bluuebunny/crossref_metadata_2025 huggingface dataset:
Comparisons of General Linear Groups and their Metaplectic Coverings I
Authors: Mezo Paul
Published: December 2010

We prepare for a comparison of global trace formulas of general linear groups and their metaplectic coverings. In particular, we generalize the local metaplectic correspondence of Flicker and Kazhdan and describe the terms expected to appear in the invariant trace formulas of the above covering groups. The conjectural trace formulas are then placed into a form suitable for comparison.
Spaces of Whitney Functions on Cantor-Type Sets
Authors: Arslan Bora , Goncharov Alexander P. , Kocatepe Mefharet
Published: December 2010

We introduce the concept of logarithmic dimension of a compact set. In terms of this magnitude, the extension property and the diametral dimension of spaces Ɛ(K) can be described for Cantor-type compact sets.
Slim Exceptional Sets for Sums of Cubes
Authors: Wooley Trevor D.
Published: December 2010

We investigate exceptional sets associated with various additive problems involving sums of cubes. By developing a method wherein an exponential sum over the set of exceptions is employed explicitly within the Hardy-Littlewood method, we are better able to exploit excess variables. By way of illustration, we show that the number of odd integers not divisible by 9, and not exceeding X, that fail to have a representation as the sum of 7 cubes of prime numbers, is O(X23/36+ε). For sums of eight cubes of prime numbers, the corresponding number of exceptional integers is O(X11/36+ε).
Théorème de Voronoï dans les espaces symétriques
Authors: Akrout H.
Published: December 2010

On démontre un théorème de Voronoï (caractérisation des maxima locaux de l’invariant d’Hermite) pour les familles de réseaux paramétrées par les espaces symétriques irréductibles non exceptionnels de type non compact.
Diagonals and Partial Diagonals of Sum of Matrices
Authors: Li Chi-Kwong , Poon Yiu-Tung
Published: December 2010

Given a matrix A, let (A) denote the orbit of A under a certain group action such as

(1)

U(m) ⊗ U(n) acting on m × n complex matrices A by (U, V) * A = UAVt,

(2)

O(m) ⊗ O(n) or SO(m) ⊗ SO(n) acting on m × n real matrices A by (U, V) * A = UAVt,

(3)

U(n) acting on n × n complex symmetric or skew-symmetric matrices A by U * A = UAUt,

(4)

O(n) or SO(n) acting on n × n real symmetric or skew-symmetric matrices A by U * A = UAUt.

Denote by

the joint orbit of the matrices A1, … , Ak. We study the set of diagonals or partial diagonals of matrices in (A1, … , Ak), i.e., the set of vectors (d1, … , dr) whose entries lie in the (1, j1), … , (r, jr) positions of a matrix in (A1, … , Ak) for some distinct column indices j1, … , jr . In many cases, complete description of these sets is given in terms of the inequalities involving the singular values of A1, … , Ak. We also characterize those extreme matrices for which the equality cases hold. Furthermore, some convexity properties of the joint orbits are considered. These extend many classical results on matrix inequalities, and answer some questions by Miranda. Related results on the joint orbit (A1, … , Ak) of complex Hermitian matrices under the action of unitary similarities are also discussed.
Resonances for Slowly Varying Perturbations of a Periodic Schrödinger Operator
Authors: Dimassi Mouez
Published: December 2010

We study the resonances of the operator . Here V is a periodic potential, φ a decreasing perturbation and h a small positive constant. We prove the existence of shape resonances near the edges of the spectral bands of , and we give its asymptotic expansions in powers of .
The Operator Biprojectivity of the Fourier Algebra
Authors: Wood Peter J.
Published: December 2010

In this paper, we investigate projectivity in the category of operator spaces. In particular, we show that the Fourier algebra of a locally compact groupGis operator biprojective if and only ifGis discrete.
On the Injectivity of C1 Maps of the Real Plane
Authors: Cobo Milton , Gutierrez Carlos , Llibre Jaume
Published: December 2010

Let X : → be a C1 map. Denote by Spec(X) the set of (complex) eigenvalues of DXp when p varies in . If there exists ∊ > 0 such that Spec(X) ∩ (− ∊, ∊) = ∅, then X is injective. Some applications of this result to the real Keller Jacobian conjecture are discussed.
Besov Spaces and Hausdorff Dimension For Some Carnot-Carathéodory Metric Spaces
Authors: Skrzypczak Leszek
Published: December 2010

We regard a system of left invariant vector fieldssatisfying the Hörmander condition and the related Carnot-Carathéodory metric on a unimodular Lie group G. We define Besov spaces corresponding to the sub-Laplacianboth with positive and negative smoothness. The atomic decomposition of the spaces is given. In consequence we get the distributional characterization of the Hausdorff dimension of Borel subsets with the Haar measure zero.
Continued Fractions Associated with SL3(Z) and Units in Complex Cubic Fields
Authors: Vulakh L. Ya.
Published: December 2010

Continued fractions associated with GL3(Z) are introduced and applied to find fundamental units in a two-parameter family of complex cubic fields.
*-Subvarieties of the Variety Generated by
Authors: Benanti Francesca , Di Vincenzo Onofrio M. , Nardozza Vincenzo
Published: December 2010

Let be a field of characteristic zero, and * = t the transpose involution for the matrix algebra M2(). Let be a proper subvariety of the variety of algebras with involution generated by . We define two sequences of algebras with involution Rp, Sq, where p, q ∊ . Then we show that T*() and T*(Rp ⊕ Sq) are *-asymptotically equivalent for suitable p, q.
Some Convexity Features Associated with Unitary Orbits
Authors: Choi Man-Duen , Li Chi-Kwong , Poon Yiu-Tung
Published: December 2010

