bluuebunny/crossref_metadata_2025_split huggingface dataset:
Prolongations and Computational Algebra
Authors: Sidman Jessica , Sullivant Seth 
Published: November 2009

Abstract.We explore the geometric notion of prolongations in the setting of computational algebra, extending results of Landsberg and Manivel which relate prolongations to equations for secant varieties. We also develop methods for computing prolongations that are combinatorial in nature. As an application, we use prolongations to derive a new family of secant equations for the binary symmetric model in phylogenetics.
Infinitesimal Invariants in a Function Algebra
Authors: Tange Rudolf 
Published: November 2009

Abstract.Let G be a reductive connected linear algebraic group over an algebraically closed field of positive characteristic and let 𝔤 be its Lie algebra. First we extend a well-known result about the Picard group of a semi-simple group to reductive groups. Then we prove that if the derived group is simply connected and 𝔤 satisfies a mild condition, the algebra K[G]𝔤 of regular functions on G that are invariant under the action of 𝔤 derived from the conjugation action is a unique factorisation domain.
Petits points d’une surface
Authors: Pontreau Corentin 
Published: November 2009

Résumé. Pour toute sous-vari ét é géométriquement irréductible $V$ du groupe multiplicatif $\mathbb{G}_{m}^{n}$, on sait qu’en dehors d’un nombre fini de translat és de tores exceptionnels inclus dans $V$, tous les points sont de hauteur minorée par une certaine quantit é $q{{(V)}^{-1}}>0$. On conna ît de plus une borne supérieure pour la somme des degrés de ces translat és de tores pour des valeurs de $q(V)$ polynomiales en le degré de $V$. Ceci n’est pas le cas si l’on exige une minoration quasi-optimale pour la hauteur des points de $V$, essentiellement linéaire en l’inverse du degré.Nous apportons ici une réponse partielle à ce problème : nous donnons une majoration de la somme des degrés de ces translat és de sous-tores de codimension 1 d’une hypersurface $V$. Les résultats, obtenus dans le cas de $\mathbb{G}_{m}^{3}$,mais complètement explicites, peuvent toutefois s’étendre à $\mathbb{G}_{m}^{n}$,moyennant quelques petites complications inhérentes à la dimension $n$.
Close Lattice Points on Circles
Authors: Cilleruelo Javier , Granville Andrew 
Published: November 2009

AbstractWe classify the sets of four lattice points that all lie on a short arc of a circle that has its center at the origin; specifically on arcs of length tR1/3 on a circle of radius R, for any given t > 0. In particular we prove that any arc of length on a circle of radius R, with , contains at most three lattice points, whereas we give an explicit infinite family of 4-tuples of lattice points, (ν1, n, ν2, n, ν3, n, ν4, n), each of which lies on an arc of length on a circle of radius Rn.
On the Local Lifting Properties of Operator Spaces
Authors: Dong Z. 
Published: November 2009

Abstract In this paper, we mainly study operator spaces which have the locally lifting property (LLP). The dual of any ternary ring of operators is shown to satisfy the strongly local reflexivity, and this is used to prove that strongly local reflexivity holds also for operator spaces which have the LLP. Several homological characterizations of the LLP and weak expectation property are given. We also prove that for any operator space V, V** has the LLP if and only if V has the LLP and V* is exact.
Monodromy Groups and Self-Invariance
Authors: Hubard Isabel , Orbanić Alen , Weiss Asia Ivić 
Published: November 2009

Abstract For every polytope 𝒫 there is the universal regular polytope of the same rank as 𝒫 corresponding to the Coxeter group 𝒞 = [∞, … ,∞]. For a given automorphism d of 𝒞, using monodromy groups, we construct a combinatorial structure 𝒫d. When 𝒫d is a polytope isomorphic to 𝒫 we say that 𝒫 is self-invariant with respect to d, or d-invariant. We develop algebraic tools for investigating these operations on polytopes, and in particular give a criterion on the existence of a d-automorphismof a given order. As an application, we analyze properties of self-dual edge-transitive polyhedra and polyhedra with two flag-orbits. We investigate properties of medials of such polyhedra. Furthermore, we give an example of a self-dual equivelar polyhedron which contains no polarity (duality of order 2). We also extend the concept of Petrie dual to higher dimensions, and we show how it can be dealt with using self-invariance.
Wirtinger's Inequalities on Time Scales
Authors: Agarwal Ravi P. , Otero-Espinar Victoria , Perera Kanishka , Vivero Dolores R. 
Published: November 2009

