bluuebunny/crossref_metadata_2025 huggingface dataset:
Lexicographic Direct Sums of Elementary C*-Algebras
Authors: Behncke Horst , Elliott George A.
Published: December 2010

Besides the simple ones, there are several other kinds of C*-algebras which it has proved interesting to try to classify. For instance, a large body of results relates to the extensions of one given C*-algebra, possibly simple, by another. Extrapolating in this direction, we have considered the class of C*-algebras which can be decomposed in the strongest possible nontrivial sense in terms of their simple subquotients, and such that these simple subquotients in turn are as uncomplicated as possible.

We have found that the classification of these C*-algebras, namely, the lexicographic direct sums of elementary C*-algebras, is to a large degree tractable, and yet involves an interesting new invariant in the antiliminary case, which is the case of no minimal ideals. Even the postliminary case, which is the case that the ordered set of simple subquotients satisfies the decreasing chain condition, is not without interest as an extension of the case of finitely many simple subquotients, analysed in the earlier papers [1] and [2].
Nonstandard Ideals in Radical Convolution Algebras on a Half-Line
Authors: Dales H. G. , McClure J. P.
Published: December 2010

This note is about the interplay between two classes of radical Banach algebras, and we begin by describing the algebras in question.

A weight sequence is a positive sequence w = (wn) defined on Z+ (the non-negative integers) and satisfying w0 = 1 and wm+n ≦ wmwn for all m and n in Z+. For such a sequence w, the Banach space

is a Banach algebra with respect to the convolution product, defined by
A Cancellation Theorem for Modules Over the Group C*-Algebras of Certain Nilpotent Lie Groups
Authors: Sheu Albert Jeu-Liang
Published: December 2010

In recent years, there has been a rapid growth of the K-theory of C*-algebras. From a certain point of view, C*-algebras can be treated as “non-commutative topological spaces”, while finitely generated projective modules over them can be thought of as “non-commutative vector bundles”. The K-theory of C*-algebras [30] then generalizes the classical K-theory of topological spaces [1]. In particular, the K0-group of a unital C*-algebra A is the group “generated” by (or more precisely, the Grothendieck group of) the commutative semigroup of stable isomorphism classes of finitely generated projective modules over A with direct summation as the binary operation. The semigroup gives an order structure on K0(A) and is usually called the positive cone in K0(A).

Around 1980, the work of Pimsner and Voiculescu [18] and of A. Connes [4] provided effective ways to compute the K-groups of C*-algebras. Then the classification of finitely generated projective modules over certain unital C*-algebras up to stable isomorphism could be done by computing their K0-groups as ordered groups. Later on, inspired by A. Connes's development of non-commutative differential geometry on finitely generated projective modules [2], the deeper question of classifying such modules up to isomorphism and hence the so-called cancellation question were raised (cf. [21] ).
Proximal Analysis and Boundaries of Closed Sets in Banach Space. Part II: Applications
Authors: Borwein J. M. , Strojwas H. M.
Published: December 2010

This paper is a direct continuation of the article “Proximal analysis and boundaries of closed sets in Banach space, Part I: Theory”, by the same authors. It is devoted to a detailed analysis of applications of the theory presented in the first part and of its limitations.

Theorem 2.1 has important consequences for geometry of Banach spaces. We start the presentation with a discussion of density and existence of R-proper points (Definition 1.3) for closed sets in Banach spaces. Our considerations will be based on the “lim inf” inclusions proven in the first part of our paper.
Inclusion Theorems for FX-Spaces
Authors: Boos Johann
Published: December 2010

The main result of this paper is Theorem 1 (in connection with Corollary 1 (e)), which says that the implication

*

holds for every separable FK-space F, for every FK-space E containing φ and for certain (for example, solid) FK-AB-spaces Y. At this, φ denotes the space of all finite sequences and WE is the set of all elements of E being weakly sectionally convergent.

This result was proved by Bennett and Kalton ([1] and [3]) in the special case that E contains all null sequences and that Y is the space m of all bounded sequences or the space of all sequences almost converging to zero.
Multiplicative Functions in Short Intervals
Authors: Hildebrand Adolf
Published: December 2010

A central problem in probabilistic number theory is to evaluate asymptotically the partial sums

of multiplicative functions f and, in particular, to find conditions for the existence of the “mean value”

1.1

In the last two decades considerable progress has been made on this problem, and the results obtained are very satisfactory.
Stable Homotopy Theory of Simplicial Presheaves
Authors: Jardine J. F.
Published: December 2010

Let C be an arbitrary Grothendieck site. The purpose of this note is to show that, with the closed model structure on the category S Pre(C) of simplicial presheaves in hand, it is a relatively simple matter to show that the category S Pre(C)stab of presheaves of spectra (of simplicial sets) satisfies the axioms for a closed model category, giving rise to a stable homotopy theory for simplicial presheaves. The proof is modelled on the corresponding result for simplicial sets which is given in [1], and makes direct use of their Theorem A.7.

This result gives a precise description of the associated stable homotopy category Ho(S Pre(C))stab, according to well known results of Quillen [6]. One will recall, however, that it is preferable to have several different descriptions of the stable homotopy category, for the construction of smash products and the like.
The Multiplicative Groups of Quasifields
Authors: Kallaher Michael J.
Published: December 2010

Let (Q, +, ·) be a finite quasifield of dimension d over its kernel K = GF(q), where q = pk with p a prime and k ≧ 1. (See p. 18-22 and p. 74 of [7] or Section 5 of [9] for the definition of quasifield.) For the remainder of this article we will follow standard conventions and omit, whenever possible, the binary operations + and · in discussing a quasifield. For example, the notation Q will be used in place of the triple (Q, +, ·) and Q* will be used to represent the multiplicative loop (Q − {0}, ·).

