bluuebunny/crossref_metadata_2025_split huggingface dataset:
Geometric and Topological Properties of Certain w* Compact Convex sets which Arise from the Study of Invariant Means
Authors: Granirer Edmond E. 
Published: December 2010

Let E be a Banach space, A a subset of its dual E*.x0 ∊ A is said to be a w*Gδ point of A if there are xn ∊ E and scalars γn, n = 1,2, 3 … such thatDenote by w*Gδ{A} the set of all w*Gδ points of A.
If S is a semigroup of maps on E* and K ⊂ E*, denote byi.e., the set of points x* in the w*closure of K which are fixed points of S (i.e., sx* = x* for each s in S}. An operator will mean a bounded linear map on a Banach space and Co B will denote the convex hull of B ⊂ E.
On Convergence of Vector valued Pramarts and Subpramarts
Authors: Frangos Nikos E. 
Published: December 2010

In [15] Millet and Sucheston introduced the notion of pramart and subpramart indexed by directed sets, generalizing that of martingale and submartingale, and studied their properties. In particular convergence theorems were proved. In this note we obtain convergence theorems for analogous Banach-valued processes.Let E be a Banach lattice with the Radon-Nikodym property. Let (Xt, , t ∊ J) be an E+-valued subpramart of class (d). Precise definitions are given below (Section 1).In [10] for J = N, Egghe proved a subpramart convergence theorem under the additional assumption that there is a subsequence {nk} ⊆ N such that converges weakly for each .
Optimization and α-Disfocality for Ordinary Differential Equations
Authors: Essén M. 
Published: December 2010

For f ∊ L−1(0, T), we define the distribution functionwhere T is a fixed positive number and |·| denotes Lebesgue measure. Let Φ:[0, T] → [0, m] be a nonincreasing, right continuous function. In an earlier paper [3], we discussed the equation(0.1)when the coefficient q was allowed to vary in the classWe were in particular interested in finding the supremum and infimum of y(T) when q was in or in the convex hull Ω(Φ) of (see below).
Differentiation of Multiparameter Superadditive Processes
Authors: Çömez Doğan 
Published: December 2010

In this article our purpose is to prove a differentiation theorem for multiparameter processes which are strongly superadditive with respect to a strongly continuous semigroup of positive L1 contractions (see Section 1 for definitions).Recently, the differentiation theorem for superadditive processes with respect to a one-parameter semigroup of positive L1-contractions has been proved by D. Feyel [9]. Another proof is given by M. A. Akçoğlu [1]. R. Emilion and B. Hachem [7] also proved the same theorem, but with an extra assumption on the process (see also [1]). The proof of this theorem for superadditive processes with respect to a Markovian semigroup of operators on L1 is given by M. A. Akçoğlu and U. Krengel [4]. Thus [1] and [9] extend the result of [4] to the sub-Markovian setting. Here we will obtain the multiparameter sub-Markovian version of this theorem, namely Theorem 3.17 below
Naturally Reductive Homogeneous Riemannian Manifolds
Authors: Gordon Carolyn S. 
Published: December 2010

The simple algebraic and geometric properties of naturally reductive metrics make them useful as examples in the study of homogeneous Riemannian manifolds. (See for example [2], [3], [15]). The existence and abundance of naturally reductive left-invariant metrics on a Lie group G or homogeneous space G/L reflect the structure of G itself. Such metrics abound on compact groups, exist but are more restricted on noncompact semisimple groups, and are relatively rare on solvable groups. The goals of this paper are(i) to study all naturally reductive homogeneous spaces of G when G is either semisimple of noncompact type or nilpotent and(ii) to give necessary conditions on a Riemannian homogeneous space of an arbitrary Lie group G in order that the metric be naturally reductive with respect to some transitive subgroup of G.
A q-Extension of Feldheim's Bilinear Sum for Jacobi Polynomials and Some Applications
Authors: Rahman Mizan 
Published: December 2010

The main objective of this paper is to find useful q-extensions of Feldheim's [6] bilinear formula for Jacobi polynomials, namely,1.1where the Appel function F4 is defined by1.2α1, α2, ρ are arbitrary complex parameters such that the series on both sides of (1.1) are convergent, and1.3is the Jacobi polynomial of degree k, (a)k being the usual shifted factorial.
Groups with Finite Dimensional Irreducible Multiplier Representations
Authors: Holzherr A. K. 
Published: December 2010

Let G be a locally compact group and ω a normalized multiplier on G. Denote by V(G) (respectively by V(G, ω)) the von Neumann algebra generated by the regular representation (respectively co-regular representation) of G. Kaniuth [6] and Taylor [14] have characterized those G for which the maximal type I finite central projection in V(G) is non-zero (respectively the identity operator in V(G)).In this paper we determine necessary and sufficient conditions on G and ω such that the maximal type / finite central projection in V(G, ω) is non-zero (respectively the identity operator in V(G, ω)) and construct this projection explicitly as a convolution operator on L2(G). As a consequence we prove the following statements are equivalent,(i) V(G, ω) is type I finite,(ii) all irreducible multiplier representations of G are finite dimensional,(iii) Gω (the central extension of G) is a Moore group, that is all its irreducible (ordinary) representations are finite dimensional.
On the Definition of C*-Algebras II
Authors: Magyar Zoltán , Sebestyén Zoltán 
Published: December 2010

