bluuebunny/crossref_metadata_2025_split huggingface dataset:
Reducible Rational Fractions of the type of Gaussian Polynomials with only Non-Negative Coefficients
Authors: Grosswald Emil 
Published: December 2010

The following problem arose in connection with the study of Poincaré polynomials for homogeneous spaces. Letgi hi positive integers and set d = (h1, h1,…, hk), the greatest common divisors of the exponents in the denominator. Let hi = dri and assume that the ri′s are comprime in pairs, i.e.
Maximum Modulus Theorems and Schwarz Lemmata for Sequence Spaces, II
Authors: Shawyer B. L. R. 
Published: December 2010

In this note, we continue the investigations of [3], proving another analogue of the maximum modulus theorem, this time for the sequence space bv, and we investigate maximal functions for such theorems. As in [3], we use the notation f∈MM if f is analytic in the disk |z| <1, continuous for |z| ≤ 1 and satisfies |f(z)| ≤ 1 on |z| = 1. We also write f∈SL if f∈MM and f(0) = 0. Whenever x={xk} is a sequence of complex numbers, we write f(x) = {f(xk)}.In [3], we proved analogues of the maximum modulus theorem for the sequence spaces 5, m and c, and analogues of the Schwarz Lemma for the sequence spaces c0, lp and bv0. We begin this note with the sequence space bv.
Covering Finite Sets by Ergodic Images
Authors: Steele J. Michael 
Published: December 2010

AbstractFor any ergodic transformation T a set A of measure less than ∈ is constructed with the property that for every finite set F there is a j = j(F) such that F ⊂ T-iA. The basic tool used to prove this is a purely combinatorial result which says there is a small subset of { l, 2, …, n } which can be shifted a small amount to cover any k set in {j: δn ≤j≤n}. Applications are given to the theory of combinatorial entropy.
A Sum of Reciprocals of Least Common Multiples
Authors: Borwein D. 
Published: December 2010

The purpose of this note is to prove the following theorem conjectured by P. Erdös.Theorem. Let a0, a1, …, ak be integers satisfying 1 ≤ a0 a1 … k, and let [ai-1 ai] denote the least common multiple of ai-1 and ai Then1with equality occurring if and only if ai = 2i for 1 ≤ i ≤ k.
On Almost Continuous Mappings and Baire Spaces
Authors: Lin Shwu-Yeng T. , Lin You-Feng 
Published: December 2010

AbstractIt is proved, in particular, that a topological space X is a Baire space if and only if every real valued function f: X →R is almost continuous on a dense subset of X. In fact, in the above characterization of a Baire space, the range space R of real numbers may be generalized to any second countable, Hausdorfï space that contains infinitely many points.
An Interpolatory Rational Approximation
Authors: Meir A. 
Published: December 2010

The classical Hermite-Fejér interpolation process is a positive linear mapping from C[-1, 1] into the space of polynomials of degree ≤2n-1. If Tn(x) denotes the Tchebisheff polynomial of degree n and xk = xnk(k = 1,2, …, n) its roots, then for any given f∈ C[-1, 1] the Hermite-Fejér image Hnf of f is defined by1.1
Note on Attaching Dold Fibrations
Authors: Heath Philip R. , Kamps Klaus Heiner 
Published: December 2010

In this note, we patch up the proof of a Theorem due to Handel on the characterization of homotopy epimorphisms ([6], 2.2) and generalize a Theorem due to Ibisch on attaching disk-bundles to Dold fibrations ([7], Satz 1).We work throughout in the category TopB of spaces over B for some fixed topological space B.
On Approximately Finite-Dimensional Von Neuman Algebras, II
Authors: Elliott George A. 
Published: December 2010

AbstractAn intrinsic characterization is given of those von Neumann algebras which are injective objects in the category of C*-algebras with completely positive maps. For countably generated von Neumann algebras several such characterizations have been given, so it is in fact enough to observe that an injective von Neumann algebra is generated by an upward directed collection of injective countably generated sub von Neumann algebras. The present work also shows that three of the intrinsic characterizations known in the countably generated case hold in general.
Linear Functional-Differential Equations in a Banach Algebra*
Authors: Fitzpatrick W. J. , Grimm L. J. 
Published: December 2010