Let m be a non-zero element of the quasifield Q; the right multiplicative mapping ρm:Q → Q is defined by

1
A Descent Theorem for Hermitian K-Theory
Authors: Snaith Victor
Published: December 2010

Let KO and KU respectively denote the real and complex periodic K-theory spectra [1, Part III]. Let KSC denote the spectrum representing self-conjugate K-theory [2, G]. Thus we have a fibring

1.1

where T is induced by complex conjugation on the unitary group.

The following result is due to R. Wood [1, p. 206] and, I believe, to D. W. Anderson.

1.2. PROPOSITION. Let generate the stable one-stem. Then there are weak equivalences of spectra

a

and

b
Three Test Problems for Quasisimilarity
Authors: Bercovici Hari
Published: December 2010

Kaplansky proposed in [7] three problems with which to test the adequacy of a proposed structure theory of infinite abelian groups. These problems can be rephrased as test problems for a structure theory of operators on Hilbert space. Thus, R. Kadison and I. Singer answered in [6] these test problems for the unitary equivalence of operators. We propose here a study of these problems for quasisimilarity of operators on Hilbert space. We recall first that two (bounded, linear) operators T and T′ acting on the Hilbert spaces and , are said to be quasisimilar if there exist bounded operators and with densely defined inverses, satisfying the relations T′X = XT and TY = YT′. The fact that T and T′ are quasisimilar is indicated by T ∼ T′. The problems mentioned above can now be formulated as follows.
On Elliptically Embedded Subgroups of Soluble Groups
Authors: Rhemtulla A. H. , Wilson J. S.
Published: December 2010

We call a subset X of a group an elliptic set if there is an integer n such that each element of the group generated by X can be written as a product of at most n elements of X ∪ X−1. The terminology is due to Philip Hall, who investigated elliptic sets in lectures given in Cambridge in the 1960's. Hall was chiefly interested in sets X which are unions of conjugacy classes, but among other things he proved that if H, K are subgroups of a finitely generated nilpotent group then their union H ∪ K is elliptic. We shall say that a subgroup H of an arbitrary group G is elliptically embedded in G, and we write H ee G, if H ∪ K is an elliptic set for each subgroup K of G. Thus H ee G if for each subgroup K there is an integer n (depending on K) such that

where the product has 2n factors.
Explicit Formulas for the Associated Jacobi Polynomials and Some Applications
Authors: Wimp Jet
Published: December 2010

In this paper we determine closed-form expressions for the associated Jacobi polynomials, i.e., the polynomials satisfying the recurrence relation for Jacobi polynomials with n replaced by n + c, for arbitrary real c ≧ 0. One expression allows us to give in closed form the [n — 1/n] Padé approximant for what is essentially Gauss' continued fraction, thus completing the theory of explicit representations of main diagonal and off-diagonal Padé approximants to the ratio of two Gaussian hypergeometric functions and their confluent forms, an effort begun in [2] and [19]. (We actually give only the [n — 1/n] Padé element, although other cases are easily constructed, see [19] for details.)

We also determine the weight function for the polynomials in certain cases where there are no discrete point masses. Concerning a weight function for these polynomials, so many writers have obtained so many partial results that our formula should be considered an epitome rather than a real discovery, see the discussion in Section 3.
Divisible Semiplanes, Arcs, and Relative Difference Sets
Authors: Jungnickel Dieter
Published: December 2010

In this paper we shall be concerned with arcs of divisible semiplanes. With one exception, all known divisible semiplanes D (also called “elliptic” semiplanes) arise by omitting the empty set or a Baer subset from a projective plane Π, i.e., D = Π\S, where S is one of the following:

(i) S is the empty set.

(ii) S consists of a line L with all its points and a point p with all the lines through it.

(iii) S is a Baer subplane of Π.

We will introduce a definition of “arc” in divisible semiplanes; in the examples just mentioned, arcs of D will be arcs of Π that interact in a prescribed manner with the Baer subset S omitted. The precise definition (to be given in Section 2) is chosen in such a way that divisible semiplanes admitting an abelian Singer group (i.e., a group acting regularly on both points and lines) and then a relative difference set D will always contain a large collection of arcs related to D (to be precise, —D and all its translates will be arcs).
On the Galois Theory of Commutative Rings II: Automorphisms induced in Residue Rings
Authors: Faith Carl
Published: December 2010

Let G be a group of automorphisms of a commutative ring K, and let KG denote the Galois subring consisting of all elements left fixed by every g in G. An ideal M is G-stable, or G-invariant, provided that g(x) lies in M for every x in M, that is, g(M) ⊆ M, for every g in G. Then, every g in G induces an automorphism in the residue ring , and if is the group consisting of all , trivially

1

When the inclusion (1) is strict, then G is said to be cleft at M, or by M, and otherwise G is uncleft at (by) M. When G is cleft at all ideals except 0, then G is cleft, and uncleft otherwise.
Idempotent Multipliers of H1(T)
Authors: Klemes I.
Published: December 2010

Let as usual T = R/2πZ be the circle, and H1 the subspace of L1(T) of all f such that for all integers n < 0. The norm

restricted to H1, makes it a Banach space. By a multiplier of H1 we mean a bounded linear operator m:H1 → H1 such that there is a sequence in C with
Inequalities in Discrete Subgroups of PSL(2, R)
Authors: Gilman Jane
Published: December 2010

Conditions for a subgroup, F, of PSL(2, R) to be discrete have been investigated by a number of authors. Jørgensen's inequality [5] gives an elegant necessary condition for discreteness for subgroups of PSL(2, C). Purzitsky, Rosenberger, Matelski, Knapp, and Van Vleck, among others [12, 13, 14, 9, 16, 17, 18, 19, 20, 7, 21] studied two generator discrete subgroups of PSL(2, R) in a long series of papers. The complete classification of two generator subgroups was surprisingly complicated and elusive. The most complete result appears in [20].

