bluuebunny/crossref_metadata_2025_split huggingface dataset:
Hausdorff Distance and a Compactness Criterion for Continuous Functions
Authors: Beer Gerald 
Published: December 2010

AbstractLet 〈X, dx〉 and 〈Y, dY〉 be metric spaces and let hp denote Hausdorff distance in X x Y induced by the metric p on X x Y given by p[(x1, y1), (x2, y2)] = max ﹛dx(x1, x2),dY(y1, y2)﹜- Using the fact that hp when restricted to the uniformly continuous functions from X to Y induces the topology of uniform convergence, we exhibit a natural compactness criterion for C(X, Y) when X is compact and Y is complete.
The Fractal Dimension of Sets Derived from Complex Bases
Authors: Gilbert William J. 
Published: December 2010

AbstractFor each positive integer n, the radix representation of the complex numbers in the base —n + i gives rise to a tiling of the plane. Each tile consists of all the complex numbers representable in the base -n + i with a fixed integer part. We show that the fractal dimension of the boundary of each tile is 2 log λn/log(n2 + 1), where λn is the positive root of λ3 - (2n - 1) λ2 - (n - 1) 2λ - (n2 + 1).
An Amalgamation Theorem For Soluble Groups
Authors: Leinen Felix 
Published: December 2010

AbstractA theorem of G. Higman about the embeddability of amalgams within the class of all finite ρ-groups is generalized to classes of soluble groups. We also give best possible bounds for the solubility lengths of the constructed completions. And, as an application, the super-soluble amalgamation bases in the class of all finite soluble π-groups are determined.
Sign Properties of Green's Functions For Two Classes of Boundary Value Problems
Authors: Eloe P. W. 
Published: December 2010

AbstractLet G(x,s) be the Green's function for the boundary value problem y(n) = 0, Ty = 0, where Ty = 0 represents boundary conditions at two points. The signs of G(x,s) and certain of its partial derivatives with respect to x are determined for two classes of boundary value problems. The results are also carried over to analogous classes of boundary value problems for difference equations.
Sharp Bounds on the Diameter of a Graph
Authors: Smyth W. F. 
Published: December 2010

AbstractLet Dn.m, be the diameter of a connected undirected graph on n ≥2 vertices and n - 1 ≤ m ≤ s(n) edges, where s(n) = n(n — l)/2. Then Dn.s(n) = 1, and for ms(n) it is shown thatThe bounds on Dn.m, are sharp.
A Hilbert Lattice With a Small Automorphism Group
Authors: Künzi Urs-Martin 
Published: December 2010

AbstractWe construct an orthomodular inner product space to answer the questions posed by R. P. Morash in his paper "Angle bisection and orthoautomorphisms in Hilbert lattices" [6]. For example we show that every automorphism of the Hilbert lattice belonging to our inner product space has the property, that no atom is orthogonal to its image.
A System of Operator Equations
Authors: Magajna Bojan 
Published: December 2010

AbstractLet be a separable Hilbert space, the algebra of all bounded operators on and Ai, Bi, ∊ , i = 1,. . . , r. It is shown that if no nontrivial linear combination of the operators Ai, is compact, then there exist X, Y ∊ such that X Ai, Y = Bi, for all i. A related (but much milder) result is discussed in other algebras with the unique maximal ideal and an application to elementary operators is given.
On the Semigroup of Probability Measures of a Locally Compact Semigroup II
Authors: Wong James C. S. 
Published: December 2010

AbstractThis is a sequel to the author's paper "On the semigroup of probability measures of a locally compact semigroup." We continue to investigate the relationship between amenability of spaces of functions and functionals associated with a locally compact semigroups S and its convolution semigroup MO(S) of probability measures and fixed point properties of actions of S and MO(S) on compact convex sets.
Lie Derivations on Skew Elements in Prime Rings With Involution
Authors: Killam Eleanor 
Published: December 2010

