bluuebunny/crossref_metadata_2025 huggingface dataset:
On the Nonemptiness of the Adjoint Linear System of Polarized Manifolds
Authors: Fukuma Yoshiaki
Published: December 2010

Let (X, L) be a polarized manifold over the complex number field with dim X = n. In this paper, we consider a conjecture of M. C. Beltrametti and A. J. Sommese and we obtain that this conjecture is true if n = 3 and h0(L) ≥ 2, or dim Bs |L| ≤ 0 for any n ≥ 3. Moreover we can generalize the result of Sommese.
On the Ideal-Triangularizability of Semigroups of Quasinilpotent Positive Operators on C(K)
Authors: Jahandideh M. T.
Published: December 2010

It is known that a semigroup of quasinilpotent integral operators, with positive lower semicontinuous kernels, on L2(X, μ), where X is a locally compact Hausdorff-Lindelöf space and μ is a σ-finite regular Borel measure on X, is triangularizable. In this article we use the Banach lattice version of triangularizability to establish the ideal-triangularizability of a semigroup of positive quasinilpotent integral operators on C(K) where K is a compact Hausdorff space.
A Characterization of Varieties with a Difference Term, II: Neutral = Meet Semi-Distributive
Authors: Lipparini Paolo
Published: December 2010

We provide more characterizations of varieties with a weak difference term and of neutral varieties. We prove that a variety has a (weak) difference term (is neutral) with respect to the TC-commutator iff it has a (weak) difference term (is neutral) with respect to the linear commutator. We show that a variety V is congruence meet semi-distributive iff V is neutral, iff M3 is not a sublattice of Con A, for A ∈ V, iff there is a positive integer n such that .
Extremal Values of
Authors: P. Codecà  , Nair M.
Published: December 2010

The function Δ(x, N) as defined in the title is closely associated via Δ(N) = supx |Δ(x, N)| to several problems in the upper bound sieve. It is also known via a classical theorem of Franel that certain conjectured bounds involving averages of Δ(x, N) are equivalent to the Riemann Hypothesis. We improve the unconditional bounds which have been hitherto obtained for Δ(N) and show that these are close to being optimal. Several auxiliary results relating Δ(Np) to Δ(N), where p is a prime with pN, are also obtained and two new conjectures stated.
Inequalities for Baer Invariants of Finite Groups
Authors: Burns John , Ellis Graham
Published: December 2010

In this note we further our investigation of Baer invariants of groups by obtaining, as consequences of an exact sequence of A. S.-T. Lue, some numerical inequalities for their orders, exponents, and generating sets. An interesting group theoretic corollary is an explicit bound for |γc+1 (G)| given that G, Zc(G) is a finite p-group with prescribed order and number of generators.
Linear Maps on Factors which Preserve the Extreme Points of the Unit Ball
Authors: Mascioni Vania , Molnár Lajos
Published: December 2010

The aim of this paper is to characterize those linear maps from a von Neumann factor A into itself which preserve the extreme points of the unit ball of A. For example, we show that if A is infinite, then every such linear preserver can be written as a fixed unitary operator times either a unital *-homomorphism or a unital *-antihomomorphism.
Dependent Automorphisms in Prime Rings
Authors: Brešar Matej , Martindale W. S. , Robert Miers C.
Published: December 2010

For each n ≥ 4 we construct a class of examples of a minimal C dependent set of n automorphisms of a prime ring R, where C is the extended centroid of R. For n = 4 and n = 5 it is shown that the preceding examples are completely general, whereas for n = 6 an example is given which fails to enjoy any of the nice properties of the above example.
Separating Singularities of Holomorphic Functions
Authors: Müller Jürgen , Wengenroth Jochen
Published: December 2010

We present a short proof for a classical result on separating singularities of holomorphic functions. The proof is based on the open mapping theorem and the fusion lemma of Roth, which is a basic tool in complex approximation theory. The same method yields similar separation results for other classes of functions.
Some Norm Inequalities for Operators
Authors: Kittaneh Fuad
Published: December 2010

Let Ai , Bi and Xi (i = 1, 2,…,n) be operators on a separable Hilbert space. It is shown that if f and g are nonnegative continuous functions on [0, ∞) which satisfy the relation f(t)g(t) = t for all t in [0, ∞), then

for every r > 0 and for every unitarily invariant norm. This result improves some known Cauchy-Schwarz type inequalities. Norm inequalities related to the arithmetic-geometric mean inequality and the classical Heinz inequalities are also obtained.
A Note on Finite Dehn Fillings
Authors: Boyer S. , Zhang X.
Published: December 2010

