bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the probable behaviour of some algorithms for finding the stability number of a graph
Authors: Pittel B. 
Published: November 2008

AbstractA class of f-driven algorithms due to Chvátal for finding the stability number of a graph are studied. It is shown that, for almost all graphs, the computation time grows subexponentially with n, the number of vertices. If, however, each edge exists with probability δ/n independently on other edges then asymptotically almost certainly the computation time is exponential. Still, for all large enough δ's, these algorithms perform noticeably better than a naive algorithm. The results are extended to random graphs with a fixed number of edges.
Determining the thickness of graphs is NP-hard
Authors: Mansfield Anthony 
Published: November 2008

AbstractThe thickness of a graph is a measure of its nonplanarity and has applications in the theory of printed circuits. To determine the thickness of an arbitrary graph is a seemingly intractable problem. This is made precise in this paper where we answer an open problem of Garey and Johnson (2) by proving that it is NP-complete to decide whether a graph has thickness two.
The S-unit equation over function fields
Authors: Silverman Joseph H. 
Published: November 2008

In the study of integral solutions to Diophantine equations, many problems can be reduced to that of solving the equationin S-units of the given ring. To accomplish this over number fields, the only known effective method is to use Baker's deep results on linear forms in logarithms, which yield relatively weak upper bounds. For function fields, R. C. Mason [2] has recently given a remarkably strong effective upper bound. In this note we give an independent proof of Mason's bound, relying only on elementary algebraic geometry, principally the Riemann-Hurwitz formula.
Characters of nilpotent groups
Authors: Carey A. L , Moran W. 
Published: November 2008

AbstractThe characters (extremal positive definite central functions) of discrete nilpotent groups are studied. The relationship between the set of characters of G and the primitive ideals of the group C*-algebra C*(G) is investigated. It is shown that for a large class of nilpotent groups these objects are in 1–1 correspondence. One proof of this exploits the fact that faithful characters of certain nilpotent groups vanish off the finite conjugacy class subgroup. An example is given where the latter property fails.
Note on propagation of classical waves: II
Authors: Kanseta H. 
Published: November 2008

1. Main results and notations. We consider Cauchy's problem for the classical wave equation in :with initial conditions u(0, x) = uo(x) and ∂tu(0, x) = u1 (x). In (1·1) δ and m2 stand for the Laplacian in and a constant respectively. Note that a second order hyper-bolic differential equation with real constants can be reduced to (1·1) ([1], p. 183). Let uj (j = 0,1) be C∞ funotions on whose support is contained in the closed ball BR = {xεl; |x| ≥R} for some R > 0. In this note we shall show that the solution u(t, x) of (1·1) possesses the following properties.
On the micro-to-macro transition in constitutive analyses of elastoplastic response at finite strain
Authors: Hill R. 
Published: November 2008

AbstractThe theoretical transition between basic properties of elastoplastic media at two levels of description is examined rigorously. At the micro-level the material response is heterogeneous, whereas at the macro-level it appears homogeneous. A broad class of constitutive relations is envisaged, and no restriction is placed on the magnitude of deformations and rotations at the micro-level. The investigation is concerned with quadratic differential forms that feature prominently in constitutive analyses, and is complementary to a previous study of bilinear differential forms. A principal objective is to access the transmissibility of measure-invariant inequalities from one level to the other.
A note on random walks in multidimensional time
Authors: Galambos Janos , Kátai Imre 
Published: November 2008

Let Kr denote the set of r-tuples n = (n1, n2, …, nr), r ≥ 1, where the components ni are positive integers. Let {X, Xn, n ∈ Kr} be a family of independent and identically distributed random variables with positive mean EX = μ < + ∞ and finite variance VX = σ2 < + ∞. In a recent work, M. Maejima and T. Mori [2] have shown that, if X is integer valued, aperiodic and E∣X∣3 < + ∞, then, for r = 2 or 3,wherethe summation being extended over all members j = (j1,j2, …, jr) of Kr that satisfy jt ≤ nt for all 1 ≤ t ≤ r.
Fronsdal *-quantization and Fell inducing
Authors: Hennings M. A. 
Published: November 2008

