bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Generalization of the Lax-Milgram Lemma
Authors: Inayatnoor K. , Noor M. Aslam 
Published: December 2010

Let H be a real Hilbert space with its dual space H'. The norm and inner product in H are denoted by ||.|| and 〈.,.〉 respectively. We denote by 〈.,.〉, the pairing between H' and H.If a(u, v) is a bilinear form and F is a real-valued continuous functional on H, then we consider I[v], a functional defined by
Some Triangle Inequalities and Generalizations
Authors: Carroll C. E. , Yang C C. , Ahn S. 
Published: December 2010

AbstractLet , where ai, s, and x are real, and II denotes the product over cyclic rearrangements of the subscripts. We show that, in five special cases, Dn, s(x)Dn, s(y) is greater than a fixed multiple of Dn, s(x + y).
On Prime Semilattices
Authors: Pawar Y. S. , Thakare N. K. 
Published: December 2010

AbstractSeveral characterizations for prime semilattices are obtained. Prime semilattices that are compactly packed by filters have been characterized. Solution to the problem, “Find a condition on a semilattice by which every filter can be expressed as the intersection of all prime filters containing it”, is furnished.
The Ruin Problem for Sums of Dependent Random Variables
Authors: Johnson Dudley Paul 
Published: December 2010

AbstractIn this paper we show how to compute the probability that a sequence Zn = X0 + … + Xn of partial sums of dependent random variables, each taking on the values ±1, will first leave an interval (a, b) at a; and how to compute the expected time it takes for the partial sums to leave the interval (a, b).
On the Non-Existence of Certain Euler Products
Authors: Subbarao M. V. 
Published: December 2010

In a paper with the above title, T. M. Apostol and S. Chowla [1] proved the following result:Theorem 1.For relatively prime integers h and k, l ≤ h ≤ k, the seriesdoes not admit of an Euler product decomposition, that is, an identity of the form1except when h = k = l; fc = 1, fc = 2. The series on the right is extended over all primes p and is assumed to be absolutely convergent forR(s)>1.
An Upper Limit Property of the Euler Function
Authors: Hausman Miriam 
Published: December 2010

If ϕ(n) denotes the Euler function, for n = p a prime we have ϕ(n)/n = (1-1/p), which implies thatIn this note we consider a refinement of this result. Namely, we prove that1where P∗(k) is the largest integer of the form where p1 < p2<…<pr are the first r primes in ascending order.
On the Topologies of R∞
Authors: Ho Chung-Wu 
Published: December 2010

AbstractLet R∞ be the set of all the finite sequences of real numbers. The author shows that there are uncountably many distinct topologies on the set R∞, each of which coincides with the usual topology when restricted to an Rn. However, under each of these topologies, R∞ is always of the same homotopy type. A generalization to some other spaces is mentioned.
A Generalization of Floyd's Theorem on Unicoherent Peano Continua with Involution
Authors: Grover A. K. , Hunt J. H. V. 
Published: December 2010

AbstractWe generalize a result of E. E. Floyd on unicoherent Peano continua with involution to unicoherent locally connected regular hereditarily Lindelöf spaces. The result has an application in the theory of connectivity functions.
An Extrapolation Theorem for Contractions with Fixed Points
Authors: Sato Ryotaro 
Published: December 2010

In [9] de la Torre proved that if is a finite measure space and T is a linear operator on a real for some fixed p, 1 < p < ∞ , such that ||T||P ≤ 1 and simultaneously ||T||∞ ≤ l, and also such that there exists with Th = h and h≠0 a.e., then the dominated ergodic theorem holds for T, i.e. for every we havede la Torre proved his result, by showing that the operator S, defined by Sf = (sgn h) - T(f • sgn h) for is positive, and by applying Akcoglu's theorem [1] to S.
Oscillation Theorems for Nonlinear Ordinary Differential Equations of Even Order
Authors: Kreith Kurt , Kusano Takaŝi 
Published: December 2010

Consider the differential equation1wherenis even andf(t, y)is subject to the following conditions:(a)f(t, y)is continuous on [0, ∞)×R;(2) (b)f(t, y)is nondecreasing inyfor each fixedt∈[0,∞);(c)yf(t, y )> 0 fory≠ 0 andt∈[0,∞).
Speculations Concerning the Range of Mahler's Measure
Authors: Boyd David W. 
Published: December 2010