Let M be a compact, connected, orientable 3-manifold whose boundary is a torus and whose interior admits a complete hyperbolic metric of finite volume. In this paper we show that if theminimal Culler-Shalen norm of a non-zero class in H1(∂M) is larger than 8, then the finite surgery conjecture holds for M. This means that there are at most 5 Dehn fillings of M which can yieldmanifolds having cyclic or finite fundamental groups and the distance between any slopes yielding such manifolds is at most 3.
Non Cohen-Macaulay Vector Invariants and a Noether Bound for a Gorenstein Ring of Invariants
Authors: Campbell H. E. A. , Geramita A. V. , Hughes I. P. , Shank R. J. , Wehlau D. L.
Published: December 2010

This paper contains two essentially independent results in the invariant theory of finite groups. First we prove that, for any faithful representation of a non-trivial p-group over a field of characteristic p, the ring of vector invariants ofmcopies of that representation is not Cohen-Macaulay for m ≥ 3. In the second section of the paper we use Poincaré series methods to produce upper bounds for the degrees of the generators for the ring of invariants as long as that ring is Gorenstein. We prove that, for a finite non-trivial group G and a faithful representation of dimension n with n > 1, if the ring of invariants is Gorenstein then the ring is generated in degrees less than or equal to n(|G| − 1). If the ring of invariants is a hypersurface, the upper bound can be improved to |G|.
Boundedness of the q-Mean-Square Operator on Vector-Valued Analytic Martingales
Authors: Peide Liu , Saksman Eero , Tylli Hans-Olav
Published: December 2010

We 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.
Homotopy of Knots and the Alexander Polynomial
Authors: Austin David , Rolfsen Dale
Published: December 2010

Any knot in a 3-dimensional homology sphere is homotopic to a knot with trivial Alexander polynomial.
Asymptotic Behavior of Optimal Circle Packings in a Square
Authors: Nurmela Kari J. , Östergård Patric R. J. , aus dem Spring Rainer
Published: December 2010

A 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

Let 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 that

where 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 that

where , 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

Let and , where λ > 0 and . Denote . We characterize those functions A(x) for which the parabolic Calderón commutator

is 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

An 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.
Type II Spectral Flow and the Eta Invariant
Authors: Kaminker Jerome , Perera Vicumpriya
Published: December 2010

The relative eta invariant of Atiyah-Patodi-Singer will be shown to be expressible in terms of the notion of Type I and Type II spectral flow.
Geometric Meaning of Isoparametric Hypersurfaces in a Real Space Form
Authors: Kimura Makoto , Maeda Sadahiro
Published: December 2010

We shall provide a characterization of all isoparametric hypersurfaces M’s in a real space form by observing the extrinsic shape of geodesics of M in the ambient manifold .
Cyclotomic Schur Algebras and Blocks of Cyclic Defect
Authors: König Steffen
Published: December 2010

An explicit classification is given of blocks of cyclic defect of cyclotomic Schur algebras and of cyclotomic Hecke algebras, over discrete valuation rings.
A Gorenstein Ring with Larger Dilworth Number than Sperner Number
Authors: Okon James S. , Vicknair J. Paul
Published: December 2010

A 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

In 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.
A Larger Class of Ornstein Transformations with Mixing Property
Authors: El Abdalaoui El Houcein
Published: December 2010

We prove that Ornstein transformations are almost surely totally ergodic provided only that the cutting parameter is not bounded. We thus obtain a larger class of Ornstein transformations with the mixing property.
Moduli Spaces of Polygons and Punctured Riemann Spheres
Authors: Foth Philip
Published: December 2010

The 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.
Some More Weak Hilbert Spaces
Authors: Androulakis George , Casazza Peter G. , Kutzarova Denka N.
Published: December 2010

We give new examples of weak Hilbert spaces.
A Dimension-Free Weak-Type Estimate for Operators on UMD-Valued Functions
Authors: Kelly Brian P.
Published: December 2010

Let 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

We 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).
Tournaments and Orders with the Pigeonhole Property
Authors: Bonato Anthony , Cameron Peter , Delić Dejan
Published: December 2010

