bluuebunny/crossref_metadata_2025 huggingface dataset:
A renorming theorem for dual spaces
Authors: Yorke A. C.
Published: April 2009

If the second dual of a Banach space E is smooth at each point of a certain norm dense subset, then its first dual admits a long sequence of norm one projections, and these projections have ranges which are suitable for a transfinite induction argument. This leads to the construction of an equivalent locally uniformly rotund norm and a Markuschevich basis for E*.
Non-reflexive double triangles
Authors: Longstaff W. E.
Published: April 2009

A double triangle subspace lattice in a Hilbert space H is a 5-element set of subspaces of H, containing (0) and H, with each pair of non-trivial elements intersecting in (0) and spanning H. It is shown that if any pair of non-trivial elements has a closed vector sum the double triangle is both non-reflexive and non-transitive. A double triangle in H⊕H is an operator double triangle if each non-trivial elements is the graph of an operator acting on H. A sufficient condition is given for any operator double triangle to be non-reflexive.
Central relations on lattices
Authors: Schweigert Dietmar
Published: April 2009

A maximal tolerance of a latticeLwithout infinite chains is either a congruence or a central relation. A finite latticeLis order-polynomially complete if and only ifLis simple and has no central relation.
The simultaneous representation of integers by products of certain rational functions
Authors: Elliott P. D. T. A.
Published: April 2009

It is proved that an arbitrary pair of positive integers can be simultaneously represented by products of the values at integer points of certain rational functions. Linear recurrences in Z-modules and elliptic power sums are applied.
On subgradient duality with strong and weak convex functions
Authors: Jeyakumar V.
Published: April 2009

A duality theorem of Wolfe for nonlinear differentiable programs is extended to nondifferentiable programs with strong and weak convex functions, by replacing gradients by local subgradient. A converse duality theorem is also proved.
Cp-classes of operators in C*-algebras
Authors: Giotopoulos S.
Published: April 2009

We construct a suitable representation of a C*-algebra that carries single elements to rank one operators. We also prove an abstract spectral theorem for compact elements in the algebra. This leads naturally to an abstract definition of Cp-classes of compact elements in the algebra.
Cumulants and partition lattices III: Multiply-indexed arrays
Authors: Speed T. P.
Published: April 2009

Earlier work of the author exploiting the role of partition lattices and their Mbius functions in the theory of cumulants, k-statistics and their generalisations is extended to multiply-indexed arrays of random variables. The natural generalisations of cumulants and k-statistics to this context are shown to include components of variance and the associated linear combinations of mean-squares which are used to estimate them. Expressions for the generalised cumulants of arrays built up as sums of independent arrays of effects as in anova models are derived in terms of the generalized cumulants of the effects. The special case of degree two, covering the unbiased estimation of components of variance, is discussed in some detail.
Semicontinuity of multifunctions connected with optimization with respect to cones
Authors: Sterna-Karwat Alicja
Published: April 2009

This paper studies topological upper and lower semicontinuity of the minimal value multifunction and the solution multifunction for optimization problems, which are defined in terms of cones, subject to perturbations in constraints. It extends the results of Tanino and Sawaragi to finite dimensions and one of Berge to multiple objective optimization problems.
Rings satisfying certain conditions either on subsemigroups or on endomorphisms
Authors: Cherubini A. , Varisco A.
Published: April 2009

We characterize rings whose multiplicative subsemigroups containing 0 and the additive inverse of each element are subrings. In addition we consider commutative rings for which every non-constant multiplicative endormorphism that preserves additive inverses is a ring endomorphism, and we show that they belong to one of three easily-described classes of rings.
Automorphism orbits of finite groups
Authors: Laffey Thomas J. , MacHale Desmond
Published: April 2009

Let G be a finite group and let Aut(G) be its automorphism group. Then G is called a k-orbit group if G has k orbits (equivalence classes) under the action of Aut(G). (For g, hG, we have g ~ h if ga = h for some Aut(G).) It is shown that if G is a k-orbit group, then kGp + 1, where p is the least prime dividing the order of G. The 3-orbit groups which are not of prime-power order are classified. It is shown that A5 is the only insoluble 4-orbit group, and a structure theorem is proved about soluble 4-orbit groups.
On a theorem of Fleischer
Authors: Mehta G.
Published: April 2009

Fleischer proved that a linearly ordered set that is separable in its order topology and has countably many jumps is order-isomorphic to a subset of the real numbers. The object of this paper is to extend Fleischer's result and to prove it in a different way. The proof of the theorem is based on Nachbin's extension to ordered topological spaces of Urysohn's separation theorem in normal topological spaces.
The ~ -representations of symmetric homogeneous algebras
Authors: Ward J. A.
Published: April 2009

In 1947 I. E. Segal proved that to each non-degenerate ~ -representation R of L1 (= L1 (G) for a compact group G) with representation space , there corresponds a continuous unitary representation W of G, also with representation space , which satisfies

for each fL1 and hk . This was extended to Lp,1 p < , in 1970 by E. Hewitt and K. A. Ross. We now generalize this result to any symmetric homogeneous convolution Banach alebra of pseudomeasures on G. Further we prove that the correspondence preserves irreduibility.
Orthogonal diagonal latin squares of order fourteen
Authors: Zhu L.
Published: April 2009

