bluuebunny/crossref_metadata_2025 huggingface dataset:
Criteria for Commutativity in Large Groups
Authors: Mohammadi Hassanabadi A. , Rhemtulla Akbar
Published: December 2010

In this paper we prove the following:

1.

Let m ≥ 2, n ≥ 1 be integers and let G be a group such that (XY)n = (YX)n for all subsets X, Y of size m in G. Then

a)

G is abelian or a BFC-group of finite exponent bounded by a function of m and n.

b)

If m ≥ n then G is abelian or |G| is bounded by a function of m and n.

2.

The only non-abelian group G such that (XY)2 = (YX)2 for all subsets X, Y of size 2 in G is the quaternion group of order 8.

3.

Let m, n be positive integers and G a group such that

for all subsets Xi of size m in G. Then G is n-permutable or |G| is bounded by a function of m and n.
Splitting Patterns and Trace Forms
Authors: Hurrelbrink Jurgen , Rehmann Ulf
Published: December 2010

The splitting pattern of a quadratic form q over a field k consists of all distinct Witt indices that occur for q over extension fields of k. In small dimensions, the complete list of splitting patterns of quadratic forms is known. We show that all splitting patterns of quadratic forms of dimension at most nine can be realized by trace forms.
On q-Exponential Functions for |q| = 1
Authors: Lubinsky D. S.
Published: December 2010

We discuss the q-exponential functions eq, Eq for q on the unit circle, especially their continuity in q, and analogues of the limit relation
Automorphisms of Metabelian Groups
Authors: Papistas Athanassios I.
Published: December 2010

We investigate the problem of determining when IA(Fn(AmA)) is finitely generated for all n and m, with n ≥ 2 and m ≠ 1. If m is a nonsquare free integer then IA(Fn(AmA)) is not finitely generated for all n and if m is a square free integer then IA(Fn(AmA)) is finitely generated for all n, with n ≠ 3, and IA(F3(AmA)) is not finitely generated. In case m is square free, Bachmuth and Mochizuki claimed in ([7], Problem 4) that TR(AmA) is 1 or 4. We correct their assertion by proving that TR(AmA) = ∞.
Uniform Approximation to Mahler’s Measure in Several Variables
Authors: Boyd David W.
Published: December 2010

If ƒ (x1,…,xk) is a polynomial with complex coefficients, the Mahler measure of ƒ , M(ƒ) is defined to be the geometric mean of |f| over the k-torus 𝕋k. We construct a sequence of approximations Mn(ƒ) which satisfy −d2−n log 2 + log Mn(ƒ) ≤ log M(ƒ) ≤ log Mn(ƒ). We use these to prove that M(ƒ) is a continuous function of the coefficients of ƒ for polynomials of fixed total degree d. Since Mn(ƒ) can be computed in a finite number of arithmetic operations from the coefficients of ƒ this also demonstrates an effective (but impractical) method for computing M(ƒ) to arbitrary accuracy.
Exponential Sums on Reduced Residue Systems
Authors: Loh W. K. A.
Published: December 2010

The aim of this article is to obtain an upper bound for the exponential sums , where the summation runs from x = 1 to x = q with (x, q) = 1 and e(α) denotes exp(2πiα).

We shall show that the upper bound depends only on the values of q and s, where s is the number of terms in the polynomial ƒ(x).
A Note on H1 Multipliers for Locally Compact Vilenkin Groups
Authors: Daly James E. , Phillips Keith L.
Published: December 2010

Kitada and then Onneweer and Quek have investigated multiplier operators on Hardy spaces over locally compact Vilenkin groups. In this note, we provide an improvement to their results for the Hardy space H1 and provide examples showing that our result applies to a significantly larger group of multipliers.
Lp-Boundedness of a Singular Integral Operator
Authors: Al-Hasan Abdelnaser J. , Fan Dashan
Published: December 2010

Let b(t) be an L∞ function on R, Ω(y′) be an H1 function on the unit sphere satisfying the mean zero property (1) and Qm(t) be a real polynomial on R of degree m satisfying Qm(0) = 0. We prove that the singular integral operator

is bounded in Lp(Rn) for 1 < p < ∞, and the bound is independent of the coefficients of Qm(t).
A Mountain Pass to the Jacobian Conjecture
Authors: Chamberland Marc , Meisters Gary
Published: December 2010

This paper presents an approach to injectivity theorems via the Mountain Pass Lemma and raises an open question. The main result of this paper (Theorem 1.1) is proved by means of the Mountain Pass Lemma and states that if the eigenvalues of are uniformly bounded away from zero for x ∊ Rn, where is a class C1 map, then F is injective. This was discovered in a joint attempt by the authors to prove a stronger result conjectured by the first author: Namely, that a sufficient condition for injectivity of class C1 maps F of Rn into itself is that all the eigenvalues of F′(x) are bounded away from zero on Rn. This is stated as Conjecture 2.1. If true, it would imply (via Reduction-of-Degree) injectivity of polynomial mapssatisfying the hypothesis, det F′(x) ≡ 1, of the celebrated Jacobian Conjecture (JC) of Ott-Heinrich Keller. The paper ends with several examples to illustrate a variety of cases and known counterexamples to some natural questions.
The Right Regular Representation of a Compact Right Topological Group
Authors: Moran Alan
Published: December 2010

