bluuebunny/crossref_metadata_2025 huggingface dataset:
Resolvent Means and Inverting
Generalized Fourier Transforms
Authors: Raphael Louise A.
Published: December 2010

Let S-L denote a singular Sturm-Liouville system on the half line with homogeneous boundary conditions, possessing a discrete negative and continuous positive spectrum. Let A be the S-L operator and Sα(f; x) the S-L eigenfunction expansion associated with the resolvent operator (z – A)–1, z complex. That is, Sα(f; x) denotes the resolvent summability means with weight function z(z – λ)–1 (or (1 + tλ)–1 where t = – 1/z).

We first study the problem of determining when

(1)

where is the Green's function associated with a certain perturbation of our system.
Extremal Properties of Constrained Tchebychev Polynomials
Authors: Pierre R.
Published: December 2010

In the sequel, πn will denote the class of real polynomials of degree at most n and ‖f(x)‖∞ the L∞-norm of a function on [–l, +1].

In a series of recent papers, Saff and Varga studied the properties of the so-called incomplete polynomials; that is to say polynomials of the form

where sl and s2 are fixed integers and q ∊ πn.

In there, they define the constrained Tchebychev polynomial as being, up to a multiplicative constant, the solution of the following minimization problem
Porosity and Approximate Derivatives
Authors: Bruckner A. M. , Laczkovich M. , Petruska G. , Thomson B. S.
Published: December 2010

In recent years, a considerable amount of research has been devoted to questions involving set porosity, particularly as it relates to differentiation theory. We may express the type of question in which we are interested by using the language of path derivatives and sequential derivatives. A path derivative of a function/is defined by writing

where at each point x a set Ex is given. A special case of the path derivative is the sequential derivative, defined by writing

where hn is a fixed sequence of nonzero numbers converging to zero.
Sufficiency and the Jacobi Condition in the Calculus of Variations
Authors: Clarke Frank H. , Zeidan Vera
Published: December 2010

Besides stating the problem and the results, we shall give in this section a brief overview of the classical necessary and sufficient conditions in the calculus of variations, in order to clearly situate the contribution of this article.

1.1 The problem. We are given an interval [a, b], two points xa, xb in Rn, and a function L (the Lagrangian) mapping [a, b] × Rn × Rn to R. The basic problem in the calculus of variations, labeled (P), is that of minimizing the functional

over some class X of functions x and subject to the constraints x(a) = xa, x(b) = xb. Let us take for now the class X of functions to be the continuously differentiable mappings from [a, b] to Rn; we call such functions smooth arcs.
(0, 2) – Interpolation of Entire Functions
Authors: Gervais R. , Rahman Q. I. , Schmeisser G.
Published: December 2010

Given a triangular matrix A whose nth row consists of the n points

(1.1)

Turán et al. ([12], [1], [2], [3]) considered the problem of existence, uniqueness, representation, convergence, etc. of polynomials f2n – 1 of degree ≧2n – 1 where the values of f2n – 1 and those of its second derivative are prescribed at the points (1.1), i.e.,

(1.2)

The choice of the points (1.1) is important. They found the zeros

(1.3)

of the polynomial

(1.1)

where Pn – 1 is the (n − 1) Legendre polynomial with the normalization Pn – 1(l) = 1 to be the most convenient.
Massey Products and Lower Central Series of Free Groups
Authors: Fenn Roger , Sjerve Denis
Published: December 2010

The purpose of this paper is to continue the investigation into the relationships amongst Massey products, lower central series of free groups and the free differential calculus (see [4], [9], [12]). In particular we set forth the notion of a universal Massey product ≪α1, …, αk≫, where the αi are one dimensional cohomology classes. This product is defined with zero indeterminacy, natural and multilinear in its variables.

In order to state the results we need some notation. Throughout F will denote the free group on fixed generators x1, …, xn and

will denote the lower central series of F. If I = (i1, …, ik) is a sequence such that 1 ≦ i1, …, ik ≦ n then ∂1 is the iterated Fox derivative and , where is the augmentation. By convention we set ∂1 = identity if I is empty.
Shifts on Type II1 Factors
Authors: Price Geoffrey L.
Published: December 2010

A shift on a unital C*-algebras is a *-endomorphism α of which fixes the identity and has the property that the intersection of the ranges of αn for n = 1, 2, 3, … consists only of multiples of the identity. In [4] R. T. Powers introduced the notion of a shift on a C*-algebra and considered both discrete and continuous one-parameter semi-groups of shifts. In this paper we focus on discrete shifts. We use a construction of Powers to obtain shifts on certain unital AF C*-algebras. These are defined by constructing a set {ui:i = 1, 2, …} of self-adjoint unitary operators which pairwise either commute or anticommute. Setting α(ui) = ui + 1, determines an endomorphism on the group algebra generated by the ui's. This algebra is called a binary shift algebra. By passing to the (unique) C*-algebra completion we obtain an AF-algebra on which a defines a shift.
Contractive Representation Theory for the Unitary Group of C(X, M2)
Authors: Paterson Alan L. T.
Published: December 2010

One motivation for studying representation theory for the unitary group of a unital C*-algebra arises from Theoretical Physics. (In the latter connection, Segal [9] and Arveson [1] have developed a representation theory for G. Their approach is in a different direction from ours.) Another motivation for studying the representation theory of G arises out of the desire to unify the theories of amenable von Neumann algebras and amenable locally compact groups.

A serious problem for such a representation theory is the absence of Haar measure on G in general.