Orthogonal diagonal latin squares of order n, ODLS(n), are orthogonal latin squares of order n with transversals on both the main diagonal and the back diagonal of each square. It has been proven that ODLS(n) exist for all n except n = 2, 3, 6, 10, 14, 15, 18 and 26, in which the first three are impossible. In this note an example of ODLS(14) is given.
On the location of critical points of polynomials
Authors: Aziz Abdul
Published: April 2009

Let all the zeros of a polynomial P(z) of degree n lie in |z|≤ 1 and a be a given complex number. In this paper we study the location of the zeros of higher derivatives of the polynomial (z – z) P(z) and obtain certain generalizations of some results of Rahman and Rubinstein. We shall also extend a result of Goodman, Rahman and Ratti for the zeros of the polar derivative of the polynomial P(z) given P(l) = 0.
Recursive causal models
Authors: Kiiveri Harri , Speed T. P. , Carlin J. B.
Published: April 2009

The notion of a recursive causal graph is introduced, hopefully capturing the essential aspects of the path diagrams usually associated with recursive causal models. We describe the conditional independence constraints which such graphs are meant to embody and prove a theorem relating the fulfilment of these constraints by a probability distribution to a particular sort of factorisation. The relation of our results to the usual linear structural equations on the one hand, and to log-linear models, on the other, is also explained
Attaching graphs to pseudo-similar vertices
Authors: Kocay W. L.
Published: April 2009

Vertices u and v of a graph G are pseudo-similar if G – u ≅ G – v, but no automorphisms of G maps u to v. Let H be a graph with a distinguished vertex a. Denote by G(u. H) and G(v. H) the graphs obtained from G and H by identifying vertex a of H with pseudo-similar vertices u and v, respectively, of G. Is it possible for G(u.H) and G(v.H) to be isomorphic graphs? We answer this question in the affirmative by constructing graphs G for which G(u. H)≅ G(v. H).
On numerical ranges of generalized derivations and related properties
Authors: Shaw Sen-Yen
Published: April 2009

This paper is concerned with the numerical range and some related properties of the operator Δ/ S: T → AT – TB(T∈S), where A, B are (bounded linear) operators on the normed linear spaces X and Y. respectively, and S is a linear subspace of the space ℒ (Y, X) of all operators from Y to X. S is assumed to contain all finite operators, to be invariant under Δ, and to be suitably normed (not necessarily with the operator norm). Then the algebra numerical range of Δ/ S is equal to the difference of the algebra numerical ranges of A and B. When X = Y and S = ℒ (X), Δ is Hermitian (resp. normal) in ℒ (ℒ(X)) if and only if A–λ and B–λ are Hermitian (resp. normal) in ℒ(X)for some scalar λ;if X: = H is a Hilbert space and if S is a C *-algebra or a minimal norm ideal in ℒ(H)then any Hermitian (resp. normal) operator in S is of the form Δ/ S for some Hermitian (resp. normal) operators A and B. AT = TB implies A*T = TB* are hyponormal operators on the Hilbert spaces H1 and H2, respectively, and T is a Hilbert-Schmidt operator from H2 to H1.
An expansion method for singular perturbation problems
Authors: Mahony J. J.
Published: April 2009

A method is proposed for obtaining a uniformly valid perturbation expansion of the solution of a non-linear partial differential equation, involving either a large or small parameter, when the solution exhibits boundary layer type dependence on the parameter. The method differs from those previously in use in that it is not based on drawing a distinction between points in the boundary layer and points in the remainder of the field. Each point is treated as belonging to both regimes and this enables a stricter control to be maintained on the error terms in the expansions. The method is devised so as to ensure that all forms of error terms are reduced in order at each step in the expansion and not merely those error terms which are mathematically most significant for limiting values of the parameter. The perturbation series can then be used for a wider range of the parameter and provides a solution even when the boundary layer is not particularly thin.

The method is presented through its application to a problem which arises in the theory of the large deflexion of thin elastic plates but the principles underlying the method are more widely applicable.
A continuous-time treatment of certain queues and infinite dams
Authors: Loynes R. M.
Published: April 2009

The continuous-time behaviour of a model which represents certain queues and infinite dams with correlated inputs is considered. It is shown how the transient behaviour may be investigated, and the asymptotic behaviour is obtained. Finally the methods are illustrated for a queue whose input consists of two superimposed renewal processes.
Single server queues with modified service mechanisms
Authors: Yeo G. F.
Published: April 2009

This paper considers a generalisation of the queueing systemM/G/I, where customers arriving at empty and non-empty queues have different service time distributions. The characteristic function (c.f.) of the stationary waiting time distribution and the probability generating function (p.g.f.) of the queue size are obtained. The busy period distribution is found; the results are generalised to an Erlangian inter-arrival distribution; the time-dependent problem is considered, and finally a special case of server absenteeism is discussed.
The continuity of derivations and module homomorphisms
Authors: Willis G. A.
Published: April 2009

This paper is concerned with the problem of automatic continuity of derivations from group algebras L1(G) is a locally compact group, and convolution algebras L1(ω), where ω is a weight function. In the case of group algebras, it is shown that either the problem reduces to the case when G is the free group on a countably infinite number of generators or there is a non-discrete group G with a discontinuous l1(G)-bimodule homomorphism from L1(G). It is also shown that every derivation from L1(G) to a commutative L1(G)-bimodule is continuous. Similar results are obtained for weighted convolution algebras.
Lattices of homomorphisms
Authors: Davey B. A. , Priestley H. A.
Published: April 2009

