bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Note on Locally Expansive and Locally Accretive Operators
Authors: Torrejon Ricardo 
Published: December 2010

AbstractLet X be a Banach space, D an open subset of X and Y a complete metric space. Assume that Y is metrically convex. For closed, locally m-expansive and mapping open subsets of D onto open subsets of Y, is is shown that y ∊ T(D) if and only if there exists x0 ∊ D such that d(Tx0, y) ≤ d(Tx, y) for all x ≤ ∂D.
Krasnosel'skii Theorems for Non-Separating Compact Sets
Authors: Stavrakas N. 
Published: December 2010

AbstractLet S ⊂ Rd, d ≥ 2, be compact and let E denote the set (d — 2) — extreme points of S. M. Breen has shown that if E is countable and S ≠ E, then S is planar. A new proof of this result is given as well as a Krasnosl'skii theorem for (d - 2) extreme points which combines and generalizes previous results.
Derivations in Prime Rings
Authors: Bergen Jeffrey 
Published: December 2010

AbstractLet R be a prime ring and d≠0 a derivation of R. We examine the relationship between the structure of R and that of d(R). We prove that if R is an algebra over a commutative ring A such that d(R) is a finitely generated submodule then R is an order in a simple algebra finite dimensional over its center.
A Multivariable form of the Fundamental Theorem of Algebra
Authors: Salzberg Pablo M. 
Published: December 2010

AbstractLet H(x) be a homogeneous polynomial in n indeterminates over an algebraically closed field K. A necesssary and sufficient condition is given for H(x) to admit a factorization of the forma, b∈ Kn, and “∘” is the usual inner product. This condition involves the linear derivatives of H(x).
Certain Characteristics of the Curvature Tensor of an Affinely Connected Manifold
Authors: Sharma Ramesh 
Published: December 2010

AbstractWe show how flatness and symmetry of an affinely connected manifold relate themselves to the symmetry of the curvature tensor and its covariant derivative in certain slots. Then we reduce Bianchi first identity to the same form as when the connexion is symmetric; even when the connexion is non-symmetric by considering other conditions.
The Shrinking Property
Authors: Rudin Mary Ellen 
Published: December 2010

AbstractA space has the shrinking property if, for every open cover {Va | a ∈ A}, there is an open cover {Wa| a ∈ A} withfor each a ∈ A.lt is strangely difficult to find an example of a normal space without the shrinking property. It is proved here that any ∑-product of metric spaces has the shrinking property.
The Equation Xk + Yk = Zk In Commuting Rational Matrices
Authors: Rush David E. 
Published: December 2010

AbstractSolutions of Xk + Yk = Zk in invertible pairwise commuting rational 2 × 2 matrices are determined for k = 3, 4, 6, 9, from the analogous results of A. Aigner for algebraic number fields.
Extra Countably Compact Spaces
Authors: Saks Victor 
Published: December 2010

AbstractA completely regular HausdorfT space is extra countably compact if every infinite subset of βX has an accumulation point in X. It is a theorem of Comfort and Waiveris that if X either an F-space or realcompact (topologically complete), then there is a set {Pξ:ξ<2C} of extra countably compact (countably compact) subspaces of αX such that Pξ ∩ Pξ = X, for ξ<ξ'<2C. Comfort and Waiveris conjecture that in all three cases, the spaces may be chosen pairwise non-homeomorphic. We prove this conjecture, using D- limits and weak P-points. We also give a partial solution to another question asked by Comfort and Waiveris.
The Height of Two-Dimensional Cohomology Classes of Complex Flag Manifolds
Authors: Broughton S. Allen , Hoffman Michael , Homer William 
Published: December 2010

AbstractFor a parabolic subgroup H of the general linear group G = Gl(n, C), we characterize the Kähler classes of G/H and give a formula for the height of any two-dimensional cohomology class. As an application, we classify the automorphisms of the cohomology ring of G/H when this ring is generated by two-dimensional classes.
Regular and Mercerian Generalized Lototsky Method
Authors: Miller J. F. , Skerry H. B. 
Published: December 2010

