bluuebunny/crossref_metadata_2025_split huggingface dataset:
Some Special Classes of Cartan Matrices
Authors: Ogg A. P. 
Published: December 2010

Let A = (Aij)l≦ij≦l be a Cartan matrix, i.e., Aii = 2 for all i and Aij is an integer ≦ 0 for i ≠ j, with Aij = 0 if Aji = 0. The size l of A is called its rank, for Lie-theoretic reasons, and may be larger than its matrix rank. We associate to A its Dynkin diagram, with vertices 1, 2, … , l, with AijAji lines joining i to j, and with an arrow pointing from i to j if Aij/Aji < 1, i.e., pointing toward the shorter root (see below). The Cartan matrix A is indecomposable if its diagram is connected, and symmetrizable if there exist positive rational numbers q1 … , ql withqiAij = qjAji for all i and j.Symmetrizability is automatic if the diagram contains no cycle.
Generalized Mellin Convolutions and their Asymptotic Expansions
Authors: Wong R. , Mcclure J. P. 
Published: December 2010

A large number of important integral transforms, such as Laplace, Fourier sine and cosine, Hankel, Stieltjes, and Riemann- Liouville fractional integral transforms, can be put in the form1.1where f(t) and the kernel, h(t), are locally integrable functions on (0,∞), and x is a positive parameter. Recently, two important techniques have been developed to give asymptotic expansions of I(x) as x → + ∞ or x → 0+. One method relies heavily on the theory of Mellin transforms [8] and the other is based on the use of distributions [24]. Here, of course, the integral I(x) is assumed to exist in some ordinary sense.If the above integral does not exist in any ordinary sense, then it may be regarded as an integral transform of a distribution (generalized function). There are mainly two approaches to extend the classical integral transforms to distributions.
Localisation Relative Associee a une Theorie de Torsion
Authors: Lemaire Claude 
Published: December 2010

Dans [3], Peter Hilton a introduit la notion de “localisation relative” d'une extension de groupes à noyau nilpotent. Etant donné une extension de groupesoú N est nilpotent, il s'agit de l'introduire dans un diagramme commutatif:oú NP est la P-localisation de N.L'idée (issue de la Topologie algébrique) est de tourner autant que possible l'absence de localisation maniable dans la catégorie des groupes. J'ai moi-même exploité cette idée dans [6], dans le cas oú une action de groupe est exercée sur G.
Compactness and Weak Compactness in Spaces of Compact-Range Vector Measures
Authors: Graves William H. , Ruess Wolfgang 
Published: December 2010

This paper features strong and weak compactness in spaces of vector measures with relatively compact ranges in Banach spaces. Its tools are the measure-operator identification of [16] and [24] and the description of strong and weak compactness in spaces of compact operators in [10], [11], and [29].Given a Banach space X and an algebra of sets, it is shown in [16] that under the usual identification via integration of X-valued bounded additive measures on with X-valued sup norm continuous linear operators on the space of -simple scalar functions, the strongly bounded, countably additive measures correspond exactly to those operators which are continuous for the coarser (locally convex) universal measure topology τ on . It is through the latter identification that the results on strong and weak compactness in [10], [11], and [29] can be applied to X-valued continuous linear operators on the generalized DF space to yield results on strong and weak compactness in spaces of vector measures.
On Explicit Decomposition for Positive Polynomials on [-1, +1] with Applications to Extremal Problems
Authors: Pierre R. 
Published: December 2010

The following well known inequality was first proved by Bernstein [2].THEOREM A. If pn(x) is a polynomial of degree n, such that |pn(x)| ≦ 1 for –1 ≦ x = +1, then1The dominant n(1 – x2)–;1/2 is best possible only at the zeros of the Tchebychev polynomialbut the bound is precise at every interior point as far as the exponent of n is concerned.Theorem A was extended to the case of higher derivatives by Duffin and Schaeffer in [4]. In that paper they make extensive use of the oscillation property of the polynomial Tn(x) and of the related function
A General form of the Functional LIL for Banach-Valued Brownian Motion
Authors: Wong H. Ship-Fah 
Published: December 2010

In a recent paper [12], C. Mueller proved a general version of the functional LIL which unifies Strassen's LIL and the Lévy modulus of continuity for Brownian motion W(t). His theorem also contains other known forms of the LIL.For each t ≧ 0, let be a family of points in the first quadrant of the plane. Let r ≦ 0; to each point (s0, l0), we associate a rectangleDefine Ar(t) to be the area of the union of these rectangles up to time t under the measure . Then, Theorem 1 [12, p. 166] states that for an increasing function h such thatthe set of limit points ofin C[0, 1] is the closed unit ball of the reproducing kernel Hilbert space (rkhs) associated with Wiener measure.
Representations of Foundation Semigroups and their Algebras
Authors: Bami M. Lashkarizadeh 
Published: December 2010