The theory of analytic differential systems in Banach algebras has been investigated by E. Hille and others, see for instance Chapter 6 in [4].In this paper we show how a projection method used by W. A. Harris, Jr., Y. Sibuya, and L. Weinberg [3] can be applied to study a class of functional differential equations in this setting. The method, based on functional analysis, had been used extensively by L. Cesari [1] in similar forms for boundary value problems, and by J. K. Hale, S. Bancroft, and D. Sweet [2]. We also obtain as corollaries several results for ordinary differential equations in Banach algebras which were proved in a different way by Hille.
Identité Pour
Authors: Mercier Armel 
Published: December 2010

Dans cet article, nous établirons un théorème sur la représentation de certaines séries de Dirichlet (ceci généralise un résultat de [3]). Avec ce nouveau résultat nous donnerons seulement quelques applications qui évidemment pourraient être augmentées de beaucoup. Par exemple, nous donnerons une expression asymptotique pour1
On Surfaces of Order Three
Authors: Bisztriczky Tibor 
Published: December 2010

A surface of order threeFin the real projective three-spaceP3is met by every line, not inF, in at most three points.In the present paper, we determine the existence and examine the distribution of elliptic, parabolic and hyperbolic points; that is, the differentiable points ofFwhich do not lie on any line contained inF.
On Basis Constants and Duality in Banach Spaces
Authors: Dor Leonard E. 
Published: December 2010

AbstractEvery Banach space with a non-shrinking (unconditional) basis (Xi) can be renormed so that the biorthogonal sequence has a much smaller (unconditional) basis constant than (xi). On the other hand, if the unconditional constant of is C < 2 then the unconditional constant of (xi) is at most C/(2—C). This estimate is sharp.
Une Double Généralisation du Théorème de Fejér-Lebesgue
Authors: Lessard Sabin 
Published: December 2010

SommaireNous nous emploierons dans cet article à démontrer la convergence presque partout pour les moyennes de projections orthogonales croissantes sur L2, qui sont ou bien u.a.c. ou bien positives, ce qui nous donnera une double généralisation du théorème classique de Fejér-Lebesgue pour les séries de Fourier. Enfin nous terminerons en énonçant un résultat général qui englobe tous ceux connus jusqu'à maintenant avec la condition u.a.c. (cf. R. Duncan, Can. Math. Bull. 20 (1977) 277-284).
The Individual Ergodic Theorem for Contractions with Fixed Points
Authors: Olsen James H. 
Published: December 2010

Let (X, I, μ) be a σ-finite measure space and let T take Lp to Lp, p fixed, 1<p<∞,‖t‖p≤1. We shall say that the individual ergodic theorem holds for T if for any uniform sequence K1, k2,… (for the definition, see [2]) and for any f∊LP(X), the limitexists and is finite almost everywhere.
Multifunctions and Inverse Cluster Sets
Authors: Joseph James E. 
Published: December 2010

AbstractIn this paper the notion of inverse cluster set, which was recently introduced and studied for functions by T. R. Hamlett and P. E. Long (Proc. Amer. Math. Soc, 53 (1975), 470-476), is extended to and investigated for multifunctions. We generalize the notion of inverse cluster set, extend to multifunctions and generalize some known results for inverse cluster sets of functions and offer some new results. In the latter sections, compactness generalizations are characterized in terms of inverse cluster sets and some results on connected and conectivity functions are extended to multifunctions.
On the Continued Fractions of Conjugate Quadratic Irrationalities
Authors: Herzog Fritz 
Published: December 2010

Let1be the simple continued fraction (SCF) of an irrational number x. The partial quotients ai which we shall sometimes refer to as the "terms" of the SCF are integers and, for i ≥ 2, they are positive. If x is a quadratic irrationality then, by Lagrange's Theorem, the right side of (1) becomes periodic from some point on.
A Construction of Approximately Finite-Dimensional Non-ITPFI Factors
Authors: Connes Alain , Woods E. J. 
Published: December 2010

