bluuebunny/crossref_metadata_2025_split huggingface dataset:
On Value Distribution Theory of Second Order Periodic ODEs, Special Functions and Orthogonal Polynomials
Authors: Chiang Yik-Man , Ismail Mourad E. H. 
Published: December 2010

AbstractWe show that the value distribution (complex oscillation) of solutions of certain periodic second order ordinary differential equations studied by Bank, Laine and Langley is closely related to confluent hypergeometric functions, Bessel functions and Bessel polynomials. As a result, we give a complete characterization of the zero-distribution in the sense of Nevanlinna theory of the solutions for two classes of the ODEs. Our approach uses special functions and their asymptotics. New results concerning finiteness of the number of zeros (finite-zeros) problem of Bessel and Coulomb wave functions with respect to the parameters are also obtained as a consequence. We demonstrate that the problem for the remaining class of ODEs not covered by the above “special function approach” can be described by a classical Heine problem for differential equations that admit polynomial solutions.
Distributions invariantes sur les groupes réductifs quasi-déployés
Authors: Courtès François 
Published: December 2010

RésuméSoit F un corps local non archimédien, et G le groupe des F-points d’un groupe réductif connexe quasi-déployé défini sur F. Dans cet article, on s’intéresse aux distributions sur G invariantes par conjugaison, et à l’espace de leurs restrictions à l’algèbre de Hecke ℋ des fonctions sur G à support compact biinvariantes par un sous-groupe d’Iwahori I donné. On montre tout d’abord que les valeurs d’une telle distribution sur ℋ sont entièrement déterminées par sa restriction au sous-espace de dimension finie des éléments de ℋ à support dans la réunion des sous-groupes parahoriques de G contenant I. On utilise ensuite cette propriété pour montrer, moyennant certaines conditions sur G, que cet espace est engendré d’une part par certaines intégrales orbitales semi-simples, d’autre part par les intégrales orbitales unipotentes, en montrant tout d’abord des résultats analogues sur les groupes finis.
The Feichtinger Conjecture for Wavelet Frames, Gabor Frames and Frames of Translates
Authors: Bownik Marcin , Speegle Darrin 
Published: December 2010

AbstractThe Feichtinger conjecture is considered for three special families of frames. It is shown that if a wavelet frame satisfies a certain weak regularity condition, then it can be written as the finite union of Riesz basic sequences each of which is a wavelet system. Moreover, the above is not true for general wavelet frames. It is also shown that a sup-adjoint Gabor frame can be written as the finite union of Riesz basic sequences. Finally, we show how existing techniques can be applied to determine whether frames of translates can be written as the finite union of Riesz basic sequences. We end by giving an example of a frame of translates such that any Riesz basic subsequence must consist of highly irregular translates.
Intégrales orbitales tordues sur GL(n, F) et corps locaux proches : applications
Authors: Henniart Guy , Lemaire Bertrand 
Published: December 2010

RésuméSoient F un corps commutatif localement compact non archimédien, G = GL(n, F) pour un entier n ≥ 2, et κ un caractère de F× trivial sur (F×)n. On prouve une formule pour les κ-intégrales orbitales régulières sur G permettant, si F est de caractéristique > 0, de les relever à la caractéristique nulle. On en déduit deux résultats nouveaux en caractéristique à 0 : le “lemme fondamental” pour l’induction automorphe, et une version simple de la formule des traces tordue locale d’Arthur reliant κ-intégrales orbitales elliptiques et caractères κ-tordus. Cette formule donne en particulier, pour une série κ-discrète de G, les κ-intégrales orbitales elliptiques d’un pseudo-coefficient comme valeurs du caractère κ-tordu.
The General Structure of G-Graded Contractions of Lie Algebras I. The Classification
Authors: Weimar-Woods Evelyn 
Published: December 2010