AbstractNecessary conditions and sufficient conditions are obtained for the generalized Lototsky summability matrix method (F, dn) to be regular and Mercerian. In particular, a set of conditions equivalent to being regular and Mercerian is given for real {dn} and for complex {dn} eventually in any closed half-plane containing the origin.
On Evaluation Subgroups of Generalized Homotopy Groups
Authors: Lim K. L. 
Published: December 2010

AbstractG(A, X) consists of all homotopy classes of cyclic maps from a space A to another space X. If A is an H-cogroup, then G(A, X) is a group. G(A, X) preserves products in the second variable and is a contravariant functor of A from the full subcategory of H-cogroups and maps into the category of abelian groups and homomorphisms. If X is an H-cogroup, then G(X, X) is a ring.
A Second Order Superlinear Oscillation Criterion
Authors: Philos Ch. G. 
Published: December 2010

AbstractA new oscillation criterion is given for general superlinear ordinary differential equations of second order of the form x″(t)+ a(t)f[x(t)]=0, where a ∈ C([t0∞,)), f∈C(R) with yf(y)>0 for y≠0 and and f is continously differentiable on R-{0} with f'(y)≥0 for all y≠O. In the special case of the differential equation (γ > 1) this criterion leads to an oscillation result due to Wong [9].
The Fixed Subring of Some Groups of Ring Automorphisms
Authors: Dowlen Mary 
Published: December 2010

AbstractLet Zm denote the ring of integers modulo an integer m > 1 and let G(Zm) be the group under composition of all Zm-automorphisms of Zm[X]. In this paper we determine Zm[X]G(zm) the subring of Zm[X] left fixed by elements of G(Zm).
A Note on Bernoulli-Goss Polynomials
Authors: Ireland K. , Small D. 
Published: December 2010

AbstractIn an important series of papers ([3], [4], [5]), (see also Rosen and Galovich [1], [2]), D. Goss has developed the arithmetic of cyclotomic function fields. In particular, he has introduced Bernoulli polynomials and proved a non-existence theorem for an analogue to Fermat’s equation for regular “exponent”. For each odd prime p and integer n, l ≤ n ≤ p2-2 we derive a closed form for the nth Bernoulli polynomial. Using this result a computer search for regular quadratic polynomials of the form x2-a was made. For primes less than or equal to 269 regular quadratics exist for p= 3, 5, 7, 13, 31.
On the Theorems of Borsuk-Ulam and Ljusternik-Schnirelmann-Borsuk
Authors: Steinlein H. 
Published: December 2010

AbstractLet p ≥ 3 be a prime number and m a positive integer, and let S be the sphere S(m-1)(p-1)-1. Let f:S→S be a map without fixed points and with fp = idS. We show that there exists an h: S→ℝm with h(x) ≠ h(f(x)) for all x ∈ S. From this we conclude that there exists a closed cover U1,…, U4m of S with Uinf(Ui) = Ø for i = 1,…, 4m. We apply these results to Borsuk-Ulam and Ljusternik-Schnirelmann-Borsuk theorems in the framework of the sectional category and to a problem in asymptotic fixed point theory.
How Good is Hadamard’s Inequality for Determinants?
Authors: Dixon John D. 
Published: December 2010

AbstractLet A be a real n × n matrix and define the Hadamard ratio h(A) to be the absolute value of det A divided by the product of the Euclidean norms of the columns of A. It is shown that if A is a random variable whose distribution satisfies some simple symmetry properties then the random variable log h(A) has mean and variance . In particular, for each ε > 0, the probability that h(A) lies in the range tends to 1 as n tends to ∞.
The Absolute Galois Group of a Rational Function Field in Characteristic Zero is a Semi-Direct Product
Authors: Van Den Dries Lou , Ribenboim Paulo 
Published: December 2010