Given a variety K of lattice-ordered algebras, A ∈ K is catalytic if for all B ∈ K, K(A, B) is a lattice for the pointwise order. The catalytic objects are determined for various varieties of distributive-lattice-ordered algebras. The characterisations obtained do not show an overall unity and exhibit diverse behaviour. Duality is employed extensively. Its usefulness in this context depends on the existence of an order-isomorphism between K(A, B) and the corresponding dual horn-set. Criteria for the existence of such an order-isomorphism are investigated for dualities of the Davey-Werner type. The relationship between catalytic objects and colattices is also discussed.
Tetrads of Möbius tetrahedra
Authors: Mandan Sahib Ram
Published: April 2009

A tetrad of Möbius tetrahedra consists of a set of 4 mutually inscribed and therefore circumscribed tetrahedra whose 16 vertices and 16 faces form a Kummer's 166 configuration (5; 11; 12; 21). As pointed out by the refere, fundamental to all work on the 166 figure are the 10 quadrics, called fundamental for the associated Kummer's quartic surface (13). To every quadric F correspond a matrix scheme of the 16 points or planes, arranged in 4 rows or columns, such that the 8 Rosenhain tetrahedra (7) formed of the rows and columns are all self-polar for F. The rows form one and the columns another tetrad of Mobius tetrahedra. Nine new schemes can be derived from one such scheme to make the total ten as explained by Baker (3, p. 133) leading to 80 Rosenhain tetrahedra in all. The 16 nodes (5; 8) or tropes of the Rummer's quartic are the 16 common elements of the 10 schemes such that the nodes and tropes are poles and polars for any one of the 10 quadrics. Each trope touches the quartic along a singular conic through the 6 points of the figure lying therein. The lines tangent to the surface at its each node N generate a quadric cone which is enveloped by the 6 tropes through N (12).
Integral operator methods for generalized axially symmetric potentials in (n+1) variables
Authors: Gilbert R. P. , Howard H. C.
Published: April 2009

In this paper we shall use the integral operator method of Bergman, B[1–6], to investigate solutions of the partial differential equation where s > −1. In particular, information concerning the growth, and location of singularities, of solutions of (1.1) will be obtained. Equations of the form (1.1) with s = 1, 2, arise from the (n+k+1)-dimensional Laplace equation Δn+k+1u = 0 in the “axially symmetric” coordinates x1, …xn, p where the relationship between cartesian and “axially symmetric” coordinates is given by
The propagation of plane waves in plastic solids
Authors: Cooper G. J. , Craggs J. W.
Published: April 2009

Equations describing a possible mode of propagation of plane waves in isotropic plastic solids are solved numerically.
On the rate of convergence of waiting times
Authors: Cheong C. K. , Heathcote C. R.
Published: April 2009

LetK(y) be a known distribution function on (−∞, ∞) and let {Fn(y),n= 0, 1,…} be a sequence of unknown distribution functions related bysubject to the initial conditionIf the sequence {Fn(y)} converges to a distribution functionF(y) thenF(y) satisfies the Wiener-Hopf equation
On functions of bounded ω-variation, II
Authors: Bhakta P. C.
Published: April 2009

Let ω(x) be a non-decreasing function defined in the interval [a, b]. We extend the definition to all x by taking ω(x) = ω(a) for x < a and ω(x) = ω(b) for x > b. R. L. Jeffery [2] has denoted by the class of functions F(x) defined as follows:
On the sign of a multiple integral
Authors: Mordell L. J.
Published: April 2009

One proof of Minkowski's fundamental theorem on lattice points in an n-dimensional parallelopiped depends upon a multiple Fourier expansion. Its terms involve multiple integrals which are easily evaluated and so are shown to have positive values. Then the expansion takes only positive values and the desired proof follows at once. It seems of interest to note a multiple integral which assumes only positive values.
On certain direct sum decompositions of L1 spaces
Authors: Edwards R. E.
Published: April 2009

Let L1 denote temporarily the usual Lebesgue space over the circle group (equivalently: the additive group of real numbers modulo 2π), and let H1 denote the Hardy space comprised of those f in L1 whose complex Fourier coefficients vanish for all negative frequencies, so tha D. J. Newman has settled a conjecture by showing [1] that there exists no continuous projuction of L1 onto H1, i.e. that there exists in L1 no topological complement to H1.
Minimal Hausdorff and maximal compact spaces
Authors: Smythe N. , Wilkins C. A.
Published: April 2009

Given two topologies J1, J2 on a set X, J1 is said to be coarser than J2, written J1 ≦ J2, if every set open under J1 is open under J2. A minimal Hausdorff space is then one for which there is no coarser Hausdorff topology etc. Vaidyanathaswamy [4] showed that every compact Hausdorff space is both maximal compact and minimal Hausdorff. This raised the question of whether there exist minimal Hausdorff non-compact spaces and/or maximal compact non-Hausdorff spaces. These questions were in fact answered in the affirmative by Ramanathan [2], Balachandran [1], and Hing Tong [3]. Their examples were, however, all on countable sets, and the topology constructed to answer one question bore no relation to the topology answering the second. In particular, the minimal Hausdorff non-compact topologies were not finer than any maximal compact topology.
On T-systems of groups
Authors: Dunwoody M. J.
Published: April 2009

Let G be an n-generator group and let g = (g1, g2, …, gn) be an ordered set of n elements which generate G, then g is called a generating n-vector of G. Let denote the set of all generating n-vectors of G.
Coefficients for the study of Runge-Kutta integration processes
Authors: Butcher J. C.
Published: April 2009

