bluuebunny/crossref_metadata_2025 huggingface dataset:
Some Characterizations of The Projection Property in Archimedean Riesz Spaces
Authors: Kutty K. K. , Quinn J.
Published: December 2010

In this paper we give some new characterizations of the projection property in Archimedean Riesz spaces. Our approach primarily explores the interrelationships between such things as the band structure or the prime ideal structure of an Archimedean vector lattice and corresponding structures of its Dedekind completion. Our results show that, in general, there is a ‘strong“ relationship if and only if the original vector lattice has the projection property. The main result of this paper is Theorem 2.6 which both summarizes and extends all of the results we obtain prior to it.
Involutory Matrices Over Finite Local Rings
Authors: McDonald B. R.
Published: December 2010

A square matrix A over a commutative ring R is said to be involutory if A2 = I (identity matrix). It has been recognized for some time that involutory matrices have important applications in algebraic cryptography and the special cases where R is either a finite field or a quotient ring of the rational integers have been extensively researched. However, there has been no detailed attempt to extend the theory to all finite commutative rings. In this paper we illustrate in detail the theory of involutory matrices over finite commutative rings with 1 having odd characteristic. The method is a careful analysis of finite local rings of odd prime power characteristic. The techniques might be also used in the examination of involutory matrices over local rings of characteristic 2λ; however, as illustrated by finite fields of characteristic 2 and Z/2λZ (Z the rational integers), the arguments are basically different. The reader will note the methods are not limited to only questions on involutory matrices.
Condition that All Irreducible Representations of a Compact Lie Group, if Restricted to a Subgroup, Contain no Representation More than Once
Authors: Goldrich Fredric E. , Wigner Eugene P.
Published: December 2010

One of the results of the theory of the irreducible representations of the unitary group in n dimensions Un is that these representations, if restricted to the subgroup Un-1 leaving a vector (let us say the unit vector e1 along the first coordinate axis) invariant, do not contain any irreducible representation of this Un-1 more than once (see [1, Chapter X and Equation (10.21)]; the irreducible representations of the unitary group were first determined by I. Schur in his doctoral dissertation (Berlin, 1901)). Some time ago, a criterion for this situation was derived for finite groups [3] and the purpose of the present article is to prove the aforementioned result for compact Lie groups, and to apply it to the theory of the representations of Un.
S-Maximal Subgroups of πl(M3)
Authors: Feustel C. D.
Published: December 2010

Let M be a compact, connected, irreducible 3-manifold. Let S be a closed, connected, 2-manifold other than the 2-sphere or projective plane. Let f be a map of S into M such that

Suppose for every closed, connected surface S1 and every map g:S1 → M such that

(1) is an injection,

(1)

Then we shall say that the subgroup is a surface maximal or S-maximal subgroup of π1(M). We may also say that the map f is S-maximal.

Let M be an irreducible 3-manifold which does not admit any embedding of the projective plane. Then we shall say that M is p2-irreducible. Throughout this paper all spaces will be simplicial complexes and all maps will be piecewise linear.
On Multipliers with Unconditionally Converging Fourier Series
Authors: Bachelis Gregory F. , Pigno Louis
Published: December 2010

Let G be a compact abelian group with dual group Γ. For 1 ≦ p < ∞, 1 ≦ q < ∞, let denote the Banach space of complex-valued functions on Γ which are multipliers of type (p, q) and the subspace of compact multipliers.

Grothendieck [10; 11] has proven that a function in LP(G), 1 ≦ p < 2, has an unconditionally converging Fourier series in LP(G) if and only if it is in L2(G), and Helgason [12] has proven that the derived algebra of LP(G), 1 ≦ p < 2, is L2(G). Using these results we show in § 2 that a multiplier of type (p, g), 1 ≦ p ≦ 2, 1 ≦ q ≦ 2, has an unconditionally converging Fourier series in if and only if it is in (Theorem 2.1), and that, for 1 ≦ p ≦ q ≦ 2, the derived algebra of is (Theorem 2.2). Statements equivalent to the above are also given.
Representation of Algebras with Involution
Authors: Maxwell George
Published: December 2010

Let K be a field with an involution J. A
*-algebra over K is an associative algebra
A with an involution * satisfying (α.a)* =
αJ.a*. A large class of
examples may be obtained as follows. Let (V, φ) be an
hermitian space over K consisting of a vector space
V and a left hermitian (w.r.t. J) form
φ on V which is nondegenerate in the
sense that φ(V,v) = 0 implies v
= 0. An endomorphism f of V
may have an adjoint f* w.r.t. φ, defined by
φ(f(u),v)
= φ(u,f*(v)); due to the nondegeneracy of
φ, f* is unique if it exists. The set B(V,
φ) of all endomorphisms of V which do have an
adjoint is easily verified to be a *-algebra.
δ-Continuous Selections of Small
Multifunction
Authors: Schirmer Helga
Published: December 2010

A multifunction φ : X → Y from a
topological space X into a topological space
Y is a correspondence such that φ(x) is
a non-empty subset of Y for every x ∊ X. A
single-valued function f : X → Y is called
a selection of φ if f(x)
∊ φ(x) for all x ∊ X; it is called a
continuous selection if f is continuous. It is well-known
that not every semi-continuous or even continuous multifunction has a
continuous selection (see e.g. [4] for a survey on selection
theory).