AbstractLet R be a prime ring with involution satisfying x/2 ∊ R whenever x ∊ R. Assume that R has two nontrivial symmetric idempotents e1, e2 whose sum is not 1, and that the subrings determined by e1, e2, 1 — (e1 + e2) are not orders in simple rings of dimension at most 4 over their centers. Then if L is a Lie derivation of the skew elements K into R there exists a subring A of R, A ⊆ , a derivation D :A → RC, the central closure of R, and a mapping T:R → C, satisfying L = D + T on K and = 0.
H-Simple H-Module Algebras
Authors: Cohen Miriam 
Published: December 2010

AbstractLet A be an H-simple commutative H-module algebra, with AH = k and dimk H ≤ dimk A < ∞. We show that this implies that A # H is isomorphic to Mn(k), a central simple algebra. We apply this to characterize certain group graded algebras, algebras acted upon by a group as automorphisms, or by a nilpotent Lie algebra as derivations.
Derivatives and Length-Preserving Maps
Authors: Yamashita Shinji 
Published: December 2010

AbstractLet a be a constant, |a| = 1. We shall prove meromorphic (M) and bounded-holomorphic (BH) versions of the following prototype: (P) Let f and g be holomorphic in a domain D. Then, |f'| = |g'| in D if and only if there exist constant a, b with f = ag + b in D. (M) Let f and g be meromorphic in D. Then, |f'|/(1 + |f|2) = |g'|/(1 + |g|2) in D if and only if there exist a, b with |b| ≦ ∞ such that f = a(g - b)/(\ + g). (BH) Let f and g be holomorphic and bounded, |f| < 1, |g| < 1, in D. Then, |f'|/ (1 - |f|2) = |g'|/(1 - |g|2) in D if and only if there exist a, b with |b| < 1, such that f = a(g - b)/(1 - g).
H-Semidirect Products
Authors: Peschke Georg 
Published: December 2010

AbstractThe concept of H-semidirect product structure on a grouplike space is introduced. It is shown that the loop space ΩX of any based CW-complex X is the H-semidirect product of the identity path-component of ΩX with π1,X. The set of free homotopy classes of maps into a Hsemidirect product inherits the structure of a semidirect product. This leads to new results concerning the nilpotency of homotopy classes of maps into a group-like space.
On a Problem Related to The Conjecture of Sendov About The Critical Points of a Polynomial
Authors: Rahman Q. I. , Tariq Q. M. 
Published: December 2010

AbstractLet P be a polynomial of degree n having all its zeros in the closed unit disk. Given that a is a zero (of P) of multiplicity k we seek to determine the radius ρ(n; k; a) of the smallest disk centred at a containing at least k zeros of the derivative P'. In the case k = 1 the answer has been conjectured to be 1 and is known to be true for n ≦ 5. We prove that ρ(n; k; a) ≦ 2k/(k + 1) for arbitrary k ∊ N and n ≦ k + 4.
Convolution with Odd Kernels Having a Tempered Singularity
Authors: Kerman R. A. 
Published: December 2010

AbstractSuppose b(t) decreases to 0 on [1, ∞). Define the singular integral operator Cb at periodic f of period 1 in L1 (T),T = ( - 1 / 2, 1/2), byThen, for a large class of b one has the rearrangement inequalityThis inequality is used to construct a rearrangement invariant function space X corresponding to a given such space Y so that Cb maps X into Y.
On Quasisimilarity for Analytic Toeplitz Operators
Authors: Takahashi Katsutoshi 
Published: December 2010

AbstractLet f be a function in H∞. We show that if f is inner or if the commutant of the analytic Toeplitz operator Tf is equal to that of Tb for some finite Blaschke product b, then any analytic Toeplitz operator quasisimilar to Tf is unitarily equivalent to Tf.
Torsion-free Abelian Groups, Valuations and Twisted Group Rings
Authors: Bastos Gervasio G. , Viswanathan T. M. 
Published: December 2010