The theory of noncommutative involutive Banach algebras (briefly Banach *-algebras) owes its origin to Gelfand and Naimark, who proved in 1943 the fundamental representation theorem that a Banach *-algebra with C*-condition(C*)is *-isomorphic and isometric to a norm-closed self-adjoint subalgebra of all bounded operators on a suitable Hilbert space.At the same time they conjectured that the C*-condition can be replaced by the B*-condition.(B*)In other words any B*-algebra is actually a C*-algebra. This was shown by Glimm and Kadison [5] in 1960.
Generalized L(f) Spaces
Authors: Hussein D. , Natsheh M. A. , Qumsiyeh I. 
Published: December 2010

Given any set Γ, let be the family of all finite subsets of . Let f:[0, ∞) → R satisfying: (1) f(x) = 0 if and only if x = 0, (2) f is increasing, (3) f(x + y) ≧ f(x) + f(y) for all x, y ≦ 0, and (4) f is continuous at zero from the right. Such an f is called a modules. Let C be the set of all moduli, and F = {fv ∊ C:v ∊ Γ). Q(Γ) will denote the set of all such F, s. For each F ∊ Q(Γ) letthe summation is taken over Γ, and setIf Γ is countable Q(Γ) will be denoted by Q and LΓ(F) by L(F). LetNote thatsee [4, 5 and 6].
The Dirichlet Problem for the Subelliptic Laplacian on the Heisenberg Group II
Authors: Gaveau Bernard , Vauthier Jacques 
Published: December 2010

Let H3 be the Heisenberg group in three dimensions, Δ the fundamental subelliptic laplacian on H3 (see Section 1 for notations and definitions) and U be an open subset of H3 If φ is a continuous function on the boundary ∂U of U, the Dirichlet problem is thus,(1)In [3], p. 104, it was asserted by the first author that, when dU is regular (see Section 1 for this definition), the problem (1) has a solution continuous on D and a probabilistic formula was given. In [3], we prove that our probabilistic formula gives a solution of the so called “martingale problem” associated to Δ on U (see [5] for this notion). But it appears that the connection between the solution in the martingale problem sense and the true solution is not at all clear in the subelliptic case; in particular it is not obvious at all that the probabilistic formula is a C2 function.
A Note on the mod 2 Cohomology of BŜOn〈l6〉
Authors: Ng Tze-Beng 
Published: December 2010

Recall BSOn is the classifying space for the special orthogonal group of rank n. It is well known that the mod 2 cohomology ring of BSOn is given as follows:where wi is the i-th mod 2 Stiefel-Whitney class. For the 3-connective cover of BSOn, BSpinn, Quillen in [4] has determined H*(BSpinn) completely for all n. Let BŜOn〈8〉, BŜOn〈16〉 be the classifying spaces for n-plane spin bundle ξ satisfying w4(ξ) = 0 and w4(ξ) = w8(ξ) = 0 respectively. This note follows the method of A. Borel [2] and gives the mod 2 cohomology ring of BŜOn〈8〉 and BŜOn〈16〉 for small n. In particular we answer the question “when is H*(BŜOn〈8〉; Z2), or H*(BŜOn〈16〉; Z2) a polynomial algebra?”
Corner Behavior of Solutions of Semilinear Dirichlet Problems
Authors: Wigley Neil M. 
Published: December 2010

In recent years there has been considerable attention paid to the behavior of solutions of elliptic boundary value problems in domains with piecewise smooth boundary. In two dimensions the study concerns the behavior of a solution near a corner, and in three (or more) dimensions two cases have been given considerable attention: a conical vertex on the boundary, or an edge.The solution of such a problem may be singular at the nonsmooth boundary points. The standard example in two dimensions is a solution in polar coordinates of the Dirichlet problem near a corner of interior angle πα;u = r1/α sin θ/α is a function which is harmonic in the sector 0 < θ < πα, has zero boundary values near the corner, and yet at the origin has unbounded derivatives of order > 1/α unless 1/α is an integer.
Automorphisms of G-Azumaya Algebras
Authors: Beattie Margaret 
Published: December 2010

Let R be a commutative ring, G a finite abelian group of order n and exponent m, and assume n is a unit in R. In [10], F. W. Long defined a generalized Brauer group, BD(R, G), of algebras with a G-action and G-grading, whose elements are equivalence classes of G-Azumaya algebras. In this paper we investigate the automorphisms of a G-Azumaya algebra A and prove that if Picm(R) is trivial, then these automorphisms are all, in some sense, inner.In fact, each of these “inner” automorphisms can be written as the composition of an inner automorphism in the usual sense and a “linear“ automorphism, i.e., an automorphism of the typewith r(σ) a unit in R. We then use these results to show that the group of gradings of the centre of a G-Azumaya algebra A is a direct summand of G, and thus if G is cyclic of order pr, A is the (smash) product of a commutative and a central G-Azumaya algebra.
A Note on the Multiplicity of Cohen-Macaulay Algebras with Pure Resolutions
Authors: Huneke Craig , Miller Matthew 
Published: December 2010

