bluuebunny/crossref_metadata_2025 huggingface dataset:
A Generalization of the Lax-Milgram Lemma
Authors: Inayatnoor K. , Noor M. Aslam
Published: December 2010

Let H be a real Hilbert space with its dual space H'. The norm and inner product in H are denoted by ||.|| and 〈.,.〉 respectively. We denote by 〈.,.〉, the pairing between H' and H.

If a(u, v) is a bilinear form and F is a real-valued continuous functional on H, then we consider I[v], a functional defined by
Some Examples of Smooth and Regular Rings(1)
Authors: Roberts Leslie G.
Published: December 2010

In this note I investigate smoothness and regularity of the ring the ring of integers. These results do not seem to be well known, especially those dealing with regularity. At any rate, several of my colleagues knew that was not smooth, but thought that it might be regular. I was surprised by the number of possibilities that can occur, as well as by the fact that A can be regular but not smooth. As expected the prime 2 plays a special role. Smoothness depends on a, b, c mod 2, and regularity depends on a, b, c mod 4.
Some Triangle Inequalities and Generalizations
Authors: Carroll C. E. , Yang C C. , Ahn S.
Published: December 2010

Let , where ai, s, and x are real, and II denotes the product over cyclic rearrangements of the subscripts. We show that, in five special cases, Dn, s(x)Dn, s(y) is greater than a fixed multiple of Dn, s(x + y).
On Prime Semilattices
Authors: Pawar Y. S. , Thakare N. K.
Published: December 2010

Several characterizations for prime semilattices are obtained. Prime semilattices that are compactly packed by filters have been characterized. Solution to the problem, “Find a condition on a semilattice by which every filter can be expressed as the intersection of all prime filters containing it”, is furnished.
The Ruin Problem for Sums of Dependent Random Variables
Authors: Johnson Dudley Paul
Published: December 2010

In this paper we show how to compute the probability that a sequence Zn = X0 + … + Xn of partial sums of dependent random variables, each taking on the values ±1, will first leave an interval (a, b) at a; and how to compute the expected time it takes for the partial sums to leave the interval (a, b).
Some Generalizations of Carathéodory′s Theorem Via Barycentres, with Application to Mathematical Programming
Authors: Tijs S. H. , Borwein J. M.
Published: December 2010

A theorem on the barycentre of a measure is proven which leads to generalization of Carathéodory′s theorem and to extension of various results. A mathematical programming problem is examined in application.
On the Non-Existence of Certain Euler Products
Authors: Subbarao M. V.
Published: December 2010

In a paper with the above title, T. M. Apostol and S. Chowla [1] proved the following result:

Theorem 1.For relatively prime integers h and k, l ≤ h ≤ k, the series

does not admit of an Euler product decomposition, that is, an identity of the form

1

except when h = k = l; fc = 1, fc = 2. The series on the right is extended over all primes p and is assumed to be absolutely convergent forR(s)>1.
An Upper Limit Property of the Euler Function
Authors: Hausman Miriam
Published: December 2010

If ϕ(n) denotes the Euler function, for n = p a prime we have ϕ(n)/n = (1-1/p), which implies that

In this note we consider a refinement of this result. Namely, we prove that

1

where P∗(k) is the largest integer of the form where p1 < p2<…<pr are the first r primes in ascending order.
A Summability Problem
Authors: Macphail M. S.
Published: December 2010

In a paper by Wilansky and the writer [4] there were five questions left open, four of which have been answered by Beekman and the writer, [1], [3]. We shall consider the fifth one, namely, “If , must for every matrix D with cD = cA?” Here A is a conservative summability matrix with column limits .
Prime z-Ideals of C(X) and Related Rings
Authors: Mason Gordon
Published: December 2010

Let C(X) be the ring of continuous real-valued functions on a (completely regular) topological space X. The structure of the prime ideals and the prime z-ideals of C(X) has been the subject of much investigation (see e-g- [1], [3], [5]). One of the surprising facts about C(X) is that the sum of two prime ideals is again prime.
A Note on Fixed Point Sets and Wedges
Authors: Martin John R. , Nadler Sam B.
Published: December 2010

A space Z is said to have the complete invariance property (CIP) provided that every nonempty closed subset of Z is the fixed point set of some continuous self-mapping of Z. In this paper it is shown that there exists a one-dimensional contractible planar continuum having CIP whose wedge with itself at a specified point is contractible, planar, and does not have CIP.
On the Topologies of R∞
Authors: Ho Chung-Wu
Published: December 2010

Let R∞ be the set of all the finite sequences of real numbers. The author shows that there are uncountably many distinct topologies on the set R∞, each of which coincides with the usual topology when restricted to an Rn. However, under each of these topologies, R∞ is always of the same homotopy type. A generalization to some other spaces is mentioned.
A Generalization of Floyd's Theorem on Unicoherent Peano Continua with Involution
Authors: Grover A. K. , Hunt J. H. V.
Published: December 2010

We generalize a result of E. E. Floyd on unicoherent Peano continua with involution to unicoherent locally connected regular hereditarily Lindelöf spaces. The result has an application in the theory of connectivity functions.
A Note on Split Extensions of Finite Groups
Authors: Pettet Martin R.
Published: December 2010

Let N and K be finite groups with K acting on N, and let G be the semidirect product NK It was shown by Zassenhaus that if (|N|, |K|) — 1 and either N or K is solvable (an assumption later rendered redundant by the Feit-Thompson theorem), then all complements of N in G are conjugate to K.
A Problem of R. H. Fox
Authors: Gupta Narain
Published: December 2010

