bluuebunny/crossref_metadata_2025_split huggingface dataset:
A simple proof of Müntz's theorem
Authors: Rogers L. C. G. 
Published: November 2008

Let 0 < λ1 < λ2 < … be an increasing sequence of positive reals tending to infinity, and let ν1, ν2 be two (finite) signed measures on ℝ+ such thatfor all k. It was originally proved by Müntz (12) that, ifthen ν1 = ν2, and, conversely, if this condition fails, then there exist distinct ν1 and ν2 satisfying (1).
Small fractional parts of quadratic and additive forms
Authors: Baker R. C. , Harman G. 
Published: November 2008

We denote by ∥…∥ the distance to the nearest integer. Let ε be an arbitrary positive number. Danicic(6) showed that for N > c1(s, ε) and a quadratic form Q(x1, …, xs) there exist integers n1, …, ns withhaving
Norm preserving interpolation sets for polydisc algebras
Authors: Globevnik Josep 
Published: November 2008

AbstractLet N > 1 and let AN be the polydisc algebra, i.e. the algebra of all continuous functions on the closed polydisc δ¯N ⊂ N, analytic on the open polydisc δN, with sup norm. Call a closed set F ⊂ δ¯N a peak interpolation set for AN if given any f ε C(F), f ≠ 0, there is an extension f ε AN of f such that ¦f˜(z)¦ < ‖ f ‖ (z ε δ¯N - F); call F a norm preserving interpolation set for AN if given any f ε C(F) there is an extension f˜ ε AN of f such that ‖f˜‖ = ‖f‖. The paper gives a complete description of norm preserving interpolation sets for AN in terms of peak interpolation sets for AM, M ≤ N.
On the tangent developable of a space curve
Authors: Mond David 
Published: November 2008

SummaryIn this paper we investigate the local form of the tangent developable of a curve in 3-space, and obtain results relating this to the order of vanishing of the torsion. In particular,Theorem 1. If at the point γ(t) on the curve γ, the torsion vanishes to order k (0 ≼ k ≼ 4), then the germ of the tangent developable at that point has one curve of self intersection if k is odd, and none if k is even.
On a class of non-homogeneous Markov chains
Authors: Cohn Harry 
Published: November 2008

AbstractSuppose that {Xn} is a countable non-homogeneous Markov chain andIf converges for any i, l, m, j with , thenwhenever lim , whereas if converges, thenwhere and . The behaviour of transition probabilities between various groups of states is studied and criteria for recurrence and transience are given.
On 2-dimensional local rings with Artin's approximation property
Authors: Brown M. L. 
Published: November 2008

AbstractExtending results of Popescu and Brown, the main result of this paper is that excellent henselian R1 and S1 2-dimensional local rings, at least in characteristic zero, have the approximation property of M. Artin.Most of the paper consists of an extension of Néron's desingularization to rings which are R1 and S1; such a theorem was previously known for factorial domains. The main theorem is then deduced from this desingularization theorem using a theorem of Elkik.Because of cohomological obstructions, the desingularization theorem is proved only for quasi-projective varieties. In the previously known case for factorial domains, these obstructions are always zero and the desingularization can be obtained by blowing up subschemes. The more general desingularization of this paper is obtained by blowing up locally free sheaves instead, the obstructions being zero for this case.
Homogeneous elements of free algebras have free idealizers
Authors: Dicks Warren 
Published: November 2008

AbstractLet k be a field, X a set, F = k 〈X〉 the free associative k-algebra, and b an element of F that is homogeneous with respect to the grading of F induced by some map . We show that the idealizer of b in F, S = {f∈F|fb∈bF}, is a free algebra.
Diophantine approximation and Dirichlet series
Authors: Everest G. R. 
Published: November 2008

1. Given a sequence an of positive integers, one expects to obtain information on the distribution of these numbers by examining the Dirichlet seriesIn this paper we are going to show how such a series arises from Fröhlich's Galoismodule theory and the use the Thue–Siegel–Roth–Schmidt Theorem as one of the tools in the study of its singularities.
A note on k-uniformly convex spaces
Authors: Bae Jong Sook , Choi Sung Kyu 
Published: November 2008

