bluuebunny/crossref_metadata_2025_split huggingface dataset:
From Path Lifting and Unique Arc Lifting to Unique Path Lifting
Authors: Bell Harold , Ungar Gerald S. 
Published: December 2010

In [4] it was conjectured that a light map p : E → B for which paths can be lifted and lifting of arcs is unique is a Serre fibration. As is well-known this implies that paths have unique liftings. In this paper we shall prove several special cases of this conjecture.The two main theorems are: (3.5) Let p be a light compact map of a metric space E onto a connected semi-locally contractible along arcs metric space B. If arcs can be lifted uniquely then p is locally trivial.
Groups and Monoids of Regular Graphs (And of Graphs with Bounded Degrees)
Authors: Hell Pavol , Nešetřil Jaroslav 
Published: December 2010

A graph X is a set V(X) (the vertices of X) with a system E(X) of 2-element subsets of V(X) (the edges of X). Let X, Y be graphs and f : V(X) → V(Y) a mapping; then/ is called a homomorphism of X into F if [f(x),f(y)] ∈ E(Y) whenever [x,y] ∈ E(X). Endomorphisms, isomorphisms and automorphisms are defined in the usual manner.Much work has been done on the subject of representing groups as groups of automorphisms of graphs (i.e., given a group G, to find a graph X such that the group of automorphisms of X is isomorphic to G). Recently, this was related to category theory, the main question being as to whether every monoid (i.e., semigroup with 1) can be represented as the monoid of endomorphisms of some graph in a given category of graphs.
Sur Les Anneaux de Groupes Semi-Parfaits
Authors: Goursaud J. M. 
Published: December 2010

Soient A un anneau unitaire, G un groupe. L'anneau de groupe AG est le A-module libre ayant pour base les éléments de G, la multiplication étant définie par :avecLe premier résultat de cet article concerne les annulateurs des idéaux à gauche engendrés par les sous-groupes finis de G, il permet d'obtenir une démonstration facile de la caractérisation des anneaux de groupes parfaits à gauche.
Chromatic Sums for Rooted Planar Triangulations, IV: The Case λ = ∞
Authors: Tutte W. T. 
Published: December 2010

SummaryThe chromial P(M, λ) of a planar near-triangulation M has the leading term λv(M), where v(M) is the number of vertices of M. The problem of finding the number of rooted planar near-triangulations of a given class S, all supposed to have the same number of vertices, can be regarded as a special case of the problem of finding chromatic sums. We can sum P(M, λ) over the members of S, divide by the appropriate power of λ and let λ → ∞. We thus get the sum of the coefficient of the leading term of P(M, λ) for all M ∈ S, that is we get the number of members of S.
Curvature and Radius of Curvature for Functions with Bounded Boundary Rotation
Authors: Noonan J. W. 
Published: December 2010

For k ≧ 2 denote by Vk the class of functions f regular in and having the representation(1.1)where μ is a real-valued function of bounded variation on [0, 2π] with(1.2)Vk is the class of functions with boundary rotation at most kπ.
Conformally Flat Spaces of Codimension 2 in a Euclidean Space
Authors: Chen Bang-Yen , Yano Kentaro 
Published: December 2010

In a previous paper [1], the authors introduced and studied the notion of special conformally flat spaces and quasi-umbilical hypersurfaces. In that paper, the authors proved that every conformally flat space of codimension one in a Euclidean space is special and, conversely, every special conformally flat space can be isometrically immersed in a Euclidean space as a quasi-umbilical hypersurface.In the present paper, the authors study the conformally flat spaces of codimension 2 in a Euclidean space. (Manifolds, mappings, functions, etc. are assumed to be sufficiently differentiate and we shall restrict ourselves only to manifolds of dimension n > 3.)
Sur des Classes de Fonctions Analytiques Dans Le Disque et Indéfiniment Dérivables à La Frontière
Authors: Chollet A.-M. 
Published: December 2010

