bluuebunny/crossref_metadata_2025_split huggingface dataset:
Word problems related to periodic solutions of a non-autonomous system
Authors: Devlin James 
Published: November 2008

In this paper, we develop an abstract formulation of a problem which arises in the investigation of the number of limit cycles of systems of the formwhere p and q are homogeneous polynomials. This is part of the much wider study of Hilbert's sixteenth problem, in which information is sought about the number of limit cycles of systems of the formwhere P and Q are polynomials, and their possible configurations.
Character-pure locally compact abelian groups and their dual groups
Authors: Takahashi Yuji 
Published: November 2008

AbstractWe give some characterizations of the class of character-pure locally compact abelian groups. As an application we supplement a result of Venkataraman characterizing the class of locally compact abelian groups which are topologically pure in their Bohr compactifications. We also study the class of locally compact abelian groups which are pure closed in their Bohr compactifications.
Representability of invariant positive sesquilinear forms on partial *-algebras
Authors: Antoine J.-P. , Inoue A. 
Published: November 2008

AbstractWe consider invariant positive sesquilinear forms on a (partial) *-algebra A without unit. First we investigate the relationship between extendability and representability for such a form ø; in particular we discuss under which conditions the two concepts are equivalent. Then we introduce the notions of weak representability and strict unrepresentability, and we show that every fully invariant positive sesquilinear form on A × A is uniquely decomposed into a weakly representable part and a strictly unrepresentable part.
A diophantine problem in harmonic analysis
Authors: Poorten A. J. Van Der , Schlickewei H. P. 
Published: November 2008

In the problem session of the Journées Arithmétiques 1989 in Luminy, Bourgain made the followingConjecture. Suppose α is an algebraic number of degree d. Assume that for each n∈ ℕThen there exists a constant c = c(α) with the following property: given any subspace W of dimension ≤ d − 1 of the d-dimensional ℚ-vector space ℚ(α), the set {n|n∈ℕ,αn∈W} contains fewer than c(α) elements.
The flow near non-trivial minimal sets on 2-manifolds
Authors: Athanassopoulos Konstantin 
Published: November 2008

In this paper we give a description of the qualitative behaviour of the orbits near a non-trivial compact minimal set of a continuous flow on a 2-manifold. The first results in this direction were obtained in [1] and the present paper can be regarded as a continuation of that work. The main result can be stated as follows:Theorem 1·1. Let (ℝ, M, f) be a continuous flow on a 2-manifold M and A ⊂ M a non-trivial compact minimal set.
On parallelepipeds of minimal volume containing a convex symmetric body in ℝn
Authors: Pelczynski A. , Szarek S. J. 
Published: November 2008

AbstractGiven a convex symmetric body C ⊂ ℝn we put a(C) = |C| sup |P|−1 where the supremum extends over all parallelepipeds containing C and |A| denotes the volume of a set A ⊂ ℝn. Let an = inf {a(C): C ⊂ ℝn}. We show thatwhich slightly improves the estimate due to Dvoretzky and Rogers [6]. In every dimension n we construct a convex symmetric polytope Wn such that the unit Euclidean ball is the ellipsoid of maximal volume inscribed into Wn and the volume of every parallelepiped containing Wn is greater thanfor large n which shows ‘the limit’ to the Dvoretzky Rogers method for bounding an below. We present an alternative proof of the result of I. K. Babenko [l] that . We show that , and that a local minimum of the function C→a(C) for C ⊂ ℝn is attained only at an equiframed convex body (that is, a body such that every point of its boundary belongs to a parallelepiped of minimal volume containing the body).
A separable quasidiagonal C*-algebra with a non-quasidiagonal quotient by the compact operators
Authors: Wassermann Simon 
Published: November 2008

A C*-algebra A of operators on a separable Hilbert space H is said to be quasidiagonal if there is an increasing sequence E1, E2, … of finite-rank projections on H tending strongly to the identity and such thatas i → ∞ for T∈A. More generally a C*-algebra is quasidiagonal if there is a faithful *-representation π of A on a separable Hilbert space H such that π(A) is a quasidiagonal algebra of operators. When this is the case, there is a decomposition H = H1 ⊕ H2 ⊕ … where dim Hi < ∞ (i = 1, 2,…) such that each T∈π(A) can be written T = D + K where D= D1 ⊕ D2 ⊕ …, with Di∈L(Hi) (i = 1, 2,…), and K is a compact linear operator on H. As is well known (and readily seen), this is an alternative characterization of quasidiagonality.
Shape-preserving polynomial approximation in C[– 1, 1]
Authors: Ditzian Z. , Jiang D. , Leviatan D. 
Published: November 2008

