bluuebunny/crossref_metadata_2025_split huggingface dataset:
Incompleteness of (nq + n - q - 2, n)-arcs in finite projective planes of even order
Authors: Wilson B. J. 
Published: November 2008

1. It was shown by Barlotti (1) that the number k of points on a (k, n)-arc of a finite projective piane of order qand that if q ≢ 0 (mod n) then for n ≥ 3.
On equimultiplicity
Authors: Herrmann M. , Orbanz U. 
Published: November 2008

This note consists of some investigations about the condition ht(A) = l(A) where A is an ideal in a local ring and l(A) is the analytic spread of A (9).In (4) we proved the following: If R is a local ring and P a prime ideal such that R/P is regular then (under some technical assumptions) ht(P) = l(P) is equivalent to the equimultiplicity e(R) = e(RP). Also for a general ideal A (which need not be prime), the condition ht(A) = l(A) can be translated into an equality of certain multiplicities (see Theorem 0).
Random uniform triangles and the alignment problem
Authors: Small Christopher 
Published: November 2008

AbstractLet n points be drawn independently and uniformly from a compact convex set K. The distribution of the shape of the resulting n–ad is determined and studied in the region corresponding to near alignment. Special attention is given to the case n ≥ 4 and a table provided to help in the assessment of practical data (e.g. megalithic ‘alignments’). The Broadbent factor, representing the effect of stretching the parent distribution, is computed explicitly.
Some orthogonal and complete sets of Bessel functions associated with the vibrating plate
Authors: Higgins J. R. 
Published: November 2008

AbstarctSome orthogonal sets of Bessel functions of real order v are identified using the equation Δ2u = utt of the vibrating plate. Our main concern is with the L2 completeness of such sets, and we prove that the well known ‘clamped edge’ type is complete for v > -1, thus completing a result of E. Dahlberg. We also study a very closely related set and show that it needs an extra (non-Bessel) function for completeness.Our method for proving the completeness is based on one given by H. Hochstadt in connection with Dini functions. We have found it necessary to reorganize Hoch-stadt's method and correct some errors contained in it.Certain isolated values of v require special attention and we treat these by subjecting the Dalzell completeness criterion to a continuity argument.
Eigen-values of Lipschitz kernels
Authors: Reade J. B. 
Published: November 2008

AbstractAsymptotic estimates are obtained for the eigen-values of symmetric kernels which satisfy a Lipschitz condition of order α, where 0 < α ≤ 1, on a bounded region. For 0 < α < 1, the eigen-values are shown to be O(1/nα+½) for general kernels, and O(1/nα+1) for positive definite kernels. For α = 1, the eigen-values are shown to be O(1/n+3/2) in general, but only O(1/n2) when the kernel is positive definite. Examples are given to show these estimates are best possible for powers of n.The estimates for general kernels are known. In 1931, Hille and Tamarkin used infinite determinants to obtain weaker estimates in the case 0 < α < 1, but the same estimates as ours for α = 1. In 1937, Smithies sharpened the estimates for 0 < α < 1 to the ones we give by a variant of the method used by Weyl in 1912 for smooth kernels. Cochran obtained the same estimates in 1972 using Fredholm determinants. Our proof uses Weyl's method in its original form for 0 < α < 1, and in Smithies' variant for α = 1, so in all cases simplifies previous proofs.The estimates for positive definite kernels are, as far as we know, new. The proofs use the method of our recent paper on smooth positive definite kernels.
Some properties of maximal measures on compact convex sets
Authors: Batty C. J. K. 
Published: November 2008

AbstractLet be a maximal measure on a compact convex set K, K* be the state space of the space of all continuous functions f: KK ℝ which are affine in the first variable, 1 be the -algebra on K generated by the Baire sets and the compact extremal subsets of K, and = {BeK1}. Then(i) For any fixed continuous function g:K ℝ and -almost all x in K, there is a closed face of K containing x on which g is constant.(ii) The image of under the map :KK* defined by f, (x) = f(x, x) is the unique maximal measure on K* representing its barycentre(iii) induces a measure on (eK) satisfying certain regularity conditions.
Minimum growth of harmonic functions and thinness of a set
Authors: Wu Jang-Mei G. 
Published: November 2008

In [3], Barth, Brannan and Hayman proved that if u(z) is any non-constant harmonic function in ℝ2, ø(r) is a positive increasing function of r for r ≥ 1 andthen there exists a path going from a finite point to ∞, such that u(z) > ø(|z|) on Γ. Moreover, they showed by example that the integral condition above cannot be relaxed.
Unsound ordinals
Authors: Mathias A. R. D. 
Published: November 2008