We show that for certain compact right topological groups, , the strong operator topology closure of the image of the right regular representation of G in L(H), where H = L2(G), is a compact topological group and introduce a class of representations, R , which effectively transfers the representation theory of over to G. Amongst the groups for which this holds is the class of equicontinuous groups which have been studied by Ruppert in [10].We use familiar examples to illustrate these features of the theory and to provide a counter-example. Finally we remark that every equicontinuous group which is at the same time a Borel group is in fact a topological group.
On the Construction of Hölder and Proximal Subderivatives
Authors: Borwein J. M. , Girgensohn R. , Wang Xianfu
Published: December 2010

We construct Lipschitz functions such that for all s > 0 they are s-Hölder, and so proximally, subdifferentiable only on dyadic rationals and nowhere else. As applications we construct Lipschitz functions with prescribed Hölder and approximate subderivatives.
On the Set of Common Differences in van der Waerden’s Theorem on Arithmetic Progressions
Authors: Brown Tom C. , Graham Ronald L. , Landman Bruce M.
Published: December 2010

Analogues of van derWaerden’s theorem on arithmetic progressions are considered where the family of all arithmetic progressions, AP, is replaced by some subfamily of AP. Specifically, we want to know for which sets A, of positive integers, the following statement holds: for all positive integers r and k, there exists a positive integer n = w′(k, r) such that for every r-coloring of [1, n] there exists a monochromatic k-term arithmetic progression whose common difference belongs to A. We will call any subset of the positive integers that has the above property large. A set having this property for a specific fixed r will be called r-large. We give some necessary conditions for a set to be large, including the fact that every large set must contain an infinite number of multiples of each positive integer. Also, no large set {an : n = 1, 2,…} can have . Sufficient conditions for a set to be large are also given. We show that any set containing n-cubes for arbitrarily large n, is a large set. Results involving the connection between the notions of “large” and “2-large” are given. Several open questions and a conjecture are presented.
Generic Partial Two-Point Sets Are Extendable
Authors: Dijkstra Jan J.
Published: December 2010

It is shown that under ZFC almost all planar compacta that meet every line in at most two points are subsets of sets that meet every line in exactly two points. This result was previously obtained by the author jointly with K. Kunen and J. vanMill under the assumption that Martin’s Axiom is valid.
Lorentz-Schatten Classes and Pointwise Domination of Matrices
Authors: Cobos Fernando , Kühn Thomas
Published: December 2010

We investigate pointwise domination property in operator spaces generated by Lorentz sequence spaces.
The Bockstein Map is Necessary
Authors: Dădărlat Marius , Eilers Søren
Published: December 2010

We construct two non-isomorphic nuclear, stably finite, real rank zero C*-algebras E and E′ for which there is an isomorphism of ordered groups which is compatible with all the coefficient transformations. The C*-algebras E and E0 are not isomorphic since there is no Θ as above which is also compatible with the Bockstein operations. By tensoring with Cuntz’s algebra one obtains a pair of non-isomorphic, real rank zero, purely infinite C*-algebras with similar properties.
Averaging Operators and Martingale Inequalities in Rearrangement Invariant Function Spaces
Authors: Kikuchi Masato
Published: December 2010

We shall study some connection between averaging operators and martingale inequalities in rearrangement invariant function spaces. In Section 2 the equivalence between Shimogaki’s theorem and some martingale inequalities will be established, and in Section 3 the equivalence between Boyd’s theorem andmartingale inequalities with change of probability measure will be established.
Cyclic Subgroup Separability of HNN-Extensions with Cyclic Associated Subgroups
Authors: Kim Goansu , Tang C. Y.
Published: December 2010

We derive a necessary and sufficient condition for HNN-extensions of cyclic subgroup separable groups with cyclic associated subgroups to be cyclic subgroup separable. Applying this, we explicitly characterize the residual finiteness and the cyclic subgroup separability of HNN-extensions of abelian groups with cyclic associated subgroups. We also consider these residual properties ofHNN-extensions of nilpotent groups with cyclic associated subgroups.
A Real Holomorphy Ring without the Schmüdgen Property
Authors: Marshall Murray A.
Published: December 2010

A preordering T is constructed in the polynomial ring A = ℝ[t1, t2, … ] (countablymany variables) with the following two properties: (1) For each f ∈ A there exists an integer N such that −N ≤ f (P) ≤ N holds for all P ∈ SperT(A)). (2) For all f ∈ A, if N + f, N − f ∈ T for some integer N, then f ∈ R. This is in sharp contrast with the Schmüdgen-Wörmann result that for any preordering T in a finitely generated ℝ-algebra A, if property (1) holds, then for any f ∈ A, f > 0 on SperT(A)) f ∈; T. Also, adjoining to A the square roots of the generators of T yields a larger ring C with these same two properties but with ∑C2 (the set of sums of squares) as the preordering.
A Generalized Rao Bound for Ordered Orthogonal Arrays and (t, m, s)-Nets
Authors: Martin W. J. , Stinson D. R.
Published: December 2010

In this paper, we provide a generalization of the classical Rao bound for orthogonal arrays, which can be applied to ordered orthogonal arrays and (t, m, s)-nets. Application of our new bound leads to improvements in many parameter situations to the strongest bounds (i.e., necessary conditions) for existence of these objects.
Prime and Primary Ideals in a Prüfer Order in a Simple Artinian Ring with Finite Dimension over its Center
Authors: Marubayashi H. , Ueda A.
Published: December 2010