A binary structure S has the pigeonhole property (𝒫) if every finite partition of S induces a block isomorphic to S. We classify all countable tournaments with (𝒫); the class of orders with (𝒫) is completely classified.
Non-Isomorphic Maximal Orders with Isomorphic Matrix Rings
Authors: Chatters A. W.
Published: December 2010

We construct a countably infinite family of pairwise non-isomorphic maximal ℚ[X]-orders such that the full 2 by 2 matrix rings over these orders are all isomorphic.
Helices, Hasimoto Surfaces and Bäcklund Transformations
Authors: Ivey Thomas A.
Published: December 2010

Travelling 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.
On the Existence of a New Class of Contact Metric Manifolds
Authors: Koufogiorgos Themis , Tsichlias Charalambos
Published: December 2010

A new class of 3-dimensional contact metric manifolds is found. Moreover it is proved that there are no such manifolds in dimensions greater than 3.
Properties of the Invariants of Solvable Lie Algebras
Authors: Ndogmo J. C.
Published: December 2010

We 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

Many 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.
The Trace Formula and Its Applications: An Introduction to the Work of James Arthur
Authors: Langlands Robert P.
Published: December 2010

In May, 1999 James Greig Arthur, University Professor at the University of Toronto was awarded the Canada Gold Medal by the National Science and Engineering Research Council. This is a high honour for a Canadian scientist, instituted in 1991 and awarded annually, but not previously to a mathematician, and the choice of Arthur, although certainly a recognition of his greatmerits, is also a recognition of the vigour of contemporary Canadian mathematics.
Extension of Maps to Nilpotent Spaces
Authors: Cencelj M. , Dranishnikov A. N.
Published: December 2010

We 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

Let c = (c1, … , cn) be such that c1 ≥ … ≥ cn. The c-numerical range of an n × n matrix A is defined by

and 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

Nousmontrons 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

Let 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.
The Distribution of Totatives
Authors: Hall R. R. , Shiu P.
Published: December 2010

D. H. Lehmer initiated the study of the distribution of totatives, which are numbers coprime with a given integer. This led to various problems considered by P. Erdős, who made a conjecture on such distributions. We prove his conjecture by establishing a theorem on the ordering of residues.
The Number of Non-Zero Digits of n!
Authors: Luca Florian
Published: December 2010

Let b be an integer with b > 1. In this note, we prove that the number of non-zero digits in the base b representation of n! grows at least as fast as a constant, depending on b, times log n.
Mahler Measures Close to an Integer
Authors: Dubickas Artūras
Published: December 2010

We prove that theMahler measure of an algebraic number cannot be too close to an integer, unless we have equality. The examples of certain Pisot numbers show that the respective inequality is sharp up to a constant. All cases when the measure is equal to the integer are described in terms of the minimal polynomials.
Globalization of Distinguished Supercuspidal Representations of GL(n)
Authors: Hakim Jeffrey , Murnaghan Fiona
Published: December 2010

An 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

H. 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 ≤ ∞.
The Transfer in the Invariant Theory of Modular Permutation Representations II
Authors: Neusel Mara D.
Published: December 2010

In this note we show that the image of the transfer for permutation representations of finite groups is generated by the transfers of special monomials. This leads to a description of the image of the transfer of the alternating groups. We also determine the height of these ideals.
Modular Subgroups, Forms, Curves and Surfaces
Authors: Sebbar Abdellah
Published: December 2010

We study a class of subgroups of PSL2(ℤ) which can be characterized in different ways, such as congruence groups, modular forms, modular curves, elliptic surfaces, lattices and graphs.
Surjectivity of mod ℓ Representations Attached to Elliptic Curves and Congruence Primes
Authors: Chen Imin
Published: December 2010

For 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

For 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

We 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

We 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

An 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.
Generalized Commutativity in Group Algebras
Authors: Bahturin Yu. A. , Parmenter M. M.
Published: December 2010

We study group algebras FG which can be graded by a finite abelian group Γ such that FG is β-commutative for a skew-symmetric bicharacter β on Γ with values in F*.
Remarques sur les points rationnels des variétés de Fermat
Authors: Bernardi D. , Halberstadt E. , Kraus A.
Published: December 2010

Soit 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

Let 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

Let 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 form

for 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

In 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

We 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

Let 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

Let 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

In 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.
L-Series of Certain Elliptic Surfaces
Authors: Long Ling
Published: December 2010

In this paper, we study the modularity of certain elliptic surfaces by determining their L-series through their monodromy groups.
The Essential Norm of a Bloch-to-Qp Composition Operator
Authors: Lindstróm Mikael , Makhmutov Shamil , Taskinen Jari
Published: December 2010