AbstractAn ordinal is termed unsound if it has subsets An (nεω) such that un-countably many ordinals are realised as order types of sets of the form ∪ {An|nε a} where a ⊆ ω. It is shown that if ω1 is regular and then the least unsound ordinal is exactly but that if ω1 is regular and the least unsound ordinal, assuming one exists, is at least . Arguments due to Kechris and Woodin are presented showing that under the axiom of determinacy there is an unsound ordinal less than ω2. The relation between unsound ordinals and ideals on w is explored. The paper closes with a list of open problems.
Best L∞-approximation of measurable, vector-valued functions
Authors: Al-Rashed Abdallah M. , Darst Richard B. 
Published: November 2008

Let (Ω, ,μ) be a probability space, and let be a sub-sigma-algebra of . Let X be a uniformly convex Banach space. Let A =L∞(Ω, , μ X) denote the Banach space of (equivalence classes of) essentially bounded μ-Bochner integrable functions g: Ω.→ X, normed by the function ∥.∥∞ defined for g ∈ A by(cf. [6] for a discussion of this space). Let B = L∞(Ω, , μ X), and let f ε A. A sufficient condition for g ε B to be a best L∞-approximation to f by elements of B is established herein.
A sequence well distributed in the square
Authors: Pinch R. G. E. 
Published: November 2008

Bollobás and Erdös[1] have posed the problem:If a is irrational, show that for 1 ≤ i < j ≤ p the number of integers t with 1 ≤ t ≤ p such that {(t–i)2a} < d and {(t–j)2a} < d, 0 < d < 1, is d2p + o(p) uniformly in i, j.
On fixed-point-free elements
Authors: Espuelas Alberto 
Published: November 2008

In Theorem 1·2 of [3] the following extension of the classical theorem of Shult is proved.Theorem. Let G be a p-solvable group and let V be a faithful KG-module, where char. Assume that G contains an element x of order pn acting fixed-pointfreely on V. If p is a Fermat prime suppose further that the Sylow 2-subgroups of G are abelian. If p = 2 assume that the Sylow q-subgroups of G for each Mersenne prime q less than 2n are abelian. Then
Filtrations, closure operations and prime divisors
Authors: Okon J. S. , Ratliff L. J. 
Published: November 2008

AbstractLet ƒ = {In}n≽ 0be a filtration on a ringR, let(In)w= {xεR;xsatisfies an equationxk+i1xk− 1+ … +ik= 0, whereijεInj} be the weak integral closure ofInand let ƒw= {(In)w}n≽ 0. Then it is shown that ƒ ↦ ƒwis a closure operation on the set of all filtrations ƒ ofR, and ifRis Noetherian, then ƒwis a semi-prime operation that satisfies the cancellation law: if ƒh≤ (gh)wand Rad (ƒ) ⊆ Rad (h), then ƒw≤gw. These results are then used to show that ifRand ƒ are Noetherian, then the sets Ass (R/(In)w) are equal for all largen. Then these results are abstracted, and it is shown that ifI↦Ixis a closure (resp.. semi-prime, prime) operation on the set of idealsIofR, then ƒ ↦ ƒx= {(In)x}n≤ 0is a closure (resp., semi-prime, prime) operation on the set of filtrations ƒ ofR. In particular, if Δ is a multiplicatively closed set of finitely generated non-zero ideals ofRand (In)Δ= ∪KεΔ(In, K: K), then ƒ ↦ ƒΔis a semi-prime operation that satisfies a cancellation law, and ifRand ƒ are Noetherian, then the sets Ass (R/(In)Δ) are quite well behaved.
Locally compact groups: maximal compact subgroups and N-groups
Authors: Bagley R. W. , Wu T. S. , Yang J. S. 
Published: November 2008

AbstractIf G is a locally compact group such thatG/G0contains a uniform compactly generated nilpotent subgroup, thenGhas a maximal compact normal subgroupKsuch thatG/Gis a Lie group. A topological groupGis an N-group if, for each neighbourhoodUof the identity and each compact setC⊂G, there is a neighbourhoodVof the identity such thatfor eachg∈G. Several results on N-groups are obtained and it is shown that a related weaker condition is equivalent to local finiteness for certain totally disconnected groups.
Tangential H∞-images of boundary curves
Authors: Rudin Walter 
Published: November 2008

