bluuebunny/crossref_metadata_2025 huggingface dataset:
Oscillation and Global Attractivity in a Periodic Delay Equation
Authors: Graef J. R. , Qian C. , Spikes P. W.
Published: December 2010

Consider the delay differential equation

whereα(t) andβ(t) are positive, periodic, and continuous functions with periodw> 0, andmis a nonnegative integer. We show that this equation has a positive periodic solutionx*(t) with periodw. We also establish a necessary and sufficient condition for every solution of the equation to oscillate aboutx*(t) and a sufficient condition forx*(t) to be a global attractor of all solutions of the equation.
Pseudo-Homogeneous Coordinates for Hughes Planes
Authors: Maier Peter , Stroppel Markus
Published: December 2010

Among the projective planes, the class of Hughes planes has received much interest, for several good reasons. However, the existing descriptions of these planes are somewhat unsatisfactory. We introduce pseudo-homogeneous coordinates which at the same time are easy to handle and give insight into the action of the group that is generated by all elations of the desarguesian Baer subplane of a Hughes plane. The information about the orbit decomposition is then used to give a description in terms of coset spaces of this group. Finally, we exhibit a non-closing Desargues configuration in terms of coordinates.
Weak*-Closed Derivations from C[0,1] into L∞[0,1]
Authors: Weaver Nik
Published: December 2010

We show that every weak*-closed derivation from C[0,1] ⊂ L∞[0, 1] into L∞[0, 1] is the inverse of integration against a function in L1[0,1].
On the Reduced Product Construction
Authors: Fantham Peter , James Ioan , Mather Michael
Published: December 2010

Under certain conditions the reduced product space JX of a space X has the same homotopy type as ΩΣX, the loop-space on the suspension of X. Several proofs can be found in the literature. The original proof [6] made unnecessarily strong assumptions. Later, in the last chapter of [3], torn Dieck, Kamps and Puppe gave a proof under much weaker conditions and showed that they could not be further weakened. The question then arose as to whether the reduced product construction could be generalized to provide combinatorial models not only of ΩΣX but also of Ω2Σ2X, Ω3Σ3X and so on. This was answered in the affirmative by May [10], using ideas of Boardman and Vogt [1], and the construction was further developed by Segal [11] and others.

The present note, however, is not concerned with these generalizations. Its purpose is to give a simple proof of the original result, without striving for maximum generality, and to show that the same method can be used to prove an equivariant version of the reduced product theorem and hence a fibrewise version. Fibrewise versions of the reduced product theorem have previously been given by Eggar [5] and, more recently, by one of us [8] but it may be useful to have a relatively simple treatment which is adequate for the majority of applications.
Self-Adjoint Fredholm Operators And Spectral Flow
Authors: Phillips John
Published: December 2010

We study the topology of the nontrivial component, , of self-adjoint Fredholm operators on a separable Hilbert space. In particular, if {Bt} is a path of such operators, we can associate to {Bt} an integer, sf({Bt}), called the spectral flow of the path. This notion, due to M. Atiyah and G. Lusztig, assigns to the path {Bt} the net number of eigenvalues (counted with multiplicities) which pass through 0 in the positive direction. There are difficulties in making this precise — the usual argument involves looking at the graph of the spectrum of the family (after a suitable perturbation) and then counting intersection numbers with y = 0.

We present a completely different approach using the functional calculus to obtain continuous paths of eigenprojections (at least locally) of the form . The spectral flow is then defined as the dimension of the nonnegative eigenspace at the end of this path minus the dimension of the nonnegative eigenspace at the beginning. This leads to an easy proof that spectral flow is a well-defined homomorphism from the homotopy groupoid of onto Z. For the sake of completeness we also outline the seldom-mentioned proof that the restriction of spectral flow to is an isomorphism onto Z.
Lattice trees and super-Brownian motion
Authors: Derbez Eric , Slade Gordon
Published: December 2010

This article discusses our recent proof that above eight dimensions the scaling limit of sufficiently spread-out lattice trees is the variant of super-Brownian motion calledintegrated super-Brownian excursion(ISE), as conjectured by Aldous. The same is true for nearest-neighbour lattice trees in sufficiently high dimensions. The proof, whose details will appear elsewhere, uses the lace expansion. Here, a related but simpler analysis is applied to show that the scaling limit of a mean-field theory is ISE, in all dimensions. A connection is drawn between ISE and certain generating functions and critical exponents, which may be useful for the study of high-dimensional percolation models at the critical point.
Derivations from Totally Ordered Semigroup Algebras into their Duals
Authors: Blackmore T. D.
Published: December 2010

For a well-behaved measureμ, on a locally compact totally ordered setX, with continuous partμc, we makeLp(X,μc) into a commutative Banach bimodule over the totally ordered semigroup algebraLp(X,μ), in such a way that the natural surjection from the algebra to the module is a bounded derivation. This gives rise to bounded derivations fromLp(X,μ) into its dual module and in particular shows that ifμcis not identically zero thenLp(X,μ) is not weakly amenable. We show that all bounded derivations fromL1(X,μ) into its dual module arise in this way and also describe all bounded derivations from Lp(X,μ) into its dual for 1 <p< ∞ the case thatXis compact andμcontinuous.
Quantum Deformations of Simple Lie Algebras
Authors: Bremner Murray
Published: December 2010