Let Q be a simple Artinian ring with finite dimension over its center. An order R in Q is said to be Prüfer if any one-sided R-ideal is a progenerator. We study prime and primary ideals of a Prüfer order under the condition that the center is Prüfer. Also we characterize branched and unbranched prime ideals of a Prüfer order.
A Class of Supercuspidal Representations of G2(k)
Authors: Savin Gordan
Published: December 2010

Let H be an exceptional, adjoint group of type E6 and split rank 2, over a p-adic field k. In this article we discuss the restriction of the minimal representation of H to a dual pair PD× × G2(k), where D is a division algebra of dimension 9 over k. In particular, we discover an interesting class of supercuspidal representations of G2(k).
Ramanujan and the Modular j-Invariant
Authors: Berndt Bruce C. , Chan Heng Huat
Published: December 2010

A new infinite product tn was introduced by S. Ramanujan on the last page of his third notebook. In this paper, we prove Ramanujan’s assertions about tn by establishing new connections between themodular jinvariant and Ramanujan’s cubic theory of elliptic functions to alternative bases. We also show that for certain integers n, tn generates the Hilbert class field of . This shows that tn is a new class invariant according to H. Weber’s definition of class invariants.
Finite Rank Operators in Certain Algebras
Authors: Bradley Sean
Published: December 2010

Let Alg(ℒ) be the algebra of all bounded linear operators on a normed linear space X leaving invariant each member of the complete lattice of closed subspaces L. We discuss when the subalgebra of finite rank operators in Alg(ℒ) is non-zero, and give an example which shows this subalgebra may be zero even for finite lattices. We then give a necessary and sufficient lattice condition for decomposing a finite rank operator F into a sum of a rank one operator and an operator whose range is smaller than that of F, each of which lies in Alg(ℒ). This unifies results of Erdos, Longstaff, Lambrou, and Spanoudakis. Finally, we use the existence of finite rank operators in certain algebras to characterize the spectra of Riesz operators (generalizing results of Ringrose and Clauss) and compute the Jacobson radical for closed algebras of Riesz operators and Alg(ℒ) for various types of lattices.
Resolutions of Associative and Lie Algebras
Authors: Adin Ron , Blanc David
Published: December 2010

Certain canonical resolutions are described for free associative and free Lie algebras in the category of non-associative algebras. These resolutions derive in both cases from geometric objects, which in turn reflect the combinatorics of suitable collections of leaf-labeled trees.
Multiplicative Structure of the RingK(S(T*ℝP2n+1))
Authors: Bousaidi M. A.
Published: December 2010

We calculate the additive and multiplicative structure of the ringusing the eta invariant.
A Property of Lie Group Orbits
Authors: Božičević Mladen
Published: December 2010

Let G be a real Lie group and X a real analytic manifold. Suppose that G acts analytically on X with finitely many orbits. Then the orbits are subanalytic in X. As a consequence we show that the micro-support of a G-equivariant sheaf on X is contained in the conormal variety of the G-action.
Eigenfunction Decay For the Neumann Laplacian on Horn-Like Domains
Authors: Edward Julian
Published: December 2010

The growth properties at infinity for eigenfunctions corresponding to embedded eigenvalues of the Neumann Laplacian on horn-like domains are studied. For domains that pinch at polynomial rate, it is shown that the eigenfunctions vanish at infinity faster than the reciprocal of any polynomial. For a class of domains that pinch at an exponential rate, weaker, L2 bounds are proven. A corollary is that eigenvalues can accumulate only at zero or infinity.
Lomonosov’s Techniques and Burnside’s Theorem
Authors: Lindström Mikael , Schlüchtermann Georg
Published: December 2010

In this note we give a proof of Lomonosov’s extension of Burnside’s theoremto infinite dimensional Banach spaces.
Perfect Non-Extremal Riemann Surfaces
Authors: Schaller Paul Schmutz
Published: December 2010

An infinite family of perfect, non-extremal Riemann surfaces is constructed, the first examples of this type of surfaces. The examples are based on normal subgroups of the modular group PSL(2, ℤ) of level 6. They provide non-Euclidean analogues to the existence of perfect, non-extremal positive definite quadratic forms. The analogy uses the function syst which associates to every Riemann surface M the length of a systole, which is a shortest closed geodesic of M.
On a Question of Buium
Authors: Voloch José Felipe
Published: December 2010

We prove that , with p ranging over all primes, is independent of 1 over the integers, assuming a conjecture in elementary number theory generalizing the infinitude ofMersenne primes. This answers a question of Buium. We also prove a generalization.
Fixed Points of Commuting Holomorphic Maps Without Boundary Regularity
Authors: Bracci Filippo
Published: December 2010

We identify a class of domains of ℂn in which any two commuting holomorphic self-maps have a common fixed point.
Controlled Homeomorphisms Over Nonpositively Curved Manifolds
Authors: Hughes Bruce , Taylor Larry , Williams Bruce
Published: December 2010

We obtain a homotopy splitting of the forget control map for controlled homeomorphisms over closed manifolds of nonpositive curvature.
The Inequalities for Polynomials and Integration over Fractal Arcs
Authors: Kats B. A.
Published: December 2010

