bluuebunny/crossref_metadata_2025_split huggingface dataset:
Characterizations for Prime Semilattices
Authors: Shum K. P. , Chan M. W. , Lai C. K. , So K. Y. 
Published: December 2010

Throughout this paper when we refer to a semilattice S we shall mean that S is a meet semilattice. We shall denote the infimum of two elements a, b of S by a ∧ b, and the supremum, if it exists, by a ∨ b. A prime semilattice is a meet semilattice such that the infimum distributes over all existing finite suprema, in the sense that if x1 ∨ x2 … ∨ xn exists then (x ∧ x1) ∨ (x ∧ x2) … ∨ (x ∧ xn) exists for any x and equals x ∧ (x1 ∨ x2 … ∨ xn). Such semilattices were first studied by Balbes [1]
and we use his terminology.A non-empty subset F of S is a filter provided that x ∧ y ∊ F if and only if x ∊ F and y ∊ F.
Directed Graphs and the Jacobi-Trudi Identity
Authors: Goulden I. P. 
Published: December 2010

Let |aij|n×n denote the n × n determinant with (i, j)-entry aij, and hk = hk(x1, …, xn) denote the kth-homogeneous symmetric function of x1, …, xn defined bywhere the summation is over all m1, …, mn ≧ 0 such that m1 + … + mn = k. We adopt the convention that hk = 0 for k < 0. For integers α1 ≧ α2 … ≧ αn ≧ 0, the Jacobi-Trudi identity (see [6], [7]) states thatIn this paper we give a combinatorial proof of an equivalent identity, Theorem 1.1, obtained by moving the denominator on the RHS to the numerator on the LHS.
Extending Algebras to Model Congruence Schemes
Authors: Berman J. , Grätzer G. , Platt C. R. 
Published: December 2010

This paper is concerned with the description of principal congruence relations. Given elementsaandbof a universal algebra, let θ(a, b) denote the smallest congruence relation oncontaining the pair 〈a, b〉. One of the earliest characterizations of θ(a, b) is Mal'cev's well-known result [5, Theorem 1.10.3], which says thatc≡d(θ(a, b))if and only if there exists a sequencez0,z1, …,znof elements ofand a sequencef1,f2, …,fnof unary algebraic functions such thatc=z0,d=zn, and for eachi= 1, …,n,Although this describes θ(a, b) in terms of a set of unary algebraic functions, it is not possible to predict the number or complexity of the unary functions used independently of the choice ofa, b, candd. Several recent papers ([1], [2], [3], [4], [6]) investigate classes of algebras in which principal congruences are simpler.
Solution of a Problem of L. Fuchs Concerning Finite Intersections of Pure Subgroups
Authors: Göbel R. , Vergohsen R. 
Published: December 2010

L. Fuchs states in his book “Infinite Abelian Groups” [6, Vol. I, p. 134] the followingProblem 13. Find conditions on a subgroup of A to be the intersection of a finite number of pure (p-pure) subgroups of A.The answer to this problem will be given as a special case of our theorem below. In order to find a better setting of this problem recall that a subgroup S ⊆ E is p-pure if pnE ∩ S = pnS for all natural numbers. Then S is pure in E if S is p-pure for all primes p. This generalizes to pσ-isotype, a definition due to L. J. Kulikov, cf. [6, Vol. II, p. 75] and [11, pp. 61, 62]. If α is an ordinal, then S is pσ-isotype if
Generators of Chevalley Groups over Z
Authors: Chang Bomshik 
Published: December 2010

Let be the universal Chevalley group ([1], p. 197) of type over a field K and where Ф is the set of roots of . Let n = {α1, α2, …, an} be a fundamental system of roots of and putThen we know from [2] (p. 950) thatwhere h is the Coxeter number of We call an element of conjugate to W a Coxeter element and an element conjugate to M a Kac element.
Proximal Analysis and Boundaries of Closed Sets in Banach Space, Part I: Theory
Authors: Borwein J. M. , Strojwas H. M. 
Published: December 2010