AbstractWe give the general structure of complex (resp., real) G-graded contractions of Lie algebras where G is an arbitrary finite Abelian group. For this purpose, we introduce a number of concepts, such as pseudobasis, higher-order identities, and sign invariants. We characterize the equivalence classes of G-graded contractions by showing that our set of invariants (support, higher-order identities, and sign invariants) is complete, which yields a classification.
Some Results on the Schroeder–Bernstein Property for Separable Banach Spaces
Authors: Ferenczi Valentin , Galego Elόi Medina 
Published: December 2010

AbstractWe construct a continuum of mutually non-isomorphic separable Banach spaces which are complemented in each other. Consequently, the Schroeder–Bernstein Index of any of these spaces is 2ℵ0. Our construction is based on a Banach space introduced by W. T. Gowers and B. Maurey in 1997. We also use classical descriptive set theory methods, as in some work of the first author and C. Rosendal, to improve some results of P. G. Casazza and of N. J. Kalton on the Schroeder–Bernstein Property for spaces with an unconditional finite-dimensional Schauder decomposition.
On the Convergence of a Class of Nearly Alternating Series
Authors: Foster J. H. , Serbinowska Monika 
Published: December 2010

AbstractLet C be the class of convex sequences of real numbers. The quadratic irrational numbers can be partitioned into two types as follows. If α is of the first type and (ck) ∈ C, then ∑(—1)⎿ck⏌ converges if and only if ck log k → 0. If α is of the second type and (ck) ∈ C, then ∑(—1)⎿ck⏌ converges if and only if ∑ ck/k converges. An example of a quadratic irrational of the first type is and an example of the second type is . The analysis of this problem relies heavily on the representation of α as a simple continued fraction and on properties of the sequences of partial sums and double partial sums .
On Two Exponents of Approximation Related to a Real Number and Its Square
Authors: Roy Damien 
Published: December 2010

AbstractFor each real number ξ, let denote the supremum of all real numbers λ such that, for each sufficiently large X, the inequalities |x0| ≤ X, |x0ξ – x1| ≤ X–λ and |x0ξ2 – x2| ≤ X–λ admit a solution in integers x0, x1 and x2 not all zero, and let denote the supremum of all real numbers ω such that, for each sufficiently large X, the dual inequalities |x0 + x1ξ + x2ξ2| ≤ X–ω, |x1| ≤ X and |x2| ≤ X admit a solution in integers x0, x1 and x2 not all zero. Answering a question of Y. Bugeaud and M. Laurent, we show that the exponent where ξ ranges through all real numbers with [ℚ(ξ):ℚ] > 2 form a dense subset of the interval while, for the same values of ξ, the dual exponents form a dense subset of . Part of the proof rests on a result of V. Jarník showing that for any real number ξ with [ℚ(ξ):ℚ] > 2.
Weighted Inequalities for Hardy–Steklov Operators
Authors: Bernardis A. L. , Martín-Reyes F. J. , Ortega Salvador P. 
Published: December 2010

AbstractWe characterize the pairs of weights (v, w) for which the operator with s and h increasing and continuous functions is of strong type (p, q) or weak type (p, q) with respect to the pair (v, w) in the case 0 < q < p and 1 < p < ∞. The result for the weak type is new while the characterizations for the strong type improve the ones given by H. P. Heinig and G. Sinnamon. In particular, we do not assume differentiability properties on s and h and we obtain that the strong type inequality (p, q), q < p, is characterized by the fact that the functionbelongs to Lr(gqw), where 1/r = 1/q – 1/p and the supremum is taken over all c and d such that c ≤ x ≤ d and s(d) ≤ h(c).
Computations of Elliptic Units for Real Quadratic Fields
Authors: Dasgupta Samit 
Published: December 2010