The paper is dealing with determination of the integral along the fractal arc γ on the complex plane by terms of polynomial approximations of the function ƒ. We obtain inequalities for polynomials and conditions of integrability for functions from the Hölder, Besov and Slobodetskii spaces.
Linéarisation symplectique en dimension 2
Authors: Currás-Bosch Carlos
Published: December 2010

In this paper the germ of neighborhood of a compact leaf in a Lagrangian foliation is symplectically classified when the compact leaf is , the affine structure induced by the Lagrangian foliation on the leaf is complete, and the holonomy of in the foliation linearizes. The germ of neighborhood is classified by a function, depending on one transverse coordinate, this function is related to the affine structure of the nearly compact leaves.
Weak Convergence Is Not Strong Convergence For Amenable Groups
Authors: Rosenblatt Joseph M. , Willis George A.
Published: December 2010

Let G be an infinite discrete amenable group or a non-discrete amenable group. It is shown how to construct a net (fα) of positive, normalized functions in L1(G) such that the net converges weak* to invariance but does not converge strongly to invariance. The solution of certain linear equations determined by colorings of the Cayley graphs of the group are central to this construction.
Inductive Limit Toral Automorphisms of Irrational Rotation Algebras
Authors: Stacey P. J.
Published: December 2010

Irrational rotation C*-algebras have an inductive limit decomposition in terms of matrix algebras over the space of continuous functions on the circle and this decomposition can be chosen to be invariant under the flip automorphism. It is shown that the flip is essentially the only toral automorphism with this property.
A Hypergraph with Commuting Partial Laplacians
Authors: Ballantine Cristina M.
Published: December 2010

LetFbe a totally real number field and let GLnbe the general linear group of rank n overF. Let р be a prime ideal ofFand Fрthe completion ofFwith respect to the valuation induced by р. We will consider a finite quotient of the affine building of the group GLnover the field Fр. We will view this object as a hypergraph and find a set of commuting operators whose sum will be the usual adjacency operator of the graph underlying the hypergraph.
Resolution of Singularities of Null Cones
Authors: Wang Weiqiang
Published: December 2010

We give canonical resolutions of singularities of several cone varieties arising from invariant theory. We establish a connection between our resolutions and resolutions of singularities of closure of conjugacy classes in classical Lie algebras.
Weak Amenability of a Class of Banach Algebras
Authors: Zhang Yong
Published: December 2010

We show that, if a Banach algebra is a left ideal in its second dual algebra and has a left bounded approximate identity, then the weak amenability of implies the (2m+ 1)-weak amenability of for all m ≥ 1.
Uniform Embeddings into Hilbert Space and a Question of Gromov
Authors: Dranishnikov A. N. , Gong G. , Lafforgue V. , Yu G.
Published: December 2010

Gromov introduced the concept of uniform embedding into Hilbert space and asked if every separable metric space admits a uniform embedding into Hilbert space. In this paper, we study uniform embedding into Hilbert space and answer Gromov’s question negatively.
Approximation On Arcs and Dendrites Going to Infinity in ℂn
Authors: Gauthier P. M. , Zeron E. S.
Published: December 2010

On a locally rectifiable arc going to infinity, each continuous function can be approximated by entire functions.
The Discriminant of a Dihedral Quintic Field Defined by a Trinomial X5 + aX + b
Authors: Spearman Blair K. , Williams Kenneth S.
Published: December 2010

Let X5 + aX + b ∈ Z[X] have Galois group D5. Let θ be a root of X5 + aX + b. An explicit formula is given for the discriminant of Q(θ).
Sur les singularités de la fonction croissance d’une variété non simplement connexe
Authors: Ardizzone Lucia , Grimaldi Renata , Pansu Pierre
Published: December 2010

Si M est une variété de dimension n, compacte non simplement connexe, on caractérise les métriques riemanniennes sur M dont la fonction croissance a exactement deux singularités.
The Spherical Functions Related to the Root SystemB2
Authors: Sawyer P.
Published: December 2010

In this paper, we give an integral formula for the eigenfunctions of the ring of differential operators related to the root systemB2.
A Note on the Automorphic Langlands Group
Authors: Arthur James
Published: December 2010

Langlands has conjectured the existence of a universal group, an extension of the absolute Galois group, which would play a fundamental role in the classification of automorphic representations. We shall describe a possible candidate for this group. We shall also describe a possible candidate for the complexification of Grothendieck's motivic Galois group.
Group Gradings on Matrix Algebras
Authors: Bahturin Yu. A. , Zaicev M. V.
Published: December 2010

Let Φ be an algebraically closed field of characteristic zero, G a finite, not necessarily abelian, group. Given a G-grading on the full matrix algebra A = Mn(Φ), we decompose A as the tensor product of graded subalgebras A = B ⊗ C, B ≅ Mp(Φ) being a graded division algebra, while the grading of C ≅ Mq(Φ) is determined by that of the vector space Φn. Now the grading of A is recovered from those of A and B using a canonical “induction” procedure.
Subalgebras of gcN and Jacobi Polynomials
Authors: De Sole Alberto , Kac Victor G.
Published: December 2010

We classify the subalgebras of the general Lie conformal algebra gcN that act irreducibly on [∂]N and that are normalized by the sl2-part of a Virasoro element. The problem turns out to be closely related to classical Jacobi polynomials , σ ∈ . The connection goes both ways—we use in our classification some classical properties of Jacobi polynomials, and we derive from the theory of conformal algebras some apparently new properties of Jacobi polynomials.
Specializations of Jordan Superalgebras
Authors: Martínez Consuelo , Efim Zelmanov
Published: December 2010