Let be the real linear space of n × n complex Hermitian matrices. The unitary (similarity) orbit of C ∈ is the collection of all matrices unitarily similar to C. We characterize those C ∈ such that every matrix in the convex hull of can be written as the average of two matrices in . The result is used to study spectral properties of submatrices of matrices in , the convexity of images of under linear transformations, and some related questions concerning the joint C-numerical range of Hermitian matrices. Analogous results on real symmetric matrices are also discussed.
On the Zariski-van Kampen Theorem
Authors: Shimada Ichiro
Published: December 2010

Let f : E → B be a dominant morphism, where E and B are smooth irreducible complex quasi-projective varieties, and let Fb be the general fiber of f. We present conditions under which the homomorphism π1(Fb) → π1(E) induced by the inclusion is injective.
Pair Correlation of Squares in p-Adic Fields
Authors: Zaharescu Alexandru
Published: December 2010

Let p be an odd prime number, K a p-adic field of degree r over Qp, O the ring of integers in K, B = {β1,…,βr} an integral basis of K over Qp, u a unit in O and consider sets of the form 𝒩 = {n1β1 + … + nrβr : 1 ≤ nj ≤ Nj, 1 ≤ j ≤ r}. We show under certain growth conditions that the pair correlation of {uz2 : z ∊ 𝒩} becomes Poissonian.
Une formule de Riemann-Roch équivariante pour les courbes
Authors: Borne Niels
Published: December 2010

SoitGun groupe fini agissant sur une courbe algébrique projective et lisseXsur un corps algébriquement closk. Dans cet article, on donne une formule de Riemann-Roch pour la caractéristique d'Euler équivariante d'unG-faisceau inversible ℒ, à valeurs dans l'anneauRk(G) des caractères du groupeG. La formule donnée a un bon comportement fonctoriel en ce sens qu'elle relève la formule classique le long du morphisme dim:Rk(G) → ℤ, et est valable même pour une action sauvage. En guise d'application, on montre comment calculer explicitement le caractère de l'espace des sections globales d'une large classe deG-faisceaux inversibles, en s'attardant sur le cas particulier délicat du faisceau des différentielles sur la courbe.
Almost-Free E-Rings of Cardinality ℵ1
Authors: Göbel Rüdiger , Shelah Saharon , Strüngmann Lutz
Published: December 2010

An E-ring is a unital ring R such that every endomorphism of the underlying abelian group R+ is multiplication by some ring element. The existence of almost-free E-rings of cardinality greater than 2ℵ0 is undecidable in ZFC. While they exist in Gödel's universe, they do not exist in other models of set theory. For a regular cardinal ℵ1 ≤ λ 2ℵ0 we construct E-rings of cardinality λ in ZFC which have ℵ1-free additive structure. For λ = ℵ1 we therefore obtain the existence of almost-free E-rings of cardinality ℵ1 in ZFC.
Homology TQFT's and the Alexander–Reidemeister Invariant of 3-Manifolds via Hopf Algebras and Skein Theory
Authors: Kerler Thomas
Published: December 2010

We develop an explicit skein-theoretical algorithm to compute the Alexander polynomial of a 3-manifold from a surgery presentation employing the methods used in the construction of quantum invariants of 3-manifolds. As a prerequisite we establish and prove a rather unexpected equivalence between the topological quantum field theory constructed by Frohman and Nicas using the homology ofU(1)-representation varieties on the one side and the combinatorially constructed Hennings TQFT based on the quasitriangular Hopf algebra= ℤ/2 n ⋊ Λ* ℝ2on the other side. We find that both TQFT's are SL(2; ℝ)-equivariant functors and, as such, are isomorphic. The SL(2; ℝ)-action in the Hennings construction comes from the natural action onand in the case of the Frohman–Nicas theory from the Hard–Lefschetz decomposition of theU(1)-moduli spaces given that they are naturally Kähler. The irreducible components of this TQFT, corresponding to simple representations of SL(2; ℤ) and Sp(2g; ℤ), thus yield a large family of homological TQFT's by taking sums and products. We give several examples of TQFT's and invariants that appear to fit into this family, such as Milnor and Reidemeister Torsion, Seiberg–Witten theories, Casson type theories for homology circlesà laDonaldson, higher rank gauge theories following Frohman and Nicas, and the ℤ=pℤ reductions of Reshetikhin.Turaev theories over the cyclotomic integers ℤ[ζp]. We also conjecture that the Hennings TQFT for quantum-sl2is the product of the Reshetikhin–Turaev TQFT and such a homological TQFT.
An Ordering for Groups of Pure Braids and Fibre-Type Hyperplane Arrangements
Authors: Kim Djun Maximilian , Rolfsen Dale
Published: December 2010

We define a total ordering of the pure braid groups which is invariant under multiplication on both sides. This ordering is natural in several respects. Moreover, it well-orders the pure braids which are positive in the sense of Garside. The ordering is defined using a combination of Artin's combing technique and the Magnus expansion of free groups, and is explicit and algorithmic.