The 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

Let 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).
Systems of Hermitian Quadratic Forms
Authors: Li Ma , Dezhong Chen
Published: December 2010

In this paper, we give some conditions to judge when a system of Hermitian quadratic forms has a real linear combination which is positive definite or positive semi-definite. We also study some related geometric and topological properties of the moduli space.
The Poincaré Inequality and Reverse Doubling Weights
Authors: Hurri-Syrjänen Ritva
Published: December 2010

We show that Poincaré inequalities with reverse doubling weights hold in a large class of irregular domains whenever the weights satisfy certain conditions. Examples of these domains are John domains.
Solvability by Real Radicals and Fermat Primes
Authors: Jensen C. U.
Published: December 2010

We give a survey of old and new results concerning the expressibility of the real roots of a solvable polynomial over a real number field by real radicals. A characterization of Fermat primes is obtained in terms of solvability by real radicals for certain ploynomials.
A Geometric Characterization of Nonnegative Bands
Authors: Marwaha Alka
Published: December 2010

A 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

In 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

We 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).
Mean Curvature Comparison with L1-norms of Ricci Curvature
Authors: Yun Jong-Gug
Published: December 2010

We prove an analogue of mean curvature comparison theorem in the case where the Ricci curvature below a positive constant is small in L1-norm.
Classifying Spaces for Monoidal Categories Through Geometric Nerves
Authors: Bullejos M. , Cegarra A. M.
Published: December 2010

The 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

For 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

D. 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

We 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.
Remarques sur l’enlacement en théorie des points critiques pour des fonctionnelles continues
Authors: Frigon M.
Published: December 2010

Dans cet article, à partir de la notion d’enlacement introduite dans [7] entre des paires d’ensembles (B, A) et (Q, P), nous établissons l’existence d’un point critique d’une fonctionnelle continue sur un espace métrique lorsqu’une de ces paires enlace l’autre. Des renseignements sur la localisation du point critique sont aussi obtenus. Ces résultats conduisent à une généralisation du théor`eme des trois points critiques. Finalement, des applications à des probl`emes aux limites pour une équation quasi-linéaire elliptique sont présentées.
A Generalization of the Erdös-Kac Theorem and its Applications
Authors: Liu Yu-Ru
Published: December 2010

We axiomatize the main properties of the classical Erdös-Kac Theorem in order to apply it to a general context. We provide applications in the cases of number fields, function fields, and geometrically irreducible varieties over a finite field.
Quantum Ergodicity of Boundary Values of Eigenfunctions: A Control Theory Approach
Authors: Burq N.
Published: December 2010

Consider M, a bounded domain in ℝd, which is a Riemanian manifold with piecewise smooth boundary and suppose that the billiard associated to the geodesic flow reflecting on the boundary according to the laws of geometric optics is ergodic. We prove that the boundary value of the eigen-functions of the Laplace operator with reasonable boundary conditions are asymptotically equidistributed in the boundary, extending previous results by Gérard and Leichtnam as well as Hassell and Zelditch, obtained under the additional assumption of the convexity of M.
Estimates of Henstock-Kurzweil Poisson Integrals
Authors: Talvila Erik
Published: December 2010

If f is a real-valued function on [−π, π] that is Henstock-Kurzweil integrable, let ur(θ) be its Poisson integral. It is shown that ∥ur∥p = o(1/(1 − r)) as r → 1 and this estimate is sharp for 1 ≤ p ≤ ∞. If μ is a finite Borel measure and ur(θ) is its Poisson integral then for each 1 ≤ p ≤ ∞ the estimate ∥ur∥p = O((1−r)1/p−1) as r → 1 is sharp. The Alexiewicz norm estimates ∥ur∥ ≤ ∥f ∥ (0 ≤ r < 1) and ∥ur − f∥ → 0 (r → 1) hold. These estimates lead to two uniqueness theorems for the Dirichlet problem in the unit disc with Henstock-Kurzweil integrable boundary data. There are similar growth estimates when u is in the harmonic Hardy space associated with the Alexiewicz norm and when f is of bounded variation.
Indecomposable Higher Chow Cycles
Authors: Kimura Kenichiro
Published: December 2010

Let X be a projective smooth variety over a field k. In the first part we show that an indecomposable element in CH2(X, 1) can be lifted to an indecomposable element in CH3(XK, 2) where K is the function field of 1 variable over k. We also show that if X is the self-product of an elliptic curve over ℚ then the ℚ-vector space of indecomposable cycles is infinite dimensional.

