bluuebunny/crossref_metadata_2025_split huggingface dataset:
Chromatic Solutions
Authors: Tutte W. T. 
Published: December 2010

Early in the Seventies I sought the number of rooted λ-coloured triangulations of the sphere with 2p faces. In these triangulations double joins, but not loops, were permitted. The investigation soon took the form of a discussion of a certain formal power series l(y, z, λ) in two independent variables y and z.The basic theory of l is set out in [1]. There l is defined as the coefficient of x2 in a more complicated power series g(x, y, z, λ). But the definition is equivalent to the following formula.1Here T denotes a general rooted triangulation. n(T) is the valency of its root-vertex, and 2p(T) is the number of its faces. P(T, λ) is the chromatic polynomial of the graph of T.
The Analytic Character of the Birkhoff Interpolation Polynomials
Authors: Lorentz G. G. 
Published: December 2010

Let E be an m × (n + 1) regular interpolation matrix with elements ei, k = (E)i, k which are zero or one, with n + 1 ones. Then for each f ∈ Cn[a, b] and each set of knots X: a ≦ x1 < … < xm ≦ b, there is a unique interpolation polynomial P(f, E, X; t) of degree ≦ n which satisfies1A recent paper [1] discussed the continuity of P, as a function of x1, …,xm(with coalescences allowed). We would like to study in this note the analytic character of P as a function of real or complex knots X: x1, …, xm. This is easy for the Lagrange or the Hermite interpolation. In this case P is a polynomial in x1, …, xm if f is a polynomial, and an entire function in x1, …, xm if f is entire.
L'Enveloppe Conjuguee D'Un Demi-Groupe Inverse a Metacentre Idempotent
Authors: Pastijn Francis 
Published: December 2010

Nous renvoyons le lecteur à [4] pour toutes les définitions non expliquées ci-dessous.Un demi-groupe inverse S est un demi-groupe pour lequel pour tout élément a ∊ S il existe un seul inverse a–1, c'est-à-dire un élément a–l qui satisfait aux conditions aa–1a = a et a–1aa–1 = a–1. Une application λ : S → S, x → λx est appelée une translation à gauche si λ(xy) = (λx)y; une application ρ : S → S, x → xρ est dite translation à droite si (xy)ρ = x(yρ). Les translations à gauche (à droite) forment un demi-groupe Λ(S) [P(S)]. L'ensembleforme un sous-demi-groupe de Λ(S) × P(S) qui est appelé l'enveloppe de translations de S. Si pour tout a ∊ S on définit λa : S → S, x → ax, et ρa : S → S, x → xa, on appellela partie interne de Ω(S).
Rearrangements that Preserve Rates of Divergence
Authors: Johnston Elgin H. 
Published: December 2010

Let Σak be an infinite series of real numbers and let π be a permutation of N, the set of positive integers. The series Σaπ(k) is then called a rearrangement of Σak. A classical theorem of Riemann states that if Σak is a conditionally convergent series and s is any fixed real number (or ± ∞), then there is a permuation π such that Σaπ(k) = s. The problem of determining those permutations that convert any conditionally convergent series into a convergent rearrangement (such permuations are called convergence preserving) has received wide attention (see, for example [6]). Of special interest is a paper by P. A. B. Pleasants [5] in which is shown that the set of convergence preserving permutations do not form a group.In this paper we consider questions similar to those above, but for rearrangements of divergent series of positive terms. We establish some notation before stating the precise problem.
KAC-Moody Lie Algebras and the Classification of Nilpotent Lie Algebras of Maximal Rank
Authors: Santharoubane L. J. 
Published: December 2010

Introduction. The natural problem of determining all the Lie algebras of finite dimension was broken in two parts by Levi's theorem:1) the classification of semi-simple Lie algebras (achieved by Killing and Cartan around 1890)2) the classification of solvable Lie algebras (reduced to the classification of nilpotent Lie algebras by Malcev in 1945 (see [10])).The Killing form is identically equal to zero for a nilpotent Lie algebra but it is non-degenerate for a semi-simple Lie algebra. Therefore there was a huge gap between those two extreme cases. But this gap is only illusory because, as we will prove in this work, a large class of nilpotent Lie algebras is closely related to the Kac-Moody Lie algebras. These last algebras could be viewed as infinite dimensional version of the semisimple Lie algebras.
A Note on Projective Capacity
Authors: Alexander H. 
Published: December 2010

