bluuebunny/crossref_metadata_2025 huggingface dataset:
Imprimitive, Irreducible Complex Characters of the Alternating Group
Authors: Djoković Dragomir Ž. , Malzan Jerry
Published: December 2010

The purpose of this paper is to list all of the characters of An, the alternating group, mentioned in the title. The same problem for the symmetric group, Sn, was dealt with by the authors in [1]. We showr here that, apart from a few exceptions, the imprimitive, irreducible complex characters of An fall naturally into two infinite families. (Throughout this paper characters are taken over the complex numbers.)
Criteria for a Hadamard Matrix to be Skew-Equivalent
Authors: Longyear Judith Q.
Published: December 2010

A matrix H of order n = 4t with all entries from the set ﹛1, —1﹜ is Hadamard if HHt = 4tI. The set of Hadamard matrices is . A matrix is of type I or is skew-Hadamard if H = S — I where St = —S (some authors also use H = S + I). The set of type I members is . A matrix P is a signed permutation matrix if each row and each column has exactly one non-zero entry, and that entry is from the set ﹛1, —1﹜.
Representing Rank Complete Continuous Rings
Authors: Handelman David
Published: December 2010

Given a suitable regular ring R, we construct a sheaf-like representation for R as a ring of continuous sections from a completely regular space to an appropriately toplogized disjoint union of factor rings corresponding to ‘'extremal“ pseudo-rank functions. Applied to rings which are complete with respect to a rank function this representation is an isomorphism, the completely regular space is extremally disconnected and compact, and the * ‘stalks” are the simple factor rings.
Homotopy Pull-Backs and Applications to Duality
Authors: Walker Marshall
Published: December 2010

The topic of homotopy pull-backs and push-outs has recently been discussed by a number of authors; Boardman and Vogt [5], Bousfield and Kan [6], Fantham [7], Mather [11], and Vogt [16]. Mather develops the theory with an eye to applications and of particular interest is his cube theorem which appears in this paper as Theorem (1.10); the significance of this theorem to applications is shown in [11]. As often occurs in homotopy theory the dual is not true. The purpose of this paper is to examine approximations to the dual in order to obtain new information concerning classical problems of duality.
Curves in Homogeneous Spaces
Authors: Hirschorn Ronald M.
Published: December 2010

Let be a Lie group with connected Lie subgroup , and let M(t), N(i) be real analytic curves in , the Lie algebra of , with . The main result in this paper is a Lie algebraic condition which is necessary and sufficient for
Sum of Squares Rings
Authors: Fine Benjamin
Published: December 2010

One of the nicest results in elementary number theory is the following, giving the relation between quadratic residues and sums of squares.
Matchings in Countable Graphs
Authors: Steffens K.
Published: December 2010

Tutte [9] has given necessary and sufficient conditions for a finite graph to have a perfect matching. Different proofs are given by Brualdi [1] and Gallai [2; 3]. The shortest proof of Tutte's theorem is due to Lovasz [5]. In another paper [10] Tutte extended his conditions for a perfect matching to locally finite graphs. In [4] Kaluza gave a condition on arbitrary graphs which is entirely different from Tutte's.
A Note on the Representation Type of Pointed Irreducible Coalgebras and Unipotent Algebras
Authors: Trushin David
Published: December 2010

In this paper the representation type of the class of pointed irreducible coalgebras is studied. We refer the reader to [4] for the basic definitions. A coalgebra is of bounded representation type if there is a bound on the dimension of finite dimensional indecomposable comodules. In Section 1, we show that the representation type is dependent upon the size of the space of primitives. Indeed, a pointed irreducible coalgebra is of bounded type if and only if it is finite dimensional and the space of primitives is onedimensional, i.e. if and only if it is a coalgebra spanned by a finite sequence of divided powers.
On Rational Subdivisions of Polyhedra with Rational Vertices
Authors: Beynon W. M.
Published: December 2010

This short paper is devoted to the proof of a single theorem, which, in its simplest form, asserts that if Q is a polyhedron in Rn which can be expressed as the union of finitely many convex polytopes whose vertices are at rational points in Rn, and if is a simplicial subdivision of Q﹜ then there is an isomorphic simplicial subdivision ” of Q in which all vertices are at rational points.
Applications of Duality in the Theory of Finitely Generated Lattice-Ordered Abelian Groups
Authors: Beynon W. M.
Published: December 2010

In a previous paper by the author [3], duality theorems for finitely generated vector lattices and lattice-ordered Abelian groups are described. In particular, the category of finitely generated semi-simple vector lattices is shown to be equivalent to a geometrical category V whose objects are topologically closed cones in Euclidean space, and whose morphisms, called ll-maps\ form a special subclass of the class of piece wise homogeneous linear maps between such cones. Under this categorical duality, finitely generated projective vector lattices and closed polyhedral cones correspond; indeed, the category of finitely generated projective vector lattices is equivalent to the dual of a category whose objects are Euclidean closed polyhedral cones and whose morphisms consist of all piecewise homogeneous linear maps between such cones.
Irreducible Automorphisms of Certainp-Groups
Authors: Djoković D. Ž. , Malzan J.
Published: December 2010

The chief purpose of this paper is to find all pairs (G, θ) whereGis a finite specialp-group, andθis an automorphism ofGacting trivially on the Frattini subgroup and irreducibly on the Frattini quotient. This problem arises in the context of describing finite groups having an abelian maximal subgroup. In fact, we solve a more general problem for a wider class ofp-groups, which we callspecial F-groups,whereFis a finite field of characteristicp.We point out that ifpis odd, then anF-group has exponentp.On the other hand, every special 2-group is also a specialGF(2)-group.
A Note on Quasi-Metrizability
Authors: Gruenhage Gary
Published: December 2010