AbstractLet K be a field of characteristic 0 and t an indeterminate. It is shown that the absolute Galois group of K(t) is the semi-direct product of a free profinite group with the absolute Galois group of K.
Asymptotic Error Expansions for Spline Interpolation
Authors: Dikshit H. P. , Sharma A. , Tzimbalario J. 
Published: December 2010

AbstractDuring the last decade or so there has been a revival of interest in the analysis of error-bounds f(s)-S(s) for different classes of functions and their interpolatory splines of odd degree on a finite interval with variations on end conditions. Our object is to present a unified treatment of the asymptotic error expansion both for even and for odd degree interpolatory splines.
A Remark on Bases in Hardy Spaces
Authors: Sjögren Peter 
Published: December 2010

AbstractThe Franklin spline system in [0,1] has been generalized by Strömberg to a system in ℝn which is an unconditional basis in Hp(ℝn) for p > n/(n + m +1). Here the natural number m is the order of the system. For some of these values of p, it was known that the Hp quasi-norm is equivalent to a certain expression containing the coefficients of the function with respect to this basis. We prove this equivalence for all p > n/(n + m +1).
A Note About Linear Systems on Curves
Authors: Tannenbaum Allen 
Published: December 2010

AbstractInverting the Castelnuovo bound in two ways, we show that for given integers p ≥ 0, d > 1, n > 1, we can find a smooth irreducible curve of genus p which contains a linear system of degree d and of maximal dimension relative to the given data p and d, and a smooth irreducible curve of genus p which contains a linear system of dimension n and of minimal degree relative to the data p and n.
Transitive Vector Spaces of Bounded Operators
Authors: Grabiner Sandy 
Published: December 2010

AbstractThe linear subspace S of B(X, Y), the space of bounded operators from the Banach space X to the Banach space Y, is said to be transitive if Sx is dense in Y for all x ≠ 0. We give a number of conditions, involving operators intertwined by S, which imply that S is not transitive, and conditions which, when X = Y, imply that the commutant of S is also not transitive.
Generalized Cesàro Matrices
Authors: Rhaly H. C. 
Published: December 2010

AbstractFor α ∈ [0, 1] the operator is the operator formally defined on the Hardy space H2 byIf α = 1, then the usual identification of H2 with l2 takes A1 onto the discrete Cesàro operator. Here we see that {Aα: α ∈ [0, 1]} is not arcwise connected, that Re Aα ≥ 0, that Aα is a Hilbert-Schmidt operator if α ∈[0, 1), and that Aα is neither normaloid nor spectraloid if α ∈(0, 1).
Approximation Par des Fonctions Lipschitziennes et Critere de Convergence Etroite D'une Suite de Probabilites
Authors: Rihaoui I. 
Published: December 2010

AbstractIn this paper, we prove that a real valued bounded function, defined on a metric space and uniformly continuous is the uniform limit of a sequence of Lipschitzian bounded functions.As a consequence, a new criterion for the weak convergence of probabilities is given.
Cycles and Harmonic Forms on Locally Symmetric Spaces
Authors: Millson John J. 
Published: December 2010

AbstractTwo constructions of cohomology classes for congruence subgroups of unit groups of quadratic forms over totally real number fields are given and shown to coincide. One is geometric, using cycles, and the other is analytic, using the oscillator (Weil) representation. Considerable background material on this representation is given.
More on Convergence of Continuous Functions and Topological Convergence of Sets
Authors: Beer Gerald 
Published: December 2010

AbstractLet C(X, Y) denote the set of continuous functions from a metric space X to a metric space Y. Viewing elements of C(X, Y) as closed subsets of X × Y, we say {fn} converges topologically to f if Li fn = Lsfn = f. If X is connected, then topological convergence in C(X,R) does not imply pointwise convergence, but if X is locally connected and Y is locally compact, then topological convergence in C(X, Y) is equivalent to uniform convergence on compact subsets of X. Pathological aspects of topological convergence for seemingly nice spaces are also presented, along with a positive Baire category result.
Extended Centroids of Skew Polynomial Rings
Authors: Rosen Jerry D. , Rosen Mary Peles 
Published: December 2010

