bluuebunny/crossref_metadata_2025_split huggingface dataset:
Some inequalities for martingales and applications to the study of L1
Authors: Dor Leonard E. 
Published: November 2008

AbstractWe obtain here estimates for the expectation of a restricted quadratic variation of L1 bounded (weak) martingales and positive submartingales, and for related functionals. These inequalities are then used to give a quantitative version of a recent result of D. J. Aldous and D. H. Fremlin concerning the L1 norms of expansions with respect to uniformly integrable L1-normalized martingale difference sequences. Another application relates precisely the degree of norm divergence of an L1-bounded martingale to the degree of non-uniform integrability of that martingale. A partial analogue of this result is proved for certain vector valued martingales with values in L1 which are related to the Radon–Nikodým property.
Existence of solutions of Hammerstein equations of compact type
Authors: Becker Ronald I. 
Published: November 2008

AbstractThe existence of solutions is considered for equations of the formfor x ∈ H (a Hilbert space), P a compact linear operator on H; Q(x) a bounded linear operator on H and continuous in x and uniformly bounded; g(x) a continuous uniformly bounded map with range in H. Two situations are considered: Q(x) lies in a weakly compact set of operators for which (a) (I − PQ(x)) is invertible (non-resonance case) or (b) (I − P(Q(x) + λI)) is invertible for 0 < λ ≤ α (resonance case).
Shearing transformation of a linear system at an irregular singular point
Authors: Gilbert Richard C. 
Published: November 2008

Consider an nth-order linear ordinary differential equationSuppose the αj(x) are holomorphic for x ∈ S, 0 < x0 ≤ |x| < ∞, where S is an open sector of the complex plane with vertex at the origin and positive central angle not exceeding π. Suppose as x → ∞ in each closed subsector of S. The problem of finding a basis for the solutions of (1) can be reduced by a sequence of transformations (see, for example, Gilbert (1)) to the problem of finding a fundamental matrix for a system of the formwhere q is a non-negative integer, A(x) is an m by m matrix which is holomorphic for x ∈ S, x0 < ≤ |x| < ∞, and as x → ∞ in each closed subsector of S. If m ≥ 2, A0 is an m by m matrix with elements all zero except for l's on the upper off-diagonal, and the elements of Ar for r ≥ 1 are all zero except possibly in the last row. (There is one such problem (2) for each root, μ of the equation with multiplicity m ≥ 2. Recall that the coefficient αn−r, 0 the first term in the asymptotic expansion of the coefficint αn−r(x) of equation (1).) We denote the elements of the last row of Ar by 1 ≤ k ≤ m. The system (2) has an irregular singular point at infinity.
A resolution of the Euler operator II
Authors: Shakiban Chehrzad 
Published: November 2008

AbstractAn exact sequence resolving the Euler operator of the calculus of variations for partial differential polynomials in several dependent and independent variables is described. This resolution provides a solution to the ‘Inverse problem of the calculus of variations’ for systems of polynomial partial equations.That problem consists of characterizing those systems of partial differential equations which arise as the Euler-Lagrange equations of some variational principle. It can be embedded in the more general problem of finding a resolution of the Euler operator. In (3), hereafter referred to as I, a solution of this problem was given for the case of one independent and one dependent variable. Here we generalize this resolution to several independent and dependent variables simultaneously. The methods employed are similar in spirit to the algebraic techniques associated with the Gelfand-Dikii transform in I, although are considerably complicated by the appearance of several variables. In particular, a simple algebraic proof of the local exactness of a complex considered by Takens(5), Vinogradov(6), Anderson and Duchamp(1), and others appears as part of the resolution considered here.
A new chain complex for the homology of the Steenrod algebra
Authors: Singer William M. 
Published: November 2008

Let A be the Steenrod algebra over the field F2. For any graded A-module M we construct here a small chain complex of A-modules EM. This complex computes the homology of the Steenrod algebra with coefficients in M, in the sense that:The complexes F2 ⊗AEM are comparable in size but slightly larger than those that arise from the Λ-algebra(4). We are motivated to introduce them because they can be used to prove an embedding theorem for the homology of the Steenrod algebra. In fact, we construct a functor K on the category of graded. A-modules, and using the complexes EM, prove that there is a natural, one-one map:
A criterion for the (e, c)-summability of Fourier series
Authors: Siddiqi Jamil A. 
Published: November 2008

