bluuebunny/crossref_metadata_2025 huggingface dataset:
Periodic Waves in a Running Stream
Authors: Shinbrot Marvin
Published: December 2010

In this paper, we discuss questions of the existence and calculation of periodic, steady flows over periodic streambeds. There are some surprises.

Problems such as this, of flows in running streams, are free-surface problems, and part of the difficulty is that the domain occupied by the fluid is not completely knowna priori.
Relative Injectives and Free Monads
Authors: Wolff Harvey
Published: December 2010

Let ∑ be a class of maps in a category An object I of is ∑-injective if is an epimorphism for all σ ∈ ∑. This paper is concerned with the question of finding “enough” S-injectives in a functorial way.
Smoothability, Strong Smoothability and Dentability in Banach Spaces1
Authors: Anantharaman R. , Lewis T. , Whitfield J. H. M.
Published: December 2010

It 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, then

1

with equality holding if and only if γ is a circle traversed a finite number of times in the same sense.
A Remark about Components of Relative Teichmüller Spaces
Authors: Gilman Jane
Published: December 2010

Our aim is to compute for all n > 2, ψ(n, h), the number of components of a certain quotient of the fixed point set of an involution in the "mod-n" Teichmuller space. This answers part of a question raised by Earle [2] and corrects and extends the answer due to Zarrow (See Theorem 2 of [6]).
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

The 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.
Remarkable Hyperplanes in Locally Convex Spaces of Dimension at Most C
Authors: Tsirulnikov Bella
Published: December 2010

Every locally convex space E of dimension at most c contains a hyperplane G with the following property: the linear hull of each bounded Banach disk in G is finite-dimensional.
Nonexpansive Uniformly Asymptotically Stable Flows are Linear
Authors: Janos Ludvik , McCann Roger C. , Solomon J. L.
Published: December 2010

We 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

We 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).
A Generalized Comparison Test
Authors: Johnston Elgin
Published: December 2010

Let ∑ cj and ∑dj be, respectively, convergent and divergent series of positive terms and let ∑ aj be a third series of positive terms. It is well known, [1, pg. 275] that ∑ aj converges if lim sup(aj/cj)<+∞, but diverges if liminf(aj/dj)>0. In this note we prove a generalized version of this comparison test that relies not on term-by-term comparison of the series, but on the relative densities of the terms of the series.
The Limit of Biased Varisolvent Chebyshev Approximation
Authors: Dunham Charles B.
Published: December 2010

Best 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

In 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.
The Solution of a Special Arithmetic Equation
Authors: Hausman Miriam
Published: December 2010

Writing ϕl(n) = ϕ(ϕl−1(n)), the integers n which are solutions of n = kϕl(n) are considered. The set of all such n is completely characterized.
A Note on Completely and Absolutely Monotone Functions
Authors: Mahajan Arvind , Ross Dieter K.
Published: December 2010

The 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?”
Multipliers for the Mellin Transformation
Authors: Rooney P. G.
Published: December 2010

In this paper we generalize the Mellin multiplier theorem we proved earlier [8] to spaces with quite general weights, satisfying an Ap-type condition. Applications are made to the Hilbert transformation.
A Note on the Fibonacci Quotient Fp-ε/p
Authors: Williams H. C.
Published: December 2010

In this note a formula analogous to Eisenstein's well known formula is presented for Fp-ε/p, where Fn is the nth Fibonacci number (F0 = 0, F1 = 1), p an odd prime, and

This formula is:
Lattice Dilations of Positive Contractions on Lp-Spaces
Authors: Nagel Rainer , Palm Günther
Published: December 2010

In 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.
Fullness of Maps
Authors: Boyarsky Abraham , Byers William
Published: December 2010

An example is given of a surjective map τ: [0,1] → [0,1] which takes every interval of [0,1] onto [0,1] eventually, but does not do so for certain other sets of positive measure.
An Example in the Theory of Bilinear Maps
Authors: Kalton N. J.
Published: December 2010

We 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

An 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

Let (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. If

exists 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

If 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.
Detection of Singular Points
Authors: Cowling V. F. , King J. P.
Published: December 2010

A theorem is proved which gives a new test for singular points on the circle of convergence of the function f(z) defined by a power series ∑anzn finite non-zero radius of convergence.
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

This 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

G. 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

It 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.
Coefficient Estimates of Some Classes of Analytic Functions
Authors: Samaris Nicolas
Published: December 2010