I would like to express my thanks to the Canadian Mathematical Society for inviting me to present this lecture. I would also like to express my appreciation to C.J. Smyth for numerous helpful conversations during his visit this year at the University of British Columbia.This paper follows reasonably closely the outline of the lecture presented in Ottawa. More details are given here though and a number of proofs which would not be otherwise accessible have been added as Appendices. The attentive reader will soon realize the appropriateness of the title.
Cutting and Pasting Zp-Manifolds(1)
Authors: Prevot Kenneth 
Published: December 2010

AbstractLet Mn and Nn be n-dimensional closed smooth oriented Zp-manifolds where p is an odd prime and Zp is the cyclic group of order p. This paper determines necessary and sufficient conditions under which Mn and Nn are equivalent under a special equivariant cut and past equivalence.The only invariants are (a) the Euler characteristics of the Zp-manifolds, (b) the Euler characteristics of the fixed point manifolds in each fixed point dimesnion with specified normal representations, and (c) the oriented Zp-stratified cobordism class of the Zp-manifolds.
On Quasisimilarity for Subnormal Operators, II
Authors: Conway John B. 
Published: December 2010

AbstractLet S be a subnormal operator and let be the weak-star closed algebra generated by S and 1. An example of an irreducible cyclic subnormal operator S is found such that there is a T in with S and T quasisimilar but not unitarily equivalent. However, if S is the unilateral shift, T ∈ and S and T are quasisimilar, then S ≅ T.
Perfect Images of Zero-Dimensional Separable Metric Spaces
Authors: Van Mill Jan , Woods R. Grant 
Published: December 2010

AbstractLet Q denote the rationals, P the irrationals, C the Cantor set and L the space C − {p} (where p ∈ C). Let f : X → Y be a perfect continuous surjection. We show: (1) If X ∈ {Q, P, Q × P}, or if f is irreducible and X ∈ {C, L}, then Y is homeomorphic to X if Y is zero-dimensional. (2) If X ∈ {P, C, L} and f is irreducible, then there is a dense subset S of Y such that f|f ← [S] is a homeomorphism onto S. However, if Z is any σ-compact nowhere locally compact metric space then there is a perfect irreducible continuous surjection from Q × C onto Z such that each fibre of the map is homeomorphic to C.
On the Non-Existence of a Projection onto the Space of Compact Operators
Authors: Feder Moshe 
Published: December 2010

AbstractLet X and Y be Banach spaces, L(X, Y) the space of bounded linear operators from X to Y and C(X, Y) its subspace of the compact operators. A sequence {Ti} in C(X, Y) is said to be an unconditional compact expansion of T ∈ L (X, Y) if ∑ Tix converges unconditionally to Tx for every x ∈ X. We prove: (1) If there exists a non-compact T ∈ L(X, Y) admitting an unconditional compact expansion then C(X, Y) is not complemented in L(X, Y), and (2) Let X and Y be classical Banach spaces (i.e. spaces whose duals are some LP(μ) spaces) then either L(X, Y) = C(X, Y) or C(X, Y) is not complemented in L(X, Y).
Antidirected Subtrees of Directed Graphs
Authors: Burr Stefan A. 
Published: December 2010

The purpose of this paper is to prove the following result:Theorem. Let T be a directed tree with k arcs and with no directed path of length 2. Then if G is any directed graph with n points and at least 4kn arcs, T is a subgraph of G.It would be appropriate to call T an antidirected tree or a source-sink tree, since every point either has all its arcs directed outward or all inward. As N. G. de Bruijn has noted (personal communication), such a linear bound in n cannot hold if T is replaced by any directed graph other than a union of such trees. The above theorem strengthens one of Graham [1], where an implicit bound of c(k)n is obtained, where c(k) is exponentially large. The proof we give here is also shorter. We first give two simple lemmas. Both are essentially due to ErdÄs, but it is not clear where either first appeared. Their proofs are easy, so we give them here for completeness; in neither case do we state quite the best possible result.
Uniformly Lipschitzian Semigroups in Hilbert Space
Authors: Downing David J. , Ray William O. 
Published: December 2010

AbstractLet K be a closed, bounded, convex, nonempty subset of a Hilbert Space . It is shown that if is a left reversible, uniformly k-lipschitzian semigroup of mappings of K into itself, with k < √2, then has a common fixed point in K.
A Note on Strong Riesz Summability
Authors: Thorpe B. 
Published: December 2010

AbstractThis note proves that if 1 ≤ p < ∞ and 1 − 1/p < k < 2 − 1/p then the space of sequences strongly Riesz summable [R, λ, k]p to 0 has AK. Using general results of Jakimovski and Russell it is then possible to deduce a best possible limitation condition and a convergence factor result for [R, λ, k]p.
On the Decomposition of Continuous Modules
Authors: Müller Bruno J. , Rizvi S. Tariq 
Published: December 2010