It is shown that every simple complex Lie algebra 𝔤 admits a 1-parameter family 𝔤q of deformations outside the category of Lie algebras. These deformations are derived from a tensor product decomposition for Uq(𝔤)-modules; here Uq(𝔤) is the quantized enveloping algebra of 𝔤. From this it follows that the multiplication on 𝔤q is Uq(𝔤)-invariant. In the special case 𝔤 = (2), the structure constants for the deformation 𝔤 (2)q are obtained from the quantum Clebsch-Gordan formula applied to V(2)q ⊗ V(2)q; here V(2)q is the simple 3-dimensional Uq(𝔤(2))-module of highest weight q2.
Finite Rank Operators and Functional Calculus on Hilbert Modules over AbelianC*-Algebras
Authors: Kucerovsky Dan
Published: December 2010

We consider the problem: IfKis a compact normal operator on a Hilbert moduleE, andf∈C0(SpK) is a function which is zero in a neighbourhood of the origin, isf(K) of finite rank? We show that this is the case if the underlyingC*-algebra is abelian, and that the range off(K) is contained in a finitely generated projective submodule ofE.
The Space of Harmonic Maps from the 2-Sphere to the Complex Projective Plane
Authors: Crawford T. Arleigh
Published: December 2010

In this paper we study the topology of the space of harmonic maps from S2 to ℂℙ2.We prove that the subspaces consisting of maps of a fixed degree and energy are path connected. By a result of Guest and Ohnita it follows that the same is true for the space of harmonic maps to ℂℙn for n ≥ 2. We show that the components of maps to ℂℙ2 are complex manifolds.
A General Approach to Littlewood-Paley Theorems for Orthogonal Families
Authors: Hare Kathryn E.
Published: December 2010

A general lacunary Littlewood-Paley type theorem is proved, which applies in a variety of settings including Jacobi polynomials in [0, 1], SU(2), and the usual classical trigonometric series in [0, 2π). The theoremis used to derive new results for Lp multipliers on SU(2) and Jacobi Lp multipliers.
On the Homology of Finite Abelian Coverings of Links
Authors: Hillman J. A. , Sakuma M.
Published: December 2010

Let A be a finite abelian group and M be a branched cover of an homology 3-sphere, branched over a link L, with covering group A. We show that H1(M; Z[1/|A|]) is determined as a Z[1/|A|][A]-module by the Alexander ideals of L and certain ideal class invariants.
On Geometric Properties of Orlicz-Lorentz Spaces
Authors: Hudzik H. , Kamińska A. , M. Mastyło
Published: December 2010

Criteria for local uniform rotundity and midpoint local uniform rotundity in Orlicz-Lorentz spaces with the Luxemburg norm are given. Strict K-monotonicity and Kadec-Klee property are also discussed.
On Compact Separable Radial Spaces
Authors: Dow Alan
Published: December 2010

If A and B are disjoint ideals on ω, there is a tower preserving σ-centered forcing which introduces a subset of ω which meets every infinite member of A in an infinite set and is almost disjoint fromeverymember of B. We can then produce a model in which all compact separable radial spaces are Fréchet, thus answering a question of P. Nyikos. The question of the existence of compact ccc radial spaces which are not Fréchet was first asked by Chertanov (see [Arh78]).
Asymptotic Existence of Tight Orthogonal Main Effect Plans
Authors: Gallant Robert , Colbourn Charles J.
Published: December 2010

Our main result is showing the asymptotic existence of tight OMEPs. More precisely, for each fixed number k of rows, and with the exception of OMEPs of the form 2 × 2 × … 2 × 2s // 4s with s odd and with more than three rows, there are only a finite number of tight OMEP parameters for which the tight OMEP does not exist.
An Answer to a Question of Kegel on Sums of Rings
Authors: Kelarev A. V.
Published: December 2010

We construct a ring R which is a sum of two subrings A and B such that the Levitzki radical of R does not contain any of the hyperannihilators of A and B. This answers an open question asked by Kegel in 1964.
The Cardinality of the Center of a PI Ring
Authors: Lanski Charles
Published: December 2010

The main result shows that if R is a semiprime ring satisfying a polynomial identity, and if Z(R) is the center of R, then card R ≤ 2cardZ(R) . Examples show that this bound can be achieved, and that the inequality fails to hold for rings which are not semiprime.
On Permanental Identities of Symmetric and Skew-Symmetric Matrices in Characteristic p
Authors: Valenti Angela
Published: December 2010

Let Mn(F) be the algebra of n × n matrices over a field F of characteristic p > 2 and let * be an involution on Mn(F). If s1,…,sr are symmetric variables we determine the smallest r such that the polynomial

is a *-polynomial identity of Mn(F) under either the symplectic or the transpose involution. We also prove an analogous result for the polynomial

where k1,…,kr, are skew variables under the transpose involution.
Genericity of Certain Classes of Unitary and Self-Adjoint Operators
Authors: Choksi J. R. , Nadkarni M. G.
Published: December 2010

In a paper [1], published in 1990, in a (somewhat inaccessible) conference proceedings, the authors had shown that for the unitary operators on a separable Hilbert space, endowed with the strong operator topology, those with singular, continuous, simple spectrum, with full support, forma dense Gδ. A similar theoremfor bounded self-adjoint operators with a given normbound (omitting simplicity) was recently given by Barry Simon [2], [3], with a totally different proof. In this note we show that a slight modification of our argument, combined with the Cayley transform, gives a proof of Simon’s result, with simplicity of the spectrum added.
Skein Homology
Authors: Bullock Doug , Frohman Charles , Kania-Bartoszyńska Joanna
Published: December 2010