AbstractIn this short note we prove that Istrǎƫescu's notion of k-uniform (k-locally uniform) convexity of a Banach space is actually equivalent to the notion of uniform (locally uniform) convexity. Thus theorem 2 in [3] and theorem 2·6·28 in [2] are trivially true.
On the Fourier series of a finitely described convex curve and a conjecture of H. S. Shapiro
Authors: Sheil-Small T. 
Published: November 2008

AbstractLet F(eis) denote a homeomorphism of the positively oriented unit circle onto a convex curve Γ and let f (eit) = F(eiΦ(t)), where Φ(t) is a non-decreasing function such that Φ(2π) – Φ(0) ≤ 2πN (N a positive integer). If f (eit) has Fourier coefficients cn, we show that is either constant or an N -valent analytic function in {|z| < 1}. We prove that where d is the distance from 0 to Γ and δ(N) > 0 depends only on N. This settles affirmatively a conjecture of H. S. Shapiro.
Proper pointed maps from ℝn+1to a σ-compact space
Authors: Hernandez Luis J. , Porter Timothy 
Published: November 2008

AbstractIn this paper we study the group of pointed proper homotopy classes of proper pointed maps from (ℝn+1, 0) to a pointed σ-compact space (X, x) and prove the existence of a diagram of exact sequences linking the groups with the Brown—Grossman groups, the Steenrod groups πn(X) and the classical Hurewicz homotopy groups πn(X).
Interpolation by analytic functions on c0
Authors: Aron Richard M. , Globevnik Josip 
Published: November 2008

AbstractLet B be the open unit ball of c0. We give a geometric characterization of the sequences {xn} ⊂ bB with the property that, given any bounded sequence {αn} ⊂ ℂ, there is a continuous function , analytic in B, such that f(xn) = αn for all n and such that supi∈B|f(x)| = supn∈N|αn|.
On the Lk-UR and L-kR spaces
Authors: Chao-Xun Nan , Jian-Hua Wang 
Published: November 2008

AbstractIn this paper, we prove that if X is a strictly convex Lk-UR space, then X is an L-kR space. However, the converse need not be true. Also, for each k ≥ 2, there exists a Lk-UR space which is URED but is not L-(k – 1)R.
Certain mapping properties of rational complex planar splines
Authors: Dikshit H. P. , Ojha A. , Sharma A. 
Published: November 2008

SummaryConsidering a certain partition of a given compact region in the complex plane, interpolatory, convergence and quasiconformal properties of interpolants from the class of continuous piecewise functions with pieces as quadratic polynomials in z and were studied recently in [3] and [7]. In the present paper we succeed in showing that the foregoing mapping properties continue to hold for interpolants from a certain class of continuous piecewise rational polynomial functions in z and
When rings of differential operators are maximal orders
Authors: Chamarie M. , Stafford J. T. 
Published: November 2008

AbstractLet A be a commutative domain, finitely generated as an algebra over a field k of characteristic zero and write (A) for the ring of k -linear differential operators. Then A is an Ore domain with quotient division ring, say Q. Our main result is that A is a maximal order in Q if and only if (i) A = ∩{Ap: height (p) = 1} and (ii) A is geometrically unibranched. In this case A is also a Krull domain with no reflexive ideals. We also determine some conditions under which A is simple.
Banach algebras whose duals consist of multipliers
Authors: Oshobi E. O. , Pym J. S. 
Published: November 2008

A few years ago, the authors considered briefly Banach algebras whose duals could be identified ‘naturally’ with their multiplier algebras [17]. In this context, naturalness can be interpreted as meaning that, for each element b of the algebra B and each pair of elements u, v of the dual B′,where 〈, 〉 denotes the dual pairing and the products are of elements of B′ regarded as left or right multipliers on B. In the present paper we return to the same circle of ideas but begin with a more general situation. We assume only that the algebra B is injectively embedded in its algebra of left, and in its algebra of right, multipliers and that its dual B′ can be injectively embedded in the algebra M(B) of double multipliers on B (definition below) in such a way that the above relation holds. From these assumptions we shall prove that there is a normed algebra A such that M(B) is the dual of A and is the algebra of continuous left multipliers on A (or, equally, right multipliers).
A note on a theorem of Stanton-Weinstein on the L4-norm of spherical harmonics
Authors: Lu Jiang-Hua 
Published: November 2008

