bluuebunny/crossref_metadata_2025_split huggingface dataset:
Extensions of the Hájek–Rényi inequality to moments of higher order
Authors: Dunnage J. E. A. 
Published: November 2008

1. Introduction. Bernoulli trials. Consider a sequence of Bernoulli trials. Let p, assumed to satisfy 0<p < 1, be the probability of success at any given trial and let q = 1–p. If Nn is the number of successes in the first n trials, it is well known that Nn/n→p almost surely as n→∞ so that for every ∈> 0,as n→∞, and it is clearly of great interest to know quantitatively how this probability depends upon n and ∈.
A Frattini-like subgroup
Authors: Tomkinson M. J. 
Published: November 2008

The Frattini subgroup φ(G) of a group G is the intersection of G and all its maximal subgroups. The following results for finite groups are well known:THEOREM A0. If G is a finite group, then the following three conditions are equivalent:(i) G is nilpotent,(ii) G/φ(G) is nilpotent,(iii) φ(G) ≥ G′.
A proof of Hartman's theorem on compact Hankel operators
Authors: Bonsall F. F. , Power S. C. 
Published: November 2008

Let U be a unilateral shift of arbitrary (perhaps uncountable) multiplicity on a Hilbert space. Following Rosenblum (5), an operator A is said to be a Hankel operator relative to U ifHartman (2) has characterized the compact Hankel operators relative to the unilateral shift of multiplicity one as the Hankel operators with symbol in H∞ + C(T). Using the usual function space model for representing the unilateral shift, Page ((4), theorem 10) has extended Hartman's theorem to unilateral shifts of countable multiplicity. We give a model-free proof of Hartman's theorem which applies to shifts of arbitrary multiplicity. The proof turns on the observation that a compact operator acts compactly on a certain algebra of operators.
On the comparison of measure functions
Authors: Hawkes John 
Published: November 2008

Suppose that f and g are measure functions and that µf and µg are the corresponding Hausdorff measures. We are interested in how relationships between f and g are reflected in relationships between µf and µg and vice versa. For example, ifRogers ((8), p. 80) has shown that there exists a metric space Ω which has subsets A and B with µf(A) = µg(B) = 0 and, µf(B) = µg(A) = ∞. We are more interested in what happens when the metric space in question is the real line. To get the above result we need to assume that both f and g are starshaped. This is just about a best possible result since if we assume only that f is a power of t the conclusion fails. Further-more we show that there exist measure functions f and g satisfying (1) such that µf and, µg are identical. We also consider related questions: when are, µf and, µg equivalent measures and when are they identical?The proofs depend on the construction in Theorem 3.1 of a Cantor set having pre-scribed measure properties. Although the construction is not difficult it turns out to be quite useful to appeal to the existence of such a set. We illustrate this remark by giving a short proof of a known theorem on cartesian product sets. We also make use of these ideas in section 5 where we discuss some properties of a class of net meastues and give a partial answer to a problem posed by Billingsley.
A compact space having the cardinality of the continuum with no convergent sequences
Authors: Fedorčuk V. V. 
Published: November 2008

1. Introduction. All spaces in this paper are Hausdorff. We recall that a space X is sequentially compact, if every countable subset of X contains a convergent sequence. Let us consider the three statements:(1) Every compact space of cardinality ≤ ʗ contains a point of countable character.(2) Every compact space of cardinality ≤ ʗ is sequentially compact.(3) Every infinite compact space of cardinality ≤ ʗ contains a convergent sequence.
On the spatial oscillations of a horizontally heated rotating fluid
Authors: Daniels P. G. , Stewartson K. 
Published: November 2008

SummaryA laboratory model simulating aspects of oceanic or atmospheric circulationconsists of a rotating fluid annulus which is subject to a temperature gradient on the lower surface and is insulated on the inner and outer curved walls and on the top surface. A theoretical study of the resulting steady axi-symmetric fluid motion in the limit of small Ekman number, E, by Daniels (2) indicated that if an appropriate convective parameter is sufficiently large, oscillatory solutions are generated in the layer which is located on the hotter of the two side-walls, which do not decay into the geostrophic interior. The present paper resolves this difficulty by using the method of multiple scales to trace the development of the oscillatory solutions in the interior of the fluid. This leads to a consistent overall flow pattern throughout the annulus, except at an infinite set of discrete values of the convective parameter at which resonance is predicted.
Families of sets whose pairwise intersections have prescribed cardinals or order types Corrigenda
Authors: Erdös P. , Milner E. C. , Rado R. 
Published: November 2008