AbstractWe prove two theorems on continuous modules:Decomposition Theorem. A continuous moduleMhas a decomposition,M=M1⊕M2, such thatM1is essential over a direct sumof indecomposable summandsAiofM, andM2has no uniform submodules; and these data are uniquely determined byMup to isomorphism.Direct Sum Theorem. A finite direct sumof indecomposable modulesAiis continuous if and only if eachAiis continuous andAj-injective for allj≠ i.
0-Distributive and P-Uniform Semilattices
Authors: Hoo C. S. , Shum K. P. 
Published: December 2010

AbstractA counter-example is provided to the conjecture of Y. S. Pawar and N. K. Thakare that a semilattice S with 0 is 0-distributive if and only if for each filter F and each ideal I such that F ∩ I = Ø, there exists a prime filter containing F and disjoint from I. This shows that 0-distributivity is not equivalent to weak distributivity. A characterization is also given of finite P-uniform semilattices in terms of 0-distributivity.
The Duals of the Camillo-Zelmanowitz Formulas for Goldie Dimension
Authors: Haack Joel K. 
Published: December 2010

AbstractThe duals of the Camillo-Zelmanowitz formulas for Goldie dimension are shown to hold for Varadarajan's notion of corank, subject to the existence of certain cocomplements. In particular, the formulas hold for modules over perfect rings. Also, if R is semiperfect, then the vector space dimension formulas hold for all modules over R for Goldie dimension iff they hold for corank iff R is semisimple.
The Exceptional Sets in the Definition of the Pn-Integral
Authors: Cross G. E. 
Published: December 2010

AbstractIt has been recently observed by S. N. Mukhopadhyay that the various definitions of the Pn-integral are not complete unless it is shown that the exceptional scattered set allowed in the definition is not important. Utilizing the fact that on the real line a scattered set is countable, and adapting known methods for coping with exceptional countable sets, it is proved that the definitions of the Pn-integral are complete. It is then clear that the concept of scattered set is not essential to the definition of the Pn-integral.
A General Inclusion Theorem for l-l Nörlund Summability
Authors: Defranza J. 
Published: December 2010

AbstractNӧrlund methods of summability are studied as mappings from I1 into I1. Conditions are given for an arbitrary l-l method to include a Nӧrlund method. In particular necessary and sufficient conditions are given for a row finite l-l method to include a Nӧrlund mean.
On Padé and Best Rational Approximation
Authors: Borwein Peter B. 
Published: December 2010

AbstractIt is reasonable to expect that, under suitable conditions, Padé approximants should provide nearly optimal rational approximations to analytic functions in the unit disc. This is shown to be the case for ez in the sense that main diagonal Padé approximants are shown to converge as expeditiously as best uniform approximants. Some more general but less precise related results are discussed.
Compactness and Almost Periodicity of Multipliers
Authors: Crombez G. 
Published: December 2010

AbstractThe question as to the existence of nontrivial compact or weakly compact multipliers between spaces of functions on groups has been investigated for several years. Until now, however, no general method which is applicable to a large class of function spaces seems to be knownIn this paper we prove that the existence of nontrivial compact multipliers between Banach function spaces on which a group acts is related to the existence of nonzero almost periodic functions.
Boolean Algebras and Raising Maps to Zero-Dimensional Spaces
Authors: van Mill Jan 
Published: December 2010

AbstractLet X be a separable metric space and let be a family of countably many self-maps of X. Then there is a countable subalgebra of the Boolean algebra of regular open subsets of X which is a base for X such that for each the function defined by Φf(B) = (f-1(B))-0 is a homomorphism.
On the Product of Ideals
Authors: Anderson David F. , Dobbs David E. 
Published: December 2010

AbstractThis article introduces the concept of a condensed domain, that is, an integral domain R for which IJ = {ij: i ∊ I, j ∊ J} for all ideals I and J of R. This concept is used to characterize Bézout domains (resp., principal ideal domains; resp., valuation domains) in suitably larger classes of integral domains. The main technical results state that a condensed domain has trivial Picard group and, if quasilocal, has depth at most 1. Special attention is paid to the Noetherian case and related examples.
Lp Spaces from Matrix Measures: A Correction and their Interpolation
Authors: Browne Patrick J. , Costa Claude 
Published: December 2010

AbstractWe discuss the construction of the spaces Lp(μij), 1 ≤ p ≤ ∞, where {μij} is an n × n positive matrix measure, correct a mistake in the literature concerning those spaces and develop an interpolation theory for them.
The Second Dual of a C*-Ternary Ring
Authors: Landesman E. M. , Russo Bernard 
Published: December 2010