AbstractAnderson and Ohm have introduced valuations of monoid rings k[Γ] where k is a field and Γ a cancellative torsion-free commutative monoid. We study the residue class fields in question and solve a problem concerning the pure transcendence of the residue fields.
On the Cardinality of Urysohn Spaces
Authors: Bella A. , Cammaroto F. 
Published: December 2010

AbstractIn this paper some cardinal inequalities for Urysohn spaces are established. In particular the following two theorems are proved:(i)If where [A]θ denotes the θ-closed hull of A, i.e., the smallest θ-closed subset of X containing A;(ii), where aL(X, X) is the smallest cardinal number m such that for every open cover of X there is a subfamily for which
Continuité des Caractères Dans les Algèbres de Fréchet à Bases
Authors: Akkar M. , El Azhari M. , Oudadess M. 
Published: December 2010

AbstractIn [1] and [2] T. Husain and J. Liang show the following results: RI. Every character on a Fréchet algebra with a Schauder basis (xi)i≧1 such that: (1) XiXj = XjXi = Xj if i ≦ j, (2) Pi(Xi) ≠ 0 and Pi(xi+1) = 0 (where (pi)i≧1 is a denumerable family of semi-norms defining the topology of the algebra) is continuous. R2. Every character on a Fréchet algebra with orthogonal and unconditional Schauder basis is continuous. The proofs of these last results are very long and introduce complex calculation without aid of spectral theory of locally ra-convex algebras. We give here short proofs of these results with aid of a characterization of elements of the spectrum in locally m-convex algebras with values of characters.
Further Theorems of the Rogers-Ramanujan Type Theorems*
Authors: Subbarao M. V. , Agarwal A. K. 
Published: December 2010

AbstractWe give three new partition theorems of the classical Rogers-Ramanujan type which are very much in the style of MacMahon. These are a continuation of four theorems of the same kind given recently by the second author. One of these new theorems, very similar to one of the original Rogers-Ramanuj an - MacMahon type theorems is as follows: Let C(n) denote the number of partitions of n into parts congruent to ±2, ± 3, ±4, ± 5, ±6, ±7 (mod 20). Let D(n) denote the number of partitions of n of the form n = b1 + b2 + … + bt, where bt ≧ 2, bt ≧ bi + 1 and if 1 ≦ i ≦ [(t - 2)/2], bi - bi + 1 ≧ 2. Then C(n) = D(n).
Characterizations of Axiomatic Categories of Models Canonically Isomorphic to (Quasi-)Varieties
Authors: Hébert Michel 
Published: December 2010

AbstractLetbe the category of all homomorphisms (i.e. functions preserving satisfaction of atomic formulas) between models of a set of sentencesTin a finitary first-order languageL.Functors between two such categories are said to becanonicalif they commute with the forgetful functors. The following properties are characterized syntactically and also in terms of closure offor some algebraic constructions (involving products, equalizers, factorizations and kernel pairs): There is a canonical isomorphism fromto a variety (resp. quasivariety) in a finitary expansion ofLwhich assigns to a model its (unique) expansion. This solves a problem of H. Volger.In the case of a purely algebraic language, the properties are equivalent to:“is canonically isomorphic to a finitary variety (resp. quasivariety)” and, for the variety case, to “the forgetful functor ofis monadic (tripleable)”.
Quadratic forms and Linkage of Quaternion Algebras
Authors: Krishnamani Vatsala , Yucas Joseph 
Published: December 2010

AbstractA field F satisfies n-linkage on a subset of Ḟ if whenever the quaternion algebrasare equal in Br(F) there exist z ∈ Ḟ withfor i = 1, 2, . . ., n. This linkage of quaternion algebras is examined and its relationship to the torsion freeness of I2(F) and to the strong approximation property is investigated.
Stability Theorems for Convex Domains of Constant Width
Authors: Groemer H. 
Published: December 2010