1. A series with partial sums {An} is said to be summable (e, c) (c > 0) ifexists, where it is to be understood that An+k = 0 when n+k < 0. The (e, c)-sum-mability method which is a regular method of summation was introduced by Hardy and Littlewood (3) (cf. also (5)) as an auxiliary method to prove the Tauberian theorem for Borel summability, viz, if Σan is summable (B) to A and an = 0(n−½), then it converges to A.
Inverse scattering problem for transparent obstacles
Authors: Petkov Vesselin 
Published: November 2008

Let K ⊂ ℝ3 be an open bounded strictly convex domain with smooth connected compact boundary ∂K. SetWe wish to study the filtered scattering amplitude, related to the transmission problemHere w± are the limiting values of w on ∂Ω; from the Ω;± side, while ∂w±/∂n are the corresponding limiting values of the normal derivative ∂w?/∂n on ∂Ω;. The function α(x) ∈ C∞(K¯), called the index of refraction, has the property α(x) > 0 for x ∈ K¯.
The join of several subnormal subgroups
Authors: Williams J. P. 
Published: November 2008

In (2) Lennox and Stonehewer proved:
Let G be a group with subnormal subgroups H and K, and let J = 〈H, K〉. Suppose that J/J′ has finite rank. Then(i) given positive integers a and b, there exists c such that γc(J) ≤ γa(H). γb(K) and(ii) J is subnormal in G.
An extremal function for contractions of graphs
Authors: Thomason Andrew 
Published: November 2008

AbstractThe function c(p) is defined for positive integers p ≥ 4 bywhere > denotes contraction. Random graph examples showIn 1968 Mader showed that c(p) ≤ 8(p − 2) [log2 (p − 2)] and more recently Kostochka showed that p√(log p) is the correct order for c(p). We present a simple argument showing c(p) ≤ 2.68p √(log2p)(l + ο(l)).
Inequalities related to Hardy's and Heinig's
Authors: Cochran James A. , Lee Cheng-Shyong 
Published: November 2008

In a 1975 paper [8], Heinig established the following three inequalities:where A = p/(p + s − λ) with p, s, λ real numbers satisfying p + s > λ,p > 0;where B = p/(2p + sp − λ −1) with p, s, λ real numbers satisfying 2p +sp > λ, + 1, p > 0;where is a sequence of nonnegative real numbers,and C = p[l + l/(p + s−λ)] with p, s, λ real numbers satisfying s > 0, p ≥ 1, and p +s > λ 0.
The transfer and Whitehead's conjecture
Authors: Kuhn Nicholas J. , Priddy Stewart B. 
Published: November 2008

In this paper we present a proof of G. W. Whitehead's conjecture about symmetric products of the sphere spectrumS.Our methods are based on the transfer, the Steinberg module, and the structure of the Hecke algebra. Our results are valid for all primes and extend those of the first author forp= 2 [7]. As originally stated, the conjecture asserts thatis zero onp-primary components in positive degrees [11]. By considering the quotientsL(k)= Σ-kSPpkS/SPk-1-S, this is seen to be equivalent to the exactness ofon homotopy groups, where ∂kis the connecting map and ε is the inclusion of the bottom cell. Here and throughout all spaces and spectra are localized atp.
Note on desuspending the Adams map
Authors: Cohen F. R. , Neisendorfer J. A. 
Published: November 2008

Let p denote a fixed prime and let Pn(pr) denote the cofibre of the degree pr map on Sn–1. We consider π*P3(pr) and show that the map q in the cofibre sequenceinduces a split epimorphism on the p-primary component of π2pS3 if p > 2. That analogous maps q: Pn(pr) →Sn, n ≥ 4, induce split epimorphisms on the p-primary component of πn+2p-3Sn, p > 2, is shown in work of J. F. Adams [1]. It is the purpose of this note to document the above computation in the case n = 3 for the use of others.
Eigenvalues of positive integral operators with certain entire kernels
Authors: Little G. 
Published: November 2008

Suppose that (an) (n ≥ 0) is a square-summable sequence of strictly positive real numbers; then the integral operator T on L2(− 1,1) given byis compact and positive and, therefore, its eigenvalues can be arranged into a sequence λ0 ≥ λ1 ≥ λ2 ≥ … of non-negative real numbers which decreases to 0.
Metric Diophantine approximation with two restricted variables I. Two square-free integers, or integers in arithmetic progressions
Authors: Harman Glyn 
Published: November 2008