AbstractA recent result of the first two authors has bridged the gap between the Timantype pointwise estimate and the norm estimate for polynomial approximation in C[– 1, 1]. Here we show that, when considering the second order modulus of smoothness, the aforementioned result holds with polynomials that preserve monotonicity, convexity and the values of the function at the end points of the interval [–1, 1]. This yields a generalization of results by Telyakovskii, Gopengauz, DeVore, Yu and the third author. Moreover, the construction here does not depend on the construction for the non-constrained approximation by polynomials.
Uniform Kadec–Klee–Huff properties of vector-valued Hardy spaces
Authors: Dowling P. N. , Lennard C. J. 
Published: November 2008

AbstractIn [8] Partington showed that a Banach space X is uniformly convex if and only if Lp([0, 1], X) has the uniform Kadec–Klee–Huff property with respect to the weak topology (UKKH (weak)), where 1 < p < ∞. In this note we will characterize the Banach spaces X such that HP(D, X) has UKKH (weak), where 1 ≤ p < ∞. Similar results for UKKH (weak*) are also obtained. These results (and proofs) are quite different from Partington's result (and proof).
Discrete least squares approximation and prewavelets from radial function spaces
Authors: Buhmann M. D. 
Published: November 2008

AbstractIn this article we study the convergence behaviour of least squares approximations of various types by radial basis functions, i.e. least squares approximations from spaces spanned by radially symmetric functions φ (‖· −xj‖). Here the xj are given ‘centres’ in ℝn which we assume to lie on a grid. The inner products with respect to which the least squares problem is considered are discrete and Sobolev, i.e. may involve derivative information. Favourable estimates for the least squares errors are found that are shown to decrease as powers of the gridspacing. The work on discrete least squares approximations also gives rise to the construction of prewavelets from radial function spaces with respect to a discrete Sobolev inner product, which are discussed in the paper as well.
Lefschetz numbers of periodic orbits of pseudo-Anosov homeomorphisms
Authors: Guaschi John 
Published: November 2008

AbstractGiven a surface homeomorphism isotopic to the identity which is pseudo-Anosov relative to a finite set, we show that the sum of the Lefschetz numbers of periodic points of any period greater than one is non-negative. If this period is odd and greater than a number which depends only on the surface, the sum is zero. If we consider sequences of periods such that each element is twice that of its predecessor, then this sum is increasing beyond a certain point also depending on the surface. As a corollary, for each periodic orbit contained within the boundary of the surface there exists one of the same period contained in the interior.
Embedding derivatives of weighted Hardy spaces into Lebesgue spaces
Authors: Girela Daniel , Lorente María , Sarrión María Dolores 
Published: November 2008

AbstractLet 1 ≤ p < ∞ and let ω be a non-negative function defined on the unit circle T which satisfies the Ap condition of Muckenhoupt. The weighted Hardy space Hp(ω) consists of those functions f in the classical Hardy space H1 whose boundary values belong to Lp(ω). Recently McPhail (Studia Math. 96, 1990) has characterized those positive Borel measures μ on the unit disc Δ for which Hp(ω) is continuously contained in Lp(dμ). In this paper we study the question of finding necessary and sufficient conditions on a positive Borel measure μ on Δ for the differentiation operator D defined by Df = f′ to map Hp(ω) continuously into Lp(dμ). We prove that a necessary condition is that there exists a positive constant C such thatwhere for any interval I ⊂ T,We prove that this condition is also sufficient in some cases, namely for 2 ≤ p < ∞ and ω(et0) = |θ|α, (|θ| ≤ π), – 1 < α < p – 1, but not in general. In the general case we prove the sufficiency of a condition which is slightly stronger than (A).
Existence of R-matrix for a quantized Kac–Moody algebra
Authors: Lyubashenko Volodimir 
Published: November 2008

AbstractThere is a pairing between two Borel subalgebras of a quantized Kac–Moody algebra, which plays the rôle of R-matrix. Over the field ℚ(q) this pairing is non-degenerate. We show the existence of a braiding in some categories of representations of a quantized Kac-Moody algebra.
Free quotients of subgroups of the Bianchi groups whose kernels contain many elementary matrices
Authors: Mason A. W. , Odoni R. W. K. 
Published: November 2008