AbstractLet K be a real quadratic field, and p a rational prime which is inert in K. Let α be amodular unit on Γ0(N). In an earlier joint article with Henri Darmon, we presented the definition of an element u(α, τ) ∊ Kxp attached to α and each τ ∈ K. We conjectured that the p-adic number u(α, τ) lies in a specific ring class extension of K depending on τ , and proposed a “Shimura reciprocity law” describing the permutation action of Galois on the set of u(α, τ). This article provides computational evidence for these conjectures. We present an efficient algorithm for computing u(α, τ), and implement this algorithm with the modular unit α(z) = Δ(z)2Δ(4z)/Δ(2z)3. Using p = 3, 5, 7, and 11, and all real quadratic fields K with discriminant D < 500 such that 2 splits in K and K contains no unit of negative norm, we obtain results supporting our conjectures. One of the theoretical results in this paper is that a certain measure used to define u(α, τ) is shown to be Z-valued rather than only Zp ∩ Q-valued; this is an improvement over our previous result and allows for a precise definition of u(α, τ), instead of only up to a root of unity.
A Weighted L2-Estimate of the Witten Spinor in Asymptotically Schwarzschild Manifolds
Authors: Finster Felix , Kraus Margarita 
Published: December 2010

AbstractWe derive a weighted L2-estimate of theWitten spinor in a complete Riemannian spin manifold (Mn, g) of non-negative scalar curvature which is asymptotically Schwarzschild. The interior geometry of M enters this estimate only via the lowest eigenvalue of the square of the Dirac operator on a conformal compactification of M.
On the Restriction to 𝒟* × 𝒟* of Representations of p-adic GL2(𝒟)
Authors: Raghuram A. 
Published: December 2010

AbstractLet be a division algebra over a nonarchimedean local field. Given an irreducible representation π of GL2(), we describe its restriction to the diagonal subgroup × . The description is in terms of the structure of the twisted Jacquet module of the representation π. The proof involves Kirillov theory that we have developed earlier in joint work with Dipendra Prasad. The main result on restriction also shows that π is × -distinguished if and only if π admits a Shalika model. We further prove that if is a quaternion division algebra then the twisted Jacquetmodule is multiplicity-free by proving an appropriate theorem on invariant distributions; this then proves a multiplicity-one theorem on the restriction to × in the quaternionic case.
Some Remarks on a Paper of McCarthy
Authors: Erdös P. 
Published: December 2010

As usual we denote the number of integers not exceeding n and relatively prime to n by Euler's ϕ function ϕ(n). Lehmer calls the ϕ(n) integersthe totatives of n.Denote by ϕ(k,l,n) the number of a's satisfyingIf nl ≡ 0 (mod k) or n(l + 1) ≡ 0 (mod k) then, since n > k, (n - l/k, n) > 1 and (n(l + 1)/k, n)>1 respectively. Thus ϕ(k, l, n) is the number of totatives of n satisfying
On a Normal Form of the Orthogonal Transformation II
Authors: Zassenhaus Hans 
Published: December 2010

In this section we continue to study the indecomposable matrix pairs adopting the same notation as in part I of this paper.If the matrix A is regular and if it is symmetric or anti-symmetric such that3.1and if the matrix pair (X, A) is indecomposable then the corresponding representation space either is indecomposable or it is the direct sum of two indecomposable invariant subspaces. These are operator isomorphic if and only if the minimal polynomial mX of X is equal to (x-δ)μ where3.2at any rate there is even a decomposition of the representation space into the direct sum of two isotropic indecomposable invariant subspaces provided the characteristic of F is not 2.
On the Distribution of Primitive Lattice Points in the Plane
Authors: Chalk J.H.H. , Erdos P. 
Published: December 2010

Let 1,θ1, θ2, …,θn be real numbers linearly independent over the rational field and let α1, α2,…, αn be arbitrary real numbers. Then, to each N > 0 and ε > 0, there correspond integerswhich satisfy the set of inequalitiesA
Solutions of the Functional Equation (f(x))2 - f(x2) = h(x)
Authors: Baker I. N. 
Published: December 2010