Let X be a set. A function d from X X X into the nonnegative real numbers is called a ﹛non-archimedean) quasi-metric on X if
Rigid Embedding of Simple Groups in the General Linear Group
Authors: Dixon John D.
Published: December 2010

Let K be a (commutative) field and n be a positive integer. Consider the K-algebra E = Mat (n, K) of all n X n matrices over K, and the corresponding general linear group GL(n, K). We shall define the set R of rigid mappings of E to consist of all a in GLK(E) which can be written in one of two possible forms: either xσ= axb for all x ϵ E or xσ = ax'b for all x ϵ E (where a and b are fixed elements of GL(n, K) and x’ denotes the transpose of x).
On Factors of a Graph
Authors: Mahmoodian Ebad
Published: December 2010

Let G be a graph with multiple edges. Let f be a function from the vertex set V(G) of G to the non-negative integers. An f-factor of G is a spanning subgraph F of G such that the degree (valence) of each vertex x in F is f(x). A theorem of Fulkerson, Hoffman and McAndrew [1] gives necessary and sufficient conditions to have an f-factor for a graph G with the odd-cycle property; i.e., if G has the property that either any two of its odd (simple) cycles have a common vertex, or there exists a pair of vertices, one from each cycle, which is joined by an edge. They proved this theorem using integer programming techniques, with a rather long proof. We show that this is a corollary of Tutte's f-factor theorem.
Weak Injectivity and Congruence Extension in Congruence-Distributive Equational Classes
Authors: Davey Brian A.
Published: December 2010

There are many concepts which arise naturally in a discussion of injectivity in an equational class; for example, weak injective algebras, absolute subretracts, essential extensions, the congruence extension property, and the amalgamation property (see [3; 9; 17; 18]). It has already been demonstrated in several papers, notably [9; 17; 26; 27; 28], that the study of these concepts is greatly enriched by the assumption that the algebras under consideration have distributive congruence lattices. In this work attention is focused on weak injective algebras (Section 2) and the congruence extension property (Section 3).
On Reflexive Compact Operators
Authors: Feintuch Avraham
Published: December 2010

Let A be a compact operator on a separable Hilbert space . The aim of this paper is to investigate the relationship between the weak closure of the algebra of polynomials in A (denoted by U(A)) and its invariant subspace lattice Lat A.
The Existence of Continuable Solutions of a Second Order Differential Equation
Authors: Butler G. J.
Published: December 2010

A much-studied equation in recent years has been the second order nonlinear ordinary differential equation

where q and f are continuous on the real line and, in addition, f is monotone increasing with yf(y) > 0 for y ≠ 0. Although the original interest in (1) lay largely with the case that q﹛t) ≧ 0 for all large values of t, a number of papers have recently appeared in which this sign restriction is removed.
Examples for the Theory of Infinite Iteration of Summability Methods
Authors: Diaconis Persi
Published: December 2010

Garten and Knopp [7] introduced the notion of infinite iteration of Césaro (C1 ) averages, which they called H∞ summability. Flehinger [6] (apparently unaware of [7]) produced the first nontrivial example of an H∞ summable sequence: the sequence ﹛ai ﹜ ∞i=1 where at is 1 or 0 as the lead digit of the integer i is one or not. Duran [2] has provided an elegant treatment of H∞ summability as a special case of summability with respect to an ergodic semigroup of transformations.
Varieties Obeying Homotopy Laws
Authors: Taylor Walter
Published: December 2010

The algebraic structure of a topological algebra influences its topological structure in a way which is profound but not well understood. (See § 7 below for various examples.) Here we examine this influence rather generally, and give a fairly complete analysis of one of the many forms it can take, namely, the influence of the identities of on the group identities obeyed by the homotopy group (or groups of the components) of .
Inequality Constraints in the Calculus of Variations
Authors: Clarke Frank H.
Published: December 2010

The classical multiplier rule. The purpose of this section is to review the multiplier rule in order to place the results of this report in perspective. Let us begin by considering the following problem of Mayer in the calculus of variations: we seek to minimize
Some Local-Global Principles for Formally Real Fields
Authors: Marshall M.
Published: December 2010

Let F be a formally real field, and let A be a preordering of F; that is, a subset of F satisfying Δ + Δ = Δ, Δ Δ = Δ, F2 ⊆ Δ. Denote by X Δ the set of all orderings P of F satisfying P ⊇ Δ. Thus Δ = ⋂ p ∈xΔP. This result is well known. It was first proved by Artin [3, Satz 1] in the case Δ = ∑ F2.
On a Transcendence Problem of K. Mahler
Authors: Kubota K. K.
Published: December 2010

K. Mahler [8] has proposed the following problem. Let Ωr for r ≧ 1 be a sequence of n X n non-negative rational integer matrices. Each Ωr — (ωrij) defines a map Ωr : Cn —⟶ Cn by
Complex Approximation and Simultaneous Interpolation on Closed Sets
Authors: Gauthier P. M. , Hengartner W.
Published: December 2010

Let ƒ be a complex-valued function denned on a closed subset F of the finite complex plane C, and let {Zn} be a sequence on F without limit points. We wish to find an analytic function g which simultaneously approximates ƒ uniformly on F and interpolates ƒ at the points {Zn}.
Best Trigonometric Approximation, Fractional Order Derivatives and Lipschitz Classes
Authors: Butzer P. L. , Dyckhoff H. , Görlich E. , Stens R. L.
Published: December 2010

Let C2π denote the space of 2π-periodic continuous functions and πn the set of trigonometric polynomials of degree ≦ n, where n ϵ P = {0, 1, … } . Given θ > 0, the well-known theorem of Stečkin and its converse state that the best approximation of an ƒ ϵ C2π with respect to the max-norm satisfies
Residuals of the Join of Ascendant Subgroups
Authors: Whitehead Jennifer
Published: December 2010