Introduction. In [1] we defined a capacity in Cn. Recently Molzon, Shiffman and Sibony [8] have introduced a different capacity which is useful for certain Bezout estimates. The object of this note is to apply the methods of [1] to study the capacity of [8]. We shall obtain an equivalent definition of this capacity via Tchebycheff polynomials, along the lines of [1]. Half of this equivalence was independently obtained by Sibony [9].To establish the full equivalence of these two approaches to capacity a notion of Jensen measures in a setting more general than uniform algebras is needed. We shall consider Jensen measures for multiplicative semigroups; these are sets of functions in which only the multiplicative structure is postulated. It will also be useful to generalize the notion of polynomial hull in Cn to a hull with respect to a multiplicative semigroup of polynomials. We can then adapt the approach of [1] to these semigroups.
On Inequalities Complementary to Jensen's
Authors: Beesack Paul R. 
Published: December 2010

In a paper published in 1975 [1, § 3], D. S. Mitrinovič and P. M. Vasič
used the so-called “centroid method” to obtain two new inequalities which are complementary to (the discrete version of) Jensen's inequality for convex functions. In this paper we shall present a very general version of such inequalities using the same geometric ideas used in [1] but not using the centroid method itself. At the same time we shall extend the domain of the inequalities (even in the discrete case), and clarify the value of the constant (λ) appearing in the inequality. We give applications of the theorems to some general means and also to the classical means. Our first result is given asTHEOREM 1. Let v be a nonnegative measure on a σ-algebra of subsets of a set D and let q, f be real v-measurable functions on D such that q(x) > 0, –∞ < x1 ≦ f(x) ≦ x2 < ∞ for all x ∊ D and ∫D qdv = 1.
The Hilbert Transform of Generalized Functions and Applications
Authors: Pandey J. N. , Chaudhry Muhammad Aslam 
Published: December 2010

The theory of Fourier transforms of tempered distributions as developed by Laurent Schwartz [17] is quite simple and elegant and has wide variety of applications, but there does not exist a corresponding neat and simple theory for the Hilbert transform of generalized functions (distributions) having wide applications. One of the objectives of this paper is to develop such a theory for the Hilbert transform of generalized functions and indicate its applicability to a variety of problems.In problems of physics sometimes we need to find harmonic functions u(x, y) in the region y > 0 whose limit as y → 0+ does not exist in pointwise sense but does exist in the distributional sense. The theory of Hilbert transform of generalized functions that we are going to develop will provide an answer to the existence and uniqueness of this problem.
The Metric Fuglede Property and Normality
Authors: Moore R. L. , Weiss G. 
Published: December 2010

In [4], H. Kamowitz considered the condition, to be satisfied by a bounded operator N on a Hilbert space , thatfor all operators X on . Kamowitz discovered that such an N must be normal and its spectrum must lie on a line or a circle; that is, N must be of the form αJ + β, where α and β are complex numbers and J is either Hermitian or unitary. G. Weiss [5] showed that the Hilbert-Schmidt norm behaves differently: N need only be normal in order thatfor all finite-rank operators X, and in fact this condition is equivalent to normality. Actually, the result in [5] removes the restriction that X be finite-rank, that is, if N is normal and X is any bounded operator, then
Uniform Approximation by Polynomials with Variable Exponents
Authors: Borwein Peter B. 
Published: December 2010

We examine questions related to approximating functions by sums of the formWe focus on approximations to functions given by the integral transformationwhere γ is a positive measure. Approximations to this class of functions (Laplace transforms in the variable — lnx) are particularly well behaved (see Theorem 1). Questions concerning existence, uniqueness and characterization of such approximations have been thoroughly examined in the equivalent setting of exponential sum approximations (see [3], [4], [6] and [9]). Less well studied is the order of convergence of the approximation. This is the problem we address. Part of the motivation for using sums of the form (1), which we shall call Gaussian sums, stems from the observation that all analytic functions with Taylor series expansion having positive coefficients are of the form (2).
Normal, Locally Compact, Boundedly Metacompact Spaces are Paracompact: an Application of Pixley-Roy Spaces
Authors: Daniels Peg 
Published: December 2010

