bluuebunny/crossref_metadata_2025 huggingface dataset:
Intersection of Two Invariant Subspaces
Authors: Nakazi Takahiko
Published: December 2010

It is shown that, if F and G are inner functions, (H2 ⊖ FH2)/(H2 ⊖ FH2) ∩ GH2 is n-dimensional if and only if G is a Blaschke product of degree n. This is an extension of the well known result for the case (H2 ⊖ FH2) ∩ GH2 = {0}.
Sur la Convergence Ponctuelle de Quelques Suites D'Operateurs
Authors: Assani I.
Published: December 2010

Let (αn.k) be a sequence of positive numbers. We define a regular sequence (resp. a weakly regular sequence) and then show the existence of a unitary operator (resp. a contraction T) L2[0, 1] → L2[0, 1] and a function f ∊ L2[0, 1] such that the pointwise convergence of the sequence of functions is not satisfied almost surely. As a first corollary the pointwise convergence of the Abel means of a contraction from L2 into L2 does not hold necessarily almost surely. As a second corollary there exists a contraction T for which the means (and powers) of Brunei's operator A do not converge pointwise a.s. We also show that, for P > 1 fixed, there exists a sequence of positive numbers αn.k for which we have the pointwise convergence in LP of the sequence of polynomials where T is a contraction of L1 and Lα. The dominated theorem does not, however, always hold for such LP-contractions.
On GL2 of a Local Ring in Which 2 is Not a Unit
Authors: Mason A. W.
Published: December 2010

Let A be a local ring with maximal ideal m, let N(m ) be the order of the residue field A/m and let N be a subgroup of GLn (A) which is normalized by SLn(A). It follows from results of Klingenberg that N is normal in GLn(A) when n ≥ 3 or . Results of Lacroix show that this is also true when n = 2 and N(m) = 3, provided that N∩2(A) ≠ SL2(A)'.

The principal aim of this paper is to provide examples of non-normal subgroups of GL2(A) which are normalized by SL2(A). In the process we extend results of Lacroix and Levesque on GL2(A)-normalized subgroups of GL2(A), where 2 ∊ m and N(m) > 2.
Distributive Modules
Authors: Erdoğdu V.
Published: December 2010

Let R be a commutative ring with identity. An R-module M is said to be distributive if the lattice of submodules of M is distributive. We characterize such modules and study their properties.
A Comparison of Methods for Constructing Probability Measures on Infinite Product Spaces
Authors: Lamb Charles W.
Published: December 2010

The construction, from a consistent family of finite dimensional probability measures, of a probability measure on a product space when the marginal measures are perfect is shown to follow from a classical theorem due to Ionescu Tulcea and known results on the existence of regular conditional probability functions.
Uniqueness of Invariant Densities for Certain Random Maps of The Interval
Authors: Boyarsky Abraham
Published: December 2010

A random map is a discrete time process in which one of a number of maps, 𝓜, is chosen at random at each stage and applied. In this note we study a random map, where 𝓜 is a set of piecewise linear Markov maps on [0, 1]. Sufficient conditions are presented which allow the determination of the unique absolutely continuous invariant measure of the process.
More on Fatou's Lemma in Several Dimensions
Authors: Balder Erik J.
Published: December 2010

Recently, Balder proved a version of FatoiTs lemma in several dimensions which, inter alia, generalizes a version of this lemma due to Artstein. Here we show how the latter result can be used to derive the former, by using Chacon's biting lemma.
Free Actions of Abelian Groups on a Cartesian Power of an Even Sphere
Authors: Hoffman Michael
Published: December 2010

We determine an algebraic condition necessary and sufficient for a group G to act freely on the nth Cartesian power of an even sphere, and characterize the abelian groups that satisfy this condition.
A Note on M-Summands in Dual Spaces
Authors: Feeman Timothy
Published: December 2010

A theorem concerning M-summands in dual spaces is used to prove that certain known M-ideals are not M-summands. In some cases where this information was already known, our procedure greatly simplifies the earlier proofs. Finally, we give a condition to determine which M-ideals in dual spaces are M-summands and which are not.
A Note on Nilpotent Jordan Rings
Authors: Martindale Wallace S.
Published: December 2010

Let R be a 2-torsion free associative ring with involution. It is shown that if the set S of symmetric elements is nilpotent as a Jordan ring then R is nilpotent.
Stable Plumbing for High Odd-Dimensional Fibred Knots
Authors: Lines Daniel
Published: December 2010

Plumbing a Hopf band on the fibre-surface of a simple fibred knot is a geometric operation that produces another such knot. We show by algebraic methods that every high odd-dimensional simple fibred knot is obtained from the unknot by using this operation and its inverse.
Empty Simplices in Euclidean Space
Authors: Bárány Imre , Füredi Zoltán
Published: December 2010

Let P - {p1,p2,. . . ,pn} be an independent point-set in ℝd (i.e., there are no d + 1 on a hyperplane). A simplex determined by d + 1 different points of P is called empty if it contains no point of P in its interior. Denote the number of empty simplices in P by fd(P). Katchalski and Meir pointed out that . Here a random construction Pn is given with , where K(d) is a constant depending only on d. Several related questions are investigated.
A Uniformly Asymptotically Regular Mapping Without Fixed Points
Authors: Lin Pei-kee
Published: December 2010

We construct a uniformly asymptotically regular, Lipschitzian mapping acting on a weakly compact convex subset of l2 which has no fixed points.
Projections in Spaces of Bimeasures
Authors: Graham Colin C. , Bertram M. Schreiber
Published: December 2010