In this paper we study specializations and one-sided bimodules of simple Jordan superalgebras.
A Note on Noncommutative Interpolation
Authors: Constantinescu T. , Johnson J. L.
Published: December 2010

In this paper we formulate and solve Nevanlinna-Pick and Carathéodory type problems for tensor algebras with data given on theN-dimensional operator unit ball of a Hilbert space. We develop an approach based on the displacement structure theory.
Properties of the ℳ-Harmonic Conjugate Operator
Authors: Lee Jaesung , Rim Kyung Soo
Published: December 2010

We define the ℳ-harmonic conjugate operator K and prove that it is bounded on the nonisotropic Lipschitz space and on BMO. Then we show K maps Dini functions into the space of continuous functions on the unit sphere. We also prove the boundedness and compactness properties of ℳ-harmonic conjugate operator with Lp symbol.
The Ramification Polygon for Curves over a Finite Field
Authors: Scherk John
Published: December 2010

A Newton polygon is introduced for a ramified point of a Galois covering of curves over a finite field. It is shown to be determined by the sequence of higher ramification groups of the point. It gives a blowing up of the wildly ramified part which separates the branches of the curve. There is also a connection with local reciprocity.
Classification of AF Flows
Authors: Dean Andrew J.
Published: December 2010

An AF flow is a one-parameter automorphism group of an AFC*-algebraAsuch that there exists an increasing sequence of invariant finite dimensional sub-C*-algebras whose union is dense inA. In this paper, a classification ofC*-dynamical systems of this form up to equivariant isomorphism is presented. Two pictures of the actions are given, one in terms of a modified Bratteli diagram/pathspace construction, and one in terms of a modifiedK0functor.
Counting the Number of Integral Points in General n-Dimensional Tetrahedra and Bernoulli Polynomials
Authors: Lin Ke-Pao , Yau Stephen S.-T.
Published: December 2010

Recently there has been tremendous interest in counting the number of integral points in n-dimensional tetrahedra with non-integral vertices due to its applications in primality testing and factoring in number theory and in singularities theory. The purpose of this note is to formulate a conjecture on sharp upper estimate of the number of integral points in n-dimensional tetrahedra with non-integral vertices. We show that this conjecture is true for low dimensional cases as well as in the case of homogeneous n-dimensional tetrahedra. We also show that the Bernoulli polynomials play a role in this counting.
Reducing Spheres and Klein Bottles after Dehn Fillings
Authors: Oh Seungsang
Published: December 2010

Let M be a compact, connected, orientable, irreducible 3-manifold with a torus boundary. It is known that if two Dehn fillings on M along the boundary produce a reducible manifold and a manifold containing a Klein bottle, then the distance between the filling slopes is at most three. This paper gives a remarkably short proof of this result.
A Basis of Bachmuth Type in the Commutator Subgroup of a Free Group
Authors: Tomaszewski Witold
Published: December 2010

We show here that the commutator subgroup of a free group of finite rank poses a basis of Bachmuth's type.
Characterizing Two-Dimensional Maps Whose Jacobians Have Constant Eigenvalues
Authors: Chamberland Marc
Published: December 2010

Recent papers have shown that C1 maps whose Jacobians have constant eigenvalues can be completely characterized if either the eigenvalues are equal or F is a polynomial. Specifically, F = (u, v) must take the form

for some constants a, b, c, d, e, f , α, β and a C1 function ϕ in one variable. If, in addition, the function ϕ is not affine, then

This paper shows how these theorems cannot be extended by constructing a real-analytic map whose Jacobian eigenvalues are ±1/2 and does not fit the previous form. This example is also used to construct non-obvious solutions to nonlinear PDEs, including the Monge—Ampère equation.
Gauss and Eisenstein Sums of Order Twelve
Authors: Gurak S.
Published: December 2010

Let q = pr with p an odd prime, and Fq denote the finite field of q elements. Let Tr : Fq → Fp be the usual trace map and set ζp = exp(2πi/p). For any positive integer e, define the (modified) Gauss sum gr(e) by

Recently, Evans gave an elegant determination of g1(12) in terms of g1(3), g1(4) and g1(6) which resolved a sign ambiguity present in a previous evaluation. Here I generalize Evans' result to give a complete determination of the sum gr(12).
On Non-Strongly Free Automorphisms of Subfactors of Type III0
Authors: Masuda Toshihiko
Published: December 2010

We determine when an automorphism of a subfactor of type III0with finite index is nonstrongly free in the sense of C. Winsløw in terms of the modular endomorphisms introduced by M. Izumi.
Representations of the Twisted Heisenberg–Virasoro Algebra at Level Zero
Authors: Billig Yuly
Published: December 2010

We describe the structure of the irreducible highest weight modules for the twisted Heisenberg–Virasoro Lie algebra at level zero. We prove that either a Verma module is irreducible or its maximal submodule is cyclic.
On Density Conditions for Interpolation in the Ball
Authors: Marco Nicolas , Massaneda Xavier
Published: December 2010