The purpose of this expository article is to familiarize the reader with one of the fundamental problems in the theory of infinite groups. We give an up-to-date account of the so-called Fox problem which concerns the identification of certain normal subgroups of free groups arising out of certain ideals in the free group rings. We assume that the reader is familiar with the elementary concepts of algebra.
The π-Full Tight Riesz Orders on A(Ω)
Authors: Davis Gary , McCleary Stephen H.
Published: December 2010

Let G be a lattice-ordered group (l-group), and let t, u∈ G+. We write tπu if t ∧ g = 1 is equivalent to u ∧ g = 1, and say that a tight Riesz order T on G is π-full if t ∈ T and t π U imply u∈T. We study the set of π-full tight Riesz orders on an l-permutation group (G, Ω), Ω a totally ordered set.
An Extrapolation Theorem for Contractions with Fixed Points
Authors: Sato Ryotaro
Published: December 2010

In [9] de la Torre proved that if is a finite measure space and T is a linear operator on a real for some fixed p, 1 < p < ∞ , such that ||T||P ≤ 1 and simultaneously ||T||∞ ≤ l, and also such that there exists with Th = h and h≠0 a.e., then the dominated ergodic theorem holds for T, i.e. for every we have

de la Torre proved his result, by showing that the operator S, defined by Sf = (sgn h) - T(f • sgn h) for is positive, and by applying Akcoglu's theorem [1] to S.
Reciprocals of Certain Large Additive Functions
Authors: De Koninck J.-M. , Erdös P. , Ivić A.
Published: December 2010

Let β(n) = ∑p|nP and B(n) = ∑Pα||nαP denote the sum of distinct prime divisors of n and the sum of all prime divisors of n respectively. Both β(n) and B(n) are additive functions which are in a certain sense large (the average order of B(n) is π2n/(6 log n), [1]).
On Gleason's Definition of Quadratic Forms
Authors: Davison T. M. K.
Published: December 2010

Suppose R is a commutative ring with identity. Let M be an R -module, and suppose f is a function from M to R. How do we characterize the property that f be a quadratic form?
A Finitely Generated Modular Ortholattice
Authors: Herrmann Christian
Published: December 2010

By an ortholattice we mean a lattice with 0 and 1 and a complementation operation which is an involutorial antiautomorphism. The free modular ortholattice on two generators has 96 elements—cf. J. Kotas [8].
On a Paper of G. Mason
Authors: Feigelstock Shalom
Published: December 2010

Mason, [1, Theorem 2.6], proved that for any near-ring R, there are no non-trivial injective R-modules. In his proof he embedded R into a simple R -module G of arbitrarily high cardinality.
On the Zeros of Power Series with Exponential Logarithmic Coefficients
Authors: Gawronski W. , Stadtmüller U.
Published: December 2010

In this paper we investigate the zeros of power series

1

for some functions of coefficients A. In particular, we derive upper and lower bounds for the number of zeros of f in its domain of analyticity.
A Characterization of Line Spaces
Authors: Whitfield J. H. M. , Yong S.
Published: December 2010

The line spaces of J. Cantwell are characterized among the axiomatic convexity spaces defined by Kay and Womble. This characterization is coupled with a recent result of Doignon to give an intrinsic solution of the linearization problem.
Oscillation Theorems for Nonlinear Ordinary Differential Equations of Even Order
Authors: Kreith Kurt , Kusano Takaŝi
Published: December 2010

Consider the differential equation

1

wherenis even andf(t, y)is subject to the following conditions:

(a)f(t, y)is continuous on [0, ∞)×R;

(2) (b)f(t, y)is nondecreasing inyfor each fixedt∈[0,∞);

(c)yf(t, y )> 0 fory≠ 0 andt∈[0,∞).
On the Approximation of Fixed Points of Locally Nonexpansive Mappings
Authors: Kirk W. A. , Morales Claudio
Published: December 2010

It is shown that techniques of Browder and Ishikawa for approximating fixed points of nonexpansive mappings extend in a more restricted sense to the locally nonexpansive case.
Speculations Concerning the Range of Mahler's Measure
Authors: Boyd David W.
Published: December 2010

I would like to express my thanks to the Canadian Mathematical Society for inviting me to present this lecture. I would also like to express my appreciation to C.J. Smyth for numerous helpful conversations during his visit this year at the University of British Columbia.

This paper follows reasonably closely the outline of the lecture presented in Ottawa. More details are given here though and a number of proofs which would not be otherwise accessible have been added as Appendices. The attentive reader will soon realize the appropriateness of the title.
Remarques Sur la Représentation de Certaines Séries de Dirichlet
Authors: Mercier Armel
Published: December 2010

Le but de la présente note est de donner une preuve différente et beaucoup moins laborieuse que celle que l'on trouve dans [1] pour obtenir la représentation de étant des entiers positifs et f étant une fonction multiplicative.
Cutting and Pasting Zp-Manifolds(1)
Authors: Prevot Kenneth
Published: December 2010

Let Mn and Nn be n-dimensional closed smooth oriented Zp-manifolds where p is an odd prime and Zp is the cyclic group of order p. This paper determines necessary and sufficient conditions under which Mn and Nn are equivalent under a special equivariant cut and past equivalence.