In [7], the author introduced the class RepdG of contractive unitary representations of G, the strong metric condition involved compensating for the lack of Haar measure.
Homologies de SHIH: Definition et Proprietes
Authors: Lalonde François
Published: December 2010

En 1977, Shih [8] a introduit, pour l'étude des sections d'une application f:X → A de classe Ck, où X et A sont des espaces de classe Ck avec 0 ≦ k ≦ ∞ (paragraphe 1), une nouvelle “homologie” appelée homologie sectionnelle (k-fois différentiable) permettant d'attacher à l'application f des invariants algébriques, et un invariant numérique quand A est une variété connexe, orientée et paracompacte, le degré sectionnel, plus fin que le degré classique.

Cette homologie, introduite d'abord dans le cadre de la résolution des systèmes d'équations aux dérivées partielles, intervient également dans les problèmes liés aux singularités des applications différentiables.
Character Correspondences and π-Special Characters in π-Separable Groups
Authors: Wolf Thomas R.
Published: December 2010

Let π be a set of primes and let G be a π-separable group (all groups considered are finite). Two subsets Xπ(G) and Bπ(G) of the set Irr(G) of irreducible characters of G play an important role in the character theory of π-separable groups and particularly solvable groups. If p is prime and π is the set of all other primes, then the Bπ characters of G give a natural one-to-one lift of the Brauer characters of G into Irr(G). More generally, they have been used to define Brauer characters for sets of primes.

The π-special characters of G (i.e., Xπ(G)) restrict irreducibly and in a one-to-one fashion to a Hall-π-subgroup of G. If an irreducible character χ is quasi-primitive, it factors uniquely as a product of a π-special character an a π′-special character. This is a particularly useful tool in solvable groups.
Decomposable Free Loop Spaces
Authors: Aguadé J.
Published: December 2010

In this paper we study the spaces X having the property that the space of free loops on X is equivalent in some sense to the product of X by the space of based loops on X. We denote by ΛX the space of all continuous maps from S1 to X, with the compact-open topology. ΩX denotes, as usual, the loop space of X, i.e., the subspace of ΛX formed by the maps from S1 to X which map 1 to the base point of X.

If G is a topological group then every loop on G can be translated to the base point of G and the space of free loops ΛG is homeomorphic to G × ΩG. More generally, any H-space has this property up to homotopy. Our purpose is to study from a homotopy point of view the spaces X for which there is a homotopy equivalence between ΛX and X × ΩX which is compatible with the inclusion ΩX ⊂ ΛX and the evaluation map ΛX → X.
Univalent and Starlike Generalized Hypergeometric Functions
Authors: Owa Shigeyoshi , Srivastava H. M.
Published: December 2010

A single-valued function f(z) is said to be univalent in a domain if it never takes on the same value twice, that is, if f(z1) = f(z2) for implies that z1 = z2. A set is said to be starlike with respect to the line segment joining w0 to every other point lies entirely in . If a function f(z) maps onto a domain that is starlike with respect to w0, then f(z) is said to be starlike with respect to w0. In particular, if w0 is the origin, then we say that f(z) is a starlike function. Further, a set is said to be convex if the line segment joining any two points of lies entirely in . If a function f(z) maps onto a convex domain, then we say that f(z) is a convex function in .
Dual Space Derivations and H2(L, F) of Modular Lie Algebras
Authors: Farnsteiner Rolf
Published: December 2010

It is well-known that the classical vanishing results of the cohomology theory of Lie algebras depend on the characteristic of the underlying base field. The theorems of Cartan and Zassenhaus, for instance, entail that non-modular simple Lie algebras do not admit non-trivial central extensions. In contrast, early results by Block [3] prove that this conclusion loses its validity if the underlying base field has positive characteristic.

Central extensions of a given Lie algebra L, or equivalently its second cohomology group H(L, F), can be conveniently described by means of derivations φ:L → L*.
Théorèmes de Convergence Locale Pour Les Résolvantes et Les Processus Abéliens à Plusieurs Paramètres
Authors: Boivin Daniel
Published: December 2010

En démontrant un lemme ergodique maximal pour une famille résolvante de contractions positives et propres de L1(σ) [5], D. Feyel a obtenu, entre autres, des théorèmes de dérivation pour les processus abéliens [7]. Grâce à un théorème taubérien, il peut déduire un théorème de convergence locale pour les processus additifs. Le but de cet article est de montrer que le lemme ergodique maximal de D. Feyel et une technique de réduction des paramètres, introduite par Dunford-Schwartz [4] et développée par Terrell [13] et Akcoglu-del Junco [1] permettent d'obtenir des théorèmes de dérivation pour les familles résolvantes à plusieurs paramètres. C'est ce qu'on fait à la Section 2. Le premier théorème ergodique local pour les semi-groupes de contractions a été obtenu par Krengel [10] et Ornstein [12]. A la Section 3, nous considérons les processus abéliens associés aux processus additifs qui ont été introduits dans [2] par Akcoglu et Krengel et dont les résultats ont ensuite été généralisés par Terrell [13], Akcoglu et del Junco [1], Emilion [5]. Comme dans le cas à un paramètre, à la Section 4, nous retrouvons un théorème local pour les processus additifs.
On the Structure of Certain Nest Algebra Modules
Authors: Knowles G. J.
Published: December 2010

Let be a nest algebra of operators on some Hilbert space H. Weakly closed -modules were first studied by J. Erdos and S. Power in [4]. It became apparent that many interesting classes of non self-adjoint operator algebras arise as just such a module. This paper undertakes a systematic investigation of the correspondence which arises between such modules and order homomorphisms from Lat into itself. This perspective provides a basis to answer some open questions arising from [4]. In particular, the questions concerning unique “determination” and characterization of maximal and minimal elements under this correspondence, are resolved. This is then used to establish when the determining homomorphism is unique.
The MOD 2 K-Homology of Ω3S3X
Authors: Mayorquin J. G.
Published: December 2010