In this paper we use the results of [20] to prove that a nonelementary subgroup F of PSL(2, R) is discrete if and only if every non-elementary subgroup, G, generated by two hyperbolics is discrete (Theorem 5.2) and that F contains no elliptics if and only if each such G is free (Theorem 5.1). Thus, we produce necessary and sufficient conditions for a non-elementary subgroup F of PSL(2, R) to be a discrete group without elliptic elements (Theorem 6.1) or a discrete group containing only hyperbolic elements (Theorem 7.1).
A Tauberian Theorem Concerning Borel-Type and Cesàro Methods of Summability
Authors: Borwein David , Markovich Tom
Published: December 2010

Suppose throughout that r ≧ 0, α > 0, αq + β > 0 where q is a non-negative integer. Let {sn} be a sequence of real numbers,

The Borel-type summability method (B, α, β) is defined as follows:

The method (B, α, β) is regular [5]; and (B, 1, 1) is the standard Borel exponential method B. For a real sequence {sn} we consider the slowly decreasing-type Tauberian condition

We shall also be concerned with the Cesàro summability method Cp(p > —1), the Valiron method Vα, and the Meyer-König method Sa (0 < a < 1) defined as follows:
Commutativity Preserving Maps of Factors
Authors: Miers C. Robert
Published: December 2010

By a von Neumann algebra M we mean a weakly closed, self-adjoint algebra of operators on a Hilbert space which contains I, the identity operator. A factor is a von Neumann algebra whose centre consists of scalar multiples of I.

In all that follows ϕ:M → N will be a one to one, *-linear map from the von Neumann factor M onto the von Neumann algebra N such that both ϕ and ϕ−1 preserve commutativity. Our main result states that if M is not of type I2 then where is an isomorphism or an antiisomorphism, c is a non-zero scalar, and λ is a *-linear map from M into ZN, the centre of N.

Our interest in this problem was aroused by several recent results. In [1], Choi, Jafarian, and Radjavi proved that if S is the real linear space of n × n matrices over any algebraically closed field, n ≧ 3, and ψ a linear operator on S which preserves commuting pairs of matrices, then either ψ(S) is commutative or there exists a unitary matrix U such that

for all A in S. They proved an analogous result for the collection of all bounded self-adjoint operators on an infinite dimensional Hilbert space when ψ is one to one. Subsequently, Omladic [7] proved that if ψ:L(X) → L(X) is a bijective linear operator preserving commuting pairs of operators where X is a non-trivial Banach space, then

where U is a bounded invertible operator on X and A′ is the adjoint of A.
Sur Les Isométries De Lp(X) Et Le Théorème Ergodique Vectoriel
Authors: Guerre S. , Raynaud Y.
Published: December 2010

Etant donné un opérateur T sur un espace LP (1 < p < ∞), la théorie ergodique s'intéresse à la convergence presque sûre des moyennes de Césaro

des itérés d'un point f de Lp par T. On dit que T vérifie le théorème ergodique si cette convergence a lieu pour tout f de Lp.

Parmi les nombreux résultats sur cette question (cf. [21]) nous citerons d'abord ceux de A. Ionescu-Tulcea ([19]) et R. Chacon-S. A. McGrath
([10]) que l'on peut réunir dans l'assertion suivante:

“Si 1 < p < ∞ et T une isométrie positive de Lp, ou si 1 < p ≠ 2 < ∞ et si T est une isométrie surjective de Lp, alors T vérifie le théorème ergodique”.

Nous nous intéressons ici à une version vectorielle de ce théorème. Plus précisément, si X est un espace de Banach réel, un opérateur linéare T sur l'espace LP(X) est dit vérifier le théorème ergodique vectoriel si la suite des moyennes de Césaro

converge presque sûrement en norme dans X, quel que soit f ∊ Lp(X).
Inclusions for Classes of Lacunary Sets
Authors: Chun C. S. , Freedman A. R.
Published: December 2010

A sequence, a1 < a2 < a3 < …, of positive integers is called lacunary if the difference sequence dn = an+l — an tends to infinity as n → ∞.

In several recent papers we have made use of these sequences in analysis and combinatorics. In [6] we show that the class of all sets which are either finite or the range of a lacunary sequence is “full” in the sense that if (tk) is a real sequence and for each then (tk) is an l1 sequence, that is,

In [3] the class of all finite unions of sets of is shown to consist of exactly those sets of integers, A, whose characteristic sequence, χA, is in the well known summability space bs + c0. More recently, in [1], we study lacunary sequences in connection with the conjecture of P.
Asymptotic Maximum Principles for Subharmonic and Plurisubharmonic Functions
Authors: Gauthier P. M. , Grothmann R. , Hengartner W.
Published: December 2010

Let Ω be a bounded open set in Rn. An immediate consequence of the maximum principle is that if s is a function continuous on and subharmonic on Ω, then

(1)

Of course (1) is no longer true if Ω is not bounded. For example in C ∼ R2 consider the functions

However, if we restrict the growth of s, then (1) may still hold even if the open set Ω is no longer bounded and such is the theme of Phragmèn-Lindelöf type theorems. If we assume even more, namely, that s is upper-bounded, then we can again infer (1) for unbounded open sets Ω. We shall return to this point later.