We consider a set of η first order simultaneous differential equations in the dependent variables y1, y2, …, yn and the independent variable x ⋮ No loss of gernerality results from taking the functions f1, f2, …, fn to be independent of x, for if this were not so an additional dependent variable yn+1, anc be introduced which always equals x and thus satisfies the differential equation
On the integration processes of A. Huťa
Authors: Butcher J. C.
Published: April 2009

Huta [1], [2] has given two processes for solving a first order differential equation to sixth order accuracy. His methods are each eight stage Runge-Kutta processes and differ mainly in that the later process has simpler coefficients occurring in it.
A family of simple groups associated with the Satake diagrams
Authors: Chonhu Cheng
Published: April 2009

Using the theory of the Satake diagrams associated with the non-compact simple Lie algebras over the real number field R, we shall construct a family of simple groups over a field K which are called the simple groups associated with the Satake diagrams. The list of these simple groups includes all Chevalley groups and twisted groups, and all simple algebraic groups of adjoint type defined over R if K is the complex number field C (except two types given by Table II′). Furthermore, the simple groups associated with the Satake diagrams of type AIII, BI, DI are identified with the simple groups obtained from the unitary or orthogonal groups of non-zero indices. The quasi-Bruhat decomposition of the “non-split” simple groups associated with the Satake diagrams which are not Chevalley groups or twisted groups will be given in this paper.
An approximation method for monotone Lipschitzian operators in Hilbert spaces
Authors: Chidume C. E.
Published: April 2009

Suppose H is a complex Hilbert space and K is a nonempty closed convex subset of H. Suppose T: K → H is a monotomc Lipschitzian mapping with constant L ≧ 1 such that, for x in K and h in H, the equation x + Tx Tx = h has a solution q in K. Given x0 in K, let {Cn}∞n=0 be a real sequence satisfying: (i) C0 = 1, (ii) 0 ≦ Cn < L-2 for all n ≧ 1, (iii) ΣnCn(1 − Cn) diverges. Then the sequence {Pn}∞n=0 in H defined by pn = (1 − Cn)xn + CnSxn, n ≧ 0, where {xn}∞n=0 in K is such that, for each n ≧ 1, ∥ xn – Pn−1 ∥ = infx ∈ k ∥ Pn−1 − x ∥, converges strongly to a solution q of x + Tx = h. Explicit error estimates are given. A similar result is also proved for the case when the operator T is locally Lipschitzian and monotone.
On extremal points of the unit ball in the Banach space of Lipschitz continuous functions
Authors: Rolewicz S.
Published: April 2009

It is shown that for arbitrary ε > 0 there is a function x(t, x) defined on the square [0,1] × [0,1] such that x(t, s) represents an extremal point of the unit ball in the space of Lipschitz continuous functions, and the gradient of x(t, s) is equal to 0 except on a set of measure at most ε.
A Riemann integral in a locally compact Hausdorff space
Authors: Ahmed S. I. , Pfeffer W. F.
Published: April 2009

We present a systematic and self-contained exposition of the generalized Riemann integral in a locally compact Hausdorff space, and we show that it is equivalent to the Perron and variational integrals. We also give a necessary and sufficient condition for its equivalence to the Lebesgue integral with respect to a suitably chosen measure.
A Property of completely monotonic functions
Authors: O'Cinneide Colm
Published: April 2009

A non-negative function f(t), t > 0, is said to be completely monotonic if its derivatives satisfy (-1)n fn (t) ≥ 0 for all t and n = 1, 2, …, For such a function, either f(t + δ) / f(t) is strictly increasing in t for each δ > 0, or f(t) = ce-dt for some constants c and d, and for all t. An application of this result is given.
Subnormal subgroups in direct products of groups
Authors: Hauck Peter
Published: April 2009

A groupGis callednormally (subnormally) detectableif the only normal (subnormal) subgroups in any direct productG1× … ×Gnof copies ofGare just the direct factorsGi. We give an internal characterization of finite subnormally detectable groups and obtain analogous results for associative rings and for Lie algebras. The main part of the paper deals with a study of normally detectable groups, where we verify a conjecture of T. O. Hawkes in a number of special cases.
Mal'cev products of varieties of completely regular semigroups
Authors: Jones P. R.
Published: April 2009

Whilst the Mal'cev product of completely regular varieties need not again be a variety, it is shown that in many important instances a variety is in fact obtained. However, unlike the product of group varieties this product is nonassociative.

Two important operators introduced by Reilly are studied in the context of Mal'cev products. These operators are shown to generate from any given variety one of the networks discovered by Pastijn and Trotter, enabling identities to be provided for the varieties in the network. In particular the join O V BG of the varieties of orthogroups and of bands of groups is determined, answering a question of Petrich.
Smooth derivations on abelian C*-dynamical systems
Authors: Robinson Derek W.
Published: April 2009

Let (A, R, σ) be an abelian C*-dynamical system. Denote the generator of σ by δ0 and define A∞ = ∩n>1D (δ0n). Further define the Lipschitz algebra
.

