bluuebunny/crossref_metadata_2025_split huggingface dataset:
Oscillation of neutral delay differential equations
Authors: Yu Jianshe , Wang Zhicheng , Qian Chuanxi 
Published: April 2009

Consider the following neutral delay differential equationwhereP∈ ℝ,T∈ (0, ∞), σ ∈ (0, ∞) andQ∈C[(t0, ∞), [0, ∞)]. We obtain a sufficient condition for the oscillation of all solutions of Equation (*) withP= −1, which does not require thatBut, for the cases −1 <P< 0 andP< −1, we show that (**) is a necessary condition for the oscillation of all solutions of Equation (*). These new results solve some open problems in the literature.
Equality algebras
Authors: Fearnley-Sander Desmond , Stokes Tim 
Published: April 2009

As part of an attempt to capture abstractly the most fundamental properties of algebraic reasoning involving equality, we introduce the notion of an equality algebra. It is a universal algebra A endowed with a binary function =iA × A → L, where L is a meet-semilattice with top element 1, called internalised equality, and satisfying, for all x, y ∈ A,1. (x =ix) = 1; and2. (x =iy)f(x) = (x =iy)f(y), where f is any function A → L derived from the Operations on A, the semilattice operations, and = i.We charecterise internalised equalities in terms of finetly many identities, give examples, and show that all are equivalent to internalised equalities defined in terms of congruences on the underlying algebra. In the special case in which A is an Abelian group or ring, the internalised equality is shown to be equivalent to the dual of a norm-like mapping taking values in semilattice.
Expansion of analytic functions of an operator in series of Faber polynomials
Authors: Hasson Maurice 
Published: April 2009

Let T: B → B be a bounded linear operator on the complex Banach space B and let f(z) be analytic on a domain D containing the spectrum Sp(T) of T. Then f(T) is defined bywhere C is a contour surrounding SP(T) and contained in D.
Approximating common fixed points of two nonexpansive mappings in Banach spaces
Authors: Atsushiba Sachiko , Takahashi Wataru 
Published: April 2009

Let C be a nonempty closed convex subset of a real Banach space E and let S, T be nonexpansive mappings of C into itself. In this paper, we consider the following iteration procedure of Mann's type for approximating common fixed points of two mappings S and T:where {αn is a sequence in [0,1]. Using some ideas in the nonlinear ergodic theory, we prove that the iterates converge weakly to a common fixed point of the nonexpansive mappings T and S in a uniformly convex Banach space which satisfies Opial's condition or whose norm is Fréchet differentiable.
A closed simplicial model category for proper homotopy and shape theories
Authors: García-Calcines J.M. , Garcia-Pinillos M. , Hernández-Paricio L.J. 
Published: April 2009

In this paper, we introduce the notion of exterior space and give a full embedding of the category P of spaces and proper maps into the category E of exterior spaces. We show that the category E admits the structure of a closed simplicial model category. This technique solves the problem of using homotopy constructions available in the localised category HoE and in the “homotopy category” π0E, which can not be developed in the proper homotopy category.On the other hand, for compact metrisable spaces we have formulated sets of shape morphisms, discrete shape morphisms and strong shape morphisms in terms of sets of exterior homotopy classes and for the case of finite covering dimension in terms of homomorphism sets in the localised category.As applications, we give a new version of the Whitehead Theorem for proper homotopy and an exact sequence that generalises Quigley's exact sequence and contains the shape version of Edwards-Hastings' Comparison Theorem.
Integral points on elliptic curves over function fields of positive characteristic
Authors: Pacheco Amílcar 
Published: April 2009

Let K be a one variable function field of genus g defined over an algebraically closed field k of characteristic p > 0. Let E/K be a non-constant elliptic curve. Denote by MK the set of places of K and let S ⊂ MK be a non-empty finite subset.Mason in his paper “Diophantine equations over function fields” Chapter VI, Theorem 14 and Voloch in “Explicit p-descent for elliptic curves in characteristic p” Theorem 5.3 proved that the number of S-integral points of a Weiertrass equation of E/K defined over RS is finite. However, no explicit upper bound for this number was given. In this note, under the extra hypotheses that E/K is semi-stable and p > 3, we obtain an explicit upper bound for this number for a certain class of Weierstrass equations called S-minimal.
Elementary equivalence for finitely generated nilpotent groups and multilinear maps
Authors: Oger Francis 
Published: April 2009