In this paper, together with [7] and [8], we shall be concerned with estimating the number of solutions of the inequalityfor almost all α (in the sense of Lebesgue measure on Iℝ), where, and bothmandnare restricted to sets of number-theoretic interest. Our aim is to prove results analogous to the following theorem (an improvement given in [2] of an earlier result of Khintchine [10]) and its quantitative developments (for example, see [11, 12,6]):Let ψ(n) be a non-increasing positive function of a positive integer variable n. Then the inequality (1·1) has infinitely many, or only finitely many, solutions in integers to, n(n > 0) for almost all real α, according to whether the sumdiverges, or converges, respectively.
A topological criterion for group decompositions
Authors: Hebda J. , Moylan P. 
Published: November 2008

AbstractGiven a connected Lie group G and a closed connected subgroup H of G we prove a necessary and sufficient condition that G decomposes into the Cartesian product of H with G/H is that a similar decomposition holds for the maximal compact subgroups of G and H. Our criterion is applied to the three series of groups for which G/H is SO0(p, q)/SO0(p, q − 1), SU(q + 1, q + 1)/S[U(q + 1, q) × U(1)], and SU(q + 1, q + 1)/SL(n, ℂ) ⋊ H(n) (p, q ≥ 1), and we list the values of p and q for which G ≅ H × G/H in each of the three cases. We describe certain decompositions for some of the groups. We show the usefulness of our criterion in obtaining characterization of the space of differentiable vectors for a unitary induced group representation, and, finally, we show by example of SU(2, 2), how the asymptotic properties of certain function spaces for induced group representations are readily obtained using our results. Our results should be of interest to those working in de Sitter and conformal field theories.
Sprays, universality and stability
Authors: Riego L. Del , Dodson C. T. J. 
Published: November 2008

AbstractAn important class of systems of second order differential equations can be represented as sprays on a manifoldMwith tangent bundleTM↠M; that is, as certain sections of the second tangent bundleTTM↠TM. We consider here quadratic sprays; they correspond to symmetric linear connections onTM↠Mand hence to principal connections on the frame bundleLM↠M. Such connections overMconstitute a system of connections, on which there is a universal connection and through which individual connections can be studied geometrically. Correspondingly, we obtain a universal spray-like field for the system of connections and each spray onMarises as a pullback of this ‘universal spray’. The Frölicher-Nijenhuis bracket determines for each spray (or connection) a Lie subalgebra of the Lie algebra of vector fields onMand this subalgebra consists precisely of those morphisms ofTTMoverTMwhich preserve the horizontal and vertical distributions; there is a universal version of this result. Each spray induces also a Riemannian structure onLM; it isometrically embeds this manifold as a section of the space of principal connections and gives a corresponding representation ofTMas a section of the space of sprays. Such embeddings allow the formulation of global criteria for properties of sprays, in a natural context. For example, ifLMis incomplete in a spray-metric then it is incomplete also in the spray-metric induced by a nearby spray, because that spray induces a nearby embedding. For Riemannian manifolds, completeness ofLMis equivalent to completeness ofMso in the above sense we can say that geodesic incompleteness is stable; it is known to be Whitney stable.
Generating families for images of Lagrangian submanifolds and open swallowtails
Authors: Janeczko Stanisław 
Published: November 2008

SummaryIn this paper we study the symplectic relations appearing as the generalized cotangent bundle liftings of smooth stable mappings. Using this class of symplectic relations the classification theorem for generic (pre) images of lagrangian submanifolds is proved. The normal forms for the respective classified puilbacks and pushforwards are provided and the connections between the singularity types of symplectic relation, mapped lagrangian submanifold and singular image, are established. The notion of special symplectic triplet is introduced and the generic local models of such triplets are studied. We show that the open swallowtails are canonically represented as pushforwards of the appropriate regular lagrangian submanifolds. Using the SL2(ℝ) invariant symplectic structure of the space of binary forms of n appropriate dimension we derive the generating families for the open swallowtails and the respective generating functions for its regular resolutions.
Wave source potentials 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 sources are obtained for the case when each fluid is of finite constant depth, neglecting effects of surface tension at the surface of separation.
Asymptotic distributions of pontograms
Authors: Csörgő Miklós , Horváth Lajos 
Published: November 2008