Let R = k[X1, …, Xn] with k a field, and let I ⊂ R be a homogeneous ideal. The algebra R/I is said to have a pure resolution if its homogeneous minimal resolution has the formSome of the known examples of pure resolutions include the coordinate rings of: the tangent cone of a minimally elliptic singularity or a rational surface singularity [15], a variety defined by generic maximal Pfaffians [2], a variety defined by maximal minors of a generic matrix [3], a variety defined by the submaximal minors of a generic square matrix [6], and certain of the Segre-Veronese varieties [1].If I is in addition Cohen-Macaulay, then Herzog and Kühl have shown that the betti numbers bi are completely determined by the twists di.
Partitioning Projective Geometries into Caps
Authors: Ebert Gary L. 
Published: December 2010

In [2] by means of a fairly lengthy argument involving Hermitian varieties it was shown that PG(2n, q2) can be partitioned into (q2n++ 1 + 1)/(q + l)-caps. Moreover, these caps were shown to constitute the “large points” of a PG(2n, q) in a natural way. In [3] a similar argument was used to show that once two disjoint (n – l)-subspaces are removed from PG(2n, q2), the remaining points can be partitioned into (q2n – 1)/(q2 – l)-caps.The purpose of this paper is to give a short proof of the results found in [2], and then use the technique developed to partition PG(2n, q) into (qn + l)-caps for n even and q any prime-power. Moreover, these caps can be treated in a natural way as the “large points” of a PG(n – 1, q).
Estimates for Solutions of Wave Equations with Vanishing Curvature
Authors: Marshall Bernard 
Published: December 2010

The solution of the Cauchy problem for a hyperbolic partial differential equation leads to a linear combination of operators Tt of the formFor example, the solution of the initial value problemis given by u(x, t) = Ttf(x) wherePeral proved in [11] that Tt is bounded from LP(Rn) to LP(Rn) if and only ifFrom the homogeneity, the operator norm satisfies ‖Tt‖ ≦ Ct for all t > 0.
Convexity Conditions on f-Rings
Authors: Larson Suzanne 
Published: December 2010

Let n be a positive integer. An f-ring A is said to satisfy the left nth-convexity property if for any u, v ∊ A such that v ≧ 0 and 0 ≧ u ≧ vn, there exists a w ∊ A such that u = wv. The right nth-convexity property is defined similarly and an f-ring is said to satisfy the nth-convexity property if it satisfies both the left and the right nth-convexity property. In this paper, we study arbitrary f-rings which satisfy one of the convexity properties.Those f-rings which satisfy one or more of these properties have been studied by several authors. In [3, 1D], L. Gillman and M. Jerison note that any C(X) satisfies the nth-convexity property for all n ≧ 2, and in [3, 14.25], they give several properties that in C(X) are equivalent to the 1st-convexity property. M. Henriksen proves some results about the ideal theory of an f-ring satisfying the 2nd-convexity property in [5] and S. Steinberg studies left quotient rings of f-rings satisfying the left 1st-convexity property in [13].
q-Series Identities and Reducibility of Basic Double Hypergeometric Functions
Authors: Srivastava H. M. , Jain V. K. 
Published: December 2010

For real or complex q, |q| < 1, let(1.1)for arbitrary λ and μ, so that(1.2)and(1.3)Define, as usual, a generalized q-hypergeometric function by (cf. [26, Chapter 3]; see also [18])(1.4)where, for convergence, |q| < 1 and |z| < ∞ when r is a positive integer, or |z| < 1 when r = 0, provided that no zeros appear in the denominator.
The Fourier Transforms of Smooth Measures on Hypersurfaces of Rn + 1
Authors: Marshall Bernard 
Published: December 2010

The Fourier transform of the surface measure on the unit sphere in Rn + 1, as is well-known, equals the Bessel functionIts behaviour at infinity is described by an asymptotic expansionThe purpose of this paper is to obtain such an expression for surfaces Σ other than the unit sphere. If the surface Σ is a sufficiently smooth compact n-surface in Rn + 1 with strictly positive Gaussian curvature everywhere then with only minor changes in the main term, such an asymptotic expansion exists. This result was proved by E. Hlawka in [3]. A similar result concerned with the minimal smoothness of Σ was later obtained by C. Herz [2].
On Sieved Orthogonal Polynomials II: Random Walk Polynomials
Authors: Charris Jairo , Ismail Mourad E. H. 
Published: December 2010

A birth and death process is a stationary Markov process whose states are the nonnegative integers and the transition probabilities(1.1)satisfy(1.2)as t → 0. Here we assume βn > 0, δn + 1 > 0, n = 0, 1, …, but δ0 ≦ 0. Karlin and McGregor [10], [11], [12], showed that each birth and death process gives rise to two sets of orthogonal polynomials. The first is the set of birth and death process polynomials {Qn(x)} generated by
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 formwhere 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 writingwhere at each point x a set Ex is given. A special case of the path derivative is the sequential derivative, defined by writingwhere 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 functionalover 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 andwill 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.
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.
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*.