The only invariants are (a) the Euler characteristics of the Zp-manifolds, (b) the Euler characteristics of the fixed point manifolds in each fixed point dimesnion with specified normal representations, and (c) the oriented Zp-stratified cobordism class of the Zp-manifolds.
On Quasisimilarity for Subnormal Operators, II
Authors: Conway John B.
Published: December 2010

Let S be a subnormal operator and let be the weak-star closed algebra generated by S and 1. An example of an irreducible cyclic subnormal operator S is found such that there is a T in with S and T quasisimilar but not unitarily equivalent. However, if S is the unilateral shift, T ∈ and S and T are quasisimilar, then S ≅ T.
Perfect Images of Zero-Dimensional Separable Metric Spaces
Authors: Van Mill Jan , Woods R. Grant
Published: December 2010

Let Q denote the rationals, P the irrationals, C the Cantor set and L the space C − {p} (where p ∈ C). Let f : X → Y be a perfect continuous surjection. We show: (1) If X ∈ {Q, P, Q × P}, or if f is irreducible and X ∈ {C, L}, then Y is homeomorphic to X if Y is zero-dimensional. (2) If X ∈ {P, C, L} and f is irreducible, then there is a dense subset S of Y such that f|f ← [S] is a homeomorphism onto S. However, if Z is any σ-compact nowhere locally compact metric space then there is a perfect irreducible continuous surjection from Q × C onto Z such that each fibre of the map is homeomorphic to C.
On the Non-Existence of a Projection onto the Space of Compact Operators
Authors: Feder Moshe
Published: December 2010

Let X and Y be Banach spaces, L(X, Y) the space of bounded linear operators from X to Y and C(X, Y) its subspace of the compact operators. A sequence {Ti} in C(X, Y) is said to be an unconditional compact expansion of T ∈ L (X, Y) if ∑ Tix converges unconditionally to Tx for every x ∈ X. We prove: (1) If there exists a non-compact T ∈ L(X, Y) admitting an unconditional compact expansion then C(X, Y) is not complemented in L(X, Y), and (2) Let X and Y be classical Banach spaces (i.e. spaces whose duals are some LP(μ) spaces) then either L(X, Y) = C(X, Y) or C(X, Y) is not complemented in L(X, Y).
Antidirected Subtrees of Directed Graphs
Authors: Burr Stefan A.
Published: December 2010

The purpose of this paper is to prove the following result:

Theorem. Let T be a directed tree with k arcs and with no directed path of length 2. Then if G is any directed graph with n points and at least 4kn arcs, T is a subgraph of G.

It would be appropriate to call T an antidirected tree or a source-sink tree, since every point either has all its arcs directed outward or all inward. As N. G. de Bruijn has noted (personal communication), such a linear bound in n cannot hold if T is replaced by any directed graph other than a union of such trees. The above theorem strengthens one of Graham [1], where an implicit bound of c(k)n is obtained, where c(k) is exponentially large. The proof we give here is also shorter. We first give two simple lemmas. Both are essentially due to ErdÄs, but it is not clear where either first appeared. Their proofs are easy, so we give them here for completeness; in neither case do we state quite the best possible result.
On Dunford-Pettis Operators
Authors: Saab Elias
Published: December 2010

Let X be a complemented subspace of a Banach lattice E. It is shown that if every Dunford-Pettis operator from L1[0,1] into X is Pettis-representable then X has the Radon-Nikodym property.
Uniformly Lipschitzian Semigroups in Hilbert Space
Authors: Downing David J. , Ray William O.
Published: December 2010

Let K be a closed, bounded, convex, nonempty subset of a Hilbert Space . It is shown that if is a left reversible, uniformly k-lipschitzian semigroup of mappings of K into itself, with k < √2, then has a common fixed point in K.
A Note on Strong Riesz Summability
Authors: Thorpe B.
Published: December 2010

This note proves that if 1 ≤ p < ∞ and 1 − 1/p < k < 2 − 1/p then the space of sequences strongly Riesz summable [R, λ, k]p to 0 has AK. Using general results of Jakimovski and Russell it is then possible to deduce a best possible limitation condition and a convergence factor result for [R, λ, k]p.
On the Decomposition of Continuous Modules
Authors: Müller Bruno J. , Rizvi S. Tariq
Published: December 2010

We prove two theorems on continuous modules:Decomposition Theorem. A continuous moduleMhas a decomposition,M=M1⊕M2, such thatM1is essential over a direct sumof indecomposable summandsAiofM, andM2has no uniform submodules; and these data are uniquely determined byMup to isomorphism.Direct Sum Theorem. A finite direct sumof indecomposable modulesAiis continuous if and only if eachAiis continuous andAj-injective for allj≠ i.
0-Distributive and P-Uniform Semilattices
Authors: Hoo C. S. , Shum K. P.
Published: December 2010

A counter-example is provided to the conjecture of Y. S. Pawar and N. K. Thakare that a semilattice S with 0 is 0-distributive if and only if for each filter F and each ideal I such that F ∩ I = Ø, there exists a prime filter containing F and disjoint from I. This shows that 0-distributivity is not equivalent to weak distributivity. A characterization is also given of finite P-uniform semilattices in terms of 0-distributivity.
The Duals of the Camillo-Zelmanowitz Formulas for Goldie Dimension
Authors: Haack Joel K.
Published: December 2010

The duals of the Camillo-Zelmanowitz formulas for Goldie dimension are shown to hold for Varadarajan's notion of corank, subject to the existence of certain cocomplements. In particular, the formulas hold for modules over perfect rings. Also, if R is semiperfect, then the vector space dimension formulas hold for all modules over R for Goldie dimension iff they hold for corank iff R is semisimple.
The Exceptional Sets in the Definition of the Pn-Integral
Authors: Cross G. E.
Published: December 2010

It has been recently observed by S. N. Mukhopadhyay that the various definitions of the Pn-integral are not complete unless it is shown that the exceptional scattered set allowed in the definition is not important. Utilizing the fact that on the real line a scattered set is countable, and adapting known methods for coping with exceptional countable sets, it is proved that the definitions of the Pn-integral are complete. It is then clear that the concept of scattered set is not essential to the definition of the Pn-integral.
A General Inclusion Theorem for l-l Nörlund Summability
Authors: Defranza J.
Published: December 2010