A von Neumann algebra is said to be approximately finite-dimensional if it is of the formwhere Mn⊆Mn+1 for each n and each Mn is a finite-dimensional matrix algebra. A factor is said to be ITPFI if it is of the form
A Characterisation of Locally Compact Amenable Subsemigroups
Authors: Wong James C. S. 
Published: December 2010

AbstractIn this paper, we prove that if S is a locally compact semigroup and T a locally compact Borel measurable subsemigroup of S, then T has a topological left invariant mean if and only if there is a topological left T-invariant mean M on S such that M(xT) = 1, where xT is the characteristic functional of T in S.
Least Positive Residues and the Quadratic Character of Two
Authors: Rosen Kenneth H. 
Published: December 2010

Let be the least positive residue modulo 2tk of (2j- l)h. Define ut to be the number of with l≤j≤2t-2k such that . At the Special Session in Combinatorial Number Theory at the 1977 Summer AMS Meeting Szekeres [2] asked for a simple proof that if (h, 2k)=1, thenHere a simple proof will be given for the following equivalent result.
Spherical Harmonics on the Heisenberg Group
Authors: Greiner Peter C. 
Published: December 2010

H1. Equip ℝ3 with the group law(1.1)where (z, t) stands for (x, y, t). This is a nilpotent Lie group, usually referred to as the first Heisenberg group, H1. In general Hk denotes ℝ2k+1 equipped with a similar group law, namely
Sur Une Equation Differentielle Fonctionnelle Analytique*
Authors: Bélair Jacques 
Published: December 2010

Nous considérons dans cette note une classe d′équations différentielles fonctionnelles linéaires dont les coefficients sont analytiques; des résultats sur l′ordre des solutions et leur comportement asymptotique seront obtenus.Il s'agit d'une généralisation à des équations du deuxiéme ordre d'une propriété d'équations d'ordre un [2]: la démonstration du théoréme principal demeure valable dans ce dernier cas.
On the Relation between the Logarithmic and Borel-Type Summability Methods
Authors: Borwein D. , Watson B. 
Published: December 2010

Suppose throughout that {sn} is a sequence of real numbers, λ > - 1, a > 0, and β is real. Let N be any non-negative integer such that αN + β > l.We are concerned primarily with the logarithmic summability method L and the Borel-type method (B, α, β). Some known results involve the Abel-type summability method Aγ.
On Certain Sequence Spaces
Authors: Kizmaz H. 
Published: December 2010

AbstractIn this paper define the spaces l∞(Δ), c(Δ), and c0(Δ), where for instance l∞(Δ) = {x=(xk):supk |xk -xk + l|< ∞}, and compute their duals (continuous dual, α-dual, β-dual and γ-dual). We also determine necessary and sufficient conditions for a matrix A to map l∞(Δ) or c(Δ) into l∞ or c, and investigate related questions.
Construction of Satisfaction Classes for Nonstandard Models
Authors: Kotlarski H. , Krajewski S. , H. Lachlan A. 
Published: December 2010

AbstractGiven a resplendent model for Peano arithmetic there exists a full satisfaction class over , i.e. an assignment of truth-values, to all closed formulas in the sense of with parameters from , which satisfies the usual semantic rules. The construction is based on the consistency of an appropriate system of -logic which is proved by an analysis of standard approximations of nonstandard formulas.
On Integrals and Summable Trigonometric Series
Authors: Lee Cheng-Ming 
Published: December 2010

AbstractIn considering a problem on certain summable (C, k) trigonometric series, R. D. James [13] used a symmetric pk+2- integral defined earlier to recapture the coefficients of the series from the sum function. James' formulas for the coefficients are more complicated than the usual Euler-Fourier form since the pk + 2 - integral is of order k + 2. It is shown that a generalized integral of order one for each non-negative integer k can be suitably defined to reduce James' formulas to the usual form.
The Integers as Differences of a Sequence
Authors: Pollington Andrew , Vanden Eynden Charles 
Published: December 2010