If G is a group, then we say H is an ascendant subgroup of G, and write H asc G, if there exists a sequence of subgroups (Gα)α ≦ ρ where ρ is some ordinal number, such that G0 = H, Gp = G, Gρ ⊲ Gα+1 for all α < ρ and G ƛ = ⋂ {Gα α| α ⊲ ƛ} for all limit ordinals λ ≦ ρ. (Gα) α ≦ ρ is said to be an ascending series from H to G.
The Weak Basis Theorem Fails in Non-Locally Convex F-Spaces
Authors: Drewnowski L.
Published: December 2010

W. J. Stiles showed in [10, Corollary 4.5] that Banach's weak basis theorem fails in the spaces lp, 0 < p < 1. Then, J. H. Shapiro [9] indicated certain general classes of non-locally convex F-spaces with the same property, and asked whether the weak basis theorem fails in every non-locally convex F-space with a weak basis. Our purpose is to answer this question in the affirmative. In [3] we observed that, essentially, the only case that remained open is that of an F-space with irregular basis (en), i.e. such that snen →0 for any scalar sequence (sn).
Homotopy Equivalence of a Cofibre Fibre Composite
Authors: Heath Philip R.
Published: December 2010

Consider the following commutative diagram in Top, the category of topological spaces

in which j and j' are cofibrations, p and p' are (Hurewicz) fibrations and ƒ0, ƒi and ƒ2 are homotopy equivalences.
Bireflectionality in Classical Groups
Authors: Ellers Erich W.
Published: December 2010

The motion groups of the real Euclidean plane and of the elliptic plane, the group of projectivities of a line, the projective general linear group PGL2(K), some orthogonal groups O3(K, Q) with char K = 2 (see [8]), are all bireflectional (zweispiegelig). There can be no doubt that bireflectional groups are of prime importance in any theory of groups that are generated by involutions. A brief look into F. Bachmann's book [1] gives convincing evidence.
Quantization and Group Representations
Authors: Cressman R.
Published: December 2010

A quantization of a fixed classical mechanical system is firstly an association between quantum mechanical observables (preferably self-adjoint operators on Hilbert space) and classical mechanical observables (i.e. real-valued functions on phase space). Secondly, a quantization should permit an interpretation of the correspondence principle that ‘classical mechanics is the limit of quantum mechanics as Planck's constant approaches zero'. With these two underlying precepts, Section 2 states the four basic requirements, I to IV, of a quantization along with an additional requirement V that characterizes the subclass of special quantizations.
Subfields and Invariants of Inseparable Field Extensions
Authors: Deveney James K. , Mordeson John N.
Published: December 2010

Let L/K be a field extension of characteristic p ≠ 0. The existence of intermediate fields over which L is regular, separable, or modular is important in recent Galois theories. For instance, see [1; 2; 3; 4; 7; 8; 9 and 14].
Norm Convergence of Tn
Authors: Luecke Glenn R.
Published: December 2010

Throughout this paper X will denote a complex Banach space and all operators T will be assumed to be continuous linear transformations from X into X. If T is an operator then ┘(T), γ(T), and R(T) will denote the spectrum of T, the spectral radius of T, and range of T, respectively. This paper contains necessary and sufficient conditions for the (norm) convergence of {Tn} when T is an operator on X.
Confluent and Related Mappings Defined by Means of Quasi-Components
Authors: Grispolakis Joachim
Published: December 2010

In 1964, J. J. Charatonik in [1] introduced a new
class of mappings, the so-called confluent mappings, which comprises the classes
of open, monotone and quasi-interior mappings (see [20]).
In 1966, A. Lelek started working on confluent mappings with applications to
continua theory (see [7]). He introduced two other classes
of mappings, the so-called weakly confluent and pseudo confluent mappings, he
proved the invariance of rational continua under open, monotone and quasi-interior
mappings and he asked about their invariance under confluent mappings. In 1976, E.
D. Tymchatyn gave an example of a confluent mapping, which does not preserve the
rationality of a curve (see [18]).
Subrings of Generated by Monomials
Authors: Anderson David F.
Published: December 2010

In this paper we study subrings A of
generated by
monomials over . If
A is normal and A ⊂
B integral, we can completely characterize
A. If dim A = 2, we show
that A is isomorphic to a subring
A’ of B generated by
monomials with A’ ⊂ B
integral. The author became interested in these rings while studying projective
modules over subrings of , For some
applications, see [1].
The Number of Closed Subsets of a Topological Space
Authors: Hodel R. E.
Published: December 2010

Let X be an infinite topological space, let
𝔫 be an infinite cardinal number with 𝔫 ≦ |X|. The basic problem
in this paper is to find the number of closed sets in X
of cardinality 𝔫. A complete answer to this question for the class of
metrizable spaces has been given by A. H. Stone in [31], where he proves the
following result. Let X be an infinite metrizable space of
weight 𝔪, let 𝔫 ≦
|X|.
Normality and the Higher Numerical Range
Authors: Marcus Marvin , Moyls Benjamin N. , Filippenko Ivan
Published: December 2010

Let
Mn(C) be
the vector space of all w-square complex matrices. Denote by (• , •) the standard
inner product in the space
C
n
of complex n-tuples. For a matrix A ∈
Mn(C)
and an n-tuple c = (c1,… ,
cn) ∈ C
n, define the c-numerical range
of A to be the set
Some Orbital Integrals and a Technique for Counting Representations of GL
2(F)
Authors: Callahan T.
Published: December 2010

