bluuebunny/crossref_metadata_2025_split huggingface dataset:
Cocharacters, Codimensions and Hilbert Series of the Polynomial Identities for 2 × 2 Matrices with Involution
Authors: Drensky Vesselin , Giambruno Antonio 
Published: December 2010

AbstractLet M2(K, *) be the algebra of 2 × 2 matrices with involution over a field K of characteristic 0. We obtain the exact values of the cocharacters, codimensions and Hilbert series of the *-T-ideal of the polynomial identities for M2(K, *).
Homomorphisms on Function Algebras
Authors: Garrido M. I. , Gómez Gil J. , Jaramillo J. A. 
Published: December 2010

AbstractLet A be an algebra of continuous real functions on a topological space X. We study when every nonzero algebra homomorphism φ: A → R is given by evaluation at some point of X. In the case that A is the algebra of rational functions (or real-analytic functions, or Cm-functions) on a Banach space, we provide a positive answer for a wide class of spaces, including separable spaces and super-reflexive spaces (with nonmeasurable cardinal).
Representations of Quantum Heisenberg Algebras
Authors: Fabbri Marc A. , Okoh Frank 
Published: December 2010

AbstractA Lie algebra is called a Heisenberg algebra if its centre coincides with its derived algebra and is one-dimensional. When is infinite-dimensional, Kac, Kazhdan, Lepowsky, and Wilson have proved that -modules that satisfy certain conditions are direct sums of a canonical irreducible submodule. This is an algebraic analogue of the Stone-von Neumann theorem. In this paper, we extract quantum Heisenberg algebras, q(), from the quantum affine algebras whose vertex representations were constructed by Frenkel and Jing. We introduce the canonical irreducible q()-module Mq and a class Cq of q()-modules that are shown to have the Stone-von Neumann property. The only restriction we place on the complex number q is that it is not a square root of 1. If q1 and q2 are not roots of unity, or are both primitive m-th roots of unity, we construct an explicit isomorphism between q1() and q2(). If q1 is a primitive m-th root of unity, m odd, q2 a primitive 2m-th or a primitive 4m-th root of unity, we also construct an explicit isomorphism between q1() and q2().
The Stability Theorems for Subgroups of and
Authors: Lari-Lavassani Ali , Lu Yung-Chen 
Published: December 2010

AbstractIn singularity theory, J. Damon gave elegant versions of the unfolding
and determinacy theorems for geometric subgroups of . and . In this work, we propose a unified treatment of the smooth stability of germs and the structural stability of versai unfoldings for a large class of such subgroups.
The Structure of C*-Convex Sets
Authors: Morenz Phillip B. 
Published: December 2010

AbstractCompact C*-convex subsets of Mn correspond exactly to n-th matrix ranges of operators. The main result of this paper is to discover the “right” analog of linear extreme points, called structural elements, and then to prove a generalised Krein-Milman theorem for C*-convex subsets of Mn. The relationship between structural elements and an earlier attempted generalisation, called C*-extreme points, is examined,
solving affirmatively a conjecture of Loebl and Paulsen [8]. An improved bound for a C* -convex version of the Caratheodory theorem for convex sets is also given.
Quasi-Multipliers and Embeddings of Hilbert C*-Bimodules
Authors: Brown Lawrence G. , Mingo James A. , Shen Nien-Tsu 
Published: December 2010

Abstract
This paper considers Hilbert C*-bimodules, a
slight generalization of imprimitivity bimodules which were introduced by Rieffel
[20]. Brown, Green, and Rieffel [7] showed that every imprimitivity bimodule X can
be embedded into a certain C*-algebra L, called the
linking algebra of X. We consider arbitrary embeddings of Hilbert
C*-bimodules into
C*-algebras; i.e. we describe the relative position of
two arbitrary hereditary C*-algebras of a
C*-algebra, in an analogy with Dixmier's description
[10] of the relative position of two subspaces of a Hilbert space.
The main result of this paper (Theorem 4.3) is taken from the doctoral
dissertation of the third author [22], although the proof here follows a different
approach. In Section 1 we set out the definitions and basic properties (mostly
folklore) of Hilbert C*-bimodules. In Section 2 we show
how every quasi-multiplier gives rise to an embedding of a bimodule. In Section 3
we show that , the enveloping
C*-algebra of the
C*-algebraA with its product perturbed by a positive
quasi-multiplier , is isomorphic to
the closure (Proposition 3.1).
Section 4 contains the main theorem (4.3), and in Section 5 we explain the analogy
with the relative position of two subspaces of a Hilbert spaces and present some
complements.
The Königsberg Bridge Problem for Peano Continua
Authors: Bula W. , Nikiel J. , Tymchatyn E. D. 
Published: December 2010

