bluuebunny/crossref_metadata_2025_split huggingface dataset:
Structural Properties of Elementary Operators
Authors: Apostol Constantin , Fialkow Lawrence 
Published: December 2010

Let and denote complex Banach algebras and let b e a left Banach module and a right Banach -module. Ifwe define the bounded linear elementary operator R(A, B), acting on , byFor the case , elementary operators were introduced by Lumer and Rosenblum [19], who studied their spectral properties. In this setting many authors subsequently studied spectral, algebraic, metric, and structural properties of elementary operators, with particular attention devoted to the inner derivations δa (δa(x) = ax – xa) [25], generalized derivations τ(a, b) (τ(a, b)(x) = ax – xb) [9, 10], and elementary multiplications S(a, b) (S(a, b)(x) = axb), including left and right multiplications La and Rb [11].
Operators on L2(I) ⊕ Cr
Authors: Kemp R. R. D. 
Published: December 2010

Several authors have considered eigenvalue problems for differential equations where the eigenvalue parameter also appears in the boundary conditions. Such problems do not appear to arise from any spectral problem associated with a linear operator on a Hilbert space. However, it is possible to reset such problems in this context. This has been done for certain second order cases by Walter [4] using a special measure on the interval in question, and by Fulton [1, 2] using the type of space indicated in the title of this article.It is our purpose here to consider a general class of operators on L2(I) ⊕ Cr, which are based on a differential expression τ of order n on I. We shall first investigate adjoints, boundary conditions, and self-adjointness for such operators. We shall then show that all eigenvalue problems of the form τy = λy, with boundary conditions which involve λ in a linear fashion, can be reset in the context of such operators.
A Variation of the Koebe Mapping in a Dense Subset of S
Authors: Bshouty D. , Hengartner W. 
Published: December 2010

Let H(U) be the linear space of holomorphic functions defined on the unit disk U endowed with the topology of normal (locally uniform) convergence. For a subset E ⊂ H(U) we denote by Ē the closure of E with respect to the above topology. The topological dual space of H(U) is denoted by H′(U).Let D, 0 ∊ D, be a simply connected domain in C. The unique univalent conformal mapping ϕ from U onto D, normalized by ϕ(0) = 0 and ϕ′(0) > 0 will be called “the Riemann Mapping onto D”. Let S be the set of all normalized univalent functions
Dirac Systems with Discrete Spectra
Authors: Hinton D. B. , Shaw J. K. 
Published: December 2010

In this paper we consider the one dimensional Dirac system1.1where αk(x) < 0, λ is a complex spectral parameter, and the remaining coefficients are suitably smooth and real valued. We regard (1.1) as regular at x = a but singular at x = b; in Section 4 we extend our result to problems having two singular endpoints.Equation (1.1) arises from the three dimensional Dirac equation with spherically symmetric potential, following a separation of variables. For the choices p(x) = k/x, αk(x) = 1,p2(x) = (z/x) + c, p1(x) = (z/x) – c, and appropriate values of the constants, (1.1) is the radial wave equation in relativistic quantum mechanics for a particle in a field of potential V = z/x [17]. Such an equation was studied by Kalf [11] in the context of limit point-limit circle criteria, which is one of the matters we consider here.
Characters of Non-Connected, Reductive p-Abic Groups
Authors: Clozel Laurent 
Published: December 2010

In this paper, we extend to non-connected, reductive groups over p-adic field of characteristic zero Harish-Chandra's theorem on the local integrability of characters.Harish-Chandra's theorem states that the distribution character of an admissible, irreducible representation of a (connected) reductive p-adic group is locally integrable. We show that this extends to any reductive group; just as in the connected case, one even gets a very precise control over the singularities of the character along the singular elements.As will be seen, the proof in the non-connected case is an easy extension of Harish-Chandra's. The reader may wonder why we have bothered to write its generalization completely. The reason is that the original article [8] does not contain proofs for the crucial lemmas, and this makes it impossible to explain why the theorem extends. Because this result is needed for work of Arthur and the author on base change, it has been thought necessary to give complete arguments.
The L-Theory of Twisted Quadratic Extensions
Authors: Ranicki Andrew 
Published: December 2010

