bluuebunny/crossref_metadata_2025_split huggingface dataset:
Translates of Sequences in Sets of Positive Measure
Authors: Borwein D. , Ditor S. Z. 
Published: December 2010

Given a measurable set A of real numbers with measure mA > 0, and a sequence {dn} of real numbers converging to zero, is there always an x such that x + dn ∈ A for all n sufficiently large?The answer to this question, which was posed to the authors by P. Erdös, is NO.
Square-Reduced Residue Systems (Mod r) and Related Arithmetical Functions
Authors: Sivaramakrishnan R. 
Published: December 2010

AbstractWe define a square-reduced residue system (mod r) as the set of integers a (mod r) such that the greatest common divisor of a and r, denoted by (a, r), is a perfect square ≥ 1 and contained in a residue system (mod r). This leads to a Class-division of integers (mod r) based on the 'square-free' divisors of r. The number of elements in a square-reduced residue system (mod r) is denoted by b(r). It is shown that(1)(2)In view of (2), b(r) is said to be 'specially multiplicative'. The exponential sum associated with a square-reduced residue system (mod r) is defined bywhere the summation is over a square-reduced residue system (mod r).B(n, r) belongs to a new class of multiplicative functions known as 'Quasi-symmetric functions' and(3)As an application, the sum is considered in terms of the Cauchy-composition of even functions (mod r). It is found to be multiplicative in r. The evaluation of the above sum gives an identity involving Pillai's arithmetic function
A Note on Bernstein's Bivariate Inequality
Authors: Mullen K. 
Published: December 2010

SummaryAn upper bound for P[Σ Xi≥tσ, Σ Yi ≥ tσ], where (Xi, Yi), i = 1, 2, …, n are bounded independent random variables, was given by Mullen (1973). An improvement to the bound is possible without further assumptions.
Local Unique Factorization in the Semigroup of Paths in ℝn
Authors: Putcha Mohan S. 
Published: December 2010

AbstractLet S denote the semigroup of all rectifiable, piecewise continuously difïerentiable paths in ℝn under concatenation. We prove a theorem to the effect that every finite collection of paths is contained in a subsemigroup of S which has the unique factorization property with respect to certain primes and straight lines. We also determine an abstract necessary sufficient condition for a subsemigroup of S to have this unique factorization property.
Complete Diagonals of Latin Squares
Authors: Chang Gerard J. 
Published: December 2010

AbstractJ. Marica and J. Schönhein [4], using a theorem of M. Hall, Jr. [3], see below, proved that if any n − 1 arbitrarily chosen elements of the diagonal of an n × n array are prescribed, it is possible to complete the array to form an n × n latin square. This result answers affirmatively a special case of a conjecture of T. Evans [2], to the effect that an n × n incomplete latin square with at most n − 1 places occupied can be completed to an n × n latin square. When the complete diagonal is prescribed, it is easy to see that a counterexample is provided by the case that one letter appears n − 1 times on the diagonal and a second letter appears once. In the present paper, we prove that except in this case the completion to a full latin square is always possible. Completion to a symmetric latin square is also discussed.
Complements of Minimal Ideals in Solvable Lie Rings
Authors: Stitzinger Ernest L. 
Published: December 2010

AbstractConditions for the existence and conjugacy of complements of certain minimal ideals of solvable Lie algebras over a Noetherian ring R are considered. Let L be a solvable Lie algebra and A be a minimal ideal of L. If L/A is nilpotent and L is not nilpotent then A has a complement in L, all such complements are conjugate and self-normalizing and if C is a complement then there exists an x∈L such that C = {y∈L; yadnx = 0 for some n = 1, 2,…}. A similar result holds if A is self-centralizing and a finitely generated R-module.
A Note on Whitney Maps
Authors: Ward L. E. 
Published: December 2010

In his recent book [3] Nadler observes that the property of admitting a Whitney map is of fundamental importance in studying the internal structure of hyperspaces, especially their arc structure. Nadler presents three distinct methods of constructing a Whitney map on the hyperspace 2X of nonempty closed subsets of a continuum.A partially ordered space is a topological space X endowed with a partial order ≤ whose graph is a closed subset of X×X. It is well-known (see, for example, [2], page 167) that if X is a regular Hausdorff space then 2X is a partially ordered space with respect to inclusion.
Sur Les M-Ideaux Dans Certains Espaces D′Operateurs Et L′Approximation Par Des Operateurs Compacts
Authors: Fakhoury H. 
Published: December 2010

