bluuebunny/crossref_metadata_2025_split huggingface dataset:
Objets compacts dans les topos
Authors: Dubuc Eduardo J. , Penon Jacques 
Published: April 2009

AbstractIt is well known that compact topological spaces are those space K for which given any point x0 in any topological space X, and a neighborhood H of the fibre -1 {x0} KXX, then there exists a neighborhood U of x0 such that -1UH. If now is an object in an arbitrary topos, in the internal logic of the topos this property means that, for any A in and B in K, we have (-1AB)=AB. We introduce this formula as a definition of compactness for objects in an arbitrary topos. Then we prove that in the gross topoi of algebraic, analytic, and differential geometry, this property characterizes exactly the complete varieties, the compact (analytic) spaces, and the compact manifolds, respectively.
On concircular transformations in Riemannian spaces
Authors: Chongshan Luo 
Published: April 2009

AbstractThis paper introduces a tensor that contains the Riemannian curvature tensor and the conformal curvature tensor as special examples in the Riemannian space (Mn, g), and by using this tensor we define C-semi-symmetric space. In this paper, we have the following main result: if there is a non-trivial concircular transformation between two C-semi-symmetric spaces, then both spaces are of quasi-constant curvature.
On vector lattice-valued measures II
Authors: Panchapagesan T. V. , Palled Shivappa Veerappa 
Published: April 2009

AbstractFor a weakly (, )-distributive vector lattice V, it is proved that a V {}-valued Baire measure 0 on a locally compact Hausdorff space T admits uniquely regular Borel and weakly Borel extensions on T if and only if 0 is strongly regular at . Consequently, for such a vector lattice V every V-valued Baire measure on a locally compact Hausdorff space T has unique regular Borel and weakly Borel extensions. Finally some characterisations of a weakly (, )-distributive vector lattice are given in terms of the existence of regular Borel (weakly Borel) extensions of certain V {}-valued Barie measures on locally compact Hausdorff spaces.
Decomposable graphs and hypergraphs
Authors: Lauritzen S. L. , Speed T. P. , Vijayan K. 
Published: April 2009

AbstractWe define and investigate the notion of a decomposable hypergraph, showing that such a hypergraph always is conformal, that is, can be viewed as the class of maximal cliques of a graph. We further show that the clique hypergraph of a graph is decomposable if and only if the graph is triangulated and characterise such graphs in terms of a combinatorial identity.
Alexander polynomials of two-bridge links
Authors: Kanenobu Taizo 
Published: April 2009

AbstractWe provide an algorithm for calculating the Alexander polynomial of a two-bridge link by putting every two-bridge link in a special type of Conway diagram. Using this algorithm, some necessary conditions for a polynomial to be the Alexander polynomial of a two-bridge link are given, in particular, certain alternating and monotonicity conditions on the coefficients, analogous to corresponding known properties of the reduced Alexander polynomial.
Monogenic inverse semigroups
Authors: Preston G. B. 
Published: April 2009

AbstractWe give a survey of some of the realisations that have been given of monogenic inverse semigroups and discuss their relation to one another. We then analyse the representations by bijections, combined under composition, of monogenic inverse semigroups, and classify these into isomorphism types. This provides a particularly easy way of classifying monogenic inverse semigroups into isomorphism types. Of interest is that we find two quite distinct representations by bijections of free monogenic inverse semigroups and show that all such representations must contain one of these two representations. We call a bijection of the form ai ↦ ai+1, i = 1,2,…, r − 1, a finite link of length r, and one of the form ai ↦ ai+1, i = 1,2…, a forward link. The inverse of a forward link we call a backward link. Two bijections u: A → B and r: C → D are said to be strongly disjoint if A ∩ C, A ∩ D, B ∩ C and B ∩ D are each empty. The two distinct representations of a free monogenic inverse semigroup, that we have just referred to, are first, such that its generator is the union of a counbtable set os finite links that are pairwise storongly disjoint part of any representation of a free monogenic inverse semigroup, the remaining part not affecting the isomorphism type. Each representation of a monogenic inverse semigroup that is not free contains a strongly disjoint part, determining it to within isomorphism, that is generated by either the strongly disjoint union of a finite link and a permutation or the strongly disjoint union of a finite and a forward link.
Perturbations of type I Aw*-algebras
Authors: Khoshkam Mahmood 
Published: April 2009