For surgery on codimension 1 submanifolds with non-trivial normal bundle the theory of Wall [13, Section 12C] has obstruction groups LN∗(π′ → π), with π a group and π′ a subgroup of index 2, such that there is defined an exact sequence involving the ordinary L-groups of rings with involutionwith the superscript w signifying a different involution on Z[π]. Geometry was used in [13] to identifywith (α, u) an antistructure on Z[π′] in the sense of Wall [14]. The main result of this paper is a purely algebraic version of this identification, for any twisted quadratic extension of a ring with antistructure.
A New Result on Comma-Free Codes of Even Word-Length
Authors: Tang Betty , Golomb Solomon W. , Graham Ronald L. 
Published: December 2010

Comma-free codes were first introduced in [1] in 1957 as a possible genetic coding scheme for protein synthesis. The general mathematical setting of such codes was presented in [3], and the biochemical and mathematical aspects of the problem were later summarized and extended in [4].Using the notation of [3], a set D of k-tuples or k-letter words, (a1a2 … ak), wherefor fixed positive integers k and n, is said to be a comma-free dictionary if and only if, whenever (a1a2 … ak) and (b1b2 … bk) are in D, the “overlaps”are not in D. This precludes codewords having a subperiod less than k; and two codewords which are cyclic permutations of one another cannot both be in D.
Existence, Unicite et Multiplicite de Solutions Periodiques D'Equations Differentielles de Duffing Non-Lineaires Avec Dissipation
Authors: Nkashama M. N. 
Published: December 2010

Nous nous intéressons à l'existence, l'unicité et la multiplicité de solutions de l'équation différentielle forcée:1.1vérifiant les conditions périodiques1.2où e ∊ L1(0, 2π), c ∊ R, c arbitraire, g:[0, 2π] × R → R satisfait les conditions de Carathéodory i.e.,g(·, x) est measurable pour tout x ∊ R, g(t, ·) est continu pour presque tout t ∊ [0, 2π].Le problème (1.1)-(1.2) a été étudié par plusieurs auteurs. Nous mentionerons les travaux [22], [18], [21], [20], [19], [7], [29], [25] et la bibliographie contenue dans ces articles.
Relations Between Mahler's Measure and Values of L-Series
Authors: Ray Gary Alan 
Published: December 2010

Mahler's measure is a natural generalization of Jensen's formula to polynomials in several variables. Its definition is as follows:The importance of Mahler's measure for polynomials in several variables lies in its connection to Lehmer's classical question which can be phrased in terms of Mahler's measure for polynomials in one variable:Given , are there any polynomials p with integer coefficients in one variable for which ?Surprisingly, Boyd [1] has shown that to answer this question, it is necessary to investigate the larger question involving polynomials in several variables.
Explicit Formulas for the Coefficients of α-Convex Functions, α ≧ 0
Authors: Todorov Pavel G. 
Published: December 2010

Let the function1be analytic in the unit disk Δ = {z│ │z│ ≤ 1), withthere, and let α be a real number. Then f(z) is said to be α-convex in Δ if and only if the inequalityholds in Δ. The class of α-convex functions was introduced in [8] and was studied in detail in the series [5]–[10], where in particular it is shown that α-convex functions are univalent and starlike for all α (−∞≦ α ≦ + ∞), that is, the inequalityholds in Δ.
Simple Type III Self-Injective Rings and Rings of Column-Finite Matrices
Authors: O'Meara K. C. 
Published: December 2010

Relatively little is known about simple, Type III, right self-injective rings Q. This is despite their common occurrence, for example as Qmax(R) for any prime, nonsingular, countable-dimensional algebra R without uniform right ideals. (In particular Q can be constructed with a given field as its centre.) As with their directly finite, SP(1), right self-injective counterparts, division rings, there are few obvious invariants apart from the centre.One reason perhaps why little interest has been shown in their structure is that the usual construction of such Q, namely as a suitable Qmax(R), is not concrete enough; in general R sits far too loosely inside Q and not enough information transfers to Q from R. Thus, for example, taking R to be a non-right-Ore domain and Q = Qmax(R) tells us little about Q (although it has been conjectured that all Q arise this way).
Compact 16-Dimensional Projective Planes with Large Collineation Groups. IV
Authors: Salzmann Helmut 
Published: December 2010

Let be a topological projective plane with compact point set P of finite (covering) dimension. In the compact-open topology (of uniform convergence), the group Σ of continuous collineations of is a locally compact transformation group of P.THEOREM. If dim Σ > 40, thenis isomorphic to the Moufang plane 6 over the real octonions (and dim Σ = 78).By [3] the translation planes with dim Σ = 40 form a one-parameter family and have Lenz type V. Presumably, there are no other planes with dim Σ = 40, cp. [17].
On the Sieve of Eratosthenes
Authors: Murty M. Ram , Saradha S. 
Published: December 2010