Abstract
Peano continua which are images of the unit interval [0,1] or the circle
S under a continuous and irreducible map are
investigated. Necessary conditions for a space to be the irreducible image of
[0,1] are given, and it is conjectured that these conditions are sufficient as
well. Also, various results on irreducible images of [0,1] and
S are given within some classes of regular curves.
Some of them involve inverse limits of inverse sequences of Euler graphs with
monotone bonding maps.
Asymptotics of the Exit Distribution for Markov Jump Processes; Application to
Atm
Authors: Iscoe I. , Mcdonald D. , Qian K. 
Published: December 2010

Abstract
We approximate the exit distribution of a Markov jump process into a set of
forbidden states and we apply these general results
to an ATM multiplexor. In this case the forbidden
states represent an overloaded multiplexor. Statistics for this overload or busy
period are difficult to obtain since this is such a rare event. Starting from the
approximate exit distribution, one may simulate the busy period without wasting
simulation time waiting for the overload to occur.
Geometric Characterization of Interpolating Varieties for the (FN)-Space A0p of Entire Functions
Authors: Berenstein Carlos A. , Li Bao Qin , Vidras Alekos 
Published: December 2010

AbstractA necessary and sufficient geometric characterization and a necessary and sufficient analytic characterization of interpolating varieties for the space of entire functions will be obtained in the paper, which as an application will also give a generalization of the well-known Pólya-Levinson density theorem.
Restricted Lie Algebras and Their Envelopes
Authors: Riley D. M. , Shalev A. 
Published: December 2010

AbstractLet L be a restricted Lie algebra over a field of characteristic p. Denote by u(L) its restricted enveloping algebra and by ωu(L) the augmentation ideal of u(L). We give an explicit description for the dimension subalgebras of L, namely those ideals of L defined by Dn(L) - L∩ωu(L)n for each n ≥ 1. Using this expression we describe the nilpotence index of ωU(L). We also give a precise characterisation of those L for which ωu(L) is a residually nilpotent ideal. In this case we show that the minimal number of elements required to generate an arbitrary ideal of u(L) is finitely bounded if and only if L contains a 1-generated restricted subalgebra of finite codimension. Subsequently we examine certain analogous aspects of the Lie structure of u(L). In particular we characterise L for which u(L) is residually nilpotent when considered as a Lie algebra, and give a formula for the Lie nilpotence index of u(L). This formula is then used to describe the nilpotence class of the group of units of u(L).
Topological Properties of the Set of Norm-Attaining Linear Functionals
Authors: Debs Gabriel , Godefroy Gilles , Raymond Jean Saint 
Published: December 2010

AbstractIf X is a separable non-reflexive Banach space, then the set NA of all norm-attaining elements of X* is not a w*-Gδ subset of X*. However if the norm of X is locally uniformly rotund, then the set of norm attaining elements of norm one is w*-Gδ. There exist separable spaces such that NA is a norm-Borel set of arbitrarily high class. If X is separable and non-reflexive, there exists an equivalent Gâteaux-smooth norm on X such that the set of all Gâteaux-derivatives is not norm-Borel.
Reducibility for Non-Connected p-Adic Groups, With G° Of Prime Index
Authors: Goldberg David 
Published: December 2010

AbstractWe determine the structure of representations induced from discrete series of parabolic subgroups of quasi-split p-adic groups G with G/G° a cyclic group of prime order. We attach to each such representation an R-group which extends the definition of the Knapp-Stein R-group. We show that this R-group has the properties predicted by Arthur. We apply our results to the case of Orthogonal groups.
Fixed Points of Automorphisms of Free Pro-p Groups of Rank 2
Authors: Herfort Wolfgang N. , Ribes Luis , Zalesskii Pavel A. 
Published: December 2010