1.Introduction. Suppose that Ω is a region (i.e. a connected open set) in ࠶n, for some fixedn≥ 1. We define (Γ, μ) to be aFatou pair inΩ if(a) Γ is a continuous family of boundary curves γwin Ω, one ending at each w ∈ ∂Ω,(b) μ is a positive finite Borel measure on ∂Ω, and(c) the conclusion of Fatou's theorem holds with respect to Γ and μ. Let us state (a) and (c) in more detail:(a) The map(w, t) → γw(t)is continuous, from ∂Ω × [0, 1) into Ω, andfor every w in the boundary ∂Ω of Ω.(c) For everyf ∈ H∞(Ω)(the class of all bounded holomorphic functions in Ω), the limitexists a.e. [μ].
Matchings and Radon transforms in lattices II. Concordant sets
Authors: Kung Joseph P. S. 
Published: November 2008

AbstractLet and ℳ be subsets of a finite lattice L. is said to be concordant with ℳ if, for every element x in L, either x is in ℳ or there exists an element x+ such that (CS1) the Möbius function μ(x, x+) ≠ 0 and (CS2) for every element j in , x ∨ j ≠ x+. We prove that if is concordant with ℳ, then the incidence matrix I(ℳ | ) has maximum possible rank ||, and hence there exists an injection σ: → ℳ such that σ(j) ≥ j for all j in . Using this, we derive several rank and covering inequalities in finite lattices. Among the results are generalizations of the Dowling-Wilson inequalities and Dilworth's covering theorem to semimodular lattices, and a refinement of Dilworth's covering theorem for modular lattices.
Uniformly asymptotic expansions for an integral with a large and a small parameter
Authors: Ursell F. 
Published: November 2008

AbstractThe integralinvolves a large real parameter N and a small real parameter ∈. Its asymptotic behaviour is non-uniform when N → ∞ and ∈ → 0. Thus, when ∈ > 0 is kept fixed and N → ∞, the integral decays exponentially at a rate depending on ∈; when ∈ → 0 the integral tends towhich decays algebraically when N → ∞. It is shown that several distinct uniformly asymptotic expansions can be obtained which each involve an infinite set of functions of the combination Certain related integrals are also treated.
On representing sets of an almost disjoint family of sets
Authors: Komjath P. , Milner E. C. 
Published: November 2008

For cardinal numbers λ, K, ∑ a (λ, K)-family is a family of sets such that || = and |A| = K for every A ε , and a (λ, K, ∑)-family is a (λ,K)-family such that |∪| = ∑. Two sets A, B are said to be almost disjoint ifand an almost disjoint family of sets is a family whose members are pairwise almost disjoint. A representing set of a family is a set X ⊆ ∪ such that X ∩ A = ⊘ for each A ε . If is a family of sets and |∪| = ∑, then we write εADR() to signify that is an almost disjoint family of ∑-sized representing sets of . Also, we define a cardinal number
Liénard systems with several limit cycles
Authors: Lloyd N. G. 
Published: November 2008

There is an extensive literature on Liénard's equationand numerous criteria for the existence of limit cycles have been developed: see the survey of Staude[7], for example. Broadly speaking, such results are proved in one of two ways: a bounded solution is shown to exist and the Poincaré–Bendixson theorem used, or an ‘a priori’ bound for periodic solutions is obtained and the methods of degree theory utilized.
Liftings of formal groups and the Artinian completion of BP
Authors: Baker Andrew , Würgler Urs 
Published: November 2008

Let BP denote the localization at υn, of the Brown-Peterson spectrum (associated to the prime p). There is a related ring spectrum E(n) with homotopy ring(as a quotient ring of in fact the cohomology theory E(n)*( ) is determined via a Conner-Floyd type isomorphism from on finite complexes, and moreover E(n) and BP are in the same Bousfield class (see [2, 14]). Although it is known (essentially from [17]) that BP cannot be a product of suspensions of E(n) in a multiplicative sense, D. Ravenel conjectured that such a splitting might occur after suitable completion of these spectra (see the introduction to [14]). This question was the original motivation of the present paper; however in proving Ravenel's conjecture we were naturally led to the consideration of some fundamental results in the theory of liftings of formal group laws and ‘change of ring’ results for Ext groups occurring in connection with the work of [10, 11, 12].
A generalization of a result of Iwasawa on the capitulation problem
Authors: Cremona J. E. , Odoni R. W. K. 
Published: November 2008

The aim of this note is to proveTheorem 1. Let n ≥ 3, and let p1, p2,…, Pn be primes in ℕ: = {z ∈ ℤ:z > 0}, each congruent to 1 (mod 4), which satisfy both of the following conditions:(i) every unit in ℚ(√(p1p2)) has norm + 1;(ii) the graph γ = γ(p1, p2, …, pn) associated with p1, p2, …, pn is odd (in the sense of [1]).
A class of representations of involutive bialgebras
Authors: Schürmann Michael 
Published: November 2008