(i) J. Baumgartner has kindly drawn our attention to the fact that Theorem 2 as stated in (1) is false. A counter example is the case in which m = ℵ2; n = ℵ1; p = ℵ0. For by reference (3) of the paper (1) there is an almost disjoint family (Aγ: γ < ω1) of infinite subsets of ω̲ Put Aν = ω̲ for ω1 ≤ ν < ω2. Then, contrary to the assertion of that theorem, all conditions of Theorem 2 are satisfied. However, Theorem 2 becomes correct if the hypothesisis strengthened toIn fact, Baumgartner has proved the desired conclusion under the weaker hypothesis
On representation of Poisson mixtures as Poisson sums and a characterization of the gamma distribution
Authors: Godambe A. V. 
Published: November 2008

AbstractA necessary and sufficient condition for a Poisson mixture with an exponential type mixing distribution to be equivalently represented as a Poisson sum is obtained. The problem of deriving a similar condition under any mixing distribution on (0, ∞) is discussed. Finally, a characterization of the gamma distribution is obtained.
Littlewood–Paley theorems for sum and difference sets
Authors: Gaudry Garth I. 
Published: November 2008

SummaryLet α be a positive integer, andEl, …,EαHadamard sets of positive integers. It is shown thatE = E1+ … +Eαdetermines a Littlewood–Paley decomposition ofZ.Suppose thatis a Hadamard set of positive integers such thatnj+1/nj≥ 2 for allj. Let α be a positive integer, andWe show thatF(α) also determines a Littlewood-Paley decomposition of Z.
On the nilpotence class of commutative Moufang loops
Authors: Smith J. D. H. 
Published: November 2008

AbstractThe nilpotence class of the free commutative Moufang loop on n generators (n > 3) is the maximum allowed by the Bruck-Slaby Theorem, namely n − 1. This is proved by setting up a presentation of an extension of the loop's multiplication group as a nilpotent group of class at most 2n − 2, and then using the Macdonald-Wamsley technique of nilpotent group theory to show that this class is exactly 2n − 2.
On centralizers of involutions in 2-groups
Authors: Ronse Christian 
Published: November 2008

1. Introduction. It is well known (see (5) and (6)) that if T is a 2-group containing an involution t such that |CT(t)| = 4, then T is dihedral, semidihedral or cyclic of order 4. Fomin(1) has studied 2-groups T containing an involution t such that |CT(t)| ≤ 8. He showed in particular that such a group has sectional 2-rank at most 4. In this paper we will prove the following:Theorem A. Let T be a 2-group containing an involution t such that |CT(t)| ≤ 16. Then T has sectional 2-rank at most 6.
The Adams–Mahowald conjecture on real projective spaces
Authors: Lin Wen-Hsiung 
Published: November 2008

Let A denote the mod 2 Steenrod algebra. Let ℤ2[x, x−l] be the (graded) ring of finite Laurent series over ℤ2 in the variable x with dim (x) = 1. ℤ2[x, x−1] is a module over the Steenrod algebra A bywhere are binomial coefficients modulo 2 and m > 0 is large compared with |k| and i. Let M be the A-submodule of ℤ2[x, x−1 ] generated by all powers xi with i ≠ −1. It is easy to see that ℤ2 [,x, x−1]/M ≅ σ−1ℤ2 (means ℤ2 on dimension − 1). Let ρ: ℤ2[x, x−1] → σ−1 ℤ2 be the projection map.
A note on a theorem of Maddox on strong almost convergence
Authors: Das G. , Mishra S. K. 
Published: November 2008

Let m be the set of all real sequences x = (xn) with norm . A linear functional L on m is said to be a Banach limit (see Banach(1), p. 32) if it has the following properties:(i) L(x) ≥ 0, if x ≥ 0 (i.e. xn ≥ 0, for all n ∈ N)(ii) L{e) = 1, where e = (1, 1, 1,…),(iii) L(Sx) = L(x), where (Sx)n = xn+1.
Absolute summability functions for Hausdorff methods
Authors: Kuttner B. 
Published: November 2008

1. Following Lorentz, we suppose throughout that Ω(n) is a non-negati ve non-decreasing function of the non-negative integer n such that Ω(n)→ ∞ as n → ∞. Consider the summability method given by the sequence-to-sequence transformation corresponding to the matrix A = (ank). We say that Ω(n) is a summability function for A (or absolute summability function for A) if the following holds: Any bounded sequence {sn} such that the number of values of ν with ν ≤ n, sν ≠ 0 does not exceed Ω(n) is summable A (or is absolutely summable A, respectively). These definitions are due to Lorentz (4), (6). We shall be concerned with the case in which A is a regular Hausdorff method, say A = H = (H, μn). Then H is given by the matrix (hnk) withwithX(0) = X(0 + ) = 0, X(1) = 1;(see e.g.(1), chapter XI). We shall suppose throughout that these conditions are satisfied. It is known that H is then necessarily also absolutely regular.
Multipole expansions for two superposed fluids, each of finite depth
Authors: Kassem S. E. 
Published: November 2008

