bluuebunny/crossref_metadata_2025_split huggingface dataset:
On Delay Differential Inequalities of Higher Order
Authors: Ladas G. , Stavroulakis I. P. 
Published: December 2010

AbstractConsider the nth order (n ≥ 1) delay differential inequalities and and the delay differential equation , where q(t) ≥ 0 is a continuous function and p, τ are positive constants. Under the condition pτe ≥ 1 we prove that when n is odd (1) has no eventually positive solutions, (2) has no eventually negative solutions, and (3) has only oscillatory solutions and when n is even (1) has no eventually negative bounded solutions, (2) has no eventually positive bounded solutions, and every bounded solution of (3) is oscillatory. The condition pτe > 1 is sharp. The above results, which generalize previous results by Ladas and by Ladas and Stavroulakis for first order delay differential inequalities, are caused by the retarded argument and do not hold when τ = 0.
Approximation De Fonctions Convexes Sur Un Espace De Mesures Et Applications
Authors: Temam R. 
Published: December 2010

AbstractIn the first part of this article we recall the definition and a few basic properties of convex functionals defined on a space of bounded measures. In the second part we show several results of approximation of the following type: Although a measure μ cannot be approximated in the sense of the norm by smooth functions, we can find an appropriate sequence of smooth functions which converge weakly to the measure μ, the corresponding value of the functional converging to the value of the functional at μ.This article is part of a series on the existence theory of solution of variational problems of mechanics (perfect plasticity), which is based on a systematic utilization of the methods of convex analysis and the calculus of variations.
Local Freeness of Profinite Groups
Authors: Pletch Andrew 
Published: December 2010

AbstractIn this paper we discuss the relationship between local properties such as freeness and projectivity of a group and the freeness or projectivity of its pro-C-completion. We show that for certain classes, C, of finite groups (e.g. p-groups, nilpotent groups, super-solvable groups) the pro-C-completion of a locally free pro-C-group is a free pro-C-group. We also show that under certain circumstances the converse is also true but we leave open the question, for example, of whether a locally free pro-p-group is free.
Rings with a Special Kind of Automorphism
Authors: Bergen Jeffrey , Herstein I. N. 
Published: December 2010

AbstractIn this paper we examine the nature of rings R with unit having an automorphism ϕ ≠ 1 such that x — ϕ(x) is 0 or invertible for every x ∊ R. We show that the only examples of such rings are R = D, R = D2, and R = D ⊕ D, where D is a division ring. Furthermore, for the case D2, we describe the division rings that are possible.
On Ergodic Extensions of Stationary Measures with Minimal Support
Authors: Krebs William B. , Robertson James B. 
Published: December 2010

AbstractLet T be an ergodic measure preserving transformation with the following property: there exists a positive integer n and a finite partition α such that the number of atom of is one more than that of , and the probability of at least one of the atoms is irrational. Then there exists a unique (up to conjugacy) transformation S such that there is a partition β with S restricted to isomorphic to T restricted to and the number of atoms in is one more than the number of atoms in for all m ≥ n. Moreover this transformation has discrete spectrum with at most two generators. If there are two generators, one of them must be a root of unity.
A Structure Theorem in Finite Topology
Authors: Ginsburg John 
Published: December 2010

AbstractSimple structure theorems or representation theorems make their appearance at a very elementary level in subjects such as algebra, but one infrequently encounters such theorems in elementary topology. In this note we offer one such theorem, for finite topological spaces, which involves only the most elementary concepts: discrete space, indiscrete space, product space and homeomorphism. Our theorem describes the structure of those finite spaces which are homogeneous.
The Poincaré Map in Mixed Exterior Algebra
Authors: Vanstone J. R. 
Published: December 2010

AbstractThe Poincaré map of mixed exterior algebra generalizes the Hodge star operator and it plays a central rôle in the proofs of many classical identities of linear algebra. The principal purpose of this paper is to derive a new formula for it. This formula is useful in circumstances when the definition is too implicit. Several applications are discussed.
Covering Problem for Idempotent Latin Squares
Authors: Heinrich Katherine 
Published: December 2010