In this paper we study interpolating sequences for two related spaces of holomorphic functions in the unit ball of Cn, n > 1. We first give density conditions for a sequence to be interpolating for the class A−∞ of holomorphic functions with polynomial growth. The sufficient condition is formally identical to the characterizing condition in dimension 1, whereas the necessary one goes along the lines of the results given by Li and Taylor for some spaces of entire functions. In the second part of the paper we show that a density condition, which for n = 1 coincides with the characterizing condition given by Seip, is sufficient for interpolation in the (weighted) Bergman space.
On Universal Schauder Bases in Non-Archimedean Fréchet Spaces
Authors: Śliwa Wiesław
Published: December 2010

It is known that any non-archimedean Fréchet space of countable type is isomorphic to a subspace of . In this paper we prove that there exists a non-archimedean Fréchet space U with a basis (un) such that any basis (xn) in a non-archimedean Fréchet space X is equivalent to a subbasis (ukn) of (un). Then any non-archimedean Fréchet space with a basis is isomorphic to a complemented subspace of U. In contrast to this, we show that a non-archimedean Fréchet space X with a basis (xn) is isomorphic to a complemented subspace of if and only if X is isomorphic to one of the following spaces: c0, c0 × . Finally, we prove that there is no nuclear non-archimedean Fréchet space H with a basis (hn) such that any basis (yn) in a nuclear non-archimedean Fréchet space Y is equivalent to a subbasis (hkn) of (hn).
Embeddability of Some Three-Dimensional Weakly Pseudoconvex CR Structures
Authors: Wang Wei
Published: December 2010

We prove that a class of perturbations of standard CR structure on the boundary of threedimensional complex ellipsoid Ep, q can be realized as hypersurfaces on ℂ2, which generalizes the result of Burns and Epstein on the embeddability of some perturbations of standard CR structure on S3.
On the Uniqueness of Wave Operators Associated with Non-Trace Class Perturbations
Authors: Xia Jingbo
Published: December 2010

Voiculescu has previously established the uniqueness of the wave operator for the problem of -perturbation of commuting tuples of self-adjoint operators in the case where the norm ideal has the property , where {Pn} is any sequence of orthogonal projections with rank(Pn) = n. We prove that the same uniqueness result holds true so long as is not the trace class. (It is well known that there is no such uniqueness in the case of trace-class perturbation.)
A Note on 4-Rank Densities
Authors: Osburn Robert
Published: December 2010

For certain real quadratic number fields, we prove density results concerning 4-ranks of tame kernels. We also discuss a relationship between 4-ranks of tame kernels and 4-class ranks of narrow ideal class groups. Additionally, we give a product formula for a local Hilbert symbol.
A Geometric Approach to Voiculescu-Brown Entropy
Authors: Kerr David
Published: December 2010

A basic problem in dynamics is to identify systems with positive entropy, i.e., systems which are “chaotic.” While there is a vast collection of results addressing this issue in topological dynamics, the phenomenon of positive entropy remains by and large a mystery within the broader noncommutative domain of C*-algebraic dynamics. To shed some light on the noncommutative situation we propose a geometric perspective inspired by work of Glasner and Weiss on topological entropy. This is a written version of the author’s talk at theWinter 2002Meeting of the CanadianMathematical Society in Ottawa, Ontario.
A Generalization of the Turán Theorem and Its Applications
Authors: Liu Yu-Ru
Published: December 2010

We axiomatize the main properties of the classical Turán Theorem in order to apply it to a general context. We provide applications in the cases of number fields, function fields, and geometrically irreducible varieties over a finite field.
A Compactness Theorem for Yang-Mills Connections
Authors: Zhang Xi
Published: December 2010

In this paper, we consider Yang-Mills connections on a vector bundle E over a compact Riemannian manifold M of dimension m > 4, and we show that any set of Yang-Mills connections with the uniformly bounded -norm of curvature is compact in C∞ topology.
Degree Homogeneous Subgroups
Authors: Dixon John D. , Barghi A. Rahnamai
Published: December 2010

Let G be a finite group and H be a subgroup. We say that H is degree homogeneous if, for each χ ∈ Irr(G), all the irreducible constituents of the restriction χH have the same degree. Subgroups which are either normal or abelian are obvious examples of degree homogeneous subgroups. Following a question by E.M. Zhmud’, we investigate general properties of such subgroups. It appears unlikely that degree homogeneous subgroups can be characterized entirely by abstract group properties, but we providemixed criteria (involving both group structure and character properties) which are both necessary and sufficient. For example, H is degree homogeneous in G if and only if the derived subgroup H′ is normal in G and, for every pair α, β of irreducible G-conjugate characters of H′, all irreducible constituents of αH and βH have the same degree.
Biorthogonal Systems in Weakly Lindelöf Spaces
Authors: Fabian M. , Montesinos V. , Zizler V.
Published: December 2010

We study countable splitting of Markushevich bases in weakly Lindelöf Banach spaces in connection with the geometry of these spaces.
Products of Conjugacy Classes in SU(2)
Authors: Jeffrey Lisa C. , Mare Augustin-Liviu
Published: December 2010

We obtain a complete description of the conjugacy classes C1, … ,Cn in SU(2) with the property that C1 … Cn = SU(2). The basic instrument is a characterization of the conjugacy classes C1, … ,Cn+1 in SU(2) with C1 … Cn+1 ∋ I, which generalizes a result of [Je-We].
On Negatively Curved Finsler Manifolds of Scalar Curvature
Authors: Mo Xiaohuan , Shen Zhongmin
Published: December 2010