AbstractLet d be a square-free positive integer and let be the ring of integers of the imaginary quadratic number field ℚ(√ − d) The Bianchi groups are the groups SL2() (or PSL2(). Let m be the order of index m in . In this paper we prove that for each d there exist infinitely many m for which SL2(m)/NE2(m) has a free, non-cyclic quotient, where NE2(m) is the normal subgroup of SL2(m) generated by the elementary matrices. When d is not a prime congruent to 3 (mod 4) this result is true for all but finitely many m. The proofs are based on the fundamental paper of Zimmert and its generalization due to Grunewald and Schwermer.The results are used to extend earlier work of Lubotzky on non-congruence subgroups of SL2(), which involves the concept of the ‘non-congruence crack’. In addition the results highlight a number of low-dimensional anomalies. For example, it is known that [SLn(m), SLnm)] = En(m), when n ≥ 3, where [SLn(m), SLn(m)] is the commutator subgroup of SL(m) and En(m) is the subgroup of SLn(m) generated by the elementary matrices. Our results show that this is not always true when n = 2.
Higher-order differential equations with a slowly decaying coefficient containing a periodic factor
Authors: Eastham M. S. P. 
Published: November 2008

Let p(x) be periodic with mean value c and let α > 0. Then the investigation of the asymptotic solution of the second-order equationcan be split into four cases: (i) α > 2, (ii) α > 1 and c = 0, (iii) 0 < α ≤ 1 and c = 0, (iv) 0 < α ≤ 2 and c ≠ 0. The first two cases are straightforward because then there are solutions y1 and y2 of (1·1) such that y1(x) ~ x and y2(x) → 1 as x → ∞ [5, theorems 2·7·2 and 2·7·5; 7, p. 375; 8]. Thus the coefficient of y in (1·1) represents a perturbation which has no effect on the dominant asymptotic behaviour of solutions. Case (iii) is less simple because here the nature of p(x) does influence the asymptotic form of solutions and, indeed, when α < 1 the solutions of (1·1) are oscillatory. This case has been fully covered by a number of authors: Atkinson, Eastham and McLeod[2, §3], Cassell[3, 4], Eastham[5, §4·13], Mahoney[10], Willett[13] and Wong[14, 15]. In addition, corresponding results for a higher-order self-adjoint analogue of (1·1) have been obtained recently by Al-Hammadi and Eastham [1, 6] as an application of general asymptotic methods for differential systems.
Studying the topology of Morin singularities from a global viewpoint
Authors: Saeki Osamu 
Published: November 2008

AbstractLetf:M→Nbe a smooth map of a closedn-manifold into ap-manifold (n≥p) having only Morin singularities [17]. We study the topology of such a map and obtain a modulo 2 congruence formula involving the Euler characteristics ofM, N, the singular sets and the regular fibres off. We also consider applications of this formula to the existence problem of maps having only fold singular points. Stable maps into 3-manifolds are also studied and we obtain a modulo 2 congruence formula involving the swallow tails and the number of triple points of the discriminant set.
A toral configuration space and regular semisimple conjugacy classes
Authors: Lehrer G. I. 
Published: November 2008

For any topological space X and integer n ≥ 1, denote by Cn(X) the configuration spaceThe symmetric group Sn acts by permuting coordinates on Cn(X) and we are concerned in this note with the induced graded representation of Sn on the cohomology space H*(Cn(X)) = ⊕iHi (Cn(X), ℂ), where Hi denotes (singular or de Rham) cohomology. When X = ℂ, Cn(X) is a K(π, 1) space, where π is the n-string pure braid group (cf. [3]). The corresponding representation of Sn in this case was determined in [5], using the fact that Cn(C) is a hyperplane complement and a presentation of its cohomology ring appears in [1] and in a more general setting, in [8] (see also [2]).
Covering properties of open continuous mappings having two valences between Riemann surfaces
Authors: Lyzzaik Abdallah 
Published: November 2008

AbstractLet be an open Riemann surface with finite genus and finite number of boundary components, and let be a closed Riemann surface. An open continuous function from to is termed a (p, q)-map, 0 < q < p, if it has a finite number of branch points and assumes every point in either p or q times, counting multiplicity, with possibly a finite number of exceptions. These comprise the most general class of all non-trivial functions having two valences between and .The object of this paper is to study the geometry of (p, q)-maps and establish a generalized embedding theorem which asserts that the image surfaces of (p, q)-maps embed in p-fold closed coverings possibly having branch points off the image surfaces.
A systematic approach to symmetric presentations. I. Involutory generators
Authors: Curtis R. T. , Hammas A. M. A. , Bray J. N. 
Published: November 2008