1. Let El (l = 0,1,2, …) be the eigenspaces of the Laplacian on the standard 2-sphere S2. Consider the function r2. 4: El −{0} → R given byStanton and Weinstein proved in [1] that r2, 4 was locally maximized by the ‘highest weight’ function . This note is to simplify part of their proof, namely that of the negativity of .
Tempered distributions with spectral gaps
Authors: Gabardo Jean-Pierre 
Published: November 2008

AbstractA tempered distribution on ℝ whose Fourier transform is supported in an interval [−Ω,Ω], where Ω>0, can be characterized by the behaviour of its successive derivatives. On the other hand, a tempered distribution on ℝ whose Fourier transform vanishes in an interval (−Ω,Ω), where Ω>0, can be characterized by the behaviour of a particular sequence of successive antiderivatives. Similar considerations apply to general convolution operators acting on J′(ℝn) and yield characterizations for tempered distributions having their Fourier transforms supported in sets of the form or , where and Ω>0.
Uniqueness of solutions for a class of non-linear Volterra integral equations with convolution kernel
Authors: Bushell P. J. , Okrasinski W. 
Published: November 2008

The non-linear Volterra integral equationhas been studied recently in connection with non-linear diffusion and percolation problems [4, 6, 10]. The existence, uniqueness and qualitative behaviour of non-negative, non-trivial solutions are the questions of physical interest.
Geometric interpretations of the ‘natural’ generators of the Mathieu groups
Authors: Curtis R. T. 
Published: November 2008

AbstractIn [1] we used the alternating group A5 to produce a set of five permutations of order three acting on 12 letters; this set was normalized by A5 and generated the Mathieu group M12. We analogously used the linear group PSL2(7) to produce a set of seven involutions acting on 24 letters which was normalized by our PSL2(7) and generated M24. In this paper we describe the combinatorial and geometric interpretations of our generators, and aim to justify our use of the word ‘natural’. The generators for M12 are defined both as permutations of twelve 5-cycles in a conjugacy class of A5, and as permutations of the faces of a dodecahedron. The outer automorphism of M12 emerges as a bonus. The generators of M24 are defined analogously both as permutations of twenty-four 7-cycles in the action of PSL2(7) on seven letters, and as permutations of the 24 faces of a certain cubic graph drawn on a surface of genus three. In addition we mention the connection between the latter construction and the binary Golay code.
Structure theory for L*-algebras
Authors: Cuenca Mira José Antonio , Martín Amable García , González Cándido Martín 
Published: November 2008

AbstractThe structure theory of separable complex L*-algebras was given by Schue in [10] and [11]. In [3] Balachandran makes a study of infinite-dimensional complex topologically simple L*-algebras of classical type and poses the question whether these algebras exhaust the class of all infinite-dimensional complex topologically simple L*-algebras. In this paper we give an affirmative answer by determining all the complex topologically simple infinite-dimensional L*-algebras. The case of the real L*-algebras was studied previously in [4], [9] and [12] also under the separability condition. Applying the result of Balachandran, our result yields the structure theory for real L*-algebras. The main tool used here is the ‘approximation’ of the L*-algebra by topologically simple separable L*-algebras via an ultraproduct construction.
Closure properties of the quasi-centre of a Banach algebra
Authors: Rennison J. F. 
Published: November 2008

Throughout the paper, A will denote a unital Banach algebra with centre Z over the complex field ℂ. An element a of A is called quasi-central if, for some K ≥ 1,The set of elements a satisfying (1) for a particular value of K will be denoted by Q(K) and Q = UK≥1Q(K) will be called the quasi-centre of A.
Radial variation of analytic functions with non-tangential boundary limits almost everywhere
Authors: Hallenbeck D. J. , Samotij K. 
Published: November 2008

The purpose of this paper is to investigate the asymptotic behaviour as r → 1− of the integralsand f is an analytic function on the unit disk Δ which has non-tangential limits at almost every point on ∂Δ. The paper is divided into three parts. In the first part we consider the case where λ ≠ 1/k, in the second the somewhat more delicate case when λ = 1/k and in the third part we concentrate on some problems related to the case λ = k = 1.
A torus reduction theorem for regular coverings of 3-manifolds by homology 3-spheres
Authors: Luft E. , Sjerve D. 
Published: November 2008

