bluuebunny/crossref_metadata_2025_split huggingface dataset:
Free Involutorial Completely Simple Semigroups
Authors: Gerhard J. A. , Petrich Mario 
Published: December 2010

An involution x → x* of a semigroup S is an antiautomorphism of S of order at most 2, that is (xy)* = y*x* and x** = x for all x, y ∊ S. In such a case, S is called an involutorial semigroup if regarded as a universal algebra with the binary operation of multiplication and the unary operation *. If S is also a completely simple semigroup, regarded as an algebra with multiplication and the unary operation x → x−1 of inversion (x−1 is the inverse of x in the maximal subgroup of S containing x), then (S, −1, *), or simply S, is an involutorial completely simple semigroup. All such S form a variety determined by the identities above concerning * andwhere x0 = xx−1.
On the Restricted Cesàro Summability of Multiple Orthogonal Series
Authors: Móricz Ferenc 
Published: December 2010

We actually treat double orthogonal series in detail, simply for the sake of brevity in notations. Multiple orthogonal series will be shortly indicated in the concluding Section 8.Let (X, , μ) be an arbitrary positive measure space and {ϕjk(x):i, k = 0, 1, …} an orthonormal system defined on X. We consider the double orthogonal series(1.1)where {ϕik:i, k = 0, 1, …} is a double sequence of real numbers (coefficients), for which(1.2)
The largest Irreducible Character Degree of a Finite Group
Authors: Gluck David 
Published: December 2010

Much information about a finite group is encoded in its character table. Indeed even a small portion of the character table may reveal significant information about the group. By a famous theorem of Jordan, knowing the degree of one faithful irreducible character of a finite group gives an upper bound for the index of its largest normal abelian subgroup.Here we consider b(G), the largest irreducible character degree of the group G. A simple application of Frobenius reciprocity shows that b(G) ≧ |G:A| for any abelian subgroup A of G. In light of this fact and Jordan's theorem, one might seek to bound the index of the largest abelian subgroup of G from above by a function of b(G). If is G is nilpotent, a result of Isaacs and Passman (see [7, Theorem 12.26]) shows that G has an abelian subgroup of index at most b(G)4.
An Ergodic Theorem for Multidimensional Superadditive Processes
Authors: Çömez Doğan 
Published: December 2010

The ergodic theorem for multidimensional strongly subadditive processes relative to a semigroup induced by a measure preserving point transformation on X was proved by R. T. Smythe [18]. His results have been generalized by M. A. Akçoğlu and U. Krengel [4] to the continuous parameter case. The definition of superadditivity they used is stronger than Smythe's but weaker than strong superadditivity. R. Emilion and B. Hachem [10] extended this result to strongly superadditive processes relative to a semigroup generated by a pair of commuting Markovian operators which are also L∞-contractions. The basic tool in the proof is a technique which may be referred to as “reduction of dimension“ and they used a version of it due to A. Brunei [6].The purpose of this paper is to show that if F = {F(uv)}u>0 is a bounded strongly superadditive process with respect to a two-dimensional strongly continuous Markovian semigroup of operators on L1, then u-2F(uu) converges a.e. as u → ∞.
Extreme Positive Contractions on Finite Dimensional lp-Spaces
Authors: Grząślewicz Ryszard 
Published: December 2010

In this paper we give a characterization of the extreme positive contractions on finite dimensional lp-spaces for 1 < p < ∞. This is related to the characterization of the extreme doubly stochastic operators. In Section 2 we present the basic properties of the facial structure of the set of doubly stochastic n × m matrices. In Section 3 we use these facts for description of the facial structure of the set of positive contractions on finite dimensional lp-space. Next is considered stability of the positive part of the unit ball of operators (Section 5). In Section 7 we prove that extreme positive contractions on are strongly exposed.1. Terminology and notation. Let (X, , m) be a a-finite measure space. As usual, we denote by LP(m), 1 < p < ∞, the Banach lattice of all p-summable real-valued functions on X with standard norm and order. If X = {1, 2 , …, n) n < ∞, and m is a counting measure we write instead of LP(m). If X = [0, 1] and m is Lebesgue measure we write briefly LP.
Centres of Rank-Metric Completions
Authors: Handelman David 
Published: December 2010