AbstractProblems dealing with the generation of internal waves at the surface separating two fluids involves the consideration of different types of singularities in one of the two fluids. In this paper the velocity potentials describing line and point multipoles are obtained for the case when each fluid is of finite constant depth, neglecting effects of surface tension at the surface of separation.
On Ext1 for semisimple groups and infinitesimal subgroups
Authors: Donkin Stephen 
Published: November 2008

Let G be an affine, connected, semisimple, simply connected algebraic group over an algebraically closed field k of non-zero characteristic p and, for a positive integer n, let Gn be the nth infinitesimal subgroup (the kernel of the nth power of the Frobenius morphism). The purpose of this note is to point out that, for certain rational G-modules V, the natural homomorphismis the zero map, for m ≽ 0. For such modules V, taking m = 0, we see from the 5-term exact sequence of Lyndon-Hochschild-Serre that the inflation-restriction sequenceis exact and thus the dimension of H1(G, V), when finite, may be calculated by adding the dimensions of the outer terms. The practical value of this result seems to lie in the special case n = 1 and V = L(λ) ⊗ L(µ), the tensor product of simple rational G-modules. In this case H1(G/G1) VG1 is H1(G, L(λ′) ⊗ L(¯′)) for λ′, ¯′ ‘smaller’ than λ µ and the above exact sequence gives an inductive procedure for computing Ext1G between simple rational (G-modules once the (G-module structure of Ext1G1 (equi valently Ext1u1 where% is the restricted enveloping algebra of the Lie algebra of G), for simple G1-modules, is known. Using the rather complicated structure of Weyl modules Cline, in (4), calculated Ext1G between simple modules for G = SL2(k) (this process was reversed in (5)). The present note has been used by S. EIB. Yehia, (17), in finding the corresponding result for SL3(k). We believe these Ext groups to be of increasing importance in view of their connection with Lusztig's conjecture, (14), on the characters of the simple rational G-modules and the related conjecture, 7–2 of (l), of Andersen.
An extremum variational principle and error estimate procedure for qIV = f(q, x)
Authors: Djukic Dj. S. , Atanackovic T. M. 
Published: November 2008

AbstractAn extremum variational principle for boundary value problems described by a non-linear fourth order differential equation qIV = f(q, x) is constructed. For approximate solutions an error estimate procedure, based on the value of the functional, is developed and applied to two concrete problems.
Transfer and ramified coverings
Authors: Smith Larry 
Published: November 2008

AbstractIn this note we introduce a general class of finite ramified coverings π X˜ ↓ X. Examples of ramified covers in our sense include: finite covering spaces, branched covering spaces and the orbit map Y ↓ Y/G where G is a finite group and Y an arbitrary G-space. For any d-fold ramified covering π: X˜ ↓ X we construct a transfer homomorphismwith the expected property thatis multiplication by d. As a consequence we obtain a simple proof of the Conner conjecture; viz. the orbit space of an arbitrary finite group action on a ℚ-acyclic space is again ℚ acyclic.
Further aspects of the evaluation of σ(m. n≠0, 0) (am2 + bnm + cn2)−s
Authors: Zucker I. J. , Robertson M. M. 
Published: November 2008

In some previous publications, Zucker and Robertson [13, 14, 15] for certain cases evaluated exactly the double sumwith a, b, c integers. In (1·1) the summation is over all integer values of m and n, both positive and negative, but excluding the case where m and n are simultaneously zero. The term ‘exact’ used here is in the sense introduced by Glasser [5], and means that S may be expressed as a linear sum of products of pairs of Dirichlet L-series. S is then said to be solvable. Whether S may be solved or not depends on the properties of the related binary quadratic form (am2 + bmn + cn2) = (a, b, c). The cases considered in [15] were when a > 0 and d = b2 − 4ac < 0, i.e. (a, b, c) was positive definite. When this is so, Glasser [5] conjectured that S was solvable if and only if (a, b, c) had one reduced form per genus, i.e. the reduced forms of (a, b, c) were disjoint. Zucker and Robertson [15] were in fact able to solve S for all (a, b, c) for which d < 0 and whose reduced forms were disjoint. A complete list of solutions may be found in [6].
On nearly uniformly convex and k-uniformly convex spaces
Authors: Istrăt‚escu V. I. , Partington J. R. 
Published: November 2008