We show that two finitely generated finite-by-nilpotent groups are elementarily equivalent if and only if they satisfy the same sentences with two alternations of quantifiers. For each integer n ≥ 2, we prove the same result for the following classes of structures:(1) the (n + 2)-tuples (A1, …, An+1, f), where A1, …, An+1 are disjoint finitely generated Abelian groups and f: A1 × … × An → An+1 is a n-linear map;(2) the triples (A, B, f), where A, B are disjoint finitely generated Abelian groups and f: An → B is a n-linear map;(3) the pairs (A, f), where A is a finitely generated Abelian group and f: An → A is a n-linear map.In the proof, we use some properties of commutative rings associated to multilinear maps.
Improvement on the bounds of permutation groups with bounded movement
Authors: Alaeiyan Mehdi 
Published: April 2009

Let G be a permutation group on a set Ω with no fixed points in Ω and let m be a positive integer. Then we define the movement of G as, m := move(G) := supΓ{|Γg \ Γ| │ g ∈ G}. Let p be a prime, p ≥ 5. If G is not a 2-group and p is the least odd prime dividing |G|, then we show that n := |Ω| ≤ 4m – p + 3.Moreover, if we suppose that the permutation group induced by G on each orbit is not a 2-group then we improve the last bound of n and for an infinite family of groups the bound is attained.
The Weyl functional calculus and two-by-two selfadjoint matrices
Authors: Ricker Werner J. 
Published: April 2009

Let D be a (2 × 2) matrix with distinct eigenvalues λ1 and λ2. There is a basic and well known functional equation which provides a formula for constructing the matrix g (D), for any ℂ-valued function g defined on a subset of ℂ containing {λ1,λ2}, namely .This equation is used to give a direct and transparent proof of the following fact due to Anderson: A pair of (2 × 2) selfadjoint matrices A1 and A2 commute if and only if the Weyl functional calculus of the pair (A1,A2), which is a matrix-valued distribution, has order zero (that is, is a measure).
On the dynamics of a periodic delay logistic equation with diffusion
Authors: Gopalasamy K. , Weng Pei-Xuan 
Published: April 2009

Sufficient conditions are obtained for the existence of a globally attractive positive periodic solution of the periodic diffusive delay logistic systemin whichτandKare positive periodic functions of periodτ, nis a positive integer and ö is a nonnegative number; sufficient conditions are also obtained for all positive solutions to be oscillatory about the periodic solution.
Extreme points in spaces between Dirichlet and Vanishing Mean Oscillation
Authors: Wirths K. J. , Xiao J. 
Published: April 2009

Forp∈ (0, ∞) defineQp0(∂Δ) as the space of all Lebesgue measurable complex-valued functionsf; on the unit circle ∂Δ for which ∫∂Δf;(z)|dz|/(2π) = 0 andas the open subarcIof ∂Δ varies. Note that eachQp,0(∂Δ) lies between the Dirichlet space and Sarason's vanishing mean oscillation space. This paper determines the extreme points of the closed unit ball ofQp,0(∂Δ) equipped with an appropriate norm.
Global existence and comparison theorem for a nonlinear parabolic equation
Authors: Hesaaraki Mahmoud , Moameni Abbas 
Published: April 2009

In this paper we consider a nonlinear parabolic equation with gradient dependent nonlinearities of the form0 < p, q and a, b ∈ ℝ, with homogeneous boundary condition in a bounded domain Ω ⊆ ℝ,N. In the case 0 < p, q ≤ 1 we prove the existence of solution for suitable initial data. A comparison theorem for the solutions with respect to supersoultions and subsolutions is proved. Using these result, uniqueness and boundedness of solutions is studied.
On uniformly distributed sequences of integers and Poincaré recurrence III
Authors: Nair R. 
Published: April 2009

Let S be a semigroup contained in a locally compact Abelian group G. Let Ĝ denote the Bohr compactification of G. We say that a sequence contained in S is Hartman uniform distributed on G iffor any character χ in Ĝ. Suppose that (Tg)g∈s is a semigroup of measurable measure preserving transformations of a probability space (X, β, μ) and B is an element of the σ-algebra β of positive μ measure. For a map T: X → X and a set A ⊆ X let T−1A denote {x ∈ X: Tx ∈ A}. In an earlier paper, the author showed that if k is Hartman uniform distributed thenIn this paper we show that ≥ cannot be replaced by =. A more detailed discussion of this situation ensues.
Analogues of the Liouville theorem for linear fractional relations in Banach spaces
Authors: Khatskevich V.A. , Ostrovskii M.I. , Shulman V.S. 
Published: April 2009