AbstractLet R be a prime ring with σ ∊ Aut (R). We determine the extended centroid of the skew polynomial ring R[x, σ] when (i) 〈σ〉 is X-outer of finite order, (ii) 〈σ〉 is X-outer and infinite, (iii) σm is X-inner and no smaller power of σ fixes the extended centroid of R.
Integrally Closed Condensed Domains are Bézout
Authors: Anderson David F. , Arnold Jimmy T. , Dobbs David E. 
Published: December 2010

AbstractIt is proved that an integral domainRis a Bézout domain if (and only if)Ris integrally closed andI J= {ij|i∊I, j ∊J} for all idealsIandJofR; that is, if (and only if) R is an integrally closed condensed domain. The article then introduces a weakening of the "condensed" concept which, in the context of thek+Mconstruction, is equivalent to a certain field-theoretic condition. Finally, the field extensions satisfying this condition are classified.
On Quasisimilarity for Toeplitz Operators
Authors: Seddighi K. 
Published: December 2010

AbstractIn this article we give a sufficient condition for quasisimilar analytic Toeplitz operators to be unitarily equivalent. We also use a result of Deddens and Wong to give a sufficient condition for an operator intertwining two analytic Toeplitz operators to intertwine their inner parts too. Analytic Toeplitz operators with univalent symbols satisfying a suitable normalization that are quasisimilar are shown to have equal symbols.
Boundary and Angular Layer Behavior in Singularly Perturbed Semilinear Systems
Authors: Chang K. W. , Liu G. X. 
Published: December 2010

AbstractSome authors have employed the method and technique of differential inequalities to obtain fairly general results concerning the existence and asymptotic behavior, as ∊ → 0+, of the solutions of scalar boundary value problems∊y" = h(t,y), a < t < b,y(a,∊) = A, y(b,∊) = B.In this paper, we extend these results to vector boundary value problems, under analogous stability conditions on the solution u = u(t) of the reduced equation 0 = h(t,u).Two types of asymptotic behavior are studied, depending on whether the reduced solution u(t) has or does not have a continuous first derivative in (a,b), leading to the phenomena of boundary and angular layers.
The Abelian Case of Solitar's Conjecture on Infinite Nielsen Transformations
Authors: Macedonska-Nosalska Olga 
Published: December 2010

AbstractThe paper proves that the group of infinite bounded Nielsen transformations is generated by elementary simultaneous Nielsen transformations modulo the subgroup of those transformations which are equivalent to the identical transformation while acting in a free abelian group. This can be formulated somewhat differently: the group of bounded automorphisms of a free abelian group of countably infinite rank is generated by the elementary simultaneous automorphisms. This proves D. Solitar's conjecture for the abelian case.
Upper Triangular Invariants
Authors: Campbell H. E. A. 
Published: December 2010

AbstractWe modify the construction of the mod 2 Dyer-Lashof (co)-algebra to obtain a (co)-algebra W which is (also) unstable over the Steenrod algebra A*. W has canonical sub-coalgebras W[k] such that the hom-dual W[k:]* is isomorphic as an A-algebra to the ring of upper triangular invariants in ℤ/2ℤ [x1, . . . , xk].
Range Inclusion for Multilinear Mappings: Applications
Authors: Fong C. K. 
Published: December 2010

AbstractThe result of S. Grabiner [5] on range inclusion is applied for establishing the following two theorems: 1. For A, B ∊ L(H), two operators on the Hilbert space H, we have DBC0(H) ⊆ DAL(H) if and only if DBC1(H) ⊆ DAL(H), where DA is the inner derivation which sends S ∊ L(H) to AS - SA, C1(H) is the ideal of trace class operators and C0(H) is the ideal of finite rank operators. 2. (Due to Fialkow [3]) For A, B ∊ L(H), we write T(A, B) for the map on L(H) sending S to AS - SB. Then the range of T(A, B)is the whole L(H) if it includes all finite rank operators L(H).
A Functional Equation for Degree two Local Factors
Authors: Gérardin Paul , Winnie Li Wen-Ch'ing 
Published: December 2010