AbstractThe process of Fronsdal inducing is discussed as a method of quantizing physical systems, and is seen to reduce to a technique for obtaining representations of *-algebras.It is asked whether this above process is at all successful, and whether it is at all related to the representation inducing methods of Fell. The two inducing techniques are shown to be equivalent for algebras satisfying three specified properties, and it is also shown that all the strictly irreducible representations of such algebras can be found by these methods.Examples are produced whereby it is shown that algebras of the type required by the theory are of physical interest.
Estimates for polynomial norms on Lp(μ) spaces
Authors: Sarantopoulos I. 
Published: November 2008

AbstractIf L is a symmetric m-linear form on a Banach space and L^ is the associated polynomial thenFor special choices of Banach space this inequality can be improved. This has been done by Harris [5] in the case of the Lp(μ) spaces. In this paper we improve his estimates and disprove one of his conjectures.
Bernstein's theorem for compact, connected Lie groups
Authors: Gaudry Garth I. , Pini Rita 
Published: November 2008

In what follows, G will denote a compact, connected Lie group.Definition. A complex-valued function f ε L2(G) lies in the space A(G) if it can be written in the formwhereThe A(G) norm of f is the infimum of all sums (2) with respect to all decompositions (1).
A generalized Bernstein approximation theorem
Authors: Prolla João B. 
Published: November 2008

A celebrated theorem of Weierstrass states that any continuous real-valued function f defined on the closed interval [0, 1] ⊂ ℝ is the limit of a uniformly convergent sequence of polynomials. One of the most elegant and elementary proofs of this classic result is that which uses the Bernstein polynomials of fone for each integer n ≥ 1. Bernstein's Theorem states that Bn(f) → f uniformly on [0, 1] and, since each Bn(f) is a polynomial of degree at most n, we have as a consequence Weierstrass' theorem. See for example Lorentz [9]. The operator Bn, defined on the space C([0, 1]; ℝ) with values in the vector subspace of all polynomials of degree at most n has the property that Bn(f) ≥ 0 whenever f ≥ 0. Thus Bernstein's Theorem also establishes the fact that each positive continuous real-valued function on [0, 1] is the limit of a uniformly convergent sequence of positive polynomials. This raises the following natural question: consider a compact Hausdorff space X and the convex cone C+(X):= {f ∈ C(X; ℝ); f ≥ 0}. Now the analogue of Bernstein's Theorem would be a theorem stating when a convex cone contained in C+(X) is dense in it. More generally, one raises the question of describing the closure of a convex cone contained in C(X; ℝ), and, in particular, the closure of A+:= {f ∈ A; f ≥ 0}, where A is a subalgebra of C(X; ℝ).
Sequence spaces defined by a modulus
Authors: Maddox I. J. 
Published: November 2008

Ruckle[4] used the idea of a modulus function ƒ (see Definition 1 below) to construct the sequence spaceThis space is an FK space, and Ruckle proved that the intersection of all such L(f) spaces is ø, the space of finite sequences, thereby answering negatively a question of A. Wilansky: ‘Is there a smallest FK-space in which the set {e1, e2, …} of unit vectors is bounded?’
Corrigenda
Authors: Antman Stuart S. , Calderer M. Carme 
Published: November 2008

‘Asymptotic shapes of inflated noncircular elastic rings’‘Asymptotic shapes of inflated spheroidal nonlinearly elastic shells’Formulae (2·12) of both papers, giving an expression for the curvature, k̅, are wrong. To correct them, let ο(s) be the angle between r̅′ = ν̅a+ηb and i. Thenwhence formulae (3·2) of both papers imply thatFormula (C) corrects the erroneous expression for k by adding the second term on the right-hand side of (C). Since this term is of order ∈, the analysis in the remainder of both papers is unaffected by this correction. (The analyses of higher-order terms do not include a study of corrections to the curvature.)
On the fundamental group of the complement of certain singular plane curves
Authors: Némethi András 
Published: November 2008

Let C be a complex algebraic curve in the projective space ℙ2. The purpose of this paper is to calculate the fundamental group G of the complement of C in the case when C = X ∩ H1 ∩ … ∩ Hn−2, whereand Hi are generic hyperplanes (i = 1, … n − 2).
On elements of order four in certain free central extensions of groups
Authors: Stöhr Ralph 
Published: November 2008