Consider a bounded linear operatorTbetween Banach spaces ℬ, ℬ′ which can be decomposed into direct sums ℬ = ℬ1⌖ ℬ2, ℬ′ = ℬ1′ ⌖ ℬ2′. Such linear operator can be represented by a 2 × 2 operator matrix of the formwhereTij∈ ℒ(ℬj, ℒi′)i, j= 1, 2. (By ℒ(ℬj, ℒi′) we denote the space of bounded linear operators acting from ℬjto ℬi′ (i, j= 1, 2).) The mapGTfromL(B1,B2) into the set of closed affine subspaces of ℒ(ℬ1′ ℬ2′), defined byis called alinear fractional relationassociated withT.Such relations can be considered as a generalisation of linear fractional transformations which were studied by many authors and found many applications. Many traditional and recently discovered areas of application of linear fractional transformations would benefit from a better understanding of the behaviour of linear fractional relations. The present paper is devoted to analogues of the Liouville theorem “a bounded entire function is constant” for linear fractional relations.
Équations de Fermat de type (5, 5,p)
Authors: Billerey Nicolas 
Published: April 2009

Soient p un nombre premier ≥ 7 et d un entier naturel sans puissances cinquièmes. Nous mettons en œuvre les différentes méthodes modulaires connues pour l'étude de l'équation diophantienne x5+y5 = dzp. Nous montrons en particulier qu'elle n'admet aucune solution propre et non triviale pour p ≥ 7 ou pour une infinité de nombres premiers, dans certains cas où d est de la forme 2α.3β.5γ. Pour d = 3, on énonce un critère permettant de vérifier, notamment, que tel est le cas lorsque p est ≤ 106.Let p be a prime number ≥ 7 and d be a positive integer fifth power free. We use the known modular methods for the study of the diophantine equation x5+y5 = dzp. We prove that this equation has no non trivial proper solution for p ≥ 7 or for infinitely many prime numbers, in some cases where d is of the form 2α.3β.5γ. For d = 3, we give a criterion which allows us to verify that this holds if p is less than 106.
Notes on the binding numbers for (a, b, k)-critical graphs
Authors: Zhou Sizhong , Jiang Jiashang 
Published: April 2009

Let G be a graph of order n, and let a, b, k be nonnegative integers with 1 ≤ a < b. An [a, b]-factor of graph G is defined as a spanning subgraph F of G such that a ≤ dF(x) ≤ b for each x ϵ V (F). Then a graph G is called an (a, b, k)-critical graph if after deleting any k vertices of G the remaining graph of G has an [a, b]-factor. In this paper, it is proved that G is an (a, b, k)-critical graph if the binding number

and
Furthermore, it is showed that the result in this paper is best possible in some sense.
A question of Paul Erdös and nilpotent-by-finite groups
Authors: Taeri Bijan 
Published: April 2009

Let n be a positive integer or infinity (denoted ∞), k a positive integer. We denote by Ωk(n) the class of groups G such that, for every subset X of G of cardinality n + 1, there exist distinct elements x, y ∈ X and integers t0, t1…, tk such that , where xi, ∈ {x, y}, i = 0, 1,…,k, x0 ≠ x1. If the integers t0, t1,…,tk are the same for any subset X of G, we say that G is in the class Ω̅k(n). The class k (n) is defined exactly as Ωk(n) with the additional conditions . Let t2, t3,…,tk be fixed integers. We denote by the class of all groups G such that for any infinite subsets X and Y there exist x ∈ X, y ∈ Y such that , where xi ∈ {x, y}, x0 ≠ x1, i = 2, 3, …, k. Here we prove that (1) If G ∈ k(2) is a finitely generated soluble group, then G is nilpotent.(2) If G ∈ Ωk(∞) is a finitely generated soluble group, then G is nilpotentby-finite.(3) If G ∈ Ω̅k(n), n a positive integer, is a finitely generated residually finite group, then G is nilpotent-by-finite.(4) If G is an infinite -group in which every nontrivial finitely generated subgroup has a nontrivial finite quotient, then G is nilpotent-by-finite.
Almost free actions on manifolds
Authors: Church Philip T. , Lamotke Klaus 
Published: April 2009

Let X be a compact, connected, oriented topological G-manifold, where G is a compact connected Lie group. Assume that the fixed point set is finite but nonempty, the action is otherwise free, and the orbit space is a manifold. It follows that either G = U(1) = S1 and dimX =4 or G = Sp(1) = S3 and dimX = 8, and the number of fixed points is even. The authors prove that these ∪(1)-manifolds (respectively, Sp(1)-manifolds) are classified up to orientation-preserving equivariant homeomorphism by (1) the orientation-preserving homeomorphism type of their orbit 3-manifolds (respectively, 5-manifolds), and(2) the (even) number of fixed points.Both the homeomorphism type in (1) and the even number in (2) are arbitrary, and all the examples are constructed. The smooth analog for U(1) is also proved.
Path decompositions of digraphs
Authors: Alspach Brian R. , Pullman Norman J. 
Published: April 2009

