bluuebunny/crossref_metadata_2025_split huggingface dataset:
Rings whose Indecomposable Injective Modules are Uniserial
Authors: Hill David A. 
Published: December 2010

A module is uniserial in case its submodules are linearly ordered by inclusion. A ring R is left (right) serial if it is a direct sum of uniserial left (right) R-modules. A ring R is serial if it is both left and right serial. It is well known that for artinian rings the property of being serial is equivalent to the finitely generated modules being a direct sum of uniserial modules [8]. Results along this line have been generalized to more arbitrary rings [6], [13].This article is concerned with investigating rings whose indecomposable injective modules are uniserial. The following question is considered which was first posed in [4]. If an artinian ring R has all indecomposable injective modules uniserial, does this imply that R is serial? The answer is yes if R is a finite dimensional algebra over a field. In this paper it is shown, provided R modulo its radical is commutative, that R has every left indecomposable injective uniserial implies that R is right serial.
Ford and Dirichlet Regions for Fuchsian Groups
Authors: Beardon A. F. , Nicholls P. J. 
Published: December 2010

There has recently been some interest in a class of limit points for Fuchsian groups now known as Garnett points [5], [8]. In this paper we show that such points are intimately connected with the structure of Dirichlet regions and the same ideas serve to show that the Ford and Dirichlet regions are merely examples of one single construction which also yields fundamental regions based at limit points (and which properly lies in the subject of inversive geometry). We examine in the general case how the region varies continuously with the construction. Finally, we consider the linear measure of the set of Garnett points.2. Hyperbolic space.Let Δ be any open disc (or half-plane) in the extended complex planeC∞: usually Δ will be the unit disc or the upper half-plane. We may regard Δ as the hyperbolic plane in the usual way and the conformai isometries of Δ are simply the Moebius transformations of Δ onto itself.
Intersection Patterns of Families of Convex Sets
Authors: Katchalski M. , Liu A. 
Published: December 2010

In this paper, we study the intersection pattern of families of convex sets. Since we only consider finite families, we may assume that the sets are also compact.As an example, we consider families of 5 convex sets in R2 such that every two intersect and no three intersect. One such family that comes immediately to mind is that of 5 lines in general position. However, this is not the only family which exhibits this intersection pattern. Fig. 1 shows a family of 3 lines (sides of the large triangle) and 2 triangles (inscribed in the large triangle) that has this property.
Chromatic Solutions, II
Authors: Tutte W. T. 
Published: December 2010

This paper is a continuation of the Waterloo Research Report CORR 81-12, (see [1]) referred to in what follows as I. That Report is entitled “Chromatic Solutions”. It is largely concerned with a power series h in a variable z2, in which the coefficients are polynomials in a “colour number” λ. By definition the coefficient of z2r, where r > 0, is the sum of the chromatic polynomials of the rooted planar triangulations of 2r faces. (Multiple joins are allowed in these triangulations.) Thus for a positive integral λ the coefficient is the number of λ-coloured rooted planar triangulations of 2r faces. The use of the symbol z2 instead of a simple letter t is for the sake of continuity with earlier papers.In I we consider the case(1)where n is an integer exceeding 4.
Non Commutative Lp Spaces II
Authors: Katavolos A. 
Published: December 2010

Let M be a w*-algebra (Von Neumann algebra), τ a semifinite, faithful, normal trace on M. There exists a w*-dense (i.e., dense in the σ(M, M*)-topology, where M* is the predual of M) *-ideal J of M such that τ is a linear functional on J, and(where |x| = (x*x)1/2) is a norm on J. The completion of J in this norm is Lp(M, τ) (see [2], [8], [7], and [4]).If M is abelian, in which case there exists a measure space (X, μ) such that M = L∞(X, μ), then Lp(X, τ) is isometric, in a natural way, to Lp(X, μ). A natural question to ask is whether this situation persists if M is non-abelian. In a previous paper [5] it was shown that it is not possible to have a linear mapping
Amenability and Translation Experiments
Authors: Paterson Alan L. T. 
Published: December 2010

