bluuebunny/crossref_metadata_2025 huggingface dataset:
Some Geometries Associated with Parabolic Representations of Groups of Lie Type
Authors: Cooperstein Bruce N.
Published: December 2010

Suppose (P, △) is an undirected graph without loops or multiple edges. We will denote by △ (x) the vertices adjacent to x and . Let (G, P) be a transitive permutation representation of a group G in a, set P, and Δ be a non-trivial self-paired (i.e. symmetric) orbit for the action of G on P X P. We identify △ with the set of all two subsets ﹛x, y﹜ with (x, y) in △. Then we have a graph (P, Δ) with G ≦ Aut (P, △), transitive on both P and △.
Some Comparison Theorems for Conjugate And σ-Points
Authors: Leighton Walter
Published: December 2010

Section 1 of this paper is concerned with the effect on conjugate and σ-points of various perturbations of q(x) for differential equations of the form
Isometric Mappings of Non-Commutative LP Spaces
Authors: Katavolos A.
Published: December 2010

If the Lp spaces of two measure spaces are “the same”, to what extent can we identify the underlying measure spaces? This question has been partially answered by Schneider [7] (extending results of Forelli [2]). He proves that a linear isometry between the Lv spaces of two finite measure spaces is in fact an (isometric) homomorphism between the corresponding L∞ spaces, if it preserves the identity.
Abelian Steiner Triple Systems
Authors: Tannenbaum Peter
Published: December 2010

A neofield of order v, Nv( + , •), is an algebraic system of v elements including 0 and 1,0 ≠ 1, with two binary operations + and • such that (Nv, + ) is a loop with identity element 0; (Nv*, •) is a group with identity element 1 (where Nv* = Nv\﹛0﹜) and every element of Nv is both right and left distributive (i.e., (y + z)x = yx + zx and x(y + z) = xy + xz for all y, z∈ Nv).
Blow Up Sequences and the Module of nth Order Differentials
Authors: Brown William C.
Published: December 2010

Let C denote an irreducible, algebraic curve defined over an algebraically closed field k. Let ? be a singular point of C. We shall employ the following notation throughout the rest of this paper: R will denote the local ring at P, K the quotient field of the integral closure of R in K, A the completion of R with respect to its radical topology, and Ā the integral closure of A in its total quotient ring.
Linear Symmetry Classes
Authors: Cummings L. J. , Robinson R. W.
Published: December 2010

A formula is derived for the dimension of a symmetry class of tensors (over a finite dimensional complex vector space) associated with an arbitrary finite permutation group G and a linear character of x of G. This generalizes a result of the first author [3] which solved the problem in case G is a cyclic group.
Gaining Units from Units
Authors: Bernstein Leon
Published: December 2010

Dirichlet was the first to give an ingenious proof of the exact (finite) number of elements in the basis of the multiplicative group of units in any algebraic number field of arbitrary degree n. These elements are called fundamental units. If the field is real and its generating number is a real root of a polynomial over Q of degree n﹜ having r1 real and r2 pairs of conjugate complex roots, so that r1 + 2r2 = n, then Dirichlet's famous result states that the exact number of fundamental units in Q(w) equals r1 + r2 — 1.
Positive Perturbations and Unitary Equivalence
Authors: Putnam C. R.
Published: December 2010

Let T be a (not necessarily bounded) self-adjoint operator on a Hilbert space H with the spectral resolution The set of elements x in H for which ||Etx||2 is absolutely continuous is a subspace, Ha, of H which reduces T. (See Halmos [1, p. 104]; Kato [2, p. 516].) If Ha ≠ 0, the restriction of T to DT ⋂ Ha is called the absolutely continuous part of T; in case H = Ha, T is said to be absolutely continuous.
The Manifold of Conformally Equivalent Metrics
Authors: Fischer Arthur E. , Marsden Jerrold E.
Published: December 2010

Ebin [8] gives a thorough study of the spaceof riemannian metrics on a compact manifoldMand of the action of the diffeomorphism groupofMon. The purpose of this paper is to study the action of the larger groupof conformorphisms, or conformai transformations, onand on. On, the L2-orthogonal decomposition induced by the action ofgives a splitting of symmetric tensors into three summands introduced by York [25;26]. We find submanifolds oftangent to the pieces of this decomposition.
Almost-P-Spaces
Authors: Levy Ronnie
Published: December 2010

A P-space is a topological space in which every Gδ-set is open. P-spaces are fairly rare. For example, the only compact (or even pseudocompact) P-spaces are finite. A larger class of spaces, the almost-P-spaces, consists of those spaces in which G δ-sets have dense interiors. The almost-P-spaces are far less restricted than the P-spaces—for example, there are infinite, compact, connected almost-P-spaces. In this paper, we study almost-P-spaces and raise a number of questions relating to them.
Torsion Elements and the Classification of Vector Bundles
Authors: Little Robert D.
Published: December 2010

There are many situations in algebraic topology when a geometric construction is possible if, and only if, a certain integral cohomology class, an obstruction is zero. When attempts are made to compute the obstruction, it often happens that it is relatively easy to show that m times the obstruction is zero, where m is an integer, and consequently the geometric construction is possible if the cohomology group in question has no elements of order m.
Neighborly 4-Polytopes and Neighborly Combinatorial 3-Manifolds with Ten Vertices
Authors: A. Altshuler
Published: December 2010