Nӧrlund methods of summability are studied as mappings from I1 into I1. Conditions are given for an arbitrary l-l method to include a Nӧrlund method. In particular necessary and sufficient conditions are given for a row finite l-l method to include a Nӧrlund mean.
Correction to a Result of Jain on a Correlated Random Walk
Authors: Nain R. B. , Sen Kanwar
Published: December 2010

The authors have found that the formula forU(t)— the probability generating function (p.g.f) of a return to the starting position, obtained by Jain [1, p. 344] is incorrect and have obtained its correct formulae.
The Best Interpolating Approximation is a Limit of Best Weighted Approximations
Authors: Keener Lee L.
Published: December 2010

Under appropriate conditions it is shown that the best interpolating approximation to a given function in the uniform norm is a limit of best unconstrained approximations with respect to a certain sequence of discontinuous weight functions.
On Padé and Best Rational Approximation
Authors: Borwein Peter B.
Published: December 2010

It is reasonable to expect that, under suitable conditions, Padé approximants should provide nearly optimal rational approximations to analytic functions in the unit disc. This is shown to be the case for ez in the sense that main diagonal Padé approximants are shown to converge as expeditiously as best uniform approximants. Some more general but less precise related results are discussed.
Compactness and Almost Periodicity of Multipliers
Authors: Crombez G.
Published: December 2010

The question as to the existence of nontrivial compact or weakly compact multipliers between spaces of functions on groups has been investigated for several years. Until now, however, no general method which is applicable to a large class of function spaces seems to be known

In this paper we prove that the existence of nontrivial compact multipliers between Banach function spaces on which a group acts is related to the existence of nonzero almost periodic functions.
Boolean Algebras and Raising Maps to Zero-Dimensional Spaces
Authors: van Mill Jan
Published: December 2010

Let X be a separable metric space and let be a family of countably many self-maps of X. Then there is a countable subalgebra of the Boolean algebra of regular open subsets of X which is a base for X such that for each the function defined by Φf(B) = (f-1(B))-0 is a homomorphism.
On the Product of Ideals
Authors: Anderson David F. , Dobbs David E.
Published: December 2010

This article introduces the concept of a condensed domain, that is, an integral domain R for which IJ = {ij: i ∊ I, j ∊ J} for all ideals I and J of R. This concept is used to characterize Bézout domains (resp., principal ideal domains; resp., valuation domains) in suitably larger classes of integral domains. The main technical results state that a condensed domain has trivial Picard group and, if quasilocal, has depth at most 1. Special attention is paid to the Noetherian case and related examples.
Uniformly Continuous Partitions of
Unity on a Metric Space
Authors: Robinson Stewart M. , Robinson Zachary
Published: December 2010

In this paper, we construct, for any open cover of a metric space, a partition of unity consisting of a family of uniformly continuous functions.
Lp Spaces from Matrix Measures: A Correction and their Interpolation
Authors: Browne Patrick J. , Costa Claude
Published: December 2010

We discuss the construction of the spaces Lp(μij), 1 ≤ p ≤ ∞, where {μij} is an n × n positive matrix measure, correct a mistake in the literature concerning those spaces and develop an interpolation theory for them.
On Comonotone Approximation
Authors: Beatson R. K. , Leviatan D.
Published: December 2010

Jackson type theorems are obtained for the comonotone approximation of piecewise monotone functions by polynomials.
The Second Dual of a C*-Ternary Ring
Authors: Landesman E. M. , Russo Bernard
Published: December 2010

The Arens extension of the triple product of an associative triple system is studied. Using a representation theorem for C*-ternary rings due to Zettl, it is shown that the second dual of a C*-ternary ring is itself a C*-ternary ring
Bipartite Score Sets
Authors: Wayland Keith
Published: December 2010

The question of what sets of integers may be the score sets of bipartite tournaments was posed recently by K. B. Reid. The main theorem of this paper establishes a sufficient condition for pairs of sets to be bipartite score sets. This simple condition yields an immediate affirmative answer for a large class of pairs of sets.
The Field Generated by the Discriminant of the Class Invariants of an Imaginary Quadratic Field
Authors: Dummit D. S. , Gold R. , Kisilevsky H.
Published: December 2010

This note determines the quadratic field generated by the square root of the discriminant of the modular equation satisfied by the special value j(α) of the modular function α for a an integer in an imaginary quadratic field.
Isotropic Immersions with Parallel Second Fundamental Form
Authors: Maeda Sadahiro
Published: December 2010

The main purpose of this paper is to give a characterization of a Veronese manifold, as a generalization of a Veronese surface, in terms of isotropic immersions. This is an improvement of Itoh and Ogiue's results.
Some Hypersurfaces of Symmetric Spaces
Authors: Matsuyama Yoshio
Published: December 2010

In this paper we consider how much we can say about an irreducible symmetric space M which admits a hypersurface N with at most two distinct principal curvatures. Then we will obtain that (1) if N is locally symmetric, then M must be a sphere, a real projective space and their noncompact duals (2) if N is Einstein, then M must be rank 1.
Ordered Fibonacci Partitions
Authors: Prodinger Helmut
Published: December 2010

Ordered partitions are enumerated by Fn = Σk k !S(n, k) where S(n, k) is the Stirling number of the second kind. We give some comments on several papers dealing with ordered partitions and turn then to ordered Fibonacci partitions of {1, ߪ, n}: If d is a fixed integer, the sets A appearing in the partition have to fulfill i, j ∈ A, i ≠ j ⟹ |i-j| ≥ d. The number of ordered Fibonacci partitions is determined.
On a Parametrized Levi Problem Involving One Complex Variable
Authors: Gilligan Bruce
Published: December 2010