AbstractA class of representations on Fock space is associated to a representation of the *-algebra structure of a cocommutative graded bialgebra with an involution. We prove that the Gelfand–Naimark–Segal (GNS) representation given by the convolution exponential of a conditionally positive linear functional can be embedded into a representation of this class. Our theory generalizes a well-known construction for infinitely divisible positive definite functions on a group. Applying our general result, we obtain a complete characterization of the GNS representations given by infinitely divisible states on involutive Lie superalgebras.
The uniform compactification of a locally compact abelian group
Authors: Filali M. 
Published: November 2008

In recent years, the Stone-Čech compactification of certain semigroups (e.g. discrete semigroups) has been an interesting semigroup compactification (i.e. a compact right semitopological semigroup which contains a dense continuous homomorphic image of the given semigroup) to study, because an Arens-type product can be introduced. If G is a non-compact and non-discrete locally compact abelian group, then it is not possible to introduce such a product into the Stone-Čech compactification βG of G (see [1]). However, let UC(G) be the Banach algebra of bounded uniformly continuous complex functions on G, and let UG be the spectrum of UC(G) with the Gelfand topology. If f∈ UC(G), then the functions f and fy defined on G byare also in UC(G).
On a question of R. Godement about the spectrum of positive, positive definite functions
Authors: Bekka Mohammed B. 
Published: November 2008

Let G be a locally compact group, and let P(G) be the convex set of all continuous, positive definite functions ø on G normalized by ø(e) = 1, where e denotes the group unit of G. For ø∈P(G) the spectrum spø of ø is defined as the set of all indecomposable ψ∈P(G) which are limits, for the topology of uniform convergence on compact subsets of G, of functions of the form(see [5], p. 43). Denoting by πø the cyclic unitary representation of G associated with ø, it is clear that sp ø consists of all ψ∈P(G) for which πψ is irreducible and weakly contained in πø (see [3], chapter 18).
On sums of two squarefull numbers
Authors: Baker R. C. , Brüdern J. 
Published: November 2008

A natural number n is said to be squarefull if p|n implies p2|n for primes p. The set of all squarefull numbers is not much more dense in the natural numbers than the set of perfect squares but their additive properties may be rather different. We are more precise only in the case of sums of two such integers as this is the problem with which we are concerned here. Let U(x) be the number of integers not exceeding x and representable as the sum of two integer squares. Then, according to a theorem of Landau [4],as x tends to infinity.
Quantum stochastic integration and quantum stochastic differential equations
Authors: Barnett Chris , Goldstein Stanisław , Wilde Ivan 
Published: November 2008

AbstractQuantum stochastic integrals are constructed using the non-commutativeLp-space theory of Haagerup. The existence and uniqueness of the solution to quantum stochastic differential equations driven by quasi-Wiener noises, or noises satisfying generalized standing hypotheses, is established as is the Markov behaviour of the solution. Various examples of the theory are discussed, and quantum Ornstein-Uhlenbeck processes are obtained as explicit solutions.
The coloured Jones function and Alexander polynomial for torus knots
Authors: Morton H. R. 
Published: November 2008

AbstractIn [2] it was conjectured that the coloured Jones function of a framed knot K, or equivalently the Jones polynomials of all parallels of K, is sufficient to determine the Alexander polynomial of K. An explicit formula was proposed in terms of the power series expansion , where JK, k(h) is the SU(2)q quantum invariant of K when coloured by the irreducible module of dimension k, and q = eh is the quantum group parameter.In this paper I show that the explicit formula does give the Alexander polynomial when K is any torus knot.
Genus of nilpotent groups of Hirsch length six
Authors: Cassidy Charles , Lajoie Caroline 
Published: November 2008

AbstractIn this paper, we characterize the genus of an arbitrary torsion-free finitely generated nilpotent group of class two and of Hirsch length six by means of a finite number of arithmetical invariants. An algorithm which permits the enumeration of all possible genera that can occur under the conditions above is also given.
Tangent sequences in Orlicz and rearrangement invariant spaces
Authors: Hitczenko Paweł , Montgomery-Smith Stephen J. 
Published: November 2008

AbstractLet (fn) and (gn) be two sequences of random variables adapted to an increasing sequence of σ-algebras (ℱn) such that the conditional distributions of fn and gn given ℱn coincide. Suppose further that the sequence (gn) is conditionally independent. Then it is known that where the number C is a universal constant. The aim of this paper is to extend this result to certain classes of Orlicz and rearrangement invariant spaces. This paper includes fairly general techniques for obtaining rearrangement invariant inequalities from Orlicz norm inequalities.
Isomorphisms between the second duals of group algebras of locally compact groups
Authors: Farhadi Hamid-Reza 
Published: November 2008