By contrast, the full braid groups (on 3 or more strings) can be ordered in such a way as to be invariant on one side or the other, but not both simultaneously. Finally, we remark that the same type of ordering can be applied to the fundamental groups of certain complex hyperplane arrangements, a direct generalization of the pure braid groups.
Hypergeometric Abelian Varieties
Authors: Archinard Natália
Published: December 2010

In this paper, we construct abelian varieties associated to Gauss’ and Appell–Lauricella hypergeometric series. Abelian varieties of this kind and the algebraic curves we define to construct them were considered by several authors in settings ranging from monodromy groups (Deligne, Mostow), exceptional sets (Cohen, Wolfart, Wüstholz), modular embeddings (Cohen, Wolfart) to CM-type (Cohen, Shiga, Wolfart) and modularity (Darmon). Our contribution is to provide a complete, explicit and self-contained geometric construction.
More Eventual Positivity for Analytic Functions
Authors: Handelman David
Published: December 2010

Eventual positivity problems for real convergent Maclaurin series lead to density questions for sets of harmonic functions. These are solved for large classes of series, and in so doing, asymptotic estimates are obtained for the values of the series near the radius of convergence and for the coefficients of convolution powers.
Polar Homology
Authors: Khesin Boris , Rosly Alexei
Published: December 2010

For complex projective manifolds we introduce polar homology groups, which are holomorphic analogues of the homology groups in topology. The polar k-chains are subvarieties of complex dimension k with meromorphic forms on them, while the boundary operator is defined by taking the polar divisor and the Poincaré residue on it. One can also define the corresponding analogues for the intersection and linking numbers of complex submanifolds, which have the properties similar to those of the corresponding topological notions.
Decay of Mean Values of Multiplicative Functions
Authors: Granville Andrew , Soundararajan K.
Published: December 2010

For given multiplicative functionf, with |f(n)| ≤ 1 for alln, we are interested in how fast its mean value (1/x) Σn≤xf(n) converges. Halász showed that this depends on the minimumM(overy∈ ℝ) of Σp≤x(1 – Re(f(p)p–iy)/p, and subsequent authors gave the upper bound ⪡ (1 +M)e–M. For many applications it is necessary to have explicit constants in this and various related bounds, and we provide these via our own variant of the Halász-Montgomery lemma (in fact the constant we give is best possible up to a factor of 10). We also develop a new type of hybrid bound in terms of the location of the absolute value ofythat minimizes the sum above. As one application we give bounds for the least representatives of the cosets of thek-th powers modp.
Locally Compact Pro-C*-Algebras
Authors: Amini Massoud
Published: December 2010

Let X be a locally compact non-compact Hausdorff topological space. Consider the algebras C(X), Cb(X), C0(X), and C00(X) of respectively arbitrary, bounded, vanishing at infinity, and compactly supported continuous functions on X. Of these, the second and third are C*-algebras, the fourth is a normed algebra, whereas the first is only a topological algebra (it is indeed a pro-C*- algebra). The interesting fact about these algebras is that if one of them is given, the others can be obtained using functional analysis tools. For instance, given the C*-algebra C0(X), one can get the other three algebras by C00(X) = K(C0(X)), Cb(X) = M(C0(X)), C(X) = Γ(K(C0(X))), where the right hand sides are the Pedersen ideal, the multiplier algebra, and the unbounded multiplier algebra of the Pedersen ideal of C0(X), respectively. In this article we consider the possibility of these transitions for general C*-algebras. The difficult part is to start with a pro-C*-algebra A and to construct a C*-algebra A0 such that A = Γ(K(A0)). The pro-C*-algebras for which this is possible are called locally compact and we have characterized them using a concept similar to that of an approximate identity.
ℤ[] is Euclidean
Authors: Harper Malcolm
Published: December 2010

We provide the first unconditional proof that the ring ℤ[] is a Euclidean domain. The proof is generalized to other real quadratic fields and to cyclotomic extensions of ℚ. It is proved that if K is a real quadratic field (modulo the existence of two special primes of K) or if K is a cyclotomic extension of ℚ then:

the ring of integers of K is a Euclidean domain if and only if it is a principal ideal domain.

The proof is a modification of the proof of a theorem of Clark and Murty giving a similar result when K is a totally real extension of degree at least three. The main changes are a new Motzkintype lemma and the addition of the large sieve to the argument. These changes allow application of a powerful theorem due to Bombieri, Friedlander and Iwaniec in order to obtain the result in the real quadratic case. The modification also allows the completion of the classification of cyclotomic extensions in terms of the Euclidean property.
Linear Operators on Matrix Algebras that Preserve the Numerical Range, Numerical Radius or the States
Authors: Li Chi-Kwong , Sourour Ahmed Ramzi
Published: December 2010

Every norm v on Cn induces two norm numerical ranges on the algebra Mn of all n × n complex matrices, the spatial numerical range

where vD is the norm dual to v, and the algebra numerical range

where is the set of states on the normed algebra Mn under the operator norm induced by v. For a symmetric norm v, we identify all linear maps on Mn that preserve either one of the two norm numerical ranges or the set of states or vector states. We also identify the numerical radius isometries, i.e., linear maps that preserve the (one) numerical radius induced by either numerical range. In particular, it is shown that if v is not the ℓ1, ℓ2, or ℓ∞ norms, then the linear maps that preserve either numerical range or either set of states are “inner”, i.e., of the formA ⟼ Q*AQ, where Q is a product of a diagonal unitary matrix and a permutation matrix and the numerical radius isometries are unimodular scalar multiples of such inner maps. For the ℓ1 and the ℓ∞ norms, the results are quite different.
A Central Limit Theorem and Law of the Iterated Logarithm for a Random Field with Exponential Decay of Correlations
Authors: Schmuland Byron , Sun Wei
Published: December 2010

In [6], Walter Philipp wrote that “… the law of the iterated logarithm holds for any process for which the Borel-Cantelli Lemma, the central limit theorem with a reasonably good remainder and a certain maximal inequality are valid.” Many authors [1], [2], [4], [5], [9] have followed this plan in proving the law of the iterated logarithm for sequences (or fields) of dependent random variables.

We carry on this tradition by proving the law of the iterated logarithm for a random field whose correlations satisfy an exponential decay condition like the one obtained by Spohn [8] for certain Gibbs measures. These do not fall into the ϕ-mixing or strong mixing cases established in the literature, but are needed for our investigations [7] into diffusions on configuration space.