SommaireIt is shown that if V=C(X) or V = L1(μ) then the subspace of compact (resp. weakly compact) operators from V into itself is not an M-ideal in the space of bounded operators. This is the contrary to what happens when V= Co(ℕ) or lp(ℕ). The main result is proved via the best approximation properties of M-ideals and some results concerning norm one projections in C(X) and L1(μ) are deduced from this fact.
Smoothability, Strong Smoothability and Dentability in Banach Spaces1
Authors: Anantharaman R. , Lewis T. , Whitfield J. H. M. 
Published: December 2010

AbstractIt is shown that dentability of the unit ball of a conjugate Banach space X* does not imply smoothability of the unit ball of X, answering a question raised by Kemp. A property called strong smoothability is introduced and is shown to be dual to dentability. The results are used to provide new proofs of the facts that X is an Asplund space whenever it has an equivalent Fréchet differentiable norm, or whenever X* has the Radon-Nikodym Property.
A Bound on the Number of Invariant Measures
Authors: Boyarsky Abraham 
Published: December 2010

For τ a piecewise C2 transformation, we present a method for obtaining an upper bound for the number of independent absolutely continuous measures invariant under τ.Let τ = [0,1] and let τ:I→ J be a piecewise C2 transformation with infI1 |dτ/dx| > 1, where I1 = I-P and P denotes the points of discontinuity of τ and τ′
The Isoperimetric Inequality for Curves with Self-Intersections
Authors: Vogt Andrew 
Published: December 2010

Banchoff and Pohl [3] have proved the following generalization of the isoperimetric inequality.Theorem. If γ is a closed, not necessarily simple, planar curve of length L, and w(p) is the winding number of a variable point p with respect to γ, then1with equality holding if and only if γ is a circle traversed a finite number of times in the same sense.
A Note on the Density Theorem
Authors: Lawrence John 
Published: December 2010

In this note we prove:Theorem. Let R be a right primitive ring with pair-wise non-isomorphic faithful irreducible modules Ml, M2,…, Mk. Let Di = EndR Mi. For each i, let be elements of Mi linearly independent over Di. For each i, let be a set of elements of Mi. Then there exists an element r of R such that uij = vijr, for i = 1, 2, …, k and j = 1, 2, …, ni.
R -Projective Modules over a Semiperfect Ring
Authors: Ketkar R. D. , Vanaja N. 
Published: December 2010

AbstractThe aim of this paper is to prove the following theorem:Let R be a semiperfect ring. Let Q be a left R -module satisfying (a) Q is R-projective and (b) J(Q) is small in Q. Then Q is projective.
Nonexpansive Uniformly Asymptotically Stable Flows are Linear
Authors: Janos Ludvik , McCann Roger C. , Solomon J. L. 
Published: December 2010

AbstractWe show that if a flow (R, X, π) on a separable metric space (X, d) satisfies (i) the transition mapping π(t, •): X → X is non-expansive for every t ≥ 0; (ii) X contains a globally uniformly asymptotically stable compact invariant subset, then the flow (R, X, π) is linear in the sense that it can be topologically and equivariantly embedded into a flow () on the Hilbert space l2 for which all of the transition mappings are linear operators on l2.
A Kronecker-Type Theorem for Complex Polynomials in Several Variables
Authors: Smyth C. J. 
Published: December 2010

AbstractWe give a classification result for "extreme-monic" polynomials in several variables having measure 1. The result implies a recent several-variable generalization, by D. W. Boyd, of Kronecker's classical theorem (that all zeros of a monic integral polynomial, with non-zero constant term and measure 1, are roots of unity).
The Limit of Biased Varisolvent Chebyshev Approximation
Authors: Dunham Charles B. 
Published: December 2010

AbstractBest biased and one-sided Chebyshev approximation with respect to a varisolvent approximating function on an interval are considered. The uniform limit of best biased approximations is the (unique) best one-sided approximation if the best one-sided approximation is of maximum degree. Examples are given where the best one-sided approximation is not of maximum degree and failure of uniform convergence and of existence occurs.
On the Solvability and Continuation Type Results for Nonlinear Equations with Applications, II
Authors: Milojevič P. S. 
Published: December 2010

AbstractIn this paper we continue our study of the solvability of nonlinear equations involving uniform limits of A-proper and pseudo A-proper maps under a new growth condition (1) that we began in [14,15]. Applications of our results to quasimonotone, ball-condensing pertubations of c -accretive maps and maps of semibounded variation and of type (M) are also given.
A Note on Completely and Absolutely Monotone Functions
Authors: Mahajan Arvind , Ross Dieter K. 
Published: December 2010

