bluuebunny/crossref_metadata_2025_split huggingface dataset:
Pairs of additive congruences to a large prime modulus
Authors: Atkinson O. D. , Cook R. J. 
Published: April 2009

AbstractThis paper is concerned with non-trivial solvability in p–adic integers, for relatively large primes p, of a pair of additive equations of degree k > 1: where the coefficients a1,…, an, b1,…, bn are rational integers.Our first theorem shows that the above equations have a non-trivial solution in p–adic integers if n > 4k and p > k6. The condition on n is best possible.The later part of the paper obtains further information for the particular case k = 5. specifically we show that when k = 5 the above equations have a non-trivial solution in p–adic integers (a) for all p > 3061 if n ≥ 21; (b) for all p execpt p = 5, 11 if n ≥ 26.
Cohomology with exotic supports and the generalized excision
Authors: Deo Satya , Jamwal Dalip Singh , Krishan Ram 
Published: April 2009

AbstractThe main result proved in this paper is the following. SupposeX1,X2are two subspaces of a spaceXsuch thatX= Int(X1)∪X2=X1∪ Int(X2). Then the pair (X1,X2) is a ϕ onX. This result settles an open question and includes all known results on ϕ-excisiveness in sheaf cohomology as its special cases. We construct several several examples to illustrate our main theorem and to show that it is, in fact, quite sharp.
The Three Gap Theorem (Steinhaus Conjecture)
Authors: van Ravenstein Tony 
Published: April 2009

AbstractThis paper is concerned with the distribution of N points placed consecutively around the circle by an angle of α. We offer a new proof of the Steinhaus Conjecture which states that, for all irrational α and all N, the points partition the circle into arcs or gaps of at least two, and at most three, different lengths. We then investigate the partitioning of a gap as more points are included on the circle. The analysis leads to an interesting geometrical interpretation of the simple continued fraction expansion of α.
Chain conditions and semigroup graded rings
Authors: Jespers E. 
Published: April 2009

AbstractThe following questions are studied: When is a semigroup graded ring left Noetherian, respectively semiprime left Goldie? Necessary sufficient conditions are proved for cancellative semigroup-graded subrings of rings weakly or strongly graded by a polycyclic-by-finite (unique product) group. For semigroup rings R[S] we also give a solution to the problem in case S is an inverse semigroup.
Rates of convergence for renewal sequences in the null-recurrent case
Authors: Isaac Richard 
Published: April 2009

AbstractMotivated by work of Garsia and Lamperti we consider null-recurrent renewal sequences with a regularly varying tail and seek information about their rate of convergence to zero. The main result shows that such sequences subject to a monotonicity condition obey a limit law whatever the value of the exponent α is, 0 < α < 1. This monotonicity property is seen to hold for a large class of renewal sequences, the so-called Kaluza sequences. This class includes moment sequences, and therefore includes the sequences generated by reversible Markov chains. Several subsidiary results are proved.
Subnormal embedding of relatively complete groups
Authors: Heineken Hermann , Soules Panagiotis 
Published: April 2009

AbstractIn this paper we show that a group A is embedded in any finite group G as a subnormal subgroup with low degree of complication, provided that the automorphism group of A satisfies a condition depending on some Fitting class (which coincides with completeness for the Fitting class of all groups). A criterion is given for these groups as to whether they can be embedded subnormally in the commutator subgroup of some finite group or not.
Scalar operators and integration
Authors: Kluvánek Igor 
Published: April 2009

AbstractThe notion of a scalar operator on a Banach space, in the sense of N. Dunford, is widened so as to cover those operators which can be approximated in the operator norm by linear combinations of disjoint values of an additive and multiplicative operator valued set function, P, on an algebra of sets in a space Ω such that P(Ω) = I, subject to some conditions guaranteeing that this definition is unambiguous. An operator T turns out to be scalar in this sense, if and only if, there exists a (not necessarily bounded) Boolean algebra of bounded projections such that the Banach algebra of operators it generates is semisimple and contains T.
Pasting infinite lattices
Authors: Fried E. , Grātzer G. 
Published: April 2009

