bluuebunny/crossref_metadata_2025_split huggingface dataset:
Inclusions for Classes of Lacunary Sets
Authors: Chun C. S. , Freedman A. R. 
Published: December 2010

A sequence, a1 < a2 < a3 < …, of positive integers is called lacunary if the difference sequence dn = an+l — an tends to infinity as n → ∞.In several recent papers we have made use of these sequences in analysis and combinatorics. In [6] we show that the class of all sets which are either finite or the range of a lacunary sequence is “full” in the sense that if (tk) is a real sequence and for each then (tk) is an l1 sequence, that is,In [3] the class of all finite unions of sets of is shown to consist of exactly those sets of integers, A, whose characteristic sequence, χA, is in the well known summability space bs + c0. More recently, in [1], we study lacunary sequences in connection with the conjecture of P.
Asymptotic Maximum Principles for Subharmonic and Plurisubharmonic Functions
Authors: Gauthier P. M. , Grothmann R. , Hengartner W. 
Published: December 2010

Let Ω be a bounded open set in Rn. An immediate consequence of the maximum principle is that if s is a function continuous on and subharmonic on Ω, then(1)Of course (1) is no longer true if Ω is not bounded. For example in C ∼ R2 consider the functionsHowever, if we restrict the growth of s, then (1) may still hold even if the open set Ω is no longer bounded and such is the theme of Phragmèn-Lindelöf type theorems. If we assume even more, namely, that s is upper-bounded, then we can again infer (1) for unbounded open sets Ω. We shall return to this point later.In the present note, we wish to prove (1) for an arbitrary subharmonic function s on an open subset Ω of Rn. In particular, we do not assume that s is bounded or even of restricted growth. Rather, we impose restrictions on the (possibly unbounded) set Ω.
Weighted Subspaces of Hardy Spaces
Authors: Kim Hong Oh , Kwon Ern Geun 
Published: December 2010

A function f in Hp on the unit disc U of the complex plane has the uniform growthWe consider in this paper a subspace of Hp with better uniform growthFor the previous results on see [5, 6, 7]. We start with proving an inequality on Hp which is related to the Hardy-Stein identity (Theorem 2.1) in Section 2. This is applied in the subsequent section to prove some space imbedding theorems related to (Theorems 3.1 and 3.5). These theorems have some known theorems as their corollaries. Finally we prove some coefficient relations on in the last section.The authors wish to thank Professor Patrick Ahern for the helpful conversations during his visit to Korea. Actually he suggested to the first author the possibility of Theorem 2.1 some years ago.
Oscillation Criteria For Second Order Superlinear Differential Equations
Authors: Philos CH. G. 
Published: December 2010

This paper is concerned with the question of oscillation of the solutions of second order superlinear ordinary differential equations with alternating coefficients.Consider the second order nonlinear ordinary differential equationwhere a is a continuous function on the interval [t0, ∞), t0 > 0, and / is a continuous function on the real line R, which is continuously differentia t e , except possibly at 0, and satisfies.
The Approximate Symmetric Integral
Authors: Preiss D. , Thomson B. S. 
Published: December 2010

By a symmetric integral is understood an integral obtained from some kind of symmetric derivation process. Such integrals arise most naturally in the study of trigonometric series and in particular to handle the following problem. Suppose that a trigonometric seriesconverges everywhere to a function À. It is known that this may occur without À being integrable in any of the more familiar senses so that the series may not be considered as a Fourier series of À; indeed Denjoy [4] has shown that if bnis a sequence of real numbers decreasing to zero but with+00 then the function À(x) = is not Denjoy-integrable. It is natural to ask then for an integration procedure that can be applied to À in order that the series be the Fourier series of À with respect to this integral.
Real Af C*-Algebras With K0 of Small Rank
Authors: Giordano T. , Handelman D. E. 
Published: December 2010