AbstractThe Arens extension of the triple product of an associative triple system is studied. Using a representation theorem for C*-ternary rings due to Zettl, it is shown that the second dual of a C*-ternary ring is itself a C*-ternary ring
The Field Generated by the Discriminant of the Class Invariants of an Imaginary Quadratic Field
Authors: Dummit D. S. , Gold R. , Kisilevsky H. 
Published: December 2010

AbstractThis note determines the quadratic field generated by the square root of the discriminant of the modular equation satisfied by the special value j(α) of the modular function α for a an integer in an imaginary quadratic field.
Some Hypersurfaces of Symmetric Spaces
Authors: Matsuyama Yoshio 
Published: December 2010

AbstractIn this paper we consider how much we can say about an irreducible symmetric space M which admits a hypersurface N with at most two distinct principal curvatures. Then we will obtain that (1) if N is locally symmetric, then M must be a sphere, a real projective space and their noncompact duals (2) if N is Einstein, then M must be rank 1.
Ordered Fibonacci Partitions
Authors: Prodinger Helmut 
Published: December 2010

AbstractOrdered partitions are enumerated by Fn = Σk k !S(n, k) where S(n, k) is the Stirling number of the second kind. We give some comments on several papers dealing with ordered partitions and turn then to ordered Fibonacci partitions of {1, ߪ, n}: If d is a fixed integer, the sets A appearing in the partition have to fulfill i, j ∈ A, i ≠ j ⟹ |i-j| ≥ d. The number of ordered Fibonacci partitions is determined.
On a Parametrized Levi Problem Involving One Complex Variable
Authors: Gilligan Bruce 
Published: December 2010

AbstractThe classical Levi problem in several complex variables characterizes domains of holomorphy in terms of a boundary condition called pseudo convexity. The purpose of this note is to give a characterization of those domains D in ℂ×ℝ, where one can always solve the -problem with C∞ parameters, in terms of a certain kind of convexity condition on their boundaries.
La Règle Du Trapèze Appliquée à Quelques Fonctions Sans Dérivées
Authors: Dubuc Serge , Todor Fabian 
Published: December 2010

RésuméPour chaque nombre α de (0, 1), nous construisons une fonction f qui est lipschitzienne d'ordre α et dont le reste Rn(f) par l'application de la règle du trapèze est précisément égal à 1/n lorsque n est une puissance entière et arbitraire de 2.
A Class of Addition Theorems†
Authors: Srivastava H. M. , Lavoie J.-L. , Tremblay Richard 
Published: December 2010

AbstractRecently, H. M. Srivastava extended certain interesting generating functions of L. Carlitz to the forms:andwhere are general oncand many-parameter sequences of functions. In the present paper some general addition formulas for analogous sequences of functions are derived, and a number of interesting applications of the main results are given.
Sets with No Empty Convex 7-Gons
Authors: Horton J. D. 
Published: December 2010

AbstractErdös has defined g(n) as the smallest integer such that any set of g(n) points in the plane, no three collinear, contains the vertex set of a convex n-gon whose interior contains no point of this set. Arbitrarily large sets containing no empty convex 7-gon are constructed, showing that g(n) does not exist for n≥l. Whether g(6) exists is unknown.
Finite Complexes and Integral Representations II
Authors: Schafer James A. 
Published: December 2010

AbstractIn the paper "Finite complexes and integral representations" [Illinois Journal of Math, 26, (1982), p 442] an exact sequence relating homotopy types of (G, d)-complexes with objects of integral representation theory together with some known calculations seemed to imply that the group of homotopy types of (G, d)- complexes was always a subquotient of (ℤ|g|)*. This paper gives a new characterization of one of the terms of the above sequence that allows one to conclude that this is not generally true.
On Subspaces of Replete and Measure Replete Spaces
Authors: Grassi Peter 
Published: December 2010

AbstractThe concepts of repleteness and more generally measure repleteness are investigated for set-theoretic lattices on specific subspaces of a lattice space. These general results are then applied to specific topological spaces, and we obtain as special cases some known theorems as well as some new results concerning for example, ∝-completeness, realcompactness, measure compactness and Borel-measure compactness.
Non-Parallelizability of Grassmann Manifolds
Authors: Trew S. , Zvengrowski P. 
Published: December 2010