Let PR(X) denote the Pixley-Roy topology on the collection of all nonempty, finite subsets of a space X. For each cardinal κ, let κ* be the cardinal κ with the co-finite topology. We use PR(κ*) to obtain a partial solution in ZFC to F. Tall's question whether every normal, locally compact, metacompact space is paracompact [6]. W.S. Watson has answered this question affirmatively assuming V = L[7]. The question also has an affirmative answer if we assume either that the space is perfectly normal [1] or that it is locally connected [4].A space X is said to be boundedly metacompact (boundedly paracompact) provided that for each open cover of X there is a positive integer n such that has a point finite (locally finite) open refinement of order n. As the main result of this paper, we show every normal, locally compact, boundedly metacompact space is paracompact.
Concerning the Cone = Hyperspace Property
Authors: Sherling Dorothy D. 
Published: December 2010

In this paper it is shown that a sufficient condition for a continuum X to have the cone = hyperspace property is that there exists a selection for C(X)\{X} which, for some Whitney map for C(X), maps each nondegenerate Whitney level homeomorphically onto X. Also, we construct an example of a one-dimensional, nonchainable, noncircle-like continuum which has the cone = hyperspace property. The continuum is described by means of inverse limits using only one bonding map. Each factor space in the inverse limit sequence is the quotient space resulting from an upper semi-continuous decomposition of a disjoint union of simple triods. The bonding map is an adaptation of the bonding map defined by W. T. Ingram in his construction of an atriodic, tree-like continuum which is not chainable [4].Definitions, notation, and terminology. By continuum we mean a nonempty, compact, connected metric space.
On the Resolution Diagrams of the Brieskorn Singularities (2,q,r) of Type II
Authors: Yamada Akio , Matsumoto Yukio 
Published: December 2010

Let p, q, r be pairwise coprime integers with 2 ≦ p < q < r. The equation defines a complex hypersurface V(p, q, r) ⊂ C3 which has an isolated singular point at the origin. We call the singularity the Brieskorn singularity (p, q, r). An algorithm of resolving this singularity is known [1]. According to the algorithm, the resolution diagram which describes the configuration of the pre-image of the singular point in the resolved surface is a star-shaped tree Γp, q, r with three branches:1.1The positive integers (weights) ai, bj, ck are given as follows: Let x, y, z, b be integers satisfying1.2
Distance-Genericity for Real Algebraic Hypersurfaces
Authors: Bruce J. W. , Gibson C. G. 
Published: December 2010

One of the original applications of catastrophe theory envisaged by Thom was that of discussing the local structure of the focal set for a (generic) smooth submanifold M ⊆ Rn + 1. Thom conjectured that for a generic M there would be only finitely many local topological models, a result proved by Looijenga in [4]. The objective of this paper is to extend Looijenga's result from the smooth category to the algebraic category (in a sense explained below), at least in the case when M has codimension 1.Looijenga worked with the compactified family of distance-squared functions on M (defined below), thus including the family of height functions on M whose corresponding catastrophe theory yields the local structure of the focal set at infinity. For the family of height functions the appropriate genericity theorem in the smooth category was extended to the algebraic case in [1], so that the present paper can be viewed as a natural continuation of the first author's work in this direction.
Supplements of Hölder's Inequality
Authors: Barnes David C. 
Published: December 2010

Given vectors and (or functions f(x) and g(x)) we define the Hölder Quotient Hpq by1or in case of functions by2Here ‖·‖p and ‖·‖q are the usual Lp and Lq norms. We assume throughout thatIf p and q are both greater than one then they are positive but if we allow p and q to be less than one then one of them must be positive and the other one must be negative. This may cause a problem if for example, some value ai is zero and p is negative. In this case we use the convention that and
Discrete Convex Functions and Proof of the Six Circle Conjecture of Fejes Tóth
Authors: Bárány Imre , Füredi Zoltán , Pach János 
Published: December 2010

A system of openly disjoint discs in the plane
is said to form a 6-neighboured circle packing if every is tangent to at least 6 other elements of (It is evident that such a system consists of infinitely many discs.) The simplest example is the regular circle packing all of whose circles are of the same size and have exactly 6 neighbours. L. Fejes Tóth conjectured that the regular circle packing has the interesting extremal property that, if we slightly “perturb” it, then there will necessarily occur either arbitrarily small or arbitrarily large circles. More precisely, he asked whether or not the following “zero or one law” (cf. [3], [6]) is valid: If is a 6-neighboured circle packing, thenwhere r(C) denotes the radius of circle C, inf and sup are taken over all C ∊
Orthogonal Polynomials with Symmetry of Order Three
Authors: Dunkl Charles F. 
Published: December 2010