In the present note, we wish to prove (1) for an arbitrary subharmonic function s on an open subset Ω of Rn. In particular, we do not assume that s is bounded or even of restricted growth. Rather, we impose restrictions on the (possibly unbounded) set Ω.
Representation Formulas for Integrable and Entire Functions of Exponential
Type I
Authors: Frappier Clément
Published: December 2010

Let Bτ
denote the class of entire functions of exponential type
τ (>0) bounded on the real axis. For the
function f ∊ Bτ
we have the interpolation formula [1, p.
143]

1.1

where t, γ are real
numbers and is the so called
conjugate function of f. Let us put

1.2

The function Gγ,f
is a periodic function of α, with period 2. For
t = 0 (the general case is obtained by translation)
the righthand member of (1) is 2τGγ,f
(1). In the following paper we suppose that
f satisfies an additional hypothesis of the form
f(x) =
O(|x|-ε), for some ε >
0, as x → ±∞ and we give an integral representation of
Gγ,f(α) which is valid for 0
≦ α ≦ 2.
Weighted Subspaces of Hardy Spaces
Authors: Kim Hong Oh , Kwon Ern Geun
Published: December 2010

A function f in Hp on the unit disc U of the complex plane has the uniform growth

We consider in this paper a subspace of Hp with better uniform growth

For the previous results on see [5, 6, 7]. We start with proving an inequality on Hp which is related to the Hardy-Stein identity (Theorem 2.1) in Section 2. This is applied in the subsequent section to prove some space imbedding theorems related to (Theorems 3.1 and 3.5). These theorems have some known theorems as their corollaries. Finally we prove some coefficient relations on in the last section.

The authors wish to thank Professor Patrick Ahern for the helpful conversations during his visit to Korea. Actually he suggested to the first author the possibility of Theorem 2.1 some years ago.
The Complexity Of Nowhere Differentiable Continuous Functions
Authors: Ramsamujh T. I.
Published: December 2010

It was not always clear that there could exist a continuous function which was differentiable at no point. (Such functions are now known as nowhere differentiable continuous functions. By “differentiable” we mean having a finite derivative.) In fact in 1806 M. Ampere [2] even tried to show that no such function could exist but his reasonings were later discovered to be fallacious. Of the early attempts at constructing a nowhere differentiable continuous function mention must be made of B. Bolzano. In a manuscript dated around 1830, (see [21]) he constructed a continuous function on an interval and showed that it was not differentiable on a dense set of points. (It was later shown by K. Rychlik [21] that this function was in fact nowhere differentiable.)
Automorphisms of Fuchsian Groups and their Lifts to Free Groups
Authors: Lustig Martin , Moriah Yoav , Rosenberger Gerhard
Published: December 2010

This paper has been motivated by earlier work of the first two authors (see [3] ), where distinct Nielsen classes of generating systems for a Fuchsian group have been established and, in the case of odd and pairwise relative prime exponents π(i),classified. As a consequence they could distinguish nonisotopic Heegaard decompositions of Seifert fibred 3-manifolds. In proving that these decompositions are actually non-homeomorphic (see [3], Section 2), they investigated the question whether the different Nielsen classes of generating systems for G remain distinct, if one passes over to the weaker notion of “Nielsen equivalence up to automorphisms” (see [12], p. 3.5, 4.11 a-c): this means that the automorphisms of G are added to the Nielsen equivalence relations on the generators.
Fractional Derivatives as Inverses
Authors: Isaacs Godfrey L.
Published: December 2010

We write formally (C, p) indicating that the integral is summable (C, p), i.e.,if this limit exists. We note here that all integrals over a finite range are taken in the Lebesgue sense, and all inversions of such iterated integrals are justifiable by Fubini's Theorem.
Equivalence of Cables Of Mutants of Knots
Authors: Przytycki Józef H.
Published: December 2010

There is the nice formula which links the Alexander polynomial of (m, k)-cable of a link with the Alexander polynomial of the link [5] [36] [38]. H. Morton and H. Short investigated whether a similar formula holds for the Jones-Conway (Homfly) polynomial and they found that it is very unlikely. Morton and Short made many calculations of the Jones-Conway polynomial of (2, q)-cables along knots (2 was chosen because of limited possibility of computers) and they get very interesting experimental material [24], [25]. In particular they found that using their method they were able to distinguish some Birman [4] and Lozano-Morton [22] examples (all which they tried) and the 942 knot (in the Rolfsen [37] notation) from its mirror image. On the other hand they were unable to distinguish the Conway knot and the Kinoshita-Terasaka knot.
Oscillation Criteria For Second Order Superlinear Differential Equations
Authors: Philos CH. G.
Published: December 2010

This paper is concerned with the question of oscillation of the solutions of second order superlinear ordinary differential equations with alternating coefficients.