The proofs are all obtained by patching together standard results from [5], [9] while keeping a careful eye on the correlations.
An Elementary Proof of a Weak Exceptional Zero Conjecture
Authors: Orton Louisa
Published: December 2010

In this paper we extend Darmon's theory of “integration on ℋp × ℋ” to cusp forms f of higher even weight. This enables us to prove a “weak exceptional zero conjecture”: that when the p-adic L-function of f has an exceptional zero at the central point, the ℒ-invariant arising is independent of a twist by certain Dirichlet characters.
Cohomology Ring of Symplectic Quotients by Circle Actions
Authors: Mohammadalikhani Ramin
Published: December 2010

In this article we are concerned with how to compute the cohomology ring of a symplectic quotient by a circle action using the information we have about the cohomology of the original manifold and some data at the fixed point set of the action. Our method is based on the Tolman-Weitsman theorem which gives a characterization of the kernel of the Kirwan map. First we compute a generating set for the kernel of the Kirwan map for the case of product of compact connected manifolds such that the cohomology ring of each of them is generated by a degree two class. We assume the fixed point set is isolated; however the circle action only needs to be “formally Hamiltonian”. By identifying the kernel, we obtain the cohomology ring of the symplectic quotient. Next we apply this result to some special cases and in particular to the case of products of two dimensional spheres. We show that the results of Kalkman and Hausmann-Knutson are special cases of our result.
Multisymplectic Reduction for Proper Actions
Authors: Śniatycki Jędrzej
Published: December 2010

We consider symmetries of the Dedonder equation arising from variational problems with partial derivatives. Assuming a proper action of the symmetry group, we identify a set of reduced equations on an open dense subset of the domain of definition of the fields under consideration. By continuity, the Dedonder equation is satisfied whenever the reduced equations are satisfied.
Similarity Classification of Cowen-Douglas Operators
Authors: Jiang Chunlan
Published: December 2010

Let ℋ be a complex separable Hilbert space and ℒ(ℋ) denote the collection of bounded linear operators on ℋ. An operator A in ℒ(ℋ) is said to be strongly irreducible, if , the commutant of A, has no non-trivial idempotent. An operator A in ℒ(ℋ) is said to be a Cowen-Douglas operator, if there exists Ω, a connected open subset of C, and n, a positive integer, such that

(a)

Ω ⊂ σ(A) = ﹛z ∈ C | A – z not invertible﹜;

(b)

ran(A – z) = ℋ, for z in Ω;

(c)

Vz∈Ω ker(A – z) = ℋ and

(d)

dim ker(A – z) = n for z in Ω.

In the paper, we give a similarity classification of strongly irreducible Cowen-Douglas operators by using the K0-group of the commutant algebra as an invariant.
Smoothness of Quotients Associated With a Pair of Commuting Involutions
Authors: Helminck Aloysius G. , Schwarz Gerald W.
Published: December 2010

Let σ, θ be commuting involutions of the connected semisimple algebraic group G where σ, θ and G are defined over an algebraically closed field , char = 0. Let H := Gσ and K := Gθ be the fixed point groups. We have an action (H × K) × G → G, where ((h, k), g) ⟼ hgk–1, h ∈ H, k ∈ K, g ∈ G. Let G//(H × K) denote the categorical quotient Spec (G)H×K. We determine when this quotient is smooth. Our results are a generalization of those of Steinberg [Ste75], Pittie [Pit72] and Richardson [Ric82] in the symmetric case where σ = θ and H = K.
Central Sequence Algebras of a Purely Infinite Simple C*-algebra
Authors: Kishimoto Akitaka
Published: December 2010

We are concerned with a unital separable nuclear purely infinite simple C*-algebra A satisfying UCT with a Rohlin flow, as a continuation of [12]. Our first result (which is independent of the Rohlin flow) is to characterize when two central projections in A are equivalent by a central partial isometry. Our second result shows that the K-theory of the central sequence algebra A′ ∩ Aω (for an ω ∈ βN\N) and its fixed point algebra under the flow are the same (incorporating the previous result). We will also complete and supplement the characterization result of the Rohlin property for flows stated in [12].
Enriques Diagrams and Adjacency of Planar Curve Singularities
Authors: Alberich-Carramiñana Maria , Roé Joaquim
Published: December 2010

We study adjacency of equisingularity types of planar complex curve singularities in terms of their Enriques diagrams. The goal is, given two equisingularity types, to determine whether one of themis adjacent to the other. For linear adjacency a complete answer is obtained, whereas for arbitrary (analytic) adjacency a necessary condition and a sufficient condition are proved. We also obtain new examples of exceptional deformations,i.e, singular curves of type𝓓′ that can be deformed to a curve of type𝓓without𝓓′ being adjacent to𝓓.
On the Size of the Wild Set
Authors: Somodi Marius
Published: December 2010

To every pair of algebraic number fields with isomorphic Witt rings one can associate a number, called the minimum number of wild primes. Earlier investigations have established lower bounds for this number. In this paper an analysis is presented that expresses the minimum number of wild primes in terms of the number of wild dyadic primes. This formula not only gives immediate upper bounds, but can be considered to be an exact formula for the minimum number of wild primes.
On the Duality between Coalescing Brownian Motions
Authors: Xiong Jie , Zhou Xiaowen
Published: December 2010

A duality formula is found for coalescing Brownian motions on the real line. It is shown that the joint distribution of a coalescing Brownian motion can be determined by another coalescing Brownian motion running backward. This duality is used to study a measure-valued process arising as the high density limit of the empirical measures of coalescing Brownian motions.
Unbounded Fredholm Operators and Spectral Flow
Authors: Booss-Bavnbek Bernhelm , Lesch Matthias , Phillips John
Published: December 2010

