bluuebunny/crossref_metadata_2025_split huggingface dataset:
The natural ordering on a strictly real Banach algebra
Authors: Miller John Boris 
Published: November 2008

AbstractA strictly real unital Banach algebra is one in which every element has real spectrum. An antilattice partial order and its associated open-interval topology are defined on by taking as positive cone the principal component of the maximal group of the algebra, and their properties are studied. The topology coincides with the semimetric topology of the spectral radius, which is a seminorm, making into a locally convex partially ordered topological algebra with continuous inversion and normal cone. Every positive element has a unique positive square root, and logarithm, and these functions and exp are continuous and monotone. The cone has the same closure in both open-interval and normal topologies, the closure being a wedge for an associated preorder on , this preorder coinciding with the preorder of Kelley and Vaught. The partial order and the associated preorder have the same dual cone. There is a modified Gelfand representation for (possibly non-commutative) , and a boundary integral representation for functionals in the order dual. The compact convex subset in the dual is metrizable if the cone of the partial order in is separable.
Annihilators in JB-algebras
Authors: Battaglia M. 
Published: November 2008

AbstractOrthogonality is defined for all elements in a JB-algebra and Topping's results on annihilators in JW-algebras are generalized to the context of JB- and JBW-algebras. A pair (a, b) of elements in a JB-algebra A is said to be orthogonal provided that a2 ∘ b equals zero. It is shown that this relation is symmetric. The annihilator S⊥ of a subset S of A is defined to be the set of elements a in A such that, for all elements s in S, the pair (s, a) is orthogonal. It is shown that the annihilators are closed quadratic ideals and, if A is a JBW-algebra, a subset I of A is a w*-closed quadratic ideal if and only if I coincides with its biannihilator I⊥⊥. Moreover, in a JBW-algebra A the formation of the annihilator of a w*-closed quadratic ideal is an orthocomplementation on the complete lattice of w*-closed quadratic ideals which makes it into a complete orthomodular lattice. Further results establish a connection between ideals, central idempotents and annihilators in JBW-algebras.
Weak precompactness, strong boundedness, and weak complete continuity
Authors: Abbott Catherine A. , Bator Elizabeth M. , Bilyeu Russell G. , Lewis Paul W. 
Published: November 2008

AbstractWeak precompactness in spaces of vector measures and in the space of Bochner integrable functions is studied. Uniform countable additivity and uniform integrability are characterized in terms of weak precompactness. Through this, a connection between strongly bounded operators and operators having weakly precompact adjoints on abstract continuous function spaces is established. These operators are compared with weakly completely continuous operators.
Short intervals containing numbers without large prime factors
Authors: Harman Glyn 
Published: November 2008

We denote, as usual, the number of integers not exceeding x having no prime factors greater than y by Ψ(x, y). We also writeThe function Ψ(x, y) is of great interest in number theory and has been studied by many researchers (see [3], [5] and [6] for example). The function Ψ(x, z, y) has also received some attention (see [2], [4–6]). In this paper we shall try to obtain a positive lower bound for Ψ(x, z, y) with y as small as possible when z is about x½ in magnitude. We note that the approach in [5] and [6] allows y to be much smaller than is permissible here, but requires x/z to be smaller than any power of x in [6] (unless some conjecture like the Riemann Hypothesis is assumed), or needs in [5]. The following result was obtained by Balog[1].
On the reciprocal Dunford-Pettis property in projective tensor products
Authors: Emmanuele G. 
Published: November 2008

AbstractWe prove the following result: if a Banach space E does not contain l1 and F has the (RDPP), then E ⊗nF has the same property, provided that L(E, F*) = K(E, F*). Hence we prove that if E ⊗n F has the (RDPP) then at least one of the spaces E and F must not contain l1. Some corollaries are then presented as well as results concerning the necessity of the hypothesis L(E, F*) = K(E, F*).
Is every quartic a conic of conics?
Authors: Wall C. T. C. 
Published: November 2008

The question of the title is to be interpreted as follows. Given a homogeneous nonzero quartic polynomial ø(x1, x2, x3), can one always find homogeneous quadraticsc, q1, q2, q3in three variables such thatI am indebted to Ulf Persson for asking this question, the answer to which is intimately related to the singularities of the projective quartic curve Γ defined by ø = 0. We work throughout over the field ℂ of complex numbers.
Analytic functions with values in lattices and symmetric spaces of measurable operators
Authors: Xu Quanhua 
Published: November 2008