Let v(n) denote the number of distinct prime factors of a natural number n. A classical theorem of Hardy and Ramanujan states that the normal order of v(n) is log log n. That is, given any , the number of natural numbers not exceeding x which fail to satisfy the inequality1is o(x) as x → ∞. A very simple proof of this was subsequently given by Turán. He showed that2
Analysis on Root Systems
Authors: Debiard Amédée , Gaveau Bernard 
Published: December 2010

A great part of mathematical analysis relies directly on the methods of separation of variables and on the successive reduction of several variables problems to one-dimensional equations and to the theory of classical special functions; for example, the theory of elliptic or parabolic equations with regular coefficients (even with non constant coefficients) can be done because we know explicitly the fundamental solutions of the Laplace operator or of the heat equation; these fundamental solutions are functions of one variable; pseudodifferential or parametrices methods are thus basically small perturbations of an explicitly known problem in one variable.On the other hand, there are many problems which are not of this type: they are related to the questions of operators with singular coefficients and to the global behaviour of the solutions; in that case, the local model cannot be reduced to a one variable problem but is fundamentally a several variables problem which cannot be treated in a detailed way by one variable methods or perturbation analysis of a one variable problem.
Generalized Variation and Functions of Slow Growth
Authors: Berman Robert D. 
Published: December 2010

Many of the basic results of HP theory on the disk Δ = {|z| < 1} are proved using the Cauchy-Stieltjes representation1.1and the Poisson-Stieltjes representation1.2Here, μ:R → C is a complex-valued function of a real variable that is of bounded variation on [0, 2π] such that μ(t + 2π) = μ(t) + μ(2t) — μ(0), t ∊ R,is the Cauchy kernel, andis the Poisson kernel. It is therefore natural to generalize these representations in such a way that some of the basic properties and results carry over. Such a generalization occurs when the assumption that μ is of bounded variation on [0, 2μ] is replaced by the requirement that it is measurable and bounded on [0, 2μ] (cf. [9]). The integrals in (1.1) and (1.2) are then defined by a formal integration by parts. After some preliminaries in Section 2, we catalogue a variety of results which remain valid in Section 3.
Shape Equivalences of Whitney Continua of Curves
Authors: Kato Hisao 
Published: December 2010

By a compactum, we mean a compact metric space. A continuum is a connected compactum. A curve is a 1-dimensional continuum. Let X be a continuum and let C(X) be the hyperspace of (nonempty) subcontinua of X, C(X) is metrized with the Hausdorff metric (e.g., see [12] or [18]). One of the most convenient tools in order to study the structure of C(X) is a monotone map ω:C(X) → [0, ω(X)] defined by H. Whitney [25]. A map ω:C(X) → [0, ω(X)] is said to be a Whitney map for C(X) provided thatThe continua {ω−1} (0 < t < ω(X)) are called the Whitney continua of X. We may think of the map ω as measuring the size of a continuum. Note that ω−1(0) is homeomorphic to X and ω−1(ω(X)) = {X}. Naturally, we are interested in the structures of ω−1(t)(0 < t < ω(X)). In [14], J. Krasinkiewicz proved that if X is a circle-like continuum and ω is any Whitney map for C(X), then for any 0 < t < ω(X)ω−1(t) is shape equivalent to X, i.e., Sh ω−1(t) = Sh X (e.g., see [1] or [17]). In [8], we proved the following: If one of the conditions (i) and (ii) is satisfied, then the shape morphismwhich is defined in [7] and [8], is a shape equivalence.
On the Analytic Continuation of c-Functions
Authors: Ringseth Paul F. 
Published: December 2010

Let G be a reductive Lie group; Γ a nonuniform lattice in G. Then the theory of Eisenstein series plays a major role in the spectral decomposition of L2(G/Γ) (cf. [5]). One of the most difficult aspects of the subject is the analytic continuation of the Eisenstein series along with its associated c-function. This was originally done by Langlands using some very difficult analysis (cf. [5]). Later Harish-Chandra was able to simplify somewhat the most difficult part of the continuation, the continuation to zero, by the introduction of the Maas-Selberg relation. The purpose of this note is to give a simplified account of this particular part of the theory.Our chief tool will be the truncation operator of Arthur (cf. [1] and [8]), the systematic utilization of which has the effect of streamlining the earlier accounts, especially in so far as continuation to zero is concerned, which is reduced to an elementary manipulation.
Conjugates of Infinite Measure Preserving Transformations
Authors: Alpern S. , Choksi J. R. , Prasad V. S. 
Published: December 2010