We study the gap (= “projection norm” = “graph distance”) topology of the space of all (not necessarily bounded) self-adjoint Fredholm operators in a separable Hilbert space by the Cayley transformand direct methods. In particular, we show the surprising result that this space is connected in contrast to the bounded case. Moreover, we present a rigorous definition of spectral flow of a path of such operators (actually alternative but mutually equivalent definitions) and prove the homotopy invariance. As an example, we discuss operator curves on manifolds with boundary.
Some New Results on L2 Cohomology of Negatively Curved Riemannian Manifolds
Authors: Cocos M.
Published: December 2010

The present paper is concerned with the study of the L2 cohomology spaces of negatively curved manifolds. The first half presents a finiteness and vanishing result obtained under some curvature assumptions, while the second half identifies a class of metrics having non-trivial L2 cohomology for degree equal to the half dimension of the space. For the second part we rely on the existence and regularity properties of the solution for the heat equation for forms.
Small Coverings with Smooth Functions under the Covering Property Axiom
Authors: Ciesielski Krzysztof , Pawlikowski Janusz
Published: December 2010

In the paper we formulate a Covering Property Axiom, CPAprism, which holds in the iterated perfect set model, and show that it implies the following facts, of which (a) and (b) are the generalizations of results of J. Steprāns.

(a) There exists a family ℱ of less than continuummany functions from ℝ to ℝ such that ℝ2 is covered by functions from ℱ, in the sense that for every 〈x, y〉 ∈ ℝ2 there exists an f ∈ ℱ such that either f (x) = y or f (y) = x.

(b) For every Borel function f : ℝ → ℝ there exists a family ℱ of less than continuum many “” functions (i.e., differentiable functions with continuous derivatives, where derivative can be infinite) whose graphs cover the graph of f.

(c) For every n > 0 and a Dn function f: ℝ → ℝ there exists a family ℱ of less than continuum many Cn functions whose graphs cover the graph of f.

We also provide the examples showing that in the above properties the smoothness conditions are the best possible. Parts (b), (c), and the examples are closely related to work of A. Olevskiĭ.
Summation Formulae for Coefficients of L-functions
Authors: Friedlander John B. , Iwaniec Henryk
Published: December 2010

With applications inmind we establish a summation formula for the coefficients of a general Dirichlet series satisfying a suitable functional equation. Among a number of consequences we derive a generalization of an elegant divisor sum bound due to F. V. Atkinson.
Local Solvability of Laplacian Difference Operators Arising from the Discrete Heisenberg Group
Authors: Kornelson Keri A.
Published: December 2010

Differential operators Dx, Dy , and Dz are formed using the action of the 3-dimensional discrete Heisenberg group G on a set S, and the operators will act on functions on S. The Laplacian operator is a difference operator with variable differences which can be associated to a unitary representation of G on the Hilbert space L2(S). Using techniques from harmonic analysis and representation theory, we show that the Laplacian operator is locally solvable.
The Resolvent of Closed Extensions of Cone Differential Operators
Authors: Schrohe E. , Seiler J.
Published: December 2010

We study closed extensions of an elliptic differential operator A on amanifold with conical singularities, acting as an unbounded operator on a weighted Lp-space. Under suitable conditions we show that the resolvent exists in a sector of the complex plane and decays like as Moreover, we determine the structure of the resolvent with enough precision to guarantee existence and boundedness of imaginary powers of .

As an application we treat the Laplace–Beltrami operator for a metric with straight conical degeneracy and describe domains yielding maximal regularity for the Cauchy problem , u(0) = 0.
Hyperbolic Group C*-Algebras and Free-Product C*-Algebras as Compact Quantum Metric Spaces
Authors: Ozawa Narutaka , Rieffel Marc A.
Published: December 2010

Let ℓ be a length function on a group G, and let Mℓ denote the operator of pointwise multiplication by ℓ on ℓ2(G). Following Connes, Mℓ can be used as a “Dirac” operator for C*r(G). It defines a Lipschitz seminorm on C*r(G), which defines a metric on the state space of C*r(G). We show that if G is a hyperbolic group and if ℓ is a word-length function on G, then the topology from this metric coincides with the weak-* topology (our definition of a “compact quantum metric space”). We show that a convenient framework is that of filtered C*-algebras which satisfy a suitable “Haagerup-type” condition. We also use this framework to prove an analogous fact for certain reduced free products of C*-algebras.
Dupin Hypersurfaces in ℝ5
Authors: Riveros Carlos M.C. , Tenenblat Keti
Published: December 2010

We study Dupin hypersurfaces in ℝ5 parametrized by lines of curvature, with four distinct principal curvatures. We characterize locally a generic family of such hypersurfaces in terms of the principal curvatures and four vector valued functions of one variable. We show that these vector valued functions are invariant by inversions and homotheties.
Motivic Haar Measure on Reductive Groups
Authors: Gordon Julia
Published: December 2010

We define a motivic analogue of the Haar measure for groups of the form G(k((t))), where k is an algebraically closed field of characteristic zero, and G is a reductive algebraic group defined over k. A classical Haar measure on such groups does not exist since they are not locally compact. We use the theory of motivic integration introduced by M. Kontsevich to define an additive function on a certain natural Boolean algebra of subsets of G(k((t))). This function takes values in the so-called dimensional completion of the Grothendieck ring of the category of varieties over the base field. It is invariant under translations by all elements of G(k((t))), and therefore we call it a motivic analogue of Haar measure. We give an explicit construction of the motivic Haar measure, and then prove that the result is independent of all the choices that are made in the process.
Existence and Multiplicity of Positive Solutions for Singular Semipositonep-Laplacian Equations
Authors: Agarwal Ravi P. , Cao Daomin , Lü Haishen , O'Regan Donal
Published: December 2010