The classical Levi problem in several complex variables characterizes domains of holomorphy in terms of a boundary condition called pseudo convexity. The purpose of this note is to give a characterization of those domains D in ℂ×ℝ, where one can always solve the -problem with C∞ parameters, in terms of a certain kind of convexity condition on their boundaries.
A Note on a Wiener-Pitt Theorem on Wiener Groups
Authors: Karanikas C.
Published: December 2010

It is shown that suitable conditions on the components of a measure in the algebra M(G) ensure that this element lies outside of all maximal bi-ideals.
Nilpotency of Derivations
Authors: Chung L. O. , Luh Jiang
Published: December 2010

It is shown that the nilpotency of a derivation on a 2-torsion free semiprime ring is always an odd number. Examples are provided to show the necessity of the assumptions.
Oscillation Properties of Weakly Time Dependent Hyperbolic Equations
Authors: Kreith Kurt
Published: December 2010

A Sturmian comparison theorem is established for a pair of linear hyperbolic differential equations. While the equations may be time dependent (in the sense of not allowing a separation of variables), a measure of the strength of such time dependence enters into the hypotheses of the theorem.
The Krall Polynomials as Solutions to a Second Order Differential Equation
Authors: Littlejohn Lance L.
Published: December 2010

A popular problem today in orthogonal polynomials is that of classifying all second order differential equations which have orthogonal polynomial solutions. We show that the Krall polynomials satisfy a second order equation of the form

1.1
La Règle Du Trapèze Appliquée à Quelques Fonctions Sans Dérivées
Authors: Dubuc Serge , Todor Fabian
Published: December 2010

Pour chaque nombre α de (0, 1), nous construisons une fonction f qui est lipschitzienne d'ordre α et dont le reste Rn(f) par l'application de la règle du trapèze est précisément égal à 1/n lorsque n est une puissance entière et arbitraire de 2.
A Class of Addition Theorems†
Authors: Srivastava H. M. , Lavoie J.-L. , Tremblay Richard
Published: December 2010

Recently, H. M. Srivastava extended certain interesting generating functions of L. Carlitz to the forms:

and

where are general oncand many-parameter sequences of functions. In the present paper some general addition formulas for analogous sequences of functions are derived, and a number of interesting applications of the main results are given.
Sets with No Empty Convex 7-Gons
Authors: Horton J. D.
Published: December 2010

Erdös has defined g(n) as the smallest integer such that any set of g(n) points in the plane, no three collinear, contains the vertex set of a convex n-gon whose interior contains no point of this set. Arbitrarily large sets containing no empty convex 7-gon are constructed, showing that g(n) does not exist for n≥l. Whether g(6) exists is unknown.
Finite Complexes and Integral Representations II
Authors: Schafer James A.
Published: December 2010

In the paper "Finite complexes and integral representations" [Illinois Journal of Math, 26, (1982), p 442] an exact sequence relating homotopy types of (G, d)-complexes with objects of integral representation theory together with some known calculations seemed to imply that the group of homotopy types of (G, d)- complexes was always a subquotient of (ℤ|g|)*. This paper gives a new characterization of one of the terms of the above sequence that allows one to conclude that this is not generally true.
On Subspaces of Replete and Measure Replete Spaces
Authors: Grassi Peter
Published: December 2010

The concepts of repleteness and more generally measure repleteness are investigated for set-theoretic lattices on specific subspaces of a lattice space. These general results are then applied to specific topological spaces, and we obtain as special cases some known theorems as well as some new results concerning for example, ∝-completeness, realcompactness, measure compactness and Borel-measure compactness.
Non-Parallelizability of Grassmann Manifolds
Authors: Trew S. , Zvengrowski P.
Published: December 2010

The fact that no real Grassmann manifolds Gk(Rn) are parallelizable (or even stably parallelizable) except for the obvious cases G1R2≅S1, G1(R4)≅G3(R4) ≅ RP3, and G1(R8)≅ G7(R8) ≅ RP7 was first noted by Hiller and Stong. Their work in turn depends on induction and the work of Oproiu, who examined detailed calculations of Stiefel-Whitney classes for k = 2, 3. In this note we give a short proof of this result, using elementary results from K-theory, that also covers the complex and quaternionic Grassmann manifolds.
A Representation Theorem for Distributive l-Monoids
Authors: Anderson Marlow , Edwards C. C.
Published: December 2010

In this note the Holland representation theorem for l-groups is extended to l-monoids by the following theorem: an l-monoid is distributive if and only if it may be embedded into the l-monoid of order-preserving functions on some totally ordered set. A corollary of this representation theorem is that a monoid is right orderable if and only if it is a subsemigroup of a distributive l-monoid; this result is analogous to the group theory case.
A Note on the Torsion of Bernstein Curves
Authors: Price Martin E.
Published: December 2010

It is shown that Bernstein Polynomials do not diminish the total “twist” of space curves in contrast to their length and curvature diminishing properties. This phenomenon is shown to be related to the fact that Bernstein Polynomials of a plane curve may have more inflections than the curve possesses.
Atoms, Primes and Implicative Lattices
Authors: Hoo C. S.
Published: December 2010

Let L be an a-implicative semilattice. We obtain a characterization of those elements which cover a. This gives a characterization of atoms in pseudocomplemented semilattices, and leads to various results on primes and irreducibles in semilattices. As an application, we prove that in a complete, atomistic lattice L, the following are equivalent (i) L is implicative (ii) L is (2, ∞) meet distributive (iii) each element of L is a meet of primes.
A Characterization of the Continuous q-Ultraspherical Polynomials
Authors: Al-Salam Waleed , Allaway WM. R. , Askey Richard
Published: December 2010

