bluuebunny/crossref_metadata_2025_split huggingface dataset:
Boundedness of the q-Mean-Square Operator on Vector-Valued Analytic Martingales
Authors: Peide Liu , Saksman Eero , Tylli Hans-Olav 
Published: December 2010

AbstractWe study boundedness properties of the q-mean-square operator S(q) on E-valued analytic martingales, where E is a complex quasi-Banach space and 2 ≤ q < ∞. We establish that a.s. finiteness of S(q) for every bounded E-valued analytic martingale implies strong (p, p)-type estimates for S(q) and all p ∈ (0, ∞). Our results yield new characterizations (in terms of analytic and stochastic properties of the function S(q)) of the complex spaces E that admit an equivalent q-uniformly PL-convex quasi-norm. We also obtain a vectorvalued extension (and a characterization) of part of an observation due to Bourgain and Davis concerning the Lp-boundedness of the usual square-function on scalar-valued analytic martingales.
Asymptotic Behavior of Optimal Circle Packings in a Square
Authors: Nurmela Kari J. , Östergård Patric R. J. , aus dem Spring Rainer 
Published: December 2010

AbstractA lower bound on the number of points that can be placed in a square of side σ such that no two points are within unit distance from each other is proven. The result is constructive, and the series of packings obtained contains many conjecturally optimal packings.
Some Properties of Rational Functions with Prescribed Poles
Authors: Aziz-Ul-Auzeem Abdul , Zarger B. A. 
Published: December 2010

AbstractLet P(z) be a polynomial of degree not exceeding n and let where |aj| > 1, j = 1, 2,…,n. If the rational function r(z) = P(z)/W(z) does not vanish in |z| < k, then for k = 1 it is known thatwhere B(Z) = W*(z)/W(z) and . In the paper we consider the case when k > 1 and obtain a sharp result. We also show thatwhere , and as a consquence of this result, we present a generalization of a theorem of O’Hara and Rodriguez for self-inversive polynomials. Finally, we establish a similar result when supremum is replaced by infimum for a rational function which has all its zeros in the unit circle.
A Generalized Characterization of Commutators of Parabolic Singular Integrals
Authors: Hofmann Steve , Li Xinwei , Yang Dachun 
Published: December 2010

AbstractLet and , where λ > 0 and . Denote . We characterize those functions A(x) for which the parabolic Calderón commutatoris bounded on L2(ℝn), where , K is smooth away fromthe origin and satisfies a certain cancellation property.
Spherical Functions on SO0(p, q)/ SO(p) × SO(q)
Authors: Sawyer P. 
Published: December 2010

AbstractAn integral formula is derived for the spherical functions on the symmetric space G/K = SO0(p, q)/ SO(p) × SO(q). This formula allows us to state some results about the analytic continuation of the spherical functions to a tubular neighbourhood of the subalgebra a of the abelian part in the decomposition G = KAK. The corresponding result is then obtained for the heat kernel of the symmetric space SO0(p, q)/ SO(p) × SO(q) using the Plancherel formula.In the Conclusion, we discuss how this analytic continuation can be a helpful tool to study the growth of the heat kernel.
A Gorenstein Ring with Larger Dilworth Number than Sperner Number
Authors: Okon James S. , Vicknair J. Paul 
Published: December 2010

AbstractA counterexample is given to a conjecture of Ikeda by finding a class of Gorenstein rings of embedding dimension 3 with larger Dilworth number than Sperner number. The Dilworth number of is computed when A is an unramified principal Artin local ring.
On the 2-Parallel Versions of Links
Authors: Chang Jae-Ho , Lee Sang Youl , Park Chan-Young 
Published: December 2010

AbstractIn this paper, we show that the absolute value of the signature of the 2-parallel version of a link is less than or equal to the nullity of it and show that the signature, nullity, andMinkowski units of the 2-parallel version of a certain class of links are always equal to 0, 2, and 1 respectively.
Moduli Spaces of Polygons and Punctured Riemann Spheres
Authors: Foth Philip 
Published: December 2010

AbstractThe purpose of this note is to give a simple combinatorial construction of the map from the canonically compactified moduli spaces of punctured complex projective lines to the moduli spaces 𝓟r of polygons with fixed side lengths in the Euclidean space 𝔼3. The advantage of this construction is that one can obtain a complete set of linear relations among the cycles that generate homology of 𝓟r. We also classify moduli spaces of pentagons.
A Dimension-Free Weak-Type Estimate for Operators on UMD-Valued Functions
Authors: Kelly Brian P. 
Published: December 2010