A combinatorial n-sphere is a simplicial n-complex whose body (i.e., the union of its members) is homeomorphic to the topological n-sphere Sn. A combinatorial n-manifold is a simplicial n-complex M such that M is connected, and for every vertex x in M the complex linker, M), the link of x in M, is a combinatorial (n — 1)-sphere. For more details the reader should consult Alexander [1] and Grünbaum [16]. All the spheres and manifolds to which we refer are combinatorial.
On Steenrod's Problem for Cyclic p-Groups
Authors: Arnold James E.
Published: December 2010

Let G be a finite group and A a Z[G] module.

Definition (1.1). A simply connected CW complex X is of type (A, n) if G operates on X cellularly, and modules.
Lebesgue Constants for Cardinal -Spline Interpolation
Authors: Tzimbalario J.
Published: December 2010

Recently the theory of cardinal polynomial spline interpolation was extended to cardinals -splines [3]. Let

be a polynomial with only real zeros. Denote the set of zeros by . If is the associated differential operator, the null-space
Translation-Invariant Operators On Lp(G), 0 < p < 1 (II)
Authors: Oberlin Daniel M.
Published: December 2010

For a locally compact group G, let LP(G) be the usual Lebesgue space with respect to left Haar measure m on G. For x ϵ G define the left and right translation operators Lx and Rx by Lx f(y) = f(xy), Rx f(y) = f(yx)(f ϵ Lp(G),y ϵ G). The purpose of this paper is to prove the following theorem.
A Class of Right-Orderable Groups
Authors: Botto Mura R. T. , Rhemtulla A. H.
Published: December 2010

A group g is called right-orderable (or an ro-group) if there exists an order relation ≦ on g such that a ≦ b implies ac ≦ be for all a, b, c in g. this is equivalent to the existence of a subsemigroup p of g such that p ⋂ p-1 = ﹛e﹜ and p ⋃ p-1 = g. given the order relation ≦, p can be taken to be the set of positive elements and conversely, given p, define a ≦ b if and only if ba-1ϵ p. a group g together with a given right-order relation on g is called right-ordered.
A Transformation with Simple Spectrum which is not Rank One
Authors: Del Junco Andrés
Published: December 2010

Following [10] an ergodic measure-preserving transformation is called rank one if it admits a sequence of approximating stacks. Rank one transformations have been studied in [1] and [2] where it was shown that any rank one transformation has simple spectrum. More generally it has been shown by Chacon [4] that a transformation of rank n has spectral multiplicity at most n. M. A. Akcoglu and J. R. Baxter have asked whether the converse is true. In particular: does simple spectrum imply rank one? In this paper we give a negative answer to this question.
Weak q-Rings
Authors: Mohamed Saad , Singh Surjeet
Published: December 2010

Throughout this paper we assume that every ring has unity and all modules are unital right modules. A ring R is called a (right) q-ring if every right ideal of R is quasi-injective [4], In this paper we study a generalization of this concept. A ring R is called a (right) weak q-ring (in short, wq-ring) if every right ideal of R, not isomorphic to RR, is quasi-injective. A ring R is called a right pq-ring if every proper right ideal of R is quasi-injective. Any upper triangular 2 X 2 matrix ring over a division ring is a wq-ring, which is not a q-ring. In Section 1, some general properties of wq-rings are established and, in particular, it is shown in (1.8) that a semiprime wq-ring has zero singular ideal.
Systems that are Purely Simple and Pure Injegtive
Authors: Okoh Frank
Published: December 2010

There has been a lot of progress made on the finite-dimensional representations of species. In [3] and [11] the finite-dimensional representations of tame species are classified and in [13] it is shown that if S is a species of finite type, then every representation of 5 is a direct sum of finite-dimensional ones. However, comparatively little is known about infinite-dimensional representations.
CPI-Extensions: Overrings of Integral Domains with Special Prime Spectrums
Authors: Boisen Monte B. , Sheldon Philip B.
Published: December 2010

Throughout this paper the term ring will denote a commutative ring with unity and the term integral domain will denote a ring having no nonzero divisors of zero. The set of all prime ideals of a ring R can be viewed as a topological space, called the prime spectrum of R, and abbreviated Spec (R), where the topology used is the Zariski topology [1, Definition 4, § 4.3, p. 99]. The set of all prime ideals of R can also be viewed simply as aposet - that is, a partially ordered set - with respect to set inclusion. We will use the phrase the pospec of R, or just Pospec (/v), to refer to this partially ordered set.
On Rank 3 Groups Having λ = 0
Authors: Atkinson M. D.
Published: December 2010

In this paper we shall consider certain rank 3 permutation groups G which act on a set Ω of size n. Thus a point stabiliser Gα will have 3 orbits { α }, △ (α), Γ (α) of sizes 1, k, I respectively. It is well known that, if |G| is even, then the orbital △ defines a strongly regular graph on Ω. In this graph, every point has valency k, every pair of adjacent points are adjacent to a constant number λ of common points, and every pair of non-adjacent points are adjacent to a constant number μ of common points. This notation is reasonably standard (see [4], where much background theory is given).
The Transfer of the Krull Dimension and the Gabriel Dimension to Subidealizers
Authors: Krause Günter , Teply Mark L.
Published: December 2010