We investigate here some connections between multifunctions which are
'almost single-valued” and selections which are ‘almost continuous”.
The Extent of the Sequence Space Associated with a
Basis
Authors: Ruckle William H.
Published: December 2010

The associated sequence space S of a sequence of vectors
{xn} in a Banach space consists of all scalar sequences
(sn) for which converges.
My primary motivation in writing this paper was to present a new proof to a
recent theorem of N. I. and V. I. Gurarii concerning limits of extent on
S when {xn} is a basis of a uniformly convex or a uniformly smooth Banach
space [5], This theorem is stated as Theorem 2.4. Several
interesting consequences of this theorem were noted by N. I. Gurarii in
[3] and [4].
Absolute Continuity of Some Vector Functions and
Measures
Authors: Knight William J.
Published: December 2010

In the theory of vector valued functions there is a theorem which states
that if a function from a compact interval I into a normed
linear space X is of weak bounded variation, then it is of
bounded variation. The proof uses in a straightforward way the Uniform
Boundedness Principle (see [2, p. 60]). The present paper grew
from the question of whether an analogous theorem holds for absolutely
continuous functions. The answer is in the negative, and an example will be
given (Theorem 7). But it will also be shown that if X is
weakly sequentially complete (e.g. an Lp space, 1 ≦ p < ∞ ), then a weakly absolutely
continuous point function from / into X is absolutely
continuous. The method of proof involves the construction of a countably
additive set function in the standard Lebesgue-Stieltjes fashion.

The paper is divided into three parts. In Section 1 extensions of finitely
additive, absolutely continuous set functions are carried out in an abstract
setting. Section 2 applies this to vector valued (point) functions on the
real line.
Integral Means and Zero Distributions of Blaschke
Products
Authors: Linden C. N.
Published: December 2010

A sequence {zn} in D = {z: |z|
< 1} is a Blaschke sequence if and only if

If 0 appears m times in {zn}
then

is the Blaschke product defined by {zn}. The set
of all Blaschke products will be denoted by . If B ∊ it is well-known that B is regular
in D, and |B(z, {zn})| < 1 when z ∊ D.

For a given pair of values p in (0, ∞) and
q in [0, ∞) we denote by ℐ(p,
g) the class of all Blaschke products
B(z, {zn}) such that

as r → 1 — 0. In the case q ≦ max(p — 1,0) the
classes of functions B and ℐ(p,
q) are identical: this is a particular case of an elementary
theorem for functions subharmonic in a disc, the analogous theorem for
functions subharmonic in a half-plane appearing in [1],
Generalisation de la Formule de Riemann-Hurwitz
Authors: Van Quê Ngô
Published: December 2010

Etant un polynôme Φ ∊ R[X1 … ,Xn] à n
indéterminés, Φ est dit de poids homogène m si

avec m =

Si E est un fibre vectoriel complexe de rang
n (i.e., n est la dimension sur
C de la fibre Ex) sur une
variété differentiate orientée compacte M de dimension
m, à tout polynôme Φ à n indéterminés
de poids homogène m, on associe un nombre de Chern:

où [M] est le cycle fondamental défini par l'orientation de
M et Ci(E) la ième classe de
Chern de E. Dans le cas où le poids homogène de Φ est
différent de la dimension de M, on pose: Φ(E, M)
= 0.
Cyclic Maps From Suspensions to Suspensions
Authors: Hoo C. S.
Published: December 2010

In [7] Varadarajan denned the notion of a cyclic map f
: A → X. The collection of all homotopy classes of such cyclic
maps forms the Gottlieb subset G(A, X) of
[A, X]. If A = S1 this reduces to the group G(X,
X0) of Gottlieb [5]. We show that a cyclic map
f maps ΩA into the centre of
ΩX in the sense of Ganea [4]. If
A and X are both suspensions, we then
show that if f : A → X
maps ΩA into the centre of ΩX, then
f is cyclic. Thus for maps from suspensions to
suspensions, Varadarajan's cyclic maps are just those maps considered by
Ganea. We also define G (Σ4, ΣX) in terms
of the generalized Whitehead product [1], This gives the
computations for G(Sn+k, Sn) in terms of Whitehead products in
π2n+k(Sn).

We work in the category of spaces with base points and having the homotopy
type of countable CW-complexes. All maps and homotopies are
with respect to base points. For simplicity, we shall frequently use the
same symbol for a map and its homotopy class.
The Equality (A∩B)n=An∩Bnfor Ideals
Authors: Gilmer Robert , Grams Anne
Published: December 2010

LetDbe an integral domain with identity, and letRbe a commutative ring. Ifnis a positive integer,Rwill be said tohave property (n), (n)′,or(n)″according as

property(n):For anyx, y∊R,(x,y)n= (xn, yn).

property(n)′: For anyx ∊ Rand any idealAofRsuch that xn∊ An, it follows thatx ∊ A.

property(n)′: For any idealsA, BofR, (A∩ B)n= An∩ Bn.

J. Ohm introduced property (n) in [7] in connection with the question: Ifn≦ 2 and ifDhas property (n), mustDbe a Prüfer domain? (The integral domainDwith identity is a Prüfer domain if each nonzero finitely generated ideal ofDis invertible; equivalently,DPis a valuation ring for each proper prime idealPofD.)Prior to Ohm's paper, it was known that ifDhas property (2) and ifDis integrally closed, thenDis Prüfer.
Maximal Quotient Rings and
S-Rings
Authors: Armendariz E. P. , McDonald Gary R.
Published: December 2010

Throughout, we assume all rings are associative with identity and all
modules are unitary. See [7] for undefined terms and [3] for
all homological concepts.

Let R be a ring, E(R) the
injective envelope of RR, and H =HomR(E(R),E(R)).
Then we obtain a bimodule RE(R)H. Let Q = HomH(E(R), E(R)). Q
is called the maximal left quotient ring of R. Q has the
property that if p, q ∈ Q, p ≠ 0, then
there exists r ∈ R such that
rp ≠ 0, rq ∈ R, i.e.,
Q is a ring of left quotients of R.