As various types of tangent cones, generalized derivatives and subgradients prove to be a useful tool in nonsmooth optimization and nonsmooth analysis, we witness a considerable interest in analysis of their properties, relations and applications.Recently, Treiman [18] proved that the Clarke tangent cone at a point to a closed subset of a Banach space contains the limit inferior of the contingent cones to the set at neighbouring points. We provide a considerable strengthening of this result for reflexive spaces. Exploring the analogous inclusion in which the contingent cones are replaced by pseudocontingent cones we have observed that it does not hold any longer in a general Banach space, however it does in reflexive spaces. Among the several basic relations we have discovered is the following one: the Clarke tangent cone at a point to a closed subset of a reflexive Banach space is equal to the limit inferior of the weak (pseudo) contingent cones to the set at neighbouring points.
The Geometry of GF(q3)
Authors: Sherk F. A. 
Published: December 2010

1. Introduction. Inversive geometry involves as basic entities points and circles [2, p. 83; 4, p. 252]. The best known examples of inversive planes (the Miquelian planes) are constructed from a field K which is a quadratic extension of some other field F. Thus the complex numbers yield the Real Inversive Plane, while the Galois field GF(q2)(q = pe, p prime) yields the Miquelian inversive plane M(q) [2, chapter 9; 4, p. 257]. The purpose of this paper is to describe an analogous geometry of M(q) which derives from GF(q3), the cubic extension of GF(q).The resulting space, is three-dimensional, involving a class of surfaces which include planes, some quadric surfaces, and some cubic surfaces. We explore these surfaces, giving particular attention to the number of points they contain, and their intersections with lines and planes of the space .
A Voronovskaya Theorem for Variation-Diminishing Spline Approximation
Authors: Marsden M. J. 
Published: December 2010

In [7] Schoenberg introduced the following variation-diminishing spline approximation methods.Let m > 1 be an integer and let Δ = {xi} be a biinfinite sequence of real numbers with xi ≧ xi + l < xi+m. To a function f associate the spline function Vf of order m with knots Δ defined by(1.1)whereand the Nj(x) are B-splines with support xj < x < xj+m normalized so that ΣjNj(x) = 1. See, e.g., [2] for a precise definition of the Nj(x) and a discussion of the properties of Vf.
Spaces on which every Continuous Map into a given Space is Constant
Authors: Iliadis S. , Tzannes V. 
Published: December 2010

This paper is concerned with topological spaces whose continuous maps into a given space R are constant, as well as with spaces having this property locally. We call these spaces R-monolithic and locally R-monolithic, respectively.Spaces with such properties have been considered in [1], [5]-[7], [10], [11], [22], [28], [31], where with the exception of [10], the given space R is the set of real-numbers with the usual topology. Obviously, for a countable space, connectedness is equivalent to the property that every continuous real-valued map is constant. Countable connected (locally connected) spaces have been constructed in papers [2]-[4], [8], [9], [11]-[21], [23]-[26], [30].
Theoremes de Bornage Pour L'Operateur de Nemyckii Dans Les Espaces Ideaux
Authors: Appell Jürgen , de Pascale Espedito 
Published: December 2010

Soit Ω un domaine borné de RN, et soit f:Ω × R → R une fonction satisfaisant à la condition de Carathéodory (i.e., f(s, ·) est continue pour presque tout s ∊ Ω, et f (·, u) est mesurable pour tout u ∊ R). Considérons l'opérateur de la superposition(1.1)(encore appelé opérateur de Nemyckii), engendré par la fonction f. Cet opérateur joue un grand rôle dans la théorie des équations intégrales, différentielles (ordinaires et aux dérivées partielles), et fonctionnelles-différentielles, où il est important de connaître les propriétés analytiques et topologiques de F dans certains espaces de fonctions mesurables, intégrables, continues, différentiables, analytiques etc., les propriétés les plus importantes étant : théorèmes de transfert, de continuité, de bornage, et de compacité. Par exemple, on connaît de nombreux résultats sur l'opérateur (1) dans les espaces de Lebesgue L (voir [10] pour une présentation assez complète); en effet, si l'opérateur (1) envoie une partie de L , d'intérieur non vide, dans L, alors, il est automatiquement continu et borné sur chaque boule.
Frobenius Induction for Higher Whitehead Groups
Authors: Nicas Andrew J. 
Published: December 2010