Let M be a right ideal of the ring T with identity. A unital subring R of T which contains M as a two-sided ideal is called a subidealizer ; the largest such subring is the idealizer I (M) of M in T. M is said to be generative if TM = T. In this case M is idempotent, and it follows from the dual basis lemma that T is finitely generated projective as a right R-module (see [7, Lemma 2.1]); we make frequent use of these two facts in this paper.
The Complete Quotient Ring of Images of Semilocal Prüfer Domains
Authors: Chuchel John , Eggert Norman
Published: December 2010

It is well known that the complete quotient ring of a Noetherian ring coincides with its classical quotient ring, as shown in Akiba [1]. But in general, the structure of the complete quotient ring of a given ring is largely unknown. This paper investigates the structure of the complete quotient ring of certain Prüfer rings. Boisen and Larsen [2] considered conditions under which a Prüfer ring is a homomorphic image of a Prüfer domain and the properties inherited from the domain. We restrict our investigation primarily to homomorphic images of semilocal Prüfer domains. We characterize the complete quotient ring of a semilocal Prüfer domain in terms of complete quotient rings of local rings and a completion of a topological ring.
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.
On Eutactic Forms
Authors: Ash Avner
Published: December 2010

Let (aij) = A be a positive definite n × n symmetric matrix with real entries. To it corresponds a positive definite quadratic form ƒ on Rn: ƒ(x) = txAx = ∑ aijXiXj for x any column vector in Rn. The set of values ƒ(y) for y in Zn — {0} has a minimum m (A) > 0 and the number of “minimal vectors“ y1, … , yr in Zn for which ƒ(yi) = m (A) is finite. By definition, ƒ and A are called eutactic if and only if there are positive numbers s1 ,… , sr such that
Radical Pairs
Authors: Divinsky N. , Sulinski A.
Published: December 2010

The search for new radicals goes on. Recently R. L. Snider ([6], see page 216) introduced the following notion. Let α and β be any two radicals. A ring R will be said to be an (α : β) ring if for any ideal A of R, we have α (R/A) ≧ β (R/A).
Lifting Problems and the Cohomology of C*-Algebras
Authors: Choi Man-Duen , Effros Edward G.
Published: December 2010

Suppose that A and B are C*-algebras, J is a closed two-sided ideal in B, and that η: B →B/J is the quotient map. Given a linear contraction φ : A →B/J, a linear map Ψ: A →B is a lifting of φ if one has a commutative diagram
Jordan Loops and Decompositions of Operators
Authors: Brown Arlen , Pearcy Carl
Published: December 2010

Let be a separable, infinite dimensional, complex Hilbert space, and let denote the algebra of all bounded linear operators on . In what follows we shall denote the spectrum, essential spectrum, and left essential spectrum of an operator T in , respectively. Furthermore, if and T1 is unitarily equivalent to a compact perturbation of an operator T2, then we write T1~ T2, and if the compact perturbation can be chosen to have norm less than e, we write T1 ~ T2(ϵ).
Local Topological Properties of Maps and Open Extensions of Maps
Authors: Kohli J. K.
Published: December 2010

A σ-discrete set in a topological space is a set which is a countable union of discrete closed subsets. A mapping ƒ : X ⟶ Y from a topological space X into a topological space Y is said to be σ-discrete (countable) if each fibre ƒ-1(y), y ϵ Y is σ-discrete (countable). In 1936, Alexandroff showed that every open map of a bounded multiplicity between Hausdorff spaces is a local homeomorphism on a dense open subset of the domain [2].
Certain Varieties and Quasivarieties of Completely Regular Semigroups
Authors: Petrich Mario
Published: December 2010

We adopt the following definition of acompletely regular semigroup S:for every elementaofS,there exists a unique elementa-1ofSsuch that
Cone Preserving Mappings for Quadratic Cones Over Arbitrary Fields
Authors: Lester J. A.
Published: December 2010

Let F be a non-singular metric vector space, that is, a vector space over a field F not of characteristic two, upon which is defined a non-singular symmetric bilinear form ( , ). For any a ϵ V, we define the cone with vertex a to be the set
On a 1-Dimensional Planar Continuum without the Fixed Point Property
Authors: Martin John R.
Published: December 2010

In [5 ; 6] the author considers the following two problems posed by Professor Lloyd Tucker.