Let X and Y be metrizable compact spaces and μ and v be nonzero continuous measures on X and Y, respectively. Then there is no bounded operator from the space of bimeasures BM(X, Y) onto the closed subspace of BM(X, Y) generated by L1 (μ X v); in particular, if X and Fare nondiscrete locally compact groups, then there is no bounded projection from BM(X, Y) onto the closed subspace of BM(X, Y) generated by L1(X X Y).
Bernoulli Maps of a Lebesgue Space
Authors: Alufohai Imohimi C.
Published: December 2010

A collection of measure preserving mappings having Bernoulli generators is considered. Only three conditions are required to be satisfied, and they are quite easy to check.
Recouvrements Ponctuellements Dénombrables
par des Ensembles Négligeables
Authors: Burke Maxim R.
Published: December 2010

Nous allons démontrer la consistance avec la théorie des ensembles ZFC de l'existence d'un recouvrement de R par une collection d'ensembles négligeables, telle que pour tout est mesurable.
On an Extremal Problem Involving Harmonic Functions
Authors: Georg Schmidt E. J. P.
Published: December 2010

Given a domain D in R” and two specified points P0 and P1 in D we consider the problem of minimizing u(p1) over all functions harmonic in D with values between 0 and 1 normalised by the requirement u(P0) = 1/2. We show that when D is suitably regular the problem has a unique solution u* which necessarily takes on boundary values 0 or 1 almost everywhere on the boundary. In the process we prove that it is possible to separate P0 and P1by a harmonic function whose boundary value is supported in an arbitrary set of positive measure. These results depend on the fact that (under suitable regularity conditions) a harmonic function which vanishes on an open subset of the boundary has a normal derivative which is almost everywhere non-vanishing in that set.
Method of Forced Monotonicity for Conjugate type Boundary Value Problems for Ordinary Differential Equations
Authors: Eloe P. W. , Saintignon P. L.
Published: December 2010

Let I = [a, b] ⊆ R and let L be an nth order linear differential operator defined on Cn(I). Let 2 ≦ k ≦ n and let a ≦ x1 < x2 < … < xn = b. A method of forced mono tonicity is used to construct monotone sequences that converge to solutions of the conjugate type boundary value problem (BVP) Ly = f(x, y),y(i-1) = rij where 1 ≦i ≦ mj, 1 ≦ j ≦ k, mj = n, and f : I X R → R is continuous. A comparison theorem is employed and the method requires that the Green's function of an associated BVP satisfies certain sign conditions.
The Number of Rooted Convex Polyhedra
Authors: Bender Edward A. , Wormald Nicholas C.
Published: December 2010

Let pij be the number of rooted convex polyhedra with i + 1 vertices and j + 1 faces. We express pij as a singly indexed summation whose terms decrease geometrically. From this we deduce that

uniformly as max(i, j) → ∞.
Derivations with Invertible Values on a Lie Ideal
Authors: Bergen Jeffrey , Carini L.
Published: December 2010

Let R be a ring which possesses a unit element, a Lie ideal U ⊄ Z, and a derivation d such that d(U) ≠ 0 and d(u) is 0 or invertible, for all u ∈ U. We prove that R must be either a division ring D or D2, the 2 X 2 matrices over a division ring unless d is not inner, R is not semiprime, and either 2R or 3R is 0. We also examine for which division rings D, D2 can possess such a derivation and study when this derivation must be inner.
Counterexamples Concerning Support Theorems for Convex Sets in Hilbert Space
Authors: Phelps R. R.
Published: December 2010

The Bishop-Phelps theorem guarantees the existence of support points and support functionals for a nonempty closed convex subset of a Banach space; equivalently, it guarantees the existence of subdifferentials and points of subdifferentiability of a proper lower semicontinuous convex function on a Banach space. In this note we show that most of these results cannot be extended to pairs of convex sets or functions, even in Hilbert space. For instance, two proper lower semicontinuous convex functions need not have a common point of subdifferentiability nor need they have a subdifferential in common. Negative answers are also obtained to certain questions concerning density of support points for the closed sum of two convex subsets of Hilbert space.
Reduced Sobolev Inequalities
Authors: Adams R. A.
Published: December 2010

The Sobolev inequality of ordermasserts that ifp≧ 1,mp<nand1/q = 1/p — m/n,then the Lq-norm of a smooth function with compact support in Rnis bounded by a constant times the sum of theLp-norms of the partial derivatives of ordermof that function. In this paper we show that that sum may be reduced to include only the completely mixed partial derivatives or orderm,and in some circumstances even fewer partial derivatives.
The Focal Locus of a Riemannian 4-Symmetric Space
Authors: Alfredo Jimenez J.
Published: December 2010

compact Riemannian 4-symmetric space M can be regarded as a fibre bundle over a Riemannian 2-symmetric space with totally geodesic fibres isometric to a 2-symmetric space. Here the result of R. Crittenden for conjugate and cut points in a 2-symmetric space is extended to the focal points of the fibres of M. Also the restriction of the exponential map of M up to the first focal locus in the normal bundle of a fibre is proved to yield a covering map onto its image. It is shown that for the noncompact dual M*, the fibres have no focal points and hence the exponential map of M* restricted to the normal bundle of a fibre is a covering map. The classification of the compact simply connected 4-symmetric spaces G/L with G classical simple provides a large class of examples of these fibrations.
Local Connectedness of the stone-Čech Compactification
Authors: Baboolal D.
Published: December 2010

A uniform space X is said to be uniformly locally connected if given any entourage U there exists an entourage V ⊂ U such that V[x] is connected for each x ∈ X. It is said to have property S if given any entourage U, X can be written as a finite union of connected sets each of which is U-small.