AbstractIn an earlier paper, we investigated for finite lattices a concept introduced by A. Slavik: LetA, B,andSbe sublattices of the latticeL,A∩B=S,A∪B=L. ThenL pastes AandBtogether overS, if every amalgamation ofAandBoverScontainsLas a sublattice. In this paper we extend this investigation to infinite lattices. We give several characterizations of pasting; one of them directly generalizes to the infinite case the characterization theorem of A. Day and J. Ježk. Our main result is that the variety of all modular lattices and the variety of all distributive lattices are closed under pasting.
Major n-connected graphs
Authors: Oellermann Ortrud R. 
Published: April 2009

AbstractAn induced subgraph H of connectivity (edge-connectivity) n in a graph G is a major n-connected (major n-edge-connected) subgraph of G if H contains no subgraph with connectivity (edge- connectivity) exceeding n and H has maximum order with respect to this property. An induced subgraph is a major (major edge-) subgraph if it is a major n-connected (major n-edge-connected) subgraph for some n. Let m be the maximum order among all major subgraphs of C. Then the major connectivity set K(G) of G is defined as the set of all n for which there exists a major n-connected subgraph of G having order m. The major edge-connectivity set is defined analogously. The connectivity and the elements of the major connectivity set of a graph are compared, as are the elements of the major connectivity set and the major edge-connectivity set of a graph. It is shown that every set S of nonnegative integers is the major connectivity set of some graph G. Further, it is shown that for each positive integer m exceeding every element of S, there exists a graph G such that every major k-connected subgraph of G, where k ∈ K(G), has order m. Moreover, upper and lower bounds on the order of such graphs G are established.
On the existence of sequences of co-prime pairs of integers
Authors: Dowe David L. 
Published: April 2009

AbstractWe say that a positive integer d has property (A) if for all positive integers m there is an integer x, depending on m, such that, setting n = m + d, x lies between m and n and x is co-prime to mn. We show that infinitely many even d and infinitely many odd d have property (A) and that infinitely many even d do not have property (A). We conjecture and provide supporting evidence that all odd d have property (A).Following A. R. Woods [3] we then describe conditions (Au) (for each u) asserting, for a given d, the existence of a chain of at most u + 2 integers, each co-prime to its neighbours, which start with m and increase, finishing at n = m + d. Property (A) is equivalent to condition (A1), and it is easily shown that property (Ai) implies property (Ai+1). Woods showed that for some u all d have property (Au), and we conjecture and provide supporting evidence that the least such u is 2.
The last problem of Harald Bohr
Authors: Kahane Jean-Pierre 
Published: April 2009

AbstractThe first and last papers of Harald Bohr deal with ordinary Dirichlet series and their order (or Lindelöf) function μ(σ) (= inf{α;f(σ + it) + 0(|t|α)}). The Lindelöf hypothesis is μ(σ) = inf(0, ½ − t) when an = (−1)n. Are there ordinary Dirichlet series with −l < μ′ (σ) < 0 for some σ? A negative answer would imply Lindelöf's hypothesis. This is the last problem of Harald Bohr. This paper gives (1) a review on Bohr's results on ordinary Dinchlet series; (2) a review on results of the author and of Queffelec on “almost sure” and “quasi sure” properties of series with the solution of a previous problem of Bohr; (3) the following answer to the last problem: μ′(σ) can approach − ½, and necessarily μ(σ + μ(σ) + ½) = 0. The characterization of the order functions of ordinary Dirichlet series remains an open question.
Recursive constructions and some properties of twofold designs with block size four
Authors: Phelps K. T. , Rosa A. 
Published: April 2009

AbstractA direct construction for partially resolvable t-partitions is presented and then used to give a recursive construction for BIBDs (ν, 4, 2). In particular, we construct BIBD(ν, 4, 2) with BIBD(ν, 4, 2) embedded in it whenever ν = 3u + a, a ∈ {1, 4, 7}. This result allows us to give simple proofs for the existence of BIBD(ν, 4, 2) with various additioinal properties.
Everywhere Nonrecursive r.e. Sets in Recursively Presented Topological Spaces
Authors: Xiang Li 
Published: April 2009

AbstractRecursively presented topological spaces are topological spaces with a recursive system of basic neighbourhoods. A recursively enumerable (r.e.) open set is a r.e. union of basic neighbourhoods. A set is everywhere r.e. open if its intersection with each basic neighbourhood is r.e. Similarly we define everywhere creative, everywhere simple, everywhere r.e. non-recursive sets and show that there exist sets both with and without these everywhere properties.
Pair-Countable, Closure-Preserving Covers of Compact Sets
Authors: Potoczny Henry 
Published: April 2009