AbstractLet A = (aij) be an idempotent latin square of order n, n ≥ 3, in which aii = i, 1 ≤ i ≤ nc. A set S ⊆ N = {1, 2, …, n} is a cover of A if (N × N)\{(i, i):i ∉ S} = {(i, j): i ∊ S, j ∊ N} ∪ {(j, i): i ∊ S, j ∊ N} ∪ {(i, j): aij ∊ S}. A cover S is minimum for A if |S| < |T| for every cover T of A and we write c(A) = |S|. We denote by c(n) the maximum value of c(A) over all idempotent latin squares A of order n and in this paper show that (7n/10)-3.8 ≤ c (n) < n - n1/3 + 1 for all n ≥ 15. The problem of determining c(n) was first raised by J. Schönheim.
Coincidence Sets of Coincidence Producing Maps
Authors: Schirmer Helga 
Published: December 2010

AbstractA theorem by H. Robbins shows that every closed and non-empty subset of the unit ball Bn in Euclidean n-space is the fixed point set of a self map of Bn. This result is extended to coincidence producing maps of Bn, where a map ƒ:X → Y is coincidence producing (or universal) if it has a coincidence with every map g:X → Y. The main result implies that if ƒ:Bn, Sn - 1 → Bn, Sn - 1 is coincidence producing and A⊂Bn closed and nonempty, then there exist a map ƒ': Bn, Sn - 1 → Bn, Sn - 1 and a map g: Bn → Bn such that ƒ' | Sn - 1 is homotopic to ƒ | Sn-1 and A is the coincidence set of ƒ' and g.
Extremal Positive Solutions of Semilinear Schrödinger Equations
Authors: Swanson C. A. 
Published: December 2010

AbstractNecessary and sufficient conditions are proved for the existence of maximal and minimal positive solutions of the semilinear differential equation Δu = -ƒ(x, u) in exterior domains of Euclidean n-space. The hypotheses are that ƒ(x, u) is nonnegative and Hölder continuous in both variables, and bounded above and below by ugi(| x |, u), i = 1, 2, respectively, where each gi(r, u) is monotone in u for each r > 0.
Optimal Stopping Under General Dependence Conditions
Authors: Longnecker M. 
Published: December 2010

AbstractLet {Xn} be a sequence of random variables, not necessarily independent or identically distributed, put and Mn =max0≤k≤n|Sk|. Effective bounds on in terms of assumed bounds on , are used to identify conditions under which an extended-valued stopping time τ exists. That is these inequalities are used to guarantee the existence of the stopping time τ such that E(ST/aτ) = supt ∈ T∞ E(|Sτ|/at), where T∞ denotes the class of randomized extended-valued stopping times based on S1, S2, … and {an} is a sequence of constants. Specific applications to stochastic processes of the time series type are considered.
An Algebraic Characterization of Remainders of Compactifications
Authors: Hatzenbuhler James , Mattson Don A. , Sizer Walter S. 
Published: December 2010

AbstractLet X be a locally compact, completely regular Hausdorff space. In this paper it is shown that all compact metric spaces are remainders of X if and only if the quotient ring C*(X)/C∞(X) contains a subring having no primitive idempotents.
Asymptotic Results for Class Number Divisibility in Cyclotomic Fields
Authors: Gerth Frank 
Published: December 2010

AbstractLet n ≥3 and m≥3 be integers. Let Kn be the cyclotomic field obtained by adjoining a primitive nth root of unity to the field of rational numbers. Let denote the maximal real subfield of Kn. Let hn (resp., ) denote the class number of Kn (resp., ). For fixed m we show that m divides hn and hn for asymptotically almost all n. Also for those Kn and with a given number of ramified primes, we obtain lower bounds for certain types of densities for m dividing hn and .
A Multiple Sequence Ergodic Theorem
Authors: Olsen James H. 
Published: December 2010