AbstractLet 0 < p,pi ≤ ∞, 0 < q,qi < ∞ (i = 1, 2) such thatLet E be a quasi-Banach lattice which fails to contain c0 and whose α-convexity constant is equal to 1 for some 0 < α < ∞. Then for every f∈H(E(q)) there exist g∈Hp, 0(E(q0)), h∈Hp1(E(q1)) such thatConsequently, E is q-concave for some finite q if and only if E is uniformly H1-convexifiable in the sense of [24]. Analogous results are also obtained for symmetric spaces of measurable operators. Another result proved in the paper says that if E is a symmetric quasi-Banach function space on (0, ∞) having the analytic Radon–Nikodym property then LE(M, τ) also possesses this property for any semifinite von Neumann algebra (M, τ).
Covering a sphere by equal circles, and the rigidity of its graph
Authors: Tarnai T. , Gáspár Zs. 
Published: November 2008

AbstractHow must a sphere be covered by n equal circles so that the angular radius of the circles will be as small as possible? In this paper, conjectured solutions of this problem for n = 15 to 20 are given and some sporadic results for n > 20 (n = 22, 26, 38, 42, 50) are presented. The local optima are obtained by using a ‘cooling technique’ based on the theory of bar-and-joint structures. Thus the graph of the coverings by circles is considered as a spherical cable net in which the edge lengths are uniformly decreased, e.g. due to a uniform decrease in the temperature, until the graph becomes rigid and tensile stresses appear in the cables.
Dimensions associated with recurrent self-similar sets
Authors: Deliu Anca , Geronimo J. S. , Shonkwiler R. , Hardin D. 
Published: November 2008

AbstractThe Hausdorff and box dimensions for measures associated with recurrent self-similar sets generated by similitudes is explicitly given. The box dimension of the attractor associated with a class of two-dimensional affine maps is also computed.
Asymptotic distributions of weighted compound Poisson bridges
Authors: Szyszkowicz Barbara 
Published: November 2008

Let S(N(t)) be defined bywhere {N(t), t ≥ 0} is a Poisson process with intensity parameter 1/μ > 0 and {Xi i ≥ 1} is a family of independent random variables which are also independent of {N(t), t ≥ 0}.
Some results of Lindelöf type involving the segmental behaviour of holomorphic functions
Authors: Bravo Francisca , Girela Daniel 
Published: November 2008

AbstractA classical theorem of Lindelöf asserts that if ƒ is a function analytic and bounded in the unit disc δ which has the asymptotic value L at a point ξ ε ∂ δ then it has the non-tangential limit L at ξ. This result does not remain true for functions f analytic in δ whose maximum modulus grows to infinity arbitrarily slowly. However, the second author has recently obtained some results of Lindelöf type valid for these functions. In this paper we obtain new results of this kind. We prove that if f is an analytic function of slow growth in δ and ξ ε ∂ δ, then certain restrictions on the growth of ƒ′ along a segment which ends at ξ do imply that ƒ has a non-tangential limit at ξ.
Skeins and mapping class groups
Authors: Roberts Justin 
Published: November 2008

AbstractThe protective unitary representations of the mapping class groups of surfaces corresponding to the Jones–Witten topological quantum field theory for SU(2) are expressed as representations in algebras of skeins in the surface. The skein-theoretic construction of the representations uses neither Kirby's surgery theorem nor a presentation of the group. Using these representations and the Reidemeister–Singer classification of Heegaard splittings gives a proof of the existence of the moduli of the Witten invariants of 3-manifolds.
Fractal properties of products and projections of measures in ℝd
Authors: Hu Xiaoyu , Taylor S. James 
Published: November 2008

AbstractBorel measures in ℝd are called fractal if locally at a.e. point their Hausdorff and packing dimensions are identical. It is shown that the product of two fractal measures is fractal and almost all projections of a fractal measure into a lower dimensional subspace are fractal. The results rely on corresponding properties of Borel subsets of ℝd which we summarize and develop.
Triple points of unknotting discs and the Arf invariant of knots
Authors: Fiedler Thomas 
Published: November 2008