Let F be a local field of characteristic zero,
with q elements in its residue field, ring of integers
uniformizer
ωF and maximal ideal . Let
GF
= GL2(F). We fix
Haar measures dg
and dz
on GF
and ZF, the centre
of GF, so that

meas(K) = meas

where K = GL2() is a maximal
compact subgroup of GF. If T is a
torus in GF we take dt to be the
Haar measure on T such that

means(TM)=1

where TM denotes the maximal compact subgroup of
T.
On Infinite Full Colourings of Graphs
Authors: Fawcett Barry
Published: December 2010

This paper answers affirmatively a question of Pavol Hell
[2]: if a graph admits a full n-colouring for every
finite n ≧
n0, does it admit an infinité
full colouring? (A colouring is full if every pair of
distinct colour classes is joined by at least one edge).
Local Boundary Behavior of Bounded Holomorphic Functions
Authors: Nagel Alexander , Rudin Walter
Published: December 2010

Let D ⊂⊂ Cn
be a bounded domain with smooth boundary
∂D, and let F be a
bounded holomorphic function on D. A generalization of
the classical theorem of Fatou says that the set E of
points on ∂D at which F
fails to have nontangential limits satisfies the condition σ
(E) = 0, where a denotes
surface area measure. We show in the present paper that this result remains true
when σ is replaced by 1-dimensional Lebesgue measure on
certain smooth curves γ in ∂D. The condition that γ
must satisfy is that its tangents avoid certain directions.
Uniqueness in Structure Theorems for LCA Groups
Authors: Armacost D. L. , Armacost W. L.
Published: December 2010

The classical Pontrjagin-van Kampen structure theorem states that any locally
compact abelian (LCA) group G can be written as the
direct product of a vector group Rm
(where R denotes the additive group of
real numbers with the usual topology, and m is a
non-negative integer) and an LCA group H which contains
a compact open subgroup. This important theorem, which van Kampen deduced from the
work of Pontrjagin, was first stated and proved in [5, p.
461].
Perturbation of Direct Sum Differential Operators
Authors: Lee S. J.
Published: December 2010

Let I be an interval, and let for 1 ≦
j ≦ I < ∞ be
abutted subintervals such that . Let τ
j
be a linear differential expression defined on I
j
. In this paper we study densely defined
operators associated with

(0.1)
Harmonic Mappings of Negatively Curved Manifolds
Authors: Har'el Zvi
Published: December 2010

Volume decreasing properties of harmonic mappings of space forms were
investigated by S. S. Chern and S. I. Goldberg [3] and the
author. In a previous paper [6], a step toward
generalization of the results was made proving the following theorem:

Theorem. Let ƒ: M —>
N be a harmonic mapping of
n-dimensional Riemannian manifolds, with C ≦ 0.
Suppose the scalar curvature of M is not less than — S, and the Ricci curvature of
N is not greater than —S/n, where S ≧ 0 and S
> 0 are constants. Then, if u has a maximum on
M,

i.e. ƒ is volume decreasing up to a constant.
Lee Polynomials of Codes and Theta Functions of Lattices
Authors: Maher David P.
Published: December 2010

Several authors [2;3;10;12] have noticed the similarities between the theory of codes and the theory of Euclidean lattices. It is interesting to compare the two theories since they share a common problem, viz. the sphere packing problem. In the theory of codes one would like to find a code over Fp, i.e. a subspace of Fpn, such that non-intersecting spheres with respect to a given metric, centered at the code vectors, pack Fpndensely.
Combinatorial Matrices with Small Determinants
Authors: Newman Morris
Published: December 2010

In this paper we will be concerned with the determinants of matrices whose elements are 0, 1 or —1, 1. Accordingly, let Sn,k be the set of n X n 0, 1 matrices with exactly k ones in each row and column; and let Hn be the set of n X n — 1, 1 matrices. Let J = Jn denote (as usual) the n X n matrix all of whose elements are one.
Riemann Surfaces Over Regular Maps
Authors: Wilson Stephen E.
Published: December 2010

The idea of one surface covering another is a useful one in the study of regular maps. Coxeter and Moser discuss a particular instance [3, p. 115] and the maps produced by Sherk [6] and Garbe [4] are formed by such coverings, though neither paper mentions that fact. In [5], Sherk explicitly constructs coverings of regular maps on the sphere.
Additivity of the Pn-Integral
Authors: Cross George
Published: December 2010

It is known that the Pn-tegral as originally defined is not additive on abutting intervals. This paper offers a slight modification in the definition of the integral and develops necessary and sufficient conditions for the integral to be additive.
On Algebras Stably Equivalent to an Hereditary Artin Algebra
Authors: Inés Platzeck María
Published: December 2010

Let Λ be an artin algebra, that is, an artin ring that is a finitely generated module over its center C which is also an artin ring. We denote by mod Λ the category of finitely generated left Λ-modules. We recall that the category of finitely generated modules modulo projectives is the category given by the following data: the objects are the finitely generated Λ-modules.
On the Homology of the General Linear Groups Over Z/4
Authors: Snaith Victor
Published: December 2010

Let p be a prime. The algebraic K-theory of Z/p2 is unknown. However it is easy to show that Ki(Z/p2) is finite if i > 0 and that it differs only in its K-torsion from Ki(Z/p) which was computed in [2]. To proceed further one surely needs the mod p (co-)homology of GLZ/p2. There is an exact sequence
Analytic Structures for H∞ of Certain Domains in Cn
Authors: Kronstadt Eric P.
Published: December 2010

Let Ω C Cn be a bounded domain; let H∞ (Ω) be the uniform algebra of bounded analytic functions on 12; and let ∑ (Ω) be the maximal ideal space of H∞ (Ω). In the weak-* topology of (H∞ (Ω))*, ∑ (Ω) is a compact Hausdorf space in which Ω is embedded in a natural fashion, so that to every g ∈ H∞ (Ω) there corresponds the Gelfand transform ĝ ∈ C(∑ (Ω)); ĝ|Ω = g.
On the Upper Majorant Property for Locally Compact Abelian Groups
Authors: Rains M.
Published: December 2010