Based on these two uniform connection properties, another proof is given of the following well known result in the theory of locally connected spaces: The Stone-Čech compactification βX is locally connected if and only if X is locally connected and pseudocompact.
Derivations on a Lie Ideal
Authors: Mauceri Silvana , Misso Paola
Published: December 2010

In this paper we prove the following result: let R be a prime ring with no non-zero nil left ideals whose characteristic is different from 2 and let U be a non central Lie ideal of R.

If d ≠ 0 is a derivation of R such that d(u) is invertible or nilpotent for all u ∈ U, then either R is a division ring or R is the 2 X 2 matrices over a division ring. Moreover in the last case if the division ring is non commutative, then d is an inner derivation of R.
Indecomposable Positive Maps in Matrix Algebras
Authors: Tanahashi Kôtarô , Tomiyama Jun
Published: December 2010

We prove that Choi's map in M3 cannot be written as the sum of a 2-positive map and a 2-copositive map. We also provide other examples of positive maps in Mn which cannot be written as the sum of an n-positive map and a 2-copositive map.
Semi-F-Spaces
Authors: Levy Ronnie
Published: December 2010

Semi-F-spaces are spaces such that given any pair of disjoint cozero sets, every countable subset of one is completely separated from the other. This generalizes the notion of an F-space and is stronger than the property that every countable subset is C*-embedded. Semi-F-spaces are studied and several examples are given.
Notes on Interpolation by Bounded Analytic Functions
Authors: Nakazi Takahiko
Published: December 2010

Let ﹛zn﹜ be a sequence in the open unit disc and write In the case of pn for all n, the interpolation problems are considered.
A New Proof of a Watson's Formula
Authors: Stempak Krzysztof
Published: December 2010

A new proof of a product formula for Laguerre polynomials, due originally to Watson, is given. Considering the commutative Banach algebra of radial functions on the Heisenberg groups Hn, n ≧ 2, we observe that Watson's formula holds for z = 1,2, 3, …. Then, applying a complex function theory argument, we establish the validity of this formula for other complex values of z, i.e. for Re z > - 1/2.
Semibounded Extensions of Singular Ordinary Differential Operators
Authors: Krall Allan M.
Published: December 2010

The self-adjoint extensions of the singular differential operator Ly = [(py’)’ + qy]/w, where p < 0, w > 0, q ≧ mw, are characterized under limit-circle conditions. It is shown that as long as the coefficients of certain boundary conditions define points which lie between two lines, the extension they help define has the same lower bound.
Sums of Idempotents in Banach Algebras
Authors: Kalton N. J.
Published: December 2010

We prove that the sum of two idempotents is in a Banach algebra is itself an idempotent if and only if it is power-bounded.
On Levi-Like Properties and some of Their Applications in Riesz Space Theory
Authors: Buskes G. , Labuda I.
Published: December 2010

Let (L, λ) be a locally solid Riesz space. (L, λ) is said to have the Levi property if for every increasing λ-bounded net (xα) ⊂ L+, sup xα exists. The Levi property, appearing in literature also as weak Fatou property (Luxemburg and Zaanen), condition (B) or monotone completeness (Russian terminology), is a classical object of investigation. In this paper we are interested in some variations of the property, their mutual relationships and applications in the theory of topological Riesz spaces. In the first part of the paper we clarify the status of two problems of Aliprantis and Burkinshaw. In the second part we study ideal-injective Riesz spaces.
Injective and Weakly Injective Rings
Authors: Gardner B. J. , Stewart P. N.
Published: December 2010

Let V be a variety of rings and let A ∊ V. The ring A is injective in V if every triangle

with C ∊ V, m a monomorphism and f a homomorphism has a commutative completion as indicated. A ring which is injective in some variety (equivalently, injective in the variety it generates) is called injective. When only triangles with f surjective are considered we obtain the notion of weak injectivity. Directly indecomposable injective and weakly injective rings are classified.
Non-Standard, Normal Subgroups and Non-Normal, Standard Subgroups of the Modular Group
Authors: Mason A.W.
Published: December 2010

Let R be a commutative ring with identity. A subgroup S of GLn(R), where n ≥ 2, is said to be standard if and only if S contains all the q-elementary matrices and all conjugates of those matrices by products of elementary matrices, where q is the ideal in R generated by Xij,xii — Xjj(i ≠ j), for all (xij) ∊ S. It is known that, when n ≧ 3, the standard subgroups of GLn(R) are precisely those normalized by the elementary matrices. To demonstrate how completely this result can break down for n = 2 we prove that GL2(Z), where Z is the ring of rational integers, has uncountably many non-normal, standard subgroups and uncountably many non-standard, normal subgroups.
On PIC(D[α]) For a Principal Ideal Domain D
Authors: Gilmer Robert , Heinzer William
Published: December 2010

Let D be a PID with infinitely many maximal ideals. J. W. Brewer has asked whether some simple ring extension D[α] of D must have nontrivial Picard group. We show that this question has a negative answer.
Montel Subspaces in the Countable Projective Limits of Lp(μ)-Spaces
Authors: Díaz J. C.
Published: December 2010

Let us suppose one of the following conditions: (a) p ≧ 2 and F is a closed subspace of a projective limit (b) p = 1 and F is a complemented subspace of an echelon Köthe space of order 1, Λ(X,β,μ,gk); and (c) 1 > p > 2 and F is a quotient of a countable product of Lp(μn) spaces. Then, F is Montel if and only if no infinite dimensional subspace of F is normable.
Solutions of Specific Diophantine Equations and their Relationship to Complex Multiplication
Authors: Wajngurt Clara
Published: December 2010