In [11] it is shown that the deficiency of a translation experiment with respect to another on a σ-finite, amenable, locally compact group can be calculated in terms of probability measures on the group. This interesting result, brought to the writer's notice by [1], does not seem to be as wellknown in the theory of amenable groups as it should be. The present note presents a simple proof of the result, removing the σ-finiteness condition and repairing a gap in Torgersen's argument. The main novelty is the use of Wendel's multiplier theorem to replace Torgersen's approach which is based on disintegration of a bounded linear operator from L1(G) into C(G)* for G σ-finite (cf. [5], VI.8.6). The writer claims no particular competence in mathematical statistics, but hopes that the discussion of the above result from the “harmonic analysis” perspective may prove illuminating.We then investigate a similar issue for discrete semigroups. A set of transition operators, which reduce to multipliers in the group case, is introduced, and a semigroup version of Torgersen's theorem is established.
Weighted and Subsequential Ergodic Theorems
Authors: Baxter J. R. , Olsen J. H. 
Published: December 2010

1. Introduction. Let (X, , μ) be a probability space, T a linear operator on ℒp(X, , μ), for some p, 1 ≦ p ≦ ∞. Let an be a sequence of complex numbers, n = 0, 1, …, which we shall often refer to as weights. We shall say that the weighted pointwise ergodic theorem holds for T on ℒp, if, for every ƒ in ℒp,1.1Let a denote the sequence (an). If (1.1) holds we shall say that a is Birkhoff for T on ℒp, or, more briefly, that (a, T) is Birkhoff.We are also interested in ergodic theorems for subsequences. Let n(k) be a subsequence. We shall say the pointwise ergodic theorem holds for the subsequence n(k) and the operator T if, for every ƒ in ℒp,1.2
Hopf Algebras from Branching Rules
Authors: Hoffman P. 
Published: December 2010

Below we work out the algebra structure of some Hopf algebras which arise concretely in restricting representations of the symmetric group to certain subgroups. The basic idea generalizes that used by Adams [1] for H*(BSU). The question arose in discussions with H. K. Farahat. I would like to thank him for his interest in the work and to acknowledge the usefulness of several stimulating conversations with him.1. Review and statement of results. A homogeneous element of a graded abelian group will have its gradation referred to as its dimension. In all such groups below there will be no non-zero elements with negative or odd dimension. A graded algebra (resp. coalgebra) will be associative (resp. coassociative), strictly commutative (resp. co-commutative) and in dimension zero will be isomorphic to the ground ring F, providing the unit (resp. counit). We shall deal amost entirely with F = Z or F = Z/p for a prime p; the cases F = 0 or a localization of Z will occur briefly. In every case, the component in each dimension will be a finitely generated free F-module, so dualization works simply.
Unitarily Invariant Operator Norms
Authors: Fong C.-K. , Holbrook J. A. R. 
Published: December 2010

1.1. Over the past 15 years there has grown up quite an extensive theory of operator norms related to the numerical radius1of a Hilbert space operator T. Among the many interesting developments, we may mention:(a) C. Berger's proof of the “power inequality”2(b) R. Bouldin's result that3for any isometry V commuting with T;(c) the unification by B. Sz.-Nagy and C. Foias, in their theory of ρ-dilations, of the Berger dilation for T with w(T) ≤ 1 and the earlier theory of strong unitary dilations (Nagy-dilations) for norm contractions;(d) the result by T. Ando and K. Nishio that the operator radii wρ(T) corresponding to the ρ-dilations of (c) are log-convex functions of ρ.
Asymptotic Behaviour of Nonoscillatory Equations
Authors: Edelson Allan L. , Perri Emilia 
Published: December 2010

For nonlinear equations of the formIthere has been considerable interest in determining the asymptotic forms of nonoscillatory solutions. We assume r(t) is continuous and positive on [0, ∞), and f(t, x) is continuous on [0, ∞) × R, and f(t, x) ≥ 0 for x ≠ 0. For n = 2, equation (I) was studied by Kusano and Naito [3], who found necessary and sufficient conditions for the existence of minimal and maximal nonoscillatory solutions. The former are the bounded solutions, while the later are those asymptotic to the function1.1Their method consisted of writing (I) in the form of an integral operator and applying the Schauder fixed point theorem. For arbitrary n, but for r(t) = 1, Kreith [2] found necessary and sufficient conditions for the existence of maximal solutions.
Local Stability and Saturation in Spaces of Orderings
Authors: Schwartz Niels 
Published: December 2010

If k is a f.r. (= formally real) field which is partially ordered with positive cone, P, XP denotes the space of total orders T of k with P ⊂ T. Suppose you have a subset A ⊂ XP and an element T ∈ XP, T ∉ A. Then the main question investigated in this paper is the following: How can T be separated from A by using elements of k? To be more specific, this is split up into two different questions.Question 1. Suppose A is closed. Then there is an n ∈ N and elements a1, …, an ∈ k such that the basic open set H = H(a1, …, an) is a neighborhood of T and has empty intersection with A. Now, if T is given, what is the least n ∊ N (if it exists) such that T has a neighborhood basis consisting of basic open sets of the form H(a1, …, an)?
Secant Spaces to Curves
Authors: von Zur Gathen Joachim 
Published: December 2010