In this paper, we prove a global rigidity theorem for negatively curved Finsler metrics on a compact manifold of dimensionn≥ 3. We show that for such a Finsler manifold, if the flag curvature is a scalar function on the tangent bundle, then the Finsler metric is of Randers type. We also study the case when the Finsler metric is locally projectively flat.
Baker-Type Estimates for Linear Forms in the Values of q-Series
Authors: Väänänen Keijo , Zudilin Wadim
Published: December 2010

We obtain lower estimates for the absolute values of linear forms of the values of generalized Heine series at non-zero points of an imaginary quadratic field II, in particular of the values of q-exponential function. These estimates depend on the individual coefficients, not only on the maximum of their absolute values. The proof uses a variant of classical Siegel's method applied to a system of functional Poincaré-type equations and the connection between the solutions of these functional equations and the generalized Heine series.
The Index Theory Associated to a Non-Finite Trace on a C*-Algebra
Authors: Murphy G. J.
Published: December 2010

The index theory considered in this paper, a generalisation of the classical Fredholm index theory, is obtained in terms of a non-finite trace on a unitalC*-algebra. We relate it to the index theory of M. Breuer, which is developed in a von Neumann algebra setting, by means of a representation theorem. We show how our new index theory can be used to obtain an index theorem for Toeplitz operators on the compact group U(2), where the classical index theory does not give any interesting result.
Discrete Sets and Associated Dynamical Systems in a Non-Commutative Setting
Authors: Yokonuma Takeo
Published: December 2010

We define a uniform structure on the set of discrete sets of a locally compact topological space on which a locally compact topological group acts continuously. Then we investigate the completeness of these uniform spaces and study these spaces by means of topological dynamical systems.
On Gâteaux Differentiability of Convex Functions in WCG Spaces
Authors: Rychtář Jan
Published: December 2010

It is shown, using the Borwein–Preiss variational principle that for every continuous convex function f on a weakly compactly generated space X, every x0 ∈ X and every weakly compact convex symmetric set K such that , there is a point of Gâteaux differentiability of f in x0 +K. This extends a Klee's result for separable spaces.
B-Stable Ideals in the Nilradical of a Borel Subalgebra
Authors: Sommers Eric N.
Published: December 2010

We count the number of strictly positive B-stable ideals in the nilradical of a Borel subalgebra and prove that the minimal roots of any B-stable ideal are conjugate by an element of the Weyl group to a subset of the simple roots. We also count the number of ideals whose minimal roots are conjugate to a fixed subset of simple roots.
A Note on Lagrangian Loci of Quotients
Authors: Foth Philip
Published: December 2010

We study Hamiltonian actions of compact groups in the presence of compatible involutions. We show that the Lagrangian fixed point set on the symplectically reduced space is isomorphic to the disjoint union of the involutively reduced spaces corresponding to involutions on the group strongly inner to the given one. Our techniques imply that the solution to the eigenvalues of a sum problem for a given real form can be reduced to the quasi-split real form in the same inner class. We also consider invariant quotients with respect to the corresponding real form of the complexified group.
On a Theorem of Kawamoto on Normal Bases of Rings of Integers, II
Authors: Ichimura Humio
Published: December 2010

Let m = pe be a power of a prime number p. We say that a number field F satisfies the property when for any a ∈ F×, the cyclic extension F(ζm, a1/m)/F(ζm) has a normal p-integral basis. We prove that F satisfies if and only if the natural homomorphism is trivial. Here K = F(ζm), and denotes the ideal class group of F with respect to the p-integer ring of F.
On a Class of Singular Integral Operators With Rough Kernels
Authors: Al-Salman Ahmad
Published: December 2010

In this paper, we study the Lp mapping properties of a class of singular integral operators with rough kernels belonging to certain block spaces. We prove that our operators are bounded on Lp provided that their kernels satisfy a size condition much weaker than that for the classical Calderón–Zygmund singular integral operators. Moreover, we present an example showing that our size condition is optimal. As a consequence of our results, we substantially improve a previously known result on certain maximal functions.
Scattering Length and the Spectrum of –Δ + V
Authors: Taylor Michael
Published: December 2010

Given a non-negative, locally integrable functionV on ℝn, we give a necessary and sufficient condition that –Δ + V have purely discrete spectrum, in terms of the scattering length ofV restricted to boxes.
On the Inequality for Volume and Minkowskian Thickness
Authors: Averkov Gennadiy
Published: December 2010

Given a centrally symmetric convex bodyBin, we denote by ℳd(B) the Minkowski space (i.e., finite dimensional Banach space) with unit ballB. LetKbe an arbitrary convex body in ℳd(B). The relationship between volumeV(K) and the Minkowskian thickness (= minimal width) ΔB(K) ofKcan naturally be given by the sharp geometric inequalityV(K) ≥ α(B) · ΔB(K)d, where α(B) > 0. As a simple corollary of the Rogers-Shephard inequality we obtain thatwith equality on the left attained if and only ifBis the difference body of a simplex and on the right ifBis a cross-polytope. The main result of this paper is that ford= 2 the equality on the right implies thatBis a parallelogram. The obtained results yield the sharp upper bound for the modified Banach–Mazur distance to the regular hexagon.
On the Membership in Bergman Spaces of the Derivative of a Blaschke Product With Zeros in a Stolz Domain
Authors: Girela Daniel , Peláez José Ángel
Published: December 2010