In a recent paper [2] Lambek and Moser have introduced the functional equations1and2in connection with some problems of number theory, in particular in dealing with the sums by pairs of sets of integers. The second may be put into the same form as (1) by the substitutions x = In z, f(ln z) = F(z), h(ln z) = H(z).
Reflexive Homomorphic Relations
Authors: Findlay G. D. 
Published: December 2010

It is well known that a symmetric and transitive relation on a set is reflexive wherever it is defined. In this note we show that a converse is true for homomorphic relations in certain classes of algebras.Consider a class of similar algebras which contains the sub-algebras and quotient algebras of each of its members. Assume also that the direct product A x B of each pair A, B in is also an algebra belonging to . The algebras of , being similar, have the same set of operations. We observe that other operations, called compound operations, may be obtained by composition from the assigned operations.
On a Problem of Erdös and Szekeres
Authors: Atkinson F. V. 
Published: December 2010

Write12where the maximum is over all real θ, and the lower bound is over all sets of positive integers a1 ≤ a2 ≤ … ≤ an. The problem of the order of magnitude of f(n) was posed by Erdös and Szekeres [1], side by side with a number of other interesting questions. Writing g(n) = log f(n), it is obvious that g(n) is sub-additive, in the sense that g(m+n) ≤ g(m) + g(n), and also that g(1) = log 2, so that g(n) ≤ n log 2.
Some Extensions of the Hausdorff-Young and Paley Theorems
Authors: Bullen P. S. 
Published: December 2010

Orthonormal sequences, o.n. s., {ϕn} defined on [0,1] and satisfying1have been studied in [3] and [1]. One of the objects of this paper is to indicate that the methods used to study such o. n. s. can be used for a much wider class, and that, although there seems to be no super theorem to cover all cases, a knowledge of the results and methods of proof in some fairly broad special cases enables one to state and prove theorems for other classes of o. n. s.
Right and Left Orthogonality
Authors: Wild Jonathan 
Published: December 2010

Let V be a vector space over an arbitrary field F. In V a bilinear formis given. If f is symmetric [(x, y) ≡ (y, x)] or skew-symmetric [(x, y) + (y, x) ≡ 0], then1Thus right and left orthogonality coincide. It is well known that (1) implies conversely that f is either symmetric or skew-symmetric in V. We wish to give a simple proof of this result.
The Exponent of a Primitive Matrix*
Authors: Dulmage A. L. , Mendelsohn N. S. 
Published: December 2010

Let A be an n by n matrix with non-negative entries. If a permutation matrix P exists such that P-1 is of the formwhere A and C are square matrices and O is a zero-matrix then A is said to be reducible. Otherwise, A is irreducible. If A is irreducible, then A is said to be primitive if there is an integer k such that Ak0, i.e., Ak has no zero entries. If A is primitive, the least integer m for which Am0 is called the exponent of A. In (4), Wielandt has shown that for n by n primitive matrices the exponent is at most (n-1)2+1. In this paper, the theory of directed graphs is used to determine conditions under which the exponent is less than (n-1)2+1. The following results are obtained. If A contains r non-zero entries along its main diagonal then its exponent is at most 2n-r-1, and this result is the best possible. If all the diagonal entries of A are zero but its graph KA (see next section for definition) contains a cycle of length d, then the exponent of A is at most d(2n-d-1). For the case where this improves Wielandt's result.
Another Remark on a Result of K. Goldberg
Authors: Marcus Marvin 
Published: December 2010

In [3] K. Goldberg showed that if A is a 0-1 matrix that satisfies(1.1)then for some permutation matrix P, PAP* is a direct sum of matrices each of
which is either zero or consists only of ones. More recently J. L. Brenner
[1] proved that if A ∦ 0 (i.e. A has non-negative entries) and satisfies (1)
then there exists a permutation matrix P such that PAP* = A1⊕ …
⊕An in in which each Ai is either 0 or all
positive, Ai > 0, and satisfies (1) as well.
A Generalization of an Inversion Formula for the Gauss
Transformation
Authors: Rooney P. G. 
Published: December 2010