On note D le disque unité ouvert du plan complexe, le disque fermé et T l'ensemble des réels modulo 2π.Soit une suite de réels positifs; on désigne par {Nn}+ la classe des fonctions f, analytiques dans D, continues ainsi que toutes leurs dérivées dans , qui vérifient la propriété suivante: il existe des constantes Af et Mf telles que pour tout z dans et tout entier n positif ou nul .
On the Existence of Normal Metacompact Moore Spaces which are not Metrizable
Authors: Tall Franklin D. 
Published: December 2010

It is known that the following classes of spaces (all spaces in this article are assumed T1) are identical:1. Images of metric spaces under continuous open maps with compact point inverses.2. Spaces with uniform bases (in the sense of Alexandrov [1]).3. Metacompact developable spaces.4. Spaces with σ-point-finite bases in which closed sets are Gδ's.
Rank r Solutions to the Matrix Equation XAXT = C, A Nonalternate, C Alternate, Over GF(2y).
Authors: Buckhiester Philip G. 
Published: December 2010

Let GF(q) denote a finite field of order q = py, p a prime. Let A and C be symmetric matrices of order n, rank m and order s, rank k, respectively, over GF(q). Carlitz [6] has determined the number N(A, C, n, s) of solutions X over GF(q), for p an odd prime, to the matrix equation1.1where n = m. Furthermore, Hodges [9] has determined the number N(A, C, n, s, r) of s × n matrices X of rank r over GF(q), p an odd prime, which satisfy (1.1). Perkin [10] has enumerated the s × n matrices of given rank r over GF(q), q = 2y, such that XXT = 0. Finally, the author [3] has determined the number of solutions to (1.1) in case C = 0, where q = 2y.
Operators with Compact Self-Commutator
Authors: Pearcy Carl , Salinas Norberto 
Published: December 2010

Let be a fixed separable, infinite dimensional complex Hilbert space, and let () denote the algebra of all (bounded, linear) operators on . The ideal of all compact operators on will be denoted by and the canonical quotient map from () onto the Calkin algebra ()/ will be denoted by π.Some open problems in the theory of extensions of C*-algebras (cf. [1]) have recently motivated an increasing interest in the class of all operators in () whose self-commuta tor is compact.
Some C*-Algebras with Outer Derivations, II
Authors: Elliott George A. 
Published: December 2010

In this paper we shall consider the class of C*-algebras which are inductive limits of sequences of finite-dimensional C*-algebras. We shall give a complete description of those C*-algebras in this class every derivation of which is inner.Theorem. Let A be a C*-algebra. Suppose that A is the inductive limit of a sequence of finite-dimensional C*-algebras. Then the following statements are equivalent:(i) every derivation of A is inner;(ii) A is the direct sum of a finite number of algebras each of which is either commutative, the tensor product of a finite-dimensional and a commutative with unit, or simple with unit.
Multiplication Rings Via Their Total Quotient Rings
Authors: Griffin Malcolm 
Published: December 2010

In the following paper ring will always mean commutative ring which may or may not have an identity. We use the letterNexclusively for nilpotents of the ringA.A ring such that, given any two idealsLandMwithL⊆Mthere exists an idealQsuch thatL=QMis called amultiplication ring. For references to early papers on multiplication rings by Krull and Mori the reader is referred to [2]. A ring in which every regular ideal is invertible is called aDedekind ring.
Extrema of a Class of Functions on a Finite Set
Authors: Lebensold Kenneth W. 
Published: December 2010

In this paper, we are concerned with the following problem: Let S be a finite set and Sm* ⊂ 2S a collection of subsets of S each of whose members has m elements (m a positive integer). Let f be a real-valued function on S and, for p ∊ Sm*, define f(P) as Σs∊pf (s). We seek the minimum (or maximum) of the function f on the set Sm*.The Traveling Salesman Problem is to find the cheapest polygonal path through a given set of vertices, given the cost of getting from any vertex to any other. It is easily seen that the Traveling Salesman Problem is a special case of this system, where S is the set of all edges joining pairs of points in the vertex set, Sm* is the set of polygons, each polygon has m elements (m = no. of points in the vertex set = no. of edges per polygon), and f is the cost function.
Sufficiency Conditions for the Existence of Transversals
Authors: Milner E. C. , Shelah S. 
Published: December 2010