AbstractLet T denote the unit circle in the complex plane, and let X be a Banach space that satisfies Burkholder’s UMD condition. Fix a natural number, N ∈ . Let P denote the reverse lexicographical order on ZN. For each f ∈ L1(TN, X), there exists a strongly measurable function such that formally, for all . In this paper, we present a summation method for this conjugate function directly analogous to the martingale methods developed by Asmar and Montgomery-Smith for scalar-valued functions. Using a stochastic integral representation and an application of Garling’s characterization of UMD spaces, we prove that the associated maximal operator satisfies a weak-type (1, 1) inequality with a constant independent of the dimension N.
Kahane-Khinchin’s Inequality for Quasi-Norms
Authors: Litvak A. E. 
Published: December 2010

AbstractWe extend the recent results of R. Latała and O. Guédon about equivalence of Lq-norms of logconcave random variables (Kahane-Khinchin’s inequality) to the quasi-convex case. We construct examples of quasi-convex bodies Kn ⊂ Rn which demonstrate that this equivalence fails for uniformly distributed vector on Kn (recall that the uniformly distributed vector on a convex body is logconcave). Our examples also show the lack of the exponential decay of the “tail” volume (for convex bodies such decay was proved by M. Gromov and V. Milman).
Helices, Hasimoto Surfaces and Bäcklund Transformations
Authors: Ivey Thomas A. 
Published: December 2010

AbstractTravelling wave solutions to the vortex filament flow generated by elastica produce surfaces in ℝ3 that carry mutually orthogonal foliations by geodesics and by helices. These surfaces are classified in the special cases where the helices are all congruent or are all generated by a single screw motion. The first case yields a new characterization for the Bäcklund transformation for constant torsion curves in R3, previously derived fromthe well-known transformation for pseudospherical surfaces. A similar investigation for surfaces in H3 or S3 leads to a new transformation for constant torsion curves in those spaces that is also derived from pseudospherical surfaces.
Properties of the Invariants of Solvable Lie Algebras
Authors: Ndogmo J. C. 
Published: December 2010

AbstractWe generalize to a field of characteristic zero certain properties of the invariant functions of the coadjoint representation of solvable Lie algebras with abelian nilradicals, previously obtained over the base field ℂ of complex numbers. In particular we determine their number and the restricted type of variables on which they depend. We also determine an upper bound on the maximal number of functionally independent invariants for certain families of solvable Lie algebras with arbitrary nilradicals.
The Dynamics of Localized Solutions of Nonlocal Reaction-Diffusion Equations
Authors: Ward Michael J. 
Published: December 2010

AbstractMany classes of singularly perturbed reaction-diffusion equations possess localized solutions where the gradient of the solution is large only in the vicinity of certain points or interfaces in the domain. The problems of this type that are considered are an interface propagation model from materials science and an activator-inhibitor model of morphogenesis. These two models are formulated as nonlocal partial differential equations. Results concerning the existence of equilibria, their stability, and the dynamical behavior of localized structures in the interior and on the boundary of the domain are surveyed for these two models. By examining the spectrum associated with the linearization of these problems around certain canonical solutions, it is shown that the nonlocal term can lead to the existence of an exponentially small principal eigenvalue for the linearized problem. This eigenvalue is then responsible for an exponentially slow, or metastable, motion of the localized structure.
Extension of Maps to Nilpotent Spaces
Authors: Cencelj M. , Dranishnikov A. N. 
Published: December 2010

AbstractWe show that every compactum has cohomological dimension 1 with respect to a finitely generated nilpotent group G whenever it has cohomological dimension 1 with respect to the abelianization of G. This is applied to the extension theory to obtain a cohomological dimension theory condition for a finite-dimensional compactum X for extendability of every map from a closed subset of X into a nilpotent CW-complex M with finitely generated homotopy groups over all of X.
Linear Operators Preserving Generalized Numerical Ranges and Radii on Certain Triangular Algebras of Matrices
Authors: Cheung Wai-Shun , Li Chi-Kwong 
Published: December 2010

AbstractLet c = (c1, … , cn) be such that c1 ≥ … ≥ cn. The c-numerical range of an n × n matrix A is defined byand the c-numerical radius of A is defined by . We determine the structure of those linear operators ϕ on algebras of block triangular matrices, satisfying
LS-catégorie algébrique et attachement de cellules
Authors: Kahl Thomas 
Published: December 2010

