bluuebunny/crossref_metadata_2025 huggingface dataset:
Characteristic p Galois Representations That Arise from Drinfeld Modules
Authors: Boston Nigel , Ose David T.
Published: December 2010

We examine which representations of the absolute Galois group of a field of finite characteristic with image over a finite field of the same characteristic may be constructed by the Galois group’s action on the division points of an appropriate Drinfeld module.
Courbes hyperelliptiques à multiplications réelles et une construction de Shih
Authors: Darmon Henri , Mestre Jean-François
Published: December 2010

Soient r et p deux nombres premiers distincts, soit , et soit 𝔽 le corps résiduel de K en une place au-dessus de p. Lorsque l’image de dans 𝔽 n’est pas un carré, nous donnons une construction géométrique d’une extension réguliere de K(t) de groupe de Galois PSL2(𝔽). Cette extension correspond à un revêtement de de « signature (r, p, p) » au sens de [3, sec. 6.3], et son existence est prédite par le critère de rigidité de Belyi, Fried, Thompson et Matzat. Sa construction s’obtient en tordant la representation galoisienne associée aux points d’ordre p d’une famille de variétés abéliennes à multiplications réelles par K découverte par Tautz, Top et Verberkmoes [6]. Ces variétés abéliennes sont définies sur un corps quadratique, et sont isogènes à leur conjugué galoisien. Notre construction généralise une méthode de Shih [4], [5], que l’on retrouve quand r = 2 et r = 3.
On Classification of Certain C*-Algebras
Authors: Elliott George , Fulman Igor
Published: December 2010

We consider C*-algebras which are inductive limits of finite direct sums of copies of . For such algebras, the lattice of closed two-sided ideals is proved to be a complete invariant.
Maximal Operators and Cantor Sets
Authors: Hare Kathryn E.
Published: December 2010

We consider maximal operators in the plane, defined by Cantor sets of directions, and show such operators are not bounded on L2 if the Cantor set has positive Hausdorff dimension.
Nonconvexity of the Generalized Numerical Range Associated with the Principal Character
Authors: Li Chi-Kwong , Zaharia Alexandru
Published: December 2010

Suppose 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 by

It 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.
An Estimate For a Restricted X-Ray Transform
Authors: Oberlin Daniel M.
Published: December 2010

This paper contains a geometric proof of an estimate for a restricted x-ray transform. The result complements one of A. Greenleaf and A. Seeger.
Harmonic Polynomials Associated With Reflection Groups
Authors: Xu Yuan
Published: December 2010

We 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.
Multiplicities of Binary Recurrences
Authors: Brindza B. , Pintér Á. , Schmidt W. M.
Published: December 2010

In this note the multiplicities of binary recurrences over algebraic number fields are investigated under some natural assumptions.
Gauss Sums of Orders Six and Twelve
Authors: Evans Ronald
Published: December 2010

Precise, elegant evaluations are given for Gauss sums of orders six and twelve.
Normal Subloops in the Integral Loop Ring of an RA Loop
Authors: Goodaire Edgar G. , Milies César Polcino
Published: December 2010

We show that an RA loop has a torsion-free normal complement in the loop of normalized units of its integral loop ring. We also investigate whether an RA loop can be normal in its unit loop. Over fields, this can never happen.
Constructing Compacta of Different Extensional Dimensions
Authors: Levin Michael
Published: December 2010

Applying the Sullivan conjecture we construct compacta of certain cohomological and extensional dimensions.
On the Density of Cyclic Quartic Fields
Authors: Ou Zhiming M. , Williams Kenneth S.
Published: December 2010

An asymptotic formula is obtained for the number of cyclic quartic fields over Q with discriminant ≤ x.
Approximation algébrique simultanée de nombres de Liouville
Authors: Roy Damien
Published: December 2010

The 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

Around 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

We 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

Let 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

We 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.
Positive Solution of a Subelliptic Nonlinear Equation on the Heisenberg Group
Authors: Wang Wei
Published: December 2010

In this paper, we establish the existence of positive solution of a nonlinear subelliptic equation involving the critical Sobolev exponent on the Heisenberg group, which generalizes a result of Brezis and Nirenberg in the Euclidean case.
On Locating Isometric 𝓁(n)1
Authors: Weston Anthony
Published: December 2010

