bluuebunny/crossref_metadata_2025_split huggingface dataset:
Time-discretised Galerkin approximations of parabolic stochastic PDE's
Authors: Grecksch W. , Kloeden P.E. 
Published: April 2009

The global discretisation error is estimated for strong time discretisations of finite dimensional Ito stochastic differential equations (SDEs) which are Galerkin approximations of a class of parabolic stochastic partial differential equation (SPDE) with a strongly monotone linear operator with eigenvalues λ1 ≤ λ2 ≤ … in its drift term. If an order γ strong Taylor scheme with time-step δ is applied to the N dimensional Ito-Galerkin SDE, the discretisation error is bounded above bywhere [x] is the integer part of the real number x and the constant K depends on the initial value, bounds on the other coefficients in the SPDE and the length of the time interval under consideration.
Structure des cones normaux contenus dans un espace de Banach ou son dual II
Authors: Becker Richard 
Published: April 2009

Let B be a Banach space and X ⊂ B a normal cone such that the norm is monotone on X for the order determinated by X.We study the sup, denoted by i(X), of the q ≥ 1 such that, for each E> 0 and each n, there are x1, …, xn in X such that:for all a1, …, an ≥ 0, where ‖ ‖q is the norm in lq.We prove that i(X) is the inf of the p for which we have:The proof use a similar theorem of Kirvine, concerning Banach Riesz spaces. Here conical measures are a useful tool. We establish a link with a preceding work in which we adapt the Maurey theory factorisation of operators with values in a LP space, to the case of normal cones, contained in a Banach space.
On the Hölder semi-norm of the remainder in polynomial approximation
Authors: Elliott David 
Published: April 2009

Suppose the qth derivative of a function f is Hölder continuous of index α, where 0 < α ≤ 1, on the interval [-1,1]. Suppose further that pn is any polynomial of degree at most n such that |τn(x)| = |f(x) - pn(x)| ≤ c {max ((1 - x2)½/n, 1/n2) } q+a [-1,1]. Ifthen it is shown that‖τn‖β ≤ cn−q−α+β, 0 < β ≤ 1.
Stationary subspaces in ordered spaces
Authors: Kemoto Nobuyuki 
Published: April 2009

In this paper, we shall characterise the B(k)-property in generalised ordered (GO) spaces as follows.For every uncountable regular cardinal K, every GO space has the B(K)-property if and only if it has no closed subspace which is homeomorphic to a stationary set in K (with the subspace topology in K).
Area and length maxima for univalent functions
Authors: Yamashita Shinji 
Published: April 2009

Let S be the family of functions f(z) = z + a2z2 + … which are analytic and univalent in |z| < 1. We find the valueas a function of r 0 < r < 1. The known lower estimate ofis improved. Relations with the growth theorem are considered and the radius of univalence of f(z)/z is discussed.
The average distance property of classical Banach spaces
Authors: Hinrichs Aicke 
Published: April 2009

A Banach space X has the average distance property (ADP) if there exists a unique real number r such that for each positive integer n and all x1,…,xn in the unit sphere of X there is some x in the unit sphere of X such that
.It is known that l2 and l∞ have the ADP, whereas lp fails to have the ADP if 1 ≤ p < 2. We show that lp also fails to have the ADP for 3 ≤ p ≤ ∞. Our method seems to be able to decide also the case 2 < p < 3, but the computational difficulties increase as p comes closer to 2.
Some Engel conditions on infinite subsets of certain groups
Authors: Abdollahi Alireza 
Published: April 2009

Let k be a positive integer. We denote by ɛk(∞) the class of all groups in which every infinite subset contains two distinct elements x, y such that [x,k y] = 1. We say that a group G is an -group provided that whenever X, Y are infinite subsets of G, there exists x ∈ X, y ∈ Y such that [x,k y] = 1. Here we prove that:(1) If G is a finitely generated soluble group, then G ∈ ɛ3(∞) if and only if G is finite by a nilpotent group in which every two generator subgroup is nilpotent of class at most 3.(2) If G is a finitely generated metabelian group, then G ∈ ɛk(∞) if and only if G/Zk (G) is finite, where Zk (G) is the (k + 1)-th term of the upper central series of G.(3) If G is a finitely generated soluble ɛk(∞)-group, then there exists a positive integer t depending only on k such that G/Zt (G) is finite.(4) If G is an infinite -group in which every non-trivial finitely generated subgroup has a non-trivial finite quotient, then G is k-Engel. In particular, G is locally nilpotent.
The Kunze–Stein phenomenon on the isometry group of a tree
Authors: Veca Alessandro 
Published: April 2009