A path decomposition of a digraph G (having no loops or multiple arcs) is a family of simple paths such that every arc of G lies on precisely one of the paths of the family. The path number, pn(G) is the minimal number of paths necessary to form a path decomposition of G.We show that pn(G) ≥ max{0, od(v)-id(v)} the sum taken over all vertices v of G, with equality holding if G is acyclic. If G is a subgraph of a tournament on n vertices we show that pn(G) ≤ with equality holding if G is transitive.We conjecture that pn(G) ≤ for any digraph G on n vertices if n is sufficiently large, perhaps for all n ≥ 4.
Anti-uniform semilattices
Authors: Howie J. M. , Schein B. M. 
Published: April 2009

An inverse semigroup which is a union of groups is called Cliffordian. A semilattice E is called universally Cliffordian if every inverse semigroup having E as semilattice of idempotents is Cliffordian. It is shown that E is universally Cliffordian if and only if it is anti-uniform, that is, if and only if no two distinct principal ideals of E are isomorphic.A semilattice E satisfying the minimum condition is anti-uniform if and only if it is a well-ordered chain. Examples are given of anti-uniform semilattices of more complicated types.
Hadamard designs
Authors: Wallis Jennifer 
Published: April 2009

In this paper it is shown that an Hadamard design with each letter repeated once and only once can exist for 2, 4 and 8 letters only.L.D. Baumert and Marshall Hall, Jr have found a design with four letters each repeated three times. Their design and the design on four letters each repeated once, found by J. Williamson, is the totality previously published.
On the extension of orders in ordered modules
Authors: Ribenboim P. 
Published: April 2009

We introduce the notion of a positively independent set of elements in an ordered module. With this concept we determine a necessary and sufficient condition which insures that on a strictly ordered module over a strictly ordered ring there exists a strict total order refining the given order. This generalizes a previous result of Fuchs, concerning the case of ordered abelian groups.As an application, let R be a strictly ordered totally ordered ring and let M be the R-module of all mappings from a set I into R, with pointwise order; then this order on M may be refined to a strict total order.
On the structure of Stone lattices
Authors: Finch P. D. 
Published: April 2009

C.C. Chen and G. Grätzer have shown that a Stone lattice is determined by a triple (C, D, ø) where C is a boolean algebra, D is a distributive lattice with 1 and ø is an e-homomorphism from C into D(D), the lattice of dual ideals of D.It is shown here that any Stone lattice is, up to an isomorphism, a subdirect product of its centre C(L) and a special Stone lattice M(L). Special Stone lattices are characterised, in the terminology of the Chen-Grätzer triple, by the fact that the e-homomorphism Φ is one to one.In this paper we characterise a special Stone lattice L as a triple (H, C, Do) where H is a distributive lattice with 0 and 1, C is a boolean e-subalgebra of the centre of H and Do is a sublattice of H with o such that
d ∈ Do & c ∈ C = d ∧ c ∈ Do, and which separates the elements of C in the sense that for any c1 ≠c2 in C there is a d in Do with d ≤ c1 but d ≰ C2. It then turns out that C is C(L) and Do is the dual of D(L).
Ext(Q,Z) is the additive group of real numbers
Authors: Wiegold James 
Published: April 2009

Standard homological methods and a theorem of Harrison on cotorsion groups are used to prove the result mentioned.In this note Z denotes an infinite cyclic group, Q the additive group of rational numbers, Zp ∞ a p–quasicyclie group, and Ip the group of p–adic integers.Pascual Llorente proves in [3] that Ext(Q,z) is an uncountable group, and gives explicitly a countably infinite subset. Very little extra effort produces the result embodied in the title, as follows.
Error bounds in the approximation of functions: Corrigenda and an acknowledgement
Authors: Sahney Badri N. , Gopal Rao V. Venu 
Published: April 2009

The following corrections should be made in the authors' paper [2]: Replace p. 12, line 4 by ‖f−Nn‖p, = 0(1/nα),The author's theorems are contained as special cases in [1], Theorem 1.
Some classes of Hadamard matrices with constant diagonal
Authors: Wallis Jennifer , Whiteman Albert Leon 
Published: April 2009