AbstractLet be a σ-finite measure space, {T1, …, Tk} a set of linear operators of , some p, 1≤p≤∞.Ifexists a.e. for all f ∊ Lp, we say that the multiple sequence ergodic theorem holds for {T1, …, Tk}. If f≥0 implies Tf≥0, we say that T is positive. If there exists an operator S such that |Tf(x)|≥S |f|(x) a.e., we say that T is dominated by S. In this paper we prove that if T1, …, Tk are dominated by positive contractions of , p fixed, 1<p<∞, then the multiple sequence ergodic theorem holds for {T1, …, Tk}.
Absolute Summability Factors in a Sequence
Authors: Baron S. 
Published: December 2010

AbstractLet α≥0 and β>— 1. The main result gives necessary and sufficient conditions for the sequence (εn) in order that the sequence (εnUn) will be absolutely summable by the Cesàro method Cβ for each sequence (Un) which is bounded or summable by the method CαAnother theorem is proven when Cα and Cβ are replaced by triangular methods A = (ank) and B=(bnk) satisfying , where (ξnk) = (ank)-1.
Primary Groups Whose Basic Subgroup Decompositions can be Lifted
Authors: Benabdallah K. , Laroche A. 
Published: December 2010

AbstractA primary group G is said to be a l.i.b. group if every idempotent endomorphism of every basic subgroup of G can be extended to an endomorphism of G. We establish the following characterization: A primary group is a l.i.b. group if and only if it is the direct sum of a torsion complete group and a divisible group. The technique used consists of a close analysis of certain subgroups of Prufer-like primary groups.
Split Graphs with Specified Dilworth Numbers
Authors: Nara Chiê , Sato Iwao 
Published: December 2010

AbstractLet G be a split graph with the independent part IG and the complete part KG. Suppose that the Dilworth number of (IG, ≼) with respect to the vicinal preorder ≼ is two and that of (KG, ≼) is an integer k. We show that G has a specified graph Hk, defined in this paper, as an induced subgraph.
(HM)-Spaces and Measurable Cardinals
Authors: Aguirre José A. Facenda 
Published: December 2010

AbstractA locally convex space E is called an (HM)-space if E has invariant nonstandard hulls. In this paper we prove that if E is an (HM)-space, then E is a T(μ)-space, where μ is the first measurable cardinal. This is equivalent to say that in an (HM)-space, with dim(E)≧μ, does not exist a continuous norm. With this result, we prove that there exists an inductive semi-reflexive space E such that the bounded sets in E are finite-dimensional but E is not an (HM)-space. Thus, we answer negatively to an open problem raised up by Bellenot. In this paper, we do not use nonstandard analysis.
Simplicite des Groupes Unitaires Definis par un Facteur Simple
Authors: Giordano Thierry , Harpe Pierre De La 
Published: December 2010

AbstractLet B be a σ-finite von Neumann factor of type II1 or III and let σ be an involutory *-antiautomorphism of B. We consider U(B) the unitary group of B and its subgroup G = {g ∈U(B) | σ(g) = g*}, which are unitary classical groups. In this paper, we prove that G has a unique non trivial normal subgroup, which is its centre {±1}.
Centralizing Mappings of Prime Rings
Authors: Mayne Joseph H. 
Published: December 2010

AbstractLet R be a prime ring and U be a nonzero ideal or quadratic Jordan ideal of R. If L is a nontrivial automorphism or derivation of R such thatuL(u)—L(u)u is in the center of R for every u in U, then the ring R is commutative.
An Elementary Probabilistic Computation of the Poisson Kernel for the n = 2 and 3 Euclidean Ball
Authors: Vauthier Jacques 
Published: December 2010

AbstractDirect and elementary derivation of the classical Poisson kernel for the ball in n = 2 or n = 3 dimensions starting with the usual expression involving the brownian motion bω, the stopping time T on the boundary, and Ex the conditional expectation on paths starting at x.
Diviseurs Dans Les Anneaux De Series Formelles En Une Infinite D’Indeterminees
Authors: Ballet B. 
Published: December 2010