In the second part we give a new definition of the group of indecomposable cycles of CH3(X, 2) and give an example of non-torsion cycle in this group.
Monotonicity Properties of the Hurwitz Zeta Function
Authors: Alzer Horst
Published: December 2010

Let

be the Hurwitz zeta function and let

whereα, β> 1 anda,b> 0 are real numbers. We prove: (i) The functionQis decreasing on (0, ∞) iffαa−βb≥ max(a−b, 0). (ii)Qis increasing on (0, ∞) iffαa−βb≤ min(a−b, 0). An application of part (i) reveals that for allx> 0 the functions⟼ [(s− 1)ζ(s,x)]1/(s−1)is decreasing on (1, ∞). This settles a conjecture of Bastien and Rogalski.
Reduction of Elliptic Curves in Equal Characteristic 3 (and 2)
Authors: Miyamoto Roland , Top Jaap
Published: December 2010

We determine conductor exponent, minimal discriminant and fibre type for elliptic curves over discrete valued fields of equal characteristic 3. Along the same lines, partial results are obtained in equal characteristic 2.
Extension of Holomorphic Functions From One Side of a Hypersurface
Authors: Baracco Luca
Published: December 2010

We give a new proof of former results by G. Zampieri and the author on extension of holomorphic functions from one side Ω of a real hypersurface M of ℂn in the presence of an analytic disc tangent to M, attached to Ω but not to M. Our method enables us to weaken the regularity assumptions both for the hypersurface and the disc.
Exceptional Sets in Hartogs Domains
Authors: Kot Piotr
Published: December 2010

Assume that Ω is a Hartogs domain in ℂ1+n, defined as Ω = ﹛(z, w) ∈ ℂ1+n : |z| < μ(w), w ∈ H﹜, where H is an open set in ℂn and μ is a continuous function with positive values in H such that –ln μ is a strongly plurisubharmonic function in H. Let Ωw = Ω ∩ (ℂ × ﹛w﹜). For a given set E contained in H of the type Gδ we construct a holomorphic function f ∈ (Ω) such that
On the Regularity of the s-Differential Metric
Authors: Mashreghi Javad , Pouryayevali Mohamad R.
Published: December 2010

We show that the injective Kobayashi–Royden differential metric, as defined by Hahn, is upper semicontinous.
Toeplitz Algebras and Extensions of Irrational Rotation Algebras
Authors: Park Efton
Published: December 2010

For a given irrational number θ, we define Toeplitz operators with symbols in the irrational rotation algebra , and we show that the C*-algebra generated by these Toeplitz operators is an extension of by the algebra of compact operators. We then use these extensions to explicitly exhibit generators of the group KK1(, ℂ). We also prove an index theorem for that generalizes the standard index theorem for Toeplitz operators on the circle.
On Finite-to-One Maps
Authors: Tuncali H. Murat , Valov Vesko
Published: December 2010

Let f : X → Y be a σ-perfect k-dimensional surjective map of metrizable spaces such that dim Y ≤ m. It is shown that for every positive integer p with p ≤ m + k + 1 there exists a dense Gδ-subset (k,m, p) of C(X, k+p) with the source limitation topology such that each fiber of f△g, g ∈ (k, m, p), contains at most max ﹛k + m – p + 2, 1﹜ points. This result provides a proof the following conjectures of S. Bogatyi, V. Fedorchuk and J. van Mill. Let f : X → Y be a k-dimensional map between compact metric spaces with dimY ≤ m. Then: (1) there exists a map h: X → m+2k such that f△h: X → Y × m+2k is 2-to-one provided k ≥ 1; (2) there exists a map h: X → m+k+1 such that f△h: X →Y × m+k+1 is (k + 1)-to-one.
Holomorphic Frames for Weakly Converging Holomorphic Vector Bundles
Authors: Daskalopoulos Georgios D. , Wentworth Richard A.
Published: December 2010

Using a modification of Webster's proof of the Newlander–Nirenberg theorem, it is shown that, for a weakly convergent sequence of integrable unitary connections on a complex vector bundle over a complex manifold, there is a subsequence of local holomorphic frames that converges strongly in an appropriate Holder class.
A Dynamical Proof of Pisot's Theorem
Authors: Kwapisz Jaroslaw
Published: December 2010