In this paper, we are primarily concerned with the behaviour of the centre with respect to the completion process for von Neumann regular rings at the pseudo-metric topology induced by a pseudo-rank function.Let R be a (von Neumann) regular ring, and N a pseudo-rank function (all terms left undefined here may be found in [6]). Then N induces a pseudo-metric topology on R, and the completion of R at this pseudo-metric, , is a right and left self-injective regular ring. Let Z( ) denote the centre of whatever ring is in the brackets. We are interested in the map .If R is simple, Z(R) is a field, so is discrete in the topology; yet Goodearl has constructed an example with Z(R) = R and Z(R) = C [5, 2.10]. There is thus no hope of a general density result.
Actions of Finite Groups on Rn+k with Fixed Set Rk
Authors: Hambleton Ian , Madsen Ib 
Published: December 2010

In this paper we study the existence problem for topological actions of finite groups on euclidean spaces Rn+k which are free outside a fixed point set Rk (embedded as a vector subspace). We refer to such an action as a semi-free action on (Rn+k, Rn) and note that all our actions will be assumed orientation-preserving.Suppose the finite group π acts semi-freely on (Rn+k, Rn), then it acts freely on (Rn+k – Rn) = Sn–l × Rk+1. Since this space is homotopy equivalent to Sn–l, π will have periodic integral cohomology and n will be a multiple of the period. In fact the orbit spaceis a finitely-dominated Poincaré complex of formal dimension n – 1 with π1W = π and as considered by Swan [41].
The smallest Prime Value of xn + a
Authors: McCurley Kevin S. 
Published: December 2010

Let a and n be positive integers such that f(x) = xn + a is irreducible over the integers. A conjecture made by Bouniakowsky [4] in 1857 would imply that there exist infinitely many integers x such that f(x) is prime. An even stronger conjecture of Bateman and Horn [1, 2] would imply thatwhere π(x;f) is the number of integers m with 0 ≧ m ≧ x for which f(m) is prime, andwhere w(p) is the number of solutions of the congruenceExcept for the trivial case n = 1, neither of these conjectures has ever been resolved.
Sur Les Operateurs a Puissances Bornees et Le Theoreme Ergodique Ponctuel Dans Lp[0, 1], 1 < p < ∞
Authors: Assani I. 
Published: December 2010

Soient Lp(X, , μ) les espaces de Banach usuels associés à un espace mesuré fini ou α-fini (X, , μ), p étant un nombre réel compris entre un et l'infini (1 < p < ∞). Notons Lp, l'espace Lp[0, 1]. Un opérateur T:Lp → Lp est dit être à puissances bornées sur Lp siLa convergence presque sure de la suite de fonctionsa été étudiée dans L2 pour T contraction [8], [1] et pour T inversible à puissances bornées dans , 1 < p ≧ 2 [9].
On C*-Diagonals
Authors: Kumjian Alexander 
Published: December 2010

Preface. The impetus for this study arose from the belief that the structure of a C*-algebra is illuminated by an understanding of the manner in which abelian subalgebras embed in it. Posed in its full generality, the question concerning abelian subalgebras would seem impossible to answer. A notion of diagonal subalgebra is, however, proposed which has the virtue that one can associate a “topological”; invariant to the pair consisting of the diagonal and the ambient algebra, from which these algebras may be retrieved.In the setting of von Neumann algebras, the analogous question was addressed in the seminal work of Feldman and Moore [13]. Their definition of Cartan subalgebra permits the abstraction of a complete invariant consisting of a Borel equivalence relation together with a certain cohomology class on the relation from which the Cartan pair may be recovered. Our development parallels theirs in spirit; differences in substance derive from the topological flavor of C*-theory.
Classification of Algebraic Surfaces with
Sectional Genus less than or Equal to Six.
II: Ruled Surfaces with dim ϕKx⊗L(x) = l
Authors: Livorni Elvira Laura 
Published: December 2010