Let G be the group of isometries of a homogeneous tree . In the first part of this paper we decompose G in terms of certain subgroups N, ℤ, and K to obtain the related integral formula
Then, by using ideas of A. Ionescu and the formula above, we prove that

and that a related maximal operator on  is bounded from L2, 1() to L2,∞(). We finally show that Lp, 1(K\G/K) is a commutative Banach algebra of convolutors for Lp(G) and give an explicit description of its Gelfand spectrum.
The average distance property of classical Banach spaces II
Authors: Hinrichs Aicke , Wenzel Jörg 
Published: April 2009

A Banach space X has the average distance property if there exists a unique real number r such that for each positive integer n and all x1,…,xn in the unit sphere of X there is some x in the unit sphere of X such that
We show that lp does not have the average distance property if p > 2. This completes the study of the average distance property for lp spaces.
On Banach spaces of vector valued continuous functions
Authors: Cembranos Pilar 
Published: April 2009

LetKbe a compact Hausdorff space and letEbe a Banach space. We denote byC(K, E) the Banach space of allE-valued continuous functions defined onK, endowed with the supremum norm.Recently, Talagrand [Israel J. Math.44(1983), 317–321] constructed a Banach spaceEhaving the Dunford-Pettis property such thatC([0, 1],E) fails to have the Dunford-Pettis property. So he answered negatively a question which was posed some years ago.We prove in this paper that for a large class of compactsK(the scattered compacts),C(K, E) has either the Dunford-Pettis property, or the reciprocal Dunford-Pettis property, or the Dieudonné property, or propertyVif and only ifEhas the same property.Also some properties of the operators defined onC(K, E) are studied.
Coloring island maps
Authors: Jackson Brad , Ringel Gerhard 
Published: April 2009

An empire map is a map where the set of countries is divided into disjoint subsets which we call empires. If one empire consists of a single country then the remaining map is called an empire island map, the single country being referred to as the ocean. If every empire consists of at most M countries then it is called an M-pire map.It is proved that an M-pire map is colorable by 6M – 2 colors. Further there exists such a map which has 6M – 2 mutually adjacent empires.If an M-pire island map has every country adjacent to the ocean, then it is colorable in 4M colors. Such a map exists with 4M mutually adjacent empires where every country is adjacent to the ocean.
Monotone method and periodic solution of non linear parabolic boundary value problem for systems
Authors: Devasahayam M. Paul 
Published: April 2009

A system of parabolic equations is considered: Lui = uit − uix = fi (x, t, u, uix) on Q, Biui(j, t) = ωij(t), t ∈ (−∞, ∞), j = 0, 1, i = 1, 2, …, n, where Bi is one of the boundary operators Biui = ui or Biui = ∂ui/∂v + βi(x, t)ui, x = 0, 1, Ω = (0, 1), Q = Ω × R, u(=(u1, …, un)): Q → Rn, v(x) is the outward normal to the boundary ∂Ω, f, u, ω0, ω1 are n-valued functions and f, ω0, ω1 are periodic in t with period T and Bi is a positive function.The paper is classified into two parts. The first part deals with the existence and uniqueness of periodic solutions of the above system of parabolic equations. The second part deals with a monotone iterative method which develops a monotone iterative scheme for the solution of the above system of equations. In this paper we establish the existence of coupled quasi-solutions of the above equation. Also we give a monotone iterative scheme for the construction of such a solution.
On the ring of locally bounded Nash meromorphic functions
Authors: Kucharz Wojciech , Rusek Kamil 
Published: April 2009

We show that the ring of locally bounded Nash meromorphic functions on a connected d-dimensional Nash submanifold of ℝn is a Prüfer domain and every finitely generated ideal in this ring can be generated by d + 1 elements.Moreover, every finitely generated ideal can be generated by d elements if and only if the Nash manifold is noncompact.
Certain classes of univalent functions with negative coefficients II
Authors: Gupta V.P. , Jain P.K. 
Published: April 2009

Let P*(α, β) denote the class of functionsanalytic and univalent in |z| < 1 for whichwhere α є [0, 1), β є (0, 1].Sharp results concerning coefficients, distortion theorem and radius of convexity for the class P*(α, β) are determined. A comparable theorem for the classes C*(α, β) and P*(α, β) is also obtained. Furthermore, it is shown that the class P*(α, ß) is closed under ‘arithmetic mean’ and ‘convex linear combinations’.
Arithmetic properties of certain functions in several variables III
Authors: Loxton J.H. , van der Poorten A.J. 
Published: April 2009