The aim of this paper is to extend to a suitable class of topological semigroups parts of well-defined theory of representations of topological groups. In attempting to obtain these results it was soon realized that no general theory was likely to be obtainable for all locally compact semigroups. The reason for this is the absence of any analogue of the group algebra Ll(G). So the theory in this paper is restricted to a certain family of topological semigroups. In this account we shall only give the details of those parts of proofs which depart from the standard proofs of analogous theorems for groups.On a locally compact semigroup S the algebra of all μ ∊ M(S) for which the mapping and of S to M(S) (where denotes the point mass at x) are continuous when M(S) has the weak topology was first studied in the sequence of papers [1, 2, 3] by A. C. and J. W. Baker.
Derivations Tangential to Compact Group Actions: Spectral Conditions in the Weak Closure
Authors: Bratteli Ola , Goodman Frederick M. 
Published: December 2010

Let G be a compact Lie group and a an action of G on a C*-algebra as *-automorphisms. Let denote the set of G-finite elements for this action, i.e., the set of those such that the orbit {αg(x):g ∊ G} spans a finite dimensional space. is a common core for all the *-derivations generating one-parameter subgroups of the action α. Now let δ be a *-derivation with domain such that Let us pose the following two problems:Is δ closable, and is the closure of δ the generator of a strongly continuous one-parameter group of *-automorphisms?If is simple or prime, under what conditions does δ have a decompositionwhere is the generator of a one-parameter subgroup of α(G) and is a bounded, or approximately bounded derivation?
Exact Sequences for the Kasparov Groups of Graded Algebras
Authors: Skandalis George 
Published: December 2010

In [11] G. G. Kasparov defined the “operatorK-functor”KK(A, B)associated with the gradedC*-algebrasAandB. If the algebrasAandBare trivially graded andAis nuclear he proves six term exact sequence theorems. He asks whether this extends to the graded case.Here we prove such “six-term exact sequence” results in the graded case. Our proof does not use nuclearity of the algebraA. This condition is replaced by a completely positive lifting condition (Theorem 1.1).Using our result we may extend the results by M. Pimsner and D. Voiculescu on theKgroups of crossed products by free groups toKKgroups [15]. We give however a different way of computing these groups using the equivariantKK-theory developed by G. G. Kasparov in [12]. This method also allows us to compute the KK groups of crossed products byPSL2(Z).
An n-Vertex Theorem for Convex Space Curves
Authors: Bisztriczky Tibor 
Published: December 2010

The classical four-vertex theorem states that a simple closed convex C2 curve in the Euclidean plane has at least four vertices (points of extreme curvature). This theorem has many generalizations with regard to both the curve and the topological space and for a history of the subject, we refer to [4] and [1]. The particular generalization of concern, credited to H. Mohrmann, is the following n-vertex theorem.Let a simple closed C3 curve on a closed convex surface be intersected by a suitable plane in n points. Then the curve has at least n inflections (vertices).The closed convex surface in the preceding is defined as having at most two points in common with any straight line. Presently, we extend this result to curves on more general convex surfaces in a real projective three-space P3.
Algebras of Analytic Operators associated with a Periodic Flow on a Von Neumann Algebra
Authors: Solel Baruch 
Published: December 2010

Let M be a σ-finite von Neumann algebra and {σt}t∊T be a σ-weakly continuous representation of the unit circle, T, as *-automorphisms of M. Let H∞(σ) be the set of all x ∊ M such thatThe structure of H∞(σ) was studied by several authors (see [2-13]).The main object of this paper is to study the σ-weakly closed subalgebras of M that contain H∞(σ). In [12] this was done for the special case where H∞(σ) is a nonselfadjoint crossed product.Let Mn, for n ∊ Z, be the set of all x ∊ M such that
Finite Projective Planes that Admit a Strongly Irreducible Collineation Group
Authors: Ho Chat Yin 
Published: December 2010