AbstractLet p be a prime number, and let F be a free pro-p group of rank two. Consider an automorphism α of F of finite order m, and let FixF(α) = {x ∈ F | α(x) = x} be the subgroup of F consisting of the elements fixed by α. It is known that if m is prime to p and α = idF, then the rank of FixF(α) is infinite. In this paper we show that if m is a finite power pr of p, the rank of FixF(α) is at most 2. We conjecture that if the rank of F is n and the order of a is a power of α, then rank (FixF(α)) ≤ n.
Analytic Range Functions of Several Variables
Authors: Cheng R. 
Published: December 2010

AbstractLet C be a separable Hilbert Space, and let Λ be the halfplane {(m, n) ∈ Ζ2 : m ≥ 1} ∪ {(0, n) ∈ Ζ2 : n ≥ 0} of the integer lattice. Consider the subspace ℳc(Λ) of on the torus spanned by the C-valued trigonometric functions {Ceims+int : с ∈ C, (m, n) ∈ Λ}. The notion of a Λ-analytic operator on ℳc(Λ) is defined with respect to the family of shift operators {Smn}Λ on ℳC(Λ) given by (Smnƒ)(eis, eit) = eims+intƒ(eis, eit). The corresponding concepts of inner function, outer function and analytic range function are explored. These ideas are applied to the spectral factorization problem in prediction theory.
Brauer Group Analogues of Results Relating the Witt Ring to Valuations and Galois Theory
Authors: Hwangk Yoon Sung , Jacob Bill 
Published: December 2010

AbstractLet F be a field of characteristic different from p containing a primitive p-th root of unity. This paper studies the cup product pairing Hl(F, p) x Hl(F, p) → H2(F, p) and its relationship to valuation theory and Galois theory. Sufficient conditions on the pairing which guarantee the existence of a valuation on the field are described. In the non p-adic case these results provide a converse to the well-known structure theory in this situation. In the p-adic case, the pairing is described using the notion of "relative rigidity". These results are analogues of results in quadratic form theory developed in the past decade, which cover the special case p = 2. Applications to the maximal pro-p Galois group of F are also described.
Voronoi Domains and Dual Cells in the Generalized Kaleidoscope with Applications to Root and Weight Lattices
Authors: Moody R. V. , Patera J. 
Published: December 2010

AbstractWe give a uniform description, in terms of Coxeter diagrams, of the Voronoi domains of the root and weight lattices of any semisimple Lie algebra. This description provides a classification not only of all the facets of these Voronoi domains but simultaneously a classification of their dual or Delaunay cells and their facets. It is based on a much more general theory that we develop here providing the same sort of information in the setting of chamber geometries defined by arbitrary reflection groups. These generalized kaleidoscopes include the classical spherical, Euclidean, and hyperbolic kaleidoscopes as special cases. We prove that under certain conditions the Delaunay cells are Voronoi cells for the vertices of the Voronoi complex. This leads to the description in terms of Wythoff polytopes of the Voronoi cells of the weight lattices.
On the Existence and the Classification of Critical Points for Non-Smooth Functionals
Authors: Fang G. 
Published: December 2010

AbstractWe extend the min-max methods used in the critical point theory of differentiable functionals on smooth manifolds to the case of continuous functionals on a complete metric space. We study the topological properties of the min-max generated critical points in this new setting by adopting the methodology developed by Ghoussoub in the smooth case. Many old and new results are extended and unified and some applications are given.
Markov Processes Associated With Positivity Preserving Coercive Forms
Authors: Ma Zhi-Ming , Röckner Michael 
Published: December 2010

AbstractCoercive closed forms on L2-spaces are studied whose associated L2-semigroups are positivity preserving. Earlier work by other authors is extended by further developing the potential theory of such forms and completed by proving an analytic characterization of those of these forms which have a probabilistic counterpart, i.e., are associated with (special standard) Markov processes. Examples with finite and infinite dimensional state spaces are discussed.
Cliques of Irreducible Representations, Quotient Groups, and Brauer's Theorems on Blocks
Authors: Ellers Harald 
Published: December 2010

