bluuebunny/crossref_metadata_2025_split huggingface dataset:
Bound Sets in Partial Orders and the Fixed Point Property
Authors: Höft Hartmut 
Published: December 2010

AbstractIn this paper we introduce several properties closely related to the fixed point property of a partially ordered set P: the comparability property, the fixed point property for cones, and the fixed point extension property. We apply these properties to the sets of common bounds of the minimal (maximal) elements of the partially ordered set P in order to derive fixed point theorems for P.
On the Kobayashi Pseudometric Reduction of Homogeneous Spaces
Authors: Gilligan Bruce 
Published: December 2010

AbstractGiven any homogeneous complex manifold X = G/H, there exists a natural coset map π :G/H → G/K satisfying π (X1) = π (x2) if and only if dx(x1 x2) = 0, where dx denotes the Kobayashi pseudometric on X. Its typical fiber Z : = K/H is a connected complex submanifold of X. Also G/K has a (7-invariant complex structure, provided K satisfies a certain technical assumption (see Theorem 3). If Z is compact as well, then G/K is biholomorphic to a homogeneous bounded domain.
Spaces of Continuous Vector Functions as Duals
Authors: Cambern Michael , Peter Greim  
Published: December 2010

AbstractA well known result due to Dixmier and Grothendieck for spaces of continuous scalar-valued functions C(X), X compact Hausdorff, is that C(X) is a Banach dual if, and only if, Xis hyperstonean. Moreover, for hyperstonean X, the predual of C(X) is strongly unique. Here we obtain a formulation of this result for spaces of continuous vector-valued functions. It is shown that if E is a Hilbert space and C(X, (E, σ *) ) denotes the space of continuous functions on X to E when E is provided with its weak * ( = weak) topology, then C(X, (E, σ *) ) is a Banach dual if, and only if, X is hyperstonean. Moreover, for hyperstonean X, the predual of C(X, (E, σ *) ) is strongly unique.
On Shift Operators
Authors: Holub J. R. 
Published: December 2010

AbstractA definition of an isometric shift operator on a Banach space is given which extends the usual definition of a shift operator on a separable Hilbert space. It is shown that there is no such shift on many of the common Banach spaces of continuous functions. The associated ideas of a semi-shift and a backward shift are also introduced and studied in the case of continuous function spaces.
The Enumeration of Maps on the Torus and the Projective Plane
Authors: Bender E. A. , Canfield E. R. , Robinson R. W. 
Published: December 2010

AbstractThe enumeration of rooted maps (embedded graphs), by number of edges, on the torus and projective plane, is studied. Explicit expressions for the generating functions are obtained. From these are derived asymptotic expressions and recurrence relations. Numerical tables for the numbers with up to 20 edges are presented.
Kummer's and Iwasawa's Version of Leopoldt's Conjecture
Authors: Sands Jonathan W. 
Published: December 2010

AbstractWe present a refinement of Iwasawa's approach to Leopoldt's conjecture on the non-vanishing of the p-adic regulator of an algebraic number field K. As an application, the conjecture for K implies the conjecture for a solvable extension L of degree g over K if g is relatively prime to p — 1 and p does not divide g, the discriminant of K, and the quotient of class numbers where is a primitive pth root of unity. This can be viewed as generalizing a theorem of Kummer on cyclotomic units.
On the Constant in the Pólya-Vinogradov Inequality
Authors: Hildebrand Adolf 
Published: December 2010

AbstractThe Pólya-Vinogradov inequality states that for any non-principal character x modulo q and any N ≧ 1,where c is an absolute constant. We show that (*) holds with c = 2/(3π2) + o(1) in the case x is primitive and x (— 1) =1 with c = 1/(3π) + o(l) in the case x is primitive and x(— 1) = — 1- This improves by a factor 2/3 the previously best-known values for these constants.
The Proximal Subgradient Formula in Banach Space
Authors: Loewen Philip D. 
Published: December 2010

AbstractThe proximal subgradient formula is a refinement due to Rockafellar of Clarke's fundamental proximal normal formula. It expresses Clarke's generalized gradient of a lower semicontinuous function in terms of analytically simpler proximal subgradients. We use the infinite-dimensional proximal normal formula recently given by Borwein and Strojwas to derive a new version of the proximal subgradient formula in a reflexive Banach space X with Frechet differentiable and locally uniformly convex norm. Our result improves on the one given by Borwein and Strojwas by referring only to the given norm on X.
Eventual Disconjugacy and Right Disfocality of Linear Difference Equations
Authors: Eloe P. W. 
Published: December 2010