AbstractIt is shown that there exists a sequence of integers a1 < a2 <... such that each positive integer is a difference of elements of the sequence in exactly one way, and such that ak does not exceed a constant times k3. In fact we construct such a sequence with each ak in [C(k -1)3, Ck3), where C is an absolute constant.
Polyedres Equilibres
Authors: Bantegnie Robert , Coxeter H. S. M. 
Published: December 2010

AbstractDans une note au C. R. Math. Rep. Ac. Se. Canada [1] qui peut servir de préliminaire, j’ai annoncé qu'on ne pouvait trouver de polyèdres convexes équilibrés non strictement équilibrés qui, à une isomorphic près, ne soient pas dans la liste de Johnson [4]. Nous donnons ici la preuve.Rappelons qu'on dit qu'un polyèdre convexe fermé borné est strictement équilibré resp. équilibré quand le cycle resp. le pseudocycle de chaque sommet est le même. Les polyèdres strictement équilibrés sont α) les polyèdres uniformes β) le polyè'dre de Miller appelé pseudo-rhombicuboctaèdre dans [9], petit rhombicuboctaèdre tordu dans [6], gyrobicupola carré allongé dans [4] et attribué à tort à Ashkinuze dans [7].
Oscillation Criteria for a Class of Perturbed Schrödinger Equations
Authors: Kusano Takaŝi , Naito Manabu 
Published: December 2010

We are concerned with the oscillatory behavior of the second order elliptic equation1where Δ is the Laplace operator inn-dimensional Euclidean spaceRn,Eis an exterior domain inRn, andc:E × R → Randf:E → Rare continuous functions.A functionv : E − Ris called oscillatory inEifv(x) has arbitrarily large zeros, that is, the set {x∈E:v(x) = 0} is unbounded. For brevity, we say that equation (1) is oscillatory inEif every solutionu∈C2(E) of (1) is oscillatory inE.
Functions in All Hp Spaces, p < ∞
Authors: Campbell Douglas M. 
Published: December 2010

AbstractLet Ĥ denote the class of functions analytic in |z| < 1 which are in every Hp class, 0 < p < ∞. The class Ĥ strictly contains H∞ and consists of those functions that are ‘almost in H∞’ in the sense of integration. L. Hansen and W. Hayman have given simple geometric conditions for a function to belong to Ĥ. The purpose of this note is to show that Hansen and Hayman's conditions are far from necessary. Using techniques from normal functions, gap series, characterizations of BMOA, subordination, Bloch functions, and VMOA, six completely different examples of functions in Ĥ are given which ‘fill the plane’.
A Group Theoretic Approach to the Equations of Plasma Physics
Authors: Marsden Jerrold E. 
Published: December 2010

AbstractThis paper concerns the interaction between group theory and classical mechanics in general and with the application of this theory to plasma physics in particular.Mechanics has had a profound role in the historical development of mathematics. Leading original thinkers in pure mathematics such as Newton, Euler, Lagrange, Jacobi, Laplace, Cauchy, Gauss, Riemann, Poincaré, Hilbert, Birkhofï, Smale and Arnold were also great original thinkers in various facets of mechanics. The interaction between mechanics and pure mathematics remains one of the most active and flourishing areas of current research. It is this flavor which I hope to convey in this lecture.
Solvable Groups of Unipotent Elements in a Ring
Authors: Klein Abraham A. 
Published: December 2010

AbstractLet R be a ring with 1 whose nil subrings are nilpotent modulo the sum of nilpotent ideals. It is proved that if G is a locally solvable group of unipotent elements in R, then the subring generated by {g −1 g ∈ G} is nil. This result implies a result of Sizer showing that a solvable group of unipotent matrices over a skew field can be simultaneously triangularized.
On the Divisibility of the Class Numbers of Q(√−p) and Q(√−2p) by 16.
Authors: Leonard Philip A. , Williams Kenneth S. 
Published: December 2010

