bluuebunny/crossref_metadata_2025_split huggingface dataset:
Smooth Maps and Real Algebraic Morphisms
Authors: Bochnak J. , Kucharz W. 
Published: December 2010

AbstractLet X be a compact nonsingular real algebraic variety and let Y be either the blowup of along a linear subspace or a nonsingular hypersurface of of bidegree (1, 1). It is proved that a C1 map f : X → Y can be approximated by regular maps if and only if , where is the subgroup of H1(X, Z/2) generated by the cohomology classes of algebraic hypersurfaces in X. This follows from another result on maps into generalized flag varieties.
A Remark on the Moser-Aubin Inequality for Axially Symmetric Functions on the Sphere
Authors: Pruss Alexander R. 
Published: December 2010

AbstractLet Sr be the collection of all axially symmetric functions f in the Sobolev space H1(𝕊2) such that vanishes for i = 1, 2, 3. We prove thatand that this infimum is attained. This complements recent work of Feldman, Froese, Ghoussoub and Gui on a conjecture of Chang and Yang concerning the Moser-Aubin inequality.
Trivial Units in Group Rings
Authors: Farkas Daniel R. , Linnell Peter A. 
Published: December 2010

AbstractLet G be an arbitrary group and let U be a subgroup of the normalized units in ℤG. We show that if U contains G as a subgroup of finite index, then U = G. This result can be used to give an alternative proof of a recent result of Marciniak and Sehgal on units in the integral group ring of a crystallographic group.
Cockcroft Properties of Thompson’s Group
Authors: Bogley W. A. , Gilbert N. D. , Howie James 
Published: December 2010

AbstractIn a study of the word problem for groups, R. J. Thompson considered a certain group F of self-homeomorphisms of the Cantor set and showed, among other things, that F is finitely presented. Using results of K. S. Brown and R. Geoghegan, M. N. Dyer showed that F is the fundamental group of a finite two-complex Z2 having Euler characteristic one and which is Cockcroft, in the sense that each map of the two-sphere into Z2 is homologically trivial. We show that no proper covering complex of Z2 is Cockcroft. A general result on Cockcroft properties implies that no proper regular covering complex of any finite two-complex with fundamental group F is Cockcroft.
On the Prime Ideals in a Commutative Ring
Authors: Dobbs David E. 
Published: December 2010

AbstractIf n and m are positive integers, necessary and sufficient conditions are given for the existence of a finite commutative ring R with exactly n elements and exactly m prime ideals. Next, assuming the Axiom of Choice, it is proved that if R is a commutative ring and T is a commutative R-algebra which is generated by a set I, then each chain of prime ideals of T lying over the same prime ideal of R has at most 2|I| elements. A polynomial ring example shows that the preceding result is best-possible.
Growth Estimates on Positive Solutions of the Equation
Authors: Leung Man Chun 
Published: December 2010

AbstractWe construct unbounded positive C2-solutions of the equation in (equipped with Euclidean metric go) such that K is bounded between two positive numbers in , the conformal metric is complete, and the volume growth of g can be arbitrarily fast or reasonably slow according to the constructions. By imposing natural conditions on u, we obtain growth estimate on the -norm of the solution and show that it has slow decay.
The Zeta Function of a Pair of Quadratic Forms
Authors: Schueller Laura Mann 
Published: December 2010

AbstractThe zeta function of a nonsingular pair of quadratic forms defined over a finite field, k, of arbitrary characteristic is calculated. A. Weil made this computation when char k ≠ 2. When the pair has even order, a relationship between the number of zeros of the pair and the number of places of degree one in an appropriate hyperelliptic function field is established.
Hecke Operators on Jacobi-like Forms
Authors: Lee Min Ho , Myung Hyo Chul 
Published: December 2010

AbstractJacobi-like forms for a discrete subgroup are formal power series with coefficients in the space of functions on the Poincaré upper half plane satisfying a certain functional equation, and they correspond to sequences of certain modular forms. We introduce Hecke operators acting on the space of Jacobi-like forms and obtain an explicit formula for such an action in terms of modular forms. We also prove that those Hecke operator actions on Jacobi-like forms are compatible with the usual Hecke operator actions on modular forms.
Ergodic Rotations of Nilmanifolds Conjugate to Their Inverses
Authors: Henniger J. P. 
Published: December 2010