The theory of induced representations has served as a powerful tool in the computations of algebraicK-theory andL-theory ([2], [7], [4, 5], [9], [10, 11, 12, 13], [14], [17], [18]). In this paper we show how to apply this theory to obtain induction theorems for the higher Whitehead groups of Waldhausen. The same technique applies to the analogs of Whitehead groups in unitaryK-theory and inL-theory.For any ringAwith unit, letK(A) be the spectrum of the algebraicK-theory ofA([8, p. 343]). Given a discrete group Γ and a subringRof the rational numbers, Loday defines a map of spectra:*where (BΓ) is the classifying space of Γ union with a disjoint base point andRΓ is the group-ring of Γ overR.
Lexicographic Direct Sums of Elementary C*-Algebras
Authors: Behncke Horst , Elliott George A. 
Published: December 2010

Besides the simple ones, there are several other kinds of C*-algebras which it has proved interesting to try to classify. For instance, a large body of results relates to the extensions of one given C*-algebra, possibly simple, by another. Extrapolating in this direction, we have considered the class of C*-algebras which can be decomposed in the strongest possible nontrivial sense in terms of their simple subquotients, and such that these simple subquotients in turn are as uncomplicated as possible.We have found that the classification of these C*-algebras, namely, the lexicographic direct sums of elementary C*-algebras, is to a large degree tractable, and yet involves an interesting new invariant in the antiliminary case, which is the case of no minimal ideals. Even the postliminary case, which is the case that the ordered set of simple subquotients satisfies the decreasing chain condition, is not without interest as an extension of the case of finitely many simple subquotients, analysed in the earlier papers [1] and [2].
Nonstandard Ideals in Radical Convolution Algebras on a Half-Line
Authors: Dales H. G. , McClure J. P. 
Published: December 2010

This note is about the interplay between two classes of radical Banach algebras, and we begin by describing the algebras in question.A weight sequence is a positive sequence w = (wn) defined on Z+ (the non-negative integers) and satisfying w0 = 1 and wm+n ≦ wmwn for all m and n in Z+. For such a sequence w, the Banach spaceis a Banach algebra with respect to the convolution product, defined by
A Cancellation Theorem for Modules Over the Group C*-Algebras of Certain Nilpotent Lie Groups
Authors: Sheu Albert Jeu-Liang 
Published: December 2010

In recent years, there has been a rapid growth of the K-theory of C*-algebras. From a certain point of view, C*-algebras can be treated as “non-commutative topological spaces”, while finitely generated projective modules over them can be thought of as “non-commutative vector bundles”. The K-theory of C*-algebras [30] then generalizes the classical K-theory of topological spaces [1]. In particular, the K0-group of a unital C*-algebra A is the group “generated” by (or more precisely, the Grothendieck group of) the commutative semigroup of stable isomorphism classes of finitely generated projective modules over A with direct summation as the binary operation. The semigroup gives an order structure on K0(A) and is usually called the positive cone in K0(A).Around 1980, the work of Pimsner and Voiculescu [18] and of A. Connes [4] provided effective ways to compute the K-groups of C*-algebras. Then the classification of finitely generated projective modules over certain unital C*-algebras up to stable isomorphism could be done by computing their K0-groups as ordered groups. Later on, inspired by A. Connes's development of non-commutative differential geometry on finitely generated projective modules [2], the deeper question of classifying such modules up to isomorphism and hence the so-called cancellation question were raised (cf. [21] ).
Proximal Analysis and Boundaries of Closed Sets in Banach Space. Part II: Applications
Authors: Borwein J. M. , Strojwas H. M. 
Published: December 2010

