bluuebunny/crossref_metadata_2025_split huggingface dataset:
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 forwhich 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 thatMust there then exist commuting self-adjoint matrices H′n and K′n for whichOne 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.
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 ⊂ XIt is easy to see that if A is a Borel set such thatthenwhere 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]).
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 is1.1whereThe 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 ofwhere 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 type1will 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 transformThese 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 setcd(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 defineThis 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 inΔ = {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 expansionthe 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 that1. every line contains n + 1 points,2. every point is on n + 1 lines,3. any two distinct lines intersect at exactly one point, and4. 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.
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’ equationsf(x + y - xy) +f(xy) =f(x) +f (y ),by Neagu [4]for the Pompeiu equationf(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 .
Sur Une Formule de Ramanujan-Bailey
Authors: Zeng Jiang 
Published: December 2010

RésuméL'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

AbstractTwo 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.
On Rings with a Certain Type of Factorization and Compact Riemann Surfaces
Authors: Ripoll Pascual Cutillas 
Published: December 2010

AbstractLet 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

AbstractThe 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.
Positive Definite and Related Functions on Hypergroups
Authors: Bloom Walter R. , Ressel Paul 
Published: December 2010

AbstractIn 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.
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.
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

AbstractWe 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

AbstractEigenvalue 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

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