AbstractAn unknotting disc is the ‘trace’ in ℝ4of a homotopy of a diagram of a knot in ℝ3, which shrinks the diagram to a point. In this paper we study unknotting discs which have as singularities only ordinary triple points. It turns out that the Arf invariant of the knot is determined by the number of triple points in which all three branches of the disc intersect pairwise with the same index. We call such a triple pointcoherent. This interpretation of the Arf invariant has a surprising consequence:LetS⊂ ℝ4be a taut immersed sphere which has as singularities only ordinary triple points. Then the number of coherent triple points inSis even. For example, it is easy to show that there is a taut immersed sphereSwith Euler number six of the normal bundle and which has exactly three ordinary double points and no other singularities. So, our result implies that the three double points ofScan not be pushed together to create an ordinary triple point without the appearance of new singularities.Here ‘taut’ means that the restriction of one of the coordinate functions onShas exactly two (non-degenerate) critical points, i.e. is a perfect Morse function.
Holonomies of Yang–Mills connections for bundles on a surface with disconnected structure group
Authors: Huebschmann Johannes 
Published: November 2008

AbstractLet Σ be a closed surface of genus ≥ 1, G a compact Lie group, not necessarily connected with Lie algebra g, ξ,: P → Σ a principal G-bundle, and suppose Σ equipped with a Riemannian metric and g with an invariant scalar product so that the Yang—Mills equations on ξ are defined. Further, letbe the universal central extension of the fundamental group π of Σ and ΓR the group obtained from Γ when its centre Z is extended to the additive group R of the reals. We show that there are bijective correspondences between various spaces of classes of Yang—Mills connections on ξ and spaces of representations of Γ and ΓR (as appropriate) in G. In particular, we show that the holonomy establishes a homeomorphism between the moduli space N(ξ) of central Yang–Mills connections on ξ and the space Repξ(Γ, G) of representations of Γ in G determined by ξ. Our results rely on a detailed study of the holonomy of a central Yang–Mills connection and extend corresponding ones of Atiyah and Bott for the case where G is connected.
Links with alternating diagrams on closed surfaces of positive genus
Authors: Hayashi Chuichiro 
Published: November 2008

AbstractWe consider links in an orientable 3-manifold M which have an alternating diagram on a closed orientable surface F of positive genus. We see that if the diagram is ‘complex’ enough and if F gives a Heegaard splitting of M, then such a link L is prime and M—L does not contain an essential torus.
A generalization of the Liouville–Arnol'd theorem
Authors: Prince G. E. , Byrnes G. B. , Sherring J. , Godfrey S. E. 
Published: November 2008

AbstractWe show that the Liouville-Arnol'd theorem concerning knowledge of involutory first integrals for Hamiltonian systems is available for any system of second order ordinary differential equations. In establishing this result we also provide a new proof of the standard theorem in the setting of non-autonomous, regular Lagrangian mechanics on the evolution space ℝ × TM of a manifold M. Both the original theorem and its generalization rely on a certain bijection between symmetries of the system and its first integrals. We give two examples of the use of the theorem for systems on ℝ2 which are not Euler-Lagrange.
Normality for elementary subgroup functors
Authors: Bak Anthony , Vavilov Nikolai 
Published: November 2008

AbstractWe define a notion of group functor G on categories of graded modules, which unifies previous concepts of a group functor G possessing a notion of elementary subfunctor E. We show under a general condition which is easily checked in practice that the elementary subgroup E(M) of G(M) is normal for all quasi-weak Noetherian objects M in the source category of G. This result includes all previous ones on Chevalley and classical groups G of rank ≥ 2 over a commutative or module finite ring M (since such rings are quasi-weak Noetherian) and settles positively unanswered cases of normality for these group functors.
Oriented bordism groups of immersions
Authors: Li Gui-Song 
Published: November 2008

Let IΩn, k denote the bordism group of immersions of closed oriented n-manifolds into (n + k)-space. The object of this paper is to study certain group extension problems arising from Pastor's calculations of IΩn, k.The bordism group of immersions was first studied by Wells [12] who calculated the unoriented bordism group I Rn, k for k = n and k = n − 1 ≡ 3(4). Later these unoriented bordism groups were completely determined by Koschorke and Olk for k ≥ n − 2 with the help of an exact sequence measuring the difference between IRn, k and Rn (see [4]). A similar program has been carried out by Pastor [7] to determine the oriented bordism group I Ωn, k for k ≥ n − 2 except for certain group extension problems and some low dimensional cases.
The distribution of the values of an entire function whose coefficients are independent random variables (II)
Authors: Offord A. C. 
Published: November 2008

