bluuebunny/crossref_metadata_2025_split huggingface dataset:
Nonconvexity of the Generalized Numerical Range Associated with the Principal Character
Authors: Li Chi-Kwong , Zaharia Alexandru 
Published: December 2010

AbstractSuppose m and n are integers such that 1 ≤ m ≤ n. For a subgroup H of the symmetric group Sm of degree m, consider the generalized matrix function on m × m matrices B = (bij) defined by and the generalized numerical range of an n × n complex matrix A associated with dH defined byIt is known that WH(A) is convex if m = 1 or if m = n = 2. We show that there exist normal matrices A for which WH(A) is not convex if 3 ≤ m ≤ n. Moreover, for m = 2 < n, we prove that a normal matrix A with eigenvalues lying on a straight line has convex WH(A) if and only if νA is Hermitian for some nonzero ν ∈ ℂ. These results extend those of Hu, Hurley and Tam, who studied the special case when 2 ≤ m ≤ 3 ≤ n and H = Sm.
Harmonic Polynomials Associated With Reflection Groups
Authors: Xu Yuan 
Published: December 2010

AbstractWe extend Maxwell’s representation of harmonic polynomials to h-harmonics associated to a reflection invariant weight function hk. Let 𝑫i, 1 ≤ i ≤ d, be Dunkl’s operators associated with a reflection group. For any homogeneous polynomial P of degree n,we prove the polynomial is a h-harmonic polynomial of degree n, where γ = ∑ki and 𝑫 = (𝑫1, … ,𝑫d). The construction yields a basis for h-harmonics. We also discuss self-adjoint operators acting on the space of h-harmonics.
Approximation algébrique simultanée de nombres de Liouville
Authors: Roy Damien 
Published: December 2010

AbstractThe purpose of this paper is to show the limitations of the conjectures of algebraic approximation. For this, we construct points of Cm which do not admit good algebraic approximations of bounded degree and height, when the bounds on the degree and the height are taken from specific sequences. The coordinates of these points are Liouville numbers.
Each Copy of the Real Line in is Removable
Authors: Zeron E. Santillan 
Published: December 2010

AbstractAround 1995, Professors Lupacciolu, Chirka and Stout showed that a closed subset of (N ≥ 2) is removable for holomorphic functions, if its topological dimension is less than or equal to N − 2. Besides, they asked whether closed subsets of homeomorphic to the real line (the simplest 1-dimensional sets) are removable for holomorphic functions. In this paper we propose a positive answer to that question.
On Quantizing Nilpotent and Solvable Basic Algebras
Authors: Gotay Mark J. , Grabowski Janusz 
Published: December 2010

AbstractWe prove an algebraic “no-go theorem” to the effect that a nontrivial Poisson algebra cannot be realized as an associative algebra with the commutator bracket. Using it, we show that there is an obstruction to quantizing the Poisson algebra of polynomials generated by a nilpotent basic algebra on a symplectic manifold. This result generalizes Groenewold’s famous theorem on the impossibility of quantizing the Poisson algebra of polynomials onR2n. Finally, we explicitly construct a polynomial quantization of a symplectic manifold with a solvable basic algebra, thereby showing that the obstruction in the nilpotent case does not extend to the solvable case.
Algebraic Homology For Real Hyperelliptic and Real Projective Ruled Surfaces
Authors: Abánades Miguel A. 
Published: December 2010

AbstractLet X be a reduced nonsingular quasiprojective scheme over such that the set of real rational points X() is dense in X and compact. Then X() is a real algebraic variety. Denote by (X(), ) the group of homology classes represented by Zariski closed k-dimensional subvarieties of X(). In this note we show that (X(), ) is a proper subgroup of H1(X(), ) for a nonorientable hyperelliptic surface X. We also determine all possible groups (X(), ) for a real ruled surface X in connection with the previously known description of all possible topological configurations of X.
Images of mod p Galois Representations Associated to Elliptic Curves
Authors: Reverter Amadeu , Vila Núria 
Published: December 2010

AbstractWe give an explicit recipe for the determination of the images associated to the Galois action on p-torsion points of elliptic curves. We present a table listing the image for all the elliptic curves defined over without complex multiplication with conductor less than 200 and for each prime number p.
On Locating Isometric 𝓁(n)1
Authors: Weston Anthony 
Published: December 2010

AbstractMotivated by a question of Per Enflo, we develop a hypercube criterion for locating linear isometric copies of in an arbitrary real normed space X.The said criterion involves finding 2n points in X that satisfy one metric equality. This contrasts nicely to the standard classical criterion wherein one seeks n points that satisfy 2n−1 metric equalities.
Exponents of Class Groups of Quadratic Function Fields over Finite Fields
Authors: Cardon David A. , Ram Murty M. 
Published: December 2010