In this paper we establish a relationship between the rational solutions (x(t), y(t)), over C(t), of the diophantine equation:

and the solutions which parametrize the elliptic curve E, y2 = 4x3 — g2x — g3 admitting complex multiplication by λ. We first characterize the form of all rational solutions of diophantine equation (1). The rational solutions are derivable from the subsititutions

in which μ = 0,ω1,ω2,ω1 + ω2 = ω3. Using techniques established in elliptic function theory, we prove that the complex multiplier λ, associated with a unique rational solution (x(t), y(t)), must be of a certain form. Next we construct all rational solutions of diophantine equation (1) by using the addition theorems valid for the Weierstrass function, Specific examples are finally worked out for the cases
A Dual characterization of Banach Spaces With the Convex Point-of-Continuity Property
Authors: Hare D. E. G.
Published: December 2010

We introduce a new type of differentiability, called cofinite Fréchet differentiability. We show that the convex point-of-continuity property of Banach spaces is dual to the cofinite Fréchet differentiability of all equivalent norms. A corresponding result for dual spaces with the weak* convex point-of-continuity property is also established.
Une Note sur les Coefficients Binomiaux de Gauss
Authors: Mercier Armel
Published: December 2010

Nous obtenons différentes identités de l'analyse combinatoire contenant des coefficients binomiaux de Gauss.
Invariant Vectors of a Nonrecurrent Markov Matrix
Authors: Foguel S. R.
Published: December 2010

Let P be an irreducible Markov matrix. Assume:

We study conditions for such a matrix to be nonrecurrent. If P is nonrecurrent we study the invariant vectors of P (invariant column vectors and invariant row vectors).
Moore G-Spaces Which are not Co-Hopf G-Spaces
Authors: Doman Ryszard
Published: December 2010

Let G be a finite group. By a Moore G-space we mean a G-space X such that for each subgroup H of G the fixed point space XH is a simply connected Moore space of type (MH,n), where MH is an abelian group depending on H, and n is a fixed integer. By a co-Hopf G-space we mean a G-space with a G-equivariant comultiplication. In this note it is shown that, in contrast to the non-equivariant case, there exist Moore G-spaces which are not co-Hopf G-spaces.
A Note on the Orthogonality of Jackson's q-Bessel Functions
Authors: Rahman Mizan
Published: December 2010

A q-analogue of the orthogonality property of the Bessel functions on the zeros is obtained in terms of a q-integral.
A Group Theoretic Characterization of the 2-Dimensional Spherical Groups
Authors: Miller Andy
Published: December 2010

It is shown that for a finite group G to be isomorphic to a subgroup of SO(3) (or, equivalently, of PSL(2, C)) it is necessary and sufficient that G satisfies the property that the normalizer of every cyclic subgroup is either cyclic or dihedral.
On the Davison Convolution of Arithmetical Functions
Authors: Haukkanen Pentti
Published: December 2010

The Davison convolution of arithmetical functions f and g is defined by where K is a complex-valued function on the set of all ordered pairs (n, d) such that n is a positive integer and d is a positive divisor of n. In this paper we shall consider the arithmetical equations f(r) = g, f(r) = fg, f o g = h in f and the congruence (f o g)(n) = 0 (mod n), where f(r) is the iterate of f with respect to the Davison convolution.
An Inculsion Theorem for Dirichlet Series
Authors: Borwein David
Published: December 2010

It is shown that under certain conditions the asymptotic relationship

between two Dirichlet series implies the same relationship with λn replaced by log λn.
Projective Socles
Authors: Stewart Patrick N.
Published: December 2010

Nicholson and Watters have recently investigated rings with projective socles and they have shown, among other things, that a ring R has a projective socle if and only if each matrix ring Mn(R), n > 1, has a projective socle. We generalize this result by showing that if S is an excellent extension of R, then the socle of R is projective if and only if the socle of S is projective. Examples of excellent extensions include, as well as matrix rings Mn(R), skew group rings R * G where G is a finite group and the order of G is invertible in R.
Families of Sequences of 0s and 1s In FK-Spaces
Authors: Sember John
Published: December 2010

A characterization is given of those families ℱ of subsets of the positive integers for which σ(ℓ1, ) is sequentially complete, where denotes the linear span of the characteristic functions of ℱ. Consequences include some known matrix results, such as Hahn's Theorem and conditions required for a matrix to "sum" the characteristic functions of the lacunary sets.
Dependent Random Variables with Independent Subsets - II
Authors: Wang Y. H.
Published: December 2010

In this paper, we consolidate into one two separate problems - dependent random variables with independent subsets and construction of a joint distribution with given marginals. Let N = {1,2,3,...} and X = {Xn; n ∊ N} be a sequence of random variables with nondegenerate one-dimensional marginal distributions {Fn; n ∊ N}. An example is constructed to show that there exists a sequence of random variables Y = {Yn; n ∊ N} such that the components of a subset of Y are independent if and only if its size is ≦ k, where k ≧ 2 is a prefixed integer. Furthermore, the one-dimensional marginal distributions of Y are those of X.
A Banach Space in Which a Ball is Contained in the Range of Some Countably Additive Measure is Superreflexive
Authors: Sun Yeneng
Published: December 2010

A nonstandard proof of the fact that a Banach space in which a ball is contained in the range of a countably additive measure is superreflexive is given. The proof is an application of a general method in which we first transfer certain standard objects to the nonstandard hull of a Banach space and then, using the quite well developed theory of nonstandard hulls, derive results about the objects in the original Banach space. It also provides us with an example of the applications of the theory of nonstandard hull valued measures.
Pseudoumbilical 2-Type Surfaces in Spheres
Authors: Garay Oscar J.
Published: December 2010

It is proved that a pseudoumbilical 2-type surface in a sphere has constant mean curvature. Moreover, the dimension of the sphere is greater than four.
Extensions that are Submodules of their Quotients
Authors: Okoh F. , Zorzitto F.
Published: December 2010