This paper is a direct continuation of the article “Proximal analysis and boundaries of closed sets in Banach space, Part I: Theory”, by the same authors. It is devoted to a detailed analysis of applications of the theory presented in the first part and of its limitations.Theorem 2.1 has important consequences for geometry of Banach spaces. We start the presentation with a discussion of density and existence of R-proper points (Definition 1.3) for closed sets in Banach spaces. Our considerations will be based on the “lim inf” inclusions proven in the first part of our paper.
Inclusion Theorems for FX-Spaces
Authors: Boos Johann 
Published: December 2010

The main result of this paper is Theorem 1 (in connection with Corollary 1 (e)), which says that the implication*holds for every separable FK-space F, for every FK-space E containing φ and for certain (for example, solid) FK-AB-spaces Y. At this, φ denotes the space of all finite sequences and WE is the set of all elements of E being weakly sectionally convergent.This result was proved by Bennett and Kalton ([1] and [3]) in the special case that E contains all null sequences and that Y is the space m of all bounded sequences or the space of all sequences almost converging to zero.
Stable Homotopy Theory of Simplicial Presheaves
Authors: Jardine J. F. 
Published: December 2010

Let C be an arbitrary Grothendieck site. The purpose of this note is to show that, with the closed model structure on the category S Pre(C) of simplicial presheaves in hand, it is a relatively simple matter to show that the category S Pre(C)stab of presheaves of spectra (of simplicial sets) satisfies the axioms for a closed model category, giving rise to a stable homotopy theory for simplicial presheaves. The proof is modelled on the corresponding result for simplicial sets which is given in [1], and makes direct use of their Theorem A.7.This result gives a precise description of the associated stable homotopy category Ho(S Pre(C))stab, according to well known results of Quillen [6]. One will recall, however, that it is preferable to have several different descriptions of the stable homotopy category, for the construction of smash products and the like.
The Multiplicative Groups of Quasifields
Authors: Kallaher Michael J. 
Published: December 2010

Let (Q, +, ·) be a finite quasifield of dimension d over its kernel K = GF(q), where q = pk with p a prime and k ≧ 1. (See p. 18-22 and p. 74 of [7] or Section 5 of [9] for the definition of quasifield.) For the remainder of this article we will follow standard conventions and omit, whenever possible, the binary operations + and · in discussing a quasifield. For example, the notation Q will be used in place of the triple (Q, +, ·) and Q* will be used to represent the multiplicative loop (Q − {0}, ·).Let m be a non-zero element of the quasifield Q; the right multiplicative mapping ρm:Q → Q is defined by1
A Descent Theorem for Hermitian K-Theory
Authors: Snaith Victor 
Published: December 2010

Let KO and KU respectively denote the real and complex periodic K-theory spectra [1, Part III]. Let KSC denote the spectrum representing self-conjugate K-theory [2, G]. Thus we have a fibring1.1where T is induced by complex conjugation on the unitary group.The following result is due to R. Wood [1, p. 206] and, I believe, to D. W. Anderson.1.2. PROPOSITION. Let generate the stable one-stem. Then there are weak equivalences of spectraa andb
On Elliptically Embedded Subgroups of Soluble Groups
Authors: Rhemtulla A. H. , Wilson J. S. 
Published: December 2010