AbstractIt is known that among all plane convex domains of given constant width Reuleaux triangles have minimal and circular discs have maximal area. Some estimates are given concerning the following associated stability problem: If K is a convex domain of constant width w and if the area of K differs at most ∊ from the area of a Reuleaux triangle or a circular disc of width w, how close (in terms of the Hausdorff distance) is K to a Reuleaux triangle or a circular disc? Another result concerns the deviation of a convex domain M of diameter d from a convex domain of constant width if the perimeter of M is close to πd.
Isomorphisms of Prime Goldie Semi-Principal Left Ideal Rings, II
Authors: Wolfson Kenneth G. 
Published: December 2010

AbstractA prime Goldie ring K, in which each finitely generated left ideal is principal is the endomorphism ring E(F, A) of a free module A, of finite rank, over an Ore domain F. We determine necessary and sufficient conditions to insure that whenever K ≅ E(F, A) ≅ E(G, B) (with A and B free and finitely generated over domains F and G) then (F, A) is semi-linearly isomorphic to (G, B). We also show, by example, that it is possible for K ≅ E(F, A ) ≅ E(G, B), with F and G, not isomorphic.
Primary Decomposition for Σ-Groups
Authors: Brunker Don , Higgs Denis 
Published: December 2010

AbstractA Σ-group is an abelian group on which is given a collection of infinite sums having properties suggested by those of absolutely convergent series in R or C. It is shown that the usual decomposition of a torsion abelian group into its p-components carries over to the case of Σ-groups when the property of being torsion is replaced by an appropriate uniform version. For a certain class of Σ-groups, it turns out that being torsion is already sufficient for primary decomposition to hold.
Decompositions of Localized Fibres and Cofibres
Authors: Oprea John 
Published: December 2010

AbstractIn this paper p-local versions of the Rational Fibre and Cofibre Decomposition Theorems are given. In particular, if there exists an element in the nth Gottlieb group of a space F such that its image under the Hurewicz map has infinite order, then Sn for almost all primes p. A dual result is proved for cofibrations.
On the Residual Finiteness of Certain Polygonal Products
Authors: Allenby R. B. J. T. , Tang C. Y. 
Published: December 2010

AbstractWe give examples to show that unlike generalized free products of groups (g.f.p.) polygonal products of finitely generated (f.g.) nilpotent groups with cyclic amalgamations need not be residually finite (R) and polygonal products of finite p-groups with cyclic amalgamations need not be residually nilpotent. However, polygonal products f.g. abelian groups are R, and under certain conditions polygonal products of finite p-groups with cyclic amalgamations are R.
A Note on Blaschke Products with Zeroes in a Nontangential Region
Authors: Jevtić Miroljub 
Published: December 2010

AbstractWe show that if B is α Blaschke product with nontangential zero set {zk} and 0 < p < 1, 1/2 < αp < 1, then the condition sup0<r<1(l — r) Mp(r, D1+αB) < ∞ is equivalent to the condition {(1 - |zk|(1/p)-αKα} ∊ l∞.
Bireflectionality in Absolute Geometry
Authors: Ljubić Dragoslav 
Published: December 2010

AbstractIf G is any group then g ∊ G is called an involution if g ≠ 1 and g o g = 1. A group G is called bireflectional if every element in G is a product of two involutions. It is known that 2- dimensional, 3- dimensional, and some types of n-dimensional (n > 3) absolute geometries (in the sense of H. Kinder) are bireflectional. In this article the author proves the general result that every n-dimensional absolute geometry is bireflectional.
Cauchy Completion Categories
Authors: Kent D. C. , Richardson G. D. 
Published: December 2010

AbstractA general procedure is introduced for identifying categories of Cauchy spaces which have completions which possess a certain convergence property P, and for constructing completion functors on such categories. These results are applied to obtain a characterization of Cauchy spaces which allow T3 completions, and to construct T3 completions for categories of Cauchy groups and Cauchy lattices.
A Stochastic Ergodic Theorem for General Additive Processes
Authors: Çömez Doḡan 
Published: December 2010