We are concerned with coefficient estimates, and other similar problems, of the typically real functions and of the functions with positive real part. Following the stream of ideas in [1], new results and generalizations of others given in [1], [2] and [3] are obtained.
A Lemma on Projective Geometries as Modular and/or Arguesian Lattices
Authors: Day Alan
Published: December 2010

A 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

In 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

Questions 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.
Divergence of Fourier Series
Authors: Oberlin Daniel M.
Published: December 2010

This note contains a strengthened version of the following well-known theorem: there exists a continuous function whose Fourier series diverges at a point.
Partitioning Intervals, Spheres and Balls into Congruent Pieces
Authors: Wagon Stanley
Published: December 2010

We survey results on partitioning some common sets into m congruent pieces, and prove that a ball in Rn cannot be so partitioned if 2 ≤ m ≤ n.
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

With 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

The 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

If (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.
An Improved Wintner Oscillation Criterion for Second Order Linear Differential Equations
Authors: Johnson George W. , Yan Jurang
Published: December 2010

An iterative technique is used to establish an oscillation theorem for the equation x″+ a(t)x=0 which relaxes the condition that a(t) satisfy

without the restriction that
Orthogonal Polynomials With Weight Function (1 - x)α( l + x)β + Mδ(x + 1) + Nδ(x - 1)
Authors: Koornwinder Tom H.
Published: December 2010

We 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

Necessary 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

In 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

It 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

The 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

The 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.
Metrization of Ranked Spaces
Authors: Ishikawa Fumie
Published: December 2010

K. Kunugi introduced the notion of ranked space as a generalization of that of metric spaces, (see [6]). In this note we define a metrizability of ranked spaces and study conditions under which a ranked space is metrizable.
The Almost Lindelöf Degree
Authors: Willard S. , Dissanayake U. N. B.
Published: December 2010

In [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

We 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.
A Brouwer Type Coincidence Theorem and the Fundamental Theorem of Algebra
Authors: Dodson M. M.
Published: December 2010

It is shown that a coincidence theorem which is a natural generalisation of Brouwer's fixed point theorem also gives a short and simple proof of the fundamental theorem of algebra.
On the Extreme Points of Quotients of L∞ by Douglas Algebras
Authors: Deeb Waleed , Younis Rahman
Published: December 2010

Let 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.
On the Pontrjagin Algebra of a Certain Class of Flags of Foliations
Authors: Carreras F. J. , Naveira A. M.
Published: December 2010

Let (𝓜,g) be a Riemannian manifold and let 1, 2, 3 be mutually orthogonal distributions on 𝓜 of dimensions p1, p2,P3 such that p1 + p2 + p3 = dim 𝓜. We assume that , and 1, ⊕ 2 are integrable and that all the geodesies of 𝓜 with initial tangent vector in 2 remain tangent to 2. Then, we prove that Pontk(2, ⊕ 3) = 0 for k > p2 + 2p3, where Pontk(2, ⊕ 3) is the subspace of the Pontrjagin algebra of 2 ⊕ 3 generated by forms of degree k.
The Fibre of the Double Suspension is an H-Space
Authors: Selick Paul
Published: December 2010

In this paper we show that the homotopy-theoretic fibre of the double suspension map E2:S2n-1 → Ω2S2n+1 is an H-space.
Groups Preserving a Class of Bilinear Functions
Authors: Greub W. H. , Malzan J. , Vanstone J. R.
Published: December 2010

Given a finite dimensional Euclidean vector space V, ( , ) and an involution τ of V, one can form the bilinear function ( , )τ defined by (x, y)τ = (τ(x), y), x,y ∊ V.

Let O(τ) = {ϕ ∊ GL(V)|(ϕx, ϕy)τ = (x, y)τ}.