Positive solutions are obtained for the boundary value problem

Heref (t, u)≥–M, (Mis a positive constant) for (t, u) ∈ [0, 1]×(0, ∞). We will show the existence of two positive solutions by using degree theory together with the upper–lower solution method.
Hausdorff and Quasi-Hausdorff Matrices on Spaces of Analytic Functions
Authors: Galanopoulos P. , Papadimitrakis M.
Published: December 2010

We consider Hausdorff and quasi-Hausdorff matrices as operators on classical spaces of analytic functions such as the Hardy and the Bergman spaces, the Dirichlet space, the Bloch spaces and BMOA. When the generating sequence of the matrix is the moment sequence of a measure μ, we find the conditions on μ which are equivalent to the boundedness of the matrix on the various spaces.
Mordell–Weil Groups and the Rank of Elliptic Curves over Large Fields
Authors: Im Bo-Hae
Published: December 2010

Let K be a number field, an algebraic closure of K and E/K an elliptic curve defined over K. In this paper, we prove that if E/K has a K-rational point P such that 2P ≠ O and 3P ≠ O, then for each σ ∈ Gal(/K), the Mordell–Weil group of E over the fixed subfield of under σ has infinite rank.
Diametrically Maximal and Constant Width Sets in Banach Spaces
Authors: Moreno J. P. , Papini P. L. , Phelps R. R.
Published: December 2010

We characterize diametrically maximal and constant width sets inC(K), whereKis any compact Hausdorff space. These results are applied to prove that the sum of two diametrically maximal sets needs not be diametrically maximal, thus solving a question raised in a paper by Groemer. A characterization of diametrically maximal sets inis also given, providing a negative answer to Groemer's problem in finite dimensional spaces. We characterize constant width sets inc0(I), for everyI, and then we establish the connections between the Jung constant of a Banach space and the existence of constant width sets with empty interior. Porosity properties of families of sets of constant width and rotundity properties of diametrically maximal sets are also investigated. Finally, we present some results concerning non-reflexive and Hilbert spaces.
Functorial Decompositions of Looped Coassociative Co-H Spaces
Authors: Selick P. , Theriault S. , Wu J.
Published: December 2010

Selick and Wu gave a functorial decomposition of Ω∑X for path-connected, p-local CW-complexes X which obtained the smallest nontrivial functorial retract Amin(X) of Ω∑X. This paper uses methods developed by the second author in order to extend such functorial decompositions to the loops on coassociative co-H spaces.
A Casselman–Shalika Formula for the Shalika Model of GLn
Authors: Sakellaridis Yiannis
Published: December 2010

The Casselman–Shalika method is a way to compute explicit formulas for periods of irreducible unramified representations of p-adic groups that are associated to unique models (i.e., multiplicity-free induced representations). We apply this method to the case of the Shalika model of GLn, which is known to distinguish lifts from odd orthogonal groups. In the course of our proof, we further develop a variant of themethod, that was introduced by Y.Hironaka, and in effect reducemany such problems to straightforward calculations on the group.
Orbites unipotentes et pôles d'ordre maximal de la fonction μ de Harish-Chandra
Authors: Heiermann Volker
Published: December 2010

Dans un travail antérieur, nous avions montré que l’induite parabolique (normalisée) d’une représentation irréductible cuspidale σ d’un sous-groupe de LeviMd’un groupep-adique contient un sous-quotient de carré intégrable, si et seulement si la fonction μ de Harish-Chandra a un pôle en σ d’ordre égal au rang parabolique deM. L’objet de cet article est d’interpréter ce résultat en termes de fonctorialité de Langlands.
On Fiber Cones of 𝑚-Primary Ideals
Authors: Jayanthan A. V. , Puthenpurakal Tony J. , Verma J. K.
Published: December 2010

Two formulas for the multiplicity of the fiber cone of an 𝑚-primary ideal of a d-dimensional Cohen–Macaulay local ring (R, 𝑚) are derived in terms of the mixed multiplicity ed–1(𝑚|I), the multiplicity e(I), and superficial elements. As a consequence, the Cohen–Macaulay property of F(I) when I has minimal mixed multiplicity or almost minimal mixed multiplicity is characterized in terms of the reduction number of I and lengths of certain ideals. We also characterize the Cohen–Macaulay and Gorenstein properties of fiber cones of 𝑚–primary ideals with a d–generated minimal reduction J satisfying ℓ(I2/JI) = 1 or ℓ(I𝑚/J𝑚) = 1.
Bol Loops of Nilpotence Class Two
Authors: Chein Orin , Goodaire Edgar G.
Published: December 2010

Call a non-Moufang Bol loopminimally non-Moufangif every proper subloop is Moufang andminimally nonassociativeif every proper subloop is associative. We prove that these concepts are the same for Bol loops which are nilpotent of class two and in which certain associators square to 1. In the process, we derive many commutator and associator identities which hold in such loops.
Le splitting pour l'opérateur de Klein–Gordon: une approche heuristique et numérique
Authors: Servat E.
Published: December 2010

Dans cet article on étudie la différence entre les deux premières valeurs propres, le splitting, d’un opérateur de Klein–Gordon semi-classique unidimensionnel, dans le cas d’un potentiel symétrique présentant un double puits. Dans le cas d’une petite barrière de potentiel, B. Helffer et B. Parisse ont obtenu des résultats analogues à ceux existant pour l’opérateur de Schrödinger. Dans le cas d’une grande barrière de potentiel, on obtient ici des estimations des tranformées de Fourier des fonctions propres qui conduisent à une conjecture du splitting. Des calculs numériques viennent appuyer cette conjecture.
Division Algebras of Prime Degree and Maximal Galois p-Extensions
Authors: Mináč J. , Wadsworth A.
Published: December 2010