In this paper we consider a question concerning the conjugacy class of an arbitrary ergodic automorphism σ of a sigma finite Lebesgue space (X, , μ) (i.e., a is a ju-preserving bimeasurable bijection of (X, , μ). Specifically we proveTHEOREM 1. Let τ, σ be any pair of ergodic automorphisms of an infinite sigma finite Lebesgue space (X, , μ). Let F be any measurable set such thatThen there is some conjugate σ' of σ such that σ'(x) = τ(x) for μ-almost every x in F.The requirement that F ∪ τF has a complement of infinite measure is, for example, satisfied when F has finite measure, and in that case, the theorem was proved by Choksi and Kakutani ([7], Theorem 6).Conjugacy theorems of this nature have proved to be very useful in proving approximation results in ergodic theory. These conjugacy results all assert the denseness of the conjugacy class of an ergodic (or antiperiodic) automorphism in various topologies and subspaces.
Maximal Homotopy Lie Subgroups of Maximal Rank
Authors: Frohliger John A. 
Published: December 2010

Let G be a compact connected Lie group with
H a connected subgroup of maximal rank. Suppose
there exists a compact connected Lie subgroup K with
H ⊂ K ⊂
G. Then there exists a smooth fiber bundle
G/H → G/K with
K/H as the fiber. (See for example
[13].) This can be incorporated into a diagram involving
the classifying spaces as follows:

(1)

Here π, ϕ, ϕ
1 and ϕ
2 denote fibrations. We also know that the homogeneous spaces
and the Lie groups, which are homotopy equivalent to the loop spaces of their
respective classifying spaces, are homotopy equivalent to connected finite
complexes.
Now suppose H is a maximal subgroup. Can there
still exist spaces, which we will call BK, K/H, and
G/K, and fibrations so that diagram (1) is still
valid? This paper will show that in many cases either
G/K or K/H will be homo
topically trivial.
Notions De Base Pour L'Arthmetique De Fq((1/t))
Authors: Hellegouarch Yves 
Published: December 2010

Le but de ce travail est de définir un certain nombre d'objets de
F

q
((1/t) et de fonctions

qui sont analogues à des objets classiques de R(ou
C) et à des fonctions classiques
R → R (ou
C → C) : par exemple
ζ(l), ζ(2), etc.,
fractions continues, domaine fondamental du “demi-plan” de Poincaré, séries
d'Eisenstein, fonctions multiplement périodiques.
Un tel travail avait été entrepris autrefois par E. Artin
[2], mais dans un autre esprit, et la fonction zéta que
j'ai définie dans [7] n'est pas celle d'Artin, mais celle
de Carlitz [3].
L'intersection de la thèse d'Artin et de ce travail n'est donc pas vide, mais
elle n'est pas non plus très étendue bien que je me sois limité aux définitions et
aux propriétés les plus élémentaires. En revanche, par son esprit, ce travail se
rapproche davantage du point de vue de Carlitz.
Certain Invariant Subspaces of H2 and L2 on a Bidisc
Authors: Nakazi Takahiko 
Published: December 2010

We let T2 be the torus that is the cartesian product of 2 unit circles in C. The usual Lebesgue spaces, with respect to the Haar measure m of T2, are denoted by Lp = Lp(T2), and Hp = Hp(T2) is the space of all f in LP whose Fourier coefficientsare 0 as soon as at least one component of (j, ℓ) is negative.A closed subspace M of L2 is said to be invariant ifWhenever this is the case, it follows that fM ⊂ M for every f in H∞. One can ask for a classification or an explicit description (in some sense) of all invariant subspaces of L2, but this seems out of reach.
Elementary Abelian Cartesian Groups Cartesian Groups
Authors: Hayden John L. 
Published: December 2010

Throughout the paper, G will denote an additively written, but not always abelian, group of finite order n; and X = (xij) will denote a square matrix of order n with entries from G and whose rows and columns are numbered 0, 1, …, n − 1. We call X a cartesian array (afforded by G) if(1.1) The sequence {−xmi + xki, i = 0,…, n – 1} contains all elements of G whenever k ≠ m.By a theorem of Jungnickel (see Theorem 2.2 in [5]), the transpose of a cartesian array is also a cartesian array. We call G a cartesian group if there is a cartesian array X afforded by G. In this case, we also call (G, X) a cartesian pair.
Products of Normal Operators
Authors: Wu Pei Yuan 
Published: December 2010