Problem 1. Does there exist a 1-dimensional continuum X without the fixed point property such that every retract of X has the fixed point property with respect to one-to-one maps?
Boundedness Criteria for Generalized Hankel Conjugate Transformations
Authors: Kerman R. A.
Published: December 2010

This paper completes a study, begun in [7], of
conditions under which a generalized Hankel conjugate transformation
H
ƛ is bounded between a pair of μα
-rearrangement invariant function spaces, the measure μα
being defined by dμα
(t) = t
α∼1dt. Examples of such spaces are the
Lp(μα)
of Lebesgue and generalizations of them due respectively to Orlicz and
Lorentz.
Affine Parts of Algebraic Theories II
Authors: Isbell J. R. , Klun M. I. , Schanuel S. H.
Published: December 2010

This paper concerns relative complexity of an algebraic theory T and its
affine part A, primarily for theories TR
of modules over a ring R. TR,
AR
and R itself are all, or none, finitely
generated or finitely related. The minimum number of relations is the same for T
R
and AR. The minimum
number of generators is a very crude invariant for these theories, being 1 for
AR if it is finite, and 2 for TR if
it is finite (and 1 ≠ 0 in R). The minimum arity of
generators is barely less crude: 2 for TR} and 2 or 3 for AR
(1 ≠ 0). AR is generated by binary operations if and only if
R admits no homomorphism onto
Z2.
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.
Sur L'Approximation Polynomiale Avec Poids exp(-|x|)
Authors: Freud G. , Giroux A. , Rahman Q. I.
Published: December 2010

Dans ce travail, nous étudions l'approximation polynomiale pondérée usuelle
et aussi unilatérale dans l'espace L. Le poids
considéré est w(x) = exp
(—|x|) ce qui constitue un cas extremal; rappelons à
ce propos quelques résultats de G. Freud. A chaque poids de la forme
wQ(x) = exp ( — (Q(#))
correspond une suite caractéristique
{qn} de nombres positifs
définis par la relation qnQ’
(qn) = n. Dans le sixième chapitre de
[1] (voir aussi [14]), Freud démontre que toute
fonction/ pour laquelle ƒwQ ∊ L peut être approchée par un
polynôme pn de degré ≤n en commettant une erreur (∫|fƒ
-Pn\w
Q) d'au plus Ω(ƒ,
qn/n) où Ω est un module de
continuité adéquat et obtient des résultats précisés lorsque la fonction ƒ est
supposée differentiate. Dans [2], Freud montre que si la r
ième dérivée f(r) est à support compact et à variation bornée
et si |ƒ| admet une majoration polynomiale, alors/ peut être approchée
unilatéralement par des polynômes de degré ≦n (pn ≦ ƒ ≦
Pn) avec une erreur (∫(Pn —
pn)wQ) inférieure à
K(ƒ)(qn/n)r+1.
Lorsque Q(x) =
|x|p, on a qn ~
n
1/p de telle sorte que, si ρ > 1,
qn/n tend vers zéro avec \/n mais, si ρ = 1, le
prolongement formel direct des résultats de Freud fournit une majoration de
l'erreur ne tendant pas vers zéro avec 1/n. Cependant, il suit des recherches de
M. Riesz [3] (voir aussi [4]) que les fonctions à croissance polynomiale peuvent
être approchées unilatéralement dans l'espace L avec poids
w et, en particulier, que les polynômes sont denses
dans cet espace.
Continuous Ergodic Extensions and Fibre Bundles
Authors: Zimmer Robert J.
Published: December 2010

If a locally compact group G acts as a measure
preserving transformation group on a Lebesgue space X,
then there is a naturally induced unitary representation of
G on
L2(X), and one can study the
action on X by means of this representation. The
situation in which the representation has discrete spectrum (i.e., is the direct
sum of finite dimensional representations) and the action is ergodic was examined
by von Neumann and Halmos when G is the integers or the
real line [7], and by Mackey for general non-abelian
G [10].
Maximal Strictly Partial Spreads
Authors: Ebert Gary L.
Published: December 2010

Let ∑ = PG(3, q) denote 3-dimensional projective
space over GF(q). A partial spread of ∑ is a collection
W of pairwise skew lines in ∑.
W is said to be maximal
if it is not properly contained in any other partial spread. If every point of ∑
is contained in some line of W, then
W is called a spread.
Since every spread of PG(3, q) consists of
q2 + 1 lines, the deficiency of a partial spread
W is defined to be the number d =
q2 + 1 — |W|. A maximal partial spread of ∑ which is not a
spread is called a maximal strictly partial spread (msp
spread) of ∑.
A Witt Theorem for Non-Defective Lattices
Authors: Morin-Strom Karl A.
Published: December 2010

In [10], Witt laid the foundation for the study of
quadratic forms over fields. Suppose Q is a quadratic
form defined on a finite dimensional vector space V
over a field of characteristic not equal to 2. Witt showed that non-zero vectors
x and y in
V satisfying Q(x) = Q(y)
can be mapped into each other via an isometry of the vector space
V. More generally, if τ :
W ⟶ W’ is an isometry
between subspaces of V, then τ extends to an isometry ϕ
of V.
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

(*)
Minimal Rates of Summability
Authors: Fridy J. A.
Published: December 2010

During the early nineteenth century much effort was spent on attempts to find a “universal comparison test“: i.e., a sequence in l1 that dominates every other member of l1. The nonexistence of such a series converging at a minimal rate was demonstrated by Abel, et al. [1; 4; 7; 9, pp. 298-304].
Some Group Presentations
Authors: Neumann B. H.
Published: December 2010