A left ideal I of R is
dense if for every x,y ∈ R,x ≠ 0, there
exists r ∈ R such that rx
≠ 0, ry ∈ I. An alternate description of Q is Q
= {x ∈ E(RR) : (R :
x) is a dense left ideal of R{, where (R : x) =
{r ∈ R : rx ∈ R}.

The left singular ideal of R is Zl(R) =
{r ∈ R : lR(r) is an essential left ideal of R},
where lR(r) = {x ∈ R : xr = 0}. If
Zl(R) = (0), then Q is a
left self-injective von Neumann regular ring [7, § 4.5]. Most of the
previous work on maximal left quotient rings has been done in this case.
Polynomial Rings with the Outer Product Property
Authors: Geramita A. V.
Published: December 2010

In [3] Lissner defined a class of rings called outer
product rings, (OP-rings). These are commutative rings
R with identity for which every
exterior vector is
decomposable, i.e., with
.

If we look only at those vectors whose
co-ordinates with respect to any basis of generate
the unit ideal in R and consider those rings
R for which all vectors of this type are decomposable,
we obtain the class of rings which have been referred to as Her
mite-rings (H-rings, see also Lissner
[3]). This class of H-rings evidently
contains the class of OP-rings.
The Hardy Space H1 on Manifolds and Submanifolds
Authors: Strichartz Robert S.
Published: December 2010

It is well-known that the space L1(Rn) of integrable functions on Euclidean space fails to be preserved by
singular integral operators. As a result the rather large
Lp theory of partial differential equations also fails for p
= 1. Since L1 is such a natural space, many substitute spaces have been
considered. One of the most interesting of these is the space we will denote
by H1(Rn) of integrable functions whose Riesz transforms are
integrable.
Counterexample to a Conjecture on Positive Definite
Functions
Authors: Stewart James
Published: December 2010

Cooper [1] called a complex-valued function f
on the real line Rpositive definite for F, where F is a set
of complex-valued functions on R, if the integral

exists as a Lebesgue integral and is nonnegative for every
ϕ in F. Let us denote by
P(F) the set of functions positive definite for
F, by the set of
functions in LP(R) with compact
support, and by the set of
functions which are locally in LP(R), i.e.,
for every
compact subset K of R. Cooper showed that
for any
p ≧ 2 and that each function in is essentially bounded and hence equal almost
everywhere to an ordinary continuous positive definite function in the sense
of Bochner.
Automorphism Groups of Algebras of Finite Type
Authors: Gould Matthew
Published: December 2010

By “algebra” we shall mean a finitary universal algebra, that is, a pair 〈A; F〉 where A and F are nonvoid sets and every element of F is a function, defined on A, of some finite number of variables. Armbrust and Schmidt showed in [1] that for any finite nonvoid set A, every group G of permutations of A is the automorphism group of an algebra defined on A and having only one operation, whose rank is the cardinality of A. In [6], Jónsson gave a necessary and sufficient condition for a given permutation group to be the automorphism group of an algebra, whereupon Plonka [8] modified Jonsson's condition to characterize the automorphism groups of algebras whose operations have ranks not exceeding a prescribed bound.
Domains of Paracompactness and Regularity
Authors: MacDonald S. , Willard S.
Published: December 2010

Given a class of topological spaces and a class of maps of topological spaces, our interest is in characterization of the class () of topological spaces whose every -image lies in . The class () is referred to as the -resolvent of and is the largest class of spaces smaller than closed under -images (provided is closed under composition and includes identity maps).

In the present paper, will be either the class of paracompact spaces or the class of regular spaces, and the conditions determining will always include separation axioms on the range, some of which can be dispensed with now by agreeing that all spaces are Hausdorff.
The Existence of Quadratic Differentials in Simply Connected Regions of the Complex Plane
Authors: Grassmann E.
Published: December 2010

The general coefficient theorem [2] and the extended general coefficient theorem [3] state that the existence of certain quadratic differentials is a sufficient condition for a function to be a solution of certain extremum problems. The purpose of this paper is to show that in the case of simply connected regions this condition is also necessary.

We shall do this by a variational method of the Schiffer-Golusin-type. The main difficulty is, that the class of admissible functions for the general coefficient theorem is restricted and we must therefore have a method of variation with restrictions.
A Note on Generalized Direct Products of Groups
Authors: Schick Marlene
Published: December 2010

In [1] Tang proved that the generalized direct product of a finite set of cyclic groups amalgamating subgroups which satisfy certain compatibility conditions always exists. In the proof, Theorem 4.1 is made use of. However, this theorem is not correct since we can construct examples of groups which satisfy the conditions of Theorem 4.1, but whose generalized direct product does not exist. Therefore, a modification of this result as pointed out by Professor Tang is given here, together with the resulting modification of the proof of the result stated above.
On the Peano Derivatives
Authors: Bullen P. S. , Mukhopadhyay S. N.
Published: December 2010

Let f be a real valued function defined in some neighbourhood of a point x. If there are numbers α1, α2, … αr-1, independent of h such that

then the number αk is called the kth Peano derivative (also called kth de la Vallée Poussin derivative [6]) of f at x and we write αk = fk(x). It is convenient to write α0 = f0(x) = f(x). The definition is such that if the mth Peano derivative exists so does the nth for 0 ≦ n ≦ m.
L'enveloppe de Translations d'un Demi-Treillis de Groupes
Authors: Petrich Mario
Published: December 2010