ResumeEtant donné un anneau commutatif unitaire A et un ensemble d’indices infini I; on peut obtenir, par passage à la limite projective, essentiellement trois anneaux A1, A2, A3 de séries formelles en des indéterminées indexées par I et à coefficients dans A. On étudie alors les implications A factoriel ⇒ A1, A2, A3 factoriels et A de Krull ⇒ A1, A2, A3 de Krull. On donne à cet effet des conditions pour qu’une limite projective d’anneaux factoriels soit factorielle.
Topological Completeness of Order Intervals in Riesz Spaces
Authors: Dodds P. G. 
Published: December 2010

AbstractIt is shown that if L is a Dedekind complete Riesz space equipped with a locally solid topology T defined by strongly (A, 0) Riesz pseudonorms, then order intervals of L are T-complete. This is an extension of a well known theorem of Nakano. The second part of the paper gives a necessary and sufficient condition for topological completeness of order intervals in a Dedekind σ-complete Riesz space which has a weak order unit and which is equipped with a locally solid σ-Fatou topology.
Mean Growth of Harmonic Functions of Beurling Type
Authors: Collier Manning G. , Kelingos John A. 
Published: December 2010

AbstractA harmonic function on the unit disc is of Beurling type ω if its Fourier (or Taylor) coefficients grow no faster than exp ω(|n|) as |n|→∞, where ω is a given increasing, concave function with ω(x)/x ↓ 0 as x → ∞. These harmonic functions are characterized by the growth rate of their L1-norms on circles of radius r as r → 1. The classical Schwartz result follows as a corollary by taking ω(x) = log(1+x). The Gevrey case is also included in the general result if one uses ω(x) = xα, 0 < α < 1.
A Decomposition Theorem for Certain Bipolynomial Hopf Algebras
Authors: Baker Andrew 
Published: December 2010

AbstractIn this note we generalise a result of D. Husemoller to certain bipolynomial Hopf algebras and are able to give Hopf algebra decompositions for these. As an easy consequence of our approach we give a simplified derivation of recent results of P. Hoffman on polynomial generators for these algebras; we also give explicit systems of “Borel generators” for a related family of quotient Hopf algebras considered by Hoffman.
On Homotopy Domination
Authors: Kwasik Sławomir 
Published: December 2010

AbstractA short proof of the following result of Bernstein and Ganea is given:“Let X be a topological space which is homotopy dominated by a closed connected n-dimensional manifold M. If Hn(X; Z2) ≠ 0 then X has the homotopy type of M”.It is also shown that the manifold in this theorem can be replaced by a Poincaré complex.
On the Commutativity of a Ring with Identity
Authors: Tong Jingcheng 
Published: December 2010

AbstractLet R be a ring with identity. R satisfies one of the following properties for all x, y ∈ R:(I)xynxmy = xm+1yn+1 and mnm! n! x≠0 except x = 0;(II)xynxm = xm + 1yn + 1 and mm! n! x≠0 except x = 0;(III)xmyn = ynxm and m! n! x≠0 except x = 0;(IV)(xpyQ)n = xpnyqn for n = k, k + 1 and N(p, q, k) x≠0 except x = 0, where N(p, q, k) is a definite positive integer. Then R is commutative.
Inequalities for Entire Functions of Exponential Type
Authors: Frappier Clément 
Published: December 2010

AbstractBernstein's inequality says that if f is an entire function of exponential type τ which is bounded on the real axis thenGenchev has proved that if, in addition, hf (π/2) ≤0, where hf is the indicator function of f, thenUsing a method of approximation due to Lewitan, in a form given by Hörmander, we obtain, to begin, a generalization and a refinement of Genchev's result. Also, we extend to entire functions of exponential type two results first proved for polynomials by Rahman. Finally, we generalize a theorem of Boas concerning trigonometric polynomials vanishing at the origin.
Tensor Products and Singularly Continuous Spectrum
Authors: White Denis A. W. 
Published: December 2010