It is known that the derivative of a Blaschke product whose zero sequence lies in a Stolz angle belongs to all the Bergman spaces Ap with 0 < p < 3/2. The question of whether this result is best possible remained open. In this paper, for a large class of Blaschke products B with zeros in a Stolz angle, we obtain a number of conditions which are equivalent to the membership of B′ in the space Ap (p < 1). As a consequence, we prove that there exists a Blaschke product B with zeros on a radius such that B′ ∉ A3/2.
On Sequences of Squares with Constant Second Differences
Authors: Browkin J. , Brzeziński J.
Published: December 2010

The aim of this paper is to study sequences of integers for which the second differences between their squares are constant. We show that there are infinitely many nontrivial monotone sextuples having this property and discuss some related problems.
A Singular Critical Potential for the Schrödinger Operator
Authors: Duyckaerts Thomas
Published: December 2010

Consider a real potential V on Rd, d ≥ 2, and the Schrödinger equation:

(LS)      i∂tu + Δu −Vu = 0, u↾t=0 = u0 ∈ L2.

In this paper, we investigate the minimal local regularity of V needed to get local in time dispersive estimates (such as local in time Strichartz estimates or local smoothing effect with gain of 1/2 derivative) on solutions of (LS). Prior works show some dispersive properties when V (small at infinity) is in Ld/2 or in spaces just a little larger but with a smallness condition on V (or at least on its negative part).

In this work, we prove the critical character of these results by constructing a positive potential V which has compact support, bounded outside 0 and of the order (log |x|)2/|x|2 near 0. The lack of dispersiveness comes from the existence of a sequence of quasimodes for the operator P := −Δ + V.

The elementary construction of V consists in sticking together concentrated, truncated potential wells near 0. This yields a potential oscillating with infinite speed and amplitude at 0, such that the operator P admits a sequence of quasi-modes of polynomial order whose support concentrates on the pole.
A Note on Giuga's Conjecture
Authors: Tipu Vicentiu
Published: December 2010

LetG(X) denote the number of positive composite integersnsatisfying. ThenG(X) ≪X1/2logXfor sufficiently largeX.
On the Lack of Inverses to C*-Extensions Related to Property T Groups
Authors: Manuilov V. , Thomsen K.
Published: December 2010

Using ideas of S. Wassermann on non-exact C*-algebras and property T groups, we show that one of his examples of non-invertible C*-extensions is not semi-invertible. To prove this, we show that a certain element vanishes in the asymptotic tensor product. We also show that a modification of the example gives a C*-extension which is not even invertible up to homotopy.
Spatial uncertainty assessment in modelling reference evapotranspiration at regional scale
Authors: Buttafuoco G. , Caloiero T. , Coscarelli R.
Published: December 2010

Abstract. Evapotranspiration is one of the major components of the water balance and has been identified as a key factor in hydrological modelling. For this reason, several methods have been developed to calculate the reference evapotranspiration (ET0). In modelling reference evapotranspiration it is inevitable that both model and data input will present some uncertainty. Whatever model is used, the errors in the input will propagate towards the output of the calculated ET0. Neglecting the information about estimation uncertainty, however, may lead to improper decision-making and water resources management. One geostatistical approach to spatial analysis is stochastic simulation, which draws alternative and equally probable, realizations of a regionalized variable. Differences between the realizations provide a measure of spatial uncertainty and allows to carry out an error propagation analysis. The aim of this paper is to assess spatial uncertainty of a monthly reference evapotranspiration model resulting from the uncertainties in the input attributes (mainly temperature) at a regional scale. A case study was presented for the Calabria region (southern Italy). Temperature data were jointly simulated by a conditional turning bands simulation with elevation as external drift and 500 realizations were generated. Among the evapotranspiration models, the Hargreaves-Samani model was used. The ET0 was then estimated for each set of the 500 realizations of the input variables, and the ensemble of the model outputs was used to infer the reference evapotranspiration probability distribution function. This approach allowed for the delineation of the areas characterised by greater uncertainty, to improve supplementary sampling strategies and ET0 value predictions.
State-space approach to evaluate spatial variability of field measured soil water status along a line transect in a volcanic-vesuvian soil
Authors: Comegna A. , Coppola A. , Comegna V. , Severino G. , Sommella A. , Vitale C. D.
Published: December 2010

Abstract. Unsaturated hydraulic properties and their spatial variability today are analyzed in order to use properly mathematical models developed to simulate flow of the water and solute movement at the field-scale soils. Many studies have shown that observations of soil hydraulic properties should not be considered purely random, given that they possess a structure which may be described by means of stochastic processes. The techniques used for analyzing such a structure have essentially been based either on the theory of regionalized variables or to a lesser extent, on the analysis of time series. This work attempts to use the time-series approach mentioned above by means of a study of pressure head h and water content θ which characterize soil water status, in the space-time domain. The data of the analyses were recorded in the open field during a controlled drainage process, evaporation being prevented, along a 50 m transect in a volcanic Vesuvian soil. The isotropic hypothesis is empirical proved and then the autocorrelation ACF and the partial autocorrelation functions PACF were used to identify and estimate the ARMA(1,1) statistical model for the analyzed series and the AR(1) for the extracted signal. Relations with a state-space model are investigated, and a bivariate AR(1) model fitted. The simultaneous relations between θ and h are considered and estimated. The results are of value for sampling strategies and they should incite to a larger use of time and space series analysis.