L'enveloppe de translations d'un demi-groupe présente un intérêt particulier pour les deux raisons suivantes : d'une part, elle apparaît d'une façon naturelle dans la construction des extensions idéales des demi-groupes, et d'autre part, elle est souvent utilisée pour des caractérisations abstraites des demi-groupes. Afin de l'appliquer aux problèmes particuliers, il est important de fournir des constructions qui, pour un demi-groupe donné sous une forme ou une autre, soient aussi explicites que possible. Un exemple d'une telle construction est celle de l'enveloppe de translations d'un demi-groupe de matrices de Rees (voir [4]) et ses nombreuses applications [5 ; 6 ; 7 ; 8].
Oscillation Criteria for y"" + p(t)f(y,y’) = 0 with f Homogeneous of Degree One
Authors: Gustafson G. B.
Published: December 2010

Let be the class of functions f : R2 → R satisfying (1) f is continuous, (2) for all t, x, y ∈ R, (4) f is locally Lipschitzian. The classical Sturm theorems, the Leighton-Wintner oscillation theorem, and perturbation theorems have been established by Bihari in [1; 2; 3] for the equation , .

This paper investigates the question of strong oscillation of

(1.1)

for p ∈ C[0, ∞ ), f ∈ . The equation is viewed as “almost linear” because of the homogeneity and sign conditions on f.
Covering Theorems for Classes of Univalent Functions
Authors: Aharonov Dov , Kirwan W. E.
Published: December 2010

Let denote the class of functions f(z) = z + that are analytic and univalent in and will denote the collection of f ∈ that map U onto a domain that is respectively starlike with respect to the origin and convex.

In [4, p. 85] Hayman used Steiner symmetrization to solve a problem, a special case of which is the following.
The Homology of Uniform Spaces
Authors: Bahauddin Mohammed , Thomas John
Published: December 2010

In the past thirty years, algebraic topologists have developed a great body of knowledge concerning the category of topological spaces. By contrast, corresponding problems in the category of uniform spaces have been barely touched. Lubkin [8] studied the notion of a covering space in the category of generalized uniform spaces, and suggested that much of algebraic topology could be profitably studied in this category. Deming [2] discussed the fundamental group of a generalized uniform space, and related it to the first Čech homology group. A slightly different version of Cech cohomology was defined by Kuzminov and Svedov in [7] and related to the dimension theory of uniform spaces.
The Character Tables for SL(3, q), SU(3, q2), PSL(3, q), PSU(3, q2)
Authors: Simpson William A. , Frame J. Sutherland
Published: December 2010

In this paper the character table of GL(3, q) (U(3, q2)), the group of all nonsingular n × n (unitary) matrices over GF(q) (GF(q2)), is used to obtain the character tables for the related subgroups SL(3, q), PSL(3, q) (SU(3, q2), PSU(3, q2)), the corresponding groups of matrices of determinant unity and the projective group respectively. There are very few abstract character tables which hold for entire families of groups. Such tables are of much greater value than tables for specific groups because, among other things, they enable one to discern various patterns common to the whole family.
The Common Points of Families of Normal Functions
Authors: Abian Alexander
Published: December 2010

In this paper we show that the common points of any nonempty “family“ of normal functions form a normal function and from this we derive various significant consequences such as Theorem 2 below.
Inclusion Theorems forK-Spaces
Authors: Bennett G. , Kalton N. J.
Published: December 2010

Asequence spaceis a vector subspace of the space ω of all real (or complex) sequences. A sequence spaceEwith a locally convex topologyτis called aK- spaceif the inclusion mapE →ω is continuous, when ω is endowed with the product topology. A K-spaceEwith a Frechet (i.e., complete, metrizable and locally convex) topology is called anFK-space;if the topology is a Banach topology, thenEis called aBK-space.
Abelian Groups in Which Every α-Pure Subgroup is β-Pure
Authors: Moore J. Douglas , Hewett Edwin J.
Published: December 2010

The determination of the abelian groups in which every neat subgroup is pure is a relatively routine exercise (see [6]). There are numerous problems of this type; for example, the determination of the groups in which every pure subgroup is isotype or the groups in which every subgroup is isotype. These are all special cases of the general problem of determining the abelian groups in which every α-pure subgroup is β-pure for arbitrary ordinal numbers α and β. The solution of this general problem is the object of this paper.
Quadratic Irrationals in the Lower Lagrange Spectrum
Authors: Davis Nancy , Kinney J. R.
Published: December 2010

We let , where the xi are positive integers and i ∈ N, the set of all integers. We define , where where . We let = [0; x1, x2, … ] where

We let

and define

The range of L(ξ) is known as the Lagrange spectrum and the range of M(ξ) as the Markov spectrum. It is known that both are closed and that the Markov spectrum includes the Lagrange spectrum.
A Procedure for Improving the Upper Bound for the Number of n-Ominoes
Authors: Klarner D. A. , Rivest R. L.
Published: December 2010

We begin with some definitions and a formulation of the problem treated in subsequent sections. Also included in this section is a brief indication of some of the known results dealing with the n-omino enumeration problem. Some of what follows together with more details may be found in [3] or [4].
Rigid and Finitely V-Determined Germs of C∞-Mappings
Authors: Bochnak Jacek , Kuo Tzee-Char
Published: December 2010

Let (respectively ) denote the ring of germs at 0 ∈ Rn of all C∞ functions (respectively Cμ functions) from Rn to R. For a given where is the space of all germs of C∞ mappings Rn → Rp, let J(φ) denote the ideal in generated by φ1, … , φp and the Jacobian determinants

where Let

Clearly, is an ideal in and where is the (unique) maximal ideal of .
Chromatic Sums for Rooted Planar Triangulations, III: The Case λ = 3
Authors: Tutte W. T.
Published: December 2010