AbstractAn example of a bounded self adjoint operator A is constructed so that A⊗I + α(I⊗A) is purely singularly continuous but A⊗1 + β(I⊗A) is purely absolutely continuous, for some real α and β. In fact α - β can be chosen arbitrarily small.
A Finite Index Property of Certain Solvable Groups
Authors: Rhemtulla A. H. , Smith H. 
Published: December 2010

AbstractA group G is said to have the FINITE INDEX property (G is an FI-group) if, whenever H≤G, xp ∈ H for some x in G and p > 0, then |〈H, x〉: H| is finite. Following a brief discussion of some locally nilpotent groups with this property, it is shown that torsion-free solvable groups of finite rank which have the isolator property are FI-groups. It is deduced from this that a finitely generated torsion-free solvable group has an FI-subgroup of finite index if and only if it has finite rank.
Another Class of Cyclicly Extensible and Reducible Properties
Authors: Lehman B. 
Published: December 2010

AbstractA space S has property P-1 if S is nonempty. For n > — 1, S has property Pn if it is locally connected, has property Pn-1 and if whenever it is written as a union, S = A ∪ B where each of A and B is closed and has property Pn-1, then A ∩ B also has property Pn-1. The purpose of this paper is to establish that for locally compact spaces, each of the properties Pn is both cyclicly extensible and reducible.
On the Branch Points in the Branched Coverings of Links
Authors: Kinoshita Shintchi 
Published: December 2010

AbstractLet l be a polygonal link in a 3-sphere S3 and a branched covering of l, which depends on the choice of a monodromy map ϕ. Let be the link in over l. In this paper we determine the exact position of in for some cases. For instance, if l is a torus link ((n + 1)p, n) and ϕ is an appropriate monodromy map of the fundamental group of S3 - l into the symmetric group of degree n + 1, then is an S3 and l is a torus link (np,n2). The 3-fold irregular branched covering of a doubled knot k is an S3, if it exists. The position of the link over k is shown in a figure. The link over knot 61 is obtained by K. A. Perko and the author, independently, and shown without proof in a paper by R. H. Fox [Can. J. Math. 22 (1970), 193-201]. The result mentioned in the above includes this case.
Approximation Theorems for Manis Valuations
Authors: Arapović Miroslav 
Published: December 2010

AbstractThroughout this paper rings are understood to be commutative with unity. In this paper we prove the general approximation theorem for valuations whose infinite ideals have large Jacobson radicals. We give an example in which it is shown that approximation theorems for Manis valuations do not hold in the general case. Also we prove that every valuation pair (Rv, Pv) of a total quotient ring T(R) whose infinite ideal has large Jacobson radical is a Prüfer valuation pair.
Germs Associated to Regular Unipotent Classes in p-adic SL(n)
Authors: Repka Joe 
Published: December 2010

AbstractFor an elliptic torus in SL(n), explicit formulae are given for the germs which are associated to the regular unipotent conjugacy classes. Using them, a formula is found for the germ associated to the "subregular" class, the class whose Jordan canonical form contains a 1 x 1 and an (n - 1) x (n - 1) block.
Scalar Products of Certain Hecke L-Series and Moments of Weighted Norm-Counting Functions
Authors: Odoni R. W. K. 
Published: December 2010

AbstractWe consider Dirichlet series R(s), constructed by taking scalar products of Hecke L-series with ray-class characters. Using a theorem of G. W. Mackey on tensor products of representations of finite groups we show that R(s) has a meromorphic continuation into Re(s) > 1/2 (obtained by more sophisticated methods in [l]-[5]); we then obtain estimates for the growth of R(s) on vertical lines. Via the Mellin transformation we deduce asymptotics for various weighted moment sums involving ideals of given ray-class and norm, in one or several fields simultaneously.
The Simplicial Helix and the Equation tan nθ = n tan θ
Authors: Coxeter H. S. M. 
Published: December 2010