AbstractThe distance between two operator algebras acting on a Hilbert space H is defined to be the Hausdorff distance between their unit balls. We investigate the structural similarities between two close AW*-algebras A and B acting on a Hilbert space H. In particular, we prove that if A is of type I and separable, then A and B are *-isomorphic.
On the conjugacy classes in the unitary, symplectic and orthogonal groups
Authors: Wall G. E. 
Published: April 2009

This paper is concerned with two mani problems:(a) the determination of the conjugacy classes in the finite-dimensional unitary, symplectic and orthogonal groups over division rings or fields;(b) the determination of the equivalence classes of non-degenerate sesquilinear forms on finite-dimensional vector spaces.
The elastodynamics of moving loads, Part 1: The field of a semi-infinite line load moving on the surface of an elastic solid with constant supersonic velocity
Authors: Papadopoulos Michael 
Published: April 2009

AbstractWhen a semi-infinite line load moves lengthways, at supersonic velocity, on the plane surface of an elastic solid, the resulting velocity field is conical. There are two characteristic cones, one associated with dilatation effects and the other with shear effects. The propagation process is more complicated than the well-known case of conical flow in supersonic aerodynamics not only because of the presence of two cones of discontinuity but also because the presence of a free surface implies interaction between shear and dilatation effects. It is the interaction process at the free surface which is examined in detail in this paper.The results of this fundamental problem may be extended by the process of superposition to more general steadily moving loads. In particular by differentiating with respect to time, the potential of a steadily moving point load is obtained explicitly.
The transient behaviour of a single server queue with batch arrivals
Authors: Brockwell P. J. 
Published: April 2009

SUMMARYA queue at which arrivals occur randomly in batches of fixed size r and for which the service times are independent negative exponential variates is considered. Expressions are obtained for the moments of the transient waiting time distribution and the distribution of the number of customers in the system just before the nth batch arrives. The distribution of the number of customers served in a busy period is also determined.
On the commutants modulo Cp of A2 and A3
Authors: Kittaneh Fuad 
Published: April 2009

AbstractWe prove the following statements about bounded linear operators on a complex separable infinite dimensional Hilbert space. (1) Let A and B* be subnormal operators. If A2X = XB2 and A3X = XB3 for some operator X, then AX = XB. (2) Let A and B* be subnormal operators. If A2X – XB2 ∈ Cp and A3X – XB3 ∈ Cp for some operator X, then AX − XB ∈ C8p. (3) Let T be an operator such that 1 − T*T ∈ Cp for some p ≥1. If T2X − XT2 ∈ Cp and T3X – XT3 ∈ Cp for some operator X, then TX − XT ∈ Cp. (4) Let T be a semi-Fredholm operator with ind T < 0. If T2X − XT2 ∈ C2 and T3X − XT3 ∈ C2 for some operator X, then TX − XT ∈ C2.
A variational method for the construction of convergent iterative sequences
Authors: Rubinstein Zalman 
Published: April 2009

AbstractConvergent iterative sequences are constructed for the polynomials fm = z + zm, m ≧ 2, with initial point the lemniscate {z: |fm (z)| ≦1}. In the particular case m = 2 convergent iterative sequences are constructed also for f-1m, (z) with an arbitrary initial point. The method is based on a certain variational principle which allows reducing the problem to the well known situation of an analytic function mapping a simply connected domain into a proper subset of itself and possessing a fixed point in the domain.
Cumulants and partition lattices IV: a.s. convergence of generalised k-statistics
Authors: Speed T. P. 
Published: April 2009

AbstractGeneralised k-statistics associated with multi-indexed arrays of random variables satisfying a generalised form of exchangeability are studied. By showing that they form multi-indexed reversed martingales and that the associated family of σ-fields possesses certain conditional independence properties, conditions for the a.s. convergence of generalised k-statistics are obtained. When the arrays of random variables are sums of independent arrays of independent effects, as is the case with the standard random effects anova models, the limits are identified as the associated generalixed cumulants.
Classical isol incomparability and ∞ · on manifold RET's
Authors: Harkleroad Leon 
Published: April 2009