AbstractThe solutions of a certain class of first order linear differential equations are shown to be either completely or absolutely monotone depending on the nature of its coefficients. This is a simple theorem which is used to deduce a number of new and interesting results dealing with the complete and absolute monotonicity of functions. In particular, a partial answer is supplied to a question posed by Askey and Pollard: “When is completely monotone?”
Lattice Dilations of Positive Contractions on Lp-Spaces
Authors: Nagel Rainer , Palm Günther 
Published: December 2010

AbstractIn the spirit of our previous paper (Math. Z. 156, 265 - 277 (1977)) we present a functional analytic proof of the following result of M. A. Akcoglu: Every positive contraction on a reflexive Lp-space has a lattice dilation.
An Example in the Theory of Bilinear Maps
Authors: Kalton N. J. 
Published: December 2010

AbstractWe give an example of a p-convex quasi-Banach space E with 0 < p < 1 such that every bilinear map B: E × E →F into a p-convex quasi-Banach space F is identically zero. This resolves a question of Waelbroeck.
Hausdorff Obstructions to Packing (N-1)-Balls in N-Space
Authors: Wilker J. B. 
Published: December 2010

AbstractAn arbitrary collection of (N — l)-flats in ℝN is called a frame and an arbitrary assignment of (N — 1))-balls to these (N — 1)-flats is called a loading. Any loading in which the designated (N — 1)-balls are mutually disjoint is called a packing. For the frame consisting of the (N — 1)-flats perpendicular to a given line, every loading is automatically a packing. Although this is obviously not the most general frame to admit a packing, we show two senses in which all frames which admit packings are "at most onedimensional." Our principal tool is the Hausdorff measure-theoretic dimension.
The Individual Weighted Ergodic Theorem for Bounded Besicovitch Sequences
Authors: Olsen James H. 
Published: December 2010

AbstractLet (X, , μ) be a σ-finite measure space, p fixed, 1 < p < ∞, T a linear operator of Lp(X,μ), {αi} a sequence of complex numbers. Ifexists and is finite a.e. we say the individual weighted ergodic theorem holds for T with the weights {αi}In this paper we show that if {αi} is a bounded Besicovitch sequence and T is a Dunford-Schwartz operator (i.e.: ||T||1≤1, ||T||∞≤1) then the individual weighted ergodic theorem holds for T with the weights {αi}.
Uncountable Discrete Sets in Extensions and Metrizability
Authors: Bell Murray , Ginsburg John 
Published: December 2010

AbstractIf X is a topological space then exp X denotes the space of non-empty closed subsets of X with the Vietoris topology and λX denotes the superextension of X Using Martin's axiom together with the negation of the continuum hypothesis the following is proved: If every discrete subset of exp X is countable the X is compact and metrizable. As a corollary, if λX contains no uncountable discrete subsets then X is compact and metrizable. A similar argument establishes the metrizability of any compact space X whose square X × X contains no uncountable discrete subsets.
On Relaxation Oscillations Governed by a Second Order Differential Equation for a Large Parameter and with a Piecewise Linear Function(1)
Authors: Anand K. K. 
Published: December 2010

AbstractThis paper deals with the differential equation: ẍ + μF(ẋ) + x = ƒ( X, ẋ, t/Tμ) for μ ≫ 1 where F is a piecewise linear function and f is a periodic function of period μT, where T is to be chosen. It is established that periodic forced vibrations exist in an annular domain R(μ) constructed for the free vibration (ƒ ≡ 0), provided ƒ is not of higher order than Subsequently with ƒ = A cos (2πt/μT*), an asymptotic treatment of the forced vibration problem is carried out, by finding the proper initial conditions and the proper period μT* of f. Finally it is concluded that μT* is close to the period of the free vibration.
Closures of Equivalence Classes of Trivectors of an Eight-Dimensional Complex Vector Space
Authors: Djoković Dragomir Ž. 
Published: December 2010

AbstractG. B. Gurevič enumerated all the orbits of GL8(ℂ) in Λ3(ℂ8). There are precisely 23 orbits (including the trivial orbit). For each of these orbits, we determine its closure (for the ordinary topology).
The Maximal Extension of a Zero-dimensional Product Space
Authors: Ohta Haruto 
Published: December 2010

AbstractIt is known that if a topological property of Tychonoff spaces is closed-hereditary, productive and possessed by all compact Hausdorff spaces, then each (0-dimensional) Tychonoff space X is a dense subspace of a (0-dimensional) Tychonoff space with such that each continuous map from X to a (0-dimensional) Tychonoff space with admits a continuous extension over . In response to Broverman's question [Canad. Math. Bull. 19 (1), (1976), 13–19], we prove that if for every two 0-dimensional Tychonoff spaces X and Y, if and only if , then is contained in countable compactness.
A Lemma on Projective Geometries as Modular and/or Arguesian Lattices
Authors: Day Alan 
Published: December 2010