In order to compute the group K*(Ω3S3X; Z/2) when X is a finite, torsion free CW-complex we apply the techniques developed by Snaith in [38], [39], [40], [41] which were used in [42] to determine the Atiyah-Hirzebruch spectral sequence ( [11], [1, Part III])

for X as above. Roughly speaking the method consists in defining certain classes in K*(Ω3S3X; Z/2) via the π-equivariant mod 2 K-homology of S2 × Y2,

([35]), π the cyclic group of order 2 (acting antipodally on S2, by permuting factors in Y2, and diagonally on S2 × Y2), Y a finite subcomplex of Ω3S3X, and then showing that the classes so produced map under the edge homomorphism to cycles (in the E1-term of the Atiyah-Hirzebruch spectral sequence for

which determine certain homology classes of H*(Ω3S3X; Z/2), thus exhibiting these as infinite cycles of the spectral sequence
K-Theory and Asymptotically Commuting Matrices
Authors: Loring Terry A.
Published: December 2010

To shed light on the following unsolved problem, several authors have considered related problems. The problem is that of finding commuting approximants to pairs of asymptotically commuting self-adjoint matrices:

Suppose that Hn and Kn are self-adjoint matrices of dimension m(n), with ║Hn║, ║Kn║ ≦ 1, which commute asymptotically in the sense that

Must there then exist commuting self-adjoint matrices H′n and K′n for which

One may alter the conditions imposed on Hn and Kn, for example, by requiring Hn to be normal and Kn to be self-adjoint, and ask whether commuting approximants H′n and K′n can be found satisfying the same conditions. Some of these related problems have been solved. This paper will examine their solutions from a K-theoretic point of view, illustrating the difficulty inherent in modifying them to work for the original problem.
On the Intersection of a Family of Maximal Subgroups Containing the Sylow Subgroups of a Finite Group
Authors: Mukherjee N. P. , Bhattacharya Prabir
Published: December 2010

Given a finite group G, the Frattini subgroup of G, Φ(G) is defined to be the intersection of all the maximal subgroups of G. Of late there have been several attempts to consider generalizations of Φ(G). For example, Gaschutz [7] and Rose [13] have investigated the intersection of all non-normal, maximal subgroups of a finite group. Deskins [6] has discussed the intersection of the family of maximal subgroups of a finite group whose indices are co-prime to a given prime. In [4-5, 12] we have considered the investigation of the family of all maximal subgroups of a finite group whose indices are composite and co-prime to a given prime. We have obtained several results about the family . In this paper which is a sequel to [4] we prove some further results about this family indicating the interesting role it plays especially when G is solvable or p-solvable. First we recall the main definition from [4].
The Eta Invariant and Equivariant SpinC Bordism for Spherical Space form Groups
Authors: Gilkey Peter B.
Published: December 2010

A finite group G is a spherical space form group if it admits a fixed point free representation τ:G → U(k) for some k; for the remainder of this paper, we assume G is such a group. The eta invariant of Atiyah et al [2] defines Q/Z valued invariants of equivariant bordism. In [6], we showed the eta invariant completely detects the reduced equivariant unitary bordism groups and completely detects all but the 2-primary part of the reduced equivariant SpinC bordism groups . The coefficient ring is without torsion; all the torsion in is of order 2. The prime 2 plays a distinguished role in the discussion of equivariant SpinC bordism and is quite different from at the prime 2. Let ker*(η, G) denote the kernel of all eta invariants and let ker*(SW, G) denote the kernel of the Z2-equivariant Stiefel-Whitney numbers (see Section 1 for details). Then:

THEOREM 0.1. Let. If M = ker*(η, G) ∩ ker*(SW, G), M = 0.
Large Deviations for Gaussian Stochastic Processes with Sample Paths in Orlicz Spaces
Authors: Lawniczak Anna T.
Published: December 2010

Let X be a complete, separable metric space, and a family of probability measures on the Borel subsets of X. We say that obeys the large deviation principle (LDP) with a rate function I( · ) if there exists a function I( · ) from X into [0, ∞] satisfying:

(i) 0 ≦ I(x) ≦ ∞ for all x ∊ X,

(ii) I( · ) is lower semicontinuous,

(iii) for each 1 < ∞ the set {x:I(x) ≦ 1} is compact set in X,

(iv) for each closed set C ⊂ X

(v) for each open set U ⊂ X

It is easy to see that if A is a Borel set such that

then

where A0 and Ā are respectively the interior and the closure of the Borel set A.
Linearization and Boundary Trajectories of Nonsmooth Control Systems
Authors: Frankowska H. , Kaśkosz B.
Published: December 2010

This paper deals with boundary trajectories of non-smooth control systems and differential inclusions.

Consider a control system

(1.1)

and denote by R(t) its reachable set at time t. Let (z, u*) be a trajectory-control pair. If for every t from the time interval [0, 1], z(t) lies on the boundary of R(t) then z is called a boundary trajectory. It is known that for systems with Lipschitzian in x right-hand side, z is a boundary trajectory if and only if z(1) belongs to the boundary of the set R(1). If z is not a boundary trajectory, that is, z(1) ∊ Int R(1) then the system is said to be locally controllable around z at time 1.