In this paper we are chiefly concerned with the chromatic sums we have called l and h, with colour-number 3. In this case h can be interpreted as enumerating the rooted Eulerian triangulations with a given number of faces, and l as enumerating such triangulations with a given number of faces and a given valency for the root-vertex. The series h has been determined already, by summation from the formula enumerating even slicings [3]. However our formula for l does not seem to have been published before, though it could presumably be derived in a similar way.
Spectral Properties for Invertible Measure Preserving Transformations
Authors: Belley Jean-Marc
Published: December 2010

An invertible measure preserving transformation T on the unit interval I generates a unitary operator U on the space L2(I) of Lebesque square integrable functions given by (Uf)(x) = f(Tx) for all f in L2(I) and x in I. By definition

for all f , g in L2(I), the bar denoting complex conjugation.
Residual Finiteness of Commutative Rings and Schemes
Authors: Simis Aron
Published: December 2010

This work grew out of a preliminary announcement (Notices of the Amer. Math. Soc. 18 (1971)). Here we modify the definition of residual finiteness given in [2]. This allows us, first of all, to consider a broader class of rings which are “essentially” residually finite and, secondly, to extend the notion to schemes. We then show that, for various topologies on the category of schemes, our notion of residual finiteness is local so that all relevant questions appear already at the ring level.
Direct Sums of Torsion-Free Covers
Authors: Cheatham Thomas
Published: December 2010

In [4, Theorem 4.1, p. 45], Enochs characterizes the integral domains with the property that the direct product of any family of torsion-free covers is a torsion-free cover. In a setting which includes integral domains as a special case, we consider the corresponding question for direct sums. We use the notion of torsion introduced by Goldie [5]. Among commutative rings, we show that the property “any direct sum of torsion-free covers is a torsion-free cover“ characterizes the semi-simple Artinian rings.
A Necessary and Sufficient Condition for the Oscillation of an Even Order Nonlinear Delay Differential Equation
Authors: Singh Bhagat
Published: December 2010

In this paper we study the oscillatory behavior of the even order nonlinear delay differential equation

(1)

where

(i)denotes the order of differentiation with respect tot. The delay termsτiσiare assumed to be real-valued, continuous, non-negative, non-decreasing and bounded by a common constantMon the half line (t0, + ∞ ) for somet0≧ 0.
Finitely Generated Subgroups of HNN Groups
Authors: Burns R. G.
Published: December 2010

In this paper we give sufficient conditions for an HNN group to have the following two properties:

(1) any two finitely generated subgroups intersect in a finitely generated subgroup;

(2) every finitely generated subgroup containing a non-trivial subnormal subgroup has finite index.

The following result is a particular case of the main theorem.
A Dual View of the Clifford Theory of Characters of Finite Groups, II
Authors: Roth Richard L.
Published: December 2010

This paper continues the analysis of Clifford theory for the case of a finite group G, K a normal subgroup of G and G/K abelian which was developed in [7]. In [7] the permutation actions of G/K on the characters of K and of (G/K)^ on the characters of G were studied in relation to their effects on induction and restriction of group characters.
Sous-Modules Purs et Sommantes Directes
Authors: Lemaire Claude
Published: December 2010

Ce travail donne des conditions sous lesquelles un sousmodule pur de M est une sommante directe, non nécessairement de M luimême, mais d'un sous-module “proche” de celui-ci. (M est supposé sans torsion, dans un certain sens.) Ces conditions sont exprimées à partir d'un module H d'endomorphismes du mondule des fractions de M, étroitement lié à la notion d'“endomorphisme partiel” d'un module sans torsion, introduite par Fuchs [3] et que nous avons étudiée dans [5] et [6].
On the Distribution of Square-Free Numbers
Authors: Hooley C.
Published: December 2010

Erdös [1] has shown that, if the square-free numbers in ascending order be denoted by s1, s2, … , sn, … , then for 0 ≦ γ ≦ 2

as x → ∞. In this paper we shall extend this result by proving that the asymptotic formula in fact holds for the wider range 0 ≦ γ ≦ 3.

Similar results have been obtained previously by the author in respect of both the sequence of numbers expressible as the sum of two squares and also sequences of numbers relatively prime to given large integers, although the method used here differs from that of the earlier papers [2; 3].
Semi-Metrics on the Normal States of a W*-Algebra
Authors: Promislow David
Published: December 2010

This paper is concerned with some extensions of the Bures metric d defined on the set of normal states of a W*-algebra [2]. Each subgroup G of the automorphism group of leads naturally to a semi-metric dG. (See Definition 1.1 below.) When G is the identity group dG = d.
Derived Ring Isomorphisms of Von Neumann Algebras
Authors: Miers C. Robert
Published: December 2010

Let M be an associative *-algebra with complex scalar field. M may be turned into a Lie algebra by defining multiplication by [A, B] = AB - BA. A Lie *-subalgebra L of M is a *-linear subspace of M such that if A, B ∈ L then [A,B] ∈ L. A Lie *-isomorphism ϕ between Lie *-subalgebras L1 and L2 of *-algebras M and N is a one-one, *-linear map of L1 onto L2 such that ϕ[A, B] = [ϕ(A), ϕ(B)] for all A , B ∈ L1.
On the Number of Structures of Reflexive and Transitive Relations
Authors: Broughan K. A.
Published: December 2010

If for each permutation the number of partial orderings fixed by that permutation is known, it is possible to count the number of non-isomorphic partial orderings on a finite set using a lemma of Burnside. In this paper it is shown that knowledge of the numbers of partial orderings fixed by permutations will enable the number of non-isomorphic pre-orderings to be counted also.
Enumerating Dissectible Polyhedra by Their Automorphism Groups
Authors: Beineke L. W. , Pippert R. E.
Published: December 2010