This paper studies how coding theory and group theory can be used to produce information about a finite projective plane π and a collineation group G of π.A new proof for Hering's bound on |G| is given in 2.5. Using the idea of coding theory developed in [9], a relation between two rows of the incidence matrix of π with respect to a tactical decomposition is obtained in 2.1. This result yields, among other things, some techniques in calculating |G|, and generalizes a result of Roth [16], [see 2.4 and 2.5].Hering [7] introduced the notion of strong irreducibility of G, that is, G does not leave invariant any point, line, triangle or proper subplane. He showed that if in addition G contains a non-trivial perspectivity, then there is a unique minimal normal subgroup of G. This subgroup is either non-abelian simple or isomorphic to the elementary abelian group Z3 × Z3 of order 9.
An Independent System of Units in Certain Algebraic Number Fields
Authors: Levesque Claude 
Published: December 2010

For Kn = Q(ω) a real algebraic number field of degree n over Q such thatwith D ∊ N, d ∊ Z, d|D2, and D2 + 4d > 0, we proved in [5] (by using the approach of Halter-Koch and Stender [6]) that ifwiththenis an independent system of units of Kn.
Singularity of Monomial Curves in A3 and Gorenstein Monomial Curves in A4
Authors: Kraft Jürgen 
Published: December 2010

Let 2 ≦ s ∊ N and {n1, …, ns) ⊆ N*. In 1884, J. Sylvester [13] published the following well-known result on the singularity degree S of the monomial curve whose corresponding semigroup is S: = 〈n1, …, ns): If s = 2, thenLet K: = –Z\S andfor all 1 ≦ i ≦ s. We introduce the invariantof S involving a correction term to the Milnor number 2δ [4] of S. As a modified version and extension of Sylvester's result to all monomial space curves, we prove the following theorem: If s = 3, thenWe prove similar formulas for s = 4 if S is symmetric.
Nilpotent by Supersolvable M-Groups
Authors: Parks Alan E. 
Published: December 2010

A character of a finite group G is monomial if it is induced from a linear (degree one) character of a subgroup of G. A group G is an M-group if all its complex irreducible characters (the set Irr(G)) are monomial.In [1], Dade gave an example of an M-group with a normal subgroup which is itself not an M-group. In his group G, the supersolvable residual N is an extra special 2-group and G/N is supersolvable of even order. Moreover, the prime 2 is used in such a way that no analogous construction is possible in the case that |N| or |G:N| is odd. This led Isaacs in [8] and Dade in [2] to consider the effect of certain “oddness“ hypotheses in the study of monomial characters.Our main results are in the same spirit. Although our techniques seem to require a restrictive assumption on the supersolvable residual of the groups we consider, our theorems provide more evidence that under fairly general circumstances normal subgroups of M-groups should be M-groups.
Euler's Criterion for Quintic Nonresidues
Authors: Katre S. A. , Rajwade A. R. 
Published: December 2010

Let e be an integer ≧ 2, and p a prime = 1 (mod e). Euler's criterion states that for D ∊ Z,(1.1)if and only if D is an e-th power residue (mod p). If D is not an e-th power (mod p), one has(1.2)for some e-th root α(≠1) of unity (mod p). Sometimes expressions for roots of unity (mod p) can be given in terms of quadratic partitions of p. For example,(1.3)are the four distinct fourth roots of unity (mod p) for a prime p ≡ 1 (mod 4) in terms of a solution (a, b) of the diophantine system(a, b unique), whereas for p ≡ 1 (mod 3), a solution (L, M) of the systemgives(1.4)as the three distinct cuberoots of unity (mod p).
Approximation by Λ-Splines on the Circle
Authors: Goodman T. N. T. , Lee S. L. , Sharma A. 
Published: December 2010

Let Λ = {λ0,…, λn} denote a set of distinct integers and let Π(Λ) denote the set of all generalized polynomials of the formFor any given ζ on the unit circle U withwe consider the set Zk of points 1, ζ, ζ2, …, ζk−1 whereWe shall denote by or the class of Λ-splines S(z) which satisfy the following conditions:(i) S(z) ∊ Cn−1(U)(ii) S(z)|Av ∊ Π(Λ) where
Generalized Spectral Theory in Complex Banach Algebras
Authors: Hile G. N. , Pfaffenberger W. E. 
Published: December 2010

Let A be an element of a complex Banach algebra with identitI. The ordinary spectrum of A, sp(A), consists of those points z in the complex plane such that A — zI has no inverse in . If Q is any other element of , we define spQ(A), the spectrum of A relative to Q, or Q-spectrum of A, as those points z such that has no inverse in . Thus if Q = 0 the Q-spectrum of A is the same as the ordinary spectrum of A.The generalized notion of spectrum, spQ(A), retains many of the properties of the ordinary spectrum, particularly when A and Q commute and the ordinary spectrum of Q does not meet the unit circle. Under these conditions the Q-spectrum of A is a nonempty compact subset of the plane, and if both sp(A) and sp(Q) are finite (or countable), so is spQ(A).
A measure on the Unipotent Variety
Authors: Arthur James 
Published: December 2010