Motivated 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

We 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

In 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).
Local VMO and Weak Convergence in h1
Authors: Dafni Galia
Published: December 2010

A local version of VMO is defined, and the local Hardy space h1 is shown to be its dual. An application to weak-* convergence in h1 is proved.
On the Poisson Integral of Step Functions and Minimal Surfaces
Authors: Weitsman Allen
Published: December 2010

Applications of minimal surface methods are made to obtain information about univalent harmonic mappings. In the case where the mapping arises as the Poisson integral of a step function, lower bounds for the number of zeros of the dilatation are obtained in terms of the geometry of the image.
On the Chow Groups of Supersingular Varieties
Authors: Fakhruddin Najmuddin
Published: December 2010

We 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

The 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

We 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.
Modular Forms Associated to Theta Functions
Authors: Ho Lee Min
Published: December 2010

We use the theory of Jacobi-like forms to construct modular forms for a congruence subgroup of SL(2, ℝ) which can be expressed as linear combinations of products of certain theta functions.
Algèbres simples centrales de degré 5 et E8
Authors: Gille Philippe
Published: December 2010

As a consequence of a theorem of Rost-Springer, we establish that the cyclicity problem for central simple algebra of degree 5 on fields containg a fifth root of unity is equivalent to the study of anisotropic elements of order 5 in the split group of type E8.
Criteria for Simultaneous Solutions of X2 − DY2 = c and x2 − Dy2 = −c
Authors: Mollin R. A.
Published: December 2010

The 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

In 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

A 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

We 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).
Polytopal Realizations of Generalized Associahedra
Authors: Chapoton Frédéric , Fomin Sergey , Zelevinsky Andrei
Published: December 2010

We prove polytopality of the generalized associahedra introduced in [5].
Weak Type Estimates of the Maximal Quasiradial Bochner-Riesz Operator On Certain Hardy Spaces
Authors: Kim Yong-Cheol
Published: December 2010

Let 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 by

If 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

Suppose 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

We 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

This 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

The 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.
Second Order Dehn Functions of Asynchronously Automatic Groups
Authors: Wang Xiaofeng
Published: December 2010

Upper bounds of second order Dehn functions of asynchronously automatic groups are obtained.
Discreteness For the Set of Complex Structures On a Real Variety
Authors: Ballico E.
Published: December 2010

Let 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

We 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

We 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

We 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.
The Grothendieck Trace and the de Rham Integral
Authors: Sastry Pramathanath , Tong Yue Lin L.
Published: December 2010

On a smoothn-dimensional complete varietyXoverwe show that the trace maparising from Lipman's version of Grothendieck duality in [L] agrees with

under the Dolbeault isomorphism.
Canonical Vector Heights on Algebraic K3 Surfaces with Picard Number Two
Authors: Baragar Arthur
Published: December 2010

Let 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 satisfies

Here, 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

Let 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

Recently [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

In 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.
A Note on the Height of the Formal Brauer Group of a K3 Surface
Authors: Goto Yasuhiro
Published: December 2010

Using weighted Delsarte surfaces, we give examples of K3 surfaces in positive characteristic whose formal Brauer groups have height equal to 5, 8 or 9. These are among the four values of the height left open in the article of Yui [11].
2-Primary Exponent Bounds for Lie Groups of Low Rank
Authors: Theriault Stephen D.
Published: December 2010

Exponent 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.
On Uniqueness of Meromorphic Functions with Shared Values in Some Angular Domains
Authors: Jian-Hua Zheng
Published: December 2010

In this paper we investigate the uniqueness of transcendental meromorphic function dealing with the shared values in some angular domains instead of the whole complex plane.
Kolakoski-(3, 1) Is a (Deformed) Model Set
Authors: Baake Michael , Sing Bernd
Published: December 2010

Unlike 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

A 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

This 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

In 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

We 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.
Spectrally Bounded Linear Maps on 𝓑(X)
Authors: Fošner Ajda , Šemrl Peter
Published: December 2010

We characterize surjective linear maps on that are spectrally bounded and spectrally bounded below.
A Reduction of the Batyrev-Manin Conjecture for Kummer Surfaces
Authors: McKinnon David
Published: December 2010

Let 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.
A Hopf Type Lemma and a CR Type Inversion for the Generalized Greiner Operator
Authors: Pengcheng Niu , Yanwu Han , Junqiang Han
Published: December 2010