A new class of homology groups associated to a 3-manifold is defined. The theories measure the syzygies between skein relations in a skein module. We investigate some of the properties of the homology theory associated to the Kauffman bracket.
Congruence Lattices of Finite Semimodular Lattices
Authors: Grätzer G. , Lakser H. , Schmidt E. T.
Published: December 2010

We prove that every finite distributive lattice can be represented as the congruence lattice of a finite (planar) semimodular lattice.
Class Number One and Prime-Producing Quadratic Polynomials Revisited
Authors: Mollin R. A.
Published: December 2010

Over a decade ago, this author produced class number one criteria for real quadratic fields in terms of prime-producing quadratic polynomials. The purpose of this article is to revisit the problem from a new perspective with new criteria.We look at the more general situation involving arbitrary real quadratic orders rather than the more restrictive field case, and use the interplay between the various orders to provide not only more general results, but also simpler proofs.
Exponentiality of Certain Real Solvable Lie Groups
Authors: Moskowitz Martin , Wüstner Michael
Published: December 2010

In this article, making use of the second author’s criterion for exponentiality of a connected solvable Lie group, we give a rather simple necessary and sufficient condition for the semidirect product of a torus acting on certain connected solvable Lie groups to be exponential.
Free Products with Amalgamation and p-Adic Lie Groups
Authors: Long D. D. , Reid A. W.
Published: December 2010

Using the theory of p-adic Lie groups we give conditions for a finitely generated group to admit a splitting as a non-trivial free product with amalgamation. This can be viewed as an extension of a theorem of Bass.
The Periodic Radical of Group Rings and Incidence Algebras
Authors: Parmenter M. M. , Spiegel E. , Stewart P. N.
Published: December 2010

Let R be a ring with 1 and P(R) the periodic radical of R. We obtain necessary and sufficient conditions for P(RG) = 0 when RG is the group ring of an FC group G and R is commutative. We also obtain a complete description of when I(X, R) is the incidence algebra of a locally finite partially ordered set X and R is commutative.
Remarks on Certain Metaplectic Groups
Authors: Sun Heng
Published: December 2010

We study metaplectic coverings of the adelized group of a split connected reductive group G over a number field F. Assume its derived group G′ is a simply connected simple Chevalley group. The purpose is to provide some naturally defined sections for the coverings with good properties which might be helpful when we carry some explicit calculations in the theory of automorphic forms on metaplectic groups. Specifically, we

1.

construct metaplectic coverings of G(A) from those of G′(A);

2.

for any non-archimedean place v, show the section for a covering of G(Fv) constructed from a Steinberg section is an isomorphism, both algebraically and topologically in an open subgroup of G(Fv);

3.

define a global section which is a product of local sections on a maximal torus, a unipotent subgroup and a set of representatives for the Weyl group.
How the Roots of a Polynomial Vary with its Coefficients: A Local Quantitative Result
Authors: Beauzamy Bernard
Published: December 2010

A well-known result, due to Ostrowski, states that if , then the roots (xj) of P and (yj) of Q satisfy , where n is the degree of P and Q. Though there are cases where this estimate is sharp, it can still be made more precise in general, in two ways: first by using Bombieri’s norm instead of the classical l1 or l2 norms, and second by taking into account the multiplicity of each root. For instance, if x is a simple root of P, we show that instead of . The proof uses the properties of Bombieri’s scalar product andWalsh Contraction Principle.
Operators with Closed Range, Pseudo-Inverses, and Perturbation of Frames for a Subspace
Authors: Christensen Ole
Published: December 2010

Recent work of Ding and Huang shows that if we perturb a bounded operator (between Hilbert spaces) which has closed range, then the perturbed operator again has closed range. We extend this result by introducing a weaker perturbation condition, and our result is then used to prove a theorem about the stability of frames for a subspace.
Ample Vector Bundles of Curve Genus One
Authors: Lanteri Antonio , Maeda Hidetoshi
Published: December 2010

We investigate the pairs (X, ε) consisting of a smooth complex projective variety X of dimension n and an ample vector bundle ε of rank n − 1 on X such that ε has a section whose zero locus is a smooth elliptic curve.
Conjugate Radius and Sphere Theorem
Authors: Paeng Seong-Hun , Yun Jong-Gug
Published: December 2010

Bessa [Be] proved that for given n and i0, there exists an depending on n, i0 such that if M admits a metric g satisfying , then M is diffeomorphic to the standard sphere. In this note, we improve this result by replacing a lower bound on the injectivity radius with a lower bound of the conjugate radius.
Mellin Transforms of Mixed Cusp Forms
Authors: Choie Youngju , Lee Min Ho
Published: December 2010

We define generalized Mellin transforms of mixed cusp forms, show their convergence, and prove that the function obtained by such a Mellin transform of a mixed cusp form satisfies a certain functional equation. We also prove that a mixed cusp form can be identified with a holomorphic form of the highest degree on an elliptic variety.
On Kloosterman Sums with Oscillating Coefficients
Authors: Deng Peiming
Published: December 2010

In this paper we prove: for any positive integers a and q with (a, q) = 1, we have uniformly

This improves the previous bound obtained by D. Hajela, A. Pollington and B. Smith [5].
Spaces of Quasi-Measures
Authors: Grubb D. J. , LaBerge Tim
Published: December 2010

We give a direct proof that the space of Baire quasi-measures on a completely regular space (or the space of Borel quasi-measures on a normal space) is compact Hausdorff. We show that it is possible for the space of Borel quasi-measures on a non-normal space to be non-compact. This result also provides an example of a Baire quasi-measure that has no extension to a Borel quasi-measure. Finally, we give a concise proof of theWheeler-Shakmatov theorem, which states that if X is normal and dim(X) ≤ 1, then every quasi-measure on X extends to a measure.
Lie Derivations in Prime Rings With Involution
Authors: Swain Gordon A. , Blau Philip S.
Published: December 2010