AbstractWe show that the Fourier transforms of the admissible irreducible representations of the group GL2 over a nonarchimedian local field F are characterized by a functional equation (MF). We also prove that the functions satisfying (MF) and having at most one pole are exactly the Fourier transforms of the irreducible representations of the quaternion group H over F. The Jacquet-Langlands correspondence between irreducible representations of H and discrete series of GL2 then follows immediately from our criteria.
On a Congruence Related to Character Sums
Authors: Chalk J. H. H. 
Published: December 2010

AbstractIf χ is a Dirichlet character to a prime-power modulus pα, then the problem of estimating an incomplete character sum of the form ∑1≤x≤h χ (x) by the method of D. A. Burgess leads to a consideration of congruences of the typef(x)g'(x) - f'(x)g(x) ≡ 0(pα),where fg(x) ≢ 0(p) and f, g are monic polynomials of equal degree with coefficients in Ζ. Here, a characterization of the solution-set for cubics is given in terms of explicit arithmetic progressions.
Cauchy Integral of Calderón on the Graphs of Functions with BMO Derivatives
Authors: Yabuta Kôzô 
Published: December 2010

AbstractWe first note that each graph (x,A(x)) of a function A(x) with BMO derivative is a chord-arc curve. Using this, Muckenhoupt's Ap theory, and the theory of Calderón-Zygmund operators, we shall derive weighted norm inequalities for the Cauchy integral on such graphs from a recent theorem of G. David on the L2-boundedness of Cauchy integral on almost-lipschitzian curves.
Non-Averaging Sets, Dimension and Porosity
Authors: Foran James 
Published: December 2010

AbstractA subset of the line is called non-averaging if, whenever two points belong to the set, their average does not. This paper provides an example of a closed set which is small in the sense that it is non-averaging and has porosity 1 at each of its points and yet large in the sense that its Hausdorff dimension is 1.
An Endpoint Estimate for Certain k-Plane Transforms
Authors: Drury S. W. 
Published: December 2010

AbstractIn this paper we extend a result of Oberlin and Stein on
Radon Transforms to /c-plane transforms for Specifically letwhere the supremum is taken over all affine k-planes ∏ parallel to the vector k-plane π. We show that F is in Ln of the Grassmann manifold Gn,k whenever f is in the Lorentz space L(n/k, 1) of ℝn. The proof relies very heavily on the ideas of M. Christ.
On the Cardinality of Subrings of a Commutative Ring
Authors: Gilmer Robert , Heinzer William 
Published: December 2010

AbstractIf R is an uncountable commutative ring, it is shown that there exists a proper subring of R having the same cardinality as R. It is also shown that if |R| = ω is an uncountable regular cardinal, and if R1 is a subring of R containing an identity of R and such that |R1| < ω, then there exists a proper R1-subalgebra S of R such that |S| = |R|.
Algebraic Elements and Sets of Uniqueness in the Group of Integers of a p-Series Field
Authors: Aubertin Bruce 
Published: December 2010

AbstractLet G be the group of integers of a p-series field. A class {E(θ)} of perfect null subsets of G is introduced and classified into M-sets and U-sets according to the arithmetical nature of the field element θ. This is analogous to the well-known classification, involving Pisot numbers, of certain Cantor sets on the circle.
H(ϕ) Spaces
Authors: W. Deeb  , M. Marzuq  
Published: December 2010

AbstractLet ψ be a non-decreasing continuous subadditive function defined on [0, ∞) and satisfy ψ(x) = 0 if and only if x = 0. The space H(ψ) is defined as the set of analytic functions in the unit disk which satisfyand the space H+ (ψ) is the space of a f ∊ H(ψ) for whichwhere almost everywhere.In this paper we study the H(ψ) spaces and characterize the continuous linear functionals on H+ (ψ).
Counterexamples to Smoothing Convex Functions
Authors: Smith Patrick Adrian Neale 
Published: December 2010