Let L be a very ample line bundle on a smooth, connected, projective, ruled not rational surface X. We have considered the problem of classifying biholomorphically smooth, connected, projected, ruled, non rational surfaces X with smooth hyperplane section C such that the genus g = g(C) is less than or equal to six and dim where is the map associated to . L. Roth in [10] had given a birational classification of such surfaces. If g = 0 or 1 then X has been classified, see [8].If g = 2 ≠ hl,0(X) by [12, Lemma (2.2.2) ] it follows that X is a rational surface. Thus we can assume g ≦ 3.Since X is ruled, h2,0(X) = 0 andsee [4] and [12, p. 390].
A Classification of Reflexive Graphs: The use of “Holes”
Authors: Jawhari El Moustafa , Pouzet Maurice , Rival Ivan 
Published: December 2010

The purpose of this article is to develop aspects of a classification theory for reflexive graphs. A first important step was already taken in [2]; throughout we follow, at least the spirit, of the classification theory for ordered sets initiated in [1].For a graph G let V(G) denote its vertex set and E(G) ⊆ V(G) × V(G) its edge set. A graph K is a subgraph of G if V(K) ⊆ V(G) and for a, b ∊ V(K), (a, b) ∊ E(K) just if (a, b) ∊ E(G). The subgraph K of G is a retract of G, and we write K ◅ G, if there is an edge-preserving map g of V(G) to V(K) satisfying g(v) = v for each v ∊ V(K); g is called a retraction. A reflexive graph is an undirected graph with a loop at every vertex. The reason for a loop at a vertex is that an edge-preserving map can send the two vertices of an adjacent pair to it. The concept is illustrated in Figure 1. From here on, though, we shall for convenience suppress the illustration of the loops in the figures of reflexive graphs.
Behavior of Coefficients of Inverses of α-Spiral Functions
Authors: Libera Richard J. , Złotkiewicz Eligiusz J. 
Published: December 2010

If f(z) is univalent (regular and one-to-one) in the open unit disk Δ, Δ = {z ∊ C:│z│ < 1}, and has a Maclaurin series expansion of the form(1.1)then, as de Branges has shown, │ak│ = k, for k = 2, 3, … and the Koebe function.(1.1)serves to show that these bounds are the best ones possible (see [3]). The functions defined above are generally said to constitute the class .
The Hausdorff Dimension Distribution of Finite Measures in Euclidean Space
Authors: Cutler Colleen D. 
Published: December 2010

Let E be a Borel set of RN. The α-outer Hausdorff measure of E has been defined to bewhereand each Bi is a closed ball. d(Bi) denotes the diameter of Bi.It is easily seen that the same value Hα(E) is obtained if we consider coverings of E by open balls or by balls which may be either open or closed.By dim(E) we will mean the usual Hausdorff-Besicovitch dimension of E, where
On Basis-Conjugating Automorphisms of Free Groups
Authors: McCool J. 
Published: December 2010

Let X = {x1, … xn} be a free generating set of the free group Fn and let H be the subgroup of Aut Fn consisting of those automorphisms α such that α(xi) is conjugate to xi for each i = 1, 2 , …, n. We call H the Z-conjugating subgroup of Aut Fn. In [1] Humphries found a generating set for the isomorphic copy H1 of H consisting of Nielsen transformationswhere each is conjugate to ui (see remark 1 below). The purpose of this paper is to find a presentation of H (and hence of H1).Let i ≠ j be elements of {1, 2, …, n}. We denote by (xi; xj) the automorphism of Fn which sends xi to and fixes xk if k ≠ i. Let S be the set of all such automorphisms.
Colour Switching and Homeomorphism of Manifolds
Authors: Ferri Massimo 
Published: December 2010