AbstractIn answer to a question posed in [3], we give sufficient conditions on a Lie nilmanifold so that any ergodic rotation of the nilmanifold is metrically conjugate to its inverse. The condition is that the Lie algebra be what we call quasi-graded, and is weaker than the property of being graded. Furthermore, the conjugatingmap can be chosen to be an involution. It is shown that for a special class of groups, the condition of quasi-graded is also necessary. In certain examples there is a continuum of conjugacies.
Real-Analytic Negligibility of Points and Subspaces in Banach Spaces, with Applications
Authors: Azagra D. , Dobrowolski T. 
Published: December 2010

AbstractWe prove that every infinite-dimensional Banach space X having a (not necessarily equivalent) real-analytic norm is real-analytic diffeomorphic to X \ {0}. More generally, if X is an infinitedimensional Banach space and F is a closed subspace of X such that there is a real-analytic seminorm on X whose set of zeros is F, and X/F is infinite-dimensional, then X and X \ F are real-analytic diffeomorphic. As an application we show the existence of real-analytic free actions of the circle and the n-torus on certain Banach spaces.
Extrapolation of Lp Data from a Modular Inequality
Authors: Bloom Steven , Kerman Ron 
Published: December 2010

AbstractIf an operator T satisfies a modular inequality on a rearrangement invariant space Lρ(Ω, μ), and if p is strictly between the indices of the space, then the Lebesgue inequality holds. This extrapolation result is a partial converse to the usual interpolation results. A modular inequality for Orlicz spaces takes the form , and here, one can extrapolate to the (finite) indices i(Φ) and I(Φ) aswell.
Invariant Measures and Natural Extensions
Authors: Haas Andrew 
Published: December 2010

AbstractWe study ergodic properties of a family of intervalmaps that are given as the fractional parts of certain real Möbius transformations. Included are the maps that are exactly n-to-1, the classical Gauss map and the Renyi or backward continued fraction map. A new approach is presented for deriving explicit realizations of natural automorphic extensions and their invariant measures.
Uniform Distribution in Model Sets
Authors: Moody Robert V. 
Published: December 2010

AbstractWe give a new measure-theoretical proof of the uniform distribution property of points in model sets (cut and project sets). Each model set comes as a member of a family of related model sets, obtained by joint translation in its ambient (the ‘physical’) space and its internal space. We prove, assuming only that the window defining themodel set ismeasurable with compact closure, that almost surely the distribution of points in any model set from such a family is uniform in the sense of Weyl, and almost surely the model set is pure point diffractive.
On the Exponent of the NK0-Groups of Virtually Infinite Cyclic Groups
Authors: Connolly Francis X. , Prassidis Stratos 
Published: December 2010

AbstractIt is known that the K-theory of a large class of groups can be computed from the K-theory of their virtually infinite cyclic subgroups. On the other hand, Nil-groups appear to be the obstacle in calculations involving the K-theory of the latter. The main difficulty in the calculation of Nil-groups is that they are infinitely generated when they do not vanish. We develop methods for computing the exponent of NK0-groups that appear in the calculation of the K0-groups of virtually infinite cyclic groups.
Joint Mean Oscillation and Local Ideals in the Toeplitz Algebra II: Local Commutivity and Essential Commutant
Authors: Xia Jingbo 
Published: December 2010

AbstractA well-known theorem of Sarason [11] asserts that if [Tf, Th] is compact for every h ∈ H∞, then f ∈ H∞ + C(T). Using local analysis in the full Toeplitz algebra τ = τ(L∞), we show that the membership f ∈ H∞ + C(T) can be inferred from the compactness of a much smaller collection of commutators [Tf, Th]. Using this strengthened result and a theorem of Davidson [2], we construct a proper C*-subalgebra τ(L)) of τ which has the same essential commutant as that of τ. Thus the image of τ(ℒ) in the Calkin algebra does not satisfy the double commutant relation [12], [1]. We will also show that no separable subalgebra Ѕ of τ is capable of conferring the membership f ∈ H∞ + C(T) through the compactness of the commutators {[Tf, S] : S ∈ Ѕ}.
The Local Möbius Equation and Decomposition Theorems in Riemannian Geometry
Authors: Fernández-López Manuel , García-Río Eduardo , Kupeli Demir N. 
Published: December 2010

AbstractA partial differential equation, the local Möbius equation, is introduced in Riemannian geometry which completely characterizes the local twisted product structure of a Riemannian manifold. Also the characterizations of warped product and product structures of Riemannian manifolds are made by the local Möbius equation and an additional partial differential equation.
Some Factorizations in Universal Enveloping Algebras of Three Dimensional Lie Algebras and Generalizations
Authors: Berman Stephen , Morita Jun , Yoshii Yoji 
Published: December 2010