AbstractIn this note we prove that every nearly uniformly convex space has normal structure and that K-uniformly convex spaces are super-reflexive.We recall [1] that a Banach space is said to be Kadec–Klee if whenever xn → x weakly and ∥n∥ = ∥x∥ = 1 for all n then ∥xn −x∥ → 0. The stronger notions of nearly uniformly convex spaces and uniformly Kadec–Klee spaces were introduced by R. Huff in [1]. For the reader's convenience we recall them here.
Various representations of a generalized hypergeometric function through statistical techniques
Authors: Anderson W. J. , Mathai A. M. 
Published: November 2008

AbstractThis paper deals with a statistical technique of deriving new results on Meijer's G-function. Multiple integral as well as computable series representations are given. The method used is to derive the density of a product of independent beta-distributed random variables by using different statistical techniques, and then compare the expressions to get the desired results. The results obtained in this article do not seem to be available through standard mathematical techniques.
Boundary conditions and reducibility of differential operators
Authors: Fisherl B. , Zahreddine Z. 
Published: November 2008

AbstractExamples were exhibited in [4] of both reducible and irreducible symmetric operators (of deficiency index (1:1)) associated with − d2/dt2 in the Hilbert space L2(I) (I = [0,1). Such symmetric operators are determined by three linearly independent boundary conditions which define their domains as restrictions of the domain of the maximal operator associated with — d2/dt2.
On Toda's fibrations
Authors: Gray Brayton 
Published: November 2008

In 1956 Toda [5] introduced two fibrations localized at p > 2:where is a subcomplex of the James construction . The construction of H′ was somewhat difficult and was discussed by Moore (see [3]). Moore's definition however is not natural (in the sense of Theorem 1 (b) below). It is our purpose to give another definition, closer to Toda's original definition, which is natural, is an H map* and behaves well with respect to the Dyer-Lashof map λ: BΣp → Q(So). We use this to settle an unanswered question in [2].
The Cauchy integral and analytic continuation
Authors: Brennan James. E. 
Published: November 2008

One of the most important concepts in the theory of approximation by analytic functions is that of analytic continuation. In a typical problem, for example, there is generally a region Ω, a Banach space B of functions analytic in Ω and a subfamily ℱ ⊂ B, each member of which is analytic in some larger open set, and one might be asked to decide whether or not ℱ is dense in B. It often happens, however, that either ℱ is dense or the only functions which can be so approximated have a natural analytic continuation across ∂Ω. A similar phenomenon is also known to occur even for approximation on sets without interior. In this article we shall describe a method for proving such theorems which can be applied in a variety of settings and, in particular, to: (1) the Bernštein problem for weighted polynomial approximation on the real line; (2) the completeness problem for weighted polynomial approximation on bounded simply connected regions; (3) the Shapiro overconvergence problem for sequences of rational functions with sparse poles; (4) the Akutowicz-Carleson minimum problem for interpolating functions. Although we shall present no new results, the method of proof, which is based on an argument of the author [6], seems sufficiently versatile to warrant exposition.
On automorphisms of unique factorization domains
Authors: Brown M. L. 
Published: November 2008

Chatters has asked whether a unique factorization domain (UFD) R, equipped with an automorphism σ transitive on the height 1 prime ideals of R, is necessarily Dedekind. If R contains an uncountable field, then Chatters observed that the answer is affirm ative. In this note was show:Theorem. Let R be a local UFD equipped with an automorphism σ which is transitive on the height 1 prime ideals of R. Suppose that σ induces an automorphism of finite order on the residue field κ of R (for example, if κ is a global or finite field), Then R is Dedekind.
Perfect powers in values of certain polynomials at integer points
Authors: Shorey T. N. 
Published: November 2008

1. For an integer v > 1, we define P(v) to be the greatest prime factor of v and we write P(1) = 1. Let m ≥ 0 and k ≥ 2 be integers. Let d1, …, dt with t ≥ 2 be distinct integers in the interval [1, k]. For integers l ≥ 2, y > 0 and b > 0 with P(b) ≤ k, we consider the equationPutso that ½ < vt ≤ ¾. If α > 1 and kα < m ≤ kl, then equation (1) implies thatfor 1 ≤ i ≤ t and hence
Fourier-Laplace transforms decaying exponentially
Authors: Kaneta H. 
Published: November 2008