Let 0 → N → E → F → 0 be a short exact sequence of torsion-free Kronecker modules. Suppose that N and F have rank one. The module F is classified by a height function h defined on the projective line. If N is finite-dimensional, h is supported on a set of cardinality less than that of its domain and h takes on the value ∞, then E embeds into F. The converse holds if all such E embed into F. This embeddability is in contrast to the situation with other rings such as commutative domains, where it never occurs.
Divisors of Integers in Arithmetic Progression
Authors: Varbanec P. D. , Zarzycki P.
Published: December 2010

Let d(n; l, k) be the number of positive divisors of n which lie in the arithmetic progression l mod k. Using the complex integration technique the formula

is proved. This formula holds uniformly in l, k and x satisfying 1 ≦ l ≦ k, (lx)1/2 ≦ k ≦ x1-∊; the exponent α ≦ 1/3.
Exemples de Dimension de Krull D'Anneaux de Polynomes
Authors: Ouertani Ahmed
Published: December 2010

For each pair (m, n) of integers such that m+1 ≦ n ≦ 2m+1, we give, by original and straightforward methods, some examples of rings A' such that dim A' = m and dim A'[X] = n.
On the Étale K-Theory of an Elliptic Curve with Complex Multiplication for Regular Primes
Authors: Wingberg Kay
Published: December 2010

Generalizing a result of Soulé we prove that for an elliptic curve E defined over an imaginary quadratic field K with complex multiplication having good ordinary reduction at the prime number p > 3 which is regular for E and the extension F of K contained in K(Ep) the dimensions of the étale K-groups are equal to the numbers predicted by Bloch and Beilinson, i.e.,
On Totally Real Submanifolds in a 6-Sphere
Authors: Bashir M. A.
Published: December 2010

The 6-dimensional sphere S6 has an almost complex structure induced by properties of Cayley algebra. With respect to this structure S6 is a nearly Kaehlerian manifold. We investigate 2-dimensional totally real submanifolds in S6. We prove that a 2-dimensional totally real submanifold in S6 is flat.
Equivariant Witt Groups
Authors: Morales Jorge F.
Published: December 2010

This paper studies for a number field K and a finite group Γ the cokernel of the residue homomorphism .
On Number of Integers Representable as Sums of Unit Fractions
Authors: Yokota Hisashi
Published: December 2010

Let N(n) be the set of all integers that can be written in the form where ∊(n) → 0 as n → ∞, answering a question of P. Erdös and R. L. Graham.
The Hexagonal Packing Lemma and Discrete Potential Theory
Authors: Aharonov Dov
Published: December 2010

One of the questions concerning the Hexagonal Packing Lemma ([1], [3], [4]) is the rate of convergence of Sn. It was suggested in [3] and [4] that Sn = 0(1/n). In the following we prove this conjecture under the additional condition of some "nice" behaviour of the "circle function".
Valuation Rings and Integral Closure
Authors: Lucas Thomas G.
Published: December 2010

A famous theorem of Krull's is that the integral closure of an integral domain D is the intersection of the valuation domains that contain D. An example is given to show that the same result need not hold for the integral closure of a ring with zero divisors.
Totally Integrally Closed Azumaya Algebras
Authors: Macoosh R. , Raphael R.
Published: December 2010

Enochs introduced and studied totally integrally closed rings in the class of commutative rings. This article studies the same question for Azumaya algebras, a study made possible by Atterton's notion of integral extensions for non-commutative rings.

The main results are that Azumaya algebras are totally integrally closed precisely when their centres are, and that an Azumaya algebra over a commutative semiprime ring has a tight integral extension that is totally integrally closed. Atterton's integrality differs from that often studied but is very natural in the context of Azumaya algebras. Examples show that the results do not carry over to free normalizing or excellent extensions.
Hankel Matrices Over Right Ordered Amenable Groups
Authors: Exel Ruy
Published: December 2010

We extend to amenable right ordered groups the theorems of Nehari and Hartman on Hankel matrices.
Invertible Elements in the Dirichlet Space
Authors: Brown Leon
Published: December 2010

It is shown that if a function in the Dirichlet space is inveritible then it is cyclic with respect to the operator of multiplication by the identity function.
Oscillation in Differential Equations with Positive and Negative Coefficients
Authors: Ladas G. , Qian C.
Published: December 2010

We obtain sufficient conditions for the oscillation of all solutions of the linear delay differential equation with positive and negative coefficients

where

Extensions to neutral differential equations and some applications to the global asymptotic stability of the trivial solution are also given.
Binary Trees and the n-Cutset Property
Authors: Arpin Peter , Ginsburg John
Published: December 2010

A partially ordered set P is said to have the n-cutset property if for every element x of P, there is a subset S of P all of whose elements are noncomparable to x, with |S| ≤ n, and such that every maximal chain in P meets {x} ∪ S. It is known that if P has the n-cutset property then P has at most 2n maximal elements. Here we are concerned with the extremal case. We let Max P denote the set of maximal elements of P. We establish the following result. THEOREM: Let n be a positive integer. Suppose P has the n-cutset property and that |Max P| = 2n. Then P contains a complete binary tree T of height n with Max T = Max P and such that C ∩ T is a maximal chain in T for every maximal chain C of P. Two examples are given to show that this result does not extend to the case when n is infinite. However the following is shown. THEOREM: Suppose that P has the ω-cutset property and that |Max P| = 2ω. If P — Max P is countable then P contains a complete binary tree of height ω
An Induction Theorem for Units of p-Adic Group Rings
Authors: Bhandari A. K. , Sehgal S. K.
Published: December 2010