A real AF C*-algebra is the norm closure of a direct limit of finite dimensional real C*-algebras (with real *-algebra maps). When we use the unadorned “AF C*-algebra”, we mean the usual complex version.Let R be a simple AF C*-algebra such that K0(R) is free of rank 2 or 3. The problem is to find (up to Morita equivalence) all real AF C*-algebras A such that AꕕC≅R. This is closely related to the problem of finding all involutions on R [3], [10].For example, when the rank is 2, generically there are 8 such classes. The exceptional cases arise when the ratio of the two generators in K0(R) is a quadratic (algebraic) number, and here there are 4, 5, or 8 Morita equivalence classes, the number depending largely on the behaviour of the prime 2 in the relevant algebraic number field.
The Stationary Phase Method for Certain Degenerate Critical Points I
Authors: Dostal Milos , Gaveau Bernard 
Published: December 2010

We consider, in this work, the asymptotic behaviour for large λ, of a Fourier integralwhere 𝜑(x) is in general a C∞ function and a(x) a C∞ function with compact support. It is well known that the asymptotic behaviour of this integral is controlled by the behaviour of 𝜑 at its critical points (i.e., points where 𝜕𝜑/𝜕xj(x) = 0) and is given by local contributions at these points ([1], [3], [7], [9]).In general, one assumes the hypothesis of non degenerate isolated critical point, namely that the determinant of the second derivative at the critical point is non zero.
On the Hyperplane Sections of Blow-Ups of Complex Projective Plane
Authors: Biancofiore Aldo 
Published: December 2010

Let L be a line bundle on a connected, smooth, algebraic, projective surface X. In this paper we have studied the following questions:1) Under which conditions is L spanned by global sections? I.e., if ɸL : X →PN denotes the map associated to the space Г(L) of the sections of L, when is ɸL a morphism?2) Under which conditions is L very ample? I.e., when does ɸL give an embedding?These problems arise naturally in the study, and in particular in the classification, of algebraic surfaces (see [8], [3], [5]).
The Approximate Jordan-Hahn Decomposition
Authors: Rüttimann Gottfried T. 
Published: December 2010

Non-commutative measure theory embraces measure theory on cr-fields of subsets of a set, on projection lattices of von Neumann algebras or JBW-algebras and on hypergraphs alike [20], [27], [33], [37], [39], [40], [41]. Due to the unifying structure of an orthoalgebra concepts can easily be transferred from one branch to the other. Additional conceptual inpetus is obtained from the logico-probabilistic foundations of quantum mechanics (see [6], [19], [21]).In the late seventies the author studied the Jordan-Hahn decomposition of measures on orthomodular posets and certain graphs. These investigations revealed an interesting geometrical aspect of this decomposition in that the Jordan-Hahn property of the convex set of probability charges on a finite orthomodular poset can be characterized in terms of the extreme points of the unit ball of the Banach space dual of the base normed space of Jordan charges.
On Moduli of Continuity for Gaussian and l2-Norm Squared Processes Generated by Ornstein-Uhlenbeck Processes
Authors: Csörgö Miklós , Lin Zhengyan 
Published: December 2010

Let be a sequence of independent Ornstein-Uhlenbeck processes with coefficients lk and ƛk,i.e., Xk(.)is a Gaussian process with EXk(t) =0 andThe process Y(.)was first studied by Dawson (1972) as the stationary solution of the infinite array of stochastic differential equationswhere are independent Wiener processes (cf. also [6],[19],and [1]).
The n-Dimensional Hilbert Transform of Distributions, Its Inversion and Applications
Authors: Singh O. P. , Pandey J. N. 
Published: December 2010

Pandey and Chaudhary [13] recently developed the theory of Hilbert transform of Schwartz distribution space (DLp)',p > 1 in one dimension using Parseval's types of relations for one dimensional Hilbert transform [17] and noted that their theory coincides with the corresponding theory for the Hilbert transform developed by Schwartz [16] by using the technique of convolution in one dimension.The corresponding theory for the Hilbert transform in n-dimension is considerably harder and will be successfully accomplished in this paper.
Tensor Products of Unitary Super-Virasoro Modules With Central Charge 7/10
Authors: Bremner Murray R. 
Published: December 2010

AbstractThe two Virasoro superalgebras, known as the Neveu- Schwarz algebra and the Ramond algebra, each have two unitary irreducible lowest weight modules with central charge . In this paper, I show how tensor products of these modules decompose into finite direct sums of irreducible modules with central charge .
A Family of Unitals in the Hughes Plane
Authors: Kestenband Barbu C. 
Published: December 2010