AbstractFor any regular covering p:M→M of 3-dimensional manifolds M, M with M a homology 3-sphere we construct a regular covering p′: M′ → M′ of 3-manifolds M′, M′ with the same group of covering transformations and a degree 1 map f:M → M′ so that M′ is a homology 3-sphere, M′ (and hence M′) is irreducible and does not contain incompressible tori, and the regular covering p:M→M is induced from the regular covering p′: M′ → M′ by the map f. Assuming Thurston's geometrization conjecture it follows that M′ (and hence M′) is either hyperbolic or Seifert fibred.
Constructive complete distributivity II
Authors: Rosebrugh Robert , Wood R. J. 
Published: November 2008

AbstractA complete lattice, L, is constructively completely distributive, (CCD) (L), if the sup map defined on down-closed subobjects has a left adjoint. It was known that in Boolean toposes (CCD) (L) is equivalent to (CCD) (Lop). We show here that the latter property for all L (sufficiently, for Ω.) characterizes Boolean toposes.
Bifurcation in the traction problem for a transversely isotropic material
Authors: Danescu A. 
Published: November 2008

SummaryThe traction problem for a transversely isotropic incompressible elastic material is considered, and it is shown that when only pure homogeneous deformations are considered, the problem can be formulated as a two-dimensional ℤ2-equivariant bifurcation problem in which the bifurcation parameter is the dead-load. Using imperfect bifurcation theory, conditions for bifurcation phenomena are given and, considering a general non-linear form for the stored energy function, the recognition problem is solved in the simplest cases. The last section treats transversely isotropic non-linear perturbations for a Mooney–Rivlin material and a neo-Hookean material and the corresponding bifurcations.
The mod-p cohomology rings of some p-groups
Authors: Leary I. J. 
Published: November 2008

Throughout this paper p denotes an odd prime. The groups we shall consider are central extensions of a cyclic subgroup by Cp ⊕ Cp, and may be presented asThe group P(n) is defined for each n ≥ 3, and has order pn. The group P(3) is the non-abelian group of order p3 and exponent p. The mod-p cohomology rings of the other groups of order p3 have been known for some time (see [14] or [5] for that of the non-abelian metacyclic group), and so this paper completes the calculation of the mod-p cohomology rings of the groups of order p3.
On pairs of additive forms modulo one
Authors: Schäffer S. 
Published: November 2008

Throughout this paper ∈ denotes an arbitrary positive number. For real α, ‖α‖ denotes the distance from α to the nearest integer. For natural numbers k we write K = 2k−1. In 1948 Heilbronn [8] showed that for any real α and N > C1(∈)This theorem has since been generalized in many ways. In particular, results of the following type have been proved for natural numbers k ≥ 2, h = 1,2 and s.
On Behrend sequences
Authors: Hall R. R. , Tenenbaum G. 
Published: November 2008

Let denote a sequence of integers exceeding 1, and let τ(n, ) be the number of those divisors of n which belong to . We say that is a Behrend sequence ifwhere, here and in the sequel, we use the notation p.p. to indicate that a relation holds on a set of asymptotic density one.
Uniform annihilation of local cohomology and of Koszul homology
Authors: Raghavan K. 
Published: November 2008

Let R be a ring (all rings considered here are commutative with identity and Noetherian), M a finitely generated R-module, and I an ideal of R. The jth local cohomology module of M with support in I is defined byIn this paper, we prove a uniform version of a theorem of Brodmann about annihilation of local cohomology modules. As a corollary of this, we deduce a generalization of a theorem of Hochster and Huneke about uniform annihilation of Koszul homology.
Symmetry characterizations of certain distributions, 2: Discounted additive functionals and large deviations
Authors: Baxter Martin , Williams David 
Published: November 2008

This paper may be read independently of Baxter and Williams [1], hereinafter denoted by [BW1].As in [BW1], we are mainly concerned with discounted additive functionals. We find that the large-deviation behaviour of the average depends on the precise average used. We derive, in certain cases, a link (but not equality) between the Cesàro average and Abel average limits, and would expect that other averages would produce other limiting behaviours. We have focused on the exponentially discounted (Abel average) case, both because of its tractability and because of its frequent appearance in decision/control problems and models of financial markets. We do give in subsection (e) the promised ‘excursion’ treatment of symmetry characterizations of the type announced in [BW1]; and this new treatment is simpler, more illuminating and more general. First, however, we focus attention on a different kind of asymptotic behaviour from that studied in [BW1], and on differential equations for exact results.
Hermitian–Einstein metrics and jumping lines forSp(n+1)-homogeneous bundles over ℙ2n+1
Authors: Vitter Al 
Published: November 2008