Let{N(x), x ≥ 0} be a Poisson process with intensity parameter λ > 0, and introduceWhen looking for the changepoint in the Land's End data, Kendall and Kendall [7] proved for all 0 < ε1 < 1 − ε2 < 1 thatwhere {V(s), − ∞ < s < ∞} is an Ornstein–Uhlenbeck process with covariance function exp (−|t − s|). D. G. Kendall has posed the problem of replacing ε1 and ε2 by zero or by sequences εi(n) → 0 (n → ∞) (i = 1, 2), in (1·1). In this paper we study the latter problem and also its L2 version. The proofs will be based on the following weighted approximation of Zn.
The 2-variable polynomial of cable knots
Authors: Morton H. R. , Short H. B. 
Published: November 2008

AbstractThe 2-variable polynomial PK of a satellite K is shown not to satisfy any formula, relating it to the polynomial of its companion and of the pattern, which is at all similar to the formulae for Alexander polynomials. Examples are given of various pairs of knots which can be distinguished by calculating P for 2-strand cables about them even though the knots themselves share the same P. Properties of a given knot such as braid index and amphicheirality, which may not be apparent from the knot's polynomial P, are shown in certain cases to be detectable from the polynomial of a 2-cable about the knot.
The maximal C*-norm and the Haagerup norm
Authors: Itoh Takashi 
Published: November 2008

AbstractThe difference between the maximal C*-norm ‖ ‖max and the Haagerup norm ‖ ‖h on the tensor product space of C*-aIgebras is studied. Let A and B be C*-algebras. It is shown that ‖ ‖max is equivalent to ‖ ‖h on A ⊗ B if and only if A or B is finite-dimensional.
Seminorms related to weak compactness and to Tauberian operators
Authors: Astala Kari , Tylli Hans-Olav 
Published: November 2008

Let E and F be Banach spaces. The semigroup Φ+(E,F) of semi-Fredholm operators consists of the bounded linear mappings E→F with closed image and finite-dimensional kernel. By a well known result of Yood we have that T∈Φ+(E,F) if and only if for any bounded set B⊂E the condition TB relatively compact implies that B is relatively compact. Lebow and Schechter[10] gave a quantitative version of the above qualitative characterization, namely the operator T belongs to Φ+(E,F) if and only if there is c ≥ 0 such thatfor all bounded B⊂E. Here γ is the well known Hausdorff measure of non-compactnesswith BE the closed unit ball of E.
Global properties of supermanifolds and their bodies
Authors: Bryant Peter 
Published: November 2008

AbstractIn supersymmetric field theories, the use of Berezin-like integrals for curved superspace presupposes the existence of a smooth manifold structure on the underlying curved space (the body). The aim of this paper is to address the following question: when does a Rogers supermanifold have a body manifold?Elementary techniques from the theory of foliations are used to derive some necessary and sufficient conditions. The main result is the necessity of regularity of the soul foliation in the sense of Catenacci, Reina and Teofilatto. Regularity is not sufficient (for example, punctured superspace is regular with non-Hausdorff body). A sufficient condition (albeit highly sensitive to the choice of charts) is the transitivity of the body relation ˜, a property enjoyed by De Witt supermanifolds.We show that the body of a quotient supermanifold S/Γ is the quotient of the body (under the induced action). Several examples in the text illustrate that this is extremely useful.New characterizations ρ-supermanifolds and their saturations are given and the saturation construction is extended to all bodied supermanifolds.
The sum of Rademacher functions and Hausdorff dimension
Authors: Hu Tian-You , Lau Ka-Sing 
Published: November 2008

AbstractFor 0 < α < 1, let for 0 ≤ x < 1, where is the sequence of Rademacher functions. We give a class of fα so that their graphs have Hausdorff dimension 2 − α. The result is closely related to the corresponding unsolved question for the Weierstrass functions.
Fibrewise separation axioms for locales
Authors: Johnstone P. T. 
Published: November 2008

AbstractIn this paper we study the weak versions of the fibrewise separation axioms for locales over a base locale, whose introduction has been made possible by the development, in a previous paper by the author, of the fibrewise notion of closure for sublocales of locales over a base. We establish the implications which hold between these axioms and the traditional separation axioms for locales, and give counter-examples to show that some of these implications are irreversible.
Copies of l∞ in an operator space
Authors: Drewnowski Lech 
Published: November 2008