Suppose that G is a reductive algebraic group defined over Q. There occurs in the trace formula a remarkable distribution on G(A)1 which is supported on the unipotent set. It is defined quite concretely in terms of a certain integral over G(Q)\G(A)1. Despite its explicit description, however, this distribution is not easily expressed locally, in terms of integrals on the groups G(QV). For many applications of the trace formula, it will be essential to do this. In the present paper we shall solve the problem up to some undetermined constants.The distribution, which we shall denote by Junip, was defined in [1] and [3] as one of a family {Jo} of distributions. It is the value at T = T0 of a certain polynomial . We shall recall the precise definition in Section 1.
Projections sur des Espaces de Fonctions Holomorphes Dans des Domaines Plans
Authors: Békollé David 
Published: December 2010

Soit Ω un domaine de Jordan à bord rectifiable du plan complexe C. Désignons par dλ la mesure de Lebesgue à l'intérieur de Ω, par dσ la mesure de Lebesgue sur le bord ∂Ω de Ω et par φ une représentation conforme de Ω sur le disque unité D du plan complexe.Par définition, la classe de Bergman Ap(Ω), 0 < p ≦ +∞, est le sous-espace de Lp(dλ) formé par les fonctions holomorphes dans Ω et le projecteur de Bergman PΩ de Ω est le projecteur orthogonal de L2(dλ) sur A2(Ω); quel que soit f dans L2(dλ), on a la formule:(1)
Continuity of the Scattering Transformation for the Korteweg de Vries Equation
Authors: Gautrin Henri-François , Klemola Tapio 
Published: December 2010

It is at present well known that, if q(x, t) is a solution of the Korteweg de Vries (K d V) equation(1)such that q(x, 0) = q0(x), where q0(x) behaves reasonably at infinity, and ifare the scattering data (see [4]) corresponding to q(x, t), then
Epimorphisms From S(X) onto S(Y)
Authors: Magill K. D. , Misra P. R. , Tewari U. B. 
Published: December 2010

1. Introduction. In this paper, the expression topological space will always mean generated space, that is any T1 space X for whichforms a subbasis for the closed subsets of X. This is not at all a severe restriction since generated spaces include all completely regular Hausdorff spaces which contain an arc as well as all 0-dimensional Hausdorff spaces [3, pp. 198-201], [4].The symbol S(X) denotes the semigroup, under composition, of all continuous selfmaps of the topological space X. This paper really grew out of our efforts to determine all those congruences σ on S(X) such that S(X)/σ is isomorphic to S(Y) for some space Y.
Induction and Restriction of π-Special Characters
Authors: Isaacs I M. 
Published: December 2010

1. Introduction. The character theory of solvable groups has undergone significant development during the last decade or so and it can now be seen to have quite a rich structure. In particular, there is an interesting interaction between characters and sets of prime numbers.Let G be solvable and let π be a set of primes. The “π-special” characters of G are certain irreducible complex characters (defined by D. Gajendragadkar [1]) which enjoy some remarkable properties, many of which were proved in [1]. (We shall review the definition and relevant facts in Section 3 of this paper.) Actually, we need not assume solvability: that G is π-separable is sufficient, if we are willing to use the Feit-Thompson “odd order” theorem occasionally. We shall state and prove our results under this weaker hypothesis, but we stress that anything of interest in them is already interesting in the solvable case where, of course, the “odd order” theorem is irrelevant.
The Dirichlet Problem on the Heisenberg Group III: Harmonic Measure of a certain Half-Space
Authors: Gaveau Bernard , Vauthier Jacques 
Published: December 2010

0. Introduction. In this short note we give an explicit computation of the harmonic measure of a half space x > 0 in the 3-dimensional Heisenberg group in terms of a degenerate hypergeometric function. A probabilistic argument reduces the whole problem to a Hermite-type equation on a half line, that we can solve in terms of the function G(l/4, 1/2; x2).A preliminary attempt to compute this kernel was done in [1] p. 107 and, cited by Huber [4]. Unfortunately a small mistake was made in [1] and the problem was still open until now. The first author is very grateful to Prof. Huber for having pointed out the weak argument of [1]. Since that time, other harmonic measures and even Green functions have been explicitly computed (see [2]).
A Tauberian Theorem of Exponential Type
Authors: Geluk J. L. , de Haan L. , Stadtmüller U. 
Published: December 2010