AbstractThis paper is devoted to the study of Wirtinger-type inequalities for the Lebesgue Δ-integral on an arbitrary time scale 𝕋. We prove a general inequality for a class of absolutely continuous functions on closed subintervals of an adequate subset of 𝕋. By using this expression and by assuming that 𝕋 is bounded, we deduce that a general inequality is valid for every absolutely continuous function on 𝕋 such that its Δ-derivative belongs to([a,b) ∩ 𝕋) and at most it vanishes on the boundary of 𝕋.
Boundedness from Below of Composition Operators on α-Bloch Spaces
Authors: Chen Huaihui , Gauthier Paul 
Published: November 2009

AbstractWe give a necessary and sufficient condition for a composition operator on an α-Bloch space with α ≥ 1 to be bounded below. This extends a known result for the Bloch space due to P. Ghatage, J. Yan, D. Zheng, and H. Chen.
On Gâteaux Differentiability of Pointwise Lipschitz Mappings
Authors: Duda Jakub 
Published: November 2009

AbstractWe prove that for every functionf:X→Y, whereXis a separable Banach space andYis a Banach space with RNP, there exists a setA∈such thatfis Gâteaux differentiable at allx∈S(f)\A, whereS(f) is the set of points wherefis pointwise-Lipschitz. This improves a result of Bongiorno. As a corollary, we obtain that everyK-monotone function on a separable Banach space is Hadamard differentiable outside of a set belonging to; this improves a result due to Borwein and Wang. Another corollary is that ifXis Asplund,f:X→ ℝ cone monotone,g:X→ ℝ continuous convex, then there exists a point inX, wherefis Hadamard differentiable andgis Fréchet differentiable.
A Multivalued Nonlinear System with the Vector p-Laplacian on the Semi-Infinity Interval
Authors: Filippakis Michael E. , Papageorgiou Nikolaos S. 
Published: November 2009

AbstractWe study a second order nonlinear system driven by the vector p-Laplacian, with a multivalued nonlinearity and defined on the positive time semi-axis ℝ+. Using degree theoretic techniques we solve an auxiliary mixed boundary value problem defined on the finite interval [0, n] and then via a diagonalization method we produce a solution for the original infinite time horizon system.
Existence of Solutions to Poisson's Equation
Authors: Hanley Mary 
Published: November 2009

AbstractLet Ω be a domain in ℝn(n≥ 2). We find a necessary and sufficient topological condition on Ω such that, for anymeasureμon ℝn, there is a functionuwith specified boundary conditions that satisfies the Poisson equation Δu=μon Δ in the sense of distributions.
Kolmogorov, Linear and Pseudo-Dimensional Widths of Classes of s-Monotone Functions in 𝕃p, 0 < p < 1
Authors: Konovalov Victor N. , Kopotun Kirill A. 
Published: November 2009

AbstractLet Bp be the unit ball in 𝕃p, 0 < p < 1, and let , s ∈ ℕ, be the set of all s-monotone functions on a finite interval I, i.e., consists of all functions x : I ⟼ ℝ such that the divided differences [x; t0, … , ts] of order s are nonnegative for all choices of (s + 1) distinct points t0, … , ts ∈ I. For the classes Bp := ∩ Bp, we obtain exact orders of Kolmogorov, linear and pseudo-dimensional widths in the spaces , 0 < q < p < 1:
The Noether–Lefschetz Theorem Via Vanishing of Coherent Cohomology
Authors: Ravindra G. V. 
Published: November 2009

AbstractWe prove that for a generic hypersurface in ℙ2n+1 of degree at least 2 + 2/n, the n-th Picard number is one. The proof is algebraic in nature and follows from certain coherent cohomology vanishing.
The Kostrikin Radical and the Invariance of the Core of Reduced Extended Affine Lie Algebras
Authors: Tocón Maribel 
Published: November 2009

AbstractIn this paper we prove that the Kostrikin radical of an extended affine Lie algebra of reduced type coincides with the center of its core, and use this characterization to get a type-free description of the core of such algebras. As a consequence we get that the core of an extended affine Lie algebra of reduced type is invariant under the automorphisms of the algebra.
Relative Homotopy in Relational Structures
Authors: Witbooi P. J. 
Published: November 2009