A first-order necessary condition for boundary trajectories of smooth systems comes from the Pontriagin maximum principle, (see e.g. [12]).
On Divisors of Sums of Integers IV
Authors: Sárközy A. , Stewart C. L.
Published: December 2010

Throughout this article c
0, c
1, c
2, … will denote effectively computable positive absolute
constants. Denote the cardinality of a set X by
|X|. Let N be a positive
integer and let A and B be
non-empty subsets of {1, …,N}. Put

In [3], Balog and Sá;rközy proved that if
N > c
0 and

(1)

then there exist a
0 and b
0 with a
0 ∊ A
0 and b
0 ∊ B
0 and a prime number p such
that

and

(2)

If follows from this result that if |A| ≫
N and |B| ≫
N then there exist a in
A and b in
B and a prime p such that
p
2|(a +
b) with
Semicontinuity and Multipliers of C*-Algebras
Authors: Brown Lawrence G.
Published: December 2010

In [5] C. Akemann and G. Pedersen defined four
concepts of semicontinuity for elements of A**, the
enveloping W*-algebra of a
C*-algebra A. For three of
these the associated classes of lower semicontinuous elements are
, and
(notation
explained in Section 2), and we will call these the classes of
strongly lsc, middle lsc,
and weakly lsc elements, respectively. There are three
corresponding concepts of continuity: The strongly continuous elements are the
elements of A itself, the middle continuous elements
are the multipliers of A, and the weakly continuous
elements are the quasi-multipliers of A. It is natural
to ask the following questions, each of which is three-fold.

(Q1) Is every lsc element the limit of a monotone increasing net of
continuous elements?

(Q2) Is every positive lsc element the limit of an increasing net of positive
continuous elements?

(Q3) If h ≧ k, where
h is lsc and k is usc,
does there exist a continuous x such that
h ≧ x ≧
k?
Cyclic Cohomology of Non-Commutative Tori
Authors: Nest Ryszard
Published: December 2010

In this paper we shall compute the cyclic cohomology of a non-commutative torus, i.e., a certain algebra associated with an antisymmetric bicharacter of a finite rank free abelian group G.

The main result is

1.1

where

The method of computation generalises the computation of the cyclic cohomology of the irrational rotation algebras given by Connes in [3]. (Our method works equally well also in the rational case, which was dealt with by a different method by Connes in [3].)

We first describe the Hochschild cohomology of in an explicit way, and then combine this description with the exact sequence of [3]:

1.2
The Empty Sphere Part II
Authors: Ryshkov S. S. , Erdahl R. M.
Published: December 2010

Blow up a sphere in one of the interstices of a lattice until it is held rigidly. There will be no lattice points in the interior and sufficiently many on the boundary so that their convex hull is a solid figure. Such a sphere was called an empty sphere by B. N. Delone in 1924 when he introduced his method for lattice coverings [3, 4]. The circumscribed polytope is called an L-polytope. Our interest in such matters stems from the following result [6, Theorems 2.1 and 2.3]: With a list of the L-polytopes for lattices of dimension ≦n one can give a geometrical description of the possible sets of integer solutions of

where f satisfies the following condition (in which Z denotes the integers):
Gorenstein Witt Rings
Authors: Fitzgerald Robert W.
Published: December 2010

Throughout R is a noetherian Witt ring. The basic example is the Witt ring WF of a field F of characteristic not 2 and finite. We study the structure of (noetherian) Witt rings which are also Gorenstein rings (i.e., have a finite injective resolution). The underlying motivation is the elementary type conjecture. The Gorenstein Witt rings of elementary type are group ring extensions of Witt rings of local type. We thus wish to compare the two classes of Witt rings: Gorenstein and group ring over local type. We show the two classes enjoy many of the same properties and are, in several cases, equal. However we cannot decide if the two classes are always equal.

In the first section we consider formally real Witt rings R (equivalently, dim R = 1). Here the total quotient ring of R is R-injective if and only if R is reduced. Further, R is Gorenstein if and only if R is a group ring over Z. This result appears to be somewhat deep.
Radial Entire Solutions of Even Order Semilinear Elliptic Equations
Authors: Kusano Takaŝi , Naito Manabu , Swanson Charles A.
Published: December 2010

Semilinear elliptic partial differential equations of the type

1

will be considered throughout real Euclidean N-space, where m ≧ 2 is a positive integer, Δ denotes the N-dimensional Laplacian, and f is a real-valued continuous function in [0, ∞) × (0, ∞). Detailed hypotheses on the structure of f are listed in Section 3.

Our objective is to prove the existence of radially symmetric positive entire solutions u(x) of (1) which are asymptotic to positive constant multiples of |x|2m−2i as |x| → ∞ for every i = 1,…, m, N ≧ 2i + 1.
On the Mapping Theorem for Lusternik-Schnirelmann Category II
Authors: Félix Yves , Lemaire Jean-Michel
Published: December 2010

Let X and Y be 1-connected spaces having the homotopy type of cw-complexes.

Definition 0.1. A continuous map f:X → Y is Ω-split if Ωf:ΩX → ΩY admits a retraction up to homotopy.

In [6] we prove the following “mapping theorem”:

THEOREM 0.1. (a) If f is Ω-split, then cat(X) ≦ cat(Y);

(b) If π*(f) is split injective and ΩY has the homotopy type of a product of Eilenberg-MacLane spaces, then f is Ω-split.
Pairs of Rings with the Same Prime Ideals, II
Authors: Anderson David F. , Dobbs David E.
Published: December 2010

Much of [2] was devoted to studying pairs of subringsA⊂Bof a field with the property thatAandBhave the same prime ideals. In this paper, we continue that investigation, but we no longer assume thatAandBare comparable. Interestingly, most of the results of [2] carry over to this more general context. Besides such extensions of [2], additional motivation for the more general context comes from the need to explicate some naturally occurring examples (see Examples 2.5, 3.6, and 4.3).