A dissectible polyhedron is a natural extension of a concept whose history dates back to at least 1758 and Euler [7]—the concept of a dissection of a polygon. An interesting historical survey of dissections of a polygon is given by Brown [4]. Some approaches to the classical problem have been given by Moon and Moser [9] and by Guy [8] ; the latter provides an approach which is the basis of the work in this paper. A summary of enumeration results on dissections of polygons and polyhedra by automorphism groups has been given by the authors [2].Recent extensions of the problem have been investigated in a series of papers by Brown and Tutte [3; 5; 14; 15] and b y Takeo [10; 11; 12; 13].
Prime Ideals in GCD-Domains
Authors: Sheldon Philip B.
Published: December 2010

A GCD-domain is a commutative integral domain in which each pair of elements has a greatest common divisor (g.c.d.). (This is the terminology of Kaplansky [9]. Bourbaki uses the term ''anneau pseudobezoutien" [3, p. 86], while Cohn refers to such rings as "HCF-rings" [4].) The concept of a GCD-domain provides a useful generalization of that of a unique factorization domain (UFD), since several of the standard results for a UFD can be proved in this more general setting (for example, integral closure, some properties of D[X], etc.). Since the class of GCD-domains contains all of the Bezout domains, and in particular, the valuation rings, it is clear that some of the properties of a UFD do not hold in general in a GCD-domain. Among these are complete integral closure, ascending chain condition on principal ideals, and some of the important properties of minimal prime ideals.
Entire Functions with Some Derivatives Univalent
Authors: Shah S. M. , Trimble S. Y.
Published: December 2010

This paper is a continuation of the author's previous work, [6; 7], on the relationship between the radius of convergence of a power series and the number of derivatives of the power series which are univalent in a given disc.

In particular, let D be the open disc centered at 0, and let f be regular there. Suppose that is a strictly-increasing sequence of positive integers such that each f(np) is univalent in D. Let R be the radius of convergence of the power series, centered at 0, that represents f. In [7], we investigated the connection between R and . We showed that, in general
Characterization of a Class of Equicontinuous Sets of Finitely Additive
Measures with an Application to Vector Valued Borel Measures
Authors: Oberle Richard Alan
Published: December 2010

Let V denote a ring of subsets of an abstract
space X, let R
+ denote the nonnegative reals, and let
N denote the set of positive integers. We denote by
C(V) the space of all
subadditive and increasing functions, from the ring V
into R
+, which are zero at the empty set. The space
C(V) is called the space
of contents on the ring V and elements are referred to
as contents.

A sequence of sets An
∊ V, n ∊
N is said to be dominated if there exists a set
B ∊ V such that
An
⊆ B, for n =
1, 2, A content p ∊
C(V) is said to be
Rickart on the ring V if lim
n

p(An
) = 0 for each dominated, disjoint sequence
An
∊ V, n ∊
N.
Pure N-high Subgroups, P-adic Topology and Direct Sums of Cyclic
Groups
Authors: Benabdallah Khalid , Irwin John
Published: December 2010

This paper is divided into two sections. In the first, we characterize the
subgroups N of a reduced abelian primary group for
which all pure N-high subgroups are bounded. This
condition on pure N-high subgroups occurs in several
instances, for instance, all pure N-high subgroups of a
primary group G are bounded if
G is the smallest pure subgroup of
G containing N; all
N-high subgroups are bounded if
N ≠ 0 and all N-high subgroups are closed in the
p-adic topology.
Limit Point Criteria for Differential Equations, II
Authors: Hinton Don
Published: December 2010

We consider here singular differential operators, and for convenience the
finite singularity is taken to be zero. One operator discussed is the operator
L defined by

where q
0 > 0 and the coefficients
q

t
are real, locally Lebesgue integrable functions defined on an interval
(a, b). For a given
positive, continuous weight function h, conditions are
given on the functions qi
for which the number of linearly independent solutions
y of
L(y) =
λhy (Re λ = 0)
satisfying.
A Note on the van Der Waerden Permanent Conjecture
Authors: Dubois Jacques
Published: December 2010

The permanent of an n-square complex matrix
P = (pij
) is defined by

where the summation extends over Sn
, the symmetric group of degree n. This
matrix function has considerable significance in certain combinatorial problems
[6; 7]. The properties and many related problems about the permanent are presented
in [3] along with an extensive bibliography.
Ideals and Subalgebras of a Function Algebra
Authors: Lund Bruce
Published: December 2010

Let X be a compact Hausdorff space and
C(X) the set of all
continuous complex-valued functions on X. A
function algebra A on X is a uniformly closed, point
separating subalgebra of
C(X) which contains the
constants. Equipped with the sup-norm, A becomes a Banach algebra. We let
MA
denote the maximal ideal space and
SA
the Shilov boundary.
Generators of Nest Algebras
Authors: Longstaff W. E.
Published: December 2010

A collection of subspaces of a Hilbert space is called a nest if it is totally ordered by inclusion. The set of all bounded linear operators leaving invariant each member of a given nest forms a weakly-closed algebra, called a nest algebra. Nest algebras were introduced by J. R. Ringrose in [9]. The present paper is concerned with generating nest algebras as weakly-closed algebras, and in particular with the following question which was first raised by H. Radjavi and P. Rosenthal in [8], viz: Is every nest algebra on a separable Hilbert space generated, as a weakly-closed algebra, by two operators? That the answer to this question is affirmative is proved by first reducing the problem using the main result of [8] and then by using a characterization of nests due to J. A. Erdos [2].
Additive Divisibility in Compact Topological Semirings
Authors: Karvellas P. H.
Published: December 2010

A topological semiring (S, + , ·) is a nonempty Hausdorff space S on which are defined continuous and associative operations, termed addition (+) and multiplication (·), such that the multiplication distributes over addition from left and right. The additive semigroup (S, +) need not be commutative.