AbstractWe find a lower bound on the number of imaginary quadratic extensions of the function fieldwhose class groups have an element of a fixed order.More precisely, letq≥ 5 be a power of an odd prime and letgbe a fixed positive integer ≥ 3. There arepolynomialsD∈with deg(D) ≤ℓsuch that the class groups of the quadratic extensionshave an element of orderg.
The Lehmer Polynomial and Pretzel Links
Authors: Hironaka Eriko 
Published: December 2010

AbstractIn this paper we find a formula for the Alexander polynomial Δp1,…,pk (x) of pretzel knots and links with (p1,…,pk,−1) twists, where k is odd and p1,…, pk are positive integers. The polynomial Δ2,3,7(x) is the well-known Lehmer polynomial, which is conjectured to have the smallest Mahler measure among all monic integer polynomials. We confirm that Δ2,3,7(x) has the smallest Mahler measure among the polynomials arising as Δp1,…,pk (x).
On the Chow Groups of Supersingular Varieties
Authors: Fakhruddin Najmuddin 
Published: December 2010

AbstractWe compute the rational Chow groups of supersingular abelian varieties and some other related varieties, such as supersingular Fermat varieties and supersingular K3 surfaces. These computations are concordant with the conjectural relationship, for a smooth projective variety, between the structure of Chow groups and the coniveau filtration on the cohomology.
On Strongly Convex Indicatrices in Minkowski Geometry
Authors: Ji Min , Shen Zhongmin 
Published: December 2010

AbstractThe geometry of indicatrices is the foundation of Minkowski geometry. A strongly convex indicatrix in a vector space is a strongly convex hypersurface. It admits a Riemannian metric and has a distinguished invariant—(Cartan) torsion. We prove the existence of non-trivial strongly convex indicatrices with vanishing mean torsion and discuss the relationship between the mean torsion and the Riemannian curvature tensor for indicatrices of Randers type.
On a Few Diophantine Equations Related to Fermat’s Last Theorem
Authors: Kihel O. , Levesque C. 
Published: December 2010

AbstractWe combine the deep methods of Frey, Ribet, Serre and Wiles with some results of Darmon, Merel and Poonen to solve certain explicit diophantine equations. In particular, we prove that the area of a primitive Pythagorean triangle is never a perfect power, and that each of the equations X4−4Y4 = Zp, X4 + 4Yp = Z2 has no non-trivial solution. Proofs are short and rest heavily on results whose proofs required Wiles’ deep machinery.
Criteria for Simultaneous Solutions of X2 − DY2 = c and x2 − Dy2 = −c
Authors: Mollin R. A. 
Published: December 2010

AbstractThe purpose of this article is to provide criteria for the simultaneous solvability of the Diophantine equations X2 − DY2 = c and x2 − Dy2 = −c when c ∊ ℤ, and D ∊ ℕ is not a perfect square. This continues work in [6]–[8].
Coordinatization Theorems For Graded Algebras
Authors: Allison Bruce , Smirnov Oleg 
Published: December 2010

AbstractIn this paper we study simple associative algebras with finite-gradings. This is done using a simple algebraFgthat has been constructed in Morita theory from a bilinear formg:U×V→Aover a simple algebraA. We show that finite-gradings onFgare in one to one correspondence with certain decompositions of the pair (U, V). We also show that any simple algebraRwith finite-grading is graded isomorphic toFgfor some bilinear fromg:U×V→A, where the grading onFgis determined by a decomposition of (U, V) and the coordinate algebraAis chosen as a simple ideal of the zero componentR0ofR. In order to prove these results we first prove similar results for simple algebras with Peirce gradings.
Diffraction of Weighted Lattice Subsets
Authors: Baake Michael 
Published: December 2010

AbstractA Dirac comb of point measures in Euclidean space with bounded complex weights that is supported on a lattice Γ inherits certain general properties from the lattice structure. In particular, its autocorrelation admits a factorization into a continuous function and the uniformlattice Dirac comb, and its diffraction measure is periodic, with the dual lattice Γ*as lattice of periods. This statement remains true in the setting of a locally compact Abelian group whose topology has a countable base.
Lie Superalgebras Graded by the Root Systems C(n), D(m, n), D(2, 1, α), F(4), G(3)
Authors: Benkart Georgia , Elduque Alberto 
Published: December 2010