We call a subset X of a group an elliptic set if there is an integer n such that each element of the group generated by X can be written as a product of at most n elements of X ∪ X−1. The terminology is due to Philip Hall, who investigated elliptic sets in lectures given in Cambridge in the 1960's. Hall was chiefly interested in sets X which are unions of conjugacy classes, but among other things he proved that if H, K are subgroups of a finitely generated nilpotent group then their union H ∪ K is elliptic. We shall say that a subgroup H of an arbitrary group G is elliptically embedded in G, and we write H ee G, if H ∪ K is an elliptic set for each subgroup K of G. Thus H ee G if for each subgroup K there is an integer n (depending on K) such thatwhere the product has 2n factors.
Explicit Formulas for the Associated Jacobi Polynomials and Some Applications
Authors: Wimp Jet 
Published: December 2010

In this paper we determine closed-form expressions for the associated Jacobi polynomials, i.e., the polynomials satisfying the recurrence relation for Jacobi polynomials with n replaced by n + c, for arbitrary real c ≧ 0. One expression allows us to give in closed form the [n — 1/n] Padé approximant for what is essentially Gauss' continued fraction, thus completing the theory of explicit representations of main diagonal and off-diagonal Padé approximants to the ratio of two Gaussian hypergeometric functions and their confluent forms, an effort begun in [2] and [19]. (We actually give only the [n — 1/n] Padé element, although other cases are easily constructed, see [19] for details.)We also determine the weight function for the polynomials in certain cases where there are no discrete point masses. Concerning a weight function for these polynomials, so many writers have obtained so many partial results that our formula should be considered an epitome rather than a real discovery, see the discussion in Section 3.
Divisible Semiplanes, Arcs, and Relative Difference Sets
Authors: Jungnickel Dieter 
Published: December 2010

In this paper we shall be concerned with arcs of divisible semiplanes. With one exception, all known divisible semiplanes D (also called “elliptic” semiplanes) arise by omitting the empty set or a Baer subset from a projective plane Π, i.e., D = Π\S, where S is one of the following:(i) S is the empty set.(ii) S consists of a line L with all its points and a point p with all the lines through it.(iii) S is a Baer subplane of Π.We will introduce a definition of “arc” in divisible semiplanes; in the examples just mentioned, arcs of D will be arcs of Π that interact in a prescribed manner with the Baer subset S omitted. The precise definition (to be given in Section 2) is chosen in such a way that divisible semiplanes admitting an abelian Singer group (i.e., a group acting regularly on both points and lines) and then a relative difference set D will always contain a large collection of arcs related to D (to be precise, —D and all its translates will be arcs).
On the Galois Theory of Commutative Rings II: Automorphisms induced in Residue Rings
Authors: Faith Carl 
Published: December 2010

Let G be a group of automorphisms of a commutative ring K, and let KG denote the Galois subring consisting of all elements left fixed by every g in G. An ideal M is G-stable, or G-invariant, provided that g(x) lies in M for every x in M, that is, g(M) ⊆ M, for every g in G. Then, every g in G induces an automorphism in the residue ring , and if is the group consisting of all , trivially1When the inclusion (1) is strict, then G is said to be cleft at M, or by M, and otherwise G is uncleft at (by) M. When G is cleft at all ideals except 0, then G is cleft, and uncleft otherwise.
Idempotent Multipliers of H1(T)
Authors: Klemes I. 
Published: December 2010

Let as usual T = R/2πZ be the circle, and H1 the subspace of L1(T) of all f such that for all integers n < 0. The normrestricted to H1, makes it a Banach space. By a multiplier of H1 we mean a bounded linear operator m:H1 → H1 such that there is a sequence in C with
Inequalities in Discrete Subgroups of PSL(2, R)
Authors: Gilman Jane 
Published: December 2010