A classical question in algebraic geometry is whether a given projection of a projective space induces an isomorphism on a given closed subvariety. To answer it, one investigates secant lines to the subvariety. There has been a lot of recent activity in this field ([12], [14],[18], [21], [23]): see [14] and [12] for references).An obvious generalization of the secant lines is provided by the secant r-planes, which intersect a given closed subvariety in r + 1 linearly independent points. The closure of the set of these secant r-planes is the secant variety, and the aim of this paper is to determine its rational equivalence class in the case of curves. There is an extensive classical literature about this problem.
On the Uniqueness of the Coefficient Ring in a Group Ring
Authors: Adjaero Isabelle , Spiegel Eugene 
Published: December 2010

LetR1andR2be commutative rings with identities,Ga group andR1GandR2Gthe group ring ofGoverR1andR2respectively. The problem that motivates this work is to determine what relations exist betweenR1andR2ifR1GandR2Gare isomorphic. For example, is the coefficient ringR1an invariant ofR1G? This is not true in general as the following example shows. LetHbe a group andIfR1is a commutative ring with identity andR2=R1H,thenbutR1needn't be isomorphic toR2.Several authors have investigated the problem whenG= <x>, the infinite cyclic group, partly because of its closeness toR[x],the ring of polynomials overR.
Some Congruences for Generalized Euler Numbers
Authors: Gessel Ira M. 
Published: December 2010

The generalized Euler numbers may be defined bySince is zero unless m divides n, we shall write for . Leeming and MacLeod [12] recently gave some congruences for these numbers. They found congruences (mod 16) for where m = 3, 6, 8, 12, and 16. Thus for m = 3, their congruence isThey also proved that , and , and they made several conjectures which may be stated as follows:C1C2C3C4
Behrend's Theorem for Dense Subsets of Finite Vector Spaces
Authors: Brown T. C. , Buhler J. P. 
Published: December 2010

The “combinatorial line conjecture” states that for all q ≧ 2 and there exists such that if , X is a q-element set, and A is any subset of X n (= cartesian product of n copies of X) with more than elements (that is, A has density greater than ), then A contains a combinatorial line. (For a definition of combinatorial line, together with statements and proofs of many results related to the combinatorial line conjecture, including all those results mentioned below, see [5]. Since we are not directly concerned with combinatorial lines in this paper, we do not reproduce the definition here.)This conjecture (which is a strengthened version of a conjecture of Moser [7]), if true, would bear the same relation to the Hales-Jewett theorem that Szemerédi's theorem bears to van der Waerden's theorem.
Injectives and Projectives in Term Finite Varieties of Algebras
Authors: McNulty George F. , Nordahl T. , Scheiblich H. E. 
Published: December 2010

Let V be a class of similar algebras. An algebra is V-injective provided and whenever and fis a one-to-one homomorphism from into and g is a homomorphism from into , then there is a homomorphism h from into such that h º f = g. So is injective provided all diagrams of the following sort can be completed.Dually, is V-projective provided and whenever and f is a homomorphism from onto and g is a homomorphism from into , then there is a homomorphism h from into such that f º h = g. So is projective provided all diagrams of the following sort can be completed:This usage of the words “projective” and “injective” differs somewhat from the usage current in category theory.
Global Positive Solutions of Semilinear Elliptic Equations
Authors: Noussair Ezzat S. , Swanson Charles A. 
Published: December 2010

The semilinear elliptic boundary value problem1.1will be considered in an exterior domain Ω ⊂ Rn, n ≥ 2, with boundary ∂Ω ∊ C2 + α, 0 < α < 1, where1.2Di = ∂/∂xi, i = 1, …, n. The coefficients aij, bi in (1.2) are assumed to be real-valued functions defined in Ω ∪ ∂Ω such that each , , and (aij(x)) is uniformly positive definite in every bounded domain in Ω. The Hölder exponent α is understood to be fixed throughout, 0 < α < 1 . The regularity hypotheses on f and g are stated as H 1 near the beginning of Section 2.
λ-Mappings Between Representation Rings of Lie Algebras
Authors: Moody R. V. , Pianzola A. 
Published: December 2010