AbstractThe fact that no real Grassmann manifolds Gk(Rn) are parallelizable (or even stably parallelizable) except for the obvious cases G1R2≅S1, G1(R4)≅G3(R4) ≅ RP3, and G1(R8)≅ G7(R8) ≅ RP7 was first noted by Hiller and Stong. Their work in turn depends on induction and the work of Oproiu, who examined detailed calculations of Stiefel-Whitney classes for k = 2, 3. In this note we give a short proof of this result, using elementary results from K-theory, that also covers the complex and quaternionic Grassmann manifolds.
A Representation Theorem for Distributive l-Monoids
Authors: Anderson Marlow , Edwards C. C. 
Published: December 2010

AbstractIn this note the Holland representation theorem for l-groups is extended to l-monoids by the following theorem: an l-monoid is distributive if and only if it may be embedded into the l-monoid of order-preserving functions on some totally ordered set. A corollary of this representation theorem is that a monoid is right orderable if and only if it is a subsemigroup of a distributive l-monoid; this result is analogous to the group theory case.
Atoms, Primes and Implicative Lattices
Authors: Hoo C. S. 
Published: December 2010

AbstractLet L be an a-implicative semilattice. We obtain a characterization of those elements which cover a. This gives a characterization of atoms in pseudocomplemented semilattices, and leads to various results on primes and irreducibles in semilattices. As an application, we prove that in a complete, atomistic lattice L, the following are equivalent (i) L is implicative (ii) L is (2, ∞) meet distributive (iii) each element of L is a meet of primes.
A Characterization of the Continuous q-Ultraspherical Polynomials
Authors: Al-Salam Waleed , Allaway WM. R. , Askey Richard 
Published: December 2010

AbstractIn his Ph.D. thesis Allaway found all polynomials
that can be represented asand a0bn≠0. We solve the essentially equivalent problem of finding all symmetric polynomials with when are orthogonal with respect to dα(x). The polynomials are the continuous q-ultraspherical polynomials and some of their limiting cases.
Separating Points and Coloring Principles
Authors: Watson W. Stephen 
Published: December 2010

AbstractIn the mid 1970's, Shelah formulated a weak version of ◊. This axiom Φ is a prediction principle for colorings of the binary tree of height ω1. Shelah and Devlin showed that Φ is equivalent to 2ℵ0 < 2ℵ1.In this paper, we formulate Φp, a "Φ for partial colorings", show that both ◊* and Fleissner's “◊ for stationary systems” imply Φp, that ◊ does not imply Φp and that Φp does not imply CH.We show that Φp implies that, in a normal first countable space, a discrete family of points of cardinality ℵ1 is separated.
Compactness in Topological Hjelmslev Planes
Authors: Lorimer J. W. 
Published: December 2010

AbstractIn the theory of ordinary topological affine and projective planes it is known that (1) An affine plane is never compact (2) a locally compact ordered projective plane is compact and archimedean (3) a locally compact connected projective plane is compact and (4) a locally compact projective plane over a coordinate ring with bi-associative multiplication is compact. In this paper we re-examine these results within the theory of topological Hjelmslev Planes and observe that while (1) remains valid (2), (3) and (4) are false. At first glance these negative results seem to suggest we are working in too general a setting. However a closer examination reveals that the absence of compactness in our setting is a natural and expected feature which in no way precludes the possibility of obtaining significant results.
On Spectral Synthesis and Ergodicity in Spaces of Vector-Valued Functions
Authors: Weit Yitzhak 
Published: December 2010

AbstractSpectral synthesis in L∞(ℝ, ℂN), N < 1, is considered. It is is proved that sets of spectral synthesis are necessarily sets of spectral resolution.These results are applied to investigate ergodic and mixing properties of some positive contractions on L1(G, ℂN).
Finite Groups Which are Automorphism Groups of Infinite Groups Only
Authors: Zimmerman Jay 
Published: December 2010

AbstractThe object of this paper is to exhibit an infinite set of finite semisimple groups H, each of which is the automorphism group of some infinite group, but of no finite group. We begin the construction by choosing a finite simple group S whose outer automorphism group and Schur multiplier possess certain specified properties. The group H is a certain subgroup of Aut S which contains S. For example, most of the PSL's over a non-prime finite field are candidates for S, and in this case, H is generated by all of the inner, diagonal and graph automorphisms of S.
The Dirichlet Problem With Denjoy-Perron Integrable Boundary Condition
Authors: Benedicks M. , Pfeffer W. F. 
Published: December 2010

AbstractThe Poisson integral of a Denjoy-Perron integrable function defined on the boundary of an open disc is harmonic in this disc. Moreover, almost everywhere on the boundary, the nontangential limits of the integral coincide with the boundary condition. This extends the classical result for Lebesgue integrable boundary conditions. By means of conformai maps, a generalization to domains bounded by a sufficiently smooth Jordan curve is also obtained.