AbstractThe homotopy groups of a finite partially ordered set (poset) can be described entirely in the context of posets, as shown in a paper by B. Larose and C. Tardif. In this paper we describe the relative version of such a homotopy theory, for pairs (X, A) where X is a poset and A is a subposet of X. We also prove some theorems on the relevant version of the notion of weak homotopy equivalences for maps of pairs of such objects. We work in the category of reflexive binary relational structures which contains the posets as in the work of Larose and Tardif.
Quantum Multiple Construction of Subfactors
Authors: Asaeda Marta 
Published: November 2009

AbstractWe construct the quantums-tuple subfactors for an AFD II1subfactor with finite index and depth, for an arbitrary natural numbers. This is a generalization of the quantum multiple subfactors by Erlijman and Wenzl, which in turn generalized the quantum double construction of a subfactor for the case that the original subfactor gives rise to a braided tensor category. In this paper we give a multiple construction for a subfactor with a weaker condition than braidedness of the bimodule system.
The Reconstruction Property in Banach Spaces and a Perturbation Theorem
Authors: Casazza Peter G. , Christensen Ole 
Published: November 2009

AbstractPerturbation theory is a fundamental tool in Banach space theory. However, the applications of the classical results are limited by the fact that they force the perturbed sequence to be equivalent to the given sequence. We will develop amore general perturbation theory that does not force equivalence of the sequences.
Real Hypersurfaces in Complex Space Forms with Reeb Flow Symmetric Structure Jacobi Operator
Authors: Cho Jong Taek , Ki U-Hang 
Published: November 2009

AbstractReal hypersurfaces in a complex space form whose structure Jacobi operator is symmetric along the Reeb flow are studied. Among them, homogeneous real hypersurfaces of type (A) in a complex projective or hyperbolic space are characterized as those whose structure Jacobi operator commutes with the shape operator.
Positive Solutions of the Falkner–Skan Equation Arising in the Boundary Layer Theory
Authors: Lan K. Q. , Yang G. C. 
Published: November 2009

AbstractThe well-known Falkner–Skan equation is one of the most important equations in laminar boundary layer theory and is used to describe the steady two-dimensional flow of a slightly viscous incompressible fluid past wedge shaped bodies of angles related to λπ/2, where λ ∈ ℝ is a parameter involved in the equation. It is known that there exists λ* < 0 such that the equation with suitable boundary conditions has at least one positive solution for each λ ≥ λ* and has no positive solutions for λ < λ*. The known numerical result shows λ* = –0.1988. In this paper, λ* ∈ [–0.4,–0.12] is proved analytically by establishing a singular integral equation which is equivalent to the Falkner–Skan equation. The equivalence result provides new techniques to study properties and existence of solutions of the Falkner–Skan equation.
Linear Equations with Small Prime and Almost Prime Solutions
Authors: Meng Xianmeng 
Published: November 2009

AbstractLet b1, b2 be any integers such that gcd(b1, b2) = 1 and c1|b1| < |b2| ≤ c2|b1|, where c1, c2 are any given positive constants. Let n be any integer satisfying gcd(n, bi) = 1, i = 1, 2. Let Pk denote any integer with no more than k prime factors, counted according to multiplicity. In this paper, for almost all b2, we prove (i) a sharp lower bound for n such that the equation b1p + b2m = n is solvable in prime p and almost prime m = Pk, k ≥ 3 whenever both bi are positive, and (ii) a sharp upper bound for the least solutions p, m of the above equation whenever bi are not of the same sign, where p is a prime and m = Pk, k ≥ 3.
Condensed and Strongly Condensed Domains
Authors: Mimouni Abdeslam 
Published: November 2009

AbstractThis paper deals with the concepts of condensed and strongly condensed domains. By definition, an integral domain R is condensed (resp. strongly condensed) if each pair of ideals I and J of R, I J = ﹛ab/a ∈ I, b ∈ J﹜ (resp. I J = a J for some a ∈ I or I J = Ib for some b ∈ J). More precisely, we investigate the ideal theory of condensed and strongly condensed domains in Noetherian-like settings, especially Mori and strong Mori domains and the transfer of these concepts to pullbacks.
On the Maximal Spectrum of Semiprimitive Multiplication Modules
Authors: Samei Karim 
Published: November 2009