The concepts of circulant and backcirculant matrices are generalized to obtain incidence matrices of subsets of finite additive abelian groups. These results are then used to show the existence of skew-Hadamard matrices of order 8(4f+1) when f is odd and 8f + 1 is a prime power. This shows the existence of skew-Hadamard matrices of orders 296, 592, 1184, 1640, 2280, 2368 which were previously unknown.A construction is given for regular symmetric Hadamard matrices with constant diagonal of order 4(2m + 1)2 when a symmetric conference matrix of order 4m + 2 exists and there are Szekeres difference sets, X and Y, of size m satisfying x є X ⇒ −xє X, y є Y ⇒ −y єY.
Maximal sum-free sets in abelian groups of order divisible by three: Corrigendum
Authors: Street Anne Penfold 
Published: April 2009

The last step of the proof in [2] was omitted. To complete the argument, we proceed in the following way. We had shown that H = H(S) = H(S+S) = H(S-S), that |S-S| = 2|S| - |H| and hence that in the factor group G* = G/H of order 3m, the maximal sum-free set S* = S/H and its set of differences S* - S* are aperiodic, withso thatBy (1) and Theorem 2.1 of [1], S* - S* is either quasiperiodic or in arithmetic progression.
On three-Engel groups
Authors: Kappe L.-C. , Kappe W.P. 
Published: April 2009

The following conditions for a group G are investigated:(i) maximal class n subgroups are normal,(ii) normal closures of elements have nilpotency class n at most,(iii) normal closures are n–Engel groups,(iv) G is an (n+1 )-Engel group.Each of these conditions is a consequence of the preceding one. The second author has shown previously that all conditions are equivalent for n = 1. Here the question is settled for n = 2 as follows: conditions (ii), (iii) and (iv) are equivalent. The class of groups defined by (i) is not closed under homomorphisms, and hence (i) does not follow from the other conditions.
Interlacing methods and large indecomposables
Authors: Dickson S. E. , Kelly G. M. 
Published: April 2009

The method of interlacing of modules, like amalgamation of groups, is a way of getting new objects from old. Briefly, the interlacing module we consider is a certain factor module of a direct sum of copies (finite or infinite) of an original module M. The conditions given in a previous paper by the first author in order that the interlacing module (using finitely many copies) be indecomposable are here greatly weakened, and we further allow the number of copies of the original to be infinite. R. Colby has shown that if R is a left artinian ring, the existence of a bound on the number of generators required for any indecomposable finitely-generated left R-module implies that R has a distributive lattice of two-sided ideals. This result is extended to rings whose identity is a sum of orthogonal local idempotents.For these rings the same distributivity is proved in case every indecomposable interlacing module of the above type which begins with an indecomposable projective M is finitely-generated. A consequence is that any finite-dimensional algebra over a field having infinitely many two-sided ideals has infinite-dimensional indecomposables.
Injective modules and soluble groups satisfying the minimal condition for normal subgroups
Authors: Hartley B. , McDougall D. 
Published: April 2009

Let p be a prime and let Q be a centre-by-finite p′-group. It is shown that the ZQ-modules which satisfy the minimal condition on submodules and have p–groups as their underlying additive groups can be classified in terms of the irreducible ZpQ-modules. If such a ZQ-module V is indecomposable it is either the ZpQ-injective hull W of an irreducible ZpQ-module (viewed as a ZQ-module) or is the submodule W[pn] of such a W consisting of the elements ω ∈ W which satisfy pnw = 0.This classification is used to classify certain abelian-by-nilpotent groups which satisfy Min-n, the minimal condition on normal subgroups. Among the groups to which our classification applies are all quasi-radicable metabelian groups with Min-n, and all metabelian groups which satisfy Min-n and have abelian Sylow p-subgroups for all p.It is also shown that if Q is any countable locally finite p'-group and V is a ZQ-module whose additive group is a p-group, then V can be embedded in a ZQ-module whose additive group is a minimal divisible group containing that of V. Some applications of this result are given.
A singular perturbation problem with a turning point
Authors: Watts A.M. 
Published: April 2009

We consider the equationεy″ + p(x)y′ + q(x)y = 0,
where ε is a small positive parameter and p vanishes in the interval. Two asymptotic forms of solution are obtained and a rigorous estimate is made of the difference between the exact solutions and the asymptotic forms.
Remarks on theorems of Thompson and Freede
Authors: Amir-Moéz A.R. , Perry C.R. 
Published: April 2009

Let A be a hermitian transformation on an n-dimensional unitary space En, with proper values a1 ≥ … ≥ an. Let M be a proper subspace of En. Suppose b1 ≥ … ≥ bh are the proper values of A/M and c1 ≥ … ≥ ck are the proper values of . Let i1. < … < ir and j1 < … < jr be sequences of positive integers, with ir ≤ k and jr ≤ h. then.This is a special case of one of the Thompson-Freede theorems which is proved by use of certain invariants.