We construct a family of unitals in the Hughes plane. We prove that they are not isomorphic with the classical unitals, and in so doing we exhibit a configuration that exists in the latter, but not in the former. This new configurational property of the classical unitals might serve in the future again as an isomorphism test.A particular instance of our construction has appeared in [11]. But it only concerns itself with the case where the matrix involved is the identity, whereas the present article treats the general case of symmetric matrices over a suitable field. Furthermore, [11] does not answer the isomorphism question. It states that (the English translation is ours) “It remains to be seen whether the unitary designs constructed in this note are isomorphic or not with known designs”.
Strongly Abelian Varieties and the Hamiltonian Property
Authors: Kiss E. , Valeriote M. 
Published: December 2010

AbstractIn this paper we show that every locally finite strongly Abelian variety satisfies the Hamiltonian property. An algebra is Hamiltonian if every one of its subuniverses is a block of some congruence of the algebra. A counterexample is provided to show that not all strongly Abelian varieties are Hamiltonian.
Minimal Convex Uscos and Monotone Operators on Small Sets
Authors: Borwein Jonathan , Fitzpatrick Simon , Kenderov Petàr 
Published: December 2010

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

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

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

AbstractFor all algebras G, such that is an algebra mentioned in the title, the modules of dimension ≤ p2 are determined. The module homomorphisms from the tensor product of these modules into a third module of the same type are described. We also give the central extensions of the algebras .
Type Preservation In Locally Finite Varieties with the CEP
Authors: Kearnes Keith A. 
Published: December 2010

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

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

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

AbstractExplicit solutions to the recurrence relation for associated continuous Hahn polynomials are derived using 3F2 contiguous relations. These solutions are used to obtain a new continued fraction and the associated absolutely continuous measure. An exceptional case is shown to yield entry 33 in Chapter 12 of Ramanujan's second notebook.
Commutative Gelfand Theory for Real Banach Algebras: Representations as Sections of Bundles
Authors: Pfaffenberger W. E. , Phillips J. 
Published: December 2010

AbstractWe are concerned here with the development of a more general real case of the classical theorem of Gelfand ([5], 3.1.20), which represents a complex commutative unital Banach algebra as an algebra of continuous functions defined on a compact Hausdorff space.In § 1 we point out that when looking at real algebras there is not always a one-to-one correspondence between the maximal ideals of the algebra B, denoted ℳ, and the set of unital (real) algebra homomorphisms from B into C, denoted by ΦB. This simple point and subsequent observations lead to a theory of representations of real commutative unital Banach algebras where elements are represented as sections of a bundle of real fields associated with the algebra (Theorem 3.5). After establishing this representation theorem, we look into the question of when a real commutative Banach algebra is already complex. There is a natural topological obstruction which we delineate. Theorem 4.8 gives equivalent conditions which determine whether such an algebra is already complex.Finally, in § 5 we abstractly characterize those section algebras which appear as the target algebras for our Gelfand transform. We dub these algebras “almost complex C*- algebras” and provide a natural classification scheme.
Primitivity in Free Groups and Free Metabelian Groups
Authors: Gupta C. K. , Gupta N. D. , Roman'kov V. A. 
Published: December 2010

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

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

AbstractInfinite sequences of exchangeable binary random variables have strong positive dependence properties; in particular, we show they are strong FKG. If the infinite exchangeable sequence is allowed to have multiple values this is no longer true. Positive dependence conditions such as association still have natural application in this context. We establish necessary and sufficient conditions for an infinite exchangeable sequence to be associated. This result shows that exchangeable Polyà urn processes are associated. We also establish necessary and sufficient conditions for finite exchangeable sequences to be weakly associated. The match set distribution of a random permutation has recently been shown to be associated by an extensive analysis of cases. Our result easily yields the weak association of such distributions.
Dedekind Completeness and the Algebraic Complexity of o-Minimal Structures
Authors: Mekler Alan , Rubin Matatyahu , Steinhorn Charles 
Published: December 2010