Consider the second order nonlinear ordinary differential equation

where a is a continuous function on the interval [t0, ∞), t0 > 0, and / is a continuous function on the real line R, which is continuously differentia t e , except possibly at 0, and satisfies.
Quasigroup Identities and Mendelsohn Designs
Authors: Bennett F. E.
Published: December 2010

A quasigroup is an ordered pair (Q, •), where Q is a set and (•) is a binary operation on Q such that the equations ax — b and ya — b are uniquely solvable for every pair of elements a,b in Q. It is well-known (see, for example, [11]) that the multiplication table of a quasigroup defines a Latinsquare, that is, a Latin square can be viewed as the multiplication table of a quasigroup with the headline and sideline removed. We are concerned mainly with finite quasigroups in this paper. A quasigroup (Q, •) is called idempotent if the identity x2 = x holds for all x in Q.
The Approximate Symmetric Integral
Authors: Preiss D. , Thomson B. S.
Published: December 2010

By a symmetric integral is understood an integral obtained from some kind of symmetric derivation process. Such integrals arise most naturally in the study of trigonometric series and in particular to handle the following problem. Suppose that a trigonometric series

converges everywhere to a function À. It is known that this may occur without À being integrable in any of the more familiar senses so that the series may not be considered as a Fourier series of À; indeed Denjoy [4] has shown that if bnis a sequence of real numbers decreasing to zero but with

+00 then the function À(x) = is not Denjoy-integrable. It is natural to ask then for an integration procedure that can be applied to À in order that the series be the Fourier series of À with respect to this integral.
Regular Germs For -Adic Sp(4)
Authors: Yangkon Kim
Published: December 2010

Shalika [6] proved the existence of germs (associated with a connected semi-simple algebraic group and a maximal torus over a non-archimedean local field), established many of their properties, and conjectured that the germ associated to the trivial unipotent class in GL(n) should be a constant. R. Howe and Harish-Chandra proved that it is a constant and J. Rogawski [5] proved that it had the value predicted previously by J. Shalika.
Existence Of Nearest Points In Banach Spaces
Authors: Borwein Jonathan M. , Fitzpatrick Simon
Published: December 2010

This paper makes a unified development of what the authors know about the existence of nearest points to closed subsets of (real) Banach spaces. Our work is made simpler by the methodical use of subderivatives. The results of Section 3 and Section 7 in particular are, to the best of our knowledge, new. In Section 5 and Section 6 we provide refined proofs of the Lau-Konjagin nearest point characterizations of reflexive Kadec spaces (Theorem 5.11, Theorem 6.6) and give a substantial extension (Theorem 5.12). The main open question is: are nearest points dense in the boundary of every closed subset of every reflexive space? Indeed can a proper closed set in a reflexive space fail to have any nearest points? In Section 7 we show that there are some non-Kadec reflexive spaces in which nearest points are dense in the boundary of every closed set.
Real Af C*-Algebras With K0 of Small Rank
Authors: Giordano T. , Handelman D. E.
Published: December 2010

A real AF C*-algebra is the norm closure of a direct limit of finite dimensional real C*-algebras (with real *-algebra maps). When we use the unadorned “AF C*-algebra”, we mean the usual complex version.

Let R be a simple AF C*-algebra such that K0(R) is free of rank 2 or 3. The problem is to find (up to Morita equivalence) all real AF C*-algebras A such that AꕕC≅R. This is closely related to the problem of finding all involutions on R [3], [10].

For example, when the rank is 2, generically there are 8 such classes. The exceptional cases arise when the ratio of the two generators in K0(R) is a quadratic (algebraic) number, and here there are 4, 5, or 8 Morita equivalence classes, the number depending largely on the behaviour of the prime 2 in the relevant algebraic number field.
Compactness of Invariant Densities for Families of Expanding, Piecewise Monotonic Transformations
Authors: Góra P. , Boyarsky A.
Published: December 2010

Let I = [0,1] and let be the space of all integrable functions on I, where m denotes Lebesque measure on I. Let ∥ ∥1 be the ℒ-1-norm and let be a measurable, nonsingular transformation on I. Let denote the space of densities. The probability measure μ is invariant under τ if for all measurable sets A, The measure μ is absolutely continuous if there exists an such that for any measurable set A We refer to ƒ* as the invariant density of τ (with respect to m). It is well-known that ƒ * is a fixed point of the Frobenius-Perron operator defined by
The Stationary Phase Method for Certain Degenerate Critical Points I
Authors: Dostal Milos , Gaveau Bernard
Published: December 2010

We consider, in this work, the asymptotic behaviour for large λ, of a Fourier integral

where 𝜑(x) is in general a C∞ function and a(x) a C∞ function with compact support. It is well known that the asymptotic behaviour of this integral is controlled by the behaviour of 𝜑 at its critical points (i.e., points where 𝜕𝜑/𝜕xj(x) = 0) and is given by local contributions at these points ([1], [3], [7], [9]).

In general, one assumes the hypothesis of non degenerate isolated critical point, namely that the determinant of the second derivative at the critical point is non zero.
On the Hyperplane Sections of Blow-Ups of Complex Projective Plane
Authors: Biancofiore Aldo
Published: December 2010

Let L be a line bundle on a connected, smooth, algebraic, projective surface X. In this paper we have studied the following questions:

1) Under which conditions is L spanned by global sections? I.e., if ɸL : X →PN denotes the map associated to the space Г(L) of the sections of L, when is ɸL a morphism?

2) Under which conditions is L very ample? I.e., when does ɸL give an embedding?