In this paper we establish a Hopf type lemma and a CR type inversion for the generalized Greiner operator. Some nonlinear Liouville type results are given.
On the Stable Basin Theorem
Authors: Parker John R.
Published: December 2010

The 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.
Algebraicity of some Weil Hodge Classes
Authors: Koike Kenji
Published: December 2010

We show that the Prym map for 4-th cyclic étale covers of curves of genus 4 is a dominant morphism to a Shimura variety for a family of Abelian 6-folds of Weil type. According to the result of Schoen, this implies algebraicity of Weil classes for this family.
On the Surjectivity of the Galois Representations Associated to Non-CM Elliptic Curves
Authors: Cojocaru Alina Carmen , Kani Ernst
Published: December 2010

Let E be an elliptic curve defined over ℚ, of conductor N and without complex multiplication. For any positive integer l, let ϕl be the Galois representation associated to the l-division points of E. From a celebrated 1972 result of Serre we know that ϕl is surjective for any sufficiently large prime l. In this paper we find conditional and unconditional upper bounds in terms of N for the primes l for which ϕl is not surjective.
Injectivity of the Connecting Maps in AH Inductive Limit Systems
Authors: Elliott George A. , Gong Guihua , Li Liangqing
Published: December 2010

LetAbe the inductive limit of a system

with, whereXn,iis a finite simplicial complex, andPn,iis a projection inM[n,i](C(Xn,i)). In this paper, we will prove thatAcan be written as another inductive limit

with, whereYn,iis a finite simplicial complex, andQn,iis a projection inM{n,i}(C(Yn,i)), with the extra condition that all the mapsψn,n+1areinjective. (The result is trivial if one allows the spacesYn,ito be arbitrary compact metrizable spaces.) This result is important for the classification of simple AH algebras. The special case that the spacesXn,iare graphs is due to the third author.
Trivial Units for Group Rings withG-adapted Coefficient Rings
Authors: Herman Allen , Li Yuanlin , Parmenter M. M.
Published: December 2010

For each finite groupGfor which the integral group ring ℤGhas only trivial units, we give ring-theoretic conditions for a commutative ringRunder which the group ringRGhas nontrivial units. Several examples of rings satisfying the conditions and rings not satisfying the conditions are given. In addition, we extend a well-known result for fields by showing that ifRis a ring of finite characteristic andRGhas only trivial units, thenGhas order at most 3.
Weighted Convolution Operators on ℓp
Authors: Borwein David , Kratz Werner
Published: December 2010

The main results deal with conditions for the validity of the weighted convolution inequality when p ≥ 1.
On Suslinian Continua
Authors: Daniel D. , Nikiel J. , Treybig L. B. , Tuncali H. M. , Tymchatyn E. D.
Published: December 2010

A continuumis said to be Suslinian if it does not contain uncountably many mutually exclusive nondegenerate subcontinua. We prove that Suslinian continua are perfectly normal and rim-metrizable. Locally connected Suslinian continua have weight atmost ω1 and under appropriate set-theoretic conditions are metrizable. Non-separable locally connected Suslinian continua are rim-finite on some open set.
The Distribution of Totatives
Authors: Germain Jam
Published: December 2010

The integers coprime to n are called the totatives of n. D. H. Lehmer and Paul Erdős were interested in understanding when the number of totatives between in/k and (i +1)n/k are 1/kth of the total number of totatives up to n. They provided criteria in various cases. Here we give an “if and only if” criterion which allows us to recover most of the previous results in this literature and to go beyond, as well to reformulate the problem in terms of combinatorial group theory. Our criterion is that the above holds if and only if for every odd character χ (mod κ) (where κ := k/ gcd(k, n/ Πp|n p)) there exists a prime p = pχ dividing n for which χ(p) = 1.
An Elementary Proof of Suslin Reciprocity
Authors: Kerr Matt
Published: December 2010

We state and prove an important special case of Suslin reciprocity that has found significant use in the study of algebraic cycles. An introductory account is provided of the regulator and norm maps on Milnor K2-groups (for function fields) employed in the proof.
Counting Multiple Cyclic Choices Without Adjacencies
Authors: McLeod Alice , Moser William
Published: December 2010