If t is self-adjoint the structure of O(t) is well known. The purpose of this paper is to detemine the structure of O(t) in the general case. This structure is also determined in the complex and quaternionic case, as well as the case when the condition on t is replaced by τ2 = ∊ι, ∊ ∈ ℝ.
The L-Functions L(s, Symm(r), π)
Authors: Moreno C. J. , Shahidi F.
Published: December 2010

The exact form for the gamma factor for the L-function corresponding to the m-th symmetric power of a cuspidal automorphic representation of PGL(2) is given. This information is used to obtain, via a theorem of Landau, bounds for the eigenvalues of Hecke operators.
Topological Spaces with a Unique Compatible Quasi-Uniformity
Authors: Künzi Hans-Peter A.
Published: December 2010

We show that a topological space X admits a unique quasiuniformity
if and only if every interior-preserving open collection of X is
finite.
Some Classes of θ-Compactness
Authors: Broverman S.
Published: December 2010

Let A and A denote the classes of ordinal spaces with the order topology and Σ-product spaces of the two point discrete space respectively. Characterizations are given in terms of ultrafiIters of clopen sets of those O-dimensional Hausdorff topological spaces that can be embedded homeomorphically as a closed subspace of a topological product of either spaces from the class Λ or the class Δ. Both classes consist of spaces that are ω0-bounded. An example is given of a O-dimensional Hausdorff ω0-bounded space that cannot be homeomorphically embedded as a closed subset of a product of spaces from either Λ or Δ, answering a question of R. G. Woods.
On Characterization of Hypersurfaces of Degrees 2 and 3 in the Complex Projective Space
Authors: Szurek Michal
Published: December 2010

Le but de cette note est de proposer une caractérisation des espaces projectifs complexes, des hyperquadriques et des hypersurfaces du troisième degré dans Pnc à l'aide de leurs points d'intersection avec l'ensemble des zéros d'une section d'un fibre positif donné sur la variété ambiante. Ceci généralise et complète ainsi certains résultats présentés par Badescu et Itoh.
Semi-Groups in L∞ And Local Ergodic Theorem
Authors: R. Emilion
Published: December 2010

We show that any W*-continuous semi-group in L∞ is L1-norm continuous. As an application we prove the n-dimensional local ergodic theorem in L∞. We also note that any bounded additive process in L∞ is absolutely continuous.

For n = 1 this local theorem improves those of R. Sato [14] and D. Feyel [6] and for n ≥ 1 it generalizes M. Lin's ones which hold for positive operators [12].
Even Covering Properties and Somewhat Normal Spaces
Authors: Künzi Hans-Peter , Fletcher Peter
Published: December 2010

A topological space X is said to be somewhat normal provided that for each open cover is a normal cover of X. We show that a completely regular somewhat normal space need not be normal, thereby answering a question of W. M. Fleischman. We note that a collectionwise normal somewhat normal space need not be almost 2-fully normal, as had previously been asserted, and that neither the perfect image nor the perfect preimage of a somewhat normal space has to be somewhat normal.
Uniqueness of Subfields
Authors: Deveney James K. , Mordeson John N.
Published: December 2010

Let L be a finitely generated field extension of a field K. The order of inseparability of L/K is the minimum of {n|[L:S] = pn where S is a separable extension of K}. If V is a subfield of L/K, then its order of inseparability is less than or equal to that of L/K. This paper examines the question of when there are unique minimal subfields of order of inseparability n — j, 0 ≤ j ≤ n.
On the Distance Between Consecutive Divisors of an Integer
Authors: Koninck Jean-Marie de , Ivić Aleksandar
Published: December 2010

Let ω(n) denote the number of distinct prime divisors of a positive integer n. Then we define and where are primes and r ≥ 2. Similarly denote by the number of divisors of n and let be defined by where are the divisors of n. We prove that there exists constants A and B such that and
Algebras with Transitive Automorphism Groups
Authors: Sweet L. G. , MacDougall J. A.
Published: December 2010

Let A be a finite dimensional algebra (not necessarily associative) over a field, whose automorphism group acts transitively. It is shown that K = GF(2) and A is a Kostrikin algebra. The automorphism group is determined to be a semi-direct product of two cyclic groups. The number of such algebras is also calculated.
On Rank One Commutators and Triangular Representations
Authors: Ma Tsoy-Wo
Published: December 2010

Starting with the extension of Lomonosov's Lemma by Tychonoff fixed point theorem, a result of Daughtry and Kim — Pearcy-Shields on rank-one commutators is extended to the context of locally convex spaces. Non-zero diagonal coefficients, eigenvalues and simultaneous triangular representations of compact operators on locally convex spaces are studied.
Goldie Dimension and Chain Conditions for Modular Lattices with Finite Group Actions
Authors: Grzeszczuk Piotr , Puczyłowski Edmund R.
Published: December 2010