Let G be a finite group and let C be the family of cyclic subgroups of G. We show that the normal subgroup H of U = U(ZpG) generated by U(ZpC), C ∊ C, where Zp is the ring of p-adic integers, is of finite index in U.
Generalised Umbilics on Embedded Spheres
Authors: Noakes J. L.
Published: December 2010

We study two kinds of generalized umbilics on smoothly embedded n-manifolds in ℝn+1. A sectional umbilic occurs where two of the principal curvatures are equal, and a split sectional umbilic is a more general
notion.
Determination of Grassmann Manifolds Which are Boundaries
Authors: Sankaran Parameswaran
Published: December 2010

LetFGn,kdenote the Grassmann manifold of allk-dimensional (left)F-vector subspace ofFnfor F = ℝ, the reals,C, the complex numbers, orHthe quaternions. The problem of determining which of the Grassmannians bound was addressed by the author in [4]. Partial results were obtained in [4] for the caseF= ℝ, including a sufficient condition, due to A. Dold, on n and k for ℝGn,kto bound. Here, we show that Dold's condition is also necessary, and obtain a new proof of sufficiency using the methods of this paper, which cover the complex and quaternionic cases as well.
Dimension-Preserving Extensions of Pro-p-Groups
Authors: Würfel Tilmann
Published: December 2010

We investigate extensions of pro-p-groups 1 —> N —> G —> Γ —> 1 where N is pro-p-free and Nab, is a free Zp[Γ]-module. In case Γ is finite we show that such an extension splits modulo the second derived
group N".
Weak Continuity of a Composition Map Between Spaces of Compact Operators and Banach Valued Continuous Functions
Authors: Asthagiri Rajappa K.
Published: December 2010

This paper characterizes the Banach space E for the sequential continuity and the continuity on bounded sets of the composition map m: C(S, E)wk x K{E,F)wk —> C(S,F)wk. Here, K(E,F) denotes the Banach space of compact linear operators on the Banach space E to the Banach space F with the usual operator norm, and for any Banach space E, Ewk denote the Banach space E with the weak topology. Also we denote by C(S, E) the Banach space of E valued continuous functions on a nonvoid compact Hausdorff space S with sup norm.
An Arithmetical Function Associated With the Rank of Elliptic Curves
Authors: Clark David
Published: December 2010

We define an arithmetical function, f(n), which gives a lower bound for the rank of elliptic curves, y2 = x3 + nx, n square-free. Thus, if f(n) is unbounded for square-free values of n, then there are elliptic curves of arbitrarily large rank. We show that f(n) is unbounded as n ranges over all integers.
Mahler's Measure of a Polynomial in Function of the Number of its Coefficients
Authors: Dobrowolski Edward
Published: December 2010

Mahler's measure of a monic polynomial is equal to the product of modules of its roots which lie outside the unit circle. By classical theorem of Kronecker it is strictly greater than 1 for any polynomial that is not a product of cyclotomic factors. In this case a number of lower bounds of the measure, depending either on the degree of the polynomial or on the number of its non-zero coefficients, has been found. Here is given an improvement of the bound of the latter type previously found by the author, A. Schinzel and W. Lawton.
Nest Algebras of Operators and the Dunford-Pettis Property
Authors: Feeman Timothy G.
Published: December 2010

A Banach space X is said to have the Dunford-Pettis Property if every weakly compact linear operator T: X —> Y, where Y is any Banach space, is completely continuous (that is, T maps weakly convergent sequences to strongly convergent ones). In this paper, we prove that if A is a nest algebra of operators on a separable, infinite dimensional Hilbert space, then A fails to have the Dunford-Pettis Property. We also investigate a certain algebra associated to A, analogous to a construction used by Bourgain and others in connection with the Dunford-Pettis Property for function algebras. We show that this algebra must lie between A and the quasi-triangular algebra A + K and we give examples to show that either extreme or something in between is possible. Finally, we consider the algebra of analytic Toeplitz operators and give a result for the corresponding associated algebra which is analogous to a result of Cima, Jansen, and Yale for H∞.
On Mennicke Groups of Deficiency Zero II
Authors: Albar Muhammad A. , Al-Shuaibi Abdul-Aziz A.
Published: December 2010

Let M be the group defined by the presentation 〈 x, y, z | xy = xm, yz = yn, zx = zr〉,m,n,r ∊ Z. M is one of the few 3-generator finite groups of deficiency zero. These groups have been considered by Mennicke [3], Macdonald, Wamsley [10], Johnson and Robertson [7], and Albar. Properties like the order of M, the nilpotency and solvability were studied. In this paper we give a better upper bound for M than the one given by Johnson and Robertson [7]. We also describe the structure of some cases of M.
On Rings With Engel Cycles
Authors: Bell H. E. , Klein A. A.
Published: December 2010

A ring R is called an EC-ring if for each x, y ∊ R, there exist distinct positive integers m, n such that the extended commutators [x, y]m and [x, y]n are equal. We show that in certain EC-rings, the commutator ideal is periodic; we establish commutativity of arbitrary EC-domains; we prove that a ring R is commutative if for each x, y ∊ R, there exists n > 1 for which [x, y] = [x, y]n.
Topological Properties of Legendrian Singularities
Authors: Izumiya Shyüichi
Published: December 2010

A wavefront set is defined to be an image of Legendrian mapping. In this note we prove that generic wavefront sets have stable local topological structures by using Mather's stratification theory.
An Order-Theoretical Characterization of Varieties of Bands
Authors: Acher August Mistlb
Published: December 2010

We give a description of band varieties by properties of the compatibility of certain quasi-orders λnand ρn.
On Sierpinski's Conjecture Concerning the Euler Totient
Authors: Subbarao M. V. , Yip L. W.
Published: December 2010

If Φk(n) denotes the Schemmel totient (so that Φ1 (n) becomes the Euler totient) we conjecture that for each k ≥ 1 and any given integer n > 1 there exist infinitely many m for which the equation Φk(x) = m has exactly n solutions. For the case k = 1, this gives Sierpinski's conjecture.