AbstractLet a ≧ 0, Ia = ﹛a, a + 1, …﹜ and consider the nth order linear difference m ∈ Ia, α0(m) = 1 on Ia. Summability conditions are placed on the coefficients αj(m), 1 ≦ j ≦ n, such that the equation Pu(m) = 0 is eventually disconjugate. Conditions for eventual right disfocality are also given.
Some Extensions of Askey-Wilson's Q-Beta Integral and the Corresponding Orthogonal Systems
Authors: Rahman Mizan 
Published: December 2010

AbstractA seven-parameter extension of Askey and Wilson's four parameter q-beta integral is written in a symmetric form as the sum of multiples of two very-well-poised balanced basic hypergeometric 10Φ9 series. Two special cases are considered in which the evaluation of the integral gives single terms by the q-Dixon formula in one case and by a special case of the Verma-Jain formula in the other. An orthogonal polynomial system is obtained in the first case and a system of biorthogonal rational function is obtained in the second. It is also shown that the biorthogonal system represents a generalization of Rogers’ q-ultraspherical polynomials.
Uniqueness of Preduals for Spaces of Continuous Vector Functions
Authors: Cambern Michael , Greim Peter 
Published: December 2010

AbstractA. Grothendieck has shown that if the space C(X) is a Banach dual then X is hyperstonean; moreover, the predual of C(X) is strongly unique. In this article we give a vector analogue of Grothendieck's result. We show that if E* is a reflexive Banach space and C(X, (E*, σ*)) denotes the space of continuous functions on X to E* when E* is provided with its weak* (= weak) topology then the full content of Grothendieck's theorem for C(X) can be established for C(X,(E*,σ*)). This improves a result previously obtained for the case in which E* is Hilbert space.
Algebraic Deformations and Bicohomology
Authors: Fox Thomas F. 
Published: December 2010

AbstractRecently we have introduced an enriched cohomology theory for categories that are tripleable (algebraic) over a category of modules. The cohomology admits a circle product, related to the obstruction problem for algebraic deformations, making the total complex a graded ring. We here offer similar constructions in two other situations - coalgebraic and bialgebraic categories. Examples include categories of bialgebras, sheaves of modules, and sheaves of algebras over a sheaf of rings.
Embedding Uncountably Many Mutually Exclusive Continua into Euclidean Space
Authors: Baker B. J. , Laidacker Michael 
Published: December 2010

AbstractUncountable collections of continua of dimension m embeddable in En are investigated, where the difference between m and n is not restricted to one. Collections of isometric copies of continua equivalent to Menger universal continua and collections of continua analogous to G. S. Young's Tn-sets are the main considerations.
A Relation Between the 2-Primary Parts of the Main Conjecture and the Birch-Tate-Conjecture
Authors: Kolster Manfred 
Published: December 2010

AbstractIt is shown that for totally real number fields the Main Conjecture in Iwasawa-Theory for p = 2 proposed by Fédérer implies the 2-primary part of the Birch-Tate-Conjecture in analogy with the case p odd.
Positive Harmonic Functions and Complete Metrics
Authors: Herron David A. , Schiff Joel L. 
Published: December 2010

AbstractWe introduce the class of Harnack domains in which a Harnack type inequality holds for positive harmonic functions with bounds given in terms of the distance to the domain's boundary. We give conditions connecting Harnack domains with several different complete metrics. We characterize the simply connected plane domains which are Harnack and discuss associated topics. We extend classical results to Harnack domains and give applications concerning the rate of growth of various functions defined in Harnack domains. We present a perhaps new characterization for quasidisks.
A Decomposition of Rings Generated by Faithful Cyclic Modules
Authors: Birkenmeier Gary F. 
Published: December 2010

AbstractA ring R is said to be generated by faithful right cyclics (right finitely pseudo-Frobenius), denoted by GFC (FPF), if every faithful cyclic (finitely generated) right R-module generates the category of right R-modules. The class of right GFC rings includes right FPF rings, commutative rings (thus every ring has a GFC subring - its center), strongly regular rings, and continuous regular rings of bounded index. Our main results are: (1) a decomposition of a semi-prime quasi-Baer right GFC ring (e.g., a semiprime right FPF ring) is achieved by considering the set of nilpotent elements and the centrality of idempotnents; (2) a generalization of S. Page's decomposition theorem for a right FPF ring.
Nilpotent-by-Noetherian Factorized Groups
Authors: Amberg Bernhard , Franciosi Silvana , de Giovanni Francesco 
Published: December 2010