Throughout this paper, we work in the PL and pseudosimplicial categories, for which we refer to [17] and [10] respectively. For the graph theory involved see [9].An h-coloured graph (Γ, γ) is a multigraph Γ = (V(Γ), E(Γ)) regular of degree h, endowed with an edge-coloration γ by h colours. If is the colour set, for each we setFor each set . For n ∊ Z, n ≧ 1, setΔn will be mostly used to denote the colour set for an (n + 1)-coloured graph.
Analytic Subalgebras of Von Neumann Algebras
Authors: Muhly Paul S. , Saito Kichi-Suke 
Published: December 2010

Let M be a von Neumann algebra and let {αt}t∊R be a σ-weakly continuous flow on M; i.e., suppose that {αt}t∊R is a one-parameter group of *-automorphisms of M such that for each ρ in the predual, M∗, of M and for each x ∊ M, the function of t, ρ(αt(x)), is continuous on R. In recent years, considerable attention has been focused on the subspace of M, H∞(α), which is defined to bewhere H∞(R) is the classical Hardy space consisting of the boundary values of functions bounded analytic in the upper half-plane. In Theorem 3.15 of [8] it is proved that in fact H∞(α) is a σ-weakly closed subalgebra of M containing the identity operator such thatis σ-weakly dense in M, and such that
Idempotents in Complex Banach Algebras
Authors: Hile G. N. , Pfaffenberger W. E. 
Published: December 2010

The concept of the spectrum of A relative to Q, where A and Q commute and are elements in a complex Banach algebra with identity I, was developed in [1]. A complex number z is in the Q-resolvent set of A if and only if is invertible in otherwise, z is in the Q-spectrum of A, or spectrum of A relative to Q. One result from [1] was the following.THEOREM. Suppose no points in the ordinary spectrum of Q have unit magnitude. Let C be a simple closed rectifiable curve which lies in the Q-resolvent of A, and let*where P is defined asxs•
On The Factorization of Partial Differential Equations
Authors: Brownawell W. Dale 
Published: December 2010

In [4] N. Steinmetz used Nevanlinna theory to establish remarkably versatile theorems on the factorization of ordinary differential equations which implied numerous previous results of various authors. (Here factorization is taken in the sense of function composition as introduced by F. Gross in [2].) The thrust of Steinmetz’ central results on factorization is that if g(z) is entire and f(z) is meromorphic in C such that the composite fog satisfies an algebraic differential equation, then so do f(z) and, degenerate cases aside, g(z). In addition, the more one knows about the equation for fog (e.g. degree, weight, autonomy), the more one can conclude about the equations for f and g.In this note we generalize Steinmetz’ work to show the following:a) Steinmetz’ two basic results, Satz 1 and Korollar 1 of [4] can be seen as one-variable specializations of a single two variable result, andb) the function g(z) can itself be allowed to be a function of several variables.
Uniqueness of Free Actions on S3 Respecting a Knot
Authors: Boileau Michel , Flapan Erica 
Published: December 2010

In this paper we consider free actions of finite cyclic groups on the pair (S3, K), where K is a knot in S3. That is, we look at periodic diffeo-morphisms f of (S3, K) such that fn is fixed point free, for all n less than the order of f. Note that such actions are always orientation preserving. We will show that if K is a non-trivial prime knot then, up to conjugacy, (S3, K) has at most one free finite cyclic group action of a given order. In addition, if all of the companions of K are prime, then all of the free periodic diffeo-morphisms of (S3, K) are conjugate to elements of one cyclic group which acts freely on (S3, K). More specifically, we prove the following two theorems.THEOREM 1. Let K be a non-trivial prime knot. If f and g are free periodic diffeomorphisms of (S3, K) of the same order, then f is conjugate to a power of g.
Uniformly Closed Algebras Generated by Boolean Algebras of Projections in Locally Convex Spaces
Authors: Ricker Werner 
Published: December 2010