AbstractAn infinite collection of indecomposable isols such that no isol is comparable to certain infinitary combinations of the others is constructed, extending a result of Dekker and Myhill. This collection is then used to investigate differences between the arithmetic of classical RET's and that of RET's on recursive manifolds, a difference relevant to the manifold equivalent of the Schröder-Bernstein Theorem.
CLT groups and wreath products
Authors: Brandl Rolf 
Published: April 2009

AbstractIn this paper the question is considered of when the wreath product of a nilpotent group with a CLT groupGis a CLT group. It is shown that if the field withPrelements is a splitting field of a HallP1–subgroup ofG, thenPwrGis a CLT group for allp–groupsPwith |P/P1|≥pr. Moreover, the class of all groupsGhaving the property thatNwrGis a CLT group for every nilpotent groupNis shown to be quite large. For exmple, every group of odd order can be embedded as a subgroup of a group belonging to this class.
The Finsler geometry of groups of isometries of Hilbert Space
Authors: Atkin C. J. 
Published: April 2009

AbstractThe paper deals with six groups: the unitary, orthogonal, symplectic, Fredholm unitary, special Fredholm orthogonal, and Fredholm symplectic groups of an infinite-dimensional Hilbert space. When each is furnished with the invariant Finsler structure induced by the operator-norm on the Lie algebra, it is shown that, between any two points of the group, there exists a geodesic realising this distance (often, indeed, a unique geodesic), except in the full orthogonal group, in which there are pairs of points that cannot be joined by minimising geodesics, and also pairs that cannot even be joined by minimising paths. A full description is given of each of these possibilities.
A perturbation approach to Bose-condensed pairs
Authors: Thompson Colin J. , Blatt John M. 
Published: April 2009

AbstractA perturbation method is developed, and is used to obtain approximate expressions for the expectation values of one-particle and two particle operators in the quasi-chemical equilibrium (pair correlation) approximation to statistical mechanics, for the case of non-extreme Bose-Einstein condensation of the correlated pairs. To lowest order, the approximate results reproduce the results obtained previously for the case of extreme Bose-Einstein condensation.
Diffraction of plane elastic waves by a crack, with application to a problem of brittle fracture
Authors: Papadopoulos M. 
Published: April 2009

AbstractA crack is assumed to be the union of two smooth plane surfaces of which various parts may be in contact, while the remainder will not. Such a crack in an isotropic elastic solid is an obstacle to the propagation of plane pulses of the scalar and vector velocity potential so that both reflected and diffracted fields will be set up. In spite of the non-linearity which is present because the state of the crack, and hence the conditions to be applied at the surfaces, is a function of the dependent variables, it is possible to separate incident step-function pulses into either those of a tensile or a compressive nature and the associated scattered field may then be calculated. One new feature which arises is that following the arrival of a tensile field which tends to open up the crack there is necessarily a scattered field which causes the crack to close itself with the velocity of free surface waves.
Basic representations of some affine Lie algebras and generalized Euler identities
Authors: Misra Kailash C. 
Published: April 2009

AbstractWe consider certain affine Kac-Moody Lie algebras. We give a Lie theoretic interpretation of the generalized Euler identities by showing that they are associated with certain filtrations of the basic representations of these algebras. In the case when the algebras have prime rank, we also give algebraic proofs of the corresponding identities.
Peripheral acyclicity in 3-manifolds
Authors: Repovš Dušan 
Published: April 2009

AbstractWe study weak and strong peripheral 1-acyclicity, a homology version of D. R. McMillan, Jr.'s weak cellularity criterion and cellularity criterion, for embeddings of compacta in 3-manifolds. In contrast with the two cellularity criteria we prove that the two peripheral acyclicities are equivalent and moreover, for compacta of dimension at most 1, independent of the embedding. We also give some results concerning regular neighborhoods of compact polyhedra in 3-manifolds.
Endomorphism rings of Butler groups
Authors: Arnold D. M. , Vinsonhaler C. I. 
Published: April 2009

AbstractThis note is devoted to the question of deciding whether or not a subring of a finite-dimensional algebra over the rationals, with additive group a Butler group, is the endomorphism ring of a Butler group (a Butler group is a pure subgroup of a finite direct sum of rank-1 torsion-free abelian groups). A complete answer is given for subrings of division algebras. Several applications are included.
Sequential binary arrays and circulant matrices
Authors: Praeger Cheryl E. , Nilrat Chaufah K. 
Published: April 2009