Let R be a non-GPI prime ring with involution and characteristic ≠ 2, 3. Let K denote the skew elements of R, and C denote the extended centroid of R. Let δ be a Lie derivation of K into itself. Then δ = ρ + ∊ where ∊ is an additive map into the skew elements of the extended centroid of R which is zero on [K, K], and ρ can be extended to an ordinary derivation of ⧼K⧽ into RC, the central closure.
Peirce Domains
Authors: Tai Yung-Sheng
Published: December 2010

A theorem of Korànyi and Wolf displays any Hermitian symmetric domain as a Siegel domain of the third kind over any of its boundary components. In this paper we give a simple proof that an analogous realization holds for any self-adjoint homogeneous cone.
Product Bases for the Rationals
Authors: Berrizbeitia P. , Elliott P. D. T. A.
Published: December 2010

A sequence of positive rationals generates a subgroup of finite index in the multiplicative positive rationals, and group product representations by the sequence need only a bounded number of terms, if and only if certain related sequences have densities uniformly bounded from below.
Characterizations of Simple Isolated Line Singularities
Authors: Zaharia Alexandru
Published: December 2010

A line singularity is a function germ with a smooth 1-dimensional critical set . An isolated line singularity is defined by the condition that for every x ≠ 0, the germ of f at (x, 0) is equivalent to . Simple isolated line singularities were classified by Dirk Siersma and are analogous of the famous A − D − E singularities. We give two new characterizations of simple isolated line singularities.
The Commutant of an Abstract Backward Shift
Authors: Barnes Bruce A.
Published: December 2010

A bounded linear operator T on a Banach space X is an abstract backward shift if the nullspace of T is one dimensional, and the union of the null spaces of Tk for all k ≥ 1 is dense in X. In this paper it is shown that the commutant of an abstract backward shift is an integral domain. This result is used to derive properties of operators in the commutant.
Sharpness Results and Knapp’s Homogeneity Argument
Authors: Iosevich Alex , Lu Guozhen
Published: December 2010

We prove that the L2 restriction theorem, and , boundedness of the surface averages imply certain geometric restrictions on the underlying hypersurface. We deduce that these bounds imply that a certain number of principal curvatures do not vanish.
Exponential Laws for the Nachbin Ported Topology
Authors: Boyd C.
Published: December 2010

We show that for U and V balanced open subsets of (Qno) Fréchet spaces E and F that we have the topological identity

Analogous results for the compact open topology have long been established. We also give an example to show that the (Qno) hypothesis on both E and F is necessary.
Stable Parabolic Bundles over Elliptic Surfaces and over Riemann Surfaces
Authors: Gantz Christian , Steer Brian
Published: December 2010

We show that the use of orbifold bundles enables some questions to be reduced to the case of flat bundles. The identification of moduli spaces of certain parabolic bundles over elliptic surfaces is achieved using this method.
Extensions of Continuous and Lipschitz Functions
Authors: Matoušková Eva
Published: December 2010

We show a result slightly more general than the following. Let K be a compact Hausdorff space, F a closed subset of K, and d a lower semi-continuous metric on K. Then each continuous function ƒ on F which is Lipschitz in d admits a continuous extension on K which is Lipschitz in d. The extension has the same supremum norm and the same Lipschitz constant.

As a corollary we get that a Banach space X is reflexive if and only if each bounded, weakly continuous and norm Lipschitz function defined on a weakly closed subset of X admits a weakly continuous, norm Lipschitz extension defined on the entire space X.
James-Hopf Invariants, Anick’s Spaces, and the Double Loops on Odd Primary Moore Spaces
Authors: Neisendorfer Joseph
Published: December 2010

Using spaces introduced by Anick, we construct a decomposition into indecomposable factors of the double loop spaces of odd primary Moore spaces when the powers of the primes are greater than the first power. If n is greater than 1, this implies that the odd primary part of all the homotopy groups of the 2n + 1 dimensional sphere lifts to a mod pr Moore space.
Infinite Classes of Covering Numbers
Authors: Bluskov I. , Greig M. , Heinrich K.
Published: December 2010

Let D be a family of k-subsets (called blocks) of a v-set X(v). Then D is a (v, k, t) covering design or covering if every t-subset of X(v) is contained in at least one block of D. The number of blocks is the size of the covering, and the minimum size of the covering is called the covering number. In this paper we consider the case t = 2, and find several infinite classes of covering numbers. We also give upper bounds on other classes of covering numbers.
Weighted Mean Operators on lp
Authors: Borwein David
Published: December 2010

Abstract. The weightedmean matrix Ma is the triangular matrix {ak/An}, where an > 0 and An := a1 + a2 + … + an. It is proved that, subject to ncan being eventually monotonic for each constant c and to the existence of for 1 < p < ∞ if and only if α < p.
Obstructions to 𝒵-Stability for Unital Simple C*-Algebras
Authors: Gong Guihua , Jiang Xinhui , Su Hongbing
Published: December 2010

Let 𝒵 be the unital simple nuclear infinite dimensional C*-algebra which has the same Elliott invariant as ℂ, introduced in [9]. A C*-algebra is called 𝒵-stable if A ≅ A ⊗ 𝒵. In this note we give some necessary conditions for a unital simple C*-algebra to be 𝒵-stable.
The Generating Degree of ℂp
Authors: Alexandru Victor , Popescu Nicolae , Zaharescu Alexandru
Published: December 2010