1. Introduction. We will be interested in Tauberian theorems concerning the limiting behaviour of a monotone function U and its Laplace transformA famous theorem of Karamata concerns the case in which the function U is regularly varying (i.e., U(tx)/U(t) → xα(t → ∞) for x > 0). Here we will consider functions U that grow faster, in fact our conditions will be in terms of log U rather than on U itself. So it is convenient to write the Laplace transform in terms of q = log U. For a function q:R+ → R such that exp q is locally integrable andwe define the function by the relation
On the Singularities of Plane Curves
Authors: Bisztriczky Tibor 
Published: December 2010

Let Γ be a differentiable curve in a real projective plane P2 met by every line of P2 at a finite number of points. The singular points of Γ are inflections, cusps (cusps of the first kind) and beaks (cusps of the second kind). Let n1(Γ), n2(Γ) and n3(Γ) be the number of these points in Γ respectively. Then Γ is non-singular ifotherwise, Γ is singular.We wish to determine when T is singular and then find the minimum value of n(Γ). A history and an analysis of this problem were presented in [1] and [2]. It was shown that we may assume that Γ is a curve of even order (even degree if Γ is algebraic), met by every line in P2. Then if Γ does not contain any multiple points or if Γ contains only a certain type of multiple point, Γ is singular. Presently, we complete this investigation
A Family of M*-Groups
Authors: May Coy L. 
Published: December 2010

A compact bordered Klein surface of (algebraic) genus g ≦ 2 is said to have maximal symmetry [5] if its automorphism group is of order 12(g – 1), the largest possible. An M*-group acts as the automorphism group of a bordered surface with maximal symmetry. M*-groups were first studied in [6], and additional results about these groups are in [5, 7, 8].Here we construct a new, interesting family of M*-groups. Each group G in the family is an extension of a cyclic group by the automorphism group of a torus T with holes that has maximal symmetry. Furthermore, G acts on a bordered Klein surface X that is a fully wound covering [7] of T, that is, an especially nice covering in which X has the same number of boundary components as T. The construction we use for the new family of M*-groups is a standard one that employs group automorphisms to define extensions of groups.
On the Spectra of Unbounded Subnormal Operators
Authors: McDonald G. , Sundberg C. 
Published: December 2010

Putnam showed in [5] that the spectrum of the real part of a bounded subnormal operator on a Hilbert space is precisely the projection of the spectrum of the operator onto the real line. (In fact he proved this more generally for bounded hyponormal operators.) We will show that this result can be extended to the class of unbounded subnormal operators with bounded real parts.Before proceeding we establish some notation. If T is a (not necessarily bounded) operator on a Hilbert space, then D(T) will denote its domain, and σ(T) its spectrum. For K a subspace of D(T), T|K will denote the restriction of T to K. Norms of bounded operators and elements in Hilbert spaces will be indicated by ‖ ‖. All Hilbert space inner products will be written 〈,〉. If W is a set in C, the closure of W will be written clos W, the topological boundary will be written bdy W, and the projection of W onto the real line will be written π(W),
Distance Functions and Orlicz-Sobolev Spaces
Authors: Edmunds D. E. , Edmunds R. M. 
Published: December 2010

Let ∧ be a bounded, non-empty, open subset of Rn and given any x in Rn, letlet k ∊ N and suppose that p ∞ (1, ∞). It is known (c.f. e.g. [4]) that if u belongs to the Sobolev space WKp(∧) and u/dk ∊ Lp(∧), then . Further results in this direction are given in [5] and [9]. Moreover, if m is the mean distance function in the sense of [2], then it turns out thatUnder appropriate smoothness conditions on the boundary of ∧, m and d are equivalent, and thus may in this case be characterized as the subspace of W1,2(∧) consisting of all functions u ∊ W1,2(∧) such that u/d ∊ L2(∧). Further results in this direction are given in [5] and [9]. Moreover, if m is the mean distance function in the sense of [2], then it turns out that
Excising States of C*-Algebras
Authors: Akemann Charles A. , Anderson Joel , Pedersen Gert K. 
Published: December 2010

A net {aα} of positive, norm one elements of a C*-algebra A excises a state f of A ifThis notion has been used explicitly by the second author [4, 5, 6] for pure states, but the present paper will explore it more fully. The name is motivated by the following example. Let K be the unit disk in the complex plane, A = C(K) and f(a) = a(0). Define an(reiθ) = ϕn(r), whereNote that the sets {t ∊ K:an(t) ∊ 0} form rings about 0 with radii tending to 0. In this sense the sequence {an} “cuts out” the state f and, in the limit, isolates it from all other states.