Section 2 begins by showing that we may reduce to the case in whichRis a quasilocal domain with nonzero maximal idealMand quotient fieldK. Proposition 2.3 establishes that the setC(R)of all subringsAofKwith Spec(A) = Spec(R) forms a complete semilattice.
Spectral Analysis on Upper Light Cone in R3 and the Radon Transform
Authors: Wawrzyñczyk Antoni
Published: December 2010

The upper light cone L in R3 is a homogeneous space of the 3-dimensional Lorentz group G. It may be identified with the space of horocycles in the upper hyperboloide H which is the symmetric space associated to G. There exists a duality between H and L (see [5] p. 144) and a general procedure leads to a generalized Radon transform:

and the dual Radon transform

These operations commute with the natural action of the group G.
Ergodic Actions of Compact Groups on Operator Algebras II: Classification of Full Multiplicity Ergodic Actions
Authors: Wassermann Antony
Published: December 2010

In the first paper of this series [17], we set up some general machinery for studying ergodic actions of compact groups on von Neumann algebras, namely, those actions for which . In particular we obtained a characterisation of the full multiplicity ergodic actions:

THEOREM A. If α is an ergodic action of G on , then the following conditions are equivalent:

(1) Each spectral subspace has multiplicity dim π for π in .

(2) Each π in admits a unitary eigenmatrix in .

(3) The W* crossed product is a (Type I) factor.

(4) The C* crossed product of the C* algebra of norm continuity is isomorphic to the algebra of compact operators on a Hilbert space.
Coprime Group Actions Fixing All Nonlinear Irreducible Characters
Authors: Isaacs I. M.
Published: December 2010

The main result of this paper is the following:

Theorem A. Let H and N be finite groups with coprime orders andsuppose that H acts nontrivially on N via automorphisms. Assume that Hfixes every nonlinear irreducible character of N. Then the derived subgroup ofN is nilpotent and so N is solvable of nilpotent length≦ 2.

Why might one be interested in a situation like this? There has been considerable interest in the question of what one can deduce about a group Gfrom a knowledge of the set

cd(G) = ﹛x(l)lx ∈ Irr(G) ﹜

of irreducible character degrees of G.Recently, attention has been focused on the prime divisors of the elements of cd(G). For instance, in [9], O. Manz and R. Staszewski consider π-separable groups (for some set π of primes) with the property that every element of cd(G) is either a 77-number or a π'-number.
Multiplication Operators
Authors: Schechter Martin
Published: December 2010

Let V(x) ≧ 0 be given on Rn and define

This constant has played a role in many investigation. For n — 3 it was shown in Courant-Hilbert [7] p. 446 that In [10], Kato estimates C2,2,2,ƛ(V) in terms of the L2 +L∞ norm of V in R3. Stummel [22] showed that C2,2,2,1(V) is bounded by in Rn, n > 2, provided α < 4. Browder [6] and Balslev [3] showed that Cs,q,q,ƛ(V) is bounded by
Weakly Close-to-Convex Meromorphic Functions
Authors: Landau-Treisner Laurellen , Livingston Albert E.
Published: December 2010

Classes of functions, meromorphic and univalent in

Δ = {z:|z|< 1}

with simple pole at z = p, 0 < p < 1, have been discussed in several places in the literature ([3], [6], [8], [10], [11], and [12]). The purpose of this paper is to discuss a class of Close-to-Convex functions with pole at p analogous to the class of Close-to-Convex functions with pole at zero studied by Libera and Robertson [9].
On the Structure of Projections and Ideals of Corona Algebras
Authors: Zhang Shuang
Published: December 2010

If K is the set of all compact bounded operators and L(H) is the set of all bounded operators on a separable Hilbert space H, then L(H) is the multiplier algebra of K. In general we denote the multiplier algebra of a C*-algebra A by M(A). For more information about M(A), readers are referred to the articles [1], [3],[7], [9], [14], [18],[20], [23], [26], [27], among others. It is well known that in the Calkin algebra L(H)/K every nonzero projection is infinite. If we assume that A is a-unital (nonunital) and regard the corona algebra M(A)/A as a generalized case of the Calkin algebra, is every nonzero projection in M(A)/A still infinite? Another basic question can be raised: How does the (closed) ideal structure of A relate to the (closed) ideal structure of M(A)/A?

In the first part of this note (Sections 1 and 2) we shall give an affirmative answer for the first question if A is a simple a-unital (nonunital) C*-algebra with FS.
Boundary Interpolation for Continuous Holomorphic Functions
Authors: Cohn William S.
Published: December 2010

Let Bn denote the unit ball in Cn with boundary S. We will be concerned with spaces of holomorphic functions on Bn and will use much of the notation and terminology found in W. Rudin's book [16]. Thus, if f is holomorphic in Bn and has homogeneous polynomial expansion

the radial derivative of f is given by
The Non-Existence of Finite Projective Planes of Order 10
Authors: Lam C. W. H. , Thiel L. , Swiercz S.
Published: December 2010

A finite projective plane of order n, with n > 0, is a collection of n2+ n + 1 lines and n2+ n + 1 points such that

1. every line contains n + 1 points,

2. every point is on n + 1 lines,

3. any two distinct lines intersect at exactly one point, and

4. any two distinct points lie on exactly one line.