In [10] Patera and Sharp conceived a new relation, subjoining, between semisimple Lie algebras. Our objective in this paper is twofold. Firstly, to lay down a mathematical formalization of this concept for arbitrary Lie algebras. Secondly, to give a complete classification of all maximal subjoinings between Lie algebras of the same rank, of which many examples were already known to the above authors.The notion of subjoining is a generalization of the subalgebra relation between Lie algebras. To give an intuitive idea of what is involved we take a simple example. Suppose is a complex simple Lie algebra of type B2. Let be a Cartan subalgebra of and Δ the corresponding root system. We have the standard root diagramInside B2 there lies the subalgebra A1 × A1 which can be identified with the sum of and the root spaces corresponding to the long roots of B2.
Spaces with a Unique Uniformity
Authors: Warren Richard H. 
Published: December 2010

The major results in this paper are nine characterizations of completely regular spaces with a unique compatible uniformity. All prior results of this type assumed that the space is Tychonoff (i.e., completely regular and Hausdorff) until the appearance of a companion paper [9] which began this study. The more important characterizations use quasi-uniqueness of R1-compactifications which relate to uniqueness of T2-comPactifications. The features of the other characterizations are: (i) compact subsets linked to Cauchy filters, (ii) C- and C*-embeddings, and (iii) lifting continuous maps to uniformly continuous maps.Section 2 contains information on T0-identification spaces which we will use later in the paper. In Section 3 several properties of uniform identification spaces are developed so that they can be used later. The nine characterizations are established in Section 4. Also it is shown that a space with a unique compatible uniformity is normal if and only if each of its closed subspaces has a unique compatible uniformity.
Maximal d-Ideals in a Riesz Space
Authors: Huijsmans Charles B. , de Pagter Ben 
Published: December 2010

We recall that the ideal I in an Archimedean Riesz space L is called a d-ideal whenever it follows from ƒ ∊ I that {ƒ}dd ⊂ I. Several authors (see [4], [5], [6], [12], [13], [15] and [18]) have considered the class of all d-ideals in L, but the set ℐd of all maximal d-ideals in L has not been studied in detail in the literature. In [12] and [13] the present authors paid some attention to certain aspects of the theory of maximal d-ideals, however neglecting the fact thatℐd, equipped with its hull-kernel topology, is a structure space of the underlying Riesz space L.The main purpose of the present paper is to investigate the topological properties of ℐd and to compare ℐd to other structure spaces of L, such as the space of minimal prime ideals and the space of all e-maximal ideals in L (where e > 0 is a weak order unit).
Pro-Categories and Multiadjoint Functors
Authors: Tholen Walter 
Published: December 2010

For a functor G:𝒜→𝔛 and a class 𝔇 of small categories containing the terminal category 1 we form the extensionand call G right 𝔇-pro-adjoint if and only if Pro (𝔇, G) is right adjoint. Here Pro (𝔇, 𝒜) is the completion of 𝒜with respect to 𝔇; it coincides with the usual pro-category of 𝒜 in case 𝔇 = directed sets. For this 𝔇 a full embedding Gis dense in the sense of Mardešić [11] if and only if it is right 𝔇-pro-adjoint in the above sense; this has been proved recently by Stramaccia [15]. The most important example is the embedding of the homotopy category of pointed CW-complexes into the homotopy category of pointed topological spaces (cf. [2]).
A Class of Homomorphisms of Pre-Hjelmslev Groups
Authors: Knüppel Frieder 
Published: December 2010

E. Salow [8] introduced the concept of pre-Hjelmslev groups, a generalization of F. Bachmann's Hjelmslev groups [1] which leads to a more natural theory of homomorphisms and permits a simpler construction of algebraic models. Basically, both types of groups are the groups of motions of a metric plane, the so-called group plane. In such a plane there is a unique perpendicular through any point to any line and the product of three collinear points (three copunctal lines) is a point (a line). Our first section contains the precise definitions and some basic facts.The homomorphic image of a pre-Hjelmslev group can be more complicated than the pre-image. For instance, there may always be a unique line through two distinct points of the pre-image but not of the image. We study regular homomorphisms of pre-Hjelmslev groups, i.e., homomorphisms with the following property: If two lines intersect at exactly one point, their images will also have precisely one point in common.
Range Sets And Bmo Norms of Analytic Functions
Authors: Kobayashi Shoji 
Published: December 2010