Let G be a compact abelian group and form the spaces LP(G) with respect to the normalized Haar measure on G.
Embedding Right Chain Rings in Chain Rings
Authors: Brungs H. H. , Törner G.
Published: December 2010

The following problem was the starting point for this investigation: Can every desarguesian affine Hjelmslev plane be embedded into a desarguesian projective Hjelmslev plane [8]? An affine Hjelmslev plane is called desarguesian if it can be coordinatized by a right chain ring R with a maximal ideal J(R) consisting of two-sided zero divisors. A projective Hjemslev plane is called desarguesian if the coordinate ring is in addition a left chain ring, i.e. a chain ring. This leads to the algebraic version of the above problem, namely the embedding of right chain rings into suitable chain rings. We can prove the following result.
Constructing Locally Flat Embeddings of Infinite Dimensional Manifolds without Tubular Neighborhoods
Authors: Chapman T. A.
Published: December 2010

All spaces in this paper will be separable and metric. A closed embedding i: M → TV is said to be locally flat (of codimension n) if for each x0 ∈ M there is an open set U in M containing xo and an open embedding h: U X Rn → N for which h(x, 0) = i(x), for all x ∈ U.
Ergodic Properties of Lamperti Operators
Authors: Kan Charn-Huen
Published: December 2010

We shall assume throughout this paper, unless otherwise specified, that p is a fixed number, 1 < p < ∞.

It is well known that to prove the poin.twise ergodic convergence of a contraction T on an Lp-space it is enough to prove a Dominated Ergodic Estimate (DEE) for T (see e.g. [11]).
A Note on Unitary Cross Sections for Operators
Authors: Fialkow Lawrence A.
Published: December 2010

This note addresses the question of characterizing the elements of a C*-algebra which have local unitary cross sections in the sense described below. Let denote a C*-algebra with identity and let denote the unitary group in .
Centered Bases, Nested Bases, and Completability of Aronszajn Spaces
Authors: Phillips Thomas M.
Published: December 2010

Definition. [1] A base B for the topology of a space S is centered provided every perfectly decreasing filterbase F in B is regular and either F is free or F converges. A centered base which contains no free perfectly decreasing filterbase is said to be complete.
Derivations and Automorphisms of Exterior Algebras
Authors: Djoković Dragomir Ž.
Published: December 2010

In this paper we study the Lie algebra of derivations of the exterior algebra of a vector space V over a field K of characteristic ≠ 2, and the group A of automorphisms of .
Some Extreme Rays of the Positive Pluriharmonic Functions
Authors: Forelli Frank
Published: December 2010

1.1. We will denote by B the open unit ball in Cn, and we will denote by H(B) the class of all holomorphic functions on B. Let

Thus N(B) is convex (and compact in the compact open topology). We think that the structure of N(B) is of interest and importance. Thus we proved in [1] that if

(1.1)

if

(1.2)

and if n≧ 2, then g is an extreme point of N(B). We will denote by E(B) the class of all extreme points of N(B). If n = 1 and if (1.2) holds, then as is well known g ∈ E(B) if and only if

(1.3)
A Theory of Uniformities for Generalized Ordered Spaces
Authors: Lindgren W. F. , Fletcher P.
Published: December 2010

Let (X, ) be a topological space equipped with a partial order ≦ and let C (≦) denote the continuous increasing functions mapping X into R (a function f : X → R is increasing provided f(x) ≦ f(y) whenever x ≦ y) Then (X,, ≦) is an N-space (in the terminology of [16], a completely regular order space) provided is the weak topology of C (≦) and if x ≦ y is false, then there is an f ∈ C (≦) such that f(y) < f(x). L. Nachbin's introduction of N-spaces was perspicacious, for these spaces now find application in a wide spectrum of mathematics.
The Asymptotic Behaviour of Equidistant Permutation Arrays
Authors: Vanstone S. A.
Published: December 2010

An equidistant permutation array (EPA) A(r λ v) is a v × r array defined on a set V of r symbols such that every row is a permutation of V and any two distinct rows have precisely λ common column entries. Define R(r, λ) to be the largest value of v for which there exists an A (r, λ; v). Deza [2] has shown that

where n = r – λ. Bolton [1] has shown that

(*)

In this paper, we show that equality holds in (*) for λ > ┌n/3┐(n2 + n). In order to do this we require several more definitions.
Labeled Bipartite Blocks
Authors: Harary F. , Robinson R. W.
Published: December 2010

Graphs which are 2-connected have been called blocks in the graph theoretic literature [3] and stars in the parlance of statistical mechanics [1]. They are also called nonseparable graphs, and in this paper include the complete graph K2 on p = 2 points. The standard terminology of graphical enumeration can be found in [3].