AbstractAnR-moduleMis called a multiplication module if for each submoduleNofM,N=IMfor some idealIofR. As defined for a commutative ringR, anR-moduleMis said to be semiprimitive if the intersection of maximal submodules ofMis zero. The maximal spectra of a semiprimitive multiplication moduleMare studied. The isolated points of Max(M) are characterized algebraically. The relationships among the maximal spectra ofM, Soc(M) and Ass(M) are studied. It is shown that Soc(M) is exactly the set of all elements ofMwhich belongs to every maximal submodule ofMexcept for a finite number. If Max(M) is infinite, Max(M) is a one-point compactification of a discrete space if and only ifMis Gelfand and for some maximal submoduleK, Soc(M) is the intersection of all prime submodules ofMcontained inK. WhenMis a semiprimitive Gelfand module, we prove that every intersection of essential submodules ofMis an essential submodule if and only if Max(M) is an almost discrete space. The set of uniform submodules ofMand the set of minimal submodules ofMcoincide. Ann(Soc(M))Mis a summand submodule ofMif and only if Max(M) is the union of two disjoint open subspacesAandN, whereAis almost discrete andNis dense in itself. In particular, Ann(Soc(M)) = Ann(M) if and only if Max(M) is almost discrete.
On Primitive Ideals in Graded Rings
Authors: Smoktunowicz Agata 
Published: November 2009

AbstractLet R = be a graded nil ring. It is shown that primitive ideals in R are homogeneous. Let A = be a graded non-PI just-infinite dimensional algebra and let I be a prime ideal in A. It is shown that either I = ﹛0﹜ or I = A. Moreover, A is either primitive or Jacobson radical.
Universal Inner Functions on the Ball
Authors: Bayart Frédéric 
Published: November 2009

AbstractIt is shown that given any sequence of automorphisms (ϕk)k of the unit ball of ℂN such that ‖ϕk(0)‖ tends to 1, there exists an inner function I such that the family of “non-Euclidean translates” (I о ϕk)k is locally uniformly dense in the unit ball of H∞().
Expected Norms of Zero-One Polynomials
Authors: Borwein Peter , Choi Kwok-Kwong Stephen , Mercer Idris 
Published: November 2009

AbstractLet = {a0 + a1z + · · · + an–1zn–1 : aj ∈ ﹛0, 1﹜¯﹜, whose elements are called zero- one polynomials and correspond naturally to the 2n subsets of [n] := ﹛0, 1, … , n – 1﹜. We also let = ﹛α(z) ∈ : α(1) = m﹜, whose elements correspond to the subsets of [n] of size m, and let , whose elements are the zero-one polynomials of degree exactly n.Many researchers have studied norms of polynomials with restricted coefficients. Using ‖α‖p to denote the usual Lp norm of α on the unit circle, one easily sees that α(z) = a0+a1z+· · ·+aNzN ∈ ℝ[z] satisfies and , where .If α(z) ∈ , say α(z) = zβ1 + · · · + zβm where β1 < · · · < βm, then ck is the number of times k appears as a difference βi – βj . The condition that α ∈ satisfies ck ∈ ﹛0, 1﹜ for 1 ≤ k ≤ n – 1 is thus equivalent to the condition that ﹛β1, … , βm﹜ is a Sidon set (meaning all differences of pairs of elements are distinct).In this paper, we find the average of over α ∈ , α ∈ , and α ∈ . We further show that our expression for the average of over yields a new proof of the known result: if m = o(n1/4) and B(n,m) denotes the number of Sidon sets of size m in [n], then almost all subsets of [n] of size m are Sidon, in the sense that .
A Result in Surgery Theory
Authors: Cavicchioli Alberto , Spaggiari Fulvia 
Published: November 2009

AbstractWe study the topological 4-dimensional surgery problem for a closed connected orientable topological 4-manifoldXwith vanishing second homotopy and π1(X) ≅A∗F(r), whereAhas one end andF(r) is the free group of rankr≥ 1. Our result is related to a theorem of Krushkal and Lee, and depends on the validity of the Novikov conjecture for such fundamental groups.
The Effective Cone of the Kontsevich Moduli Space
Authors: Coskun Izzet , Harris Joe , Starr Jason 
Published: November 2009

AbstractIn this paper we prove that the cone of effective divisors on the Kontsevich moduli spaces of stable maps, , stabilize when r ≥ d. We give a complete characterization of the effective divisors on . They are non-negative linear combinations of boundary divisors and the divisor of maps with degenerate image.
C*-Algebras Associated with Mauldin–Williams Graphs
Authors: Ionescu Marius , Watatani Yasuo 
Published: November 2009