We prove that the set A of additively divisible elements of a compact semiring S is a two-sided multiplicative ideal, containing the set E[+] of additive idempotents, with the property that (A.S) ∪ (S.A) ⊂ E[+].
On Gaussian and Geodesic Curvature of Riemannian Manifolds
Authors: Rummler Hansklaus
Published: December 2010

In [1], S. S. Chern gave a very elegant and simple proof of the Gauss-Bonnet formula for closed (i.e. compact without boundary) oriented Riemannian manifolds of even dimension:

Here, c is a suitable constant depending on the dimension of M and Ω is an n-form (n = dim M) which may be calculated from its curvature tensor. W. Greub gave a coordinate-free description of this integrand Ω (cf. [4]).
On the Selection of Compact Subsets of Positive Measure from Analytic Sets of Positive Measure
Authors: Larman D. G.
Published: December 2010

An important but seemingly difficult problem is to decide whether or not an analytic set A of positive h-measure, for some continuous Hausdorff function h, contains a compact subset C of positive h-measure, in every complete separable metric space Ω.

By extending some earlier work of R. O. Davies [1], M. Sion and D. Sjerve [8] proved that

(i)

the selection of the set C is always possible in a σ-compact metric space Ω. More recently Davies [2] has shown that it is always possible to select C

(ii)

when h(t) = ts, t ≧ 0, for some fixed positive number s,

(iii)

when Ω is finite dimensional in the sense of [4],

(iv)

when A has σ-finite h-measure, and

(v)

when Ω is an ultra metric space.
On a Family of Generalized Numerical Ranges
Authors: Lin C.-S.
Published: December 2010

Throughout this note, an operator will always mean a bounded linear operator acting on a Hilbert space X into itself, unless otherwise stated. The class Cρ (0 < ρ < ∞ ) of operators, considered by Sz.-Nagy and Foiaş [5], is defined as follows: An operator T is in Cρ if Tnx = pPUnx for all x ∊ X, n = 1, 2, . . . , where U is a unitary operator on some Hilbert space Y containing X as a subspace, and P is the orthogonal projection of Y onto X. In [2] Holbrook defined the operator radii wρ(·) (0 < ρ ≦ ∞ ) as the generalized Minkowski distance functionals on the Banach algebra of bounded linear operators on X, i.e.,

and w∞(T) = r(T), the spectral radius of T [2, Theorem 5.1].
Determination of Brauer Characters
Authors: Puttaswamaiah B. M.
Published: December 2010

The purpose of this note is to show that the values of an irreducible (Brauer) character are the characteristic values of a matrix with non-negative rational integers. The construction of these integral matrices is done by a description of a representation of the Grothendieck ring of the category of modules over the group algebra. In particular a result of Solomon on characters and a result of Burnside on vanishing of a non-linear character on some conjugate class are generalized.
Riesz Decompositions
Authors: Nagel Alexander , Rudin Walter
Published: December 2010

All functions mentioned in this paper will be real-valued. If f1, f2, g are nonnegative functions on a set S that satisfy g ≦ f1 + f2, the Riesz decomposition problem associated with these data is to find functions gi on S such that

The formula

always furnishes a solution. The problem becomes more interesting if one asks under what conditions one can find solutions that are, roughly speaking, as smooth as the data.
Easton's Results Via Iterated Boolean-Valued Extensions
Authors: Pelletier Donald H.
Published: December 2010

The purpose of this article is to show how the main result of Easton [1] can be obtained as a special case of a general theory, which was developed in [6], of Boolean-valued models of ZF when the Boolean algebra is a proper class in the ground model. Indeed [1] was the motivating example for [6], Thus the present article together with [6] contain a presentation of Easton's forcing argument in the context of Boolean-valued models. This presentation is not, however, an automatic translation of Easton's argument from the language of forcing to that of Boolean-valued models. In fact, we hope to illuminate the "black magic" referred to in Rosser [8, p. 169].
Existence Theorems for Nonlinear Boundary Value Problems
Authors: McCandless W. L.
Published: December 2010

Let C(I) denote the linear space of continuous functions from the compact interval I = [a, b] into n-dimensional real arithmetic space Rn, and let C′(I) be the subspace of continuously differentiable functions on I. A general boundary value problem for a first-order system of n ordinary differential equations on I is given by
Oscillation Criteria for Quasilinear Equations
Authors: Allegretto W.
Published: December 2010

Several authors have recently considered the problem of establishing sufficient criteria to guarantee the oscillation or non-oscillation of all solutions of a second order elliptic equation or system. We mention in particular the papers of C. A. Swanson, [15; 16], K. Kreith [9], Kreith and Travis [10], Noussair and Swanson [13], Allegretto and Swanson [3], Allegretto and Erbe [2] and the references therein.
A Bound for the Degree of H2(G, Zp)
Authors: Sharma Sneh
Published: December 2010

Let G be a group and N a trivial G-module. We say an element ξ ∊ H2 (G, N) is of degree ≦ n if a 2-cocycle representative of ξ is a polynomial 2-cocycle of degree ≦ n [1], Let PnH2(G, N) denote the subgroup of H2(G, N) consisting of elements with degree ≦ n. Then we have a nitration

of H2(G, N). We say that the degree of H2(G, N) is ≦ n if PnH2(G, N) = H2(G, N).
The Structure of Quasi-Frobenius Rings
Authors: Müller Bruno J.
Published: December 2010

Utilizing a matrix representation of semiperfect rings by a family of bimodules over local rings, we describe the structure of generalized quasi-Frobenius rings in two steps: a cyclic generalized quasi-Frobenius ring is a matrix ring over a cycle of Morita dualities between local rings, and an arbitrary generalized quasi-Frobenius ring is a matrix ring over a family of cyclic generalized quasi-Frobenius rings.