Which bounded linear operator on a complex, separable Hilbert space can be expressed as the product of finitely many normal operators? What is the answer if “normal” is replaced by “Hermitian”, “nonnegative” or “positive”? Recall that an operator T is nonnegative (resp. positive) if (Tx, x) ≧ 0 (resp. (Tx, x) ≥ 0) for any x ≠ 0 in the underlying space. The purpose of this paper is to provide complete answers to these questions.If the space is finite-dimensional, then necessary and sufficient conditions for operators expressible as such are already known. For normal operators, this is easy. By the polar decomposition, every operator is the product of two normal operators. An operator is the product of Hermitian operators if and only if its determinant is real; moreover, in this case, 4 Hermitian operators suffice and 4 is the smallest such number (cf. [10]).
The Modular Group Algebras of P-Groups of Maximal Class
Authors: Bagiński C. , Caranti A. 
Published: December 2010

The isomorphism problem for modular group algebras of finite p-groups appears to be still far from a solution (see [7] for a survey of the existing results). It is therefore of interest to investigate the problem for special classes of groups.The groups we consider here are the p-groups of maximal class, which were extensively studied by Blackburn [1]. In this paper we solve the modular isomorphism problem for such groups of order not larger than pp+1, having an abelian maximal subgroup, for odd primes p.What we in fact do is to generalize methods used by Passman [5] to solve the isomorphism problem for groups of order p4. In Passman's paper the case of groups of maximal class is actually the most difficult one.
Starlike Univalent Functions Bounded on the Real Axis
Authors: Fournier Richard 
Published: December 2010

We denote by E the open unit disc in C and by H(E) the class of all analytic functions f on E with f(0) = 0. Let (see [3] for more complete definitions)S = {ƒ ∈ H(E)|ƒ is univalent on E}S0 = {ƒ ∈ H(E)|ƒ is starlike univalent on E}TR = {ƒ ∈ H(E)|ƒ is typically real on E}.The uniform norm on (— 1, 1) of a function ƒ ∈ H(E) is defined by
Positive Forms on Nuclear *-Algebras and Their Integral Representations
Authors: Bélanger Alain , Thomas Erik G. F. 
Published: December 2010

Abstract.The main result of this paper establishes the existence and uniqueness of integral representations of KMS functionals on nuclear *- algebras. Our first result is about representations of *-algebras by means of operators having a common dense domain in a Hilbert space. We show, under certain regularity conditions, that (Powers) self-adjoint representations of a nuclear *-algebra, which admit a direct integral decomposition, disintegrate into representations which are almost all self-adjoint. We then define and study the class of self-derivative algebras. All algebras with an identity are in this class and many other examples are given. We show that if is a self-derivative algebra with an equicontinuous approximate identity, the cone of all positive forms on is isomorphic to the cone of all positive invariant kernels on These in turn correspond bijectively to the invariant Hilbert subspaces of the dual space This shows that if is a nuclear -space, the positive cone of has bounded order intervals, which implies that each positive form on has an integral representation in terms of the extreme generators of the cone. Given a continuous exponentially bounded one-parameter group of *-automorphisms of we can define the subcone of all invariant positive forms satisfying the KMS condition. Central functionals can be viewed as KMS functionals with respect to a trivial group action. Assuming that is a self-derivative algebra with an equicontinuous approximate identity, we show that the face generated by a self-adjoint KMS functional is a lattice. If is moreover a nuclear *-algebra the previous results together imply that each self-adjoint KMS functional has a unique integral representation by means of extreme KMS functionals almost all of which are self-adjoint.
Bicyclic Bicubic Fields
Authors: Parry Charles J. 
Published: December 2010

There is an extensive body of literature on the bicyclic biquadratic fields. These fields provide the simplest examples of abelian noncyclic extensions ofQ.In sharp contrast, there is a dearth of literature on the bicyclic bicubic extensions of the rational numbers. These fields together with the abelian noncyclic octic extensions provide the next simplest abelian noncyclic extensions.In this article, we shall study abelian bicyclic bicubic extensions ofQof degree 9. Hasse [4, v-ix] has stated as important objectives: the computation of an integral basis, the determination of class number and the calculation of fundamental units for abelian fields. In this article, we will solve the first problem completely, and show that the solution to the unit problem leads to a solution of the class number problem. Moreover, we shall give a method for determining the unit group up to a subgroup which has index 1 or 3 and so determine the class number up to a factor of 3.