It is known that a plane of order n exists if n is a prime power. The first value of n which is not a prime power is 6. Tarry [18] proved in 1900 that a pair of orthogonal latin squares of order 6 does not exist, which by Bose's 1938 result [3] implies that a projective plane of order 6 does not exist.
On a Stein And Weiss Property of the Conjugate Function
Authors: Asmar Nakhlé
Published: December 2010

(1.1) The conjugate function on locally compact abelian groups. Let G be a locally compact abelian group with character group Ĝ. Let μ denote a Haar measure on G such that μ(G) = 1 if G is compact. (Unless stated otherwise, all the measures referred to below are Haar measures on the underlying groups.) Suppose that Ĝ contains a measurable order P: P + P ⊆P; PU(-P)= Ĝ; and P⋂(—P) =﹛0﹜. For ƒ in ℒ2(G), the conjugate function of f (with respect to the order P) is the function whose Fourier transform satisfies the identity for almost all χ in Ĝ, where sgnP(χ)= 0, 1, or —1, according as χ =0, χ ∈ P\\﹛0﹜, or χ ∈ (—P)\﹛0﹜.
The Pexider Functional Equations in Distributions
Authors: Deeba E. Y. , Koh E. L.
Published: December 2010

The Cauchy functional equations have been studied recently for Schwartz distributions by Koh in [3]. When the solutions are locally integrate functions, the equations reduce to the classical Cauchy equations (see [1]):

(1) f(x+y)=f﹛x)+f(y)

(2) f(x+y)=f(x)f(y)

(3) f(xy)=f(x)+f(y)

(4) f(xy)=f(x)f(y).

Earlier efforts to study functional equations in distributions were given by Fenyö [2]for the Hosszu’ equations

f(x + y - xy) +f(xy) =f(x) +f (y ),

by Neagu [4]for the Pompeiu equation

f(x+y+xy)=f(x)+f(y)+f(x)f(y)

and by Swiatak [6].
Disjointly Additive Operators and Modular Spaces
Authors: Labuda Iwo
Published: December 2010

By now the literature concerning the representation of disjointly additive functionals and operators is quite extensive. A few entries on the subject are [6, 7, 8, 11, 20, 21]. In [7, 8, 17] further references can be found, in [7] the “prehistory” of the subject is also discussed.

To quote a typical result, we may take a 1967 theorem of Drewnowski and Orlicz ([6] Th. 3.2, [17] 12.4) which asserts that, under proper assumptions, an abstract modular (= disjointly countably additive functional) p on a “substantial“ subspace D of L° can be realized by the formula .
Proto-Differentiation of Subgradient Set-Valued Mappings
Authors: Poliquin René A.
Published: December 2010

Set-valued mappings arise quite naturally in optimization and nonsmooth analysis. In optimization, typically one has a family of optimization problems that depend on some parameter. One can then associate to this family of problems the set-valued mappings that assign to the parameter the set of optimal solutions, the set of feasible solutions or the set of multipliers. Many of these set-valued mappings encountered in optimization have been shown to be “proto-differentiable” (see Rockafellar [16]) i.e., in some sense these set-valued mappings are “differentiable”. Using estimates provided by the proto-derivatives, see Proposition 2.1, one can then obtain information on how the sets depend on the parameter. The concept of proto-differentiation is described in Section 2.
Sur Une Formule de Ramanujan-Bailey
Authors: Zeng Jiang
Published: December 2010

L'identité de Ramanujan-Bailey, qui établit une relation symétrique entre deux séries hypergéométriques 3F2, est généralisée en une relation symétrique entre deux séries hypergéométriques 4F3. On construit également un modèle symétrique qui rend compte de cette symétrie.
Two Families of Associated Wilson Polynomials
Authors: Ismail M. E. H. , Letessier J. , Valent G. , Wimp J.
Published: December 2010

Two families of associated Wilson polynomials are introduced. Both families are birth and death process polynomials, satisfying the same recurrence relation but having different initial conditions. Contiguous relations for generalized hypergeometric functions of the type 7F6 are derived and used to find explicit representations for the polynomials and to compute the corresponding continued fractions. The absolutely continuous components of the orthogonality measures of both families are computed. Generating functions are also given.
Restricting Representations of Completely Solvable Lie Groups
Authors: Lipsman R. L.
Published: December 2010

We are concerned here with the problem of describing the direct integral decomposition of a unitary representation obtained by restriction from a larger group. This is the dual problem to the more commonly investigated problem of decomposing induced representations. In this paper we work in the context of completely solvable Lie groups—more general than nilpotent, but less general than exponential solvable. Moreover, the groups involved are simply connected. The restriction problem was considered originally in [2] and in [6] for nilpotent groups.
Weighted Interpolation Inequalities and Embeddings in Rn
Authors: Brown R. C. , Hinton D. B.
Published: December 2010

This paper is a continuation of [3] which initiated a systematic study of sufficient conditions for the weighted interpolation inequality of sum form, 1.1 to hold. Here ϕ, θ are non-negative functions of m, j, p, q, r, Ω is a bounded or unbounded domain in Rn, ∊ belongs to an interval Γ=(0, ∊0), u is in a certain Banach space E(Ω), and N, W, P are measurable real functions satisfying N≧ 0, W, P > 0, as well as additional conditions stated below. Finally the constant K does not depend on u although it may depend on the other parameters.
Eigenvalues of the Curvature Operator for Certain Homogeneous Manifolds
Authors: D'Atri J. E. , Miatello I. Dotti
Published: December 2010

Given a Riemannian manifold M, the Riemann tensor R induces the curvature operator on the exterior power of the tangent space, defined by the formula where the inner product is defined by From the symmetries of R, it follows that ρ is self-adjoint and so has only real eigenvalues. R also induces the sectional curvature function K on 2-planes in is an orthonormal basis of the 2-plane π.
On Rings with a Certain Type of Factorization and Compact Riemann Surfaces
Authors: Ripoll Pascual Cutillas
Published: December 2010