AbstractIt is shown that a soluble-by-finite product G = AB of a nilpotent-by-noetherian group A and a noetherian group B is nilpotentby- noetherian. Moreover, a bound for the torsion-free rank of the Fitting factor group of G is given, in terms of the torsion-free rank of the Fitting factor group of A and the torsion-free rank of B.
A Regular Space on Which Every Real-Valued Function with a Closed Graph is Constant
Authors: Baggs Ivan 
Published: December 2010

AbstractAn example is given of a regular space on which every real-valued function with a closed graph is constant. It was previously known that there are regular spaces on which every continuous function is constant. It is also shown here that there are regular spaces that support only constant real-valued continuous functions, but support non-constant real-valued functions with a closed graph.
On Katětov Spaces
Authors: Porter Jack , Tikoo Mohan 
Published: December 2010

AbstractRecent work by Krystock, Porter, and Vermeer has emphasized the importance of the concepts of Katětov spaces and H-sets in the theory of H-closed spaces. These properties are closely related to being the θ-closure of some set and being the adherence of an open filter. This relationship is developed by establishing, among other facts, that an H-closed space in which every closed set is the θ-closure of some set is compact and the θ-closure of a subset of an H-closed space is Katětov and characterizing the open filter adhérences of a space as precisely those sets which are the image of a closed set of the absolute of the space. Also, examples are given of a countable, scattered space which is not Katětov and an H-closed space with an H-closed subspace which is not the θ-closure of any subset of the given space.
Quadratic Non-Residues and Prime-Producing Polynomials
Authors: Mollin R. A. , Williams H. C. 
Published: December 2010

AbstractWe will be looking at quadratic polynomials having positive discriminant and having a long string of primes as initial values. We find conditions tantamount to this phenomenon involving another long string of primes for which the discriminant of the polynomial is a quadratic non-residue. Using the generalized Riemann hypothesis (GRH) we are able to determine all discriminants satisfying this connection.
lp-Norms of Some Generalized Hausdorff Matrices
Authors: Rhoades B. E. 
Published: December 2010

AbstractIn a recent paper D. Borwein [Math. Z. 183(1983), 483- 487] obtained an upper bound for the lp -norms of some generalized Hausdorff matrices, where the sequence (λn) satisfies the condition λn+1 ≦ λn + c, for some positive c. In this paper we obtained the lp -norms of these generalized Hausdorff matrices for which the mass functions are totally monotone.
On Skew Linear Groups Associated with Certain Soluble-by-Finite Groups
Authors: Wehrfritz B. A. F. , Shirvani M. 
Published: December 2010

AbstractLet O1 denote the class of groups G such that every group ring of G (over a field) is an Ore domain. Several approaches to the correction of the proof of a result concerning subrings generated by certain O1-groups are given.
Exponential Estimates for the Conjugate Function on Locally Compact Abelian Groups
Authors: Asmar Nakhlé Habib 
Published: December 2010

AbstractLet G be a locally compact Abelian group, with character group X. Suppose that X contains a measurable order P. For the conjugate function of f is the function whose Fourier transform satisfies the identity for almost all χ in X where sgnp(χ) = - 1 , 0, 1, according as We prove that, when f is bounded with compact support, the conjugate function satisfies some weak type inequalities similar to those of the Hilbert transform of a bounded function with compact support in ℝ. As a consequence of these inequalities, we prove that possesses strong integrability properties, whenever f is bounded and G is compact. In particular, we show that, when G is compact and f is continuous on G, the function is integrable for all p > 0.
Factors of Fields
Authors: Deveney James K. , Yanik Joe 
Published: December 2010

AbstractLet L be a finitely generated extension of a field k. L is a k-rational factor if there is a field extension K of k such that the total quotient ring of L ꕕk K is a rational (pure transcendental) extension of K. We present examples of non-rational rational factors and explicitly determine both factors.
Nearness Convergence
Authors: Naimpally S. A. , Tikoo Mohan L. 
Published: December 2010

AbstractIn this paper, a concept of nearness convergence is introduced which contains the proximal convergence of Leader as a special case. It is proved that uniform convergence and this nearness convergence are equivalent on totally bounded uniform nearness spaces. One of the features of this convergence is that it lies between uniform convergence and pointwise convergence, and implies uniform convergence on compacta. Some other weaker notions of nearness convergence which are sufficient to preserve nearness maps are also discussed.
A Furstenberg Transformation of the 2-Torus Without Quasi-Discrete Spectrum
Authors: Rouhani H. 
Published: December 2010