These problems arise naturally in the study, and in particular in the classification, of algebraic surfaces (see [8], [3], [5]).
The Approximate Jordan-Hahn Decomposition
Authors: Rüttimann Gottfried T.
Published: December 2010

Non-commutative measure theory embraces measure theory on cr-fields of subsets of a set, on projection lattices of von Neumann algebras or JBW-algebras and on hypergraphs alike [20], [27], [33], [37], [39], [40], [41]. Due to the unifying structure of an orthoalgebra concepts can easily be transferred from one branch to the other. Additional conceptual inpetus is obtained from the logico-probabilistic foundations of quantum mechanics (see [6], [19], [21]).

In the late seventies the author studied the Jordan-Hahn decomposition of measures on orthomodular posets and certain graphs. These investigations revealed an interesting geometrical aspect of this decomposition in that the Jordan-Hahn property of the convex set of probability charges on a finite orthomodular poset can be characterized in terms of the extreme points of the unit ball of the Banach space dual of the base normed space of Jordan charges.
A Schensted Algorithm Which Models Tensor Representations of the Orthogonal Group
Authors: Proctor Robert A.
Published: December 2010

This paper is concerned with a combinatorial construction which mysteriously “mimics” or “models” the decomposition of certain reducible representations of orthogonal groups. Although no knowledge of representation theory is needed to understand the body of this paper, a little familiarity is necessary to understand the representation theoretic motivation given in the introduction. Details of the proofs will most easily be understood by people who have had some exposure to Schensted's algorithm or jeu de tacquin.
On Moduli of Continuity for Gaussian and l2-Norm Squared Processes Generated by Ornstein-Uhlenbeck Processes
Authors: Csörgö Miklós , Lin Zhengyan
Published: December 2010

Let be a sequence of independent Ornstein-Uhlenbeck processes with coefficients lk and ƛk,i.e., Xk(.)is a Gaussian process with EXk(t) =0 and

The process Y(.)was first studied by Dawson (1972) as the stationary solution of the infinite array of stochastic differential equations

where are independent Wiener processes (cf. also [6],[19],and [1]).
The n-Dimensional Hilbert Transform of Distributions, Its Inversion and Applications
Authors: Singh O. P. , Pandey J. N.
Published: December 2010

Pandey and Chaudhary [13] recently developed the theory of Hilbert transform of Schwartz distribution space (DLp)',p > 1 in one dimension using Parseval's types of relations for one dimensional Hilbert transform [17] and noted that their theory coincides with the corresponding theory for the Hilbert transform developed by Schwartz [16] by using the technique of convolution in one dimension.

The corresponding theory for the Hilbert transform in n-dimension is considerably harder and will be successfully accomplished in this paper.
Tensor Products of Unitary Super-Virasoro Modules With Central Charge 7/10
Authors: Bremner Murray R.
Published: December 2010

The two Virasoro superalgebras, known as the Neveu- Schwarz algebra and the Ramond algebra, each have two unitary irreducible lowest weight modules with central charge . In this paper, I show how tensor products of these modules decompose into finite direct sums of irreducible modules with central charge .
Restricted Determinantal Homomorphisms and Locally Free Class Groups
Authors: Snaith Victor
Published: December 2010

Let K be a number field and let OK denote the integers of K. The locally free class groups, Cl(OK[G]), furnish a fundamental collection of invariants of a finite group, G. In this paper I will construct some new, non-trivial homomorphisms, called restricted determinants, which map the NGH-invariant idèlic units of Ok([Hab] to Cl(OK[G]). These homomorphisms are constructed by means of the Horn-description of Cl(OK[G]), which describes the locally free class group in terms of the representation theory of G, and the technique of Explicit Brauer Induction, which was introduced in [5].
The Homotopy Set of the Axes of Pairings
Authors: Oda Nobuyuki
Published: December 2010

Varadarajan [13] named a map f: A → X a cyclic map when there exists a map F: X × A → X such that for the folding map ∇X: X ∨ X → X. He defined the generalized Gottlieb set G(A, X) of the homotopy classes of the cyclic maps F: A → X and studied the fundamental properties of G(A, X) If A is a co-Hopf space, then the Varadarajan set G(A, X) has a group structure [13]. The group G(A,X) is a generalization of G(X) and Gn(X) of Gottlieb [2,3]. Some authors studied the properties of the Varadarajan set, its dual and related topics [4, 5, 6, 7,12,15,16,17].
On Bounded and Compact Composition Operators in Polydiscs
Authors: Jafari F.
Published: December 2010

Recently MacCluer and Shapiro [6] have characterized the compact composition operators in Hardy and weighted Bergman spaces of the disc, and MacCluer [5] has made an extensive study of these opertors in the unit ball of Cn. Angular derivatives and Carleson measures have played an essential role in these studies. In this article we study composition operators in poly discs and characterize those operators which are bounded or compact in Hardy and weighted Bergman spaces. In addition to Carleson measure theorems resembling those of [5], [6], we give necessary and sufficient conditions satisfied by the maps inducing bounded or compact composition operators. We conclude by considering the role of angular derivatives on the compactness question explicitly.
Repercussions of a Problem of Erdős and Ulam on Density Ideals
Authors: Just Winfried
Published: December 2010

By P(ω) we denote the Boolean algebra of all subsets of the set ω of natural numbers. We identify each natural number with the set of its predecessors and define: the ideal of sets of density zero, and the ideal of sets of logarithmic density zero.
Non-Nilpotent Groups in Which Every Product of Four Elements Can be Reordered
Authors: Maj M. , Stonehewer S. E.
Published: December 2010