Let the group be presented on three generators a, b, c with three defining relations

where p, q, r, s, t, u are integers, the “parameters” of the presentation.
Blocking Sets in Projective Spaces
Authors: Ebert Gary L.
Published: December 2010

Blocking sets in projective spaces have been of interest for quite some time, having applications to game theory (see [6; 7]) as well as finite nets and partial spreads (see [5]). In [4] Bruen showed that if B is a blocking set in a projective plane of order n, then
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.
The Space Groups of Two Dimensional Minkowski Space
Authors: Maxwell George
Published: December 2010

LetEbe an n-dimensional real affine space,Vits vector space of translations andA(E)the affine group ofE.Suppose that (. , .) is a nondegenerate symmetric bilinear form on F of signature(n —1, 1), O(V) its orthogonal group andS(V)its group of similarities.
A Commutativity Theorem for Rings with Involution
Authors: Chacron M.
Published: December 2010

A ring with involution R is an associative ring endowed with an antiautomorphism * of period 2. One of the first commutativity results for rings with * is a theorem of S. Montgomery asserting that if R is a prime ring, in which every symmetric element s = s* is of the form s — sn(s) (n(s) ≧ 2), then either R is commutative or R is the 2 X 2 matrices over a field, which is a nice generalization of a well-known theorem of N. Jacobson on rings all of whose elements x = xn(x).
A Note on a Class of Slit Conformal Mappings
Authors: Kirwan W. E. , Pell R. W.
Published: December 2010

We denote by 5 the class of functions, f(z), that are analytic and univalent in U = ﹛z: |z| < 1﹜ and have the normalization
Simple Factors in the Jacobian of a Fermat Curve
Authors: Koblitz Neal , Rohrlich David
Published: December 2010

Let

denote 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.
Topologies Determined by -Ideals on ω1
Authors: Broverman S. , Ginsburg J. , Kunen K. , Tall F. D.
Published: December 2010

σ-ideals (collections of sets which are closed under subset and countable union) are certainly important mathematically—consider first category sets, sets of measure zero, nonstationary sets, etc.—but aside from the observation that in certain spaces the first category σ-ideal is proper, cr-ideals have not been extensively studied by topologists. In this note we study a natural topology determined by a d-ideal, exploiting the interplay between the set-theoretic properties of the σ-ideal and the topological properties of the associated space.
Factoring Ideals into Semiprime Ideals
Authors: Vaughan N. H. , Yeagy R. W.
Published: December 2010

Let D be an integral domain with 1 ≠ 0 . We consider “property SP” in D, which is that every ideal is a product of semiprime ideals. (A semiprime ideal is equal to its radical.) It is natural to consider property SP after studying Dedekind domains, which involve factoring ideals into prime ideals. We prove that a domain D with property SP is almost Dedekind, and we give an example of a nonnoetherian almost Dedekind domain with property SP.
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
Invariant Complements to Closed Invariant Subspaces
Authors: Thomas M. P.
Published: December 2010

The question under what conditions a closed invariant subspace possesses a closed invariant complement is of major importance in operator theory. In general it remains unanswered. In this paper we drop the requirement that the invariant complement be closed. We show in section 1 that the question is answerable under fairly mild conditions for a quasinilpotent operator (Theorem 1.5). These conditions will cover the case of a quasinilpotent operator with dense range and no point spectrum. In section 2 we discuss the consequences for the Volterra operator V. Since V is unicellular, its proper closed invariant subspaces do not possess closed invariant complements. However, they are all algebraically complemented (Proposition 2.1).
An Inductive Rearrangement Theorem
Authors: Chong Kong-Ming
Published: December 2010

In [2, Theorem 3.2, p. 429] and [3, Theorem 2.1, p. 155], the author established two induction theorems which gave rise to a series of fundamental results in spectral and rearrangement inequalities. In particular, the classical inequalities of Hardy-Littlewood-Pólya [4, Theorem 108, p. 89] and Pólya [6] were derived and conditions for equalities obtained (see [2, Theorem 3.8, p. 433] and [3, Theorem 2.6, p. 157]). In [5, Theorem 6, p. 651 ; and Theorem 20, p. 569], Fischer and Holbrook also gave alternative conditions for equalities to hold in the aforesaid inequalities. In this paper, we show that the result of Fischer and Holbrook can be proved by induction using an inductive rearrangement theorem which turns out to be a stronger version of the induction theorems given in [2, Theorem 3.2, p. 429] and [3, Theorem 2.1, p. 155].
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 chainable

In [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].
The Schur Subgroup of a p-Adic Field
Authors: Spiegel Eugene , Trojan Allan
Published: December 2010

Let K be a field. The Schur subgroup, S(K), of the Brauer group, B(K), consists of all classes [△] in B(K) some representative of which is a simple component of one of the semi-simple group algebras, KG, where G is a finite group such that char K ∤ G. Yamada ([11], p. 46) has characterized S(K) for all finite extensions of the p-adic number field, Qp. If p is odd, [△] ∈ S(K) if and only if

where c is the tame ramification index of k/Qp, k the maximal cyclotomic subfield of K, and s = ((p – 1)/c, [K : k]). invp △ is the Hasse invariant. Yamada showed this by proving first that S(K) is the group of classes containing cyclotomic algebras and then determining the invariants of such algebras.
An Alternative Approach to Laguerre Polynomial Identities in Combinatorics
Authors: Barrett Wayne W.
Published: December 2010