If δ is a *-derivation from A∞ into A½, then it follows that δ is closable, and its closure generates a strongly continuous one-parameter group of *-automorphisms of A. Related results for local dissipations are also discussed.
A concrete realization of the dual space of L1-spaces of certain vector and operator-valued measures
Authors: Ricker Werner
Published: April 2009

For a given vector measure n, an important problem, but in practice a difficult one, is to give a concrete description of the dual space of L1(n). In this note such a description is presented for an important class of measures n, namely the spectral measures (in the sense of N. Dunford) and certain other vector and operator-valued measures that they naturally induce. The basic idea is to represent the L1-spaces of such measures as a more familiar space whose dual space is known.
The ℋ-equivalence in a compact semigroup II
Authors: Anderson L. W. , Hunter R. P.
Published: April 2009

In [1] we considered various aspects of the quotient semigroup H. · H2 where H is an ℋ-class of a semigroup S. In particular, the action of the Schützenberger group of H upon SH was studied to obtain various results on the existence of subcontinua. Crucial in [1] was the notion of the (right handed) core of an ℋ-class which may be considered as a generalization of the notion of the core of a homogroup, [2].
Irreducible continua and generalization of hereditarily unicoherent continua by means of membranes
Authors: Dickman R. F. , Rubin L. R. , Swingle P. M.
Published: April 2009

In [2] we defined an irreducible B(J)-cartesian membrane, and used this to obtain a characterization of an n-sphere by generalizing the definition of simple closed curve given by Theorem 1.2 below. There B(J) is a class A(n) of (n−1)-spheres, but here it is a class of mutually homeomorphic continua. In Theorem 1.1 we give a definition of hereditarily unicoherent continua and generalize this in Section 3 by means of B(J)-cartesian membranes. To do this we paraphrase by a translation some of Wilder's work in [7]. In his Unified Topology [8: p. 674] he gives a principle: “The connectedness of a domain is a special case of the bounding properties of its i-cycles”. We substitute the element J of B(J) for the i-cycle and for “bound” we substitute that “J membrane-bases an irreducible B(J)-cartesian membrane. The very nature of an i-cycle seems to limit the complexity of the point set studied, although the restriction to “nice” manifolds is due partly to the difficulty of the subject matter treated. There are similar difficulties here, but also advantages, in the very general set-theoretic approach by means of B(J)-membranes.
A queueing system with moving average input process and batch arrivals
Authors: Pearce C.
Published: April 2009

In a recent paper by P. D. Finch and myself [1], the solution for the limiting distribution of a moving average queueing system was obtained. In this paper the system is generalised to the case of batch arrivals in batches of size ρ > 1.
On symmetry in periodic solutions of hamiltonian systems
Authors: Jones Arthur R.
Published: April 2009

In this paper the theory of periodic solutions of analytic Hamiltonian systems of differential equations, which is due to Cherry [5], is specialized to systems which have one symmetry property.
On the measure of the one-skeleton of the sum of convex compact sets
Authors: Dalla Leoni
Published: April 2009

For any two compact convex sets in a Euclidean space, the relation between the volume of the sum of the two sets and the volume of each of them is given by the Brünn-Minkowski inequality. In this note we prove an analogous relation for the one-dimensional Hausdorff measure of the one-skeleton of the above sets. Also, some counterexamples are given which show that the above results are the best possible in some special cases.
Exact coverings of triples with specified longest block length
Authors: Stanton R. G. , Allston J. L.
Published: April 2009

A minimal (1,3; ν) covering occurs when we have a family of proper subsets selected from ν elements with the property that every triple occurs exactly once in the family and no family of smaller cardinality possesses this property. Woodall developed a lower bound W for the quantity g(k)(1, 3; ν) which represents the cardinality of a minimal family with longest block of length k. The Woodall bound is only accurate in the region when k ≥ ν/2. We develop an expression for the excess of the true value over the Woodall bound and apply this to show that, when k ≥ ν/2, the value of g(1,3; ν) = W + 1 when k is even and W + 1 + when k is odd.
A note on a functional equation
Authors: An Chung-Ming
Published: April 2009

The object of this note is to give an aspect to the problem of the functional equation of the generalized gamma function and Dirichlet series which are defined in [1]. In general, we cannot answer the problem yet. But it is worthy to attack this problem for some special cases.
On orders and types of an entire function over 𝒞k
Authors: Krishna J. Gopala , Rao I. H. Nagaraja
Published: April 2009

The concepts of order and type associated with an entire function over the complex plane admit different “natural” extensions, most of which are in vogue, for the case of an entire function over 𝒞k, the cartesian product of k copies of the complex plane. This work is concerned with the relations among such extended concepts and with the analogous properties of the concepts.
A note on central group extensions
Authors: Hauptfleisch G. J.
Published: April 2009

If A, B, H, K are abelian group and φ: A → H and ψ: B → K are epimorphisms, then a given central group extension G of H by K is not necessarily a homomorphic image of a group extension of A by B. Take for instance A = Z(2), B = Z ⊕ Z, H = Z(2), K = V4 (Klein's fourgroup). Then the dihedral group D8 is a central extension of H by K but it is not a homomorphic image of Z ⊕ Z ⊕ Z(2), the only group extension of A by the free group B.
Denominator sequences of continued fractions II
Authors: Worley R. T.
Published: April 2009

In part I, I considered the problem of discovering when, given an irrational α which has a simple continued fraction representation with convergents pn/qn, there exists α' for which the denominator sequence for convergents is a subsequence of (qn). It was shown that such an α' exists if the continued fraction representation was “nearly periodic” with odd period. The following is a generalization of the results of part I to semi-regular continued fractions, where the problem seems to fit more naturally.
Fibre bundles and Yang-Mills fields
Authors: Smrz P. K.
Published: April 2009

Since 1954, when Yang and Mills [7] presented their idea of isotopic gauge transformation, the method of introducing interactions into field theories by using general gauge invariance has been extensively studied.