We give a particularly elementary solution to the following well-known problem. What is the number of k-subsets X ⊆ In = {1, 2, 3, … , n} satisfying “no two elements of X are adjacent in the circular display of In”? Then we investigate a new generalization (multiple cyclic choices without adjacencies) and apply it to enumerating a class of 3-line latin rectangles.
Short Geodesics of Unitaries in the L2 Metric
Authors: Andruchow Esteban
Published: December 2010

Let ℳ be a type II1 von Neumann algebra, τ a trace in ℳ, and L2 (ℳ, τ) the GNS Hilbert space of τ . We regard the unitary group Uℳ as a subset of L2(ℳ, τ) and characterize the shortest smooth curves joining two fixed unitaries in the L2 metric. As a consequence of this we obtain that Uℳ, though a complete (metric) topological group, is not an embedded riemannian submanifold of L2(ℳ, τ)
Trigonometric Multipliers on H2π
Authors: Daly J. E. , Fridli S.
Published: December 2010

In this paper we consider multipliers on the real Hardy space H2π. It is known that the Marcinkiewicz and the Hörmander–Mihlin conditions are sufficient for the corresponding trigonometric multiplier to be bounded on , 1 < p < ∞. We show among others that the Hörmander– Mihlin condition extends to H2π but the Marcinkiewicz condition does not.
Uniform Estimates of Ultraspherical Polynomials of Large Order
Authors: De Carli Laura
Published: December 2010

In this paper we prove the sharp inequality

where is the classical ultraspherical polynomial of degree n and order . This inequality can be refined in [0, ] and [, 1], where denotes the largest zero of .
On the Garsia Lie Idempotent
Authors: Patras Frédéric , Reutenauer Christophe , Schocker Manfred
Published: December 2010

The orthogonal projection of the free associative algebra onto the free Lie algebra is afforded by an idempotent in the rational group algebra of the symmetric groupSn, in each homogenous degreen. We give various characterizations of this Lie idempotent and show that it is uniquely determined by a certain unit in the group algebra ofSn−1. The inverse of this unit, or, equivalently, the Gram matrix of the orthogonal projection, is described explicitly. We also show that the Garsia Lie idempotent is not constant on descent classes (in fact, not even on coplactic classes) inSn.
Degeneracy of 2-Forms and 3-Forms
Authors: Fehér L. M. , Némethi A. , Rimányi R.
Published: December 2010

We study some global aspects of differential complex 2-forms and 3-forms on complex manifolds. We compute the cohomology classes represented by the sets of points on a manifold where such a form degenerates in various senses, together with other similar cohomological obstructions. Based on these results and a formula for projective representations, we calculate the degree of the projectivization of certain orbits of the representation Λkℂn.
Evaluation of the Dedekind Eta Function
Authors: Chapman Robin , Hart William
Published: December 2010

We extend the methods of Van der Poorten and Chapman for explicitly evaluating the Dedekind eta function at quadratic irrationalities. Via evaluation of HeckeL-series we obtain new evaluations at points in imaginary quadratic number fields with class numbers 3 and 4. Further, we overcome the limitations of the earlier methods and via modular equations provide explicit evaluations where the class number is 5 or 7.
A Double Triangle Operator Algebra From SL2(ℝ+)
Authors: Levene R. H.
Published: December 2010

We consider the w*-closed operator algebra generated by the image of the semigroup SL2(ℝ+) under a unitary representation ρ of SL2(ℝ) on the Hilbert space L2(ℝ). We show that is a reflexive operator algebra and = Alg where is a double triangle subspace lattice. Surprisingly, is also generated as a w*-closed algebra by the image under ρ of a strict subsemigroup of SL2(ℝ+).
Weighted Brianchon-Gram Decomposition
Authors: Agapito J.
Published: December 2010

We give in this note a weighted version of Brianchon and Gram's decomposition for a simple polytope. We can derive from this decomposition the weighted polar formula of Agapito and a weighted version of Brion's theorem, in a manner similar to Haase, where the unweighted case is worked out. This weighted version of Brianchon and Gram's decomposition is a direct consequence of the ordinary Brianchon–Gram formula.
On the Relation Between the Gaussian Orthogonal Ensemble and Reflections, or a Self-Adjoint Version of the Marcus–Pisier Inequality
Authors: Wagner Roy
Published: December 2010