In this paper we are concerned with the space BMOA of analytic functions of bounded mean oscillation for Riemann surfaces, and it is shown that for any analytic function on a Riemann surface the area of its range set bounds the square of its BMO norm, from which it is seen as an immediate corollary that the space BMOA includes the space AD of analytic functions with finite Dirichlet integrals.Let R be an open Riemann surface which possesses a Green's function, i.e., R ∉ OG, and f b e an analytic function defined on R. The Dirichletintegral DR(f) = D(f) of f on R is defined by1.1and we denote by AD(R) the space of all functions f analytic on R for which D(f) < +∞.
On Isomorphisms of Lattices of Closed Subspaces
Authors: Fillmore P. A. , Longstaff W. E. 
Published: December 2010

By a projectivityof vector spaces Xand Yover fields F and G is meant an isomorphism Ψ:(X) → (Y) of their lattices of subspaces. A basic theorem of projective geomtry [2, p. 44] asserts that, for spaces of dimension at least 3, any such projectivity is of the form Ψ(M) = SM for a bijection S:X → Y which is semi-linear in the sense that S is an additive mapping for which there exists an isomorphism σ:F→ G such thatS(λx) = σ(λ)Sx for all λ ∈ Fand all x∈ X.In [12] Mackey obtained a continuous version of this result: for real normed linear spaces Xand Y, the lattices and of closed subspaces are isomorphic if and only if X and Yare isomorphic (i.e., via a bicontinuous linear bijection).
Some Spectral Properties of Polar Decompositions
Authors: Cain Bryan E. 
Published: December 2010

The results in this paper respond to two rather natural questions about a polar decomposition A = UP, where U is a unitary matrix and P is positive semidefinite. Let λ1, …, λn be the eigenvalues of A. The questions are:(A) When will |λ1|, …, |λn| be the eigenvalues of P?(B) When will λ1/|λ1|, …, λn/|λn| be the eigenvalues of U?The complete answer to (A) is “if and only if U and P commute.” In an important special case the answer to (B) is “if and only if U2 and P commute.“Since these matters are best couched in terms of two different inertias, we begin with a unifying definition of inertia which views all inertias from a single perspective.For each square complex matrix A and each complex number z let m(A, z) denote the multiplicity of z as a root of the characteristic polynomial
Discrete Open and Closed Mappings on Generalized Continua and Newman's Property
Authors: McAuley Louis F. , Robinson Eric E. 
Published: December 2010

In 1930, M. H. A. Newman proved a rather remarkable theorem which has become one of the classical theorems in topology. It has many important applications. A special case of Newman's Theorem is that a periodic homeomorphism of periodn> 1 of a sphereSonto itself must have some orbit which is not contained in a “cap” smaller than a hemisphere. The general theorem is as follows:THEOREM ([15]).Suppose that Mnis a connected (metric) n-manifold, U is a domain in Mn, andp is an integer greater than1.Then there is a positive number d such that no uniformly continuous homeomorphism h of Mnonto itself of period p moves every point of U a distance < d. That is, there is x ∊ U so that the orbit of x under h has diameter ≦ d.
Subclasses of Starlike Functions Subordinate to Convex Functions
Authors: Silverman H. , Silvia E. M. 
Published: December 2010

Let S denote the class of functions of the formthat are analytic and univalent in the unit disk Δ = {z:|z| < 1}, with S*(α) and K(α) designating the subclasses of S that are, respectively, starlike of order a and convex of order α, 0 ≦ α < 1. If f(z) and g(z) are analytic in Δ, we say that f(z) is subordinate to g(z), written f ≺ g, if there exists a Schwarz function w(z), w(0) = 0 and |w(z)| < 1 in Δ, such that f(z) = g(w(z)). A function f(z) = z + … is said to be in S*[A, B] if(1)and in K[A, B] if(2)
Resultats Nouveaux sur les Faisceaux Quasi-Unipotents
Authors: Mathieu Philippe 
Published: December 2010

Dans cette note, nous donnons une réponse à un problème posé dans [5]: nous démontrerons que le niveau de quasi-unipotence de la monodromie avec coefficients est le meilleur possible (voir le paragraphe 2 pour l'énoncé précis).1. Faisceaux quasi-unipotents. Nous rappelons ici la définition et les propriétés fondamentales de ces faisceaux (voir [3], cf. [5]).Par D nous désignons un disque ouvert de C centré à l'origine et de
rayon aussi petit qu'on veut. Un faisceau V lisse (ou, suivant une autre terminologie, localement constant) constructible sur D* = D – {0} est dit quasi-unipotent (de niveau d) si la monodromie T opérant sur la fibre générique de V vérifie (Ta – 1)b = 0, où a et b sont des entiers non-négatifs (et b ≦ d).Définition (1.1). Soient X un espace analytique, Y un sous-espace analytique de X, et V un faisceau constructible sur X – Y.