AbstractA periodic binary array on the sequare grid is said to be sequential if and only if each row and each column of the array contains a given periodic binary sequence or some cyclic shift or reversal of this sequence. Such arrays are of interest in connection with experimental layouts. This paper extends previous results by characterizing sequential arrays on sequences of the type (1,…,1,0,…,0) and solving the problem of equivalence of such arrays (including a computation of the number of equivalence classes).
Lipschitz and differentiable dependence of solutions on a parameter in a scalarization method
Authors: Sterna-Karwat Alicia 
Published: April 2009

AbstractThis paper is concerned with a vector optimization problem set in a normed space where optimality is defined through a convex cone. The vector problem can be solved using a parametrized scalar problem. Under some convexity assumptions, it is shown that dependence of optimal solutions on the parameter is Lipschitz continuous. Hence differentiable dependence on the solutions on the parameter is derived.
Incomplete self-orthogonal latin squares
Authors: Heinrich Katherine , Zhu L. 
Published: April 2009

AbstractWe show that for all n ≥ 3k + 1, n ≠ 6, there exists an incomplete self-orthogonal latin square of order n with an empty order k subarray, called an ISOLS(n;k), except perhaps when (n;k) ∈ {(6m + i;2m):i = 2, 6}.
Generalizations of F. E. Browder's sharpened form of the schauder fixed point theorem
Authors: Tan Kok-Keong 
Published: April 2009

AbstractLet E be a Hausdorff topological vector space, let K be a nonempty compact convex subset of E and let f, g: K → 2E be upper semicontinuous such that for each x ∈ K, f(x) and g(x) are nonempty compact convex. Let Ω ⊂ 2E be convex and contain all sets of the form x − f(x), y − x + g(x) − f(x), for x, y ∈ K. Suppose p: K × Ω →, R satisfies: (i) for each (x, A) ∈ K × Ω and for ε > 0, there exist a neighborhood U of x in K and an open subset set G in E with A ⊂ G such that for all (y, B) ∈ K ×Ω with y ∈ U and B ⊂ G, | p(y, B) - p(x, A)| < ε, and (ii) for each fixed X ∈ K, p(x, ·) is a convex function on Ω. If p(x, x − f(x)) ≤ p(x, g(x) − f(x)) for all x ∈ K, and if, for each x ∈ K with f(x) ∩ g(x) = ø, there exists y ∈ K with p(x, y − x + g(x) − f(x)) < p(x, x − f(x)), then there exists an x0 ∈ K such that f(x0) ∩ g(x0) ≠ ø. Another coincidence theorem on a nonempty compact convex subset of a Hausdorff locally convex topological vector space is also given.
Well-bounded operators of type (B) in a class of Banach spaces
Authors: Ricker Werner 
Published: April 2009

AbstractIt is shown that in a Grothendieck space with the Dunford-Pettis property, the class of well-bounded operators of type (B) coincides with the class of scalar-type spectral operators with real spectrum. It turns out that in such Banach spaces, analogues of the classical theorems of Hille-Sz. Nagy and Stone concerned with the integral representation of C0-semigroups of normal operators and strongly continuous unitary groups in Hilbert spaces, respectively, are of a very special nature.
The kernel of integral cup product
Authors: Hillman Jonathan A. , Rubinstein J. H. 
Published: April 2009

AbstractWe compute the kernel of cup product of 1-dimensional cohomology classes for a group G acting trivially on Z or F2, by means of the naturality of cup product and the 5-term exact sequence of low degree of a suitable LHS spectral sequence. We determine thereby when cup product is injective, and when it is null.
Extension of Riesz homomorphisms. III
Authors: Buskes Gerard 
Published: April 2009

AbstractIn this paper we prove an analogue of the separable version of Nachbin's characterization of injective Banach spaces in the setting of Banach lattices. The mappings involved are continuous Riesz homomorphisms defined on ideals of separable Banach lattices which can be extended to Riesz homomorphisms on the whole Banach lattice. We discuss applications to simultaneous extension operators and to extension of continuous mappings between certain topological spaces.
A Construction for Fitting-Schunck classes
Authors: Cossey John , Ormerod Elizabeth A. , Lausch H. 
Published: April 2009