The theory of operator algebras in Banach spaces generated by Boolean algebras of projections is by now well known. It is systematically exposed in the penetrating studies of W. Bade, [1], [2] and [6, Chapter XVII]. Many of these results, a priori independent on normability of the underlying space, have recently been extended to the setting of locally convex spaces; see [3], [4], [5], [11] and [15], for example.However, one of Bade's fundamental results, stating that the closed algebra generated by a complete Boolean algebra in the uniform operator topology is the same as the closed algebra that it generates in the weak operator topology, has remained remarkably resistant in attempts to extend it to locally convex spaces. Recently however, a class of Boolean algebras in non-normable spaces, called boundedly σ-complete Boolean algebras, was exhibited in which the analogue of Bade's result is valid, [14; Theorem 5.3].
Harmonic Mappings onto Convex Domains
Authors: Abu-Muhanna Yusuf , Schober Glenn 
Published: December 2010

Let D be a simply-connected domain and w0 a fixed point of D. Denote by SD the set of all complex-valued, harmonic, orientation-preserving, univalent functions f from the open unit disk U onto D with f(0) = w0. Unlike conformai mappings, harmonic mappings are not essentially determined by their image domains. So, it is natural to study the set SD.In Section 2, we give some mapping theorems. We prove the existence, when D is convex and unbounded, of a univalent, harmonic solution f of the differential equationwhere a is analytic and |a| < 1, such that f(U) ⊂ D and
The Heat Equation for the -Neumann Problem, II
Authors: Beals Richard , Stanton Nancy K. 
Published: December 2010

Let Ω be a compact complex n + 1-dimensional Hermitian manifold with smooth boundary M. In [2] we proved the following.THEOREM 1. Suppose satisfies condition Z(q) with 0 ≦ q ≦ n. Let □p,q denote the -Laplacian on (p, q) forms onwhich satisfy the -Neumann boundary conditions. Then as t → 0;,(0.1)(If q = n + 1, the -Neumann boundary condition is the Dirichlet boundary condition and the corresponding result is classical.)Theorem 1 is a version for the -Neumann problem of results initiated by Minakshisundaram and Pleijel [8] for the Laplacian on compact manifolds and extended by McKean and Singer [7] to the Laplacian with Dirichlet or Neumann boundary conditions and by Greiner [5] and Seeley [9] to elliptic boundary value problems on compact manifolds with boundary. McKean and Singer go on to show that the coefficients in the trace expansion are integrals of local geometric invariants.
Regularite De Fonctions Holomorphes Sur Des Wedges
Authors: Coupet Bernard 
Published: December 2010

Nous traitons de la régularité d'une fonction holomorphe sur un ouvert de Cn à partir de celle de la fonction ou de la partie réelle connue sur une sous-variété totalement réelle maximale (de dimension n) incluse dans le bord de l'ouvert de définition.Un théorème classique de Privalov assure qu'une fonction continue sur un disque fermé de C, holomorphe sur le disque ouvert, de partie réelle lipschitzienne d'ordre α sur le bord du disque vérifie une condition de même ordre α sur tout le disque. De façon analogue, le module de continuité d'une fonction holomorphe sur un ouvert borné de Cn, continue sur l'adhérence est contrôlé par celui de la fonction restreinte au bord [2] et [5], Le bord de l'ouvert peut être remplacé par la frontière de Shilov dans le cas d'un polyèdre analytique [4].E. L. Stout [9] étudie la régularité sur une sous-variété totalement réelle maximale M de classe Cp, d'une fonction holomorphe f définie sur un ouvert Ω de classe Cq dont le bord contient M et telle que M soit l'ensemble sur lequel |f| est maximum; il démontre que f|M est Cp−0 lorsque q > p et Cp−1 lorsque q = p pour p supérieur ou égal à 3.
Pointwise Convergence of Alternating Sequences
Authors: Akcoglu M. A. , Sucheston L. 
Published: December 2010