AbstractWe introduce the notion of Lie algebras with plus-minus pairs as well as regular plus-minus pairs. These notions deal with certain factorizations in universal enveloping algebras. We show that many important Lie algebras have such pairs and we classify, and give a full treatment of, the three dimensional Lie algebras with plus-minus pairs.
Local Complexity of Delone Sets and Crystallinity
Authors: Lagarias Jeffrey C. , Pleasants Peter A. B. 
Published: December 2010

AbstractThis paper characterizes when a Delone set X in is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the heterogeneity of their distribution. For a Delone set X, let NX(T) count the number of translation-inequivalent patches of radius T in X and let MX(T) be the minimum radius such that every closed ball of radius MX(T) contains the center of a patch of every one of these kinds. We show that for each of these functions there is a “gap in the spectrum” of possible growth rates between being bounded and having linear growth, and that having sufficiently slow linear growth is equivalent to X being an ideal crystal.Explicitly, for NX(T), if R is the covering radius of X then either NX(T) is bounded or NX(T) ≥ T/2R for all T > 0. The constant 1/2R in this bound is best possible in all dimensions.For MX(T), either MX(T) is bounded or MX(T) ≥ T/3 for all T > 0. Examples show that the constant 1/3 in this bound cannot be replaced by any number exceeding 1/2. We also show that every aperiodic Delone set X has MX(T) ≥ c(n)T for all T > 0, for a certain constant c(n) which depends on the dimension n of X and is > 1/3 when n > 1.
Pure Discrete Spectrum for One-dimensional Substitution Systems of Pisot Type
Authors: Sirvent V. F. , Solomyak B. 
Published: December 2010

AbstractWe consider two dynamical systems associated with a substitution of Pisot type: the usual -action on a sequence space, and the -action, which can be defined as a tiling dynamical system or as a suspension flow. We describe procedures for checking when these systems have pure discrete spectrum (the “balanced pairs algorithm” and the “overlap algorithm”) and study the relation between them. In particular, we show that pure discrete spectrum for the -action implies pure discrete spectrum for the -action, and obtain a partial result in the other direction. As a corollary, we prove pure discrete spectrum for every -action associated with a two-symbol substitution of Pisot type (this is conjectured for an arbitrary number of symbols).
Crossed Products by Semigroups of Endomorphisms and Groups of Partial Automorphisms
Authors: Larsen Nadia S. 
Published: December 2010

AbstractWe consider a class (A; S; α) of dynamical systems, where S is an Ore semigroup and α is an action such that each αs is injective and extendible (i.e. it extends to a non-unital endomorphism of the multiplier algebra), and has range an ideal of A. We show that there is a partial action on the fixed-point algebra under the canonical coaction of the enveloping group G of S constructed in [15, Proposition 6.1]. It turns out that the full crossed product by this coaction is isomorphic to A ⋊αS. If the coaction is moreover normal, then the isomorphism can be extended to include the reduced crossed product. We look then at invariant ideals and finally, at examples of systems where our results apply.
On Certain Finitely Generated Subgroups of Groups Which Split
Authors: Moon Myoungho 
Published: December 2010

AbstractDefine a group G to be in the class 𝒮 if for any finitely generated subgroup K of G having the property that there is a positive integer n such that gn ∈ K for all g ∈ G, K has finite index in G. We show that a free product with amalgamation A *CB and an HNN group A *C belong to 𝒮, if C is in 𝒮 and every subgroup of C is finitely generated.
Torsion Points on Certain Families of Elliptic Curves
Authors: Wieczorek Małgorzata 
Published: December 2010

AbstractFix an elliptic curve y2 = x3 + Ax + B, satisfying A, B ∈ , A ≥ |B| > 0. We prove that the -torsion subgroup is one of (0), /3, /9. Related numerical calculations are discussed.
Beurling-Dahlberg-Sjögren Type Theorems for Minimally Thin Sets in a Cone
Authors: Miyamoto Ikuko , Yanagishita Minoru , Yoshida Hidenobu 
Published: December 2010

AbstractThis paper shows that some characterizations of minimally thin sets connected with a domain having smooth boundary and a half-space in particular also hold for the minimally thin sets at a corner point of a special domain with corners, i.e., the minimally thin set at ∞ of a cone.
Group Cohomology and Lp-Cohomology of Finitely Generated Groups
Authors: Puls Michael J. 
Published: December 2010