We obtain a general transcendence theorem for the solutions of a certain type of functional equation. A particular and striking consequence of the general result is that, for any irrational number w, the functiontakes transcendental values at all algebraic points α with 0 < |α| < 1.
On a conjecture of Mahler
Authors: Dumir V.C. , Hans-Gill R.J. 
Published: April 2009

Let R be the field of real numbers. For α in R, let ‖α‖ be the distance of α from the nearest integer. The following conjecture of Kurt Mahler [Bull. Austral. Math. Soc. 14 (1976), 463–465] is proved.Let m, n be two positive integers n ≥ 2m. Let S be a finite or infinite set of positive integers with the following properties:(Q1) S contains the integers m, m+1, …, n−m;(Q2) every element of S satisfiesThen
On vector spaces of certain modular forms of given weights
Authors: Aggarwal A.R. , Agrawal M.K. 
Published: April 2009

Let p be a rational prime and Qp be the field of p–adic numbers. Jean-Pierre Serre [Lecture Notes in Mathematics, 350, 191–268 (1973)] had defined p–adic modular forms as the limits of sequences of modular forms over the modular group SL2(Z). He proved that with each non-zero p–adic modular form there is associated a unique element called its weight k. The p–adic modular forms having the same weight form a Qp–vector space.The object of this paper is to obtain a basis of p–adic modular forms and thus to know precisely all p–adic modular forms of a given weight k. The dimension of such modular forms as a Qp–vector space is countably infinite.
Coefficient estimates for starlike functions
Authors: Mogra M.L. , Juneja O.P. 
Published: April 2009

Let (α β) denote the class of functionsanalytic in the unit disc Δ ≡{z: |z| < 1} and satisfyingfor some α, β (0 ≤ α < 1, 0 < β ≤ 1) and for all z ∈ Δ. In the present paper, sharp coefficient estimates for functions in (α, β) have been obtained. The results thus obtained not only generalize the corresponding results of Thomas H. MacGregor (Michigan Math. J. 10 (1963), 277–281), A.V. Boyd (Proc. Amer. Math. Soc. 17 (1966), 1016–1018) and others, but also give rise to analogous results for various other subclasses of starlike functions.
Some results on weighing matrices
Authors: Wallis Jennifer Seberry , Whiteman Albert Leon 
Published: April 2009

It is shown that if q is a prime power then there exists a circulant weighing matrix of order q2 + q + 1 with q2 nonzero elements per row and column.This result allows the bound N to be lowered in the theorem of Geramita and Wallis that “given a square integer k there exists an integer N dependent on k such that weighing matrices of weight k and order n and orthogonal designs (1, k) of order 2n exist for every n > N”.
A note on Hausdorff groups
Authors: Fay Temple H. 
Published: April 2009

It is well known that in the category of Hausdorff groups continuous homomorphisms having dense image are epic. That these homomorphisms are precisely the epics is a conjecture. If one could prove that proper closed subgroups (endowed with the subspace topology) cannot have epic inclusions, then the conjecture would be shown to be true. Closed subgroups fall into two classifications:(a) open (and hence closed) subgroups and(b) nowhere dense closed subgroups.In this note it is shown that proper open subgroups cannot have epic inclusion. To do so an algebraic construction of Peter J. Hilton is topologized. The nowhere dense case remains open.
Nonstandard topological extensions: Addendum
Authors: Herrmann Robert A. 
Published: April 2009

It has recently come to my attention that, independent from my investigations in [1], Professor K.D. Stroyan [2] obtains for a Tychonoff space X and a normal base β a quotient space on *X which is homeomorphic to the Wallman-Frink Hausdorff compactification w(X, β). Consequently, if X is Tychonoff, then Corollary 4.1 in [1] implies that Stroyan's space is homeomorphic to the space w(X, β)S which is constructed in Theorem 4.1 in [1]. Stroyan's result is obtained by use of a monadic closure operator.I regret not mentioning Professor Stroyan's result in my paper [1].
Duality for generalized problems in complex programming
Authors: Mahajan D.G. , Vartak M.N. 
Published: April 2009

Weak duality and direct duality theorems are proved, under appropriate assumptions, for the following pair of programming problems in complex space:The objective function may be nondifferentiable and the constraints are of a more general nature than those considered earlier by various authors. Several well-known results are shown to be special cases of the results proved here.
A note on locally finite varieties
Authors: Wilson John S. 
Published: April 2009