When its points are colored using two distinct colors in such a way that adjacent points receive different colors, a graph is called 2-colored. If the colors are considered interchangeable, such a graph is called bicolored. A graph which can be bicolored is called bicolorable. It is obvious that a connected bicolorable graph has a unique bicoloring, and so one can speak of the sizes of its color classes.
The Structure of Semisimple Symmetric Spaces
Authors: Rossmann W.
Published: December 2010

A semisimple symmetric space can be defined as a homogeneous space G/H, where G is a semisimple Lie group, H an open subgroup of the fixed point group of an involutive automorphism of G. These spaces can also be characterized as the affine symmetric spaces or pseudo-Riemannian symmetric spaces or symmetric spaces in the sense of Loos [4] with semisimple automorphism groups [3, 4]. The connected semisimple symmetric spaces are all known: they have been classified by Berger [2] on the basis of Cartan's classification of the Riemannian symmetric spaces. However, the list of these spaces is much too long to make a detailed case by case study feasible. In order to do analysis on semisimple symmetric spaces, for example, one needs a general structure theory, just as in the case of Riemannian symmetric spaces and semisimple Lie groups.
Criteres deG-Stabilite en Termes de Transversalite
Authors: Gervais Jean-Jacques
Published: December 2010

1.1. Introduction.SoitGun sous-groupe de Lie, de dimensionq, du groupeGLP(R). SoientGi(n)=Ci0,e(Rn,G) le groupe des germes en 0 des applicationsgde classeCideRndansGtelles queg(0) =e(oùeest l'élément neutre deG); Diffi(n) le groupe des germes en 0 des difféomorphismesτd'un voisinage de 0 dansRnsur un voisinage de 0 dansRntels queτ(0) = 0;C0i(Rn,Rp) l'ensemble des germes en 0 des applications de classeCideRndansRp;l'anneau des germes en 0 des fonctions numériques de classeC∞surRnetmson idéal maximal. Pour ƒ ∈C0∞(Rn,Rp), nous désignerons parjr(ƒ) le jet d'ordrerde ƒ en 0. On munit l'ensemblede la structure de groupe définie par la multiplication:
α-Speedable and non α-Speedable Sets
Authors: Jacobs Barry E.
Published: December 2010

α-Recursion theory was invented simultaneously by Kripke [15] and Platek [22] and served to generalize the theories of Takeuti [34], Machover [20], Kreisel and Sacks [14] and others. Kripke (in [16]) derived machinery to construct an analogue to Kleene's T-predicate enabling him to assert that all of unrelativized ordinary recursion theory (as found in Kleene [13]) lifted to α-recursion theory. As a result, we were able to set down in [8] α-analogues to Blum's [1] well-studied axioms, thus, introducing the study of α-computational complexity theory.
Solvable Subgroups and their Lie Algebras in Characteristic p
Authors: Winter David J.
Published: December 2010

1. Introduction. Throughout this paper, G is a connected linear algebraic group over an algebraically closed field whose characteristic is denoted p. For any closed subgroup H of G, denotes the Lie algebra of H and H0 denotes the connected component of the identity of H.

A Borel subalgebra of is the Lie algebra of some Borel subgroup B of G. A maximal torus of is the Lie algebra of some maximal torus T of G. In [4], it is shown that the maximal tori of are the maximal commutative subalgebras of consisting of semisimple elements, and the question was raised in § 14.3 as to whether the set of Borel subalgebras of is the set of maximal triangulable subalgebras of .
Multiplicative Groups Under Field Extension
Authors: May Warren
Published: December 2010

Let K be a field and L an extension field. L. Fuchs [2, Problem 98] has suggested studying the change in multiplicative groups in going from K* to L*. We wish to indicate difficulties that arise in trying to relate the group theoretic structure of L* to that of K*, even when K* has particularly simple structure and the extension is quadratic.

First let us note a trivial fact. If [L : K] = n < ∞ and K* has a free direct factor A, then L* has a free direct factor isomorphic to A. To see this, let ϕ be the composite L* → K* → A of the norm map followed by the projection map. Then L* has a free direct factor isomorphic to ϕ(L*). But the image of the norm map contains (K*)n, hence ϕ(L*) ≅ A.
Graded π-rings
Authors: Anderson D. D. , Matijevic J.
Published: December 2010

All rings considered will be commutative with identity. By a graded ring we will mean a ring graded by the non-negative integers.

A ring R is called a π-ring if every principal ideal of R is a product of prime ideals. A π-ring without divisors of zero is called a π-domain. A graded ring (domain) is called a graded π-ring (-domain) if every homogeneous principal ideal is a product of homogenous prime ideals. A ring R is called a general ZPl-ring if every ideal is a product of primes. A graded ring is called a graded general ZPl-ring if every homogenous ideal is a product of homogeneous prime ideals.
Sequence Enumeration and the de Bruijn-Van Aardenne Ehrenfest-Smith-Tutte Theorem
Authors: Jackson D. M. , Goulden I. P.
Published: December 2010

The de Bruijn—van Aardenne Ehrenfest— Smith—Tutte theorem [1] is a theorem which connects the number of Eulerian dicircuits in a directed graph with the number of rooted spanning arborescences. In this paper we obtain a proof of this theorem by considering sequences over a finite alphabet, and we show that the theorem emerges from the generating function for a certain type of sequence. The generating function for the set of sequences is obtained as the solution of a linear system of equations in Section 2. The power series expansion for the solution of this system is obtained by means of the multivariate form of the Lagrange theorem for implicit functions, and is given in Section 3, together with a restatement of the theorem as a matrix identity.
Unitaries in Simple Artinian Rings
Authors: Chacron M.
Published: December 2010

Let R be a 2-torsion free simple artinian ring with involution*. The element u of R is said to be unitary if u is invertible with inverse u*. In this paper we shall be concerned with the subalgebras W of R over its centre Z such that uWu* ⊆ W, for all unitaries u of R. We prove that if R has rank superior to 1 over a division ring D containing more than 5 elements and if R is not 4-dimensional then any such subalgebra W must be one of the trivial subalgebras 0, Z or R, under one of the following extra finiteness assumptions: W contains inverses, W satisfies a polynomial identity, the ground division ring D is algebraic, the involution is a conjugate-transpose involution such that D equipped with the induced involution is generated by unitaries.
The Order of Inseparability of Fields
Authors: Deveney James K. , Mordeson John N.
Published: December 2010