AbstractWe determine the Lie superalgebras that are graded by the root systems of the basic classical simple Lie superalgebras of type C(n), D(m, n), D(2, 1, α) (α ∈ \ {0, −1}), F(4), and G(3).
Weak Type Estimates of the Maximal Quasiradial Bochner-Riesz Operator On Certain Hardy Spaces
Authors: Kim Yong-Cheol 
Published: December 2010

AbstractLet be the dilation group in generated by the infinitesimal generator M where At = exp(M log t), and let be a At-homogeneous distance function defined on . For , we define the maximal quasiradial Bochner-Riesz operator of index δ > 0 byIf At = tI and is a smooth convex hypersurface of finite type, then we prove in an extremely easy way that is well defined on Hp() when δ = n(1/p − 1/2) − 1/2 and 0 < p < 1; moreover, it is a bounded operator from Hp() into Lp,∞().If At = tI and , we also prove that is a bounded operator from Hp() into Lp() when δ > n(1/p − 1/2) − 1/2 and 0 < p < 1.
Rationality and Orbit Closures
Authors: Levy Jason 
Published: December 2010

AbstractSuppose we are given a finite-dimensional vector space V equipped with an F-rational action of a linearly algebraic group G, with F a characteristic zero field. We conjecture the following: to each vector v ∈ V(F) there corresponds a canonical G(F)-orbit of semisimple vectors of V. In the case of the adjoint action, this orbit is the G(F)-orbit of the semisimple part of v, so this conjecture can be considered a generalization of the Jordan decomposition. We prove some cases of the conjecture.
Euclidean Sections of Direct Sums of Normed Spaces
Authors: Litvak A. E. , Milman V. D. 
Published: December 2010

AbstractWe study the dimension of “random” Euclidean sections of direct sums of normed spaces. We compare the obtained results with results from [LMS], to show that for the direct sums the standard randomness with respect to the Haar measure on Grassmanian coincides with a much “weaker” randomness of “diagonal” subspaces (Corollary 1.4 and explanation after). We also add some relative information on “phase transition”.
Rigidity of Hamiltonian Actions
Authors: Rochon Frédéric 
Published: December 2010

AbstractThis paper studies the following question: Given an ω′-symplectic action of a Lie group on a manifoldMwhich coincides, as a smooth action, with a Hamiltonian ω-action, when is this action a Hamiltonian ω′-action? Using a result of Morse-Bott theory presented in Section 2, we show in Section 3 of this paper that such an action is in fact a Hamiltonian ω′-action, provided thatM is compact and that the Lie group is compact and connected. This result was first proved by Lalonde-McDuff-Polterovich in 1999 as a consequence of a more general theory that made use of hard geometric analysis. In this paper, we prove it using classical methods only.
A Coincidence Theorem for Holomorphic Maps toG/P
Authors: Sankaran Parameswaran 
Published: December 2010

AbstractThe purpose of this note is to extend to an arbitrary generalized Hopf and Calabi-Eckmann manifold the following result of Kalyan Mukherjea: Letdenote a Calabi-Eckmann manifold. If f, g : Vn→are any two holomorphic maps, at least one of them being non-constant, then there exists a coincidence: f(x) = g(x) for some x ∈ Vn. Our proof involves a coincidence theorem for holomorphic maps to complex projective varieties of the formG/PwhereGis complex simple algebraic group andP⊂Gis a maximal parabolic subgroup, where one of the maps is dominant.
Discreteness For the Set of Complex Structures On a Real Variety
Authors: Ballico E. 
Published: December 2010

AbstractLet X, Y be reduced and irreducible compact complex spaces and S the set of all isomorphism classes of reduced and irreducible compact complex spaces W such that X × Y ≅ X × W. Here we prove that S is at most countable. We apply this result to show that for every reduced and irreducible compact complex space X the set S(X) of all complex reduced compact complex spaces W with X × Xσ ≅ W × Wσ (where Aσ denotes the complex conjugate of any variety A) is at most countable.
Some Questions about Semisimple Lie Groups Originating in Matrix Theory
Authors: Ðoković Dragomir Ž. , Tam Tin-Yau 
Published: December 2010

AbstractWe generalize the well-known result that a square traceless complex matrix is unitarily similar to a matrix with zero diagonal to arbitrary connected semisimple complex Lie groups G and their Lie algebras under the action of a maximal compact subgroup K of G. We also introduce a natural partial order on : x ≤ y if f (K · x) ⊆ f (K · y) for all f 2 *, the complex dual of . This partial order is K-invariant and induces a partial order on the orbit space /K. We prove that, under some restrictions on , the set f (K · x) is star-shaped with respect to the origin.
Homogeneity of the Pure State Space of a Separable C*-Algebra
Authors: Kishimoto Akitaka , Ozawa Narutaka , Sakai Shôichirô 
Published: December 2010