Evidence is presented which suggests that the following assertions about a variety ⊻ of groups may be equivalent:(a) ⊻ is locally finite,(b) all ⊻-groups satisfying the maximal condition for normal subgroups are finite, and(c) all ⊻-groups satisfying the minimal condition for normal subgroups are finite.
A case of boundedness in Littlewood's problem on oscillatory differential equations
Authors: Morris G.R. 
Published: April 2009

It is shown that all solutions of ẍ + 2x3 = p(t) are bounded, the notation indicating that p is periodic. It is not necessary to have a small parameter multiplying p.The essential step is to show by appeal to Moser's theorem that, under the mapping (of the initial-value plane) which corresponds to the equation, there are invariant simple closed curves. This implies also that there is an uncountable infinity of almost-periodic solutions and, for each positive integer m, an infinity of periodic solutions of least period 2mπ (2π being taken as the least period of p ).It is suggested that for a large class of equations the same attack would show all solutions of ẍ + g(x) = p(t) bounded. However, in order to show the method clearly, no generalisation is attempted here.
Amicable orthogonal designs
Authors: Robinson Peter J. 
Published: April 2009

A powerful tool in the construction of orthogonal designs has been amicable orthogonal designs. Recent results in the construction of Hadamard matrices has led to the need to find amicable orthogonal designs A, B in order n and of types (u1, U2, …, u6) and (ν1, ν2, …, νr) respectively satisfying At = -A, Bt = B, and ABt = BAt withFor simplicity, we say A, B are amicable orthogonal designs of type (u1, u2, …, us; v1, v2, …, vr).We completely answer the question in order 8 by showing (1, 2, 2, 2; 8), (1, 2, 4; 2, 2, 4), (2, 2, 3; 2, 6), (7, 1, 7) and those designs derived from the above are the only possible.We use our results to obtain new orthogonal designs in order 32.
Doubly transitive permutation groups involving the one-dimensional projective special linear groups
Authors: Praeger Cheryl E. 
Published: April 2009

Let G be a doubly transitive permutation group on a finite set Ω, and for α in Ω suppose that Gα has a set Σ of non-trivial blocks of imprimitivity in Ω - {α}. If Gα is 2-transitive but not faithful on Σ, when is it true that the stabiliser in Gα of a block of Σ does not act faithfully on that block (that is, there is a nontrivial element in Gα which fixes every point of the block)? In a previous paper this question was answered when is the alternating or symmetric group, or a Mathieu group in its usual representation. In this paper we answer the question when , permuting the q + 1 points of the projective line, for some prime power q. We show that the only groups which arise satisfy either(i) PSL(3, q) ≤ G ≤ PΓL(3, q) in its natural representation, or(ii) G is a group of collineations of an affine translation plane of order q, and contains the translation group.
On the transcendency of the solutions of a special class of functional equations: Corrigendum
Authors: Mahler Kurt 
Published: April 2009

Mr V.E. Hoggatt, Jr, has pointed out an error in the examples of my paper [2], IfFmdenotes themth Fibonacci number, these examples asserted thatis transcendental. This is in fact false, for by a theorem of Good [1],for it happens thatis a rational and not a transcendental function ofz, so that Theorem 1 of my paper cannot be applied. The value ofsfollows from (1) on putting.Hence the following changes have to be made in [2].On p. 390, lines 7 and 10, the casek= 1 must each time be excluded, and in Theorem 2 the two numbersrandsmay not be both be 0.
The class of a nilpotent wreath product
Authors: Shield David 
Published: April 2009

Let G be a group with a normal subgroup H whose index is a power of a prime p, and which is nilpotent with exponent a power of p. Gilbert Baumslag (Proc. Cambridge Philos. Soc. 55 (1959), 224–231) has shown that such a group is nilpotent; the main result of this paper is an upper bound on its nilpotency class in terms of parameters of H and G/H. It is shown that this bound is attained whenever G is a wreath product and H its base group.A descending central series, here called the cpp-series, is involved in these calculations more closely than is the lower central series, and the class of the wreath product in terms of this series is also found.Two tools used to obtain the main result, namely a useful basis for a finite p-group and a result about the augmentation ideal of the integer group ring of a finite p-group, may have some independent interest. The main result is applied to the construction of some two-generator groups of large nilpotency class with exponents 8, 9, and 25.
An extension of the essential supremum concept with applications to normal integrands and multifunctions
Authors: Balder E.J. 
Published: April 2009