Let p be an odd prime number, and let F be a field of characteristic not p and not containing the group μp of p-th roots of unity. We consider cyclic p-algebras over F by descent from L = F(μp). We generalize a theorem of Albert by showing that if μpn ⊆ L, then a division algebra D of degree pn over F is a cyclic algebra if and only if there is d ∈ D with dpn ∈ F – Fp. Let F(p) be the maximal p-extension of F. We show that F(p) has a noncyclic algebra of degree p if and only if a certain eigencomponent of the p-torsion of Br(F(p)(μp)) is nontrivial. To get a better understanding of F(p), we consider the valuations on F(p) with residue characteristic not p, and determine what residue fields and value groups can occur. Our results support the conjecture that the p torsion in Br(F(p)) is always trivial.
Operator Amenability of the Fourier Algebra in the cb-Multiplier Norm
Authors: Forrest Brian E. , Runde Volker , Spronk Nico
Published: December 2010

Let G be a locally compact group, and let Acb(G) denote the closure of A(G), the Fourier algebra of G, in the space of completely boundedmultipliers of A(G). If G is a weakly amenable, discrete group such that C*(G) is residually finite-dimensional, we show that Acb(G) is operator amenable. In particular, Acb() is operator amenable even though , the free group in two generators, is not an amenable group. Moreover, we show that if G is a discrete group such that Acb(G) is operator amenable, a closed ideal of A(G) is weakly completely complemented in A(G) if and only if it has an approximate identity bounded in the cb-multiplier norm.
Hp-Maximal Regularity and Operator Valued Multipliers on Hardy Spaces
Authors: Bu Shangquan , Merdy Christian Le
Published: December 2010

We consider maximal regularity in the Hp sense for the Cauchy problem u′(t) + Au(t) = f(t) (t ∈ ℝ), where A is a closed operator on a Banach space X and f is an X-valued function defined on ℝ. We prove that if X is an AUMD Banach space, then A satisfies Hp-maximal regularity if and only if A is Rademacher sectorial of type < . Moreover we find an operator A with Hp-maximal regularity that does not have the classical Lp-maximal regularity. We prove a related Mikhlin type theorem for operator valued Fourier multipliers on Hardy spaces Hp(ℝ X), in the case when X is an AUMD Banach space.
On Gap Properties and Instabilities of p-Yang–Mills Fields
Authors: Chen Qun , Zhou Zhen-Rong
Published: December 2010

We consider the p-Yang–Mills functional (p ≥ 2) defined as . We call critical points of YMp( · ) the p-Yang–Mills connections, and the associated curvature R∇ the p-Yang–Mills fields. In this paper, we prove gap properties and instability theorems for p-Yang–Mills fields over submanifolds in ℝn+k and .
On a Conjecture of Jacquet, Lai, and Rallis: Some Exceptional Cases
Authors: Ginzburg David , Lapid Erez
Published: December 2010

We prove two spectral identities. The first one relates the relative trace formula for the spherical variety GSpin(4, 3)/G2with a weighted trace formula forGL2. The second relates a spherical variety pertaining toF4to one of GSp(6). These identities are in accordance with a conjecture made by Jacquet, Lai, and Rallis, and are obtained without an appeal to a geometric comparison.
Restricted Partitions of Finite Sets
Authors: Miksa F.L. , Moser L. , Wyman M.
Published: December 2010

In this paper we consider the following combinatorial problem. In how many ways can n distinguishable objects be placed into an unrestricted number of indistinguishable boxes, if each box can hold at most r objects? Let us denote this number by Gn, r

Special cases of this problem have been the object of considerable study. In the case r = 2 we have the numbers Gn, 2 = Tn which have been treated by Rothe [12] as early as 1800. Tn is also the number of solutions of x2 = 1 in the symmetric group on n letters , and in this and related guises has been studied by Touchard [13], Chowla, Herstein and Moore [3] and two of the present authors [7].
Asymptotic Formulas for Some Arithmetic Functions
Authors: Erdős P.
Published: December 2010

Let f(x) be an increasing function. Recently there have been several papers which proved that under fairly general conditions on f(x) the density of integers n for which (n, f(n)) = 1 is 6/π2 and that (d(n) denotes the number of divisors of n)

In particular both of these results hold if f(x) = xα, 0 < α < 1 and the first holds if f(x) = [α x], α irrational.
On the Relative Widths of Coverings by Convex Bodies
Authors: Moser W.O.J.
Published: December 2010

The purpose of this note is to give an elementary proof of a special case of a theorem suggested by Th. Bang (2; 3) and proved by Lee et al (5; see also 1; 4; 6; 7; 8).
A Generalized Ring of Quotients II
Authors: Findlay G.D. , Lambek J.
Published: December 2010

A partial homomorphism ϕ from B into A will be called a fractional homomorphism if dom ϕ ≤ B (A). Every extension of a fractional homomorphism is again fractional, and each fractional homomorphism has a unique irreducible extension.
On a Note by H. Schwerdtfeger
Authors: Scherk Peter
Published: December 2010

Let x, y denote real column vectors with n elements. Let A be a regular symmetric real n×n matrix. Dashes indicate transposition.

If x is fixed, x' Ax > 0, the discriminant of A at x is the quadratic form

y' where S= S(x)= x'x'Ax ¨ Axx'A.