A relation between Goldie dimensions of a modular lattice L and its sublattice LG of fixed points under a finite group G of automorphisms of L is obtained. The method used also gives a relation between ACC (DCC) for L and for LG. The results obtained are applied to rings and modules.
Free Subgroups and the Residual Nilpotence of the Group of Units of Modular and p-Adic Group Rings
Authors: Gonçalves Jairo Zacarias
Published: December 2010

Let G be a group, let RG be the group ring of the group G over the unital commutative ring R and let U(RG) be its group of units. Conditions which imply that U(RG) contains no free noncyclic group are studied, when R is a field of characteristic p ≠ 0, not algebraic over its prime field, and G is a solvable-by-finite group without p-elements. We also consider the case R = ℤp, the ring of p-adic integers and G torsionby- nilpotent torsion free group. Finally, the residual nilpotence of U(ℤpG) is investigated.
The Herzog-Schönheim Conjecture for Finite Nilpotent Groups
Authors: Berger Marc A. , Felzenbaum Alexander , Fraenkel Aviezri
Published: December 2010

The purpose of this note is to prove the Herzog-Schônheim [3] conjecture for finite nilpotent groups. This conjecture states that any nontrivial partition of a group into cosets must contain two cosets of the same index (Corollary IV below). See Porubský [4, Section 8] for a perspective on coset partitions.
The Integration of Exact Peano Derivatives
Authors: Cross G. E.
Published: December 2010

It is well known that the Riemann-complete integral (or equivalently the Perron integral) integrates an everywhere finite ordinary first derivative (which may be thought of as a Peano derivative of order one). It is also known that the Cesàro-Perron integral of order(n- 1) integrates an everywhere finite Peano derivative of ordern.The present work concerns itself with necessary and sufficient conditions for the Riemann-complete integrability of an exact Peano derivative of ordern.It is shown that when the integral exists, it can be expressed as the ‘Henstock' limit of the sum of a particular kind of interval function. All functions considered will be real valued.
Uniform Paracompactness and Uniform Para-Lindelöfness
Authors: Alas O. T.
Published: December 2010

Relations between uniform paracompactness and uniform para-Lindelöfness of a uniform space and its uniform weight are established.
Note on Continuous and Purely Finitely Additive Set Functions
Authors: Siebe Wilfried
Published: December 2010

The Sobczyk-Hammer respectively Yosida-Hewitt decomposition ([17], [19]) generates the class of continuous respectively purely finitely additive charges. In this paper, attention is limited to hereditable properties for these classes. It is proved that the property of continuity is preserved with respect to extensions and that if all extensions of a charge to a charge on a given field are continuous, then the original charge is continuous. An analogous heredity theorem for purely finite additivity holds true in the monogenic case.
Probability Density Function of the Product and Quotient of Two Correlated Exponential Random Variables
Authors: Malik Henrick J. , Roger Trudel
Published: December 2010

This article deals with the distributions of the product and the quotient of two correlated exponential random variables. We consider here three types of bivariate exponential distributions: Marshall-Olkin's bivariate exponential distribution, Gumbel's Type I bivariate exponential distribution, and Gumbel's Type II bivariate exponential distribution.
Sur Une Representation Explicite des Solutions Optimales D'un Programme Lineaire
Authors: Bilodeau Martin
Published: December 2010

This paper gives a sharper explicit representation of the set of optimal solutions for a class of linear programs than those obtained by A. Ben-Israel, A. Charnes and S. Zlobec since 1968. The representation is used to determine bounds on the coefficients of the objective function that produce the same set of optimal solutions (sensitivity analysis).
Bi-Positive Sequences the Bilateral Moment Problem
Authors: Vinuesa Jaime , Guadalupe Rafael
Published: December 2010

We pose a “moment problem” in a more general setting than the classical one. Then we find a necessary and sufficient condition for a sequence to have a solution of the “problem“

where σ is a “distribution function”.
Integral Group Rings Without Proper Units
Authors: Hoechsmann K. , Sehgal S.K.
Published: December 2010

If A is an elementary abelian ρ-group and C one of its cyclic subgroups, the integral group rings ZA contains, of course, the ring ZC. It will be shown below, for A of rank 2 and ρ a regular prime, that every unit of ZA is a product of units of ZC, as C ranges over all cyclic subgroups.
The Algebra of Stable Operations For ρ-Local Complex K-Theory
Authors: Johnson Keith
Published: December 2010