Let (T, T, μ) be a σ-finite measure space and X a Suslin space. Let A be a class of normal integrands on T × X. We discuss the existence of an essential supremum of A, namely, a normal integrand l withwhere A0 is a countable subclass of A, and, for each α ∈ A,In this way we obtain an extension of the classical essential supremum concept. The applications include a result on measurable selectors of nonmeasurable multifunctions.
Approximation by smooth embedded hypersurfaces with positive mean curvature
Authors: Lin Fang Hua 
Published: April 2009

Here we initiate the study of the following problem. Let Ω be a compact domain in a Riemannian manifold such that ∂Ω is of minimum area for the contained volume. Can ∂Ω be approximated by smooth hypersurfaces of positive mean curvature? It reduces to the question of whether or not a stable (or minimizing) hypercone in a Euclidian space can be approximated by smooth hypersurfaces of positive mean curvature. The positive solution to the problem may be useful for studying the curvature and topology of Ω.We show in this paper that such approximation is possible provided that the given minimal cone satisfies some additional hypothesis.
The limiting behaviour of certain sequences of continued fractions
Authors: Angell David 
Published: April 2009

We investigate the set of limit points of the continued fractionswhere x1, x2, … is a given sequence of positive integers. We show that this set is closed, and that it may include any given countable subset of [0, 1] if the integers xk are chosen appropriately. Our main result, which has applications in transcendence theory, is that the sequence of continued fractions has no rational limit point when the sequence {xk} of partial quotients is bounded.
Oscillatory properties of the solutions of linear equations of neutral type
Authors: Bainov D.D. , Myshkis A.D. , Zahariev A.I. 
Published: April 2009

In this paper the oscillatory and asymptotic properties of solutions of the equationare investigated where δ = ±1, τ > 0, σ > 0, the functionsr(s) andare non- decreasing and.
A Class of functional equations which have entire solutions
Authors: Walker Peter L. 
Published: April 2009

We consider the Abelian functional equationwhere φ is a given entire function and g is to be found. The inverse function f = g−1 (if one exists) must satisfyWe show that for a wide class of entire functions, which includes φ(z) = ez − 1, the latter equation has a non-constant entire solution.
Corrigendum: How complete are categories of algebras
Authors: Adámek Jiří 
Published: April 2009

Proposition 1.6 states that the category Alg(P*) is hypercomplete but non-compact. This is true, but the argument for non-compactness must be corrected as follows.Let A be the category of algebras (X, x′, x″) where x′, x″: P*X → X are operations with x′(φ) = x″(φ), and homomorphisms are mappings which are P*-homomorphisms with respect to both operations. The embedding E: Alg(P*) → A with E(X, x) = (X, x, x) preserves colimits, although it is not a left adjoint. In fact, the preservation of colimits C = colim D is obvious in case C is finite, and for the infinite case the original argument presented in the paper is correct (namely, one of the colimit maps is onto). E is not a left adjoint because given A = (X, x′, x″) in A with X infinite and x′(M) ≠ x″(M) for any M ≠ φ, then there is no universal arrow into A with respect to E.
Perturbations of a Hamiltonian family of cubic vector fields
Authors: Urbina A.M. , Cañas M. , de la Barra G. León , de la Barra M. León 
Published: April 2009

This paper is related with the configurations of limit cycles for cubic polynomial vector fields in two variables (χ3).It is an open question to decide whether every limit cycle configuration in χ3 can be obtained by perturbation of a corresponding Hamiltonian configuration of centres and graphs.In this work, by considering perturbations of the Hamiltonian vector field XH = (Hy, − Hx), where H(x, y) = [a(x + h)2 + by2 − 1] [a(x − h)2 + by2 − 1], we make a global analysis of the possible cases.The vector field XH has three centres (C−, C+ and the origin) and two saddles. By means of quadratic perturbations the centres become fine foci where C−and C+ have the same type of stability but opposed to that one of the origin and infinity. Further introducing cubic perturbations changes the stability of C−, C+ and the cycle at infinity and generates limit cycles. Lastly extra linear terms change the stability of the origin and generate another limit cycle.Finally, we analyse the rupture of saddle connection of the Hamiltonian field under perturbation, via Melnikov's integral, in order to complete the study of the global phase portrait and to consider the possibility of new limit cycles emerging from the Hamiltonian graph.
Minimal partial clones
Authors: Börner F. , Haddad L. , Pöschel R. 
Published: April 2009

LetAbe a finite set. A partial clone on A is a composition closed set of operations containing all projections. It is well known that the partial clones on A, ordered by inclusion, form a lattice. We show that the minimal partial clones onAare:(a) minimal clones of full operations or(b) generated by partial projections defined on a totally reflexive and totally symmetric domain.