RésuméNousmontrons que la A-catégorie d’un espace simplement connexe de type fini est inférieure ou égale à n si et seulement si son modèle d’Adams-Hilton est un rétracte homotopique d’une algèbre différentielle à n étages. Nous en déduisons que l’invariant Acat augmente au plus de 1 lors de l’attachement d’une cellule à un espace.
On Cyclic Fields of Odd Prime Degree p with Infinite Hilbert p-Class Field Towers
Authors: Gerth Frank 
Published: December 2010

AbstractLet k be a cyclic extension of odd prime degree p of the field of rational numbers. If t denotes the number of primes that ramify in k, it is known that the Hilbert p-class field tower of k is infinite if t > 3 + 2 . For each t > 2 + , this paper shows that a positive proportion of such fields k have infinite Hilbert p-class field towers.
Globalization of Distinguished Supercuspidal Representations of GL(n)
Authors: Hakim Jeffrey , Murnaghan Fiona 
Published: December 2010

AbstractAn irreducible supercuspidal representation π of G = GL(n, F), where F is a nonarchimedean local field of characteristic zero, is said to be “distinguished” by a subgroup H of G and a quasicharacter χ of H if HomH(π, χ) ≠ 0. There is a suitable global analogue of this notion for an irreducible, automorphic, cuspidal representation associated to GL(n). Under certain general hypotheses, it is shown in this paper that every distinguished, irreducible, supercuspidal representation may be realized as a local component of a distinguished, irreducible automorphic, cuspidal representation. Applications to the theory of distinguished supercuspidal representations are provided.
On the Smirnov Class Defined by the Maximal Function
Authors: Nawrocki Marek 
Published: December 2010

AbstractH. O. Kim has shown that contrary to the case of Hp-space, the Smirnov class M defined by the radial maximal function is essentially smaller than the classical Smirnov class of the disk. In the paper we show that these two classes have the same corresponding locally convex structure, i.e. they have the same dual spaces and the same Fréchet envelopes. We describe a general form of a continuous linear functional on M and multiplier from M into Hp, 0 < p ≤ ∞.
Surjectivity of mod ℓ Representations Attached to Elliptic Curves and Congruence Primes
Authors: Chen Imin 
Published: December 2010

AbstractFor a modular elliptic curve E/, we show a number of links between the primes ℓ for which the mod ℓ representation of E/ has projective dihedral image and congruence primes for the newform associated to E/.
On Deformations of the Complex Structure on the Moduli Space of Spatial Polygons
Authors: Kamiyama Yasuhiko , Tsukuda Shuichi 
Published: December 2010

AbstractFor an integer n ≥ 3, let Mn be the moduli space of spatial polygons with n edges. We consider the case of odd n. Then Mn is a Fano manifold of complex dimension n − 3. Let ΘMn be the sheaf of germs of holomorphic sections of the tangent bundle TMn. In this paper, we prove Hq(Mn, ΘMn) = 0 for all q ≥ 0 and all odd n. In particular, we see that the moduli space of deformations of the complex structure on Mn consists of a point. Thus the complex structure on Mn is locally rigid.
A New Class of Representations of EALA Coordinated by Quantum Tori in Two Variables
Authors: Rao S. Eswara , Batra Punita 
Published: December 2010

AbstractWe study the representations of extended affine Lie algebraswhereqisN-th primitive root of unity (ℂqis the quantum torus in two variables). We first prove that⊕for a suitable number of copies is a quotient of. Thus any finite dimensional irreducible module for⊕lifts to a representation of. Conversely, we prove that any finite dimensional irreducible module forcomes from above. We then construct modules for the extended affine Lie algebraswhich is integrable and has finite dimensional weight spaces.
An Aspect of Icosahedral Symmetry
Authors: Rauschning Jan , Slodowy Peter 
Published: December 2010

AbstractWe embed the moduli space Q of 5 points on the projective line S5-equivariantly into (V), where V is the 6-dimensional irreducible module of the symmetric group S5. This module splits with respect to the icosahedral group A5 into the two standard 3-dimensional representations. The resulting linear projections of Q relate the action of A5 on Q to those on the regular icosahedron.
Condensed Domains
Authors: Anderson D. D. , Dumitrescu Tiberiu 
Published: December 2010