A general formalism was presented by Utiyama [6]. Reference [6] also contains the first application of the formalism to the theory of gravitation. A more general approach to the Young-Mills formalism applied to general relativity was described by Kibble [3]. In a special case of interacting Dirac field the gauge invariance group can still be enlarged, leading to the possibility of describing short-range interactions together with gravitation and electromagnetism [5]. It is, therefore important to have a definite formulation of the common geometrical content of such theories.
Compactifications of semitopological semigroups
Authors: Milnes Paul
Published: April 2009

Suppose S is a semitopological semigroup. We consider various subspaces of C(S) and determine what topological algebraic structure can be introduced into the spaces of means on the subspaces and into the spectra of the C*-sub-algebras of C(S) they generate.
An expansion for the permanent of a doubly stochastic matrix
Authors: Griffiths R. C.
Published: April 2009

The permanent of an n-square matrix A = (aij) is defined by where Sn is the symmetric group of order n. Kn will denote the convex set of all n-square doubly stochastic matrices and K0n its interior. Jn ∈ Kn will be the matrix with all elements equal to 1/n. If M ∈ K0n, then M lies on a line segment passing through Jn and another B ∈ Kn — K0n. This note gives an expansion for the permanent of such a line segment as a weighted average of permanents of matrices in Kn. For a survey article on permanents the reader is referred to Marcus and Mine [3].
Modular inverse semigroups
Authors: Johnston Katherine G. , Jones Peter R. , Hall T. E.
Published: April 2009

An inverse semigroup S is said to be modular if its lattice 𝓛𝓕 (S) of inverse subsemigroups is modular. We show that it is sufficient to study simple inverse semigroups which are not groups. Our main theorem states that such a semigroup S is modular if and only if (I) S is combinatorial, (II) its semilattice E of idempotents is “Archimedean” in S, (III) its maximum group homomorphic image G is locally cyclic and (IV) the poset of idempotents of each 𝓓-class of S is either a chain or contains exactly one pair of incomparable elements, each of which is maximal. Thus in view of earlier results of the second author a simple modular inverse semigroup is “almost” distributive. The bisimple modular inverse semigroups are explicitly constructed. It is remarkable that exactly one of these is nondistributive.
Congruences and Green's relations on eventually regular semigroups
Authors: Edwards P. M. , Hall T. E.
Published: April 2009

A semigroup is eventually regular if each of its elements has some power that is regular. Let 𝓚 be one of Green's relations and let ρ be a congruence on an eventually regular semigroupS. It is shown for 𝓚 = 𝓛, 𝓡 and 𝓓 that ifAandBare regular elements ofS/ρ that are 𝓚-related inS/ρ then there exist elementsa∈A,b∈Bsuch thataandbare 𝓚-related inS. The result is not true for 𝓗 or 𝓙.
A non-absolutely summing operator
Authors: Maddox I. J. , Price J. F.
Published: April 2009

In the case when 0 < p < 1 it is proved, using a method of Macphail that the identity map i: lp → lp is not (r, s)-absolutely summing for any r, s.
A uniformly strongly prime radical
Authors: Olson D. M. , Lidl R.
Published: April 2009

The class of all uniformly strongly prime rings is shown to be a special class of rings which generates a radical class which properly contains both the right and left strongly prime radicals and which is independent of the Jacobson and Brown-McCoy radicals.
On the Spectrum of almost periodic solutions of an abstract differential equation
Authors: Rao Aribindi Satyanarayan , Hengartner Walter
Published: April 2009

If a linear operator A in a Banach space satisfies certain conditions, then the spectrum of any almost periodic solution of the differential equation u′ = Au + f is shown to be identical with the spectrum of f, where f is a Stepanov almost periodic function.
Semirings with a completely 0-simple additive semigroup
Authors: Grillet Mireille P.
Published: April 2009

In a previous paper [2], we gave an explicit description of the structure of all semirings with a completely simple additive semigroup. The next step is then clearly to consider semirings with a completely 0-simple additive semigroup. We are able to classify these semirings according to the multiplicative nature of their additive zero. Let R be a semiring whose additive semigroup is completely 0-simple with zero ∞. First, if ∞ ∞ ≠ ∞, then the multiplication of R is trivial. Besides these trivial semirings, another class of semirings with a completely 0-simple additive semigroup can be easily obtained by adjoining an element ∞ which is together an additive zero and a multiplicative zero.
Connectedness in the scale of uniform subspaces of R
Authors: Richardson G. D.
Published: April 2009

Kent [4] showed that each uniform space (S, u) could be embedded in a complete, uniform lattice, called the scale of (S, u). The scale was first introduced by Bushaw [3] for studying stability in topological dynamics. In [5], the notions of connectedness and local connectedness were studied. This note is a follow-up of [5]; the purpose being to characterise the uniform subspaces of the reals, R, which have connected (locally connected) scales. The reader is asked to refer to [5] for definitions and notation not given here.
A special class of near rings
Authors: Ligh Steve
Published: April 2009