Let G be a group and n(≧ 2) an integer. We say that G belongs to the class of groups Pn if every product of n elements can be reordered, i.e. for all n-tuples , there exists a non-trivial element σ in the symmetric group Σn such that Let P denote the union of the classes Pn, n ≧ 2. Clearly every finite group belongs to P and each class Pn is closed with respect to forming subgroups and factor groups.
A Family of Unitals in the Hughes Plane
Authors: Kestenband Barbu C.
Published: December 2010

We construct a family of unitals in the Hughes plane. We prove that they are not isomorphic with the classical unitals, and in so doing we exhibit a configuration that exists in the latter, but not in the former. This new configurational property of the classical unitals might serve in the future again as an isomorphism test.

A particular instance of our construction has appeared in [11]. But it only concerns itself with the case where the matrix involved is the identity, whereas the present article treats the general case of symmetric matrices over a suitable field. Furthermore, [11] does not answer the isomorphism question. It states that (the English translation is ours) “It remains to be seen whether the unitary designs constructed in this note are isomorphic or not with known designs”.
On Nonabelian H2for Profinite Groups
Authors: Ulbrich K.-H.
Published: December 2010

Let G be a profinite group. We define an extension (E.j) of G by a group A to consist of an exact sequence of groupstogether with a section j : G → E of к satisfying:for some open normal subgroup S of G,and the map is continuous (A being discrete).
Strongly Abelian Varieties and the Hamiltonian Property
Authors: Kiss E. , Valeriote M.
Published: December 2010

In this paper we show that every locally finite strongly Abelian variety satisfies the Hamiltonian property. An algebra is Hamiltonian if every one of its subuniverses is a block of some congruence of the algebra. A counterexample is provided to show that not all strongly Abelian varieties are Hamiltonian.
The Symmetries of Genus One Handlebodies
Authors: Kalliongis John , Miller Andy
Published: December 2010

The symmetries of manifolds are a focal point of study in low-dimensional topology and yet, outside of some totally asymmetrical 3- and 4-manifolds, there are very few cases in which a complete classification has been attained. In this work we provide such a classification for symmetries of the orientable and nonorientable 3-dimensional handlebodies of genus one. Our classification includes a description, up to isomorphism, of all of the finite groups which can arise as symmetries on these manifolds, as well as an enumeration of the different ways in which they can arise. To be specific, we will classify the equivalence, weak equivalence and strong equivalence classes of (effective) finite group actions on the genus one handlebodies.
Minimal Convex Uscos and Monotone Operators on Small Sets
Authors: Borwein Jonathan , Fitzpatrick Simon , Kenderov Petàr
Published: December 2010

We generalize the generic single-valuedness and continuity of monotone operators defined on open subsets of Banach spaces of class (S) and Asplund spaces to monotone operators defined on convex subsets of such spaces which may even fail to have non-support points. This yields differentiability theorems for convex Lipschitzian functions on such sets. From a result about minimal convex uscos which are densely single-valued we obtain generic differentiability results for certain Lipschitzian realvalued functions.
Bernstein and Markov Type Inequalities for Generalized Non-Negative Polynomials
Authors: Tamás Erdélyi
Published: December 2010

Generalized polynomials are defined as products of polynomials raised to positive real powers. The generalized degree can be introduced in a natural way. Several inequalities holding for ordinary polynomials are expected to be true for generalized polynomials, by utilizing the generalized degree in place of the ordinary one. Based on Remez-type inequalities on the size of generalized polynomials, we establish Bernstein and Markov type inequalities for generalized non-negative polynomials, obtaining the best possible result up to a multiplicative absolute constant.
A Characterization of Multi-Dimensional Perron Integrals and the Fundamental Theorem
Authors: Jurkat W. B. , Knizia R. W.
Published: December 2010

In this paper weak Perron integrals are characterized as n-dimensional interval functions F which are additive, differentiable almost everywhere in the weak sense and which satisfy a new continuity condition concerning the singular set. Before, only one-dimensional Perron integrals were characterized by the theorem of Hake- Alexendrov-Looman, and analogous results for strong Perron integrals (which are best analyzed, but more restrictive) are not available in higher dimensions yet. In order to formulate our continuity condition we introduce an outer measure μ by means of a new weak variation of F which is required to vanish on all null sets. The same condition is also necessary and sufficient for the integral of the weak derivative to yield the original interval function. This “fundamental theorem” is split into two fundamental inequalities of very general nature which contain additional singular terms involving our variation. These inequalities are very useful also for Lebesgue integrals.
Representations of the (р2 - 1)-Dimensional Lie Algebras of R. E. Block
Authors: Strade Helmut
Published: December 2010

For all algebras G, such that is an algebra mentioned in the title, the modules of dimension ≤ p2 are determined. The module homomorphisms from the tensor product of these modules into a third module of the same type are described. We also give the central extensions of the algebras .
Equivariant Fixed Point Index and the Period-Doubling Cascades
Authors: Erbe L. H. , Gęba K. , Krawcewicz W.
Published: December 2010