1. In their paper “Permutation Problems and Special Functions,” Askey and Ismail [1] give the following striking identity. Consider three boxes containing j, k, m distinguishable balls, and consider all possible rearrangements of these balls such that each box still has the same number of balls; i.e., j end up in the first, k in the second, m in the third. One disregards the order of the balls within a box so there are (j + k + m)!/(j!k!m!) possible rearrangements. Let RE be the number of rearrangements where an even number of balls change boxes and R0 the number of rearrangements where an odd number change boxes. The identity is

(1.1)

where

(1.2)

is the jth Laguerre polynomial. These polynomials are orthonormal with respect to the weight function e–x; i.e.
A Measure of Linear Independence for Some Exponential Functions II
Authors: Brownawell W. Dale
Published: December 2010

This paper continues the investigations in [1] and [2] and extends the results of the latter paper to functions of several complex variables. Namely let λ : R>0 —> R>0 be monotonically increasing. (If λ is non-constant, we also require that log r = 0(λ(r)). We write / = 0(g) to mean that there is a constant C > 0 such that f(r) ≦ Cg(r) except possibly on a set of intervals of finite total length.) Let 0\ denote the set of meromorphic / on Cn for which the Nevanlinna characteristic function [5, p. 174] T(f, r) satisfies T(f, r) = 0(λ(r)).
Factorization of Affinities
Authors: Ellers Erich W.
Published: December 2010

The decomposition of mappings into a minimal number of simple mappings is a common sight in geometry. One well-known instance is the representation of a plane motion by three reflections (see e.g. H. S M. Coxeter [3]) or the representation of equiaffinities by a minimal number of shears or reflections ([14], [5], [7], [8]). Theorems of this nature not only give valuable insight into the nature of the mapping, but they are also often used as a base for characterization theories (see e.g. F. Bachmann [2], M. Götzky [10]). A more abstract version of the same type of results is the famous Cartan-Dieudonné theorem. Its usefulness is indisputable. P. Scherk [13] gave a refined version of this theorem.
Stable Homeomorphisms of the Pseudo-Arc
Authors: Lewis Wayne
Published: December 2010

Noting that certain restrictions are placed on homeomorphisms of the pseudo-arc, since it is hereditarily indecomposable, in 1955 [4] R. H. Bing asked if the identity is the only stable homeomorphism of the pseudo-arc. In this paper we prove the following theorem.

THEOREM. Let U be an open subset of the pseudo-arc P. Let p and q be distinct points of P such that the subcontinuum M irreducible between p and q does not intersect cl(U). Then there exists a homeomorphism h : P → P with h (p) = q andh│U = 1U.

1. Definitions. A chain C is a collection of open sets C = {C(i))}i≧n such that C(i) ∩ C(j) ≠ ∅ if and only if |i – j| ≦ 1, cl|(C(i)) ∩ cl(C(j)) ≠ ∅ if and only if |i – j| ≦ 1, C(0) – C(l) ≠ ∅, and C(n) – C(n – 1) ≠ ∅. Each C(i) is called a link of C.
Transformations of n-Space which Preserve a Fixed Square-Distance
Authors: Lester J. A.
Published: December 2010

1. Introduction. Our interest here lies in the following theorem:

THEOREM 1. Assume there is defined on Rn (n ≧ 3) a “square-distance” of the form

where (gij) is a given symmetric non-singular matrix over the reals and x = (x1, …, xn), y = (y1, …, yn) ∈ Rn. Assume further that f is a bijection ofRnwhich preserves a given fixed square-distance ρ, i.e. d(x, y) = ρ if and only if d(ƒ(x),ƒ(y)) = ρ. Then (unless ρ = 0 and (gij) is positive or negative definite) ƒ(x) = Lx + ƒ(0), where L is a linear bijection ofRnsatisfying d(Lx, Ly) = ±d(x, y) for all x, y ∈ Rn (the – sign is possible if and only if ρ = 0 and (gij) has signature 0).
Lower Bounds on the Number of Points in the Lower Spectrum of Elliptic Operators
Authors: Allegretto Walter
Published: December 2010

Let G denote an unbounded domain of Euclidean m-space Em with regular boundary, and let L be a self-adjoint operator generated in L2(G) by a second order elliptic expression. We denote by S(L) the spectrum of L, by µ the least point of the essential spectrum Se(L) and by N(L) the number of bound states of L; that is, the number of points in (–∞, µ) ∩ S(L). There are many results in the literature dealing with the localization, significance and properties of µ, of Se(L) and of (–∞, µ)⌒ S(L), with most of the emphasis on the cases where G = Em or G is the exterior of a closed surface in Em. We refer the reader to the books by Glazman [12], Schechter [19], Reed and Simon [18], and Paris [9], where extensive references are also found.
Hamiltonian Cubic Graphs and Centralizers of Involutions
Authors: Babai László , Frankl Péter , Kollár János , Sabidussi Gert
Published: December 2010

In 1948, R. Frucht [5] proved that, given a finite group G, there are infinitely many connected cubic graphs X such that the automorphism group Aut X is isomorphic to G. In a letter, Professor Frucht has proposed the problem, whether in addition X can be required to be hamiltonian. One of the aims of the present note is to answer this question affirmatively.