AbstractLet h(m) denote the class number of the quadratic field Q(√m). In this paper necessary and sufficient conditions for h (m) to be divisible by 16 are determined when m = −p, where p is a prime congruent to 1 modulo 8, and when m = −2p, where p is a prime congruent to ±1 modulo 8.
Discrete Sets and Discrete Maps
Authors: Warren Richard H. 
Published: December 2010

AbstractA subset of a topological space is called discrete iff every point in the space has a neighborhood which meets the set in at most one point. Discrete sets are useful for decomposing the images of certain maps and for generalizing closed maps. All discrete sets are closed iff the space is T1. As a result of characterizing discrete and countably discrete maps, theorems due to Vaĭnšteĭn and Engelking are extended to these maps.
The Extended Center of Coproducts
Authors: Martindale Wallace S. 
Published: December 2010

AbstractThe sole purpose of this paper is to prove that if R1 and R2 are algebras with 1 over a common field F, with each (Ri:F) > 1 and at least one (Ri:F) > 2, then the extended center of the coproduct R1∐R2 is equal to F.
A Counterexample in the Perturbation Theory of C*-Algebras
Authors: Johnson B. E. 
Published: December 2010

AbstractThe strongest positive results in the stability theory of C*-algebras assert that if are sufficiently close C*-subalgebras of (H) of certain kinds, then there is a unitary operator U on H near I, such that . We give examples of C*-algebras , both isomorphic to the algebra of continuous functions from [0, 1] to the algebra of compact operators on Hilbert space, which can be as close as we like, yet for which there is no isomorphism α: → with . Thus the	results mentioned do not extend to these C*-algebras.
K0 D’Un Anneau Dont Les Localises Centraux Sont Simples Artiniens
Authors: Burgess W. D. , Goursaud J.-M. 
Published: December 2010

AbstractThe purpose of the note is to calculate the group K0(A) where A is a ring all of whose Pierce stalks are simple artinian. This generalizes known results for A self injective of type In. For A regular, with injective hull, Â, of type In, a characterization is given for when A → Â it induces an isomorphism K0(A) → K0(Â).
Abel Transformations Into I1
Authors: Fridy J. A. 
Published: December 2010

AbstractLet t be a sequence in (0,1) that converges to 0, and define the Abel matrix At by ank = tn(1-tn)k. The matrix At determines a sequence-to-sequence variant of the classical Abel summability method. The purpose of this paper is to study these transformations as l-l summability methods: e.g., At maps l1 into l1 if and only if t is in l1. The Abel matrices are shown to be stronger l-l methods than the Euler-Knopp means and the Nӧrlund means. Indeed, if t is in l1 and Σ xk has bounded partial sums, then Atx is in l1. Also, the Abel matrix is shown to be translative in an l-l sense, and an l-l Tauberian theorem is proved for At.
Bounded Solutions of a Functional Inequality
Authors: Albert Michael , Baker John A. 
Published: December 2010

AbstractIt is known that if f is a real valued function on a rational vector space V, δ > 0,1and if f is unbounded then f(x + y) = f(x)f(y) for all x, y ∊ V. In response to a problem of E. Lukacs, in this paper we study the bounded solutions of (1). For example, it is shown that if f is a bounded solution of (1) then - δ ≤ f(x) ≤ (1 + (1 + 4δ)1/2)/2 for all x ∊ V and these bounds are optimal.
The Local Class Group of a Krull Domain
Authors: Bouvier A. 
Published: December 2010

AbstractThe local class group of a Krull domain A is the quotient group G(A) = CI(A)/Pic(A). A Krull domain A is locally factorial if and only if G(A) = 0. In this paper, we characterize the Krull domains for which G(A) is a torsion group. We evaluate the local class group of several examples and finally, we explain why every abelian group is the local class group of a Krull domain.
On Uniform Semigroup-Valued Additive Set Functions
Authors: Fox Geoffrey , Morales Pedro 
Published: December 2010