Stable holomorphic vector bundles over complex projective space ℙnhave been studied from both the differential-geometric and the algebraic-geometric points of view.On the differential-geometric side, the stability ofE-→ ℙncan be characterized by the existence of a unique hermitian–Einstein metric onE, i.e. a metric whose curvature matrix has trace-free part orthogonal to the Fubini–Study Kähler form of ℙn(see [6], [7], and [13]). Very little is known about this metric in general and the only explicit examples are the metrics on the tangent bundle of ℙnand the nullcorrelation bundle (see [9] and [10]).
The packing measure of self-affine carpets
Authors: Peres Yuval 
Published: November 2008

AbstractWe show that the seif-affine sets considered by McMullen [15] and Bedford [2] have infinite packing measure in their packing dimension θ except when all non-empty rows of the initial pattern have the same number of rectangles. More precisely, the packing measure is infinite in the gauge tθ|logt|−1 and zero in the gauge tθ|logt|−1−δ for any δ > 0.
The ideal lattices of the complex group rings of finitary special and general linear groups over finite fields
Authors: Hartley B. , Zalesskii A. E. 
Published: November 2008

Letqbe a prime power, which will be fixed throughout the paper, letkbe a field, and letbe the field withqelements. LetGn(k)be the general linear groupGL(n, k), andSn(k)the special linear groupSL(n, k). The corresponding groups overwill be denoted simply byGnandSn. We may embedGn(k)inGn+1(k)via the mapForming the direct limit of the resulting system, we obtain thestable general linear groupG∞(k) overk.
Almost transitivity of some function spaces
Authors: Greim Peter , Jamison James E. , Kamińska Anna 
Published: November 2008

AbstractThe almost transitive norm problem is studied for Lp (μ, X), C(K, X) and for certain Orlicz and Musielak-Orlicz spaces. For example if p ≠ 2 < ∞ then Lp (μ) has almost transitive norm if and only if the measure μ is homogeneous. It is shown that the only Musielak-Orlicz space with almost transitive norm is the Lp-space. Furthermore, an Orlicz space has an almost transitive norm if and only if the norm is maximal. Lp (μ, X) has almost transitive norm if Lp(μ) and X have. Separable spaces with non-trivial Lp-structure fail to have transitive norms. Spaces with nontrivial centralizers and extreme points in the unit ball also fail to have almost transitive norms.
The self-affine carpets of McMullen and Bedford have infinite Hausdorff measure
Authors: Peres Yuval 
Published: November 2008

AbstractWe show that the self-affine sets considered by McMullen in [11] and by Bedford in [1] have infinite Hausdorff measure in their dimension, except in the (rare) cases where the Hausdorff dimension coincides with the Minkowski (≡ box) dimension. More precisely, the Hausdorff measure of such a self-affine set K is infinite in the gauge(where γ is the Hausdorff dimension of K, and c > 0 is small). The Hausdorff measure of K becomes zero if 2 is replaced by any smaller number in the formula for the gauge ø.
Looking at bent wires – -codimension and the vanishing topology of parametrized curve singularities
Authors: Mond David 
Published: November 2008

Projecting a knot onto a plane – or, equivalently, looking at it through one eye – one sees a more or less complicated plane curve with a number of crossings (‘nodes’); viewing it from certain positions, some other more complicated singularities appear. If one spends a little time experimenting, looking at the knot from different points of view, then provided the knot is generic, one can convince oneself that there is only a rather short list of essentially distinct local pictures (singularities) – see Fig. 3 below. All singularities other than nodes are unstable: by moving one's eye slightly, one can make them break up into nodes. For each type X the following two numbers can easily be determined experimentally:1. the codimension in ℝ3 of the set View(X) of centres of projection (viewpoints) for which a singularity of type X appears, and2. the maximum number of nodes n into which the singularity X splits when the centre of projection is moved.
Reflexivity for a class of subspace lattices
Authors: Katsoulis E. G. 
Published: November 2008

AbstractThe complete lattice generated by a totally atomic CSL ℒ and the projection lattice of a von Neumann algebra ℛ, commuting with ℒ, is reflexive. From this it follows that the strongly closed lattice generated by any CSL ℒ and the projection lattice of a properly infinite von Neumann algebra ℛ, commuting with ℒ, is reflexive.