AbstractIn this article, we obtain the stochastic ergodic theorem for general additive processes. That is, we prove that there exists , such that whenever α > 0 and A is a measurable set with μ(A) < ∞, where and {U(ij)}} an arbitrary (two dimensional) semigroup of L1 -contractions. This result generalizes the stochastic ergodic theorem (SET) of U. Krengel and the SET of M. A. Akcoglu and L. Sucheston.
Sur une Propriete des Fonctions Propres de L'Operateur de Laplace-Beltrami
Authors: Chipot M. , Oliker V. 
Published: December 2010

AbstractSi M est une variété riemannienne de dimension n, n ≧ 2, et de métrique g on s'intéresse au problème: trouver toutes les fonctions régulières F : M → IR qui sont valeurs propres ainsi que leur carré de l'opérateur de Laplace-Beltrami, Δ, associé à g.
A Remark on the Loewy-Series of Certain Hopf Algebras
Authors: Röhl Frank 
Published: December 2010

AbstractAn easy proof will be given to show that for finite dimensional Hopf-algebras with nilpotent augmentation ideal over the field of p elements, the upper and lower Loewy-series coincide. In particular, this holds for the restricted universal envelope of nilpotent Lie-p-algebras with
nilpotent p-map.
Grammar as Mathematics
Authors: Lambek J. 
Published: December 2010

AbstractWhile there are a small number of reasonably deep theorems in mathematical linguistics, I wish to argue that grammar is mathematics at a very basic level, albeit "trivial" mathematics. Linguistic activities such as the production and recognition of sentences are quite analogous to the mathematical activities of proving theorems or making calculations, while learning a language involves something akin to the discovery or invention of postulates.
Conformally Flat Riemannian Manifolds as Hypersurfaces of the Light Cone
Authors: Asperti A. C. , Dajczer M. 
Published: December 2010

AbstractSimply connected conformally flat Riemannian manifolds are characterized as hypersurfaces in the light cone of a standard flat Lorentzian space, transversal to its generators. Some applications of this fact are given.
Convolution Orthogonality and the Jacobi Polynominals
Authors: Allaway Wm. R. 
Published: December 2010

AbstractLet α and β be any two real numbers and let be the Jacobi polynomial sequences. For any non-zero real number a, is an orthogonal polynomial sequence with respect to convolution if and only if either (i) b = 1, α = 0 and β + 1 is not equal to a negative integer or (ii) b = — 1, β = 0 and α + 1 is not equal to a negative integer.
A Characterization of a Sparse Blaschke Product
Authors: Guillory Carroll 
Published: December 2010

AbstractWe give a characterization of a sparse Blaschke product b in terms of the separation of support sets of its zeros in M(H∞ + C) and the structure of the nonanalytic points. We use this characterization to give a sufficient condition on an interpolating Blaschke product q to have the following property: there exists a non trivial Gleason part P on which q is nonzero and less than one.
Differential Equation for Classical-Type Orthogonal Polynomials
Authors: Ronveaux A. , Marcellan F. 
Published: December 2010

AbstractThe second order differential equation of Littlejohn-Shore for Laguerre type orthogonal polynomials is generalized in two ways. First the positive Dirac mass can be situated at any point and secondly the weight can be any classical weight modified by an arbitrary number of Dirac distributions.
On Spaces of Compact Operators in Non-Archimedean Banach Spaces
Authors: Kiyosawa Takemitsu 
Published: December 2010

AbstractLet K be a non-trivial complete non-Archimedean valued field and let E be an infinite-dimensional Banach space over K. Some of the main results are:(1) K is spherically complete if and only if every weakly convergent sequence in l∞ is norm-convergent.(2) If the valuation of K is dense, then C0 is complemented in E if and only if C(E,c0) is n o t complemented in L(E,c0), where L(E,c0) is the space of all continuous linear operators from E to c0 and C(E,c0) is the subspace of L(E, c0) consisting of all compact linear operators.
Sur les Sous-Groupes Purifiables des Groupes Abéliens Primaires
Authors: Benabdallah K. , Piché C. 
Published: December 2010