Let F be a non-cyclic free group, R a normal subgroup of F and G = F/R, i.e.where π is the natural projection of F onto G, is a free presentation of G. Let R′ denote the commutator subgroup of R. The quotient F/[R′,F] is a free central extensionof the group F/R′, the latter being a free abelianized extension of G. While F/R′ is torsion-free (see, e.g. [2], p. 23), elements of finite order may occur in R′/[R′,F], the kernel of the free central extension (l·2). Since C. K. Gupta [1] discovered elements of order 2 in the free centre-by-metabelian group F/[F″,F] (i.e. (1·2) in the case R = F′), torsion in F/[R′,F] has been studied by a number of authors (see, e.g. [4–13]). Clearly the elements of finite order in F/[R′,F] form a subgroup T of the abelian group R′/[R′,F]. It will be convenient to write T additively. By a result of Kuz'min [5], any element of T has order 2 or 4. Moreover, it was pointed out in [5] that elements of order 4 may really occur. On the other hand, it has been shown in [11] that, if G has no 2-torsion, then T is an elementary abelian 2-group isomorphic to H4(G, ℤ2). So if T contains an element of order 4, then G must have 2-torsion. We also mention a result of Zerck [13], who proved that 2T is an invariant of G, i.e. it does not depend on the particular choice of the free presentation (1·1).
Periodic groups with permutable subgroup products
Authors: Longobardi Patrizia , Maj Mercede , Rhemtulla Akbar 
Published: November 2008

AbstractLet G be a group. If there exists an integer n > 1 such that for each n-tuple (H1, …, Hn) of subgroups of G there is a non-identity permutation σ of Σn such that the complexes H1,…Hn and Hσ(1)…Hσ(n) are equal, then G is said to have the property of permutable subgroup products, or to be a PSP group. We show that periodic groups with this property are locally finite and investigate the structure of such groups.
Uniform upper bounds for the complex divisor function
Authors: Hall R. R. 
Published: November 2008

The functionhas had several applications in the analytic theory of numbers. It was used by Ingham [10] to give a new proof that ζ(1 + iθ) ≠ 0. In [1] we introduced the modern notation on the left above and used τ(n, θ) to show that for almost all n the numbers log d are asymptotically uniformly distributed (mod 1). If we definethen it is known (Hall [2], Kátai[10]) that(where p.p. means ‘on a sequence of asymptotic density 1’). It is still an open problem whether or not we may strike out the term (log 4/π) = 0.24156 & from the exponent in (3).
On the geometry of harmonic morphisms
Authors: Gudmundsson Sigmundur 
Published: November 2008

AbstractLet π:M→B be a horizontally conformal submersion. We give necessary curvature conditions on the manifolds M and B, which lead to non-existence results for certain horizontally conformal maps, and harmonic morphisms. We then classify all such maps between open subsets of Euclidean spaces, which additionally have totally geodesic fibres and are horizontally homothetic. They are orthogonal projections on each connected component, followed by a homothety.
Effective mean value estimates for complex multiplicative functions
Authors: Hall R. R. , Tenenbaum G. 
Published: November 2008

Quantitative estimates for finite mean valuesof multiplicative functions are highly applicable tools in analytic and probabilistic number theory. Extending a result of Hall [4], Halberstam and Richert[3] proved a useful inequality valid for real, non-negative g satisfying for instance a Wirsing type condition, viz for all primes p, with constants λ1 ≥ 0, 0 ≤ λ2 < 2. Their upper bound is sharp to within a factor (l + o(l)), but even a weaker and easier to prove estimate, such as(where the implied constants depend on λ1 and λ2), may become a surprisingly strong device. For instance, setting g(p) = l ± ε, where ε is an arbitrarily small positive number, provides immediately a proof of the famous Hardy–Ramanujan theorem on the normal order of the number of prime factors of an integer. This example, and many others, are discussed in detail in our book [5] where we make extensive use of (2) for various problems connected with the structure of the set of divisors of a normal number.
Hall–Littlewood polynomials at roots of 1 and modular representations of the symmetric group
Authors: Morris A. O. , Sultana N. 
Published: November 2008

We first give a brief introduction to Hall–Littlewood functions; we follow closely the notation used in Macdonald [3].Let λ = (λ1,…,λm) be a be a partition of n; that is λ1 + … + λm = n, λ1 ≥ λ2 ≥ … ≥ λm >0. We shall sometimes write l(λ) for m and refer to l(λ) as the length of λ and we shall write |λ| for ∑λi. Let x1, x2, … be an infinite set of indeterminates and t an indeterminate independent of the xi (i = 1,2, …). Let Pλ(x;t) = Pλ(x1, x2, …t) and Qλ(x,t) = Qλ(xl, x2, …t) be the Hall–Littlewood P- and Q-functions defined as in Macdonald.
Fractional parts of powers of rational numbers
Authors: Bennett M. 
Published: November 2008