AbstractR. Ji asked whether or not a Furstenberg transformation of the 2-torus of the form (x,y) → (e2πiθx, f(x)y), where θ is irrational and f : T —> T is continuous with non-zero degree k, is topologically conjugate to the Anzai transformation (x, y) → (e2πiθx, xk y) or its inverse. In this paper this question is settled in the negative. Further, some sufficient conditions are given under which the crossed product C*-algebra associated with a Furstenberg transformation of the 2-torus has a unique tracial state.
The Stability of a Functional Analogue of the Wave Equation
Authors: Bean Michael , Baker John A. 
Published: December 2010

AbstractFor h € ℝ and ϕ : ℝ2 → ℝ define Lhϕ: ℝ2 → ℝ by (Lhϕ)(x, y) = ϕ (x + h, y) + ϕ (x — h,y) — ϕ (x,y + h) — ϕ (x,y — h) for all (x,y) € ℝ2. The aim of the paper is to establish the following "stability" theorem concerning the functional equationif δ > 0, f : ℝ2 → ℝ andthen there exists ɛ > 0 ami ϕ : ℝ2 → ℝ such that (Lhϕ)(x, y ) = 0 for all x, y,h ∊ ℝ and
On Completely Positive Maps Defined by an Irreducible Correspondence
Authors: Anantharaman-Delaroche C. 
Published: December 2010

AbstractCompletely positive maps defined by an irreducible correspondence between two von Neumann algebras M and N are introduced. We give results about their structure and characterize, among them, those which are extreme points in the convex set of all unital completely positive maps from M to N. As particular cases we obtain known results of M. D. Choi [4] on completely positive maps between complex matrices and of J. A. Mingo [8] on inner completely positive maps.
LP Approximation by Reciprocals of Trigonometric and Algebraic Polynomials
Authors: Devore Ronald A. , Leviatan D. , Yu Xiang Ming 
Published: December 2010

AbstractWe give an estimate for the error of Lp approximation by reciprocals of polynomials. These estimates are the analogues of the Jackson and Ditzian - Totik estimates for polynomial approximation.
On An Affine Connection Which Admits A Volume-Like Form
Authors: Chi D. P. , Yoon Y. D. 
Published: December 2010

AbstractA necessary and sufficient condition to obtain a volumelike form from an affine connection is given in terms of the Čech cohomology, after the volume-like form is naturally defined without a Riemannian metric. A necessary condition for an affine connection to be a Riemannian connection for some metric is also given.
The Limiting Behavior of Sequences of Quasiconformal Mappings
Authors: Aebischer Beat 
Published: December 2010

AbstractThe limiting behavior of sequences of quasiconformal homeomorphisms of the n-sphere Sn is studied using a substitute to the Poincaré extension of Möbius transformations introduced by Tukia. Adapted versions of the limit set and the conical limit set known in the theory of Kleinian groups are utilized. Most of the results also hold for families of homeomorphisms of Sn with the convergence property introduced by Gehring and Martin.
The Coherence Number of 2-Groups
Authors: McCool James 
Published: December 2010

AbstractLet G be a finite group. A natural invariant c(G) of G has been defined by W.J. Ralph, as the order (possibly infinite) of a distinguished element of a certain abelian group associated to G. Ralph has shown that c(Zn) = 1 and c(Z2 ⴲ Z2) = 2. In the present paper we show that c(G) is finite whenever G is a dihedral group or a 2-group, and obtain upper bounds for c(G) in these cases.
Units in Group Rings of the Infinite Dihedral Group
Authors: Mirowicz Maciej 
Published: December 2010

AbstractThis paper studies the group of units U(RD∞) of the group ring of the infinite dihedral group D∞ over a commutative integral domain R. The structures of U(Z2D∞) and U(Z3D∞) are determined, and it is shown that U(ZD∞) is not finitely generated.
Comparing Graded Versions of the Prime Radical
Authors: Beattie M. A. , S.X. Liu , Stewart P. N. 
Published: December 2010

AbstractLet G be a group with identity e, let λ be a normal supernilpotent radical in the category of associative rings and let λref be the reflected radical in the category of G-graded rings. Then for A a G-graded ring, λref(A) is the largest graded ideal of A whose intersection with Ae is λ (Ae). For λ = B, the prime radical, we compare Bref(A) to BG(A) = B(A)G, the largest graded ideal in B(A).
On Extending Projectives of Finite Group-Graded Algebras
Authors: Harris Morton E. 
Published: December 2010