Properties of fixed points of equivariant maps have been studied by several authors including A. Dold (cf. [2], 1982), H. Ulrich (cf. [9], 1988), A. Marzantowicz (cf. [7], 1975) and others. Closely related is the work of R. Rubinsztein (cf. [8], 1976) in which he investigated homotopy classes of equivariant maps between spheres. There have been many attempts to introduce and effectively apply these concepts to nonlinear problems. In particular we mention the work of E. Dancer (cf. [1], 1982) in which some applications to nonlinear problems are given.
Type Preservation In Locally Finite Varieties with the CEP
Authors: Kearnes Keith A.
Published: December 2010

Assume that A is a finite algebra contained in a variety that has the congruence extension property and that B is a subalgebra of A. If α ≺ β in Con A and α |B ≠ β |B, then we show that α |B ≺ β |B and that there is a close connection between the type labellings of the quotients 〈α, α〉 and 〈α|B, β|B〉.
Monotone Semiflows Generated by Neutral Functional Differential Equations With Application to Compartmental Systems
Authors: Wu Jianhong , Freedman H. I.
Published: December 2010

This paper is devoted to the machinery necessary to apply the general theory of monotone dynamical systems to neutral functional differential equations. We introduce an ordering structure for the phase space, investigate its compatibility with the usual uniform convergence topology, and develop several sufficient conditions of strong monotonicity of the solution semiflows to neutral equations. By applying some general results due to Hirsch and Matano for monotone dynamical systems to neutral equations, we establish several (generic) convergence results and an equivalence theorem of the order stability and convergence of precompact orbits. These results are applied to show that each orbit of a closed biological compartmental system is convergent to a single equilibrium.
Weighted Generalized Hardy Inequalities for Nonincreasing Functions
Authors: Andersen Kenneth F.
Published: December 2010

The nonnegative weight function pairs u, v for which the operator maps the nonnegative nonincreasing functions in LP(v) boundedly into weak Lq(u) are characterized. This result is used, in particular, both to generalize and to provide an alternate proof of certain strong type inequalities recently obtained by Ariño and Muckenhouptfor the Hardy averaging operator restricted to nonnegative nonincreasing functions.
Associated Continuous Hahn Polynomials
Authors: Gupta Dharma P. , Ismail Mourad E. H. , Masson David R.
Published: December 2010

Explicit solutions to the recurrence relation for associated continuous Hahn polynomials are derived using 3F2 contiguous relations. These solutions are used to obtain a new continued fraction and the associated absolutely continuous measure. An exceptional case is shown to yield entry 33 in Chapter 12 of Ramanujan's second notebook.
Local Properties of Light Harmonic Mappings
Authors: Lyzzaik Abdallah
Published: December 2010

The object of this paper is to study the local properties of light harmonic mappings.
Commutative Gelfand Theory for Real Banach Algebras: Representations as Sections of Bundles
Authors: Pfaffenberger W. E. , Phillips J.
Published: December 2010

We are concerned here with the development of a more general real case of the classical theorem of Gelfand ([5], 3.1.20), which represents a complex commutative unital Banach algebra as an algebra of continuous functions defined on a compact Hausdorff space.

In § 1 we point out that when looking at real algebras there is not always a one-to-one correspondence between the maximal ideals of the algebra B, denoted ℳ, and the set of unital (real) algebra homomorphisms from B into C, denoted by ΦB. This simple point and subsequent observations lead to a theory of representations of real commutative unital Banach algebras where elements are represented as sections of a bundle of real fields associated with the algebra (Theorem 3.5). After establishing this representation theorem, we look into the question of when a real commutative Banach algebra is already complex. There is a natural topological obstruction which we delineate. Theorem 4.8 gives equivalent conditions which determine whether such an algebra is already complex.

Finally, in § 5 we abstractly characterize those section algebras which appear as the target algebras for our Gelfand transform. We dub these algebras “almost complex C*- algebras” and provide a natural classification scheme.
Primitivity in Free Groups and Free Metabelian Groups
Authors: Gupta C. K. , Gupta N. D. , Roman'kov V. A.
Published: December 2010

Let Mn, c denote the free n-generator metabelian nilpotent group of class c. For m ≤ n – 2, every primitive system of m elements of Mn, c can be lifted to a primitive system of m elements of the absolutely free group Fn of rank n. The restriction on m cannot be improved.
An Application of Homogenization Theory to Harmonic Analysis: Harnack Inequalities And Riesz Transforms on Lie Groups of Polynomial Growth
Authors: Alexopoulos G.
Published: December 2010

We prove a homogenization formula for a sub-Laplacian are left invariant Hörmander vector fields) on a connected Lie group Gof polynomial growth. Then using a rescaling argument inspired from M. Avellanedaand F. H. Lin [2], we prove Harnack inequalities for the positive solutions of the equation (∂/∂t+ L)u= 0. Using these inequalities and further exploiting the algebraic structure of Gwe prove that the Riesz transforms , are bounded on Lq,1 < q <+∞ and from L1to weak-L1.
Positive Dependence of Exchangeable Sequences
Authors: Burton R. M. , Dabrowski A. R.
Published: December 2010

Infinite sequences of exchangeable binary random variables have strong positive dependence properties; in particular, we show they are strong FKG. If the infinite exchangeable sequence is allowed to have multiple values this is no longer true. Positive dependence conditions such as association still have natural application in this context. We establish necessary and sufficient conditions for an infinite exchangeable sequence to be associated. This result shows that exchangeable Polyà urn processes are associated. We also establish necessary and sufficient conditions for finite exchangeable sequences to be weakly associated. The match set distribution of a random permutation has recently been shown to be associated by an extensive analysis of cases. Our result easily yields the weak association of such distributions.