Let L be a finitely generated field extension of a field K of characteristic p ≠ 0. By Zorn's Lemma there exist maximal separable extensions of K in L and L is finite dimensional purely inseparable over any such field. If ps is the smallest of the dimensions of L over such maximal separable extensions of K in L, then s is Wiel's order of inseparability of L/K [11]. Dieudonné [2] also investigated maximal separable extensions D of K in L and established that there must be at least one D such that L ⊆ Kp–∞(D) (such fields are termed distinguished). Kraft [5] showed that the distinguished maximal separable subfields are precisely those over which L is of minimal degree. This concept of distinguished subfield has been the basis of a number of results on the structure of inseparable field extensions, for example see [1], [3], [5], and [6].
Neighbor Relation and Neighbor Homomorphism of Hjelmslev Groups
Authors: Knüppel Frieder , Kunze Michael
Published: December 2010

The geometry of Hjelmslev groups is a comprehensive plane metric geometry. It supplies, for example, an approach to euclidean, hyperbolic, elliptic, Minkowskian and Galilean geometry.

The subject of this geometry are Hjelmslev groups and their group planes. (The definition of Hjelmslev groups and some basic concepts and propositions of this theory can be found in the second edition of Bachmann's book [1] (pages 318-328). A similar report in English is the lecture [3]. A comprehensive introduction is developed in the key work [2]. The first part of this work was translated by Garner [4]. An abstract is given in Math. Rev. 52, 9066 (1976).) The group plane arises from giving geometric names to some group theoretical facts. The group plane of a Hjelmslev group is an incidence structure with orthogonality, and the Hjelmslev group acts on this plane as a group of motions.
L-Indistinguishability For SL (2)
Authors: Labesse J-P. , Langlands R. P.
Published: December 2010

The notion of L-indistinguishability, like many others current in the study of L-functions, has yet to be completely defined, but it is in our opinion important for the study of automorphic forms and of representations of algebraic groups. In this paper we study it for the simplest class of groups, basically forms of SL(2). Although the definition we use is applicable to very few groups, there is every reason to believe that the results will have general analogues [12].

The phenomena which the notion is intended to express have been met–and exploited–by others (Hecke [5] § 13, Shimura [17]). Their source seems to lie in the distinction between conjugacy and stable conjugacy. If F is a field, G a reductive algebraic group over F, and the algebraic closure of F then two elements of G(F) may be conjugate in without being conjugate in G(F).
A Remark on Disintegrations With Almost All Components Non -Additive
Authors: Dang-Ngoc Nghiem
Published: December 2010

We extend a theorem of L. E. Dubins on “purely finitely additive disintegrations” of measures (cf. [4]) and apply this result to the disintegrations of extremal Gibbs states with respect to the asymptotic algebra enlarging another result of L. E. Dubins on the symmetric coin tossing game.

We recall the following definition of L. E. Dubins (cf. [3], [4]): Let (X , , μ) be a measure space, a sub σ-algebra of . A real function σx (A), is called a measurable-disintegration of μ if:

(i) ∀x ∊ X , σx(.) is a finitely additive measure .

(ii) ∀A ∊ , σ. (A) is constant on each -atom.

(iii) For each A ∊ , σ. (A) is measurable with respect to the completion of by μ and

(iv)σx(B) = 1 if x ∊ B ∊ .
Remarks on k-Leviflat Complex Manifolds
Authors: Gilligan B. , Huckleberry A.
Published: December 2010

In the theory of functions of several complex variables one is naturally led to study non-compact complex manifolds which have certain types of exhaustions. For example, on a Stein manifold X there is a strictly plurisubharmonic function ϕ: X → R+ so that the pseudoballs Bc = {φ < c } exhaust X. Conversely, a manifold which has such an exhaustion is Stein. The purpose of this note is to study a class of manifolds which have exhaustions along the lines of those on holomorphically convex manifolds, namely the k-Leviflat complex manifolds. Unlike the Stein case, the Levi form may have positive dimensional 0-eigenspaces. In the holomorphically convex case these are tangent to the generic fiber of the Remmert reduction.
The Group of Units in K-Theory Modulo an Odd Prime
Authors: Steiner R. J.
Published: December 2010

1. Introduction. There are several multiplicative cohomology theories for which the group of units in the zeroth term is the zeroth term of another cohomology theory. Examples, due to Segal, May and others, are given by ordinary cohomology with rather general graded coefficients, real and complex K-theory with integral coefficients, and various bordism theories, also with integral coefficients [8, 7, 2, 5, IV]. The object of this paper is to show that complex K-theory modulo an odd prime p provides a counter-example.

To state the theorem precisely we recall the result of Araki and Toda that there is a unique anticommutative associative admissible multiplication in K*( ;Z/p) for p an odd prime [3, 3, 7, 10]; admissible is defined in [3] and means essentially that the reduction homomorphism K*( ) → K*( ; Z/p) preserves products.
Levitzki Radical for certain Varieties
Authors: Pokrass David
Published: December 2010

Let A be a nonassociative algebra. We let An denote the subalgebra generated by all products of n elements from A. Inductively we define A(0) = A and A(n+1) = (A(n))2. We say that A is nilpotent if, for some n, An = {0}. A is solvable if A(n) = {0} for some n. An algebra is locally nilpotent (locally solvable) if each finitely generated subalgebra is nilpotent (solvable). In this paper will always be some variety of algebras defined by a set of homogeneous identities. We say that local nilpotence is a radical property in if each contains a maximal locally nilpotent ideal L and A/L has no non-zero locally nilpotent ideals. The ideal L is then called the Levitzki radical of A.
Quadratic forms over Quadratic Extensions of Fields with Two Quaternion Algebras
Authors: Cordes Craig M. , Ramsey John R.
Published: December 2010

In this paper, we analyze what happens with respect to quadratic forms when a square root is adjoined to a field F which has exactly two quaternion algebras. There are many such fields—the real numbers and finite extensions of the p-adic numbers being two familiar examples. For general quadratic extensions, there are many unanswered questions concerning the quadratic form structure, but for these special fields we can clear up most of them.

