteration of f(z) one studies the sequence {fn(z)}, n = 0, 1, 2, … in a neighbourhood of z = 0, fn(z) benig defined by For many values of the multiplier a1, including 0 < |a1| < 1 and |a1| > 1, the local iteration of f(z) is completely mastered by the introduction of Schröder's functional equation.
On the Clifford collineation, transform and similarity groups. (III) Generators and involutions
Authors: Bolt Beverley
Published: April 2009

In this paper the Clifford groups PCT(pm), p > 2, PCG(pm) and CS'(pm), and the factor groups ½CS' (pm), which were defined in Paper I of this series (Bolt, Room and Wall [1]), are considered as transformations of projective [pm–1] over the complex field, C. We note that the geometrical results are the same if any of the corresponding groups CT, CG or GG and CS, respectively, are considered instead.
On certain identities involving basic spinors and curvature spinors
Authors: Buchdahl H. A.
Published: April 2009

The spinor analysis of Infeld and van der Waerden [1] is particularly well suited to the transcription of given flat space wave equations into forms which constitute possible generalizations appropriate to Riemann spaces [2]. The basic elements of this calculus are (i) the skew-symmetric spinor Γμν, (ii) the hermitian tensor-spinor σκ(img)ν(generalized Pauli matrices), and (iii) the curvature spinor Ρμνκι. When one deals with wave equations in Riemann spaces V4 one is apt to be confronted with expressions of somewhat bewildering appearance in so far as they may involve products of a large number of σ-symbols many of the indices of which may be paired in all sorts of ways either with each other or with the indices of the components of the curvature spinors. Such expressions are generally capable of great simplification, but how the latter may be achieved is often far from obvious. It is the purpose of this paper to present a number of useful relations between basic tensors and spinors, commonly known relations being taken for granted [3], [4], [5]. That some of these new relations appear as more or less trivial consequences of elementary identities is largely the result of a diligent search for their simplest derivation, once they had been obtained in more roundabout ways.