AbstractIn this paper we conduct a systematic, computerized search for groups generated by small, but highly symmetric, sets of involutions. Many classical groups are readily obtained in this way, as are a number of sporadic simple groups. The techniques of symmetric generation developed elsewhere are described afresh, and the results are presented in a convenient tabular form.
On the zeros and Fourier transforms of entire functions in the Paley–Wiener space
Authors: Dyakonov Konstantin M. 
Published: November 2008

AbstractLet f be an entire function of the formwhere ø is a function in L2(ℝ) with compact support. If f|ℝ is real-valued then, for obvious reasons,
(a) the supporting interval for ø is symmetric with respect to the origin, andAssuming that f has no zeros in {Im z > 0}, we prove that the converse is also true: (a) and (b) together imply that f|ℝ takes values in αℝ, where α is a fixed complex number.The proof relies on a certain formula involving the Dirichlet integral, which may be interesting on its own.
Packing dimension, Hausdorff dimension and Cartesian product sets
Authors: Xiao Yimin 
Published: November 2008

AbstractWe show that the dimension adim introduced by R. Kaufman (1987) coincides with the packing dimension Dim, but the dimension aDim introduced by Hu and Taylor [7] is different from the Hausdorff dimension. These results answer questions raised by Hu and Taylor.
On the length formula of Hoskin and Deligne and associated graded rings of two-dimensional regular local rings
Authors: Johnston Bernard L. , Verma Jugal 
Published: November 2008

Let (R, m) be a 2-dimensional regular local ring and I an m-primary ideal. The aim of this paper is to find conditions on I so that the associated graded ring of I,and the Rees ring of I,where t is an indeterminate, are Cohen–Macaulay (resp. Gorenstein). To this end, we use the results and techniques from Zariski's theory of complete ideals ([14], appendix 5) and its later generalizations and refinements due to Huneke [7] and Lipman[8]. The main result is an application of three deep theorems: (i) a generalization of Macaulay's classical theorem on Hilbert series of Gorenstein graded rings [13], (ii) a generalization of the Briançon–Skoda theorem due to Lipman and Sathaye [9], and (iii) a formula for the length of R/I, where I is a complete m-primary ideal, due to Hoskin[4] and Deligne[1].
Matrix generators for Fischer's group Fi24
Authors: Wilson Robert A. 
Published: November 2008

AbstractIn this paper we show how to construct 781 × 781 matrices over GF(3), generating the largest of the three Fischer groups. For some purposes these are more useful than the permutations on 306936 points, as they require only one-sixth of the storage space. We also construct generators for its triple cover, as 1566 × 1566 matrices over GF(2), and for the derived group thereof, as 783 × 783 matrices over GF(4).
Operators in finite distributive subspace lattices, I
Authors: Spanoudakis N. K. 
Published: November 2008

AbstractThe purpose of this paper is to settle in the negative an open problem in operator theory, which asks whether in a finite distributive subspace lattice ℒ on a Hilbert space, every finite rank operator of Alg ℒ can be written as a finite sum of rank one operators from Alg ℒ. The counter-example constructed is on a specific Hilbert space realization of the free distributive lattice on three generators and the operator which fails the above property has rank two.
A rational invariant for certain infinite discrete groups
Authors: Johnson F. E. A. 
Published: November 2008

We introduce a rational-valued invariant which is capable of distinguishing between the commensurability classes of certain discrete groups, namely, the fundamental groups of smooth closed orientable aspherical manifolds of dimensional 4k(k ≥ 1) whose Euler characteristic χ(Λ) is non-zero. The invariant in question is the quotientwhere Sign (Λ) is the absolute value of the signature of the intersection formand [Λ] is a generator of H4k(Λ; ℝ).
On H-balls and canonical regions of loxodromic elements in complex hyperbolic space
Authors: Kamiya Shigeyasu 
Published: November 2008