It is assumed char F ≠ 2 and K = F (√a) where a ∊ Ḟ – Ḟ2. Ḟ denotes the non-zero elements of F. Generally the letters a, b, c, … and α, β, … refer to elements from Ḟ and x, y, z, … come from .
Dispersed Factorization Structures
Authors: Herrlich H. , Salicrup G. , Vazquez R.
Published: December 2010

Factorization structures on a category form a useful categorical tool. As is known, any , satisfying suitable completeness—and smallness—conditions, has a sufficient supply of factorization structures; in fact, there is a bijection between the class of all epireflective (full and isomorphism- closed) subcategories of and the class of all so called perfect factorizationstructures of In this paper, for an arbitrary category supplied with a fixed factorization structure (E, M), a similar bijection between the class of all E-reflective (full and isomorphism-closed) subcategories of and the class of all (E, M)-dispersed factorization structures on , introduced in this paper, will be established.
Subgroups of the Power Semigroup of a Finite Semigroup
Authors: Putcha Mohan S.
Published: December 2010

Throughout this paper, S will denote a finite semigroup and Z+ the set of positive integers. E = E(S) denotes the set of idempotents of S. Let . If , then let AB = {ab| a ∈ A, b ∈ B}. has been studied by many authors, including [2, 3, 5, 6, 7]. If X is a set, then |X| denotes the cardinality of X. For undefined terms in this paper, see [1,4].

THEOREM 1. Let I be an ideal of S, a subgroup of . Then has a normal subgroups such that is isomorphic to a subgroup of and is isomorphic to a subgroup of .
A Decomposition for Sets Having a Segment Convexity Property
Authors: Breen Marilyn
Published: December 2010

Let 5 be a subset of Euclidean space. The set 5 is said to be m-convex, m ≥ 2, if and only if for every m distinct points of S, at least one of the line segments determined by these points lies in 5. Clearly any union of m mdash — 1 convex sets will be m-convex, yet the converse is false. However, several decomposition theorems have been proved which allow us to write any closed planar m-convex set as a finite union of convex sets, and actual bounds for the decomposition in terms of m have been obtained ([6], [4], [3]). Moreover, with the restriction that (int cl S) ∼ S contain no isolated points, an arbitrary planar m-convex set S may be decomposed into a finite union of convex sets ([1].

Here we strengthen the m-convexity condition to define an analogous combinatorial property for segments.
Non-Amphicheiral Codimension 2 Knots
Authors: González-Acuña F. , Montesinos José M.
Published: December 2010

An n-knot (Sn+2, Sn) is amphicheiral if there is an orientation reversing autohomeomorphism of Sn+2 leaving Sn invariant as a set. It is invertible if there is an orientation preserving autohomeomorphism of Sn+2 whose restriction to Sn is an orientation reversing autohomeomorphism of Sn onto itself. In 1961 Fox [8, Problem 35] asked if there exist non-amphicheiral locally flat 2-knots. We will prove the following THEOREM 1. For any integer n there are smooth n-knots which are neither amphicheiral nor invertible.

A knot (Sn+2, Sn) is + amphicheiral (resp. —amphicheiral) if there is an orientation reversing autohomeomorphism f of Sn+2 leaving Sn invariant such that f| Snpreserves (resp. reverses) orientation.
Generalized Directional Derivatives and Subgradients of Nonconvex Functions
Authors: Rockafellar R. T.
Published: December 2010

Studies of optimization problems and certain kinds of differential equations have led in recent years to the development of a generalized theory of differentiation quite distinct in spirit and range of application from the one based on L. Schwartz's “distributions.” This theory associates with an extended-real-valued function ƒ on a linear topological space E and a point x ∈ E certain elements of the dual space E* called subgradients or generalized gradients of ƒ at x. These form a set ∂ƒ(x) that is always convex and weak*-closed (possibly empty). The multifunction ∂ƒ: x →∂ƒ(x) is the sub differential of ƒ.

Rules that relate ∂ƒ to generalized directional derivatives of ƒ, or allow ∂ƒ to be expressed or estimated in terms of the subdifferentials of other functions (whenƒ = ƒ1 + ƒ2,ƒ = g o A, etc.), comprise the sub differential calculus.
The Duality of Distributive Continuous Lattices
Authors: Banaschewski B.
Published: December 2010

Various aspects of the prime spectrum of a distributive continuous lattice have been discussed extensively in Hofmann-Lawson [7]. This note presents a perhaps optimally direct and self-contained proof of one of the central results in [7] (Theorem 9.6), the duality between distributive continuous lattices and locally compact sober spaces, and then shows how the familiar dualities of complete atomic Boolean algebras and bounded distributive lattices derive from it, as well as a new duality for all continuous lattices. As a biproduct, we also obtain a characterization of the topologies of compact Hausdorff spaces.

Our approach, somewhat differently from [7], takes the open prime filters rather than the prime elements as the points of the dual space. This appears to have conceptual advantages since filters enter the discussion naturally, besides being a well-established tool in many similar situations.
Some Properties of the q-Hermite Polynomials
Authors: Allaway WM. R.
Published: December 2010

Heine [7, p. 93] gave the following representation for the Legendre Polynomial {Pn(x)}∞n=o

where fo,n = 1 and

Szegö [7, p. 96] generalized this result to the Ultraspherical Polynomial set ﹛Cnλ(x)﹜∞n=o and obtained

where