AbstractLet G be a locally compact group and L1(G) be the group algebra of G. We show that G is abelian or compact if every continuous automorphism of L1(G)** maps L1(G) onto L1(G) This characterizes all groups with this property and answers a question raised by F. Ghahramani and A. T. Lau in [7]. We also show that if G is a compact group and θ is any (algebra) isomorphism from L1(G)** onto L1(H)**, then H is compact and θ maps L1(G) onto L1(H).
Path homomorphisms
Authors: Nešetřil Jaroslav , Zhu Xuding 
Published: November 2008

AbstractWe investigate homomorphisms between finite oriented paths. We demonstrate the surprising richness of this perhaps simplest case of homomorphism between graphs by proving the density theorem for oriented paths. As a consequence every two dimensional countable poset is represented finite paths and their homomorphisms, and every finite dimensional poset is represented finite oriented trees and their homomorphisms. We then consider related problems of universal representability and extendability and on-line representability.
Hilbert schemes of points on some K3 surfaces and Gieseker stable bundles
Authors: Bruzzo Ugo , Maciocia Antony 
Published: November 2008

AbstractBy using a Fourier-Mukai transform for sheaves on K3 surfaces we show that for a wide class of K3 surfacesXthe Hilbert schemes Hilbn(X) can be identified for alln≥ 1 with moduli spaces of Gieseker stable vector bundles onX. We also introduce a new Fourier-Mukai type transform for such surfaces.
Minimal ideals in group algebras and their biduals
Authors: Baker J. W. , Filali M. 
Published: November 2008

AbstractLetGbe a locally compact group andFa left introverted subalgebra ofC(G). For each of the algebrasL1(G),M(G),F* andL∞(G)* we determine the finite-dimensional minimal left ideals of the algebra (if any); in some cases we also determine the finite-dimensional minimal two-sided ideals, and in certain cases show that all minimal ideals of the algebra are finite-dimensional.
Continuous linear operators onC(K, X) and pointwise weakly precompact subsets ofC(K, X)
Authors: lger A. 
Published: November 2008

AbstractLetKbe a compact Hausdorif space,Xa Banach space andC(K, X) the Banach space of all continuous functions :KXequipped with the supremum norm. A subsetHofC(K, X) is pointwise weakly precompact if, for eachtinK, the setHt) = {(t):H} is weakly precompact. In this note we study the images of a bounded pointwise weakly precompact subsetHofC(K, X) under several classes of linear operators onC(K, X).
Interpolation problems for ideals in nest algebras
Authors: Anoussis M. , Katsoulis E. G. , Moore R. L. , Trent T. T. 
Published: November 2008

AbstractGiven vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equation Txt = yt, for i = 1, 2,, n. In this article, we continue the investigation of the one-vector interpolation problem for nest algebras that was begun by Lance. In particular, we require the interpolating operator to belong to certain ideals which have proved to be of importance in the study of nest algebras, namely, the compact operators, the radical, Larson's ideal, and certain other ideals. We obtain necessary and sufficient conditions for interpolation in each of these cases.
On Fréchet Montel spaces and their projective tensor product
Authors: Díaz Juan Carlos , Miñarro M.Angeles 
Published: November 2008

AbstractThe main result in this note is as follows. Let E be a Fréchet Montel space which belongs to the large class of decomposable (FG)-spaces introduced by Bonet, Díaz, Taskinen and let F be a Fréchet Montel (resp. distinguished) space. Then the projective tensor product is Montel (resp. distinguished). We also give examples of Montel decomposable (FG)-spaces without an unconditional basis.
On the Liénard system which has no periodic solutions
Authors: Sugie Jitsuro , Yoneyama Toshiaki 
Published: November 2008

The problem of periodicity of solutions of the generalized Liénard equationhas attracted much attention. Many efforts have been made to give sufficient conditions to guarantee the existence and the uniqueness of periodic solutions (limit cycles) of (1·1). There are also some papers on the number of limit cycles of (1·1) (see, for example, [3, 5, 6, 13]). However, there are only a few results on non-existence of periodic solutions of (1·1).
On the propagation of disturbances in a laminar boundary layer. II
Authors: Brown S. N. , Stewartson K. 
Published: November 2008

AbstractThe assumption that disturbances are confined to the neighbourhood of the wall in the problem of Part I is invalidated by an exact solution of the resulting equation which shows that disturbances rapidly travel out of the region in which the equation is applicable. The asymptotic methods of Part I are also applied to this equation, which was studied by Lam and Rott (1), and an assessment is made of the role of the eigensolutions found by these authors.