AbstractThe author uses Padé approximation techniques and an elementary lemma on primes dividing binomial coefficients to sharpen a theorem of F. Beukers on fractional parts of powers of rationals. In particular, it is proven that ‖((N+ l)/N)k‖ > 3–k holds for all positive integers N and k satisfying 4 ≤ N ≤ k · 3k. Other results are described including an effective version of a theorem of K. Mahler for a restricted class of rationals.
On Ford isometric spheres in complex hyperbolic space
Authors: Parker John R. 
Published: November 2008

AbstractThe complex hyperbolic version of Shimizu's lemma gives an upper bound on the radii of isometric spheres of maps in a discrete subgroup of PU(n, 1) containing a vertical Heisenberg translation. The purpose of this paper is to show that in a neighbourhood of this bound radii of isometric spheres only take values in a particular discrete set. When the group contains certain ellipto-parabolic maps this upper bound can be improved and the set of values of the radii is more restricted. Examples are given that show that these results cannot be improved.
Hausdorff dimension of sets of non-differentiability points of Cantor functions
Authors: Darst Richard 
Published: November 2008

AbstractEach number a in the segment (0, ½) produces a Cantor set, Ca, by putting b = 1 − 2a and recursively removing segments of relative length b from the centres of the interval [0, 1] and the intervals which are subsequently generated. The distribution function of the uniform probability measure on Ca is a Cantor function, fa. When a = 1/3 = b, Ca is the standard Cantor set, C, and fa is the standard Cantor function, f. The upper derivative of f is infinite at each point of C and the lower derivative of f is infinite at most points of C in the following sense: the Hausdorff dimension of C is ln(2)/ln(3) and the Hausdorff dimension of S = {x ∈ C: the lower derivative of f is finite at x} is [ln(2)/ln(3)]2. The derivative of f is zero off C, the derivative of f is infinite on C — S, and S is the set of non-differentiability points of f. Similar results are established in this paper for all Ca: the Hausdorff dimension of Ca is ln (2)/ln (1/a) and the Hausdorff dimension of Sa is [ln (2)/ln (1/a)]2. Removing k segments of relative length b and leaving k + 1 intervals of relative length a produces a Cantor set of dimension ln(k + l)/ln(1/a); the dimension of the set of non-differentiability points of the corresponding Cantor function is [ln (k + l)/ln (1/a)]2.
An example concerning Alexeev's boundedness results on log surfaces
Authors: Blache Raimund 
Published: November 2008

AbstractIn this note, we construct a sequence of l.t. surfaces (Xn)n ∈ ℕ such that KXn is ample for all n and such that (K2Xn)n ∈ ℕ is a strictly increasing series with limit equal to 1. This answers (in the affirmative) a question by Alexeev, cf. [Al], 11·1. Here, an l.t. surface is a normal complex projective surface with at most quotient singularities (which is the same as ‘at most log terminal singularities’). A main result of [Al] implies that it is impossible to find a sequence (Xn)n ∈ ℕ of l.t. surfaces with KXn ample for all n such that K2Xn is strictly decreasing. Although our construction is not too difficult, the example is new and has several interesting implications, see Section 4.Without further explanation, we use some fundamental tools concerning l.t. surfaces like Mumford's intersection theory or the notion of minimality; the reader should consult [Blb] and the references quoted there.
Pointwise convergence of spherical means
Authors: Seeger Andreas , Wainger Stephen , Wright James 
Published: November 2008

For a function f ∈ Lp(ℝd) we define the spherical meanswhere dσ is the rotationally invariant measure on Sd−1, normalized such that σ(Sd−1) = 1. We consider the problem of pointwise convergence of the means , for any particular sequence tj → 0.
Strong and weak duality principles for fractal dimension in Euclidean space
Authors: Cutler Colleen D. 
Published: November 2008