The multiplicative structure of the algebra of stable operations for ρ-local complex K-theory is studied, and the units and zero divisors are identified.
Cocyclic Maps and Coevaluation Subgroups
Authors: Lim K. L.
Published: December 2010

For any space X, DG(X, A) is an abelian subgroup of [X, A] when A is an H-group. DG(X, X) is a ring for any H-group X.
Some Remarks on Artin's Conjecture
Authors: Ram Murty M. , Srinivasan S.
Published: December 2010

It is a classical conjecture of E. Artin that any integer a > 1 which is not a perfect square generates the co-prime residue classes (mod ρ) for infinitely many primes ρ. Let E be the set of a > 1, a not a perfect square, for which Artin's conjecture is false. Set E(x) = card(e ∊ E: e ≤ x). We prove that E(x) = 0(log6 x) and that the number of prime numbers in E is at most 6.
On Weighted Geodesics in Groups
Authors: Lipschutz Seymour
Published: December 2010

A word W in a group G is a geodesic (weighted geodesic) if W has minimum length (minimum weight with respect to a generator weight function α) among all words equal to W. For finitely generated groups, the word problem is equivalent to the geodesic problem. We prove: (i) There exists a group G with solvable word problem, but unsolvable geodesic problem, (ii) There exists a group G with a solvable weighted geodesic problem with respect to one weight function α1, but unsolvable with respect to a second weight function α2. (iii) The (ordinary) geodesic problem and the free-product geodesic problem are independent.
Comment on the Nullenstellensatz for Regular Rings
Authors: Gentle Ron
Published: December 2010

An elementary proof of the Nullstellensatz for commutative regular rings is given.
On the Semigroup of Probability Measures of a Locally Compact Semigroup
Authors: Wong James C.S.
Published: December 2010

We show that a locally compact semigroup S is topological left amenable iff a certain space of left uniformly continuous functions on the convolution semigroup of probability measures M0(S) on S is left amenable or equivalently iff the convolution semigroup M0(S) has the fixed point property for uniformly continuous affine actions on compact convex sets.
Separating Splitting Tilting Modules and Hereditary Algebras
Authors: Assem Ibrahim
Published: December 2010

Let A be a finite-dimensional algebra over an algebraically closed field. By module is meant a finitely generated right module. A module T^ is called a tilting module if and there exists an exact sequence 0 → A^ → T' → T" → 0 with T'. T" direct sums of summands of T. Let B = End T^·T^ is called separating (respectively, splitting) if every indecomposable A-module M (respectively, B-module N) is such that either Hom^(T,M) = 0 or (respectively, N ⊗ T = 0 or . We prove that A is hereditary provided the quiver of A has no oriented cycles and every separating tilting module is splitting.
On the Ergodic Hilbert Transform for Operators In Lp, 1 < p < ∞
Authors: Sato Ryotaro
Published: December 2010

In this paper the ergodic Hilbert transform is investigated at the operator theoretic level. Let T be an invertible positive operator on Lp = Lp(X, , μ) for some fixed p, 1 < p < ∞, such that sup{||Tn||p: — ∞ < n < ∞} < ∞. It is proved that the limit

exists almost everywhere and in the strong operator topology, where the prime denotes that the term with zero denominator is omitted. Related results are also proved.
Units in Integral Group Rings of Some Metacyclic Groups
Authors: Allen P. J. , Hobby C.
Published: December 2010

Let p be odd prime and suppose that G = 〈a, b〉 where ap-1 = bp = 1, a-1 ba = br, and r is a generator of the multiplicative group of integers mod p. An explicit characterization of the group of normalized units V of the group ring ZG is given in terms of a subgroup of GL(p - 1, Z). This characterization is used to exhibit a normal complement for G in V.
Mixed Groups of Finite Nilstufe
Authors: Wilson George V.
Published: December 2010

This paper constructs a class of examples to show that for torsion-free groups H with finite nilstufe v(H) = n < ∞ there can be divisible torsion groups D with v(H ⊕ D) - n + k for all k ≤ n + 1. This answers a question of Feigelstock. The construction is based on a proposition which bounds v(H ⊕ D) in terms of v(H) and rank (D).
On Knopp's Inequality for Convex Functions
Authors: Pečarić J. E. , Beesack P. R.
Published: December 2010