AbstractBuckminster Fuller has coined the name tetrahelix for a column of regular tetrahedra, each sharing two faces with neighbours, one 'below' and one 'above' [A. H. Boerdijk, Philips Research Reports 7 (1952), p. 309]. Such a column could well be employed in architecture, because it is both strong and attractive. The (n — 1)-dimensional analogue is based on a skew polygon such that every n consecutive vertices belong to a regular simplex. The generalized twist which shifts this polygon one step along itself is found to have the characteristic equation(λ - 1)2{(n - 1)λn-2 + 2(n - 2)λn-3 + 3(n - 3)λn-4 + . . . + (n - 2)2λ + (n - 1)} = 0,which can be derived from tan nθ = n tan θ by setting λ = exp (2θi).
A Multiple Exponential Sum to Modulus p2
Authors: Heath-Brown D. R. 
Published: December 2010

AbstractFor suitable polynomials f(x) ∊ ℤ[x] in n variables, of total degree d, it is shown thatThis is, formally, a precise analogue of a theorem of Deligne [1] on exponential sums (mod p). However the proof uses no more than elementary algebraic geometry.
The Estimation of Complete Exponential Sums
Authors: Loxton J. H. , Vaughan R. C. 
Published: December 2010

AbstractThis paper proves a conjecture of Loxton and Smith about the size of the exponential sum S(f;q) formed by summing exp (2πif(x)/q) over x mod q, where f is a polynomial of degree n with integer coefficients. It is shown that |S(f;q)| ≤ Cfdn(q)qe/(e+1), where e is the maximum of the orders of the complex zeros of f'. An estimate is also obtained for Cf in terms of n, e and the different of f, and a number of examples are given to show that the estimate is best possible.
Une Remarque Sur les Deformations d'un Germe D'Hypersurfaces a Type Topologique Constant
Authors: Pnevmatikos Spyros N. 
Published: December 2010

ResuméSoit f un germe de fonction holomorphe centré à l'origine de ℂn à singularité isolée et F une déformation centrée de f de base ℂp. On se propose d'établir que lorsque la déformation Xt, = (0) de l'hypersurface X0 = f-l(0) est à type topologique constant alors la factorisation de F à travers la déformation miniverselle centrée de f concernant les espaces de paramètres correspondants est unique. Il en résulte en particulier immédiatement le théorème classique de détermination finie pour les fonctions ainsi que pour leurs déformations.
Perron Integrability Versus Lebesgue Integrability
Authors: Schurle Arlo W. 
Published: December 2010

AbstractThe paper investigates the relationship between Perron - Stieltjes integrability and Lebesgue-Stieltjes integrability within the generalized Riemann approach. The main result states that with certain restrictions a Perron-Stieltjes integrable function is locally Lebesgue-Stieltjes integrable on an open dense set. This is then applied to show that a nonnegative Perron-Stieltjes integrable function is Lebesgue-Stieltjes integrable. Finally, measure theory is invoked to remove the restrictions in the main result.
On the Number of Binomial Coefficients Which are Divisible by their Row Number: II
Authors: Robbins Neville 
Published: December 2010

AbstractIf n is a natural number, let A(n) denote the number of integers, k, such that 0 < k < n and n divides . Let ϕ(n) denote Euler's totient function. Necessary and sufficient conditions are given so that A(n) = ϕ(n) when n is square-free.
An Almost Krull Domain with Divisorial Height One Primes
Authors: Arnold J. T. , Matsuda Ryuki 
Published: December 2010

AbstractE. Pirtle has conjectured that if D is an almost Krull domain in which the height one prime ideals are divisorial then D is a Krull domain. An example is given to show that this is not the case. Further, let U = and let denote the set of prime ideals of D which are minimal over some ideal (a):(b), where a, b ∈ D. If Dp is a valuation ring for each let then Huckaba and Papick have asked whether D[x]U must be a Prufer domain. The given example shows that it need not be.