AbstractTricot [27] provided apparently dual representations of the Hausdorff and packing dimensions of any analytic subset of Euclidean d-space in terms of, respectively, the lower and upper pointwise dimension maps of the finite Borel measures on ℝd. In this paper we show that Tricot's two representations, while similar in appearance, are in fact not duals of each other, but rather the duals of two other ‘missing’ representations. The key to obtaining these missing representations lies in extended Frostman and antiFrostman lemmas, both of which we develop in this paper. This leads to the formulation of two distinct characterizations of dim (A) and Dim (A), one which we call the weak duality principle and the other the strong duality principle. In particular, the strong duality principle is concerned with the existence, for each analytic set A, of measures on A that are (almost) of the same exact dimension (Hausdorff or packing) as A. The connection with Rényi (or information) dimension and a variational principle of Cutler and Olsen[12] is also established.
Compact tripotents in bi-dual JB*-triples
Authors: Edwards C. Martin , Rüttimann Gottfried T. 
Published: November 2008

AbstractThe set consisting of the partially ordered set of tripotents in a JBW*-triple C with a greatest element adjoined forms a complete lattice. This paper is mainly concerned with the situation in which C is the second dual A** of a complex Banach space A and, more particularly, when A is itself a JB*-triple. A subset of consisting of the set of tripotents compact relative to A (denned in Section 4) with a greatest element adjoined is studied. It is shown to be an atomic complete lattice with the properties that the infimum of an arbitrary family of elements of is the same whether taken in or in and that every decreasing net of non-zero elements of has a non-zero infimum. The relationship between the complete lattice and the complete lattice where B is a Banach space such that B** is a weak*-closed subtriple of A** is also investigated. When applied to the special case in which A is a C*-algebra the results provide information about the set of compact partial isometries relative to A and are closely related to those recently obtained by Akemann and Pedersen. In particular it is shown that a partial isometry is compact relative to A if and only if, in their terminology, it belongs locally to A. The main results are applied to this and other examples.
Semigroups whose idempotents form a subsemigroup
Authors: Almeida J. , Pin J.-E. , Weil P. 
Published: November 2008

AbstractWe prove that every semigroup S in which the idempotents form a subsemigroup has an E-unitary cover with the same property. Furthermore, if S is E-dense or orthodox, then its cover can be chosen with the same property. Then we describe the structure of E-unitary dense semigroups. Our results generalize Fountain's results on semigroups in which the idempotents commute, and are analogous to those of Birget, Margolis and Rhodes, and of Jones and Szendrei on finite E-semigroups.
Knots, matroids and the Ising model
Authors: Schwärzler W. , Welsh D. J. A. 
Published: November 2008

AbstractA polynomial is defined on signed matroids which contains as specializations the Kauffman bracket polynomial of knot theory, the Tutte polynomial of a matroid, the partition function of the anisotropic Ising model, the Kauffman–Murasugi polynomials of signed graphs. It leads to generalizations of a theorem of Lickorish and Thistlethwaite showing that adequate link diagrams do not represent the unknot. We also investigate semi-adequacy and the span of the bracket polynomial in this wider context.
Convergence in distribution of lightly trimmed and untrimmed sums are equivalent
Authors: Kesten Harry 
Published: November 2008

AbstractWe show that trimming a fixed number of terms from sums of i.i.d. random variables (so-called light trimming) can have only a modest effect on limiting behaviour. More specifically, the trimmed sums, after centralization and normalization, have a limit distribution, if and only if the untrimmed sums have a limit distribution (with the same centralization and normalization constants).
A “Scale-of-two” High-Speed Counter Using Hard Vacuum Triodes
Authors: Lewis W. B. 
Published: November 2008

A high-speed recording counter circuit is described which has proved very reliable. The basic circuit element employs two triodes in a symmetrical circuit which has two stable conditions. The circuit is triggered alternately from one stable state to the other by the applied impulses acting through a circuit comprising two “Westector” cuprous oxide rectifiers and an inductance.It is easily possible to make a counter operate accurately at a speed of 20,000 random impulses a minute, provided that the associated recording meter operates in less than 1/100 sec.A “watch-dog” thyratron recording circuit is also described. This is useful where the slow speed of the mechanical recording meter would introduce loss.
Modelling operating system structures by timed stream processing functions
Authors: Broy Manfred , Dendorfer Claus 
Published: November 2008

AbstractSome extensions of the basic formalism of stream processing functions are useful to specify complex structures such as operating systems. In this paper we give the foundations of higher order stream processing functions. These are functions which send and accept not only messages representing atomic data, but also complex elements such as functions. Some special notations are introduced for the specification and manipulation of such functions. A representation of time is outlined, which enables us to model time dependent behaviour. Finally, we demonstrate how characteristic operating system structures can be modelled by timed higher order stream processing functions.