In his Ph.D. thesis Allaway found all polynomials
that can be represented as

and a0bn≠0. We solve the essentially equivalent problem of finding all symmetric polynomials with when are orthogonal with respect to dα(x). The polynomials are the continuous q-ultraspherical polynomials and some of their limiting cases.
Continuous Families of Smooth Curves and Grünbaum’s Conjecture
Authors: Zamfirescu Tudor , Zucco Andreana
Published: December 2010

First we construct spreads consisting of analytic curves (circular arcs and segments), without points of finite multiplicity. Then we see that, in the sense of Baire categories, most such spreads have no points of finite multiplicity.
Separating Points and Coloring Principles
Authors: Watson W. Stephen
Published: December 2010

In the mid 1970's, Shelah formulated a weak version of ◊. This axiom Φ is a prediction principle for colorings of the binary tree of height ω1. Shelah and Devlin showed that Φ is equivalent to 2ℵ0 < 2ℵ1.

In this paper, we formulate Φp, a "Φ for partial colorings", show that both ◊* and Fleissner's “◊ for stationary systems” imply Φp, that ◊ does not imply Φp and that Φp does not imply CH.

We show that Φp implies that, in a normal first countable space, a discrete family of points of cardinality ℵ1 is separated.
Compactness in Topological Hjelmslev Planes
Authors: Lorimer J. W.
Published: December 2010

In the theory of ordinary topological affine and projective planes it is known that (1) An affine plane is never compact (2) a locally compact ordered projective plane is compact and archimedean (3) a locally compact connected projective plane is compact and (4) a locally compact projective plane over a coordinate ring with bi-associative multiplication is compact. In this paper we re-examine these results within the theory of topological Hjelmslev Planes and observe that while (1) remains valid (2), (3) and (4) are false. At first glance these negative results seem to suggest we are working in too general a setting. However a closer examination reveals that the absence of compactness in our setting is a natural and expected feature which in no way precludes the possibility of obtaining significant results.
On Spectral Synthesis and Ergodicity in Spaces of Vector-Valued Functions
Authors: Weit Yitzhak
Published: December 2010

Spectral synthesis in L∞(ℝ, ℂN), N < 1, is considered. It is is proved that sets of spectral synthesis are necessarily sets of spectral resolution.

These results are applied to investigate ergodic and mixing properties of some positive contractions on L1(G, ℂN).
Finite Groups Which are Automorphism Groups of Infinite Groups Only
Authors: Zimmerman Jay
Published: December 2010

The object of this paper is to exhibit an infinite set of finite semisimple groups H, each of which is the automorphism group of some infinite group, but of no finite group. We begin the construction by choosing a finite simple group S whose outer automorphism group and Schur multiplier possess certain specified properties. The group H is a certain subgroup of Aut S which contains S. For example, most of the PSL's over a non-prime finite field are candidates for S, and in this case, H is generated by all of the inner, diagonal and graph automorphisms of S.
The Dirichlet Problem With Denjoy-Perron Integrable Boundary Condition
Authors: Benedicks M. , Pfeffer W. F.
Published: December 2010

The Poisson integral of a Denjoy-Perron integrable function defined on the boundary of an open disc is harmonic in this disc. Moreover, almost everywhere on the boundary, the nontangential limits of the integral coincide with the boundary condition. This extends the classical result for Lebesgue integrable boundary conditions. By means of conformai maps, a generalization to domains bounded by a sufficiently smooth Jordan curve is also obtained.
Equal Integrals of Functions
Authors: Cater F. S.
Published: December 2010

Let f1, . . . , fk be finitely many L1-functions on a measurable set E, and let d and r be numbers such that ∫E, fj, — d > r > 0 for all j. Then there is a measurable subset S of E such that ∫s fj = r for all j.
A Local Ergodic Theorem for Multiparameter Superadditive Processes
Authors: Sato Ryotaro
Published: December 2010

In this paper a local ergodic theorem is proved for positive (multiparameter) superadditive processes with respect to (multiparameter) semiflows of nonsingular point transformations on a a-finite measure space. The theorem obtained here generalizes Akcoglu-Krengel's [2] local ergodic theorem for superadditive processes with respect to semiflows of measure preserving transformations. The proof is a refinement of Akcoglu-Krengel's argument in [2]. Also, ideas of Feyel [3] and the author [4], [5] are used.
Zero Multipliers of Bergman Spaces
Authors: Axler Sheldon
Published: December 2010

This paper proves that if р < s, then 0 is the only function that multiplies a Bergman Lр space into a Bergman Ls space.
Relations Between the Genera and Between the Hasse-Witt Invariants of Galois Coverings of Curves
Authors: Kani Ernst
Published: December 2010

Let G ⊂ Aut (C) be a (finite) group of automorphisms of a curve C defined over a field K and, for each subgroup H ≤ G, let gH denote the genus of the quotient curve CH = C/H (briefly: quotient genus of H).