AbstractWe prove that the pure state space is homogeneous under the action of the automorphism group (or the subgroup of asymptotically inner automorphisms) for all the separable simple C*-algebras. The first result of this kind was shown by Powers for the UHF algbras some 30 years ago.
Potential Theory of the Farthest-Point Distance Function
Authors: Laugesen Richard S. , Pritsker Igor E. 
Published: December 2010

AbstractWe study the farthest-point distance function, which measures the distance fromz∈to the farthest point or points of a given compact setEin the plane.The logarithm of this distance is subharmonic as a function ofz, and equals the logarithmic potential of a unique probability measure with unbounded support. This measureσEhas many interesting properties that reflect the topology and geometry of the compact setE. We proveσE(E) ≤for polygons inscribed in a circle, with equality if and only ifEis a regularn-gon for some oddn. Also we showσE(E) =for smooth convex sets of constant width. We conjectureσE(E) ≤for allE.
Canonical Vector Heights on Algebraic K3 Surfaces with Picard Number Two
Authors: Baragar Arthur 
Published: December 2010

AbstractLet V be an algebraic K3 surface defined over a number field K. Suppose V has Picard number two and an infinite group of automorphisms A = Aut(V/K). In this paper, we introduce the notion of a vector height h: V → Pic(V) ⊗ and show the existence of a canonical vector height with the following properties:where σ ∈ A, σ* is the pushforward of σ (the pullback of σ−1), and hD is a Weil height associated to the divisor D. The bounded function implied by the O(1) does not depend on P. This allows us to attack some arithmetic problems. For example, we show that the number of rational points with bounded logarithmic height in an A-orbit satisfiesHere, μ(P) is a nonnegative integer, s is a positive integer, and ω is a real quadratic fundamental unit.
Symmetries of Kirchberg Algebras
Authors: Benson David J. , Kumjian Alex , Christopher Phillips N. 
Published: December 2010

AbstractLet G0 and G1 be countable abelian groups. Let γi be an automorphism of Gi of order two. Then there exists a unital Kirchberg algebra A satisfying the Universal Coefficient Theorem and with [1A] = 0 in K0(A), and an automorphism α ∈ Aut(A) of order two, such that K0(A) ≅ G0, such that K1(A) ≅ G1, and such that α* : Ki(A) → Ki(A) is γi. As a consequence, we prove that every -graded countable module over the representation ring R() of is isomorphic to the equivariant K-theory K (A) for some action of on a unital Kirchberg algebra A.Along the way, we prove that every not necessarily finitely generated []-module which is free as a -module has a direct sum decomposition with only three kinds of summands, namely [] itself and on which the nontrivial element of acts either trivially or by multiplication by −1.
On Harmonic Theory in Flows
Authors: Pak Hong Kyung 
Published: December 2010

AbstractRecently [8], a harmonic theory was developed for a compact contact manifold from the viewpoint of the transversal geometry of contact flow. A contact flow is a typical example of geodesible flow. As a natural generalization of the contact flow, the present paper develops a harmonic theory for various flows on compact manifolds. We introduce the notions of H-harmonic and H*-harmonic spaces associated to a Hörmander flow. We also introduce the notions of basic harmonic spaces associated to a weak basic flow. One of our main results is to show that in the special case of isometric flow these harmonic spaces are isomorphic to the cohomology spaces of certain complexes. Moreover, we find an obstruction for a geodesible flow to be isometric.
On Newton's Method and Rational Approximations to Quadratic Irrationals
Authors: Burger Edward B. 
Published: December 2010

AbstractIn 1988 Rieger exhibited a differentiable function having a zero at the golden ratio (−1 + )/2 for which when Newton's method for approximating roots is applied with an initial value x0 = 0, all approximates are so-called “best rational approximates”—in this case, of the form F2n/F2n+1, where Fn denotes the n-th Fibonacci number. Recently this observation was extended by Komatsu to the class of all quadratic irrationals whose continued fraction expansions have period length 2. Here we generalize these observations by producing an analogous result for all quadratic irrationals and thus provide an explanation for these phenomena.
2-Primary Exponent Bounds for Lie Groups of Low Rank
Authors: Theriault Stephen D. 
Published: December 2010