AbstractThe class of primary abelian groups whose subsocles are purifiable is not yet completely characterized and it contains the class of direct sums of cyclic groups and torsion complete groups. In sharp constrast with this, the class of groups whose p2-bounded subgroups are purifiable consist only of those groups which are the direct sum of a bounded and a divisible group. Various tools are developed and a short application to the pure envelopes of cyclic subgroups is given in the last section.
A Simple Proof for the Unicity of the Limit Cycle in the Bogdanov-Takens System
Authors: Li Chengzhi , Rousseau Christiane , Wang Xian 
Published: December 2010

AbstractWe show that the Bogdanov-Takens system has at most one limit cycle. Similarly we show that the maximum number of limit cycles in the universal unfolding of the symmetric cusp of order 2 (resp. 3) is one (resp. 2). The proof uses the elementary technique of Liénard's equation, yielding a global result for all values of the parameters.
Sur les Fonctions Analytiques Multiformes dont les Valeurs Sont des Segments
Authors: Baribeau Une 
Published: December 2010

AbstractAnalytic multivalued functions are a powerful tool in spectral theory. In this paper we study analytic multivalued functions λ → K(λ) whose values are segments. Under the additional assumption that K is continuous, we prove that the endpoints of K vary locally holomorphically.
Distribution of Weierstrass Points on Rational Cuspidal Curves
Authors: Little John B. 
Published: December 2010

AbstractWe study the set W(𝓛) of Weierstrass points of all positive tensor powers of an invertible sheaf 𝓛 on an irreducible rational curve X with g ≧ 2 ordinary cusps. Using an idea from B. Olsen's study of the analogous question on smooth curves, and an explicit formula for the "theta function" of a cuspidal rational curve, we show that W(𝓛) is never dense on X (in contrast to the case of smooth curves of genus g ≧ 2).
Product of Two Commutators as a Square in a Free Group
Authors: Comerford Jonell A. , Lee Y. 
Published: December 2010

AbstractWe show that, if [s,t][u, v] = x2 in a free group, x need not be a commutator. We arrive at our example by use of a result of D. Piollet which characterizes solutions of such equations using an algebraic interpretation of the mapping class group of the corresponding surface.
A Homotopical Conner-Raymond Theorem and a Question of Gottlieb
Authors: Oprea John 
Published: December 2010

AbstractA homotopy theoretic version is given of the following result of Conner and Raymond: If the circle acts on a space so that the orbit map induces an injection in homology, then the space fibres over the circle with finite structure group. This homotopical analogue is related to recent results pertaining to the effect of the fundamental group's structure on the Euler characteristic. It is also used in the construction of a compact, simple 7-manifold with trivial Gottlieb group which, together with an infinite dimensional example of Ganea, answers a question of Gottlieb.
Proof of a Conjecture of Chowla and Zassenhaus on Permutation Polynomials
Authors: Cohen Stephen D. 
Published: December 2010

AbstractThe following conjecture of Chowla and Zassenhaus ( 1968) is proved. If f(x) is an integral polynomial of degree ≧ 2 and p is a sufficiently large prime for which f (considered modulo p) is a permutation polynomial of the finite prime field Fp, then for no integer c with 1 ≦ c < p is f(x) + cx a permutation polynomial of Fp.
On Products of Conditional Expectation Operators
Authors: Zaharopol Radu 
Published: December 2010

AbstractLet (X, Σ, μ) be a probability space, let f1, f2, ..., Fk be k σ-subalgebras of Σ, and let p ∊ R be such that 1 < p < + ∞. Let Pi :LP(X, Σ, μ) → LP(X, Σ, μ) be the conditional expectation operator corresponding to fi for every i = 1,2,…, k, and set T = P1 . . . Pk. Our goal in the note is to give a new and simpler proof of the fact that for every f ∊ LP(X, Σ, μ), the sequence (Tnf)n∊N converges in the norm topology of LP(X, Σ, μ), and that its limit is the conditional expectation of f with respect to f1 ∩ f2 ∩ … ∩ Fk.