A near ring is a triple (R, +, · ) such that (R, + ) is a group, (R, ·) is a semigroup, and · is left distributive over +; i.e. w(x + z) = wx + wz for each w, x, z in R. A normal subgroup K of a near ring R is an ideal if (i) (m + k)n − mn is in K for all m, n in R and k in K, and (ii) RK ⊆ K. In particular, kernels of near ring homomorphisms are ideals. For various other definitions and elementary facts about near rings, see [5,8]. For each x in a near ring R, let A(x) = {y ∈ R: xy = 0}. A survey on several recent papers on near rings [2,3,6,7,8] shows that the concept of A(x) being an ideal was the main technique. The purpose of this note is to initiate a study of near rings having the property that each A(x) is an ideal.
A remark on free topological groups with no small subgroups
Authors: Thompson H. B.
Published: April 2009

For a completely regular space X let G(X) be the Graev free topological group on X. While proving G(X) exists for completely regular spaces X, Graev showed that every pseudo-metric on X can be extended to a two-sided invariant pseudo-metric on the abstract group G(X). The free group topology on G(X) is usually strictly finer than this pseudo-metric topology. In particular this is the case when X is not totally disconnected (see Morris and Thompson [7]). It is of interest to know when G(X) has no small subgroups (see Morris [5]). Morris and Thompson [6] showed that this is the case if and only if X admits a continuous metric. The proof relied on properties of the free group topology and it is natural to ask if G(X) with its pseudo-metric topology has no small subgroups when and only when X admits a continuous metric. We show that this is the case. Topological properties of G(X) associated with the pseudo-metric topology have recently been studied by Joiner [3] and Abels [1].
Generalised Markovian control systems
Authors: Kloeden P. E.
Published: April 2009

The qualitative behaviour of control systems based on ordinary differential equations has been investigated with clarity and elegance using axiomatically defined General Control Systems. Here an attainablity set function, evolving in semigroup fashion, is the main entity of interest [1], [2], [3], [4].
Ideal topology on a distrbutive lattice
Authors: Murty P. V. Ramana
Published: April 2009

In [1] Atherton has asked whether the ideal topology (see [1]) is Hausdorff on every distributive lattice. He also gave some sufficient conditions (Kent's conditions cl and c3 [1]) under which the ideal topology on a complete distributive lattice is Hausdorff. In this paper we determine some more classes of lattices in which the ideal topology is Hausdorff and give examples to show that the classes determined are independent even in a complete distributive lattice. We also show by an example that Atherton's conditions are not necessary even in the case of a complete distributive lattice.
A geometrical approach to approximations by continued fractions
Authors: Kopetzky H. G. , Schnitzer F. J.
Published: April 2009

By simple geometrical considerations new proofs for some classical results are given and also new theorems about approximation by continued fractions are derived. This geometrical approach presents an instructive visualisation of the nature of proximation theorems.
A class of hypergeometric polynomials
Authors: Srivastava H. M.
Published: April 2009

The object of the present paper is first to derive an interesting unification (and generalization) of a fairly large number of finite summation formulas including, for example, those that appeared in this Journal recently. We then briefly remark on its various (known or new) special cases which are associated with certain classes of hypergeometric polynomials in one and two variables. We also give several further generalizations (involving multiple series with essentially arbitrary terms) which are shown to be applicable in the derivation of analogous summation formulas for hypergeometric series (and polynomials) in three and more variables. Finally, with a view to presenting relevance of these types of results in various seemingly diverse areas of applied sciences and engineering, some indication of applicability is provided.
Irreducibility of the analytic continuation of the principal series of a free group
Authors: Mantero Anna Maria , Zappa Anna
Published: April 2009

In this paper it is proved that the principal series of representations of Γ = Z2*…*Z2 may be analytically continued to give uniformly bounded representations on the same Hilbert space, and that these representations are irreducible. Further, the reducibility of the restrictions to Γ ⊂ SL(2, Qp) of the irreducible unitary representations of SL(2, Qp) is examined.
Coin tossing and sum sets
Authors: Brown Gavin , Williamson John H.
Published: April 2009

We consider the distribution μ of numbers whose binary digits are generated from infinitely many tosses of a biased coin. It is shown that, if E has positive μ measure, then some n-fold sum of E with itself must contain an interval. This contrasts with the known result that all convolution powers of μ are singular.
The Hadamard conjecture and integer lattices
Authors: McCall J. , Little C. H. C.
Published: April 2009

Let L be an integer lattice, and S a set of lattice points in L. We say that S is optimal if it minimises the number of rectangular sublattices of L (including degenerate ones) which contain an even number of points in S. We show that the resolution of the Hadamard conjecture is equivalent to the determination of |S| for an optimal set S in a (4s-1) × (4s-1) integer lattice L. We then specialise to the case of 1 × n integer lattices, characterising and enumerating their optimal sets.
On equivalence of analytic functions to rational regular functions
Authors: Kucharz Wojciech
Published: April 2009

We give sufficient conditions for an analytic function from Rnto R to be analytically equivalent to a rational regular function.
Orthogonality relations on Abelian groups
Authors: Davis G.
Published: April 2009

Abstract: An orthogonality relation is an abstract relation on a group having properties similar to the relation on a l-group given by x ⊥ y if ¦x¦ ∧¦y│ = 0. A group G with an orthogonality relation ⊥ is isomorphically represented as a subgroups of the group Γ of continuous global sections of a sheaf of groups. If the stalks of the sheaf are torsion-free and G has and element 1 satisfying 1 ⊥ = (0) then Γ can be ordered so that is is an l-group and x ⊥ y if and only if │x¦ ∧ ¦y¦ = 0 in Γ. An l-group G is complemented if for all x, y ∈ G there is an a ∈ x⊥ ⊕ x⊥⊥ with y ∈ a⊥⊥: equivalent conditions are given for G to be complemented.
Generalized Boolean lattices
Authors: Byrd Richard D. , Mena Roberto A. , Troy Linda A.
Published: April 2009