Let be a compact Riemann surface, be the complement of a nonvoid finite subset of and A() be the ring of finite sums of meromorphic functions in with finite divisor. In this paper it is proved that every nonzero f ∈ A() can be decomposed as a product αβ, where α is either a unit or a product of powers of irreducible elements of A(), uniquely determined by f up to multiplication by units, and β is a product of functions of the type eφ – 1, with φ holomorphic and nonconstant in . Furthermore, a similar result is obtained for a certain class of subrings of A().
On The Convolution of a Box Spline With a Compactly Supported Distribution: Linear Independence for the Integer Translates
Authors: Chui Charles K. , Ron Amos
Published: December 2010

The problem of linear independence of the integer translates of μ * B, where μ is a compactly supported distribution and B is an exponential box spline, is considered in this paper. The main result relates the linear independence issue with the distribution of the zeros of the Fourier-Laplace transform, of μ on certain linear manifolds associated with B. The proof of our result makes an essential use of the necessary and sufficient condition derived in [12]. Several applications to specific situations are discussed. Particularly, it is shown that if the support of μ is small enough then linear independence is guaranteed provided that does not vanish at a certain finite set of critical points associated with B. Also, the results here provide a new proof of the linear independence condition for the translates of B itself.
Boolean Congruence Lattices of Orthodox Semigroups
Authors: Auinger Karl
Published: December 2010

The problem of characterizing the semigroups with Boolean congruence lattices has been solved for several classes of semigroups. Hamilton [9] and the author of this paper [1] studied the question for semilattices. Hamilton and Nordahl [10] considered commutative semigroups, Fountain and Lockley [7,8] solved the problem for Clifford semigroups and idempotent semigroups, in [1] the author generalized their results to completely regular semigroups. Finally, Zhitomirskiy [19] studied the question for inverse semigroups.
Positive Definite and Related Functions on Hypergroups
Authors: Bloom Walter R. , Ressel Paul
Published: December 2010

In this paper we make use of semigroup methods on the space of compactly supported probability measures to obtain a complete Lévy-Khinchin representation for negative definite functions on a commutative hypergroup. In addition we obtain representation theorems for completely monotone and completely alternating functions. The techniques employed here also lead to considerable simplification of the proofs of known results on positive definite and negative definite functions on hypergroups.
The Weyl-Von Neumann Theorem for Multipliers Of Some Af-Algebras
Authors: Higson Nigel , Rørdam Mikael
Published: December 2010

A well known theorem of Weyl-von Neumann asserts that if X is a self-adjoint operator acting on a separable Hilbert space, then there is a decomposition 1 = Σ en of the identity into finite rank projections so that we may write X = Σ ƛnen + y, where the ƛnare scalars and y is a compact operator with small norm. In other words, X can be approximately diagonalized.
On Induced Operators
Authors: Bradley R. E.
Published: December 2010

We show that when a positive contraction of type (p, q) is equipped with a positive norming function having full support, then it is related in a natural way to operators on other Lp spaces.
Ramanujan Congruences For p-k(n) Modulo Powers Of 17
Authors: Hughes Kim
Published: December 2010

For each integer r we define the sequence pr(n) by We note that p-1(n) = p(n), the ordinary partition function. On account of this some authors set r = — k to make positive values of k correspond to positive powers of the generating function for p(n): We follow this convention here. In [3], Atkin proved the following theorem.
Structure of р-Solvable Groups With Three р-Regular Classes
Authors: Ninomiya Yasushi
Published: December 2010

One of the important invariants of a р-block B of a group algebra is ℓ (B), the number of non-isomorphic simple B-modules. A number of authors calculated ℓ (B) for various types of defect groups of B. In particular, by Olsson [6], it has been proved that if p = 2 and the defect groups of the block B are dihedral or semi-dihedral or generalized quaternion, then ℓ (B) is at most 3. In this paper, we restrict our attention to the principal p-block B0 of a finite р-solvable group with ℓ (B0) ≤ 3. Let Γ be a finite р-solvable group and k a splitting field for Γ with characteristic р.
Homotopy Theory of Diagrams and CW-Complexes Over a Category
Authors: Piacenza Robert J.
Published: December 2010

The purpose of this paper is to introduce the notion of a CW complex over a topological category. The main theorem of this paper gives an equivalence between the homotopy theory of diagrams of spaces based on a topological category and the homotopy theory of CW complexes over the same base category.

A brief description of the paper goes as follows: in Section 1 we introduce the homotopy category of diagrams of spaces based on a fixed topological category. In Section 2 homotopy groups for diagrams are defined. These are used to define the concept of weak equivalence and J-n equivalence that generalize the classical definition. In Section 3 we adapt the classical theory of CW complexes to develop a cellular theory for diagrams. In Section 4 we use sheaf theory to define a reasonable cohomology theory of diagrams and compare it to previously defined theories. In Section 5 we define a closed model category structure for the homotopy theory of diagrams. We show this Quillen type homotopy theory is equivalent to the homotopy theory of J-CW complexes. In Section 6 we apply our constructions and results to prove a useful result in equivariant homotopy theory originally proved by Elmendorf by a different method.
Points of Spherical Maxima and Solvability of Semilinear Elliptic Equations
Authors: Schechter Martin , Tintarev Kyril
Published: December 2010

We give mild sufficient conditions on a nonlinear functional to have eigenvalues. These results are intended for the study of boundary value problems for semilinear elliptic equations.
A Criterion of Convergence of Generalized Processes and an Application to a Supercritical Branching Particle System
Authors: Fernández Begoña , Gorostiza Luis G.
Published: December 2010

The problem of convergence in distribution of a large class of generalized semimartingales to a continuous process is considerably simplified by a recent theorem of Aldous [1], in conjunction with a result of Cremers and Kadelka [3] on convergence of integral functional, and the results of Mitoma [15] and Fouque [8] for generalized processes. We will give a convenient convergence criterion in this setting. The proof amounts to a direct combination of the results of the abovementioned authors, requiring only a minor extension (of a special case) of the theorem of Cremers and Kadelka.
Probleme De Cauchy a Deux Variables Fuchsiennes
Authors: Madi Nour Saïd
Published: December 2010

Nous allons considérer ici un opérateur de Cauchy à deux variables Fuchsiennes de la forme: Puis nous allons chercher, sous certaines conditions d'hyperbolicité sur les racines caractéristiques Fuchsiennes, des solutions de l'équation 𝓟u = f, dans le cas o ù ƒ est régulière par rapport aux variables Fuchsiennes et analytique par rapport aux autres.