AbstractA projective geometry of dimension (n - 1) can be defined as modular lattice with a spanning n-diamond of atoms (i.e.: n + 1 atoms in general position whose join is the unit of the lattice). The lemma we show is that one could equivalently define a projective geometry as a modular lattice with a spanning n-diamond that is (a) is generated (qua lattice) by this n-diamond and a coordinating diagonal and (b) every non-zero member of this coordinatizing diagonal is invertible. The lemma is applied to describe certain freely generated modular and Arguesian lattices.
Dual Numbers and Topological Hjelmslev Planes
Authors: Lorimer J. W. 
Published: December 2010

AbstractIn 1929 J. Hjelmslev introduced a geometry over the dual numbers ℝ+tℝ with t2 = Q. The dual numbers form a Hjelmslev ring, that is a local ring whose (unique) maximal ideal is equal to the set of 2 sided zero divisors and whose ideals are totally ordered by inclusion. This paper first shows that if we endow the dual numbers with the product topology of ℝ2, then we obtain the only locally compact connected hausdorfT topological Hjelmslev ring of topological dimension two. From this fact we establish that Hjelmslev's original geometry, suitably topologized, is the only locally compact connected hausdorfr topological desarguesian projective Hjelmslev plane to topological dimension four.
The Usual Behaviour of Rational Approximations
Authors: Borwein Peter B. 
Published: December 2010

AbstractQuestions concerning the convergence of Padé and best rational approximations are considered from a categorical point of view in the complete metric space of entire functions. The set of functions for which a subsequence of the mth row of the Padé table converges uniformly on compact subsets of the complex plane is shown to be residual.The speed of convergence of best uniform rational approximations and Padé approximations on the unit disc is compared. It is shown that, in a categorical sense, it is expected that subsequences of these approximants will converge at the same rate.Likewise, it is expected that the poles of certain sequences of best uniform rational approximations wil be dense in the entire plane.
The Gauss-Bonnet Integrand for a Class of Riemannian Manifolds Admitting Two Orthogonal Complementary Foliations
Authors: Gil-Medrano O. , Naveira A. M. 
Published: December 2010

AbstractWith the general assumption that the manifold admits two orthogonal complementary foliations, one of which is totally geodesic, we study the components of the curvature tensor field of the characteristic connection.In the case where the manifold is compact, orientable of dimension 6 or 8 and the dimension of the totally geodesic foliation is 4, we relate the sign of the Euler characteristic of the manifold and that of the sectional curvature of the leaves of both foliations.
Analytic Continuation of Power Series by Regular Generalized Weighted Means
Authors: Shawyer Bruce L. R. , Tomm Ludwig 
Published: December 2010

AbstractThe behaviour of summability transforms of power series outside their circles of convergence has been studied by many authors. In the case of the geometric series Luh [6] and Tomm [10] showed that there exist regular methods A which provide an analytic continuation into any given simply connected region G that contains the unit disc but not the point 1. Moreover, the Atransforms of the geometric series may be required to converge to any chosen analytic function on prescribed regions outside the unit circle. In this paper, these results are extended to power series representing other meromorphic functions. It is also shown that the summability methods involved may be chosen to be generalized weighted means previously introduced by Faulstich [1].
Additive Functionals on Lorentz Spaces
Authors: Ghatage Pratibha G. 
Published: December 2010

AbstractIf (X, β, μ) is a σ-finite, non-atomic measure space, and ϕ is an increasing non-negative concave function defined on the positive real numbers, we give a set of necessary and sufficient conditions for an additive functional T on the Lorentz space Nϕ to have an integral representation with a Caratheodory kernel. In the special case when T is statistical we classify the functional properties (enjoyed by the kernels) in terms of the Lorentz norm on the space.
Orthogonal Polynomials With Weight Function (1 - x)α( l + x)β + Mδ(x + 1) + Nδ(x - 1)
Authors: Koornwinder Tom H. 
Published: December 2010

AbstractWe study orthogonal polynomials for which the weight function is a linear combination of the Jacobi weight function and two delta functions at 1 and — 1. These polynomials can be expressed as 4F3 hypergeometric functions and they satisfy second order differential equations. They include Krall’s Jacobi type polynomials as special cases. The fourth order differential equation for the latter polynomials is derived in a more simple way.
Asymptotic Theory of Singular Semilinear Elliptic Equations
Authors: Kusano Takaŝi , Swanson Charles A. 
Published: December 2010