We prove a self-adjoint analogue of the Marcus–Pisier inequality, comparing the expected value of convex functionals on random reflection matrices and on elements of the Gaussian orthogonal (or unitary) ensemble.
A Free Logarithmic Sobolev Inequality on the Circle
Authors: Hiai Fumio , Petz Dénes , Ueda Yoshimichi
Published: December 2010

Free analogues of the logarithmic Sobolev inequality compare the relative free Fisher information with the relative free entropy. In the present paper such an inequality is obtained for measures on the circle. The method is based on a random matrix approximation procedure, and a large deviation result concerning the eigenvalue distribution of special unitary matrices is applied and discussed.
Vector-Valued Modular Forms of Weight Two Associated With Jacobi-Like Forms
Authors: Lee Min Ho
Published: December 2010

We construct vector-valued modular forms of weight 2 associated to Jacobi-like forms with respect to a symmetric tensor representation of Γ by using the method of Kuga and Shimura as well as the correspondence between Jacobi-like forms and sequences of modular forms. As an application, we obtain vector-valued modular forms determined by theta functions and by pseudodifferential operators.
Conjugacy Classes of Subalgebras of the Real Sedenions
Authors: Chan Kai-Cheong , Đoković Dragomir Ž.
Published: December 2010

By applying the Cayley–Dickson process to the division algebra of real octonions, one obtains a 16-dimensional real algebra known as (real) sedenions. We denote this algebra by A4. It is a flexible quadratic algebra (with unit element 1) but not a division algebra.

We classify the subalgebras of A4 up to conjugacy (i.e., up to the action of the automorphismgroup G of A4) with one exception: we leave aside the more complicated case of classifying the quaternion subalgebras. Any nonzero subalgebra contains 1 and we show that there are no proper subalgebras of dimension 5, 7 or > 8. The proper non-division subalgebras have dimensions 3, 6 and 8. We show that in each of these dimensions there is exactly one conjugacy class of such subalgebras. There are infinitely many conjugacy classes of subalgebras in dimensions 2 and 4, but only 4 conjugacy classes in dimension 8.
On Non-Integral Dehn Surgeries Creating Non-Orientable Surfaces
Authors: Teragaito Masakazu
Published: December 2010

For a non-trivial knot in the 3-sphere, only integral Dehn surgery can create a closed 3-manifold containing a projective plane. If we restrict ourselves to hyperbolic knots, the corresponding claim for a Klein bottle is still true. In contrast to these, we show that non-integral surgery on a hyperbolic knot can create a closed non-orientable surface of any genus greater than two.
Approximation and the Topology of Rationally Convex Sets
Authors: Zeron E. S.
Published: December 2010

Considering a mappinggholomorphic on a neighbourhood of a rationally convex setK⊂ ℂn, and range into the complex projective space ℂℙm, the main objective of this paper is to show that we can uniformly approximategonKby rational mappings defined from ℂninto ℂℙm. We only need to ask that the second Čech cohomology groupȞ2(K, ℤ) vanishes.
van der Pol Expansions of L-Series
Authors: Borwein David , Borwein Jonathan
Published: December 2010

We provide concise series representations for various L-series integrals. Different techniques are needed below and above the abscissa of absolute convergence of the underlying L-series.
Invariant Metrics with Nonnegative Curvature on Compact Lie Groups
Authors: Brown Nathan , Finck Rachel , Spencer Matthew , Tapp Kristopher , Wu Zhongtao
Published: December 2010

We classify the left-invariant metrics with nonnegative sectional curvature on SO(3) and U(2).
Tensor Square of the Minimal Representation ofO(p,q)
Authors: Dvorsky Alexander
Published: December 2010

In this paper, we study the tensor product π = σmin⊗ σminof the minimal representation σminofO(p,q) with itself, and decompose π into a direct integral of irreducible representations. The decomposition is given in terms of the Plancherel measure on a certain real hyperbolic space.
Hermitian Harmonic Maps into Convex Balls
Authors: Li Zhen Yang , Zhang Xi
Published: December 2010

In this paper, we consider Hermitian harmonic maps from Hermitian manifolds into convex balls. We prove that there exist no non-trivial Hermitian harmonic maps from closed Hermitian manifolds into convex balls, and we use the heat flow method to solve the Dirichlet problem for Hermitian harmonic maps when the domain is a compact Hermitian manifold with non-empty boundary.
On the Structure of the Set of Symmetric Sequences in Orlicz Sequence Spaces
Authors: Sari Bünyamin
Published: December 2010