The generating degree gdeg(A) of a topological commutative ring A with char A = 0 is the cardinality of the smallest subset M of A for which the subring [M] is dense in A. For a prime number p, denotes the topological completion of an algebraic closure of the field of p-adic numbers. We prove that gdeg() = 1, i.e., there exists t in such that [t] is dense in . We also compute where A(U) is the ring of rigid analytic functions defined on a ball U in . If U is a closed ball then = 2 while if U is an open ball then is infinite. We show more generally that is finite for any affinoid U in ℙ1() and is infinite for any wide open subset U of ℙ1().
A Technique of Studying Sums of Central Cantor Sets
Authors: Anisca Razvan , Ilie Monica
Published: December 2010

This paper is concernedwith the structure of the arithmetic sum of a finite number of central Cantor sets. The technique used to study this consists of a duality between central Cantor sets and sets of subsums of certain infinite series. One consequence is that the sum of a finite number of central Cantor sets is one of the following: a finite union of closed intervals, homeomorphic to the Cantor ternary set or an M-Cantorval.
Quantization of Bending Deformations of Polygons In , Hypergeometric Integrals and the Gassner Representation
Authors: Kapovich Michael , Millson John J.
Published: December 2010

The Hamiltonian potentials of the bending deformations of n-gons instudied in [KM] and [Kly] give rise to a Hamiltonian action of the Malcev Lie algebra𝓟nof the pure braid groupPnon the moduli spaceMrofn-gon linkages with the side-lengthsr = (r1, … , rn)in. Ife∈Mris a singular point wemay linearize the vector fields in𝓟nate. This linearization yields a flat connection ∇ on the spaceof n distinct points on. We show that the monodromy of ∇ is the dual of a quotient of a specialized reduced Gassner representation.
The Tangent Bundle of an Almost Complex Manifold
Authors: Lempert László , Szőke Róbert
Published: December 2010

Motivated by deformation theory of holomorphic maps between almost complex manifolds we endow, in a natural way, the tangent bundle of an almost complexmanifold with an almost complex structure. We describe various properties of this structure.
On a New Exponential Sum
Authors: Lieman Daniel , Shparlinski Igor
Published: December 2010

Let p be prime and let be of multiplicative order t modulo p. We consider exponential sums of the form

and prove that for any ε > 0
Convolution Equation in —Propagation of Singularities
Authors: Pilipović Stevan
Published: December 2010

The singular spectrum of u in a convolution equation μ*u = f, where μ and f are tempered ultra distributions of Beurling or Roumieau type is estimated by

The same is done for SS*u.
A Necessary Condition for Multipliers of Weak Type (1, 1)
Authors: Wojciechowski Michał
Published: December 2010

Simple necessary conditions for weak type (1, 1) of invariant operators on L(ℝd) and their applications to rational Fourier multiplier are given.
Exceptional Sets of Slices for Functions From the Bergman Space in the Ball
Authors: Jakóbczak Piotr
Published: December 2010

Let BN be the unit ball in and let f be a function holomorphic and L2-integrable in BN. Denote by E(BN, f) the set of all slices of the form , where L is a complex one-dimensional subspace of , for which is not L2-integrable (with respect to the Lebesgue measure on L). Call this set the exceptional set for f. We give a characterization of exceptional sets which are closed in the natural topology of slices.
Extending the Archimedean Positivstellensatz to the Non-Compact Case
Authors: Marshall M.
Published: December 2010

A generalization of Schmüdgen’s Positivstellensatz is given which holds for any basic closed semialgebraic set in (compact or not). The proof is an extension of Wörmann’s proof.
An Analogue of Napoleon’s Theorem in the Hyperbolic Plane
Authors: McKay Angela
Published: December 2010

There is a theorem, usually attributed to Napoleon, which states that if one takes any triangle in the Euclidean Plane, constructs equilateral triangles on each of its sides, and connects the midpoints of the three equilateral triangles, one will obtain an equilateral triangle. We consider an analogue of this problem in the hyperbolic plane.
Spectral Transformations of the Laurent Biorthogonal Polynomials, II. Pastro Polynomials
Authors: Vinet Luc , Zhedanov Alexei
Published: December 2010

We continue to study the simplest closure conditions for chains of spectral transformations of the Laurent biorthogonal polynomials (LBP). It is shown that the 1-1-periodic q-closure condition leads to the LBP introduced by Pastro. We introduce classes of semi-classical and Laguerre-Hahn LBP associated to generic closure conditions of the chain of spectral transformations.
Hilbert Bimodules with Involution
Authors: Weaver Nik
Published: December 2010

We examine Hilbert bimodules which possess a (generally unbounded) involution. Topics considered include a linking algebra representation, duality, locality, and the role of these bimodules in noncommutative differential geometry
A Note on p-Harmonic 1-Forms on Complete Manifolds
Authors: Zhang Xi
Published: December 2010

In this paper we prove that there is no nontrivial Lq-integrably p-harmonic 1-form on a complete manifold with nonnegatively Ricci curvature (0 < q < ∞).
Finite Groups Generated by Involutions on Lagrangian Planes of C2
Authors: Falbel E.
Published: December 2010

We classify finite subgroups of SO(4) generated by anti-unitary involutions. They correspond to involutions fixing pointwise a Lagrangian plane. Explicit descriptions of the finite groups and the configurations of Lagrangian planes are obtained.
Approximation by Meromorphic Functions with Mittag-Leffler Type Constraints
Authors: Gauthier P. M. , Pouryayevali M. R.
Published: December 2010