In an earlier paper [3] we considered an inversion formula for the Gauss
transformation G defined by1.1We noted there that formally G is inverted by,1.2and we showed that if e-D2 is interpreted via the power series for the exponential function,
that is if1.3then under certain conditions on φ,1.4
The Lebesgue Constants for (γ, r) Summation of Fourier Series
Authors: Lorch Lee , Newman Donald J. 
Published: December 2010

The (γ, r) summation method, 0 < r < 1, is the "circle method" employed by G. H. Hardy and J. E. Littlewood. It is also known as the Taylor method. Its Lebesgue constants, say L(Tr, n), n = 1, 2, …, were studied by K. Ishiguro [1] in the notation L*(n;1-r). He noted that1where Im{z} denotes the imaginary part of the complex number z, and proved that2Here3
Remarks on a Problem of Obreanu
Authors: Erdös P. , Rényi A. 
Published: December 2010

Let a1 < a2 < … be any sequence of integers. Assume that the infinite sequence of numbers un satisfies the following condition: To every ɛ > 0 there is an no = no (ɛ) such that for all n > no and all k1Obreanu asked (Problem P. 35 Can. Math. Bull.) under what conditions on the sequence a1 < a2 < … does (1) imply that the sequence u is convergent. N. G. de Bruijn and P. Erdos proved that a necessary and sufficient condition for (1) to imply the convergence of un is that the sequence {an} be infinite and that the greatest common divisor of the a1 should be 1.
On a Paper by M. Iosifescu and S. Marcus
Authors: Neugebauer C. J. 
Published: December 2010

In this paper we will construct an example showing that the problem posed in [1] has a negative answer. Two more theorems on the subject treated in [1] will be included.Let Io = [0, 1], R the reals, and let, for A ⊂ R, Ao be the interior of A. Let {xn} be a sequence in [0, 1> such that 0 = x1 < x2 < … and lim xn = 1. For each n, let In be closed interval having x as its midpoint (except for n = 1 in which case x1 is the left endpoint of I1) such that In ∩ Im= ϕ, and the metric density relative to Io of at 1 is zero. Let Jn be a closed interval in In concentric with In (except for n = 1, where J1 has x1 as its left endpoint) whose length is half that of In
On a Factorisation of Positive Definite Matrices
Authors: Majindar Kulendra N. 
Published: December 2010

All our matrices are square with real elements. The Schur product of two n × n matrices B = (bij) and C = (cij) (i, j, = 1, 2, …, n), is an n × n matrix A = (aij) with aij = bij cij, (i, j = 1, 2, …, n).A result due to Schur [1] states that if B and C are symmetric positive definite matrices then so is their Schur product A. A question now a rises. Can any symmetric positive definite matrix be expressed as a Schur product of two symmetric positive definite matrices? The answer is in the affirmative as we show in the following theorem.
Remarks on a Paper by S. Trott
Authors: Moser W. O. J. 
Published: December 2010

There are several statements in [3] which require clarification.Theorem 1 [3, p. 246] states that U3= U2U4 U2-1U4 U2 U4. In fact this is (essentially) the relation O = PUPU-1PU given in [1, p. 91, (7.35)]. To see this we note that 0 = U3, P = U4, U = U4U2U4 (as explained in [1, p. 88]); since U42, = E,
Notes on Numerical Analysis IV. On Accelerating Iteration Procedures With Superlinear Convergence
Authors: Kotzé Wesley 
Published: December 2010

In the study of algorithms for the iterative solution of an arbitrary analytic equation f(z) = 0, acceleration procedures are of importance in practice and of considerable interest in the theory of the subject. Let.be an iteration formula which has a zero ξ of f(z) as attractive fixed point. An algorithm of this type is said to converge towards a root ξ of f(z) = 0 for all initial approximations z = z0 in a vicinity of ξ, of order k > 0, when1.
On Some Divisibility Properties of
Authors: Erdös P. 
Published: December 2010