AbstractLet G be a finitely generated, infinite group, let p > 1, and let Lp(G) denote the Banach space . In this paper we will study the first cohomology group of G with coefficients in Lp(G), and the first reduced Lp-cohomology space of G. Most of our results will be for a class of groups that contains all finitely generated, infinite nilpotent groups.
Cartan Subalgebras of
Authors: Neeb Karl-Hermann , Penkov Ivan 
Published: December 2010

AbstractLet V be a vector space over a field of characteristic zero and V* be a space of linear functionals on V which separate the points of V. We consider V ⊗ V* as a Lie algebra of finite rank operators on V, and set (V, V*) := V ⊗ V*. We define a Cartan subalgebra of (V, V*) as the centralizer of a maximal subalgebra every element of which is semisimple, and then give the following description of all Cartan subalgebras of (V;V*) under the assumption that is algebraically closed. A subalgebra of (V, V*) is a Cartan subalgebra if and only if it equals for some one-dimensional subspaces Vj ⊆ V and (Vj)* ⊆ V* with (Vi)* (Vj) = δij and such that the spaces . We then discuss explicit constructions of subspaces Vj and (Vj)* as above. Our second main result claims that a Cartan subalgebra of (V, V*) can be described alternatively as a locally nilpotent self-normalizing subalgebra whose adjoint representation is locally finite, or as a subalgebra h which coincides with the maximal locally nilpotent h-submodule of (V, V*), and such that the adjoint representation of is locally finite.
Existence of Leray's Self-Similar Solutions of the Navier-Stokes Equations In 𝒟 ⊂ ℝ3
Authors: He Xinyu 
Published: December 2010

AbstractLeray's self-similar solution of the Navier-Stokes equations is defined bywhere . Consider the equation for U(y) in a smooth bounded domain D of with non-zero boundary condition:We prove an existence theorem for the Dirichlet problem in Sobolev space W1,2(D). This implies the local existence of a self-similar solution of the Navier-Stokes equations which blows up at t = t* with t* < +∞, provided the function is permissible.
Suborbit Structure of Permutation p-Groups and an Application to Cayley Digraph Isomorphism
Authors: Alspach Brian , Du Shaofei 
Published: December 2010

AbstractLet P be a transitive permutation group of order pm, p an odd prime, containing a regular cyclic subgroup. The main result of this paper is a determination of the suborbits of P. The main result is used to give a simple proof of a recent result by J. Morris on Cayley digraph isomorphisms.
On Maximal k-Sections and Related Common Transversals of Convex Bodies
Authors: Makai Endre , Martini Horst 
Published: December 2010

AbstractGeneralizing results from [MM1] referring to the intersection body IK and the cross-section body CK of a convex body K ⊂ , d ≥ 2, we prove theorems about maximal k-sections of convex bodies, k ∈ {1, … ,d − 1}, and, simultaneously, statements about common maximal (d − 1)- and 1-transversals of families of convex bodies.
A New Characterization of Hardy Martingale Cotype Space
Authors: Bekjan Turdebek N. 
Published: December 2010

AbstractWe give a new characterization of Hardy martingale cotype property of complex quasi- Banach space by using the existence of a kind of plurisubharmonic functions. We also characterize the best constants of Hardy martingale inequalities with values in the complex quasi-Banach space.
A Residue Formula for SU(2)-Valued Moment Maps
Authors: Plamenevskaya Olga 
Published: December 2010

AbstractJeffrey and Kirwan gave expressions for intersection pairings on the reduced space M0 = μ−1(0)/G of a Hamiltonian G-space M in terms of multiple residues. In this paper we prove a residue formula for symplectic volumes of reduced spaces of a quasi-Hamiltonian SU(2)-space. The definition of quasi-Hamiltonian G-spaces was introduced by Alekseev, Malkin and Meinrenken.
Diagonal Plus Tridiagonal Representatives for Symplectic Congruence Classes of Symmetric Matrices
Authors: Đoković D. Ž. , Szechtman F. , Zhao K. 
Published: December 2010

AbstractLet n = 2m be even and denote by Spn(F) the symplectic group of rank m over an infinite field F of characteristic different from 2. We show that any n × n symmetric matrix A is equivalent under symplectic congruence transformations to the direct sum of m × m matrices B and C, with B diagonal andC tridiagonal. Since the Spn(F)-module of symmetric n × n matrices over F is isomorphic to the adjoint module spn(F), we infer that any adjoint orbit of Spn(F) in spn(F) has a representative in the sum of 3m − 1 root spaces, which we explicitly determine.
On the Generalized d’Alembert's and Wilson's Functional Equations on a Compact Group
Authors: Bouikhalene Belaid 
Published: December 2010