Hashimoto (1952; Theorems 8.3 and 8.5) proved the following theorems: Theorem A. If L, is a distributive lattice, then there exists a generalized Boolean alegbra Lr and an isomorphism from the lattice of all congruence relations of L onto the lattice of all congruence relations of Lr.
Finitely generated pseudocomplemented distributive lattices
Authors: Berman J. , Dwinger ph.
Published: April 2009

If L is a pseudocomplemented distributive lattice which is generated by a finite set X, then we will show that there exists a subset G of L which is associated with X in a natural way that ¦G¦ ≦ ¦X¦ + 2¦x¦ and whose structure as a partially ordered set characterizes the structure of L to a great extent. We first prove in Section 2 as a basic fact that each element of L can be obtained by forming sums (joins) and products (meets) of elements of G only. Thus, L considered as a distributive lattice with 0,1 (the operation of pseudocomplementation deleted), is generated by G. We apply this to characterize for example, the maximal homomorphic images of L in each of the equational subclasses of the class Bω of pseudocomplemented distributive lattices, and also to find the conditions which have to be satisfied by G in order that X freely generates L.
Typical Convex Sets of Convex Sets
Authors: Schwarz T. , Zamfirescu T.
Published: April 2009

There exists a natural notion of convexity in the space of all compact convex sets in D. Thus, we may consider the space of all bounded closed convex families of compact convex sets. We present here a strange generic extremal behaviour of the elements of this space.
Convolutions of Distributions With Exponential and Subexponential Tails
Authors: Cline Daren B. H.
Published: April 2009

Distribution tails F(t) = F(t, ∞) are considered for which and as t → ∞. A real analytic proof is obtained of a theorem by Chover, Wainger and Ney, namely that .

In doing so, a technique is introduced which provides many other results with a minimum of analysis. One such result strengthens and generalizes the various known results on distribution tails of random sums.

Additionally, the closure and factorization properties for subexponential distributions are investigated further and extended to distributions with exponential tails.
On a Conjecture of Carlitz
Authors: Daqing Wan
Published: April 2009

A conjecture of Carlitz on permutation polynomials is as follow: Given an even positive integer n, there is a constant Cn, such that if Fq is a finite field of odd order q with q > Cn, then there are no permutation polynomials of degree n over Fq. The conjecture is a well-known problem in this area. It is easily proved if n is a power of 2. The only other cases in which solutions have been published are n = 6 (Dickson [5]) and n = 10 (Hayes [7]); see Lidl [11], Lausch and Nobauer [9], and Lidl and Niederreiter [10] for remarks on this problem. In this paper, we prove that the Carlitz conjecture is true if n = 12 or n = 14, and give an equivalent version of the conjecture in terms of exceptional polynomials.
Motion Groups and Absolutely Convergent Fourier Transforms
Authors: Gaudry Garthi , Pini Rita
Published: April 2009

According to an extension of a classical theorem of Bernstein, due to C. Herz, a function on Rn belonging to a Besov space of appropriate order has an absolutely convergent Fourier transform. We establish extensions of this result to Cartan motion groups, for Besov spaces defined with respect to both isotropic and non-isotropic differences.
Banach Algebras Which are a Direct Sum of Division Algebras
Authors: Lopez Antonio Fernandez , Rus Eulalia Garcia
Published: April 2009

In this note it is proved that a (real or complex) semiprime Banach algebra A satisfying xAx = x2Ax2 for every x ∈ A is a direct sum of a finite number of division Banach algebras.
An Inequality Implicit Function Theorem
Authors: Ng Kung-Fu
Published: April 2009

Let f be a continuous function, and u a continuous linear function, from a Banach space into an ordered Banach space, such that f − u satisfies a Lipschitz condition and u satisfies an inequality implicit-function condition. Then f also satisfles an inequality implicit-function condition. This extends some results of Flett, Craven and S. M. Robinson.
On the Integral Modulus of Continuity of Fourier Series
Authors: Ram Babu , Kumari Suresh
Published: April 2009

For a wide class of sine trigonometric series we obtain an estimate for the integral modulus of continuity.
On Dual Radicals and Ring Elements
Authors: De La Rosa B. , Wiegandt R.
Published: April 2009

If a property P of ring elements satisfies conditions (a)-(d), then the largest homomorphically closed class having no non-zero P-element is a dual radical in the sense of Andrunakievič, and every dual radical can be obtained in this way. Also properties defined by polynomials are considered and as an application we get various characterizations of the Behrens radical.
Sampling Without Replacement: Approximation to the Probability Distribution
Authors: Darroch J. N. , Jirina M. , Speed T. P.
Published: April 2009

Let P be the probability distribution of a sample without replacement of size n from a finite population represented by the set N={1,2,…N}. For each r=0, 1, …, an approximation Pr is described such that the uniform norm ‖P − Pr‖ is of order (n2/N)r+1 if n2/N→0. The approximation Pr is a linear combination of uniform probability product-measures concentrated on certain subspaces of the sample space Nn.