A transversal of a family of non-empty sets is a 1-1 mapsuch that φ(v) ∊ Fv (v ∊ I) . A number of problems in combinatorial mathematics reduce to the question of whether or not a certain family of sets has a transversal. An up-to-date account of this theory is to be found in the book by Mirsky [9]. The best known result of this kind is the following theorem.
The Polycyclic Length of Linear and Finite Polycyclic Groups
Authors: Fisher R. K. 
Published: December 2010

In what follows, a polycyclic series, for the group G, is any finite seriesG = G0 ≧ G1 ≧ . . . ≧ Gl = 1of subgroups of G, such that Gi+1 ⊲ Gi and Gi/Gi+1 is cyclic, for all i = 0, . . ., l — 1. A group that has a polycyclic series is called a polycyclic group, and if G is a polycyclic group, then the polycyclic length of G, which we denote by ρ(G), is the number of non-trivial factors of a polycyclic series for G of shortest length.
On The Number of Classes of a Finite Group Invariant for Certain Substitutions
Authors: van Zanten A. J. , de Vries E. 
Published: December 2010

In this paper we consider representations of groups over the field of the complex numbers.The nth-Kronecker power σ⊗n of an irreducible representation σ of a group can be decomposed into the constituents of definite symmetry with respect to the symmetric group Sn. In the special case of the general linear group GL(N) in N dimensions the decomposition of the defining representation at once provides irreducible representations of GL(N) [9; 10; 11].
Homeomorphism and Isomorphism of Abelian Groups
Authors: Scheinberg Stephen 
Published: December 2010

An abelian topological group can be considered simply as an abelian group or as a topological space. The question considered in this article is whether the topological group structure is determined by these weaker structures. Denote homeomorphism, isomorphism, and homeomorphic isomorphism by ≈, ≅ , and =, respectively. The principal results are these.Theorem 1. If G1andG2are locally compact and connected, then G1≈ G2implies G1= G2.
Ln Sets and the Closures of Open Connected Sets
Authors: Stavrakas Nick M. 
Published: December 2010

F. A. Valentine in [4] proved the following two theorems.THEOREM 1. Let S be a closed connected subset of Rd which has at most n points of local nonconvexity. Then S is an Ln+i set.THEOREM 2. Let S be a closed connected subset of Rd whose points of local nonconvexity are decomposable into n closed convex sets. Then S is an L2n+i set.These results have been extended by a number of authors, but always with stronger hypothesis. (See [1] and [2].) Using a minimal arc technique, new pr∞fs of Theorems 1 and 2 were given in [3].Valentine remarks in [4] that Theorem 2 might be improved in the case that 5 is the closure of an open connected set. The goal of this paper is to give such an improvement for sets satisfying a particular local connectivity property.
Filter Monads, Continuous Lattices and Closure Systems
Authors: Day Alan 
Published: December 2010

The notion of a monad (triple) has become increasingly important as an extension of the classical universal algebraic approach to “algebraic” categories. Indeed the categories of algebras arising from a monad seem to be the most natural generalization of Birkhoffs equational classes. Moreover in [2], Barr's concept of a relational model of a monad also coincides nicely with both the concepts of partial algebras (when suitably restricted) and (Moore) closure systems.In this paper, we wish to examine two particular monads determined by filters. The first is the filter monad F = (F, η, 𝛍) over Sets where FX is the set of all (not necessarily proper) filters on X.
Norm Convergence of Riesz-Bochner Means For Radial Functions
Authors: Welland G. V. 
Published: December 2010