In this paper we show that certain idempotent relations in the rational group ring [G] imply relations between the quotient genera {gH}H=G this generalizes two theorems of Accola. Moreover, we show that in the case of char (K) = p ≠ 0, a similar statement holds for the Hasse-Witt invariants σH of the curves CH
Which Rationals are Ratios of Pisot Sequences?
Authors: Boyd David
Published: December 2010

A Pisot sequence is a sequence of integers defined recursively by the formula - . If 0 < a0 < a1 then an+1/an converges to a limit θ. We ask whether any rational p/q other than an integer can ever occur as such a limit. For p/q > q/2, the answer is no. However, if p/q < q/2 then the question is shown to be equivalent to a stopping time problem related to the notorious 3x + 1 problem and to a question of Mahler concerning the powers of 3/2. Although some interesting statistical properties of these stopping time problems can be established, we are forced to conclude that the question raised in the title of this paper is perhaps more intractable than it might appear.
The Cohomology of the Units in Certain Zp-Extensions
Authors: Kisilevsky H.
Published: December 2010

For K/k a Zp-extension with Galois group Γ Iwasawa in [4], poses the question of determining the cohomology groups Hn (Γ, E) of the unit group E of K. In this article we compute the cohomology of the units (up to finite groups) for a certain class of Zp-extensions.
Products of Elations and Harmonic Homologies
Authors: Ellers Erich W.
Published: December 2010

The projective special linear group PSL(V) is generated by dations. Among all factorizations of p ∈ PSL(V) into dations there will be one (or more) with the least number of factors. We determine this number, i.e. we solve the length problem for the projective special linear group. We solve a similar problem for the projective unimodular group which is generated by harmonic homologies. The projective special linear group and the projective unimodular group are the most important special cases of projective hyperreflection groups. We also solve the length problem for the general case.
Linear Maps on Hermitian Matrices: The Stabilizer of an Inertia Class
Authors: Johnson Charles R. , Pierce Stephen
Published: December 2010

Let T be a linear transformation acting on the space of n x n complex matrices. Let G(k) be the set of all hermitian matrices with k positive and n — k negative eigenvalues. Let T map some indefinite inertia class G(k) onto itself. We classify all such T. The possibilities are congruence, congruence followed by transposition, and, if n = 2k, it is possible that — T can be a congruence or a congruence followed by transposing. In other words, negation is an admissible transformation when n = 2k.
On the Analytic Determination of the Trace Form
Authors: Perlis Robert
Published: December 2010

The Dedekind zeta function of an algebraic number field E determines the rational equivalence class of the trace form of E. The Hasse symbols of the trace form are related to the local Artin root numbers of the zeta function by formulas of Serre and Deligne. This is used to settle the question of which families of complex numbers appear as the local Artin root numbers of a continuous real representation of the absolute Galois group of ℚ.
Mean Oscillation and Besov Spaces
Authors: Dorronsoro Jose R.
Published: December 2010

The homogeneous Besov-Lipschitz spaces, usually defined by difference operators or Fourier transform, are studied in terms of mean oscillation, and several equivalent characterisations are given.
On the Criteria of D.D. Anderson for Invertible and Flat Ideals
Authors: Dobbs David E.
Published: December 2010

Let R be an integral domain. It is proved that if a nonzero ideal I of R can be generated by n < ∞ elements, then I is invertible (i.e., flat) if and only if I(∩ Rai) = ∩ Iai for all { a1, . . ., a n﹜ ⊂ I. The article's main focus is on torsion-free R-modules E which are LCM-stable in the sense that E(Ra ∩ Rb) = Ea ∩ Eb for all a, b ∈ R. By means of linear relations, LCM-stableness is shown to be equivalent to a weak aspect of flatness. Consequently, if each finitely generated ideal of R may be 2-generated, then each LCM-stable R-module is flat. Finally, LCM-stableness of maximal ideals serves to characterize Prüfer domains, Dedekind domains, principal ideal domains, and Bézout domains amongst suitably larger classes of integral domains.
Co-Rank of a Composition Operator
Authors: Harrington David J.
Published: December 2010

A composition operator CT on L2(X, Σ,m) is a bounded linear transformation induced by a mapping T : X → X via CTf = f∘ T.

If m has no atoms then the co-rank of CT (i.e., dim is either zero or infinite. As a corollary, when m has no atoms, CT is a Fredholm operator iff it is invertible.
An Optimization Problem Related to the Zeta-function
Authors: Guiasu Silviu
Published: December 2010

S. Golomb noticed that Riemann's zeta function ζ induces a probability distribution on the positive integers, for any s > 1, and studied some of its properties connected to divisibility. The object of this paper is to show that the probability distribution mentioned above is the unique solution of an entropy-maximization problem.
A Generalization of Smith's Determinant
Authors: McCarthy P. J.
Published: December 2010

We shall evaluate the determinants ofnxnmatrices of the form[f(i,j)],wheref (w, r)is an even function of m (modr).Among the examples of determinants of this kind are H. J. S. Smith's determinant det[(i,j)],where(m, r)is the greatest common divisor ofmandr,and a generalization of Smith's determinant due to T. M. Apostol.
On Complete Intersections Over an Algebraically Non-Closed Field
Authors: Marinari Maria Grazia , Raimondo Mario
Published: December 2010

We give a criterion in order that an affine variety defined over any field has a complete intersection (ci.) embedding into some affine space. Moreover we give an example of a smooth real curve C all of whose embeddings into affine spaces are c.i.; nevertheless it has an embedding into ℝ3 which cannot be realized as a c.i. by polynomials.
Fixed Point Theorems for Proximately Nonexpansive Semigroups
Authors: Kiang Mo Tak , Tan Kok-Keong
Published: December 2010

A commutative semigroup G of continuous, selfmappings on (X, d) is called proximately nonexpansive on X if for every x in X and every (β > 0, there is a member g in G such that d(fg(x),fg(y)) ≤ (1 + β) d (x, y) for every f in G and y in X. For a uniformly convex Banach space it is shown that if G is a commutative semigroup of continuous selfmappings on X which is proximately nonexpansive, then a common fixed point exists if there is an x0 in X such that its orbit G(x0) is bounded. Furthermore, the asymptotic center of G(x0) is such a common fixed point.
Groups Admitting only Finitely Many Nilpotent Ring Structures
Authors: Feigelstock Shalom
Published: December 2010