We prove that on the basis of Schinzel's Hypothesis H, our conjecture holds for any k ≥ 3 of the form where p0 is an odd prime and α ∊ N. In 1961 Schinzel proved the case k = 1 assuming his Hypothesis H.
The Converse of the Dominated Ergodic Theorem in Hurewicz Setting
Authors: Szabó László I.
Published: December 2010

The converse of the dominated ergodic theorem in infinite measure spaces is extended to non-singular transformations, i.e. transformations that only preserve the measure of null sets. An inverse weak maximal inequality is given and then applied to obtain related results in Orlicz spaces.
Pullback-Flat Acts are Strongly Flat
Authors: Bulman-Fleming Sydney
Published: December 2010

Let 5 be a monoid. A right S-system A is called strongly flat if the functor A ⊗ — (from the category of left S-systems into the category of sets) preserves pullbacksand equalizers. (This concept arises in B. Stenström, Math. Nachr. 48(1971), 315-334 under the name weak flatness). The main result of the present paper is a proof that for A to be strongly flat it is in fact sufficient that A ⊗ — preserve only pullbacks. The approach taken is to develop an "interpolation" condition for pullback-preservation, and then to show its equivalence to Stenström's conditions for strong flatness.
Multipliers Between Sobolev Spaces
Authors: Fabec R. C.
Published: December 2010

A sufficient condition for the boundedness of a multiplier from a Sobolev space of index t > 1 / 4 to one of opposite index — t is obtained. The condition relates the indices of the Sobolev spaces to which the multiplier belongs to the pairs of Sobolev spaces between which the multiplier is bounded. The result is applied to homogeneous multipliers and a description of these multipliers in this setting is presesented. Extensions to higher dimensions are indicated.
Similarité Entre Certains Quotients de A+et des Quotients D'Algèbres Uniformes
Authors: Koua Konin
Published: December 2010

LetA(D) be the usual disc algebra, and letA+be the subalgebra ofA(D) consisting in thosef € A(D) which have an absolutely convergent series of Taylor coefficients. Setm1= {f€A(D) |f(1) = 0},m=m1∩A+, letGbe the functionandK = A+∩ I1.

We show that the quotient algebrasm1/I1andm/Kare similar in the sense of J. Esterle.
Basic Double Series, Quadratic Transformations and Products of Basic Series
Authors: Nassrallah Bassam
Published: December 2010

A basic double series is expressed in terms of two 5ϕ4 series which extends Bailey's transformation of an 8ϕ7 series into two 4ϕ3 's. From this formula we derive some quadratic transformations; one of them is a new q-analogue of a transformation due to Whipple. Product formulas as well as Gasper-Rahman's q-Clausen formula are also given as special cases.
Asymptotics for Semilinear Elliptic Systems
Authors: Noussair Ezzat S. , Swanson Charles A.
Published: December 2010

A class of weakly coupled systems of semilinear elliptic partial differential equations is considered in an exterior domain in ℝN, N > 3. Necessary and sufficient conditions are given for the existence of a positive solution (componentwise) with the asymptotic decay u(x) = O(|x|2-N) as |x| —> ∞. Additional results concern the existence and structure of positive solutions u with finite energy in a neighbourhood of infinity.
On Complete Intersections and Their Hilbert Functions
Authors: Reid Les , Roberts Leslie G. , Roitman Moshe
Published: December 2010

We deal here with the existence of half-way nonzero divisors for complete intersections and with related properties of their Hilbert functions.
Ranks of Chain Complexes Over the Complex Polynomial Ring
Authors: Zelewski Piotr M.
Published: December 2010

Using LePotier's vanishing theorem, we establish a lower bound on the rank of nontrivial free differential complex in terms of the dimension of the support for its cohomology. Our bound specializes to the one predicted by the syzygy theorem of Evans and Griffith.
Note on the Space Bmoa
Authors: Choa Jun Soo
Published: December 2010

Let D be the unit disc in the complex plane. It is shown that

(i) for 0 < p < 2, there exists an analytic function f ∊ BMOA for which

and

(ii) for 2 < p < ∞, there exists an analytic function f ∉ BMOA for which

This settles the question of Stroethoff [5] on BMOA.
A Relation Between S1 and S3-Invariant Homotopy In The Stable Range
Authors: Gilbert Shirley M. F. , Zvengrowski Peter
Published: December 2010

For any X and any q > 0, one has natural inclusions where the groups S1 and S3 act on S4q-1 in the standard way and are the G-invariant homotopy subsets, G = S1 or G = S3. It is proved here that for any space X of the homotopy type of a CW-complex and for π4q-1 (X) in the c3 cl stable range, the inclusion is m fact an equality when localized away from the prime 2.
Annihilating Polynomials and Positive Forms
Authors: Lewis D. W.
Published: December 2010

The annihilating polynomials for trace forms, as discovered recently by Conner, are shown to also annihilate many other classes of positive quadratic forms over a field F provided that F satisfies suitable conditions.
Finite Lattices of Projections in Factors and Approximately Finite C*-Algebras
Authors: Power S. C.
Published: December 2010