Let X and Y be Banach spaces. Then Kw*(X*, Y) denotes the Banach space of compact and weak*-weakly continuous linear operators from X* into Y, endowed with the usual operator norm. Let us write E⊃l∞ to indicate that a Banach space E contains an isomorphic copy of l∞. The purpose of this note is to prove the followingTheorem. Kw*(X*, Y) ⊃ l∞if and only if either X ⊃ l∞or Y ⊃ l∞.
Jones polynomial invariants for knots and satellites
Authors: Morton H. R. , Strickland P. 
Published: November 2008

AbstractResults of Kirillov and Reshetikhin on constructing invariants of framed links from the quantum group SU(2)q are adapted to give a simple formula relating the invariants for a satellite link to those of the companion and pattern links used in its construction. The special case of parallel links is treated first. It is shown as a consequence that any SU(2)q-invariant of a link L is a linear combination of Jones polynomials of parallels of L, where the combination is determined explicitly from the representation ring of SU(2). As a simple illustration Yamada's relation between the Jones polynomial of the 2-parallel of L and an evaluation of Kauffman's polynomial for sublinks of L is deduced.
SchurQ-functions and cohomology of isotropic Grassmannians
Authors: Józefiak Tadeusz 
Published: November 2008

AbstractWe prove that for homogeneous spaces of isotropic Grassmannians the Borel map sends the basis of a truncated algebra of SchurQ-functions consisting ofQ-functions orP-functions (depending on a case) onto the basis dual to the basis of Schubert cycles.
On the dimension of the non-Cohen–Macaulay locus of local rings admitting dualizing complexes
Authors: Cuong Nguyen Tu 
Published: November 2008

In this paper we mainly consider local rings admitting dualizing complexes. It is well-known that if a Noetherian local ring A admits a dualizing complex, then the non-Cohen–Macaulay (abbreviated CM) locus of A is closed in the Zariski topology (cf. [8, 10]). If the dimension of this locus is zero and A is equidimensional, i.e. the punctured spectrum of A is locally CM and dim(A/P) = dim (A) for all minimal prime ideals P ∈ Ass (A), then A is a generalized CM ring and its structure is well-understood (see [2, 12]). For instance, one of the characterizations of generalized CM rings is the conditions that for any parameter ideal q contained in a large power of the maximal ideal m of A, the difference between length and multiplicityis independent of the choice of q. However, if the dimension of the non-CM locus is larger than zero, little is known about how this dimension is related to the structure of the local ring A. The purpose of this paper is to show that if M is a finitely generated A-module, then there exist systems of parameters x = (x1, …, xd) (where d = dim M) such that the differenceis a polynomial in n1, …, nd for all positive integers n1, …, nd and the degree of IM(n1, …, nd;x) is independent of the choice of x. We shall also give various characterizations of this degree by using the notion of reducing systems of parameters of Auslander and Buchsbaum[l]. In particular, if the module M is equidimensional we shall show that the degree of IM(n1, …, nd;x) is equal to the dimension of the non-CM locus of M.
Square-full numbers in short intervals
Authors: Heath-Brown D. R. 
Published: November 2008

A positive integer n is called square-full if p2|n for every prime factor p of n. Let Q(x) denote the number of square-full integers up to x. It was shown by Bateman and Grosswald [1] thatBateman and Grosswald also remarked that any improvement in the exponent would imply a ‘quasi-Riemann Hypothesis’ of the type for . Thus (1) is essentially as sharp as one can hope for at present. From (1) it follows that, for the number of square-full integers in a short interval, we havewhen and y = o (x½). (It seems more suggestive) to write the interval as (x, x + x½y]) than (x, x + y], since only intervals of length x½ or more can be of relevance here.)
Derivations on a Fréchet convolution algebra associated with a weight
Authors: McClure J. P. 
Published: November 2008

AbstractFor certain Fréchet convolution algebras associated with a weight w on the half-line [0, ∞), we are interested in the question of which Radon measures on [0, ∞) determine the derivations on the algebra. For particular weights, we show that the derivations are determined by those measures in the multiplier algebra of the original algebra. However, we also give an example of a weight for which that characterization fails. The results show a connection between the space of derivations and the behaviour for large y of the ratio w(x + y)/w(x) w(y).
Mean growth of the derivative of certain classes of analytic functions
Authors: Girela Daniel 
Published: November 2008

AbstractIn this paper we study the question of characterizing those positive Borel measures μ on the unit disc Δ for which the differentiation operator D defined by Df = f′ maps the Hardy space Hp continuously into the Bergman space Bp(dμ) of all functions f analytic in Δ which belong to Lp (Δ, dμ).