Let 1 < p < ∞ and let Lp be the usual Banach Space of complex valued functions on a σ-finite measure space. Let (Tn), n ≧ 1, be a sequence of positive linear contractions on Lp. Hence and , where is the part of Lp that consists of non-negative Lp functions. The adjoint of Tn is denoted by which is a positive linear contraction of Lq with q = p/(p — 1).Our purpose in this paper is to show that the alternating sequences associated with (Tn), as introduced in [2], converge almost everywhere. Complete definitions will be given later. When applied to a non negative function, however, this result is reduced to the following theorem.(1.1) THEOREM. If (Tn) is a sequence of positive contractions of Lp then (1.2) exists a.e. for all.
Tensor Products of Fundamental Representations
Authors: Kempf George , Ness Linda 
Published: December 2010

Let G be a reductive group over a field of characteristic zero. Fix a Borel subgroup B of G which contains a maximal torus T. For each dominant weight X we have an irreducible representation V(X) of G with highest weight X. For two dominant representation X1 and X2 we have a decompositionThis decomposition is determined by the elementof the group ring of the group of characters of T.The objective of this paper is to compute r(X1, X2) for all pairs X1 and X2 of fundamental weights. This will be used to compute the equations for cones over homogeneous spaces. This problem immediately reduces to the case when G has simple type; An, Bn, Cn, Dn, E6, E7, E8, F4 and G2. We will give complete details for the classical types. For the case An we will work with GLn.
On the Selmer Group of Twists of Elliptic Curves with Q-Rational Torsion Points
Authors: Frey G. 
Published: December 2010

(1) The symbols p and q stand for prime numbers and throughout the paper we assume that p is fixed and contained in {3, 5, 7}. Let L be an algebraic number field (i.e., L is a finite extension of Q). Then prime divisors of L dividing p (resp. q) are denoted by (resp. ). The completion of L with respect to is denoted by . Let S be a finite set of prime numbers, and let M/L be a Galois extension with abelian Galois group of exponent p.Definition. M/L is said to be little ramified outside S if for primes q ∉ S and all one haswith k ∊ N and . Here ζp is a pth root of unity, u1, …, uk are elements in and is the normed valuation belonging to . In particular M/L is unramified at all divisors of primes q ∉ S ∪ {p}.
The Quantificational Tangent Cones
Authors: Ward Doug 
Published: December 2010

Nonsmooth analysis has provided important new mathematical tools for the study of problems in optimization and other areas of analysis [1, 2, 6-12, 28]. The basic building blocks of this subject are local approximations to sets called tangent cones.Definition 1.1. Let E be a real, locally convex, Hausdorff topological vector space (abbreviated l.c.s.). A tangent cone (on E) is a mapping A:2E × E → 2E such that A(C, x) is a (possibly empty) cone for all nonempty C in 2E and x in E.In the sequel, we will say that a tangent cone has a certain property (e.g. “A is closed” or “A is convex“) if A(C, x) has that property for all non-empty sets C and all x in C. (If A(C, x) is empty, it will be counted as having the property trivially.)
Some Differential Equations Related to Iteration Theory
Authors: Aczél J´nos , Gronau Detlef 
Published: December 2010

In connection with the translation equation(T)three differential equations arise together with a differential initial condition. They are satisfied by the differentiable solutions of (T) and of the initial condition(I)These equations are attributed in [9] to E. Jabotinsky who seems to have been the first who treated these equations in connection with the theory of analytic iteration (see [6], cf. [7, 8], but see also [1, 2, 3]).Gronau (see [9]) asked whether, conversely, it is true that all solutions of each of these “Jabotinsky differential equations”, possibly with some further initial conditions added, are also solutions of the translation equation. In this paper we give counter examples but also partial positive answers to these questions. First we show how one obtains the Jabotinsky equations from (T) and (I).