It is well known now that certain spherical methods in k (≧2) dimensions are rather poor for reconstructing a function from its Fourier transform. Consider a function f in L1(Rk), k ≧ 2,andwhere both integrals are integrals in Rk, the first over the whole space the second over the ball of radius R; x • y is the usual Euclidean inner product of x and y in Rk and \z\2 = z • z.
Rice Theorems For D.R.E. Sets
Authors: Hay Louise 
Published: December 2010

Two of the basic theorems in the classification of index sets of classes of recursively enumerable (r.e.) sets are the following:(i) The index set of a class C of r.e. sets is recursive if and only if C is empty or contains all r.e. sets; and(ii) the index set of a class C or r.e. sets is recursively enumerable if and only if C is empty or consists of all r.e. sets which extend some element of a canonically enumerable class of finite sets.The first theorem is due to Rice [7, p. 364, Corollary B]. The second was conjectured by Rice [7, p. 361] and proved independently by McNaughton, Shapiro, and Myhill [6].
Partially Bounded Solutions of Linear Ordinary Differential Equations
Authors: Lovelady David Lowell 
Published: December 2010

Let R, R+, and R- be the intervals (-∞, ∞), [0, ∞), and ( — ∞, 0] respectively. Let m be a positive integer, and let be the algebra of all m X m matrices. Let A be a locally integrable function from R to We propose to study the problems(NH) u‘(t) = f(t) + A﹛t)u﹛t)and(H) v‘(t) =A(t)v(t)in Rm. (H) and (NH) will denote whole-line problems, whereas (H)+, (NH)+, (H)-, and (NH)- will denote corresponding semi-axis problems.In [1] (see also [2, Theorem 1, p. 131]), W. A. Coppel obtained necessary and sufficient conditions for each bounded Continuous/ on R+ to yield at least one bounded solution u of (NH)+. The present author [3] has determined that an analogous result holds for (NH).
Center Points Of Nets
Authors: Anderson C. L. , Hyams W. H. , McKnight C. K. 
Published: December 2010

Suppose x = (x∝) is a net with values in a metric space X having metric ρ. If a point z in X can be found to minimizethen z is called a center point (c.p.) of x. The space X is (netwise) c.p. complete if every bounded net has at least one c.p.; it is sequentially c.p. complete if every bounded sequence has a c.p. Netwise c.p. completeness implies sequential c.p. completeness, and the latter implies completeness since any c.p. of a Cauchy sequence will necessarily be a limit point of that sequence.These notions are related to the set centers of Calder et al. [2].
Holomorphic Mappings of the Hyperbolic Space into the Complex Euclidean Space and the Bloch Theorem
Authors: Hahn Kyong T. 
Published: December 2010

This paper is to study various properties of holomorphic mappings defined on the unit ball B in the complex euclidean space Cn with ranges in the space Cm. Furnishing B with the standard invariant Kähler metric and Cm with the ordinary euclidean metric, we define, for each holomorphic mapping f : B → Cm, a pair of non-negative continuous functions qf and Qf on B ; see § 2 for the definition.Let (Ω), Ω > 0, be the family of holomorphic mappings f : B → Cn such that Qf(z) ≦ Ω for all z ∈ B. (Ω) contains the family (M) of bounded holomorphic mappings as a proper subfamily for a suitable M > 0.
Certain Submodules of Simple Rings with Involution, II
Authors: Herstein I. N. 
Published: December 2010

Let R be a simple ring, of characteristic not 2, having an involution *. Let 5 = ﹛x G R|x* = x﹜ and K = ﹛x £ R|x* = — x﹜ be the set of symmetric and skew elements, respectively, of R.In [1] we discuss the structure of S as a Jordan ring and K as a Lie ring. In [2] we considered cross-over submodules, namely additive subgroups U ⊂ K, V ⊂ S such that
Equality of Decomposable Symmetrized Tensors
Authors: Merris Russell 
Published: December 2010