AbstractAn integral domain D with identity is condensed (resp., strongly condensed) if for each pair of ideals I, J of D, IJ = {ij ; i ∈ I; j ∈ J} (resp., IJ = iJ for some i ∈ I or IJ = Ij for some j ∈ J). We show that for a Noetherian domain D, D is condensed if and only if Pic(D) = 0 and D is locally condensed, while a local domain is strongly condensed if and only if it has the two-generator property. An integrally closed domain D is strongly condensed if and only if D is a Bézout generalized Dedekind domain with at most one maximal ideal of height greater than one. We give a number of equivalencies for a local domain with finite integral closure to be strongly condensed. Finally, we show that for a field extension k ⊆ K, the domain D = k + XK[[X]] is condensed if and only if [K : k] ≤ 2 or [K : k] = 3 and each degree-two polynomial in k[X] splits over k, while D is strongly condensed if and only if [K : k] ≤ 2.
Remarques sur les points rationnels des variétés de Fermat
Authors: Bernardi D. , Halberstadt E. , Kraus A. 
Published: December 2010

RésuméSoit K un corps de nombres de degré sur inférieur ou égal à 2. On se propose dans ce travail de faire quelques remarques sur la question de l'existence de deux éléments non nuls a et b de K, et d'un entier n ≥ 4, tels que l'équation axn + byn = 1 possède au moins trois points distincts non triviaux. Cette étude se ramène à la recherche de points rationnels sur K d'une variété projective dans de dimension 3, ou d'une surface de .
Power Residue Criteria for Quadratic Units and the Negative Pell Equation
Authors: Bülow Tommy 
Published: December 2010

AbstractLet d > 1 be a square-free integer. Power residue criteria for the fundamental unit εd of the real quadratic fields modulo a prime p (for certain d and p) are proved by means of class field theory. These results will then be interpreted as criteria for the solvability of the negative Pell equation x2 − dp2y2 = −1. The most important solvability criterion deals with all d for which has an elementary abelian 2-class group and p ≡ 5 (mod 8) or p ≡ 9 (mod 16).
Linear Maps Transforming the Unitary Group
Authors: Cheung Wai-Shun , Li Chi-Kwong 
Published: December 2010

AbstractLet U(n) be the group of n × n unitary matrices. We show that if ϕ is a linear transformation sending U(n) into U(m), then m is a multiple of n, and ϕ has the formfor some V, W ∈ U(m). From this result, one easily deduces the characterization of linear operators that map U(n) into itself obtained by Marcus. Further generalization of the main theorem is also discussed.
On Frankel’s Theorem
Authors: Petersen Peter , Wilhelm Frederick 
Published: December 2010

AbstractIn this paper we show that two minimal hypersurfaces in a manifold with positive Ricci curvature must intersect. This is then generalized to show that in manifolds with positive Ricci curvature in the integral sense two minimal hypersurfaces must be close to each other. We also show what happens if a manifold with nonnegative Ricci curvature admits two nonintersecting minimal hypersurfaces.
An Explicit Cell Decomposition of the Wonderful Compactification of a Semisimple Algebraic Group
Authors: Renner Lex E. 
Published: December 2010

AbstractWe determine an explicit cell decomposition of the wonderful compactification of a semisimple algebraic group. To do this we first identify the B × B-orbits using the generalized Bruhat decomposition of a reductive monoid. From there we show how each cell is made up from B × B orbits.
Linear Maps on Selfadjoint Operators Preserving Invertibility, Positive Definiteness, Numerical Range
Authors: Li Chi-Kwong , Rodman Leiba , Šemrl Peter 
Published: December 2010

AbstractLet H be a complex Hilbert space, and be the real linear space of bounded selfadjoint operators on H. We study linear maps ϕ: → leaving invariant various properties such as invertibility, positive definiteness, numerical range, etc. The maps ϕ are not assumed a priori continuous. It is shown that under an appropriate surjective or injective assumption ϕ has the form , for a suitable invertible or unitary T and ξ ∈ {1, −1}, where Xt stands for the transpose of X relative to some orthonormal basis. Examples are given to show that the surjective or injective assumption cannot be relaxed. The results are extended to complex linear maps on the algebra of bounded linear operators on H. Similar results are proved for the (real) linear space of (selfadjoint) operators of the form αI + K, where α is a scalar and K is compact.
An Inductive Limit Model for the K-Theory of the Generator-Interchanging Antiautomorphism of an Irrational Rotation Algebra
Authors: Stacey P. J. 
Published: December 2010

AbstractLet Aθ be the universal C*-algebra generated by two unitaries U, V satisfying VU = e2πiθUV and let Φ be the antiautomorphism of Aθ interchanging U and V. The K-theory of Rθ = { a ∈ Aθ: Φ(a) = a*} is computed. When θ is irrational, an inductive limit of algebras of the form is constructed which has complexification Aθ and the same K-theory as Rθ.
Subdifferentials Whose Graphs Are Not Norm × Weak* Closed
Authors: Borwein Jonathan , Fitzpatrick Simon , Girgensohn Roland 
Published: December 2010