THEOREM 1.1. Given a finite group G there are infinitely many finite hamiltonian cubic graphs Y such that Aut Y ≌ G.

In fact, we prove the following:

THEOREM 1.2. Given a finite cubic graph X having no component isomorphic to K4, there exists a hamiltonian cubic graph Y such that Aut Y ≌ Aut X and |V(Y)| = 6|V(X)|.

This implies 1.1 by the theorem of Frucht [5] mentioned above.
Sur La Classification Des Symetries Des C*-Algebres UHF
Authors: Fack Th. , Marechal O.
Published: December 2010

Cet article contient une classification détaillée des symétries des C*-algèbres uniformément hyperfinies. Soient une symétrie de ; on associe à θ un entier généralisé N(θ), un réel Tr (θ) ∈ [0, 1], et on a les résultats suivants:

Il existe une symétrie unique à conjugaison près qui possède une suite centrale (Un) d'unitaires vérifiant ‖θ(Un) + Un‖ → 0(n → ∞). Cette symétrie est la seule dont l'algèbre des points fixes est uniformément hyperfinie.
Chain Conditions for Modular Lattices with Finite Group Actions
Authors: Fisher Joe W.
Published: December 2010

This paper establishes the following combinatorial result concerning the automorphisms of a modular lattice.

THEOREM. Let M be a modular lattice and let G be a finite subgroup of the automorphism group of M. If the sublattice, MG, of (common) fixed points (under G) satisfies any of a large class of chain conditions, then M satisfies the same chain condition. Some chain conditions in this class are the following: the ascending chain condition; the descending chain condition; Krull dimension; the property of having no uncountable chains, no chains order-isomorphic to the rational numbers; etc.
Infinite Systems of Differential Equations II
Authors: McClure J. P. , Wong R.
Published: December 2010

This paper is a continuation of earlier work [6], in which we studied the existence and the stability of solutions to the infinite system of nonlinear differential equations

(1.1)

i = 1, 2, …. Here s is a nonnegative real number, Rs = {t ∈ R: t ≧ s}, and denotes a sequence-valued function. Conditions on the coefficient matrix A(t) = [aij(t)] and the nonlinear perturbation were established which guarantee that for each initial value c= {ct} ∈ l1, the system (1.1) has a strongly continuous l1valued solution x(t) (i.e., each is continuous and converges uniformly on compact subsets of Rs). A theorem was also given which yields the exponential stability for the nonlinear system (1.1).
Lifting Isomorphisms of Modules
Authors: Reiner Irving
Published: December 2010

Throughout this note, let R be a discrete valuation ring with prime element π, residue class field , and quotient field K. Let Λ be an R-order in a finite dimensional K-algebra A. A Λ-lattice is an R-free finitely generated left Λ-module. For k > 0, we set

where M is any Λ-lattice. Obviously, for Λ-lattices M and N,

Maranda [1] and D. G. Higman [3] considered the reverse implication, and Proved

THEOREM. Let Λ be an R-order in a separable K-algebra A. Then there exists a positive integer k (which depends on Λ) with the following property: for each pair of Λ-lattices M and N,

Indeed,m it suffices to choose k so that

Maranda proved this result for the special case where Λ is the integral group ring RG of a finite group G.
A Basically Disconnected Normal Space Φ With |βΦ – Φ| = 1
Authors: Douwen Eric K. van
Published: December 2010

All spaces considered are completely regular. C*(X) denotes the set of bounded continuous real-valued functions in X. A subspace S of X is called C*-embedded in X if for every f ∈ C*(S) there is ϕ ∈ C*(X) with ϕ⥤S = f.

A space X is called almost compact if |βX – X| ≦ 1; basically disconnected if every cozero-set has open closure; extremally disconnected if every open set has open closure; an F-space if every cozero-set is C*-embedded; small if |C*(X)| = 2ω; and weakly Lindelöf if every open cover has a subfamily with and ⋃ dense. A point p of a space X is called a P-point of X if every Gδ-set in X which contains p is a neighborhood of p.

ω(X) denotes the weight of X.
Projections on Bergman Spaces Over Plane Domains
Authors: Burbea Jacob
Published: December 2010

Let D be a bounded plane domain and let Lp(D) stand for the usual Lebesgue spaces of functions with domain D, relative to the area Lebesque measure dσ(z) = dxdy. The class of all holomorphic functions in D will be denoted by H(D) and we write Bp(D) = Lp(D) ∩ H(D). Bp(D) is called the Bergman p-space and its norm is given by

Let be the Bergman kernel of D and consider the Bergman projection

(1.1)

It is well known that P is not bounded on Lp(D), p = 1, ∞, and moreover, it can be shown that there are no bounded projections of L∞(Δ) onto B∞(Δ).
Fourier Transforms of Unbounded Measures
Authors: Stewart James
Published: December 2010