Let V be an n-dimensional vector space over the field F. Let ꕕm V be the rath tensor power of V. If ᓂ ∈ Sm, the symmetric group, there exists a linear operator P (ᓂ1) on ꕕm V such thatfor all x1, … , xm ∈ V. (Here, x1 ꕕ … ꕕ xm denotes the decomposable tensor product of the indicated vectors.) If c is any function of Sm taking its values in F, we define
Coefficient Behavior of a Class of Meromorphic Functions
Authors: Noonan J. W. 
Published: December 2010

With , denote by Λk the class of functions ƒ of the formwhich are analytic in and which map y onto the complement of a domain with boundary rotation at most . It is known [2] that ƒ ∈ Λk if and only if there exist regular starlike functions s1 and s2, withsuch that
Localizations of Hi and Di Rings
Authors: Houston Evan G. 
Published: December 2010

In this paper we study conditions under which certain localizations of semilocal Hi and Di rings satisfy the second chain condition. Two of these results are as follows.1) If P is a prime in a semilocal Hi ring with depth P > i ≧ height P — 1, then RP satisfies the second chain condition.2) If P is a prime in a semilocal Dt ring with depth P ≧ i, then RP satisfies the second chain condition.
Relations Between Generalized Growth Conditions and Several Classes of Convexoid Operators
Authors: Furuta Takayuki 
Published: December 2010

In this paper we shall discuss some classes of bounded linear operators on a complex Hilbert space. If T is a bounded linear operator T acting on the complex Hilbert space H, then the following two inequalities always hold:where σ(T) indicates the spectrum of T, W(T) denotes the numerical range of T defined by W(T) = {(Tx, x) : ||x|| = 1 and x ∊ H} and means the closure of W(T) respectively.
A Finiteness Criterion for Orthomodular Lattices
Authors: Bruns Günter 
Published: December 2010

The main result of this paper is the following:
THEOREM. Every finitely generated orthomodular lattice L with
finitely many
maximal Boolean subalgebras (blocks) is finite.

If L has one block only, our theorem reduces to
the well-known fact that every finitely generated Boolean algebra is finite. On
the other hand, it is known that a finitely generated orthomodular lattice without
any further restrictions can be infinite. In fact, in [2] we constructed an
orthomodular lattice which is generated by a three-element set with two comparable
elements, has infinitely many blocks and contains an infinite chain.
On Certain Properties of Subnormal Subgroups
Authors: Whitehead Jennifer 
Published: December 2010

Main results. Let G be a
group generated by two subnormal subgroups H and
K. Denoting the class of nilpotent groups by
𝔑, and the limit of the lower central series by
G𝔑, Wielandt showed in
[14], for groups with a composition series that
(*)
Regular Representation of Finite Groups by Hypergraphs
Authors: Foldes Stephane , Singhi Navin M. 
Published: December 2010

All structures considered in this paper will be finite.The product στ of two permutations σ and τ of a set V is defined by στ(x) = στ(X)) for every x ∈ V. The set Sv of all permutations of F is a group under this operation. A permutation group on F is a subgroup of Sv.
Simple Factors in the Jacobian of a Fermat Curve
Authors: Koblitz Neal , Rohrlich David 
Published: December 2010

Letdenote theNth Fermat curve. The period lattice ofF(N)is contained with finite index in the product of certain latticesLr,s(see [6]), and to this inclusion of lattices there corresponds an isogeny of the Jacobian ofF(N)onto a product of abelian varieties. The purpose of this paper is to determine when two factors in this product are isogenous overC, and whether they are absolutely simple.
On the Embedding into a Ring of an Archimedean ι-Group
Authors: Hager Anthony W. , Robertson Lewis C. 
Published: December 2010