The measure (x1x2x3)2adm(x) on the unit sphere in R3 is invariant under sign-changes and permutations of the coordinates; here dm denotes the rotation-invariant surface measure. The more general measurecorresponds to the measureon the triangle(where ). Appell ([1] Chap. VI) constructed a basis of polynomials of degree n in v1, v2 orthogonal to all polynomials of lower degree, and a biorthogonal set for the case γ = 0. Later Fackerell and Littler [6] found a biorthogonal set for Appell's polynomials for γ ≠ 0. Meanwhile Pronol [10] had constructed an orthogonal basis in terms of Jacobi polynomials.
On Unbounded Volterra Operators
Authors: Hughes Rhonda J. 
Published: December 2010

Similarity invariants of certain families of Volterra operators acting in Lp[0, 1] were first determined by Kalisch in [4] and [5]. Subsequently, Kantorovitz made an extensive study of perturbations of the form Tα = M + αN, where M is the operation of multiplication by x, and N is the Volterra operatorboth acting in Lp[0, 1], and determined that Re α is a similarity invariant for the class of Tα's (cf. [7], and earlier work cited there). This result was eventually generalized to unbounded M (cf. [6]), and one direction was proved in [2] for both M and N unbounded: if Re α = Re β, then Tα is similar to Tβ. Properties of the Riemann-Liouville semigroup of fractional integration play a key role, for in all cases the ensuing similarity turns out to be implemented by N(i(lm(α — β))), where {N(iγ)} is the boundary group of the semigroup of fractional integration.
Modularity in the Lattice of Projections of a von Neumann Algebra
Authors: Bures Donald 
Published: December 2010

We say that two elements e and f of a lattice are moderately separated provided e ∧ f = 0 and both (e′, f′) and (f′, e′) are modular pairs for all e′ ≦ e and f′ ≦ f. Here (e′, f′) a modular pair means that, for all g ≧ e′,In the lattice of projections of a factor we show that e and f, with e ∧ f = 0, are modularly separated if and only if ‖(e – k)f‖ < 1 for some finite projection k ≦ e. From there we can show that a kind of “independence property” holds for modular separation in this case: if e and f are modularly separated and if e ∨ f and g are modularly separated, then e and f ∧ g are modularly separated.
On Torsion-Free Groups of Finite Rank
Authors: Meier David , Rhemtulla Akbar 
Published: December 2010

This paper deals with two conditions which, when stated, appear similar, but when applied to finitely generated solvable groups have very different effect. We first establish the notation before stating these conditions and their implications. If H is a subgroup of a group G, let denote the setWe say G has the isolator property if is a subgroup for all H ≦ G. Groups possessing the isolator property were discussed in [2]. If we define the relation ∼ on the set of subgroups of a given group G by the rule H ∼ K if and only if , then ∼ is an equivalence relation and every equivalence class has a maximal element which may not be unique. If , we call H an isolated subgroup of G.
More on Compact Hausdorff Spaces and Finitary Duality
Authors: Banaschewski B. 
Published: December 2010

It is an old conjecture by P. Bankston that the category CompHaus of compact Hausdorff spaces and their continuous maps is not dually equivalent to any elementary P-class of finitary algebras (taken as a category with all homomorphisms between its members as maps), where elementary means defined by first order axioms, and a P-class is one closed under arbitrary (cartesian) products. One motivation for this conjecture is the fact that such a dual equivalence would make ultracopowers of compact Hausdorff spaces correspond to ultrapowers of finitary algebras, and one might expect this to have contradictory consequences.As a possible step towards proving his conjecture, Bankston [2] showed that no elementary SP-class of finitary algebras can be dually equivalent to CompHaus. However, it was subsequently proved in [1] that the same holds for any SP-class of finitary algebras, using an argument independent of ultrapowers.
On basic Cycles of An, Bn, Cn and Dn
Authors: Britten D. J. , Lemire F. W. 
Published: December 2010

In this paper, we investigate a conjecture of Dixmier [2] on the structure of basic cycles. Our interest in basic cycles arises primarily from the fact that the irreducible modules of a simple Lie algebra L having a weight space decomposition are completely determined by the irreducible modules of the cycle subalgebra of L. The basic cycles form a generating set for the cycle subalgebra.First some notation: F denotes an algebraically closed field of characteristic 0, L a finite dimensional simple Lie algebra of rank n over F, H a fixed Cartan subalgebra, U(L) the universal enveloping algebra of L, C(L) the centralizer of H in U(L), Φ the set of nonzero roots in H*, the dual space of H, Δ = {α1, …, αn} a base of Φ, and Φ+ = {β1, …, βm} the positive roots corresponding to Δ.
A Technique to Generate -Ary Free Lattices from Finitary Ones
Authors: Grätzer George , Kelly David 
Published: December 2010