1. Introduction. One of the basic objects of study in harmonic analysis is the Fourier transform (or Fourier-Stieltjes transform) μ of a bounded (complex) measure μ on the real line R:

(1.1)

More generally, if μ is a bounded measure on a locally compact abelian group G, then its Fourier transform is the function

(1.2)

where Ĝ is the dual group of G and One answer to the question “Which functions can be represented as Fourier transforms of bounded measures?” was given by the following criterion due to Schoenberg [11] for the real line and Eberlein [5] in general: f is a Fourier transform of a bounded measure if and only if there is a constant M such that

(1.3)

for all ϕ ∈ L1(G) where
Coefficient Regions for Univalent Trinomials
Authors: Rahman Q. I. , Waniurski J.
Published: December 2010

The problem of determining necessary and sufficient conditions bearing upon the numbers a2 and a3 in order that the polynomial z + a2z2 + a3z3 be univalent in the unit disk |z| < 1 was solved by Brannan ([3], [4]) and by Cowling and Royster [6], at about the same time. For his investigation Brannan used the following result due to Dieudonné [7] and the well-known Cohn rule [9].

THEOREM A (Dieudonné criterion). The polynomial

1

is univalent in |z| < 1 if and only if for every Θ in [0, π/2] the associated polynomial

2

does not vanish in |z| < 1. For Θ = 0, (2) is to be interpreted as the derivative of (1).

The procedure of Cowling and Royster was based on the observation that is univalent in |z| < 1 if and only if for all α such that 0 ≧ |α| ≧ 1, α ≠ 1 the function

is regular in the unit disk.
Isometric Preduals of James Spaces
Authors: Brown Leon , Ito Takashi
Published: December 2010

A Banach space B is called an isometric predual, or simply a predual, of a Banach space X if the dual B* of B is isometrically isomorphic to X. A Banach space X is said to have a unique (isometric) predual if X has a predual and all preduals are mutually isometrically isomorphic. In general a Banach space does not have a unique predual even if it has a predual. A simple example of this is the space l1, because c0 and c are isometric preduals of l1 but not isometrically isomorphic. A. Grothendieck [3] first noticed that L∞-spaces have unique preduals, and then S. Sakai generalized this to von Neumann algebras (see p. 30 of [9]).
A Characterization of PSL(2, 31) and its Geometry
Authors: Perkel Manley
Published: December 2010

The aim of this paper is the characterization of PSL(2, 31) in terms of its action on a certain polygonal graph. A polygonal graph is a pair (, ) consisting of a graph which is regular, connected and has girth m for some m ≧ 3, and a set of m-gons (circuits of length m) of such that every 2-claw (i.e. path of length 2) of is contained in a unique element of , (See Section 2 for the definitions of the terms used here.) If is the set of all m-gons of H, so that there is in a unique m-gon on every one of its 2-claws, then we write for (, ) and call a strict polygonal graph. If we wish to emphasize the integer m, then we call (, ) an m-gon-graph (respectively, a strict m-gon-graph). For convenience, a strict 5-gon-graph will be called a pentagraph.
Algebres Simples de Groupes a Gauche
Authors: Handelman David
Published: December 2010

SoitRun anneau et soit Gopun sous groupe de Aut(R).Formons l'anneau de groupe à gauche (“skew group ring”)RSG,en imposant, sur le module libre à gauche avec une baseG,la multiplicationrg=grg.(On écrit Gopau lieu deGcar, siG <Inn(R) =le groupe d'automorphismes intérieurs, la conditiong–rg = rg; implique que le homomorphisme naturelest vraiment un anti-homomorphisme).

Nous considérons le cas oùR=MnF, Fun corps,MnFl'anneau de matrices, d'ordren,et Gopun sous-groupe (généralement) fini, dePGL(n, F)= Inn(R).Ce travail est consacré à l'étude de la simplicité deRSG.
Ideals with Trivial Conormal Bundle
Authors: Geramita A. V. , Weibel C. A.
Published: December 2010

Throughout this paper all rings considered will be commutative, noetherian with identity. If R is such a ring and M is a finitely generated R-module, we shall use v(M) to denote that non-negative integer with the property that M can be generated by v(M) elements but not by fewer.

Since every ideal in a noetherian ring is finitely generated, it is a natural question to ask what v(I) is for a given ideal I. Hilbert's Nullstellensatz may be viewed as the first general theorem dealing with this question, answering it when I is a maximal ideal in a polynomial ring over an algebraically closed field.

More recently, it has been noticed that the properties of an R-ideal I are intertwined with those of the R-module I/I2.
k-Discreteness and k-Analytic Sets
Authors: Freiwald Ronald C.
Published: December 2010

All spaces considered here are metrizable. k will always denote an infinite cardinal. The successor of k will be denoted by k+.

Of particular interest will be the Baire spaces where each Tn is a discrete space of cardinal k. The product topology on B(k) is the same as the topology given by the (complete) “first-difference” metric, p : p(s, t) = 1/n if Si = ti for 1 ≦ i ≦ n —1 and sn = tn. A great deal of information about these spaces can be found in [4].

A subset A of X is called k-analytic (in X) if there exist, for each t ∈ B(k), closed subsets F(t1), …, F(t1, …, tn), … of X such that