In Can. Math. Bull. 1, pp. 175-179, Dr. Schwerdtfeger proved the equivalence of the following properties of A:

(i)

A is of the congruence type [+, -,..., -].

(ii)

y' Sy≤ 0 for all y, equality holding if and only if y is a multiple of x. His note is of particular interest because he also discusses the eigen-values of S. If only the quoted result is aimed at, the following procedure may be shorter.
On the Katětov and Stone-Čech Extensions
Authors: Banaschewski Bernhard
Published: December 2010

In general topology, one knows several standard extension spaces defined for one class of spaces or another and it is a natural question concerning any two such extensions which are defined for the same space whether they can ever be equal to each other. In the following, this problem will be considered for the Stone-Čech compactification βE of a completely regular non-compact Hausdorff space E[4] and Katětov's maximal Hausdorff extension κE of E[5]. It will be shown that βEκE always holds or, what amounts to the same, that κE can never be compact. As an application of this it will be proved that any completely regular Hausdorff space is dense in some non-compact space in which the Stone-Weierstrass approximation theorem holds.
On the Inversion of General Transformations*
Authors: Rooney P. G.
Published: December 2010

Let k be the kernel of a “general transformation”; that is, k(x) / x ϵ L2(0,∞), and if x and y are positive

1

Then it is well known (see for example [8; Theorems 129 and 131]) that if the transform of fϵL2(0,∞) is g, that is, if

2

then the inverse transform is given by

3

In practice, the inversion formula (3) is often hard to use. For example, the integral may be too difficult to evaluate; moreover, since (2) requires a differentiation, it is not well suited for numerical calculation. Hence it seems worthwhile to find other methods for inverting the transformation.
On the Ring of Quotients of a Boolean Ring
Authors: Brainerd B. , Lambek J.
Published: December 2010

Two important mathematical constructions are: the construction of the rational s from the integers and the construction of the reals from the rationals. The first process can be carried out for any ring, producing its maximal ring of quotients [4, 5]. The second process can be carried out for any partially ordered set producing its Dedekind-MacNeille completion [2, p. 58]. We will show that for Boolean rings, which are both rings and partially ordered sets, the two constructions coincide.
Existence of Certain Analytic Homeomorphisms
Authors: Melzak Z. A.
Published: December 2010

This note has its origin in the following problem: do there exist non-trivial increasing continuous functions on [0, l] to [0, l], which map the following sets in [0, l] onto themselves: the rational, the algebraic and the transcendental numbers? One such function is obviously f(x) = x; more generally, f(x) = (c + l)x/(cx + 1), with c rational and non-negative, satisfies the conditions. Let G denote the space of order-preserving homeomorphisms of [0, l} onto [0, l], in the uniform metric. It follows from Theorem 1 below that the set S of all such functions i s dense in G. S is clearly a subgroup of G and one may ask what a r e its group-theoretic properties. We shall not consider these questions.
A Class of Star-Shaped Bodies
Authors: Melzak Z.A.
Published: December 2010

The more important properties of the class κ of all bounded convex bodies in E3 with non-empty interior include: uniform approximability by polyhedra, existence of volume and surface area, and Blaschke's selection principle, [l ], [2 ]. In this note we define and consider a class ℋ of star-shaped bodies in E3, which enjoys many properties of κ, among them the above-mentioned ones, and is considerably larger. Roughly speaking, ℋ consists of closed bounded sets in E3 with nonempty interior, whose boundary is completely visible from every point of a set with non-empty interior. It turns out that ℋ is identifiable with the class of all real-valued positive functions on the sphere S3 which satisfy a Lipschitz condition.
On Common Multiples of Transfinite Numbers
Authors: Zakon Elias
Published: December 2010

In his well known monograph [l] (p. 81) H. Bachmann indicates that two ordinal numbers > 1 always have a common left multiple > 1, but not always have a right multiple (RM). The monograph does not, however, contain any further analysis of right multiples. The purpose of the present note is to supplement this by formulating the following propositions which, despite their simplicity, seem not yet to be known.
On a Problem of L. Moser
Authors: Guttman Irwin
Published: December 2010

In [l], Moser derives a recurrence relation and studies the limiting behaviour of the Expectations En of the following game. “A real number is drawn at random from [0,1]. We may either keep the number selected, or reject it and draw again. We can then either keep the second number chosen or reject it, and draw again, and so on. Suppose we have at most n choices. What stopping rule gives the largest En and how can we estimate En?”
A Determinant Expression of Tchebychev Polynomials
Authors: Korsak A. , Schubert C.
Published: December 2010

A certain n x n determinant, namely that in (1), provides a rather simple expression for the Tchebychev polynomial Tn(x) = cos n(cos-1x). This determinant also leads to an interesting combinatorial interpretation of the coefficients in that polynomial.
Introduction to Von Neumann Algebras and Continuous Geometry
Authors: Halperin Israel
Published: December 2010

What is a von Neumann algebra? What is a factor (i) of type I, (ii) of type II, (iii) of type III? What is a projection geometry? And finally, what is a continuous geometry?

The questions recall some of the most brilliant mathematical work of the past 30 years, work which was done by John von Neumann, partly in collaboration with F. J. Murray, and which grew out of von Neumann1 s analysis of linear operators in Hilbert space.
An Enumeration of the Five Parallelohedra
Authors: Moser William
Published: December 2010

A parallelohedron is a convex polyhedron, in real affine three-dimensional space, which can be repeated by translation to fill the whole space without interstices. It has centrally symmetrical faces [4, p. 120] and hence is centrally symmetrical.

Let Fi denote the number of faces each having exactly i edges, Vi denote the number of vertices each incident with exactly i edges, E denote the number of edges, n denote the number of sets of parallel edges, F denote the total number of faces, V denote the total number of vertices.