Let U(1, n; ℂ) be the automorphism group of the Hermitian formfor . We can regard an element of U(1, n; ℂ) as a transformation acting on , where is the closure of the complex unit ballThe non-trivial elements of U(1, n; ℂ) fall into three conjugacy types, depending on the number and the location of their fixed points. Let g be a non-trivial element of U(1, n; ℂ). We call g elliptic if it has a fixed point in Bn and g parabolic if it has exactly one fixed point and this lies on the boundary ∂Bn. An element g will be called loxodromic if it has exactly two fixed points and they lie on ∂Bn.
The relativistic clock problem
Authors: Mikhail F. I. 
Published: November 2008

AbstractThe so-called ‘clock paradox’ is concerned with the difference in the time-intervals reckoned by two observers in relative motion for the lapse of time between two encounters. In this paper the problem is treated purely by general relativity by considering a particular example in which the two observers are attached to two test-particles moving freely in the field of a gravitating mass; one of these makes complete revolutions in a circular orbit while the other moves radially outwards and inwards. The time-interval between two successive encounters is shorter in the reckoning of the former than in that of the latter. The difference is found to agree qualitatively with a naïve application of special relativity.
Some results on the product of distributions
Authors: Fisher B. 
Published: November 2008

The product of two distributions f and g on the open interval (a, b), where −∞ ≤ a < b ≤ ∞, was defined(1) as the limit of the sequence {fngn}, provided this sequence is regular on (a, b), wherefor n = 1, 2, … and ρ is a fixed infinitely differentiable function having the following properties:(1) ρ(x) = 0 for |x| ≥ 1,(2) ρ(x) ≥ 0,(3) ρ(x) = ρ(−x),
On the congruence y2 ≡ x5 − a (mod p)
Authors: Rajwade A. R. 
Published: November 2008

The object of this paper is to complete the half proved theorem 2 of (1).Let be a primitive fifth root of unity. Any element of Z[ζ] is a polynomial f(ζ) in ζ of degree ≤ 3 since 1 + ζ + ζ2 + ζ3 + ζ4 = 0. The units of Z[ζ] are ± ζi(1 + ζ)i or better still , with 0 ≤ i ≤ 4, j ε Z, where is the fundamental unit of the maximal real subfield of Q(ζ).
On the historical development of the theory of finite inhomogeneous Markov chains
Authors: Seneta E. 
Published: November 2008

AbstractThe main purpose of the note is to compare necessary and sufficient conditions for weak ergodicity of finite inhomogeneous Markov chains given by Doeblin (3) and Hajnal (4), the former paper being little known; and more generally to expand on the nature and consequences of Doeblin's approach as compared to Hajnal's in some detail. A consequence is some insight into the relation between various ‘coefficients of ergodicity’.
Type inference with simple subtypes
Authors: Mitchell John C. 
Published: November 2008

AbstractSubtyping appears in a variety of programming languages, in the form of the ‘automatic coercion’ of integers to reals, Pascal subranges, and subtypes arising from class hierarchies in languages with inheritance. A general framework based on untyped lambda calculus provides a simple semantic model of subtyping and is used to demonstrate that an extension of Curry's type inference rules are semantically complete. An algorithm G for computing the most general typing associated with any given expression, and a restricted, optimized algorithm GA using only atomic subtyping hypotheses are developed. Both algorithms may be extended to insert type conversion functions at compile time or allow polymorphic function declarations as in ML.
Metamorph – a formal methods toolkit with application to the design of digital hardware
Authors: Brumfitt P.J. 
Published: November 2008

AbstractMetaMorph is a software tool that supports transformation and proof for an equational non-strict functional language. It was developed as a vehicle for research into the synthesis of digital logic, but is equally suitable for reasoning about functional programs. The theorem prover may be used for verifying new reusable transforms and to assist the search for transformation sequences having a constrained goal. The paper provides an overview of all aspects of the project, and a brief discussion of its application to hardware.
An incremental, exploratory and transformational environment for lazy functional programming
Authors: Runciman Colin , Toyn Ian , Firth Mike 
Published: November 2008

AbstractMost programming environments for functional languages offer a single tool used to evaluate programs – either a batch compiler or an interpreter with a read-eval-print loop. This paper presents a programming environment that supports not only evaluation, but also a range of other programming activities including transformation. The environment is designed to encourage working in an incremental and exploratory style, avoiding constraints on the order in which things must be done yet guarenteeing security. What has already been done towards the development of a program automatically persists, as does information about what has yet to be done. For instance, new laws can be introduced as conjectures and used in program transformation, but full details of proof obligations and dependencies are maintained.The paper outlines the functional language supported by the environment, and uses an extended example to illustrate program construction, execution, tracing, modification and transformation.