We study the structure of the sets of symmetric sequences and spreading models of an Orlicz sequence space equipped with partial order with respect to domination of bases. In the cases that these sets are “small”, some descriptions of the structure of these posets are obtained.
An Infinite Dimensional Vector Space of Universal Functions for H∞ of the Ball
Authors: Aron Richard , Gorkin Pamela
Published: December 2010

We show that there exists a closed infinite dimensional subspace of H∞(Bn) such that every function of norm one is universal for some sequence of automorphisms of Bn.
Plane Quartic Twists of X(5, 3)
Authors: Fernández Julio , González Josep , Lario Joan-C.
Published: December 2010

Given an odd surjective Galois representation ϱ: Gℚ → PGL2(3) and a positive integer N, there exists a twisted modular curve X(N, 3)ϱ defined over ℚ whose rational points classify the quadratic ℚ-curves of degree N realizing ϱ. This paper gives a method to provide an explicit plane quartic model for this curve in the genus-three case N = 5.
Elliptic K3 Surfaces with Geometric Mordell–Weil Rank 15
Authors: Kloosterman Remke
Published: December 2010

We prove that the elliptic surface y2 = x3 + 2(t8 + 14t4 + 1)x + 4t2(t8 + 6t4 + 1) has geometric Mordell–Weil rank 15. This completes a list of Kuwata, who gave explicit examples of elliptic K3-surfaces with geometric Mordell–Weil ranks 0, 1, … , 14, 16, 17, 18.
AF-Skeletons and Real Rank Zero Algebras with the Corona Factorization Property
Authors: Kucerovsky D. , Ng P. W.
Published: December 2010

Let A be a stable, separable, real rank zeroC*-algebra, and suppose that A has an AF-skeleton with only finitely many extreme traces. Then the corona algebra (A)/A is purely infinite in the sense of Kirchberg and Rørdam, which implies that A has the corona factorization property.
Second Order Mock Theta Functions
Authors: McIntosh Richard J.
Published: December 2010

In his last letter to Hardy, Ramanujan defined 17 functions F(q), where |q| < 1. He called them mock theta functions, because as q radially approaches any point e2πir (r rational), there is a theta function Fr(q) with F(q) − Fr(q) = O(1). In this paper we establish the relationship between two families of mock theta functions.
On Cauchy–Liouville–Mirimanoff Polynomials
Authors: Tzermias Pavlos
Published: December 2010

Let p be a prime greater than or equal to 17 and congruent to 2 modulo 3. We use results of Beukers and Helou on Cauchy–Liouville–Mirimanoff polynomials to show that the intersection of the Fermat curve of degree p with the line X + Y = Z in the projective plane contains no algebraic points of degree d with 3 ≤ d ≤ 11. We prove a result on the roots of these polynomials and show that, experimentally, they seem to satisfy the conditions of a mild extension of an irreducibility theorem of Pólya and Szegö. These conditions are conjecturally also necessary for irreducibility.
Expansions in Complex Bases
Authors: Komornik Vilmos , Loreti Paola
Published: December 2010

Beginning with a seminal paper of Rényi, expansions in noninteger real bases have been widely studied in the last forty years. They turned out to be relevant in various domains of mathematics, such as the theory of finite automata, number theory, fractals or dynamical systems. Several results were extended by Daróczy and Kátai for expansions in complex bases. We introduce an adaptation of the so-called greedy algorithm to the complex case, and we generalize one of their main theorems.
Discriminants of Complex Multiplication Fields of Elliptic Curves over Finite Fields
Authors: Luca Florian , Shparlinski Igor E.
Published: December 2010

We show that, for most of the elliptic curves E over a prime finite field p of p elements, the discriminant D(E) of the quadratic number field containing the endomorphism ring of E over p is sufficiently large. We also obtain an asymptotic formula for the number of distinct quadratic number fields generated by the endomorphism rings of all elliptic curves over p.
Generalizations of Frobenius’ Theorem on Manifolds and Subcartesian Spaces
Authors: Śniatycki Jędrzej
Published: December 2010

Let be a family of vector fields on a manifold or a subcartesian space spanning a distribution D. We prove that an orbit O of is an integral manifold of D if D is involutive on O and it has constant rank on O. This result implies Frobenius’ theorem, and its various generalizations, on manifolds as well as on subcartesian spaces.