Functions defined on closed sets are simultaneously approximated and interpolated by meromorphic functions with prescribed poles and zeros outside the set of approximation.
Some Adjunction Properties of Ample Vector Bundles
Authors: Ishihara Hironobu
Published: December 2010

Let ε be an ample vector bundle of rank r on a projective variety X with only log-terminal singularities. We consider the nefness of adjoint divisors KX +(t−r) det ε when t ≥ dim X and t > r. As an application, we classify pairs (X, ε) with cr-sectional genus zero.
Matching of Weighted Orbital Integrals for Metaplectic Correspondences
Authors: Mezo Paul
Published: December 2010

We prove an identity between weighted orbital integrals of the unit elements in the Hecke algebras of GL(r) and its n-fold metaplectic covering, under the assumption that n is relatively prime to any proper divisor of every 1 ≤ j ≤ r.
Polycharacters of Cocommutative Hopf Algebras
Authors: Bahturin Yuri , Kochetov Mikhail , Montgomery Susan
Published: December 2010

In this paper we extend a well-known theorem of M. Scheunert on skew-symmetric bicharacters of groups to the case of skew-symmetric bicharacters on arbitrary cocommutative Hopf algebras over a field of characteristic not 2. We also classify polycharacters on (restricted) enveloping algebras and bicharacters on divided power algebras.
Modular Equations and Discrete, Genus-Zero Subgroups of SL(2, ℝ) Containing Γ(N)
Authors: Cummins C. J.
Published: December 2010

Let G be a discrete subgroup of SL(2, ℝ) which contains Γ(N) for some N. If the genus of X(G) is zero, then there is a unique normalised generator of the field of G-automorphic functions which is known as a normalised Hauptmodul. This paper gives a characterisation of normalised Hauptmoduls as formal q series using modular polynomials.
Images of Additive Polynomials in 𝔽q((t)) Have the Optimal Approximation Property
Authors: van den Dries Lou , Kuhlmann Franz-Viktor
Published: December 2010

We show that the set of values of an additive polynomial in several variables with arguments in a formal Laurent series field over a finite field has the optimal approximation property: every element in the field has a (not necessarily unique) closest approximation in this set of values. The approximation is with respect to the canonical valuation on the field. This property is elementary in the language of valued rings.
The Topological Interpretation of the Core Group of a Surface inS4
Authors: Przytycki Józef H. , Rosicki Witold
Published: December 2010

We give a topological interpretation of the core group invariant of a surface embedded inS4[F-R], [Ro]. We show that the group is isomorphic to the free product of the fundamental group of the double branch cover ofS4with the surface as a branched set, and the infinite cyclic group. We present a generalization for unoriented surfaces, for other cyclic branched covers, and other codimension two embeddings of manifolds in spheres.
Biquadratic Extensions with One Break
Authors: Byott Nigel P. , Griffith Elder G.
Published: December 2010

We explicitly describe, in terms of indecomposable ℤ2[G]-modules, the Galois module structure of ideals in totally ramified biquadratic extensions of local number fields with only one break in their ramification filtration. This paper completeswork begun in [Elder: Canad. J.Math. (5) 50(1998), 1007–1047].
Griffiths Groups of Supersingular Abelian Varieties
Authors: Gordon B. Brent , Joshi Kirti
Published: December 2010

The Griffiths group Grr(X) of a smooth projective variety X over an algebraically closed field is defined to be the group of homologically trivial algebraic cycles of codimension r on X modulo the subgroup of algebraically trivial algebraic cycles. The main result of this paper is that the Griffiths group Gr2() of a supersingular abelian variety over the algebraic closure of a finite field of characteristic p is at most a p-primary torsion group. As a corollary the same conclusion holds for supersingular Fermat threefolds. In contrast, using methods of C. Schoen it is also shown that if the Tate conjecture is valid for all smooth projective surfaces and all finite extensions of the finite ground field k of characteristic p > 2, then the Griffiths group of any ordinary abelian threefold over the algebraic closure of k is non-trivial; in fact, for all but a finite number of primes l ≈ p it is the case that Gr2() ⊗ ℤl ≈ 0.
Residue: A Geometric Construction
Authors: de Salas Fernando Sancho
Published: December 2010

A new construction of the ordinary residue of differential forms is given. This construction is intrinsic, i.e., it is defined without local coordinates, and it is geometric: it is constructed out of the geometric structure of the local and global cohomology groups of the differentials. The Residue Theorem and the local calculation then follow from geometric reasons.
C*-Algebras of Infinite Graphs and Cuntz-Krieger Algebras
Authors: Brenken Berndt
Published: December 2010

The Cuntz-Krieger algebra 𝓞B is defined for an arbitrary, possibly infinite and infinite valued, matrix B. A graph C*-algebra G*(E) is introduced for an arbitrary directed graph E, and is shown to coincide with a previously defined graph algebra C*(E) if each source of E emits only finitely many edges. Each graph algebra G*(E) is isomorphic to the Cuntz-Krieger algebra 𝓞B where B is the vertex matrix of E.
Mellin Transforms of Whittaker Functions
Authors: Deitmar Anton
Published: December 2010

In this note we show that for an arbitrary reductive Lie group and any admissible irreducible Banach representation the Mellin transforms of Whittaker functions extend to meromorphic functions. We locate the possible poles and show that they always lie along translates of walls of Weyl chambers.
On the Singular Behavior of the Inverse Laplace Transforms of the Functions
Authors: Iakovlev Serguei
Published: December 2010