AbstractA method for constructing Fitting-Schunck classes is given: the method is an adaptation of one given by C. L. Kanes for constructing Fitting formations, and generalizes the Fitting-Schunck class construction given by Cossey in 1981. A criterion for deciding which of the Fitting-Schunck classes so constructed are formations is given.
Permutation polynomials in several variables over residue class rings
Authors: Kaiser H. K. , Nöbauer W. 
Published: April 2009

AbstractThe concept of a permutation polynomial function over a commutative ring with 1 can be generalized to multiplace functions in two different ways, yielding the notion of a k-ary permutation polynomial function (k > 1, k ∈ N) and the notion of a strict k-ary permutation polynomial function respectively. It is shown that in the case of a residue class ring Zm of the integers these two notions coincide if and only if m is squarefree.
Some properties of vector measures taking values in a topological vector space
Authors: Giannakoulias Efstathios 
Published: April 2009

AbstractIn this paper we study some properties of vector measures with values in various topological vector spaces. As a matter of fact, we give a necessary condition implying the Pettis integrability of a function f: S → E, where S is a set and E a locally convex space. Furthermore, we prove an iff condition under which (Q, E) has the Pettis property, for an algebra Q and a sequentially complete topological vector space E. An approximating theorem concerning vector measures taking values in a Fréchet space is also given.
Characterisation theorems for compact hypercomplex manifolds
Authors: Nag S. , Hillman J. A. , Datta B. 
Published: April 2009

AbstractWe have defined and studied some pseudogroups of local diffeomorphisms which generalise the complex analytic pseudogroups. A 4-dimensional (or 8-dimensional) manifold modelled on these ‘Further pseudogroups’ turns out to be a quaternionic (respectively octonionic) manifold.We characterise compact Further manifolds as being products of compact Riemann surfaces with appropriate dimensional spheres. It then transpires that a connected compact quaternionic (H) (respectively O) manifold X, minus a finite number of circles (its ‘real set’), is the orientation double covering of the product Y × P2, (respectively Y×P6), where Y is a connected surface equipped with a canonical conformal structure and Pn is n-dimensonal real projective space.A corollary is that the only simply-connected compact manifolds which can allow H (respectively O) structure are S4 and S2 × S2 (respectively S8 and S2×S6).Previous authors, for example Marchiafava and Salamon, have studied very closely-related classes of manifolds by differential geometric methods. Our techniques in this paper are function theoretic and topological.
Uniqueness and non-uniqueness of solutions of Vlasov-McKean equations
Authors: Scheutzow Michael 
Published: April 2009

AbstractWe study the equation dY(t)/dt = f(Y(t), Eh(Y(t))) for random initial conditions, where E denotes the expected value. It turns out that in contrast to the deterministic case local Lipschitz continuity of f and h are not sufficient to ensure uniqueness of the solutions. Finally we also state some sufficient conditions for uniqueness.
On the error in a certain interpolation formula and in the Gaussian integration formula
Authors: Luke Yudell L. 
Published: April 2009

AbstractWe first prove a basic theorem that if a set of polynomials satisfies an orthogonality relation with respect to integration, the set also satisfies an orthogonality relation with respect to summation. This result is then used to derive the Gaussian quadrature formula. The orthogonality relations give rise to interpolation formulas and a connection between the coefficients in these interpolation formulas is established. Finally, the analysis is used to get an estimate of the error in the Gaussian quadrature formula. Some error coefficients are evaluated in the cases where the orthogonal polynomials are those of Jacobi, Laguerre, Hermite and Bessel.
A Note On the Hadamard Kth Root of a Rational Function
Authors: Rumely Roberts , Van der Poorten A. J. 
Published: April 2009

AbstractSuppose the sequence of Taylor coefficients of a rational function f consists of kth powers of elements all belonging to some finitely generated extension field F of Q. Then it is a generalisation of a conjecture of Pisot that there is a rational function with Taylor coefficients term-by-term kth roots of those of f. The authors show that it suffices to prove the conjecture in the case that the field of definition is a number field and prove the conjecture in that case subject to the constraint that f has a dominant pole, that is, that there is a valuation with respect to which f has a unique pole either of maximal or of minimal absolute value.
Correction to “Construction methods for Bhaskar Rao and related designs”
Authors: Gibbons Petter B. , Mathon Rudolf 
Published: April 2009

The above paper, by Peter B. Gibbons and Rudolf Mathon, appeared in Volume 42 (1987), 5-30.Pages 10 and 11 are misplaced, and should appear between pages 17 and 18