AbstractAn ordered structure is o-minimal if every definable subset is the union of finitely many points and open intervals. A theory is o-minimal if all its models are ominimal. All theories considered will be o-minimal. A theory is said to be n-ary if every formula is equivalent to a Boolean combination of formulas in n free variables. (A 2-ary theory is called binary.) We prove that if a theory is not binary then it is not rc-ary for any n. We also characterize the binary theories which have a Dedekind complete model and those whose underlying set order is dense. In [5], it is shown that if T is a binary theory, is a Dedekind complete model of T, and I is an interval in , then for all cardinals K there is a Dedekind complete elementary extension of , so that . In contrast, we show that if T is not binary and is a Dedekind complete model of T, then there is an interval I in so that if is a Dedekind complete elementary extension of .
On the Decomposition of a Representation of SOn When Restricted to SOn-1
Authors: Gross Benedict H. , Prasad Dipendra 
Published: December 2010

Let k be a local field, with char(k) ≠ 2. A quadratic space V over k is a finite dimensional vector space together with a non-degenerate quadratic form Q: V → k.The special orthogonal group SO(V) consists of all linear maps T: V → V which satisfy:Q(Tv) = Q(v) for all ν and det T = 1.
Quartic Algebras
Authors: Farsi Carla , Watling Neil 
Published: December 2010

AbstractIn this paper we study the fixed point algebra of the automorphism of the rotation algebra , θ = p/q with p, q coprime positive integers, given by u → v-1, v → u. We give a general characterization of the fixed point algebra, determine its K-theory and consider the related crossed-product algebra ⋊Ƭ Z4.
Relative Kloosterman Integrals for GL(3): II
Authors: Jacquet Hervé 
Published: December 2010

AbstractLet G′ be a quasi–split reductive group over a local field F, ƒ′ the characteristic function of a maximal compact subgroup K′ of G′, N′ a maximal unipotent subgroup of G′. We consider the orbits of maximal dimension for the action of N′ × N′ on G′ and the weighted orbital integral of f′ on such an orbit, the weight being a generic character. The resulting integral, we call a Kloosterman integral. A relative version of this construction is to consider a symmetric space S associated to a quasi-split group G, a maximal unipotent subgroup N of G, a maximal compact K of G and the orbits of maximal dimension for the action of N on S. The weighted orbital integral of the characteristic function f of K ∩ S on such an orbit is what we call a relative Kloosterman integral; the weight is an appropriate character of N. We conjecture that a relative Kloosterman integral is actually a Kloosterman integral for an appropriate group G′. We prove the conjecture in a simple case: E is an unramified quadratic extension of F,G is GL(3, E), S is the set of 3 × 3 matrices s such that the group G′ is then the quasi-split unitary group in three variables.
The Pierce-Birkhoff Conjecture for Curves
Authors: Marshall Murray 
Published: December 2010

AbstractThe results obtained extend Madden’s result for Dedekind domains to more general types of 1-dimensional Noetherian rings. In particular, these results apply to piecewise polynomial functions t:C → R where R is a real closed field and C ⊆ Rn is a closed 1-dimensional semi-algebraic set, and also to the associated “relative” case where t, C are defined over some subfield K ⊆ R.
Homogeneous Polynomials, Centralizers and Derivations in Rings
Authors: Divincenzo Onofrio Mario , Sagona Rosa 
Published: December 2010

AbstractLetdbe a non-zero derivation on a primitive ringRandƒ(x1,…,xn) a homogeneous polynomial of degreem. We prove that the conditiond(ƒ(r1,…,rn)t) = 0, for allr1,…,rn∈R, withtdepending onr1,…,rn, forcesRto be a finite dimensional central simple algebra andƒpower-central valued onR. We also obtain bounds on [R:Z(R)] in terms ofm.
Projective and Multigraded Representations of Monomial and Multisigned Groups I. Graded Representations of a Twisted Product
Authors: Hoffman Peter 
Published: December 2010

AbstractMotivated by the problem of giving a functorial (or at least uniform) description of the projective representations for wreath productsGʅSnin terms of those for G, we study a certain binary operationon the class of “cyclic covering groups with parities”. Along with setting up the basic machinery associated to representations graded by (Ζ/2)ℓ, the main result is a description of the irreducibles forin terms of a (tensorlike) product of those forAand forB.Finally we describe a programme for producing a PSH-algebra theory in this context, analogous to that of Zelevinsky for the case ℓ=0, and that of the author with with Michael Bean (structure) and with John Humphreys (applications) for the case ℓ=1