Exact analytical expressions for the inverse Laplace transforms of the functions are obtained in the form of trigonometric series. The convergence of the series is analyzed theoretically, and it is proven that those diverge on an infinite denumerable set of points. Therefore it is shown that the inverse transforms have an infinite number of singular points. This result, to the best of the author’s knowledge, is new, as the inverse transforms of have previously been considered to be piecewise smooth and continuous. It is also found that the inverse transforms have an infinite number of points of finite discontinuity with different left- and right-side limits. The points of singularity and points of finite discontinuity alternate, and the sign of the infinity at the singular points also alternates depending on the order n. The behavior of the inverse transforms in the proximity of the singular points and the points of finite discontinuity is addressed as well.
Postcards from the Edge, or Snapshots of the Theory of Generalised Moonshine
Authors: Gannon Terry
Published: December 2010

We begin by reviewing Monstrous Moonshine. The impact of Moonshine on algebra has been profound, but so far it has had little to teach number theory. We introduce (using ‘postcards’) a much larger context in which Monstrous Moonshine naturally sits. This context suggests Moonshine should indeed have consequences for number theory. We provide some humble examples of this: new generalisations of Gauss sums and quadratic reciprocity.
Fermionic and Bosonic Representations of the Extended Affine Lie Algebra
Authors: Gao Yun
Published: December 2010

We construct a class of fermions (or bosons) by using a Clifford (or Weyl) algebra to get two families of irreducible representations for the extended affine Lie algebra of level (1, 0) (or (−1, 0)).
Classification of Quantum Tori with Involution
Authors: Yoshii Yoji
Published: December 2010

Quantum tori with graded involution appear as coordinate algebras of extended affine Lie algebras of type A1, C and BC. We classify them in the category of algebras with involution. From this, we obtain precise information on the root systems of extended affine Lie algebras of type C.
Multi-Sided Braid Type Subfactors, II
Authors: Erlijman Juliana
Published: December 2010

We show that the multi-sided inclusion R⊗l ⊂ R of braid-type subfactors of the hyperfinite II1 factor R, introduced in Multi-sided braid type subfactors [E3], contains a sequence of intermediate subfactors: R⊗l ⊂ R⊗l−1 ⊂ … ⊂ R⊗2 ⊂ R. That is, every t-sided subfactor is an intermediate subfactor for the inclusion R⊗l ⊂ R, for 2 ≤ t ≤ l. Moreover, we also show that if t > m then R⊗t ⊂ R⊗m is conjugate to R⊗t−m+1 ⊂ R. Thus, if the braid representation considered is associated to one of the classical Lie algebras then the asymptotic inclusions for the Jones-Wenzl subfactors are intermediate subfactors.
Cercles de remplissage for the Riemann Zeta Function
Authors: Gauthier P. M.
Published: December 2010

The celebrated theorem of Picard asserts that each non-constant entire function assumes every value infinitely often, with at most one exception. The Riemann zeta function has this Picard behaviour in a sequence of discs lying in the critical band and whose diameters tend to zero. According to the Riemann hypothesis, the value zero would be this (unique) exceptional value.
Sur les invariants d'Iwasawa des tours cyclotomiques
Authors: Jaulent Jean-François , Maire Christian
Published: December 2010

We carry out the computation of the Iwasawa invariantsassociated to abelianT-ramifiedS-decomposedℓ-extensions over the finite stepsKnof the cyclotomic-extensionK∞/Kof a number field of CM-type.
Branched Covers of Tangles in Three-balls
Authors: Ishiwata Makiko , Przytycki Józef H. , Yasuhara Akira
Published: December 2010

We give an algorithm for a surgery description of a p-fold cyclic branched cover of B3 branched along a tangle. We generalize constructions of Montesinos and Akbulut-Kirby.
Approximating Positive Polynomials Using Sums of Squares
Authors: Marshall M.
Published: December 2010

The paper considers the relationship between positive polynomials, sums of squares and the multi-dimensional moment problem in the general context of basic closed semi-algebraic sets in realn-space. The emphasis is on the non-compact case and on quadratic module representations as opposed to quadratic preordering presentations. The paper clarifies the relationship between known results on the algebraic side and on the functional-analytic side and extends these results in a variety of ways.
Strongly Perforated K0-Groups of Simple C*-Algebras
Authors: Toms Andrew
Published: December 2010

In the sequel we construct simple, unital, separable, stable, amenable C*-algebras for which the ordered K0-group is strongly perforated and group isomorphic to Z. The particular order structures to be constructed will be described in detail below, and all known results of this type will be generalised.
A Multiplicative Analogue of Schur's Tauberian Theorem
Authors: Yeats Karen
Published: December 2010

A theorem concerning the asymptotic behaviour of partial sums of the coefficients of products of Dirichlet series is proved using properties of regularly varying functions. This theorem is a multiplicative analogue of Schur's Tauberian theorem for power series.
On the Composition of Differentiable Functions
Authors: Bachir M. , Lancien G.
Published: December 2010

We prove that a Banach space X has the Schur property if and only if every X-valued weakly differentiable function is Fréchet differentiable. We give a general result on the Fréchet differentiability of f ○ T, where f is a Lipschitz function and T is a compact linear operator. Finally we study, using in particular a smooth variational principle, the differentiability of the semi norm ‖ ‖lip on various spaces of Lipschitz functions.
Weakly Stable Relations and Inductive Limits ofC*-algebras
Authors: Monteiro Martha Salerno
Published: December 2010

We show that ifAis a class ofC*-algebras for which the set of formal relationsRis weakly stable, thenRis weakly stable for the classBthat containsAand all the inductive limits that can be constructed with theC*-algebras inA.