Knopp's inequality for convex functions ϕ on an interval I = [m,M] states that

for an explicit functional H, and all integrable g: [0, 1] → I. In this paper we give results of this kind in which the integral operator, ∫, is replaced by a general isotonic linear functional.
Weierstrass Points on Rational Nodal Curves of Genus 3
Authors: Lax R. F. , Widland Carl
Published: December 2010

We determine, except for one unsettled case, which combinations of Weierstrass weights can occur on irreducible rational nodal curves of arithmetic genus three. It is shown that the number of nonsingular Weierstrass points on such curves can be any integer between 0 and 6, except 1.
Comportement Asymptotique de
Authors: Mercier Armel
Published: December 2010

Let {x} denote the fractional part of x. We find an asymptotic formula of , where k is any positive integer and a is any real number ≥ 1, and so for the sum ∑n<xf(n), where f(n) belongs to a class of additive functions.
Sums of Squares Formulae With Integer Coefficients
Authors: Yiu Paul Y. H.
Published: December 2010

Hidden behind a sums of squares formula are other such formulae not obtainable by restriction. This drastically simplifies the combinatorics involved in the existence problem of sums of squares formulae, and leads to a proof that the product of two sums of 16 squares cannot be rewritten as a sum of 28 squares, if only integer coefficients are permitted. We also construct all [10, 10, 16] formulae.
Generic Matrix Sign-Stability
Authors: Yamada Takeo
Published: December 2010

A new concept of generic sign-stability is proposed, and a necessary and sufficient condition for this property is given. This result shows that the condition proposed by Quirk and Ruppert [12] is correct almost everywhere, and helps to clarify the counterexample presented by Jeffries [4].
A Decomposition Theorem for Complex Nilmanifolds
Authors: Loeb Jean-Jacques , Oeljeklaus Karl , Richthofer Wolfgang
Published: December 2010

A complex nilmanifold X is isomorphic to a product X ⋍ ℂp x N/┌, where N is a simply connected nilpotent complex Lie group and ┌ is a discrete subgroup of N not contained in a proper connected complex subgroup of N. The pair (N, ┌) is uniquely determined up to holomorphic group isomorphisms.
The Spectrum of Weighted Mean Operators
Authors: Rhoades B. E.
Published: December 2010

Recently J. B. Reade determined the spectrum of C, the Cesaro matrix of order 1, considered as an operator on c0, the space of null sequences. Previously F. P. A. Cass and the author had determined the spectra for a large class of weighted mean operators on c, the space of convergent sequences. Subsequently the author determined the fine spectra of these operators over c. This paper examines the spectra and fine spectra of weighted mean operators on c0, obtaining the result of Reade as a special case.
Uniform Mazur's Intersection Property of Balls
Authors: Whitfield J. H. M. , Zizler V.
Published: December 2010

We give a dual characterization of the following uniformization of the Mazur's intersection property of balls in a Banach space X: for every ∊ > 0 there is a K > 0 such that whenever a closed convex set C ⊂ X and a point p ∊ X are such that diam C ≤ 1/∊ and dist(p, C) ≤ ∊, then there is a closed ball B of radius ≤ K with B ⊃ C and dist(p,B) ≥ ∊/2.
Borel Sets in Metric Spaces With Small Separable Subsets
Authors: Daniels P. , Gruenhage G.
Published: December 2010

Let X be a metric space such that every separable subspace of X has size less than the continuum. We answer a question of D. H. Fremlin by showing that MA + ┐CH does not necessarily imply that every subset of X is analytic.
On Hloosterman Sums with Oscillating Coefficients
Authors: Hajela D. , Pollington A. , B. Smith
Published: December 2010

An estimate for Kloosterman sums with oscillating coefficients is presented. Precisely we show: for any ϵ > 0 and a, b positive integers with (a, b) — 1 we have,

Similar techniques may be used to estimate other Kloosterman sums with oscillating coefficients which are not smooth.
Generalization of a Result of E. Lucas
Authors: Macleod R. A.
Published: December 2010

A well-known result of E. Lucas enables one to obtain the residue modulo p of in terms of the base-p digits of M and N. Using a recent result of P. W. Haggard and J. O. Kiltenen, a proof of N. J. Fine has been adapted to yield the corresponding residue modulo pr.
A Function Theoretic Proof of Axler's Zero Multiplier Theorem
Authors: Izuchi Keiji
Published: December 2010