We give a geometric proof of classical results that characterize Pisot numbers as algebraic λ > 1 for which there is x ≠ 0 with λnx → 0 (mod 1) and identify such x as members of ℤ[λ–1]· ℤ[λ]* where ℤ[λ]* is the dual module of ℤ[λ].
The Geometry of d2y1/dt2 = f (y, ẏ, t) and d2y2/dt2 = g(y, ẏ, t), and Euclidean Spaces
Authors: Atkins Richard
Published: December 2010

This paper investigates the relationship between a system of differential equations and the underlying geometry associated with it. The geometry of a surface determines shortest paths, or geodesics connecting nearby points, which are defined as the solutions to a pair of second-order differential equations: the Euler–Lagrange equations of the metric. We ask when the converse holds, that is, when solutions to a system of differential equations reveals an underlying geometry. Specifically, when may the solutions to a given pair of second order ordinary differential equations d2y1/dt2 = f (y, ẏ, t) and d2y2/dt2 = g(y, ẏ, t) be reparameterized by t → T(y, t) so as to give locally the geodesics of a Euclidean space? Our approach is based upon Cartan's method of equivalence. In the second part of the paper, the equivalence problem is solved for a generic pair of second order ordinary differential equations of the above form revealing the existence of 24 invariant functions.
On Inductive Limit Type Actions of the Euclidean Motion Group on Stable UHF Algebras
Authors: Dean Andrew J.
Published: December 2010

An invariant is presented which classifies, up to equivariant isomorphism, C*-dynamical systems arising as limits from inductive systems of elementary C*-algebras on which the Euclidean motion group acts by way of unitary representations that decompose into finite direct sums of irreducibles.
Endomorphisms That Are the Sum of a Unit and a Root of a Fixed Polynomial
Authors: Nicholson W. K. , Zhou Y.
Published: December 2010

If C = C(R) denotes the center of a ring R and g(x) is a polynomial in C[x], Camillo and Simón called a ring g(x)-clean if every element is the sum of a unit and a root of g(x). If V is a vector space of countable dimension over a division ring D, they showed that end DV is g(x)-clean provided that g(x) has two roots in C(D). If g(x) = x – x2 this shows that end DV is clean, a result of Nicholson and Varadarajan. In this paper we remove the countable condition, and in fact prove that end RM is g(x)-clean for any semisimple module M over an arbitrary ring R provided that g(x) ∈ (x – a)(x – b)C[x] where a, b ∈ C and both b and b – a are units in R.
Orbits and Stabilizers for Solvable Linear Groups
Authors: Riedl Jeffrey M.
Published: December 2010

We extend a result of Noritzsch, which describes the orbit sizes in the action of a Frobenius group G on a finite vector space V under certain conditions, to a more general class of finite solvable groups G. This result has applications in computing irreducible character degrees of finite groups. Another application, proved here, is a result concerning the structure of certain groups with few complex irreducible character degrees.
Affine Completeness of Generalised Dihedral Groups
Authors: Ecker Jürgen
Published: December 2010

In this paper we study affine completeness of generalised dihedral groups. We give a formula for the number of unary compatible functions on these groups, and we characterise for everyk∈ N thek-affine complete generalised dihedral groups. We find that the direct product of a 1-affine complete group with itself need not be 1-affine complete. Finally, we give an example of a nonabelian solvable affine complete group. For nilpotent groups we find a strong necessary condition for 2-affine completeness.
Inner E0-Semigroups on Infinite Factors
Authors: Floricel Remus
Published: December 2010

This paper is concerned with the structure of inner E0-semigroups. We show that any inner E0-semigroup acting on an infinite factor M is completely determined by a continuous tensor product system of Hilbert spaces in M and that the product system associated with an inner E0-semigroup is a complete cocycle conjugacy invariant.
Intermediate Model Structures for Simplicial Presheaves
Authors: Jardine J. F.
Published: December 2010

This note shows that any set of cofibrations containing the standard set of generating projective cofibrations determines a cofibrantly generated proper closed model structure on the category of simplicial presheaves on a small Grothendieck site, for which the weak equivalences are the local weak equivalences in the usual sense.
Cyclic Cubic Fields of Given Conductor and Given Index
Authors: Silvester Alan K. , Spearman Blair K. , Williams Kenneth S.
Published: December 2010

The number of cyclic cubic fields with a given conductor and a given index is determined.