Conditions for a subgroup, F, of PSL(2, R) to be discrete have been investigated by a number of authors. Jørgensen's inequality [5] gives an elegant necessary condition for discreteness for subgroups of PSL(2, C). Purzitsky, Rosenberger, Matelski, Knapp, and Van Vleck, among others [12, 13, 14, 9, 16, 17, 18, 19, 20, 7, 21] studied two generator discrete subgroups of PSL(2, R) in a long series of papers. The complete classification of two generator subgroups was surprisingly complicated and elusive. The most complete result appears in [20].In this paper we use the results of [20] to prove that a nonelementary subgroup F of PSL(2, R) is discrete if and only if every non-elementary subgroup, G, generated by two hyperbolics is discrete (Theorem 5.2) and that F contains no elliptics if and only if each such G is free (Theorem 5.1). Thus, we produce necessary and sufficient conditions for a non-elementary subgroup F of PSL(2, R) to be a discrete group without elliptic elements (Theorem 6.1) or a discrete group containing only hyperbolic elements (Theorem 7.1).
A Tauberian Theorem Concerning Borel-Type and Cesàro Methods of Summability
Authors: Borwein David , Markovich Tom 
Published: December 2010

Suppose throughout that r ≧ 0, α > 0, αq + β > 0 where q is a non-negative integer. Let {sn} be a sequence of real numbers,The Borel-type summability method (B, α, β) is defined as follows:The method (B, α, β) is regular [5]; and (B, 1, 1) is the standard Borel exponential method B. For a real sequence {sn} we consider the slowly decreasing-type Tauberian conditionWe shall also be concerned with the Cesàro summability method Cp(p > —1), the Valiron method Vα, and the Meyer-König method Sa (0 < a < 1) defined as follows:
Commutativity Preserving Maps of Factors
Authors: Miers C. Robert 
Published: December 2010

By a von Neumann algebra M we mean a weakly closed, self-adjoint algebra of operators on a Hilbert space which contains I, the identity operator. A factor is a von Neumann algebra whose centre consists of scalar multiples of I.In all that follows ϕ:M → N will be a one to one, *-linear map from the von Neumann factor M onto the von Neumann algebra N such that both ϕ and ϕ−1 preserve commutativity. Our main result states that if M is not of type I2 then where is an isomorphism or an antiisomorphism, c is a non-zero scalar, and λ is a *-linear map from M into ZN, the centre of N.Our interest in this problem was aroused by several recent results. In [1], Choi, Jafarian, and Radjavi proved that if S is the real linear space of n × n matrices over any algebraically closed field, n ≧ 3, and ψ a linear operator on S which preserves commuting pairs of matrices, then either ψ(S) is commutative or there exists a unitary matrix U such thatfor all A in S. They proved an analogous result for the collection of all bounded self-adjoint operators on an infinite dimensional Hilbert space when ψ is one to one. Subsequently, Omladic [7] proved that if ψ:L(X) → L(X) is a bijective linear operator preserving commuting pairs of operators where X is a non-trivial Banach space, thenwhere U is a bounded invertible operator on X and A′ is the adjoint of A.
Sur Les Isométries De Lp(X) Et Le Théorème Ergodique Vectoriel
Authors: Guerre S. , Raynaud Y. 
Published: December 2010

Etant donné un opérateur T sur un espace LP (1 < p < ∞), la théorie ergodique s'intéresse à la convergence presque sûre des moyennes de Césarodes itérés d'un point f de Lp par T. On dit que T vérifie le théorème ergodique si cette convergence a lieu pour tout f de Lp.Parmi les nombreux résultats sur cette question (cf. [21]) nous citerons d'abord ceux de A. Ionescu-Tulcea ([19]) et R. Chacon-S. A. McGrath
([10]) que l'on peut réunir dans l'assertion suivante:“Si 1 < p < ∞ et T une isométrie positive de Lp, ou si 1 < p ≠ 2 < ∞ et si T est une isométrie surjective de Lp, alors T vérifie le théorème ergodique”.Nous nous intéressons ici à une version vectorielle de ce théorème. Plus précisément, si X est un espace de Banach réel, un opérateur linéare T sur l'espace LP(X) est dit vérifier le théorème ergodique vectoriel si la suite des moyennes de Césaroconverge presque sûrement en norme dans X, quel que soit f ∊ Lp(X).