A unique factorisation theorem is obtained for tensor products of finite lattices of commuting projections in a factor. This leads to unique tensor product factorisations for reflexive subalgebras of the hyperfinite II1 factor which have irreducible finite commutative invariant projection lattices. It is shown that the finite refinement property fails for simple approximately finite C*-algebras, and this implies that there is no analogous general result for finite lattice subalgebras in this context.
Automorphisms and Derivations of Skew Polynomial Rings
Authors: Rosen Mary P. , Rosen Jerry D.
Published: December 2010

For a prime ring R and σ ∊ Aut(R), we determine the group of Rstabilizing automorphisms of the skew polynomial ring R[x; σ]. In the case where R is simple, we characterize the X-inner automorphisms of R[x; σ]. We also provide necessary and sufficient conditions for a σ -commuting derivation of a prime ring R to extend to a derivation of R[x; σ].
On Tate-Drinfeld Modules
Authors: Bae Sunghan , Kang Pyung-Lyun
Published: December 2010

The Tate-Drinfeld module is defined by Gekeler. We define the Tate- Drinfeld map and show the analogous properties concerning Tate elliptic curves and Tate map.
Deformations of Secondary Classes for Subfoliations
Authors: Domínguez Demetrio
Published: December 2010

The purpose of this paper is to study the rigidity and deformations of secondary characteristic classes for subfoliations.
Module Homomorphisms of the Dual Modules of Convolution Banach Algebras
Authors: Ghahramani F. , Mcclure J. P.
Published: December 2010

Suppose that A is either the group algebra L1 (G) of a locally compact group G, or the Volterra algebra or a weighted convolution algebra with a regulated weight. We characterize: a) Module homomorphisms of A*, when A* is regarded an A** left Banach module with the Arens product, b) all the weak*-weak* continuous left multipliers of A**.
Regular Elliptic Classes and the Stable Relative Trace Formula
Authors: Lai K. F.
Published: December 2010

We study the relative trace formula of a reductive group over an algebraic number field. Following Langlands we stabilize the geometric side of the relative trace formula contributed by the elliptic regular double cosets.
Reflexive Modules Over QF-3 Rings
Authors: Masaike Kanzo
Published: December 2010

We give a characterization of reflexive modules over QF-3 rings generalizing the concept of linearly compact modules. Further, we study necessary and sufficient conditions for left QF-3 rings to be right QF-3.
Representation of p-Lattice Summing Operators
Authors: Pomares Beatriz Porras
Published: December 2010

In this paper we study some aspects of the behaviour of p-lattice summing operators. We prove first that an operator T from a Banach space E to a Banach lattice X is p-lattice summing if and only if its bitranspose is. Using this theorem we prove a characterization for 1 -lattice summing operators defined on a C(K) space by means of the representing measure, which shows that in this case 1 -lattice and ∞-lattice summing operators coincide. We present also some results for the case 1 ≤ p < ∞ on C(K,E).
On the Limitations of Sketches
Authors: Barr Michael , Wells Charles
Published: December 2010

Call a category "sketchable" if it is the category of models in sets of some sketch. This paper explores the subtle boundary between sketchable and non-sketchable categories. We show that the category of small categories that have at least one initial object and functors that take an initial object to an initial object is sketchable. The same is true for weak initial objects, but is false for subinitial objects (that every object has at most one arrow to). Analogous results hold if we substitute finite limits for terminal object. We also show that the category of groups and center-preserving homomorphisms is not sketchable. We describe briefly how "higher-order" sketches can fill these gaps.
Factorization into Symmetries and Transvections of Given Conjugacy Classes
Authors: Knüppel Frieder
Published: December 2010

The u-invariant u(K) of a field K is the smallest number such that every k-dimensional regular quadratic form over K is universal. Let O(V,f) be the orthogonal group of a finite-dimensional regular metric vector space over a field K of characteristic distinct from 2. Let π ∊ 0(V), B(π) := V(π - 1), dim[B(π) ∩ kernel(π - 1)] > u(K). Given λ1,..., λm ∊ K* where m := dim B(π) - u(K) + 1. Then π = σ1······σk where k := dim B(π) and σi is a symmetry with negative space Kai and f(ai, ai) = λi for i ∊ { 1 , . . . , m}. We prove similar theorems also for symplectic groups where transvections are taken as generators.
A Variational Characterization of Contact Metric Manifolds With Vanishing Torsion
Authors: Blair D. E. , Perrone D.
Published: December 2010

Chern and Hamilton considered the integral of the Webster scalar curvature as a functional on the set of CR-structures on a compact 3-dimensional contact manifold. Critical points of this functional can be viewed as Riemannian metrics associated to the contact structure for which the characteristic vector field generates a 1-parameter group of isometries i.e. K-contact metrics. Tanno defined a higher dimensional generalization of the Webster scalar curvature, computed the critical point condition of the corresponding integral functional and found that it is not the K-contact condition. In this paper two other generalizations are given and the critical point conditions of the corresponding integral functionals are found. For the second of these, this is the K-contact condition, suggesting that it may be the proper generalization of the Webster scalar curvature.
Divisors on Varieties Over a Real Closed Field
Authors: Kucharz W.
Published: December 2010

Let X be a projective nonsingular variety over a real closed field R such that the set X(R) of R-rational points of X is nonempty. Let ClR(X) = Cl(X)/Γ(X), where Cl(X) is the group of classes of linearly equivalent divisors on X and Γ(X) is the subgroup of Cl(X) consisting of the classes of divisors whose restriction to some neighborhood of X(R) in X is linearly equivalent to 0. It is proved that the group ClR(X) is isomorphic to (Z/2)s for some non-negative integer s. Moreover, an upper bound on s is given in terms of the Z/2-dimension of the group cohomology modules of Gal(C/R), where , with values in the Néron-Severi group and the Picard variety of Xc = X xR C.