AbstractIn this paper, we prove the following results: (1) if a topological space X has a pair-countable, closure-preserving cover of compact sets, then X is locally paracompact at each point of X and X has a dense open subspace which is locally σ-compact. In addition, if X is also collectionwise-T2, then X is paracompact. Locally paracompact is taken to mean that each point X has an open set with paracompact closure.
The lateral completion of an arbitrary lattice group
Authors: Bernau S. J. 
Published: April 2009

SummaryThis paper shows that every lattice groupGcan be densely embedded in a unique laterally complete lattice groupH(the lateral completion ofG). All reasonable structure properties ofGare inherited byHand we have the following relationships between the ideal radicalL(G), the distributive radicalD(G) and the radicalR(G) ofGand the corresponding radicals ofH..
Gauge invariant interactions of classical fields
Authors: Smrz P. K. 
Published: April 2009

AbstractThe theory of Yang-Mills fields is explicity formulated in terms of the theory of connections in principal and associated fiber bundles. Special attention is paid to the fiber bundles with Lorentz and Poincaré structures. Equations of the form ∇ψ = 0, where ∇ is a generalized convariant derivative, are shown to contain “mass” terms if the connection in the Poincaré fiber bundle is cononically associated to the connection in the Lorentz fiber bundle.
On the homotopy theory of monoids
Authors: Hurwitz Carol M. 
Published: April 2009

AbsractIn this paper, it is shown that any connected, small category can be embedded in a semi-groupoid (a category in which there is at least one isomorphism between any two elements) in such a way that the embedding includes a homotopy equivalence of classifying spaces. This immediately gives a monoid whose classifying space is of the same homotopy type as that of the small category. This construction is essentially algorithmic, and furthermore, yields a finitely presented monoid whenever the small category is finitely presented. Some of these results are generalizations of ideas of McDuff.
Continuity properties of the superposition operator
Authors: Appell Jürgen , Zabrejko Pjotr P. 
Published: April 2009

AbstractVarious continuity conditions (in norm, in measure, weakly etc.) for the nonlinear superposition operatorF x(s) =f(s, x(s)) between spaces of measurable functions are established in terms of the generating functionf = f(s, u). In particular, a simple proof is given for the fact that, ifFis continuous in measure, thenfmay be replaced by a functionfwhich generates the same superposition operatorFand satisfies the Carathéodory conditions. Moreover, it is shown that integral functional associated with the function f are proved.
The structure of crossed products by smooth actions
Authors: Williams Dana P. 
Published: April 2009

AbsractLet ξ be a C*;-bundle over T with fibres {At}t∈A. Suppose that A is the C*-algebra of sections of ξ which vanish at infinity, and that (A, G, α) is a C*-dymanical system that, for each t ∈ T, the ideal It = {f ∈ A|f(t) =; 0} is G-invariant. If in addition, the stabiliser group of each P ∈ Prim(A) is amenable, then A ⋊αG is the section algebra of a C*-bundle with fibres {At ⋊αG}t∈T.The above theorem may be used to prove a structure theorem for crossed products built from C*-dynamical systems (A, G, α) where the action of G on A is smooth. Assuming that the stabiliser groups are amenable, then A ⋊αG has a composition series such that each quotient is a section algebra of a C*-bundle where the fibres are of the form Aσ ⋊αG; moreover, the Aσ correspond to locally closed subsets of Prim(A), and G acts transitively on Prim(Aσ). In many cases, in particular when (G, A) is separable, the Aσ ⋊αG have been computed explicitly by other authors.These results are actually proved for twisted C*dynamical systems.
The volumes of simplices, or, find the penguin
Authors: Klebaner Fima C. , Sudbury Aidan , Watterson G. A. 
Published: April 2009

AbstractGiven the equations for the n + 1 hyperplanes that bound an n-simplex in Rn, simple formulae are derived for the contents of the n − r simplices (0 ≦ r < n) embedded in it. For example, when n = 3, the formulae include the volume of the tetrahedron, the areas of its faces and the lengths of its edges.
On discontinuity of l2-angle
Authors: Jakóbczak Piotr , Mazur Tomasz 
Published: April 2009