AbstractIn this note we give examples of convex functions whose subdifferentials have unpleasant properties. Particularly, we exhibit a proper lower semicontinuous convex function on a separable Hilbert space such that the graph of its subdifferential is not closed in the product of the norm and bounded weak topologies. We also exhibit a set whose sequential normal cone is not norm closed.
The Essential Norm of a Bloch-to-Qp Composition Operator
Authors: Lindstróm Mikael , Makhmutov Shamil , Taskinen Jari 
Published: December 2010

AbstractThe Qp spaces coincide with the Bloch space for p > 1 and are subspaces of BMOA for 0 < p ≤ 1. We obtain lower and upper estimates for the essential norm of a composition operator from the Bloch space into Qp, in particular from the Bloch space into BMOA.
Rational Integer Invariants of Regular Cyclic Actions
Authors: Little Robert D. 
Published: December 2010

AbstractLet g : M2n → M2n be a smooth map of period m ≥ 2 which preserves orientation. Suppose that the cyclic action defined by g is regular and that the normal bundle of the fixed point set F has a g-equivariant complex structure. Let F ⋔ F be the transverse self-intersection of F with itself. If the g-signature Sign(g, M) is a rational integer and n < ϕ(m), then there exists a choice of orientations such that Sign(g, M) = Sign F = Sign(F ⋔ F).
A Geometric Characterization of Nonnegative Bands
Authors: Marwaha Alka 
Published: December 2010

AbstractA band is a semigroup of idempotent operators. A nonnegative band S in having at least one element of finite rank and with rank (S) > 1 for all S in S is known to have a special kind of common invariant subspace which is termed a standard subspace (defined below).Such bands are called decomposable. Decomposability has helped to understand the structure of nonnegative bands with constant finite rank. In this paper, a geometric characterization of maximal, rank-one, indecomposable nonnegative bands is obtained which facilitates the understanding of their geometric structure.
Counting Rational Points on Ruled Varieties
Authors: McKinnon David 
Published: December 2010

AbstractIn this paper, we prove a general result computing the number of rational points of bounded height on a projective variety V which is covered by lines. The main technical result used to achieve this is an upper bound on the number of rational points of bounded height on a line. This upper bound is such that it can be easily controlled as the line varies, and hence is used to sum the counting functions of the lines which cover the original variety V.
Linear Relations Among the Values of Canonical Heights from the Existence of Non-Trivial Endomorphisms
Authors: Naumann Niko 
Published: December 2010

AbstractWe study the interplay between canonical heights and endomorphisms of an abelian variety A over a number field k. In particular we show that whenever the ring of endomorphisms defined over k is strictly larger than there will be -linear relations among the values of a canonical height pairing evaluated at a basis modulo torsion of A(k).
Classifying Spaces for Monoidal Categories Through Geometric Nerves
Authors: Bullejos M. , Cegarra A. M. 
Published: December 2010

AbstractThe usual constructions of classifying spaces for monoidal categories produce CW-complexes withmany cells that,moreover, do not have any proper geometricmeaning. However, geometric nerves ofmonoidal categories are very handy simplicial sets whose simplices have a pleasing geometric description: they are diagrams with the shape of the 2-skeleton of oriented standard simplices. The purpose of this paper is to prove that geometric realizations of geometric nerves are classifying spaces for monoidal categories.
Biprojectivity and Biflatness for Convolution Algebras of Nuclear Operators
Authors: Pirkovskii A. Yu. 
Published: December 2010

AbstractFor a locally compact group G, the convolution product on the space 𝒩(Lp(G)) of nuclear operators was defined by Neufang [11]. We study homological properties of the convolution algebra 𝒩(Lp(G)) and relate them to some properties of the group G, such as compactness, finiteness, discreteness, and amenability.
Uniqueness of Almost Everywhere Convergent Vilenkin Series
Authors: Wade W. R. 
Published: December 2010

AbstractD. J. Grubb [3] has shown that uniqueness holds, under a mild growth condition, for Vilenkin series which converge almost everywhere to zero. We show that, under even less restrictive growth conditions, one can replace the limit function 0 by an arbitrary f ∈ Lq, when q > 1.
High Frequency Resolvent Estimates and Energy Decay of Solutions to the Wave Equation
Authors: Cardoso Fernando , Vodev Georgi 
Published: December 2010

AbstractWe prove an uniform Hölder continuity of the resolvent of the Laplace-Beltrami operator on the real axis for a class of asymptotically Euclidean Riemannian manifolds. As an application we extend a result of Burq on the behaviour of the local energy of solutions to the wave equation.