AbstractThe main results of this paper are the following: (1) An extension theorem for a uniform semigroup-valued measure on a ring to the generated σ-ring. This result unifies the classieal Hahn-Carathéodory theorem, the extension theorem of Sion and a more recent result of Weber.(2) A theorem stating that every monocompact additive uniform semigroup-valued set function on a semiring is σ-additive. This result generalizes several earlier theorems of Alexandroff, Dinculeanu-Kluvanek, Glicksberg, Huneycutt, Mallory, Marczewski, Millington and Topsøe.
A Topological Characterization of Gleason Parts of Real Function Algebras
Authors: Kulkarni S. H. , Limaye B. V. 
Published: December 2010

AbstractIt is well-known that a topological space is a Gleason part of some complex function algebra if and only if it is completely regular and σ-compact. In the present paper, a Gleason part of a real function algebra is characterized as a completely regular σ-compact topological space which admits an involutoric homeomorphism.
A Banach Space which is Fully 2-Rotund but not Locally Uniformly Rotund
Authors: Polak T. , Sims Brailey 
Published: December 2010

AbstractA Banach space is fully 2-rotund if (xn) converges whenever ‖xn + xm‖ converges as m, n → ∞ and locally uniformly rotund if xn → x whenever ‖xn‖ and ‖(xn + x)/2‖ → ‖x‖.We show that I2 with the equivalent normis fully 2-rotund but not locally uniformly rotund, thus answering in the negative a question first raised by Fan and Glicksberg in 1958.
A Regular Summability Method which Sums the Geometric Series to its Proper Value in the Whole Complex Plane
Authors: Tomm Ludwig 
Published: December 2010

AbstractIn this paper an explicit regular sequence-to-sequence summability method is presented which sums the geometric series to the value 1/(1-z) in all of ℂ\{1} and to infinity at the point 1. The method also provides compact convergence in ℂ \ [ 1, ∞) and therefore improves well-known results by Le Roy, Lindelöf and Mittag-Leffler.
Hülder Conditions and the Topology of Simply Connected Domains*
Authors: Aharonov Dov 
Published: December 2010

AbstractLet ƒ be regular univalent and normalized in the unit disc U (i.e. ƒ ∊ S) and continuous on U ∈ T, where T denotes the boundary of U.Recently Essén proved [5] a conjecture of Piranian [7] stating that if the derivative of ƒ ∊ S is bounded in U and ƒ(z1) = ƒ(z2) = … = ƒ(zn) for Zj ∊ T, 1 ≤ j ≤ n, then n ≤ 2. In fact, Essén proved a more general result, using a deep result on harmonic functions. The aim of the following article is to replace Essén's proof by a completely different proof which is based only on Goluzin's inequalities and is much more elementary.
Sur Les Sous-Groupes Normaux De SL2 Sur Un Anneau Local
Authors: Lacroix N. H. J. , Levesque C. 
Published: December 2010

ResumeSoit GLn (υ) le groupe des matrices inversibles n × n sur υ et soit SLn (υ) le groupe des matrices n × n de déterminant 1 sur υ. Lorsque υ est un anneau local avec idéal maximal p, W. Klingenberg (Amer. J. Math. 1961) a classifié les sous-groupes normaux de GLn(υ) et de SLn(υ) au moyen de certains groupes de congruences déterminés par les idéaux de o, sauf lorsque n = 2 et 2 ∊ p ou υ/p = 𝔽3. Ces cas furent étudiés par N. H. J. Lacroix (Can. J. Math. 1969) qui trouva (lorsque υ/p≠𝔽2) la même classification pour les sous-groupes normaux de GL2(υ) ; sa méthode donne simultanément la même classification également pour les sous-groupes normaux de SL2(υ) si l'anneau o satisfait à une forte condition appelée Propriété T.Au cours de cette note, nous précisons que les sous-groupes normaux de SL2(υ) obéissent à la classification de Klingenberg si et seulement si υ a la Propriété T. Par la suite nous montrons qu'en l'absence de cette condition, l'on n'a pas de vraie classification basée sur les transvections. Divers résultats sur les sous-groupes normaux illustrent ce qu'on peut attendre d'une entreprise visant à décrire les sous-groupes normaux de SL2(υ) en l'absence de la Propriété T.