SummaryThis is a study of entire functions whose coefficients are independent random variables. When the space of such functions is symmetric it is shown that independence of the coefficients alone is sufficient to ensure that almost all such functions will, for large z, be large except in certain small neighbourhoods of the zeros called pits. In each pit the function takes every not too large value and these pits have a certain uniform distribution.
Glueing operation for R-matrices, quantum groups and link-invariants of Hecke type
Authors: Majid Shahn , Markl Martin 
Published: November 2008

AbstractWe introduce an associative glueing operation ⊕q on the space of solutions of the Quantum Yang–Baxter Equations of Hecke type. The corresponding glueing operations for the associated quantum groups and quantum vector spaces are also found. The former involves 2×2 quantum matrices whose entries are themselves square or rectangular quantum matrices. The corresponding glueing operation for link-invariants is introduced and involves a state-sum model with Boltzmann weights determined by the link invariants to be glued. The standard su(n) solution, its associated quantum matrix group, quantum space and link-invariant arise at once by repeated glueing of the one-dimensional case.
Truncated symmetric powers and modular representations of GLn
Authors: Doty Stephen , Walker Grant 
Published: November 2008

AbstractSeveral results are obtained relating to the modular representation theory of the general linear group GLn in the defining characteristic p > 0. In Section 1, embeddings of certain simple modules in symmetric powers of the natural module, or in tensor products of truncated symmetric powers, are constructed. In Section 2, cases are found where simple quotientsof Schur modules H0(λ) can be constructed by extending theidea of truncation to these modules in a natural way. In Section 3, the characters of those simple modules which can be constructed as twisted tensor products of truncated symmetric powers are expressed in terms of Schur functions.
Harmonic typically real mappings
Authors: Bshouty D. , Hengartner W. , Hossian O. 
Published: November 2008

AbstractWe give an example of a univalent orientation-preserving harmonic mapping f = h + g¯ defined on the unit disc U which is real on the real axis, satisfies and is not typically real. Furthermore, we give a geometric characterization for univalent, harmonic and typically real mappings.
Positivity of more Jacobi polynomial sums
Authors: Brown Gavin , Koumandos Stamatis , Wang Kun-Yang 
Published: November 2008

Our main result can be stated as follows:Theorem.for all λ ≥ λ0, where λ0 is the unique root in (0, 1) of the equationandis the Gegenbauer polynomial of degree 2k and order λ. The only cases of equality in (1·1) are when θ = 0 and n is odd.
On Hausdorff and packing dimension of product spaces
Authors: Howroyd J. D. 
Published: November 2008

AbstractWe show that for arbitrary metric spaces X and Y the following dimension inequalities hold:where ‘dim’ denotes Hausdorff dimension and ‘Dim’ denotes packing dimension. The main idea of the proof is to use modified constructions of the Hausdorff and packing measure to deduce appropriate inequalities for the measure of X × Y.
The local model of an isotropic map-germ arising from one-dimensional symplectic reduction
Authors: Ishikawa Goo 
Published: November 2008

AbstractIn this paper, we classify generic isotropic map-germs arising from the symplectic reduction process relative to a hypersurface (i.e. one-dimensional reduction), up to symplectic equivalence in the C category. These models are open Whitney umbrellas of arbitrary dimension and their suspensions. These singularities appear in the generalized Cauchy problem for HamiltonJacobi equations.
The characterization of orders for regular functions
Authors: Linden C. N. 
Published: November 2008

For a given function f, regular in the unit disk D(0, 1), logarithmic means of order p may be defined in terms of integrals by the formulaefor 0 < p < , and bywhen 0 < r < 1. Associated p-orders are subsequently defined byfor 0 < p .
Some remarks on the restriction of the Fourier transform to surfaces
Authors: Drury S. W. , Guo K. 
Published: November 2008

AbstractFor a class of kernels, we prove the Lp estimate for the exotic Riesz potential, with which a restriction theorem of the Fourier transform to surfaces of half the ambient dimension is proved. A simpler proof of Barcelo's result is given. We also find that it is possible to combine the Hausdorff–Young theorem with the Fefferman–Zygmund method to prove some optimal results on the restriction theorem.
Infinite loop spaces with trivial Dyer-Lashof operations
Authors: Slack Michael 
Published: November 2008