A set of formal relationsRis said to beweakly stablefor a classofC*-algebras if, in anyC*-algebra A ∈, close to an approximate representation of the setRinAthere is an exact representation ofRinA.
The Operator Amenability of Uniform Algebras
Authors: Runde Volker
Published: December 2010

We prove a quantized version of a theorem by M. V. Sheĭnberg: A uniform algebra equipped with its canonical, i.e., minimal, operator space structure is operator amenable if and only if it is a commutative C*-algebra.
On the Generalized Cyclic Eilenberg-Zilber Theorem
Authors: Khalkhali M. , Rangipour B.
Published: December 2010

We use the homological perturbation lemma to give an algebraic proof of the cyclic Eilenberg-Zilber theorem for cylindrical modules.
Point Sets and Dynamical Systems In the Autocorrelation Topology
Authors: Moody Robert V. , Strungaru Nicolae
Published: December 2010

This paper is about the topologies arising from statistical coincidence on locally finite point sets in locally compact Abelian groupsG. The first part defines a uniform topology (autocorrelation topology) and proves that, in effect, the set of all locally finite subsets ofGis complete in this topology. Notions of statistical relative denseness, statistical uniform discreteness, and statistical Delone sets are introduced.

The second part looks at the consequences of mixing the original and autocorrelation topologies, which together produce a new Abelian group, the autocorrelation group. In particular the relation between its compactness (which leads then to aG-dynamical system) and pure point diffractivity is considered. Finally for generic regular model sets it is shown that the autocorrelation group can be identified with the associated compact group of the cut and project scheme that defines it. For such a set the autocorrelation group, as aG-dynamical system, is a factor of the dynamical local hull.
Invariant Subspaces on 𝕋Nand ℝN
Authors: Seto Michio
Published: December 2010

LetNbe an integer which is larger than one. In this paper we study invariant subspaces of L2() under the double commuting condition. A main result is anN-dimensional version of the theorem proved byMandrekar and Nakazi. As an application of this result, we have anN-dimensional version of Lax's theorem.
Recurrent Geodesics in Flat Lorentz 3-Manifolds
Authors: Charette Virginie , Goldman William M. , Jones Catherine A.
Published: December 2010

Let M be a complete flat Lorentz 3-manifold M with purely hyperbolic holonomy Γ. Recurrent geodesic rays are completely classified when Γ is cyclic. This implies that for any pair of periodic geodesics γ1, γ2, a unique geodesic forward spirals towards γ1 and backward spirals towards γ2.
A Strong Form of a Problem of R. L. Graham
Authors: Ford Kevin
Published: December 2010

If A is a set of M positive integers, let G(A) be the maximum of ai/gcd(ai, aj) over ai, aj ∈ A. We show that if G(A) is not too much larger than M, then A must have a special structure.
On the Diophantine Equation n(n + d) · · · (n + (k − 1)d) = byl
Authors: Győry K. , Hajdu L. , Saradha N.
Published: December 2010

We show that the product of four or five consecutive positive terms in arithmetic progression can never be a perfect power whenever the initial term is coprime to the common difference of the arithmetic progression. This is a generalization of the results of Euler and Obláth for the case of squares, and an extension of a theorem of Győry on three terms in arithmetic progressions. Several other results concerning the integral solutions of the equation of the title are also obtained. We extend results of Sander on the rational solutions of the equation in n, y when b = d = 1. We show that there are only finitely many solutions in n, d, b, y when k ≥ 3, l ≥ 2 are fixed and k + l > 6.
Multiplicity of Resonances in Black Box Scattering
Authors: Nedelec L.
Published: December 2010

We apply the method of complex scaling to give a natural proof of a formula relating the multiplicity of a resonance to the multiplicity of a pole of the scattering matrix.
Strong Multiplicity One for the Selberg Class
Authors: Soundararajan K.
Published: December 2010

We investigate the problem of determining elements in the Selberg class by means of their Dirichlet series coefficients at primes.
A Characterization of PSU11(q)
Authors: Iranmanesh A. , Khosravi B.
Published: December 2010

Order components of a finite simple group were introduced in [4]. It was proved that some non-abelian simple groups are uniquely determined by their order components. As the main result of this paper, we show that groups PSU11(q) are also uniquely determined by their order components. As corollaries of this result, the validity of a conjecture of J. G. Thompson and a conjecture of W. Shi and J. Bi both on PSU11(q) are obtained.
Compactness of Hardy-Type Operators over Star-Shaped Regions in
Authors: Jain Pankaj , Jain Pawan K. , Gupta Babita
Published: December 2010

We study a compactness property of the operators between weighted Lebesgue spaces that average a function over certain domains involving a star-shaped region. The cases covered are (i) when the average is taken over a difference of two dilations of a star-shaped region in , and (ii) when the average is taken over all dilations of star-shaped regions in . These cases include, respectively, the average over annuli and the average over balls centered at origin.
C*-Algebras and Factorization Through Diagonal Operators
Authors: Randrianantoanina Narcisse
Published: December 2010

Let A be a C*-algebra and E be a Banach space with the Radon-Nikodym property. We prove that if j is an embedding of E into an injective Banach space then for every absolutely summing operator T : A → E, the composition j ○ T factors through a diagonal operator from l2 into l1. In particular, T factors through a Banach space with the Schur property. Similarly, we prove that for 2 < p < ∞, any absolutely summing operator from A into E factors through a diagonal operator from lp into l2.