AbstractExponent information is proven about the Lie groups SU(3), SU(4), Sp(2), and G2 by showing some power of the H-space squaring map (on a suitably looped connected-cover) is null homotopic. The upper bounds obtained are 8, 32, 64, and 28 respectively. This null homotopy is best possible for SU(3) given the number of loops, off by at most one power of 2 for SU(4) and Sp(2), and off by at most two powers of 2 for G2.
Kolakoski-(3, 1) Is a (Deformed) Model Set
Authors: Baake Michael , Sing Bernd 
Published: December 2010

AbstractUnlike the (classical) Kolakoski sequence on the alphabet {1, 2}, its analogue on {1, 3} can be related to a primitive substitution rule. Using this connection, we prove that the corresponding biin finite fixed point is a regular generic model set and thus has a pure point diffraction spectrum. The Kolakoski-(3, 1) sequence is then obtained as a deformation, without losing the pure point diffraction property.
Countable Amenable Identity Excluding Groups
Authors: Jaworski Wojciech 
Published: December 2010

AbstractA discrete group G is called identity excluding if the only irreducible unitary representation of G which weakly contains the 1-dimensional identity representation is the 1-dimensional identity representation itself. Given a unitary representation π of G and a probability measure μ on G, let Pμ denote the μ-average ∫π(g)μ(dg). The goal of this article is twofold: (1) to study the asymptotic behaviour of the powers , and (2) to provide a characterization of countable amenable identity excluding groups. We prove that for every adapted probability measure μ on an identity excluding group and every unitary representation π there exists and orthogonal projection Eμ onto a π-invariant subspace such that for every a ∈ supp μ. This also remains true for suitably defined identity excluding locally compact groups. We show that the class of countable amenable identity excluding groups coincides with the class of FC-hypercentral groups; in the finitely generated case this is precisely the class of groups of polynomial growth. We also establish that every adapted random walk on a countable amenable identity excluding group is ergodic.
Super-Brownian Motion and Critical Spatial Stochastic Systems
Authors: Perkins Ed 
Published: December 2010

AbstractThis article is a short introduction to super-Brownian motion. Some of its properties are discussed but our main objective is to describe a number of limit theorems which show super-Brownian motion is a universal limit for rescaled spatial stochastic systems at criticality above a critical dimenson. These systems include the voter model, the contact process and critical oriented percolation.
Near Triangularizability Implies Triangularizability
Authors: Yahaghi Bamdad R. 
Published: December 2010

AbstractIn this paper we consider collections of compact operators on a real or complex Banach space including linear operators on finite-dimensional vector spaces. We show that such a collection is simultaneously triangularizable if and only if it is arbitrarily close to a simultaneously triangularizable collection of compact operators. As an application of these results we obtain an invariant subspace theorem for certain bounded operators. We further prove that in finite dimensions near reducibility implies reducibility whenever the ground field isor.
Combinatorics of Words and Semigroup Algebras Which Are Sums of Locally Nilpotent Subalgebras
Authors: Drensky Vesselin , Hammoudi Lakhdar 
Published: December 2010

AbstractWe construct new examples of non-nil algebras with any number of generators, which are direct sums of two locally nilpotent subalgebras. Like all previously known examples, our examples are contracted semigroup algebras and the underlying semigroups are unions of locally nilpotent subsemigroups. In our constructions we make more transparent than in the past the close relationship between the considered problem and combinatorics of words.
A Reduction of the Batyrev-Manin Conjecture for Kummer Surfaces
Authors: McKinnon David 
Published: December 2010

AbstractLet V be a K3 surface defined over a number field k. The Batyrev-Manin conjecture for V states that for every nonempty open subset U of V, there exists a finite set ZU of accumulating rational curves such that the density of rational points on U − ZU is strictly less than the density of rational points on ZU. Thus, the set of rational points of V conjecturally admits a stratification corresponding to the sets ZU for successively smaller sets U.In this paper, in the case that V is a Kummer surface, we prove that the Batyrev-Manin conjecture for V can be reduced to the Batyrev-Manin conjecture for V modulo the endomorphisms of V induced by multiplication by m on the associated abelian surface A. As an application, we use this to show that given some restrictions on A, the set of rational points of V which lie on rational curves whose preimages have geometric genus 2 admits a stratification of Batyrev-Manin type.
On the Stable Basin Theorem
Authors: Parker John R. 
Published: December 2010

AbstractThe stable basin theorem was introduced by Basmajian and Miner as a key step in their necessary condition for the discreteness of a non-elementary group of complex hyperbolic isometries. In this paper we improve several of Basmajian and Miner’s key estimates and so give a substantial improvement on the main inequality in the stable basin theorem.