AbstractLetpbe any prime. It is well known that the modp Dyer-Lashof algebra acts trivially on the modphomology of an Eilenberg-MacLane space. The main result of this paper is a converse of this fact. Specifically, it is shown that any connected infinite loop space with trivial action of the modpDyer-Lashof algebra is (localized atp) homotopy equivalent to a product of Eilenberg-MacLane spaces. It is then shown that this equivalence does not necessarily respect the infinite loop structures involved.
Poincaré and Friedrichs inequalities in abstract Sobolev spaces
Authors: Edmunds D. E. , Opic B. , Pick L. 
Published: November 2008

Given any domain Ω in ℝNwe consider spacesX = X(Ω),Y = Y(Ω) which are Banach function spaces in the sense of Luxemburg [12]. From these we form what we call the abstract Sobolev spaceW(X, Y), which is denned to be the linear space of allƒ ∈ Xsuch that fori= 1, …,N, the distributional derivative ∂ƒ/∂xibelongs toY; equipped with the normW(X, Y)is a Banach space. The closure of(Ω) inW(X, Y)is denoted byW0(X, Y). Letwto bea weight function on Ω, that is, a measurable function which is positive and finite almost everywhere on Ω. We say that [w, X, Y] supports the (weighted) Poincaré inequality if there is a positive constantKsuch that for allu ∈ W(X, Y),analogously, [X, Y] is said to support the Friedrichs inequality if there is a positive constant K such that for allu ∈ W0(X, Y),
The Brauer group of cubic surfaces
Authors: Swinnerton-Dyer Sir Peter 
Published: November 2008

1. Let V be a non-singular rational surface defined over an algebraic number field k. There is a standard conjecture that the only obstructions to the Hasse principle and to weak approximation on V are the Brauer–Manin obstructions. A prerequisite for calculating these is a knowledge of the Brauer group of V; indeed there is one such obstruction, which may however be trivial, corresponding to each element of Br V/Br k. Because k is an algebraic number field, the natural injectionis an isomorphism; so the first step in calculating the Brauer–Manin obstruction is to calculate the finite group H1 (k), Pic .
The Hopf invariant and homotopy groups of spheres
Authors: Hilton P. J. 
Published: November 2008

In (5), Whitehead introduced a generalization of the Hopfinvariant in the form of a homomorphism H: πr(Sn) → πr(S2n−1), valid† if r < 3n − 3. In (2), the author extended Whitehead's definition to cover the cases r ≤ 4n − 4; r = 5, n = 2; r = 13, n = 4. He also defined, without restriction, a homomorphismwhich was related to H, whenever H was defined, by the equation H* = FH, F being the Freudenthal suspension
The three-dimensional inverse scattering problem for the Helmholtz equation
Authors: Sleeman B. D. 
Published: November 2008

In this paper we are concerned with solutions of the three-dimensional Helmholtz equation which are of class C2 (i.e. regular) in the exterior of a bounded domain D. In cylindrical polar coordinates (r, z, φ) such solutions satisfy the equationin which we have dimensionalized the radial coordinate r so that the wave number is normalized to unity. If we further assume that u satisfies the Sommerfeld radiation conditionthen u may be regarded as being generated by volume sources, surface sources, or point singularities, all of which are contained in D.
A study of sparse matrix representations for solving linear systems in a functional language
Authors: Wainwright Roger L. , Sexton Marian E. 
Published: November 2008

AbstractThis paper compares three different sparse matrix representations in Miranda for solving linear systems of equations: quadtrees, binary trees and run-length encoding. It compares the three data structures in each of two common linear system solvers, Conjugate Gradient and SOR. The test problems used in the paper arise from a simple reservoir model.
Implementing lazy functional languages on stock hardware: the Spineless Tagless G-machine
Authors: Jones Simon L. Peyton 
Published: November 2008

AbstractThe Spineless Tagless G-machine is an abstract machine designed to support non-strict higher-order functional languages. This presentation of the machine falls into three parts. Firstly, we give a general discussion of the design issues involved in implementing non-strict functional languages. Next, we present the STG language, an austere but recognizably-functional language, which as well as a denotational meaning has a well-defined operational semantics. The STG language is the ‘abstract machine code’ for the Spineless Tagless G-machine. Lastly, we discuss the mapping of the STG language onto stock hardware. The success of an abstract machine model depends largely on how efficient this mapping can be made, though this topic is often relegated to a short section. Instead, we give a detailed discussion of the design issues and the choices we have made. Our principal target is the C language, treating the C compiler as a portable assembler.