The abelian groups which are the additive groups of only finitely many non-isomorphic (associative) nilpotent rings are studied. Progress is made toward a complete classification of these groups. In the torsion free case, the actual number of non-isomorphic nilpotent rings these groups support is obtained.
Remarks on the Intersection of Finitely Generated Subgroups of a Free Group
Authors: Burns R. G. , Imrich Wilfried , Servatius Brigitte
Published: December 2010

The first result gives a (modest) improvement of the best general bound known to date for the rank of the intersectionU ∩ Vof two finite-rank subgroups of a free groupFin terms of the ranks ofUandV. In the second result it is deduced from that bound that ifAis a finite-rank subgroup ofFandB < Fis non-cyclic, then the index ofA ∩ BinB, if finite, is less than 2(rank(A) - 1), whence in particular if rank (A) = 2, thenB ≤ A. (This strengthens a lemma of Gersten.) Finally a short proof is given of Stallings' result that ifU, V(as above) are such thatU ∩ Vhas finite index in bothUandV, then it has finite index in their join 〈U, V〉.
The Nilpotency Class Of The p-Sylow Subgroups of GL(n, q) Where (p, q) = 1
Authors: Bialostocki Arie
Published: December 2010

Formulae for the nilpotency class of the p-sylow subgroups of GL(n, q) where (p, q) = 1 are derived. These formulae are used in author's following paper: “On the other pα qβ theorem of Burnside”.
Sommes Contenant des Coefficients Binomiaux de Gauss
Authors: Armel Mercier
Published: December 2010

Identities containing the Gaussian binomial coefficient are obtained. From these results, we deduce some identities of the combinatorial analysis which contain the binomial coefficient
Lattice Partitions with a Straight Line
Authors: Brownrigg D. R. K.
Published: December 2010

In [1], the solution of a problem of distinct digital filter enumeration was expressed in terms of enumerating partitions of a rectangular set of lattice points with a straight line, under certain restrictions. Here, firstly, an explicit expression is derived for the number of such partitions in that and a more general case. Secondly, the asymptotic ratio of partitions to square of lattice dimensions is derived for a square lattice.
Some Results on Generalized Lototsky Summability
Authors: Miller J. F.
Published: December 2010

The (F, dn) method is investigated with respect to perfectness, strong regularity, and summing bounded divergent sequences. In the process the columns of the inverse matrix are characterized in terms of {dn}.
A Method for Constructing Square Roots in Finite Full Transformation Semigroups
Authors: Higgins Peter M.
Published: December 2010

Let Tn denote the full transformation semigroup on the set X = {1,2,. . .,n}, that is the set of all mappings from X to X, the semigroup operation being composition of mappings. The aim of this paper is to provide a method for the construction of all square roots of an arbitrary element α ∈ Tn, by employing a representation of the members of Tn as special directed graphs.
Some Properties of Bounded Holomorphic Mappings Defined on Bounded Homogeneous Domains
Authors: Kubota Yoshihisa
Published: December 2010

Let F be a bounded holomorphic mapping defined on a bounded homogeneous domain in ℂN. We study the relation between the Jacobian JF(z) and the radius dF(z) of uni valence of F.
Generalized Solutions of Autonomous Algebraic Differential Equations
Authors: Rubel Lee A.
Published: December 2010

In an earlier paper, the author introduced the notions of N-solutions and IN-solutions of algebraic differential equations (ADE's). Here it is shown, in contradistinction to the situation for Cn solutions, that every N-solution of an ADE is an N-solution of an autonomous ADE. The corresponding result also holds for IN-solutions.
Homogeneous Bundles and Universal Potentials
Authors: Fegan H. D.
Published: December 2010

This paper studies complex potentials on homogeneous bundles over a compact Lie group. It extends the previous work of V. Guillemin and A. Uribe on potentials isospectral to the zero potential. Then the notion of a universal potential is introduced, that is a potential which acts on sections by a group representation rather than as a scalar. Finally the inverse question of whether the spectral data of a complex potential on all bundles over S2 determines the potential is answered negatively.
Oscillations of Neutral Delay Differential Equations
Authors: Ladas G. , Sficas Y. G.
Published: December 2010

The oscillatory behavior of the solutions of the neutral delay differential equation

where p, τ, and a are positive constants and Q ∊ C([t0, ∞), ℝ+), are studied.
The Meet Operator in the Lattice of Group Topologies
Authors: Clark Bradd , Schneider Victor
Published: December 2010

It is well known that the lattice of topologies on a set forms a complete complemented lattice. The set of topologies which make G into a topological group form a complete lattice L(G) which is not a sublattice of the lattice of all topologies on G.

Let G be an infinite abelian group. No nontrivial Hausdorff topology in L(G) has a complement in L(G). If τ1 and τ2 are locally compact topologies then τ1Λτ2 is also a locally compact group topology. The situation when G is nonabelian is also considered.
Examples of Factorial Rings in Algebraic Geometry
Authors: Bochnak Jacek , Kucharz Wojciech
Published: December 2010

We show that the ring of complex-valued regular functions on an affine irreducible nonsingular real algebraic variety X is factorial if dim X = 1 or dim X = 2 and X has no compact connected components or X is compact and the second cohomology group of X with integral coefficients vanishes.
SP Transform and Uniform Convergence of Laurent and Power Series
Authors: Settu S.A.
Published: December 2010

If the Laurent series

is transformed to

it is shown that convergence of the former at z = 1 implies the uniform convergence of the latter on a symmetric arc of |z - 1/P| = 1/P - 1 not containing z = 1 and that the uniform convergence of the former over a symmetric arc of |z| = 1 containing z = 1 implies uniform convergence of the latter on the entire circle |z — 1/P| = 1/P — 1.