Baouendi et Goulaouic ont traité dans [1] ce même type d'opérateurs dans le cas d'une seule variable Fuchsienne. Dans [3] a été étudié le cas de plusieurs variables Fuchsiennes pour certains opérateurs de Goursat.
Complex Weight Functions for Classical Orthogonal Polynomials
Authors: Ismail Mourad E. H. , Masson David R. , Rahman Mizan
Published: December 2010

We give complex weight functions with respect to which the Jacobi, Laguerre, little q-Jacobi and Askey-Wilson polynomials are orthogonal. The complex functions obtained are weight functions in a wider range of parameters than the real weight functions. They also provide an alternative to the recent distributional weight functions of Morton and Krall, and the more recent hyperfunction weight functions of Kim.
Gyroscopically Stabilized Systems: A Class Of Quadratic Eigenvalue Problems With Real Spectrum
Authors: Barkwell Lawrence , Lancaster Peter , Markus Alexander S.
Published: December 2010

Eigenvalue problems for selfadjoint quadratic operator polynomials L(λ) = Iλ2 + Bλ+ C on a Hilbert space H are considered where B, C∈ℒ(H), C >0, and |B| ≥ kI + k-l C for some k >0. It is shown that the spectrum of L(λ) is real. The distribution of eigenvalues on the real line and other spectral properties are also discussed. The arguments rely on the well-known theory of (weakly) hyperbolic operator polynomials.
Lower Bounds for Matrices, II
Authors: Bennett Grahame
Published: December 2010

Our main result is the following monotonicity property for moment sequences μ. Let p be fixed, 1 ≤ p < ∞: then

is an increasing function of r(r = 1,2,…). From this we derive a sharp lower bound for an arbitrary Hausdorff matrix acting on ℓp.The corresponding upper bound problem was solved by Hardy.
A Criterion for Versality Of Deformations of Tubular Neighborhoods of Strongly Pseudo Convex Boundaries
Authors: Akahori Takao
Published: December 2010

We extend the famous Kodaira-Spencer's completeness theorem for a family of deformations of complex structures (see [12]). As an application, we show that the canonical family constructed in [9] is versai.
Doubling Constructions in Lattice Theory
Authors: Day Alan
Published: December 2010

This paper examines the simultaneous doubling of multiple intervals of a lattice in great detail. In the case of a finite set of W-failure intervals, it is shown that there in a unique smallest lattice mapping homomorphically onto the original lattice, in which the set of W-failures is removed. A nice description of this new lattice is given. This technique is used to show that every lattice that is a bounded homomorphic image of a free lattice has a projective cover. It is also used to give a sufficient condition for a fintely presented lattice to be weakly atomic and shows that the problem of which finitely presented lattices are finite is closely related to the problem of characterizing those finite lattices with a finite W-cover.
Univalent Harmonic Ring Mappings Vanishing on the Interior Boundary
Authors: Hengartner Walter , Szynal Jan
Published: December 2010

We give a characterization of univalent positively oriented harmonic mappings ƒ defined on an exterior neighbourhood of the closed unit disk { z: | z| ≤1} such that .
Continuations of Riemann Surfaces
Authors: Sakai Makoto
Published: December 2010

We shall show that if a Riemann surface is continuable, then it admits one of three types of continuations. Using this classification of continuations, we construct two nontrivial examples of two-sheeted unlimited covering Riemann surfaces of the unit disk one of which is continuable and the other is not.
On Nonabelian H2 for 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 groups together with a section j : G → E of K satisfying: for some open normal subgroup Sof G, and the map is continuous (A being discrete).
A Bivariant Chern Character, II
Authors: Wang Xiaolu
Published: December 2010

In [Con2] Connes introduced cyclic cohomology HC*(A) for an associative algebra A. When A is a complex algebra he constructed a Chern character for p-summable Fredholm modules over A taking values in HC*(A). As a very special case, when X is a closed C∞-manifold and A = C∞ (X), this construction recovers the usual Chern character, which is a rational isomorphism from the K-homology K0(X) to , the even dimensional deRham homology of X.
The Real Spectrum of Higher Level of a Commutative Ring
Authors: Barton Susan Maureen
Published: December 2010

The following paper defines a new type of ordering of higher level on a commutative ring. This definition allows the set of all orderings of levelnto be given a topology which we show is consistent with the topology of the real spectrum.
Slicings, Selections and Their Applications
Authors: Ghoussoub N. , B. Maurey  , Schachermayer W.
Published: December 2010

In the past few years, much progress have been made on several open problems in infinite dimensional Banach space theory. Here are some of the most recent results:

1)

The existence of boundedly complete basic sequences in a large class of Banach spaces including the ones with the so-called Radon-Nikodym property ([G-M2], [G-M4]).

2)

The embedding of separable reflexive Banach spaces into reflexive spaces with basis (fZl).

3)

The existence of long sequences of projections and hence of locally uniformly convex norms in the duals of Asplund spaces. ([F-G])