AbstractLet G be a finite group, let k be a field and let R be a finite dimensional fully G-graded k-algebra. Also let L be a completely reducible R-module and let P be a projective cover of R. We give necessary and sufficient conditions for P|R1 to be a projective cover of L|R1 in Mod (R1). In particular, this happens if and only if L is R1-projective. Some consequences in finite group representation theory are deduced.
Jacobi Sums, Irreducible Zeta-Polynomials, and Cryptography
Authors: Koblitz Neal 
Published: December 2010

AbstractWe find conditions under which the numerator of the zeta-function of the curve y2+y = xd over Fp, where d — 2g +1 is a prime, d ≠ p, is irreducible over Q. This leads to the generalized Mersenne problem of "almost primality" of the number of points on the jacobian of such a curve over an extension of Fp, which has application to public key cryptography.
Simultaneous Triangularization of Algebras of Polynomially Compact Operators
Authors: Radjabalipour M. 
Published: December 2010

AbstractIf A is a norm closed algebra of compact operators on a Hilbert space and if its Jacobson radical J(A) consists of all quasinilpotent operators in A then A/ J(A) is commutative. The result is not valid for a general algebra of polynomially compact operators.
Two Continua Having A Property of J. L. Kelley
Authors: Ingram W. T. , Sherling D. D. 
Published: December 2010

AbstractIn proving the contractibility of certain hyperspaces J. L. Kelley identified and defined a certain uniformnessproperty which he called Property 3.2. It is known that the classes of locally connected continua, homogeneous continua and hereditarily indecomposable continua have Property 3.2. In this paper we prove that two examples of indecomposable continua developed respectively by the authors have Property 3.2. One is the example of a nonchainable atriodic tree-like continuum with positive span which was defined by the first author, and the other is a nonchainable, noncircle-like continuum which has the cone=hyperspace property which was defined by the second author. Each of the examples is an inverse limit of an inverse system having a single bonding map.
Special Principal Ideal Rings and Absolute Subretracts
Authors: Jespers Eric 
Published: December 2010

AbstractA ringRis said to be an absolute subretract if for any ringSin the variety generated byRand for any ring monomorphismffromRintoS, there exists a ring morphismgfromStoRsuch that gf is the identity mapping. This concept, introduced by Gardner and Stewart, is a ring theoretic version of an injective notion in certain varieties investigated by Davey and Kovacs.Also recall that a special principal ideal ring is a local principal ring with nonzero nilpotent maximal ideal. In this paper (finite) special principal ideal rings that are absolute subretracts are studied.
The Entrance Space of a Measure-Valued Markov Branching Process Conditioned on Non-Extinction
Authors: Evans Steven N. 
Published: December 2010

AbstractWe explicitly identify the possible probability entrance laws for a class of measure-valued processes that are constructed by taking a particular measure-valued Markov branching process and conditioning it to stay away from the zero measure trap. The set of extreme points of the entrance space is larger than the state space of the conditioned process, and contains elements which correspond tostartingthe conditioned process at the zero measure.
The Hausdorff Dimension of an Ergodic Invariant Measure for a Piecewise Monotonic Map of the Interval
Authors: Hofbauer Franz , Raith Peter 
Published: December 2010

AbstractWe consider a piecewise monotonie and piecewise continuous map T on the interval. If T has a derivative of bounded variation, we show for an ergodic invariant measure μ with positive Ljapunov exponent λμ that the Hausdorff dimension of μ equals hμ / λμ.
The Poset of Conjugacy Classes and Decomposition of Products in the Symmetric Group
Authors: Bédard François , Goupil Alain 
Published: December 2010

AbstractThe action by multiplication of the class of transpositions of the symmetric group on the other conjugacy classes defines a graded poset as described by Birkhoff ([2]). In this paper, the edges of this poset are given a weight and the structure obtained is called the poset of conjugacy classes of the symmetric group. We use weights of chains in the posets to obtain new formulas for the decomposition of products of conjugacy classes of the symmetric group in its group algebra as linear combinations of conjugacy classes and we derive a new identity involving partitions of
n.
Universal Compact T1 -Spaces
Authors: Mysior Adam 
Published: December 2010

AbstractFor every infinite cardinal k we construct a space Ck universal for all compact T1 -spaces of weight ≤ k. It follows, in particular, that there are only 2k topologically different compact T1 -spaces. We show that Cw is universal for all second countable developable T1 -spaces. The existence of closely universal compact T1 -spaces is discussed.