AbstractIn this note the L2-angle between two concentric rings and between the ring and the exterior of the disc in the complex plane are calculated. In the second part we prove that the L2-angles between domains A and B and between A × C and B × C are equal. We give also some examples of discontinuity of the L2-angle between domains.
Sufficient conditions for the strong stability of the differential equation [p(D)+f(t)q(D)]y= 0
Authors: Howe A. 
Published: April 2009

AbstractA number of sufficient conditions for stability or strong stability, as used in the context of Hamiltonian systems, are found for the differential equationwhere the continuous functionf(t)is periodic ω int, D =d/dtandp(s),q(s)are real monic polynomials having special properties which allow the differential equation to be transformed into a canonical system ofksecond order equations.
On properly separable quotients of strict (LF) Spaces
Authors: Robertson W. J. 
Published: April 2009

AbstractAll known Banach spaces have an infinite-dimensional separable quotient and so do all nonnormable Fréchet spaces, although the general question for Banach spaces is still open. A properly separable topological vector space is defined, in such a way that separable and properly separable are equivalent for an infinite-dimensional complete metrisable space. The main result of this paper is that the strict inductive limit of a sequence of non-normable Fréchet spaces has a properly separable quotient.
Non-weak compactness of the integration map for vector measures
Authors: Okada S. , Ricker W. J. 
Published: April 2009

AbstractLet m be a vector measure with values in a Banach space X. If L1(m) denotes the space of all m integrable functions then, with respect to the mean convergence topology, L1(m) is a Banach space. A natural operator associated with m is its integration map Im which sends each f of L1(m) to the element ∫fdm (of X). Many properties of the (continuous) operator Im are closely related to the nature of the space L1(m). In general, it is difficult to identify L1(m). We aim to exhibit non-trivial examples of measures m in (non-reflexive) spaces X for which L1(m) can be explicitly computed and such that Im is not weakly compact. The examples include some well known operators from analysis (the Fourier transform on L1 ([−π, π]), the Volterra operator on L1 ([0, 1]), compact self-adjoint operators in a Hilbert space); such operators can be identified with integration maps Im (or their restrictions) for suitable measures m.
On minimal Fitting classes of periodic, infinite groups
Authors: McCann Brendan 
Published: April 2009

AbstractExamples of Fitting classes generated by certain periodic infinite groups are presented in this paper. The groups in question are finite extensions of direct products of quasi-cyclic (Prüfer) groups and are, in particular, Černikov groups. The methods applied follow closely those used for constructing Fitting classes of finite groups, especially in the case of nilpotent length three.
Ideal extensions of Γ-rings
Authors: Snyders A. J. M. , Veldsman S. 
Published: April 2009

AbstractGiven Γ-rings N1 and N2, a construction similar to the Everett sum of rings to find all possible extensions of N1 by N2 is given. Unlike the case of rings, it is not possible to find for any Γ-ring M an ideal extension that has a unity. Furthermore, contrary to the ring case, a Γ-ring with unity can not be characterized as a Γ-ring which is a direct summand in every extension thereof.
Homotopical aspects of Lie algebras
Authors: Ellis Graham J. 
Published: April 2009

AbstractThe Hurewicz theorem, Mayer-Vietoris sequence, and Whitehead's certain exact sequence are proved for simplicial Lie algebras. These results are applied, using crossed module techniques, to obtain information on the low dimensional homology of a Lie algebra, and information on aspherical presentations of Lie algebras.
Hyperbolic manifolds and degenerating handle additions
Authors: Scharlemann Martin , Wu Ying-Qing 
Published: April 2009

AbstractA 2-handle addition on the boundary of a hyperbolic 3-manifold M is called degenerating if the resulting manifold is not hyperbolic. There are examples that some manifolds admit infinitely many degenerating handle additions. But most of them are not ‘basic’. (See Section 1 for definitions). Our first main theorem shows that there are only finitely many basic degenerating handle additions. We also study the case that one of the handle additions produces a reducible manifold, and another produces a ∂-reducible manifold, showing that in this case either the two attaching curves are disjoint, or they can be isotoped into a once-punctured torus. A byproduct is a combinatorial proof of a similar known result about degenerating hyperbolic structures by Dehn filling.
Almost identical imitations of (3,1)-dimensional manifold pairs and the manifold mutation
Authors: Kawauchi Akio 
Published: April 2009