L. Moser [3] recently gave a very simple proof that1.has no solutions. In the present note we shall first of all prove that for , which by the fact that there is a prime p satisfying n < p ≤ 2n immediately implies that2.has no solutions. It is easy to see on the other hand that3.has infinitely many non-trivial solutions.
On Differentiable Functions having an Everywhere Dense set of Intervals of Constancy
Authors: Bruckner A. M. , Leonard John L. 
Published: December 2010

The Cantor function C [2; p. 213], which appears in analysis as a simple example of a continuous increasing function which is not absolutely continuous, has the following properties:(i)C is defined on [0,1], with C(0) = 0, C (l) = l;(ii)C is continuous and non-decreasing on [0,1];(iii)C is constant on each interval contiguous to the perfect Cantor set P;(iv)C fails to be constant on any open interval containing points of P;(v)The set of points at which C is non-differentiable is non-denumerable.
On the General Theory of Differentiable Manifolds with Almost Tangent Structure
Authors: Eliopoulos Hermes A. 
Published: December 2010

Some of the most important G-Structures of the first kind [1] are those defined by linear operators satisfying algebraic relations. If the linear operator J acting on the complexified space of a differentiable manifold V satisfies a relation of the formwhere I is the identity operator, the manifold has an almost complex structure ([2] [3]). The structures defined byare the almost product structures ([3] [4]).
A Generalization of the Bang-Bang Principle of Linear Control Theory*
Authors: Datko Richard 
Published: December 2010

In a paper by LaSalle [l] on linear time optimal control the following lemma is proved:Let Ω be the set of all r-dimensional vector functions U(τ) measurable on [ 0, t] with |ui(τ)≦1. Let Ωo be the subset of functions uo(τ) with |uoi(τ) = 1. Let Y(τ) be any (n × r ) matrix function in L1([ 0, t]).
Lebesgue Constants for Regular Taylor Summabllity
Authors: Forbes R. L. 
Published: December 2010

The nth Taylor mean of order r of a sequence {sn} is given by1.1where1.2Cowling [l] has shown that this method is regular if and only if 0 ≦ r < 1. Since r = 0 corresponds to ordinary convergence, it will be assumed here that 0 < r < 1.
On the Reducibility of Appelles Function F4*
Authors: Saxena R.K. 
Published: December 2010

It is a well-known fact in the theory of Appell's hypergeometric function of two variables F4, defined by1where |x|1/2 + |y|1/2 < 1, that it can be expressed interms of products of ordinary hypergeometric functions when γ + γ' = α + β + 1.
On Subtournaments of a Tournament
Authors: Moon J. W. 
Published: December 2010

Beineke and Harary [l] recently showed that the maximum number of strong tournaments with k nodes that can be contained in a tournament with n nodes isif 3 ≤ k ≤ n. The object of this note is to obtain some additional results of this type. We will use essentially the same terminology as was used in [ l ], so we will not repeat the standard definitions here.
On Periodic Solutions of x‴ + ax″ + b′ + g(x) = 0
Authors: Kemp R.R.D. 
Published: December 2010

In [1] J. O. C. Ezeilo asks whether the equation1has periodic solutions for a ≠ 0. Since (1) has a two-dimensional space of solutions of period 2π if sin x is approximated by x, it is plausible to conclude, by analogy with x″ + sin x = 0, that (1) does have periodic solutions. However, when one applies the standard theory of perturbation of periodic solutions (treating a as small, see [2]), one finds that the only real periodic solutions obtainable in this manner are the trivial ones x(t, a) = nπ for some integer n.
A Discrete Analogue of Opial's Inequality
Authors: Wong James S. W. 
Published: December 2010

In a number of papers [1] - [7], successively simpler proofs were given for the following inequality of Opial [1], in case p=1.Theorem 1. If x(t) is absolutely continuous with x(0)=0, then for any p ≧ 0,(1)Equality holds only if x(t) = Kt for some constant K.