We shall prove the following about the “ringification” ρA of [2] and [5] of an archimedean l-group A: (a) Any “minimal ring” containing A is ρA; (b) A ↦ ρA is a reflector; (c) ρA need not be laterally complete when A is. These constitute the solutions to the problems posed in [2] by Paul Conrad.1. The embedding into a ring. Let be the category which has objects archimedean l-groups A with distinguished positive weak unit eA, and morphisms l-group homomorphisms h: A → B with h(eA) = eB. Let be the category with objects archimedean f-rings R with identity 1R which is a weak unit, and morphisms l-ring homomorphisms h: R → S with h(lR) = 1S.
Polynomial Approximation and Growth of Generalized Axisymmetrig Potentials
Authors: McCoy Peter A. 
Published: December 2010

Generalized axisymmetric potentials Fα (GASP) are regular solutions to the generalized axisymmetric potential equation(1.1)in some neighborhood Ω of the origin where they are subject to the initial data(1.2)along the singular line y = 0. In Ω, these potentials may be uniquely expanded in terms of the complete set of normalized ultraspherical polynomials(1.3)defined from the symmetric Jacobi polynomials Pn(α, α)(ξ) of degree n with parameter α as Fourier series(1.4)
Characterizations of Finite Lattices that are Bounded-Homomqrphic Images or Sublattices of Free Lattices
Authors: Day Alan 
Published: December 2010

In [8], McKenzie introduced the notion of a bounded homomorphism between lattices, and, using this concept, proved several deep results in lattice theory. Some of these results were intimately connected with the work of Jónsson and Kiefer in [6] where an attempt was made to characterize finite sublattices of free lattices. McKenzie's characterization and others that followed (see [7] and [5]) still have not answered the (now) celebrated Jônsson conjecture:A finite lattice is a sublattice of a free lattice if and only if it satisfies (SD∨), (SD∨) and (W).(The properties mentioned here are defined in the text.)
Comments On a Discreteness Condition for Subgroups of SL(2, C)
Authors: Jørgensen Troels 
Published: December 2010

SL(2,C) is the group of all complex unimodular 2 × 2 matrices. A subgroup of SL(2, C) is said to be discrete if it does not contain any convergent sequence of distinct elements. A subgroup is said to be elementary if the commutator of any two elements of infinite order has trace 2. The discreteness condition which this note relates to is the following:PROPOSITION 1. If two complex, unimodular 2 × 2 matrices X and Y generatea non-elementary, discrete group, then
Embedding Smooth Dendroids in Hyperspaces
Authors: Grispolakis J. , Tymchatyn E. D. 
Published: December 2010

A continuum will be a connected, compact, metric space. By a mapping we mean a continuous function. By a partially ordered space X we mean a continuum X together with a partial order which is closed when regarded as a subset of X × X. We let 2x (resp. C(X)) denote the hyperspace of closed subsets (resp. subcontinua) of X with the Vietoris topology which coincides with the topology induced by the Hausdorff metric. The hyperspaces 2X and C(X) are arcwise connected metric continua (see [3, Theorem 2.7]). If A ⊂ X we let C(A) denote the subspace of subcontinua of X which lie in A.If X is a partially ordered space we define two functions L, M : X → 2X by setting for each x ∊ X
Some Properties of Hyperspaces with Applications to Continua Theory
Authors: Grispolakis J. , Nadler Sam B. , Tymchatyn E. D. 
Published: December 2010

In 1972, Lelek introduced the notion of Class (W) in his seminar at the University of Houston [see below for definitions of concepts mentioned here]. Since then there has been much interest in classifying and characterizing continua in Class (W). For example, Cook has a result [5, Theorem 4] which implies that any hereditarily indecomposible continuum is in Class (W) Read [21, Theorem 4] showed that all chainable continua are in Class (W), and Feuerbacher proved the following result:(1.1) THEOREM [7, Theorem 7]. A non-chainable circle-like continuum is in Class (W) if and only if it is not weakly chainableIn [14, 4.2 and section 6], a covering property (denoted here and in [18] by CP) was defined and studied primarily for the purpose of proving that indecomposability is a Whitney property for the class of chainable continua [14, 4.3].