AbstractNecessary and sufficient conditions are found for the existence of two positive solutions of the semilinear elliptic equation Δu + q(|x|)u = f(x, u) in an exterior domain Ω⊂ℝn, n ≥ 1, where q, f are real-valued and locally Hölder continuous, and f(x, u) is nonincreasing in u for each fixed x∈Ω. An example is the singular stationary Klein-Gordon equation Δu — k2u = p(x)u-λ where k and λ are positive constants. In this case NASC are given for the existence of two positive solutions ui(x) in some exterior subdomain of Ω such that both |x|m exp[(-l)i-1k|x|]ui(x) are bounded and bounded away from zero in this subdomain, m = (n —1)/2, i = 1, 2.
Some Remarks on Translative Coverings of Convex Domains by Strips
Authors: Groemer H. 
Published: December 2010

AbstractIn the euclidean plane let K be a compact convex set and Sl, S2,… strips of respective widths wl, w2,… Some conditions on Σ wi are given that imply that K can be covered by translates of the strips Si. These conditions involve the perimeter, the diameter, or the minimal width of K and yield improvements of previously known results.
A Monotonicity Theorem and a Bernoulli-L’Hospital-Ostrowski Rule
Authors: Lee Chang-Ming 
Published: December 2010

AbstractIt is proved that a function is nondecreasing if it is Baire one and Darboux and fulfills Lusin’s condition (N), and if its derivative is non-negative for almost every point at which the function is derivable. Using this result, a process to formulate various results on the existence and the valuation of indeterminate forms via various monotonicity theorems is illustrated. In particular, the ordinary Bernoulli-L’Hospital rule and some of its variations obtained recenty by A. M. Ostrowski are generalized.
On Chain Conditions in Integral Domains
Authors: Barucci Valentina , Dobbs David E. 
Published: December 2010

AbstractThe following two theorems are proved. If R is an Archimedean conducive integral domain, then R is quasilocal and dim(R) ≤1. If each overring of an integral domain R has ascending chain condition on divisorial ideals, then the integral closure of R is a Dedekind domain. Both theorems sharpen results already known in the Noetherian case. The second theorem leads to a strengthened converse of the Krull-Akizuki Theorem. We also investigate the effect of restricting the hypothesis in the second theorem to the proper overrings of R.
Block Sizes in Pairwise Balanced Designs
Authors: Colbourn Charles J. , Phelps Kevin T. , Rödl Vojtěch 
Published: December 2010

AbstractThe number of sets of integers which are realizable as block sizes of a pairwise balanced design of order n is between and ; in contrast, when the multiplicity of each block size is also specified, the number of multisets which can be realized is between and . Although this gives a reasonable bound on the number of multisets which can be realized, a good characterization is not likely to exist; deciding whether a multiset can be so realized is NP-complete.
The Almost Lindelöf Degree
Authors: Willard S. , Dissanayake U. N. B. 
Published: December 2010

AbstractIn [A], Arhangel'skii showed that for any T2 space X, |X|≤2L(x)χ(x), where L(X) is the Lindelöf degree of X and χ(X) is the character of X.In [B], Bell, Ginsburg and Woods improved this result, assuming normality, by showing that for T4 spaces X, |X|≤2wL(x)χ(x), where wL(X) is the weak Lindelöf degree of X.We introduce below a new cardinal function aL(X), the almost Lindelöf degree of X, which agrees with L(X) on T3 spaces, but which is often smaller than L(X) on T2 spaces, and show that for T2 spaces X,
On the Monotonic Variation of the Zeros of Ultraspherical Polynomials with the Parameters
Authors: Spigler Renato 
Published: December 2010

AbstractWe show that increases with λ, for 0< λ < 1, being the kth zero of the ultraspherical polynomial and f(λ) a suitable function of λ. As a consequence, some inequalities for and an estimate for can be obtained.
On the Extreme Points of Quotients of L∞ by Douglas Algebras
Authors: Deeb Waleed , Younis Rahman 
Published: December 2010

AbstractLet B be a Douglas algebra which admits best approximation. It will be shown that the following are equivalent: (1) The unit ball of (L∞/B) has no extreme points; (2) For any Blaschke product b with , there exists h ∈ B such that and h|E≢0, where E is the essential set of B.It will also be proven that if B⊇H∞+C and its essential set E contains a closed Gδ set, then the unit ball of (L∞/B) has no extreme points. Many known results concerning this subject will follow from these results.