Letbe an infinite regular cardinal. A posetLis called an-lattice if and only if for allXLsatisfying 0 < |X| <m, ∧Xand ∨Xexist.This paper is a part of a sequence of papers,[5], [6], [7], [8], developing the theory of-lattices. For a survey of some of these results, see [9].The-latticeis described in [6]; γ denotes the zero and γ′ the unit of. In particular, formulas for-joins and meets are given. (We repeat the essentials of this description in Section 4.)In [6] we proved the theorem stated below. Our proof was based on characterization of(the free-lattice onP) due to [1]; as a result, our proof was very computational.
The Method of Upper and Lower Solutions for Some Nonlinear Boundary Value Problems in Unbounded Domains
Authors: Các Nguyên Phuong 
Published: December 2010

Let D be a bounded domain in the Euclidean space RN(N ≦ 2) and let where is the closure of D. We assume that the boundary ∂G of G is smooth. Consider the boundary value problem (abbreviated to BVP in the sequel).(1)(1)where A is a nonlinear elliptic differential operator in divergence form of Leray-Lions type, ∇u = grad u, f is a distribution on G and p(x, t, η) is a function defined on G × R × RN. Among other hypotheses we shall, roughly speaking, assume that p has completely unrelated growth rates in the first and the third variables. In this paper we prove the solvability of the BVP (1), (2) under the assumption that it has both an upper solution ψ and a lower solution φ with φ ≧ ψ.
Beyond the Enveloping Algebra of sl3
Authors: Flath Daniel E. , Biedenharn L. C. 
Published: December 2010

The problem which motivated the writing of this paper is that of finding structure behind the decomposition of the sl3 representation spaces V* ⊗ W = Hom(V, W) for finite dimensional irreducible sl3-modules V and W. For sl2 this extends the classical Clebsch-Gordon problem. The question has been considered for sl3 in a computational way in [5]. In this paper we build a conceptual algebraic framework going beyond the enveloping algebra of sl3.For each dominant integral weight α let Vα be an irreducible representation of sl3 of highest weight α. It is well known that, for weights α, μ, λ, the multiplicity of Vλ in Hom(Vα, Vα+μ) is bounded by the multiplicity of μ in Vλ, with equality for generic α. This suggests the possibility of a single construction of highest weight vectors of weight X in Hom(Vα, Vα+μ) which is valid for all a.
Application of a Selection Theorem to Hyperspace Contractibility
Authors: Curtis D. W. 
Published: December 2010

For X a metric continuum, 2X denotes the hyper space of all nonempty subcompacta, with the topology induced by the Hausdorff metric H, and C(X) ⊂ 2X the hyperspace of subcontinua. These hyperspaces are continua, in fact are arcwise-connected, since there exist order arcs between each hyperspace element and the element X. They also have trivial shape, i.e., maps of the hyperspaces into ANRs are homotopic to constant maps. For a detailed discussion of these and other general hyperspace properties, we refer the reader to Nadler's monograph [4].The question of hyperspace contractibility was first considered by Wojdyslawski [8], who showed that 2X and C(X) are contractible if X is locally connected. Kelley [2] gave a more general condition (now called property K) which is sufficient, but not necessary, for hyperspace contractibility. The continuum X has property K if for every there exists δ > 0 such that, for every pair of points x, y with d(x, y) < δ and every subcontinuum M containing x, there exists a subcontinuum N containing y with .
Projections on Tree-Like banach Spaces
Authors: Andrew A. D. 
Published: December 2010

1. In this paper, we investigate the ranges of projections on certain Banach spaces of functions defined on a diadic tree. The notion of a “tree-like” Banach space is due to James 4], who used it to construct the separable space JT which has nonseparable dual and yet does not contain l1. This idea has proved useful. In [3], Hagler constructed a hereditarily c0 tree space, HT, and Schechtman [6] constructed, for each 1 ≦ p ≦ ∞, a reflexive Banach space, STp with a 1-unconditional basis which does not contain lp yet is uniformly isomorphic to for each n.In [1] we showed that if U is a bounded linear operator on JT, then there exists a subspace W ⊂ JT, isomorphic to JT such that either U or (1 — U) acts as an isomorphism on W and UW or (1 — U)W is complemented in JT. In this paper, we establish this result for the Hagler and Schechtman tree spaces.