Our results provide a complete classification of generalized quasi-Frobenius rings, modulo the classification of local rings with Morita duality, of certain bimodules over such rings, and of certain rest families of multiplication maps.
Some Results on Weak Covering Conditions
Authors: Gittings Raymond F.
Published: December 2010

A space X is called countdbly metacompact (countably paracompact) if every countable open cover has a point finite (locally finite) open refinement. According to Hodel [5], a space X is called countably subparacompact if every countable open cover has a σ-discrete closed refinement. It is well-known (see Mansfield [10] and Dowker [4]) that in normal spaces all of the preceding notions are equivalent. Also, according to Hodel [5], a countably subparacompact space is countably metacompact and the reverse implication is false.
A Class of Almost Commutative Nilalgebras
Authors: Myung Hyo Chul
Published: December 2010

The purpose of this paper is to investigate a class of nonassociative nilalgebras which have absolute zero divisors. If a nilalgebra is nilpotent, it, of course, possesses an absolute zero divisor. For the nilpotence of nonassociative nilalgebras, the situation however becomes quite complicated even in the finite-dimensional case. For example, Gerstenhaber [3] has conjectured the nilpotence of commutative nilalgebras. While Gerstenhaber and Myung [4] prove that any commutative nilalgebra of dimension ≦ 4 in characteristic ≠ 2 is nilpotent, Suttles [9] discovered an example of a 5-dimensional commutative nilalgebra which is solvable but not nilpotent.
Structure Species and Constructive Functors
Authors: Blanchard Andrew A.
Published: December 2010

This communication is in essence a note tying together the structure theory of Bourbaki and the categorical structure theory exemplified in the works of Sonner, and Hedrlin, Pultr, and Trnkova, to name a few. The work of Bourbaki [1] appeared in 1957, and quietly succumbed to the explosion of category theory. Sonner [6] used the nomenclature of Bourbaki to classify certain types of functors, while Hedrlin et al use the functor approach, studying structures by way of the associated forgetful functors. More discussion of this approach appears in section 3.
Topological Properties of Limits of Inverse Systems Of Measures
Authors: Mallory Donald J.
Published: December 2010

It has been shown (Mallory and Sion [6]) that the problem of finding "limit" measures for inverse systems of measure spaces (Xi,μi)i∊Ican be successfully attacked by establishing the existence of a “limit” measureon the product space, then considering the restriction to the inverse limit set.

In this paper we use a similar point of view to establish conditions under which a system of Radón measures has a “limit” measure which is also Radón.
Perfect Maps and Epi-Reflective Hulls
Authors: Hager Anthony W.
Published: December 2010

The main theorems concern the relation between the - compact spaces and the -regular spaces, and their analogues in uniform spaces. In either of the categories of Tychonoff spaces or uniform spaces, let be a class of spaces, let be the epi-reflective hull of se (closed subspaces of products of members of ), let be the “onto-reflective” hull of (all subspaces of products of members of ), and let r and o be the associated functors. Let be the class of spaces which admit a perfect map into a member of . Then, is epi-reflective (and in Tych, = but in Unif, the equality fails); call the functor p.
On Maximal Torsion Radicals, II
Authors: Beachy John A.
Published: December 2010

Let R be an associative ring with identity, and let denote the category of unital left R-modules. The Walkers [6] raised the question of characterizing the maximal torsion radicals of , and showed that if R is commutative and Noetherian, then there is a one-to-one correspondence between maximal torsion radicals and minimal prime ideals of R [6, Theorem 1.29]. Popescu announced [5, Theorem 2.5] that the result remains valid for commutative rings with Gabriel dimension (in the terminology of [2]). Theorem 4.6 below shows that the result holds for rings (not necessarily commutative) with Krull dimension on either the left or right, extending the previous theorem for right Noetherian rings which appeared in [1].
Compact Operators in Reductive Algebras
Authors: Azoff Edward A.
Published: December 2010

Let be a Hilbert space and denote the collection of (bounded, linear) operators on by . Throughout this paper, the term ‘algebra’ will refer to a subalgebra of ; unless otherwise stated, it will not be assumed to contain I or to be closed in any topology.

An algebra is said to be transitive if it has no non-trivial invariant subspaces. The following lemma has revolutionized the study of transitive algebras. For a pr∞f and a general discussion of its implications, the reader is referred to [5].
One-Sided Inverses in Rings
Authors: Peterson Roger D.
Published: December 2010

Following Herstein [2], we will call a ring R with identity von Neumann finite (vNf) provided that xy = 1 implies yx — WnR. Kaplansky [4] showed that group algebras over fields of characteristic zero are vNf rings, and further, that full matrix rings over such rings are also vNf. Herstein [2] has posed the problem for group algebras over fields of arbitrary characteristic. If group algebras over fields are always vNf, then it is easily seen that group algebras over commutative rings are always vNf. What conditions on the underlying ring of scalars would force the vNf property for all group rings over it?
Analogues of Entire Function Inequalities for an Analytic Function
Authors: Bajpai S. K. , Tanne Joseph
Published: December 2010

1. Let be an analytic function with radius of convergence R (0 < R < ∞). Set

and let the order p and lower order ⋋ of f(z) be defined by

where x = Rr/(R — r). If 0 < ᑭ < ∞, we define the type T and lower type t of f(z) by

Also, if 0 < ᑭ < ∞, define the “growth numbers” 𝛄 and δ by

The purpose of our discussion will be to obtain some inequalities involving the growth constants defined above.