AbstractLet G be a compact group.Let σ be a continuous involution of G. In this paper, we are concerned by the following functional equationwhere f , g, h: G ⟼ ℂ, to be determined, are complex continuous functions on G such that f is central. This equation generalizes d’Alembert's and Wilson's functional equations. We show that the solutions are expressed by means of characters of irreducible, continuous and unitary representations of the group G.
Separation of Variables for
Authors: Lopes Samuel A. 
Published: December 2010

AbstractLet be the positive part of the quantized enveloping algebra . Using results of Alev–Dumas and Caldero related to the center of , we show that this algebra is free over its center. This is reminiscent of Kostant's separation of variables for the enveloping algebra U(g) of a complex semisimple Lie algebra g, and also of an analogous result of Joseph–Letzter for the quantum algebra Ŭq(g). Of greater importance to its representation theory is the fact that is free over a larger polynomial subalgebra N in n variables. Induction from N to provides infinite-dimensional modules with good properties, including a grading that is inherited by submodules.
Hyperplanes of the Form f1(x, y)z1 + · · · + fk(x, y)zk + g(x, y) Are Variables
Authors: Vénéreau Stéphane 
Published: December 2010

AbstractThe Abhyankar–Sathaye Embedded Hyperplane Problem asks whether any hypersurface of ℂn isomorphic to ℂn–1 is rectifiable, i.e., equivalent to a linear hyperplane up to an automorphism of ℂn. Generalizing the approach adopted by Kaliman, Vénéreau, and Zaidenberg, which consists in using almost nothing but the acyclicity of ℂn–1, we solve this problem for hypersurfaces given by polynomials of ℂ[x, y, z1, … , zk] as in the title.
Going-Down Results for Ci-Fields
Authors: Bevelacqua Anthony J. , Motley Mark J. 
Published: December 2010

AbstractWe search for theorems that, given a Ci-field K and a subfield k of K, allow us to conclude that k is a Cj -field for some j. We give appropriate theorems in the case K = k(t) and K = k((t)). We then consider the more difficult case where K/k is an algebraic extension. Here we are able to prove some results, and make conjectures. We also point out the connection between these questions and Lang's conjecture on nonreal function fields over a real closed field.
Additive Riemann–Hilbert Problem in Line Bundles Over ℂℙ1
Authors: Dwilewicz Roman J. 
Published: December 2010

AbstractIn this note we consider -problem in line bundles over complex projective space ℂℙ1 and prove that the equation can be solved for (0, 1) forms with compact support. As a consequence, any Cauchy-Riemann function on a compact real hypersurface in such line bundles is a jump of two holomorphic functions defined on the sides of the hypersurface. In particular, the results can be applied to ℂℙ2 since by removing a point from it we get a line bundle over ℂℙ1.
Character Degree Graphs of Solvable Groups of Fitting Height 2
Authors: Lewis Mark L. 
Published: December 2010

AbstractGiven a finite group G, we attach to the character degrees of G a graph whose vertex set is the set of primes dividing the degrees of irreducible characters of G, and with an edge between p and q if pq divides the degree of some irreducible character of G. In this paper, we describe which graphs occur when G is a solvable group of Fitting height 2.
The Spectrum and Isometric Embeddings of Surfaces of Revolution
Authors: Engman Martin 
Published: December 2010

AbstractA sharp upper bound on the first S1 invariant eigenvalue of the Laplacian for S1 invariant metrics on S2 is used to find obstructions to the existence of S1 equivariant isometric embeddings of such metrics in (ℝ3, can). As a corollary we prove: If the first four distinct eigenvalues have even multiplicities then the metric cannot be equivariantly, isometrically embedded in (ℝ3, can). This leads to generalizations of some classical results in the theory of surfaces.
On the Modularity of Three Calabi–Yau Threefolds With Bad Reduction at 11
Authors: Schütt Matthias 
Published: December 2010

AbstractThis paper investigates the modularity of three non-rigid Calabi–Yau threefolds with bad reduction at 11. They are constructed as fibre products of rational elliptic surfaces, involving the modular elliptic surface of level 5. Their middle ℓ-adic cohomology groups are shown to split into two-dimensional pieces, all but one of which can be interpreted in terms of elliptic curves. The remaining pieces are associated to newforms of weight 4 and level 22 or 55, respectively. For this purpose, we develop a method by Serre to compare the corresponding two-dimensional 2-adic Galois representations with uneven trace. Eventually this method is also applied to a self fibre product of the Hesse-pencil, relating it to a newform of weight 4 and level 27.