AbstractA Mauldin–Williams graphis a generalization of an iterated function system by a directed graph. Its invariant setKplays the role of the self-similar set. We associate aC*-algebra(K) with a Mauldin–Williams graphand the invariant setK, laying emphasis on the singular points. We assume that the underlying graphGhas no sinks and no sources. Ifsatisfies the open set condition inK, andGis irreducible and is not a cyclic permutation, then the associatedC*-algebra(K) is simple and purely infinite. We calculate theK-groups for some examples including the inflation rule of the Penrose tilings.
Expansion of the Riemann Ξ Function in Meixner–Pollaczek Polynomials
Authors: Kuznetsov Alexey 
Published: November 2009

AbstractIn this article we study in detail the expansion of the Riemann Ξ function in Meixner– Pollaczek polynomials. We obtain explicit formulas, recurrence relation and asymptotic expansion for the coefficients and investigate the zeros of the partial sums.
On Tensor Products of Polynomial Representations
Authors: Purbhoo Kevin , van Willigenburg Stephanie 
Published: November 2009

AbstractWe determine the necessary and sufficient combinatorial conditions for which the tensor product of two irreducible polynomial representations of GL(n, ℂ) is isomorphic to another. As a consequence we discover families of Littlewood–Richardson coefficients that are non-zero, and a condition on Schur non-negativity.
Vanishing Theorems in Colombeau Algebras of Generalized Functions
Authors: Valmorin V. 
Published: November 2009

AbstractUsing a canonical linear embedding of the algebra of Colombeau generalized functions in the space of -valued ℂ-linear maps on the space of smooth functions with compact support, we give vanishing conditions for functions and linear integral operators of class . These results are then applied to the zeros of holomorphic generalized functions in dimension greater than one.
Summation of Series over Bourget Functions
Authors: Vidanović Mirjana V. , Tričković Slobodan B. , Stanković Miomir S. 
Published: November 2009

AbstractIn this paper we derive formulas for summation of series involving J. Bourget's generalization of Bessel functions of integer order, as well as the analogous generalizations by H. M. Srivastava. These series are expressed in terms of the Riemann ζ function and Dirichlet functions η, λ, β, and can be brought into closed form in certain cases, which means that the infinite series are represented by finite sums.
Augmented currents of an HCN2 variant in patients with febrile seizure syndromes
Authors: Dibbens Leanne M. , Reid Christopher A. , Hodgson Bree , Thomas Evan A. , Phillips Alison M. , Gazina Elena , Cromer Brett A. , Clarke Alison L. , Baram Tallie Z. , Scheffer Ingrid E. , Berkovic Samuel F. , Petrou Steven 
Published: November 2009

AbstractThe genetic architecture of common epilepsies is largely unknown. HCNs are excellent epilepsy candidate genes because of their fundamental neurophysiological roles. Screening in subjects with febrile seizures and genetic epilepsy with febrile seizures plus revealed that 2.4% carried a common triple proline deletion (delPPP) in HCN2 that was seen in only 0.2% of blood bank controls. Currents generated by mutant HCN2 channels were ∼35% larger than those of controls; an effect revealed using automated electrophysiology and an appropriately powered sample size. This is the first association of HCN2 and familial epilepsy, demonstrating gain of function of HCN2 current as a potential contributor to polygenic epilepsy. ANN NEUROL 2010;67:542–546
What role for genetics in the prediction of multiple sclerosis?
Authors: Sawcer Stephen , Ban Maria , Wason James , Dudbridge Frank 
Published: November 2009

AbstractFor most of us, the foundations of our understanding of genetics were laid by considering Mendelian diseases in which familial recurrence risks are high, and mutant alleles are both necessary and sufficient. One consequence of this deterministic teaching is that our conceptualization of genetics tends to be dominated by the notion that the genetic aspects of disease are caused by rare alleles exerting large effects. Unfortunately, the preconceptions that flow from this training are frequently erroneous and misleading in the context of common traits, where familial recurrence risks are modest, and for the most part the relevant alleles are neither rare, necessary, nor sufficient. For these common traits, the genetic architecture is far more complex, with susceptibility rather than causality resulting from the combined effects of many alleles, each exerting only a modest effect on risk. None of these alleles is sufficient to cause disease on its own, and none is essential for the development of disease. Furthermore, most are carried by large sections of the population, the vast majority of which does not develop the disease. One consequence of our innate belief in the Mendelian paradigm is that we have an inherent expectation that knowledge about the genetic basis for a disease should allow genetic testing and thereby accurate risk prediction. There is an inevitable feeling that the same should be true in complex disease, but is it? ANN NEUROL 2010;67:3–10