A function theoretic proof of Axler's zero multiplier theorem of Bergman spaces is given.
The Conjugate Function in Plane Curves
Authors: Guadalupe Jose J. , Luisa Rezola Ma
Published: December 2010

We prove that the conjugate function operator is bounded in Lp(Г, wds), 1 < p < ∞, if and only if w ∈ Ap(Г), where Г is a quasiregular curve.
Some Results in the Connective K-Theory of Lie Groups
Authors: Magalhães L.
Published: December 2010

In this paper we give a description of:

(1) the Hopf algebra structure of k*(G; L) when G is a compact, connected Lie group and L is a ring of type Q(P) so that H*(G; L) is torsion free;

(2) the algebra structure of k*(G2; L) for L = Z2 or Z.
Comparaison de la Méthode des Constantes de Lyapunov et de la Bifurcation de Hopf*
Authors: Bonin Guy , Josée Legault
Published: December 2010

Dans cet article, nous démontrons l'équivalence théorique de la méthode des constantes de Lyapunov et de la bifurcation de Hopf, pour l'étude de l'apparition ou de la disparition de cycles limites dans un système d'équations différentielles ordinaires.
The Rank Theorem for Locally Lipschitz Continuous Functions
Authors: Butler G. J. , Timourian J. G. , Viger C.
Published: December 2010

The Rank Theorem is proved for locally Lipschitz continuous functions f:Rn → Rp with generalized derivative of constant rank.
Nuclearity
Authors: Rowe K. A.
Published: December 2010

The notion of nuclear object in an autonomous category is studied. It is shown that the full subcategory determined by the nuclear objects is also autonomous.
Some Consequences of lašnev's Theorem in Shape Theory
Authors: Alonso Moron M.
Published: December 2010

In this paper we use the Lašnev Theorem in order to give some properties of a class of metrizable spaces having compact metric shape.
A Partial Generalization of Mann's Theorem Concerning Orthogonal Latin Squares
Authors: Parker E. T. , Somer Lawrence
Published: December 2010

Letn = 4t+- 2, where the integert ≧ 2. A necessary condition is given for a particular Latin squareLof ordernto have a complete set ofn — 2mutually orthogonal Latin squares, each orthogonal toL.This condition extends constraints due to Mann concerning the existence of a Latin square orthogonal to a given Latin square.
Strong Morita equivalence for the Denjoy C*-Algebras
Authors: Putnam Ian F.
Published: December 2010

The C*-algebras associated with irrational rotations of the circle were classified up to strong Morita equivalence by M. A. Rieffel. As a corollary, he gave a complete classification of the C*-algebras arising from irrational or Kronecker flows on the 2-torus up to *-isomorphism. Here, we extend the result to the socalled Denjoy homeomorphisms. Specifically, we give a necessary and sufficient condition for the strong Morita equivalence of two C*-algebras arising from homeomorphisms of the circle without periodic points. As a corollary, we show that two C*-algebras arising from flows on the 2-torus obtained from such homeomorphisms by the “flow under constant function” construction are *-isomorphic if and only if the flows themselves are topologically conjugate.
A Note on the Dubois-Efroymson Dimension Theorem
Authors: Kucharz Wojciech
Published: December 2010

Let X ⊂ Rnn be an irreducible nonsingular algebraic set and let Z be an algebraic subset of X with dim Z ≦ dim X — 2. In this paper it is shown that there exists an irreducible algebraic subset Y of X satisfying the following conditions: dim Y = dim X — 1, Z ⊂ Y and that the ideal of regular functions on X vanishing on Y is principal.
Tree self-embeddings
Authors: Ross David
Published: December 2010

Elementary proofs are given of the following two statements: (1) Every infinite tree of height at most ω properly embeds into itself. (2) There is a tree of height ω + 1 that does not properly embed into itself.
Norm Inequalities for Generators of Analytic Semigroups and Cosine Operator Functions
Authors: Siddiqi Jamil A. , Elkoutri Abdelkader
Published: December 2010

We prove that if A is the infinitesimal generator of a bounded analytic semigroup in a sector {z ∊ C : |arg z| ≦ (απ)/2} of bounded linear operators on a Banach space, then the following inequalities hold:

for any x ∊ D(An) and for any 0 < β < α. This result helps us to answer in affirmative a question raised by M. W. Certain and T. G. Kurtz [3]. Similar inequalities are proved for cosine operator funtions.