Let ƒ(x) be a C-valued function which is integrable with respect to a positive measure m on the Borel σ-field of R = (– ∞, ∞). We shall give necessary and sufficient conditions under which the following Fourier-Laplace transform f(λ) of ƒ(x) decays exponentially as λ → ∞:where θ is a constant with –π/2 ≤ θ ≤ π/2.
The quasi-centre of a Banach algebra
Authors: Rennison J. F. 
Published: November 2008

An element a of a Banach algebra A over ࠶ will be called quasi-central if, for some K ≥ 1,The set Q(A) of all quasi-central elements of A will be called the quasi-centre of A and the set of elements a which satisfy (1) for a particular value of K will be denoted by Q(K, A). The motivation for these definitions is the result of Le Page ([1], proposition 3) that Q(1, A) coincides with the centre Z(A) of A. The reader is referred to [2] and [3] for a study of the properties of quasi-central elements.
Symmetry relations for connection matrices in the phase-integral method
Authors: Fröman Nanny , Fröman Per Olof , Lundborg Bengt 
Published: November 2008

AbstractIn many cases of practical interest there is some kind of symmetry associated with an ordinary second-order differential equation of the Schrödinger type. This symmetry is reflected in certain relations between different F-matrices or different elements of the same F-matrix of the phase-integral method. These symmetry relations imply in turn further relations between the Stokes constants, in addition to those which exist for a general cluster of transition points, and thereby reduce the number of independent Stokes constants. The present paper deals with two important kinds of symmetry relations.
Vanishing sums in function fields
Authors: Brownawell W. D. , Masser D. W. 
Published: November 2008

Let k be a field of zero characteristic, and let F be a function field over k of genus g. We normalize each valuation v on F so that its order group consists of all rational integers, and for elements u1, …, un of F, not all zero, we define the (projective) height asThe sum formula on F shows that this is really a height on the projective space .
Inclusions between FK spaces and Kuttner's theorem
Authors: Maddox I. J. 
Published: November 2008

The result known as Kuttner's theorem [2] asserts that if 0 < p < 1 and A is a Toeplitz matrix then there is a sequence which is strongly Cesàro summable with index p but which is not A summable. This theorem was extended by Maddox[3] to coregular matrices, and Thorpe [9] gave a further extension by showing that if 0 < p < 1 and X is a locally convex FK space with X ⊃ w0(p) then X ⊃ l∞. Here, w0(p) denotes the space of sequences strongly summable to 0, i.e. x∈w0(p) if and only ifand l∞ denotes the space of bounded sequences. Other proofs of Thorpe's extension and related results appear in Maddox[4, 5].
Units in real cyclic quartic fields
Authors: Cusick T. W. 
Published: November 2008

Let F be a totally real quartic field. For any α in F, let α, α′, α″, α‴ or α(0) = α(1), α(2), α(3) denote the conjugates of α. Define the function T(α) byWe define a triple of units ε1, ε2, ε3 in F as follows. Let ε1 be a unit which gives the least value of T(ε) for any unit ε ≠ = ± 1 in F. Let ε2 be a unit which gives the least value of T(ε) for any unit ε ≠ = ± ε1m with m a rational integer. Let ε3 be a unit which gives the least value of T(ε) for ε ≠ = ± ε1m ε2n with m and n rational integers. We call ε1, ε2, ε3 the successive unit minima for T(ε).
A uniqueness theorem for the coagulation-fragmentation equation
Authors: Stewart I. W. 
Published: November 2008

This paper presents a uniqueness result for solutions to the general nonlinear coagulation-fragmentation equationwhereEquation (1·1) has many applications in the applied sciences (cf. [1, 3, 8, 13, 15]) and a brief physical interpretation can be found in Melzak [12] or the survey article by Drake[7]. c(x, t), for x ≥ 0, t ≥ 0, denotes the number of particles of size x at time t and the non-negative kernels K and F describe, respectively, the rates at which particles of size x coalesce with those of size y and particles of size (x + y) break-up into those of sizes x and y.
Probabilistic factorization of a quadratic matrix polynomial
Authors: Kennedy Joanne , Williams David 
Published: November 2008

A purely algebraic result. We begin by stating the following theorem. Theorem. Let E be a finite set, and letdenote the set of real E × E matrices with non-negative off-diagonal elements and with non-positive row sums. Let A be a symmetric element of, and let V be a diagonal real E × E matrix. Then there exists a unique pair (H+, H−) of elements ofsuch thatI denoting the identity E × E matrix, and the superscript T signifying transpose. It is an immediate consequence that