AbstractGreene and Wu have shown that any continuous strongly convex function on a Riemannian manifold can be uniformly approximated by infinitely differentiable strongly convex functions. This result is not true if the word “strongly” is omitted; in this paper, we give examples of manifolds on which convex functions cannot be approximated by convex functions (k = 0, 1,2,...).
On Indecomposable Projective Modules
Authors: O'Neill John D. 
Published: December 2010

AbstractIf P is an indecomposable projective R-module generated by a countable set X, then, for some countable subring S of R, P contains an indecomposable projective S-module generated by X. The subring S may be chosen to inherit many standard ring-theoretic properties from R.
Reciprocal Algebraic Integers Whose Mahler Measures are Non-Reciprocal
Authors: Boyd David W. 
Published: December 2010

AbstractThe Mahler measure M (α) of an algebraic integer α is the product of the moduli of the conjugates of α which lie outside the unit circle. A number α is reciprocal if α- 1 is a conjugate of α. We give two constructions of reciprocal a for which M (α) is non-reciprocal producing examples of any degree n of the form 2h with h odd and h ≥ 3, or else of the form with s ≥ 2. We give explicit examples of degrees 10, 14 and 20.
Centralizing Mappings of Semiprime Rings
Authors: Bell H. E. , Martindale W. S. 
Published: December 2010

AbstractLet R be a ring with center Z, and S a nonempty subset of R. A mapping F from R to R is called centralizing on S if [x, F(x)] ∊ Z for all x ∊ S. We show that a semiprime ring R must have a nontrivial central ideal if it admits an appropriate endomorphism or derivation which is centralizing on some nontrivial one-sided ideal. Under similar hypotheses, we prove commutativity in prime rings.
Kepler-Poinsot-Type Realizations of Regular Maps of Klein, Fricke, Gordan and Sherk
Authors: Schulte E. , Wills J. M. 
Published: December 2010

AbstractThe paper describes polyhedral realizations for Felix Klein's map {3, 7}8 of genus 3, for Gordan's map {4, 5}6 of genus 4, and for two maps of genus 5, the Klein-Fricke map of type {3, 8} and Sherk's map of type {4, 6}. The polyhedra have self-intersections but high symmetry and thus are close analogues to the Kepler-Poinsot-polyhedra.
On Modulus of Noncompact Convexity and Its Properties
Authors: Banaś Józef 
Published: December 2010

AbstractIn this paper we prove some properties of the so-called modulus of noncompact convexity. This notion was recently introduced by K. Goebel and T. Sȩkowski [6] and it appears to be an interesting and useful generalization of the classical Clarkson modulus of convexity. We extend the results obtained in [6] showing that the modulus of noncompact convexity is continuous and has some extra properties in reflexive Banach spaces. The properties applicable in the fixed point theory are also stated.
Lower Bounds For Induced Forests in Cubic Graphs
Authors: Bondy J. A. , Hopkins Glenn , Staton William 
Published: December 2010

AbstractIf G is a connected cubic graph with ρ vertices, ρ > 4, then G has a vertex-induced forest containing at least (5ρ - 2)/8 vertices. In case G is triangle-free, the lower bound is improved to (2ρ — l)/3. Examples are given to show that no such lower bound is possible for vertex-induced trees.
On the Number of Maximal Elements in a Partially Ordered Set
Authors: Ginsburg John 
Published: December 2010

AbstractLet P be a partially ordered set. For an element x ∊ P, a subset C of P is called a cutset for x in P if every element of C is noncomparable to x and every maximal chain in P meets {x} ∪ C. The following result is established: if every element of P has a cutset having n or fewer elements, then P has at most 2n maximal elements. It follows that, if some element of P covers k elements of P then there is an element x ∊ P such that every cutset for x in P has at least log2k elements.