AbstractIn this paper, we construct from any given good (3,1)-dimensional manifold pair finitely many almost identical imitations of it whose exteriors are mutative hyperbolic 3-manifolds. The equivariant versions with the mutative reduction property on the isometry group are also established. As a corollary, we have finitely many hyperbolic 3-manifolds with the same volume and the same isometry group.
On 4-manifolds with universal covering space a compact geometric manifold
Authors: Hillman Jonathan A. 
Published: April 2009

AbstractThere are 11 closed 4-manifolds which admit geometries of compact type (S4,CP2orS2×S2) and two other closely related bundle spaces (S2×S2and the total space of the nontrivialRP2-bundle overS2). We show that the homotopy type of such a manifold is determined up to an ambiguity of order at most 4 by its quadratic 2-type, and this in turn is (in most cases) determined by the Euler characteristic, fundamental group and Stiefel-Whitney classes. In (at least) seven of the 13 cases, a PL 4-manifold with the same invariants as a geometric manifold or bundle space must be homeomorphic to it.
Cusps, triangle groups and hyperbolic 3-folds
Authors: Conder Marston D. E. , Martin Gaven J. 
Published: April 2009

AbstractWe provide a number of explicit examples of small volume hyperbolic 3-manifolds and 3-orbifolds with various geometric properties. These include a sequence of orbifolds with torsion of orderqinterpolating between the smallest volume cusped orbifold (q= 6) and the smallest volume limit orbifold (q→ ∞), hyperbolic 3-manifolds with automorphism groups with large orders in relation to volume and in arithmetic progression, and the smallest volume hyperbolic manifolds with totally geodesic surfaces. In each case we provide a presentation for the associated Kleinian group and exhibit a fundamental domain and an integral formula for the co-volume. We discuss other interesting properties of these groups.
On Mahler's compound bodies
Authors: Burger Edward B. 
Published: April 2009

AbstractLet 1 ≤ M ≤ N − 1 be integers and K be a convex, symmetric set in Euclidean N-space. Associated with K and M, Mahler identified the Mth compound body of K, (K)m, in Euclidean (MN)-space. The compound body (K)M is describable as the convex hull of a certain subset of the Grassmann manifold in Euclidean (MN)-space determined by K and M. The sets K and (K)M are related by a number of well-known inequalities due to Mahler.Here we generalize this theory to the geometry of numbers over the adèle ring of a number field and prove theorems which compare an adelic set with its adelic compound body. In addition, we include a comparison of the adelic compound body with the adelic polar body and prove an adelic general transfer principle which has implications to Diophantine approximation over number fields.
Tubular sets and multivariate Polya algorithm
Authors: Huotari Robert 
Published: April 2009

AbstractSome new results concerning tubular sets are presented, with applications to the convergence of the Polya algorithm in the contexts of simultaneous approximation and approximation of multivariate functions by univariate functions. (The Polya algorithm constructs a best uniform approximation from the limit, as p → ∞, of best Lp approximations.)
Pairs of rings with a bijective correspondence between the prime spectra
Authors: Jespers E. , Wauters P. 
Published: April 2009

AbstractLet A be a subring of a commutative ring B. If the natural mapping from the prime spectrum of B to the prime spectrum of A is injective (respectively bijective) then the pair (A, B) is said to have the injective (respectively bijective) Spec-map. We give necessary and sufficient conditions for a pair of rings A and B graded by a free abelian group to have the injective (respectively bijective) Spec-map. For this we first deal with the polynomial case. Let l be a field and k a subfield. Then the pair of polynomial rings (k[X], l[X]) has the injective Spec-map if and only if l is a purely inseparable extension of k.
Hyperidentity bases for rectangular bands and other semigroup varieties
Authors: Wismath Shelly L. 
Published: April 2009

AbstractHyperidentities were introduced by Taylor, and their properties have been studied by Taylor, Bergman, Penner, Graczynska, Schweigert, Wismath, and others. In particular, Penner has produced bases for the hyperidentities of various types satisfied by the variety of semilattices.In this paper, we look at bases for the hyperidentities satisfied by some other varieties of semigroups. We first investigate solid and hyper-associative varieties of semigroups, and use a result of Graczynska's to form a basis for the hyperidentities of type (2) for varieties with these properties. We then produce bases for the hyperidentities satisfied by the variety R B of rectangular bands, and prove that the collection of all hyperidentities satisfied by R B is not finitely based. Finally, we use the R B results to give hyperidentity bases for some varieties of nilpotent semigroups.