AbstractAssumekis an algebraically closed field of characteristicpandGis a finite group. IfPis ap-subgroup ofGsuch thatG=PCG(P), and ifHis a normal subgroup ofGwithP≤H, then the number ofH-cliques of irreduciblek[G]-modules is the same as the number ofH/P-cliques of irreduciblek[G/P]-modules.
Consistency of Moment Systems
Authors: Lewis A. S. 
Published: December 2010

AbstractAn important question in the study of moment problems is to determine when a fixed point in ℝn lies in the moment cone of vectors , with μ a nonnegative measure. In associated optimization problems it is also important to be able to distinguish between the interior and boundary of the moment cone. Recent work of Dachuna-Castelle, Gamboa and Gassiat derived elegant computational characterizations for these problems, and for related questions with an upper bound on μ. Their technique involves a probabilistic interpretation and large deviations theory. In this paper a purely convex analytic approach is used, giving a more direct understanding of the underlying duality, and allowing the relaxation of their assumptions.
Proof, Disproof and Advances Concerning Certain Conjectures on Real Quadratic Fields
Authors: Mollin R. A. , Williams H. C. 
Published: December 2010

AbstractThe purpose of this paper is to address conjectures raised in [2]. We show that one of the conjectures is false and we advance the proof of another by proving it for an infinite set of cases. Furthermore, we give hard evidence as to why the conjecture is true and show what remains to be done to complete the proof. Finally, we prove a conjecture given by S. Louboutin, for Mathematical Reviews, in his discussion of the aforementioned paper.
q-Hermite Polynomials and Classical Orthogonal Polynomials
Authors: Berg Christian , Ismail Mourad E. H. 
Published: December 2010

AbstractWe use generating functions to express orthogonality relations in the form of q-beta. integrals. The integrand of such a q-beta. integral is then used as a weight function for a new set of orthogonal or biorthogonal functions. This method is applied to the continuous q-Hermite polynomials, the Al-Salam-Carlitz polynomials, and the polynomials of Szegö and leads naturally to the Al-Salam-Chihara polynomials then to the Askey-Wilson polynomials, the big q-Jacobi polynomials and the biorthogonal rational functions of Al-Salam and Verma, and some recent biorthogonal functions of Al-Salam and Ismail.
Bergman Spaces on Disconnected Domains
Authors: Aleman Alexandru , Richter Stefan , Ross William T. 
Published: December 2010

AbstractFor a bounded region G ⊂ ℂ and a compact set K ⊂ G, with area measure zero, we will characterize the invariant subspaces ℳ (under ƒ → zƒ) of the Bergman space (G \ K), 1 ≤ p < ∞, which contain (G) and with dim(ℳ/(z - λ)ℳ) = 1 for all λ ∈ G \ K. When G \ K is connected, we will see that dim(ℳ/(z - λ)ℳ) = 1 for all λ ∈ G \ K and thus in this case we will have a complete description of the invariant subspaces lying between (G) and (G \ K). When p = ∞, we will remark on the structure of the weak-star closed z-invariant subspaces between H∞(G) and H∞(G \ K). When G \ K is not connected, we will show that in general the invariant subspaces between (G) and (G \ K) are fantastically complicated. As an application of these results, we will remark on the complexity of the invariant subspaces (under ƒ → ζƒ) of certain Besov spaces on K. In particular, we shall see that in the harmonic Dirichlet space , there are invariant subspaces ℱ such that the dimension of ζℱ in ℱ is infinite.
Acyclic Models
Authors: Barr Michael 
Published: December 2010

AbstractAcyclic models is a powerful technique in algebraic topology and homological algebra in which facts about homology theories are verified by first verifying them on "models" (on which the homology theory is trivial) and then showing that there are enough models to present arbitrary objects. One version of the theorem allows one to conclude that two chain complex functors are naturally homotopic and another that two such functors are object-wise homologous. Neither is entirely satisfactory. The purpose of this paper is to provide a uniform account of these two, fixing what is unsatisfactory and also finding intermediate forms of the theorem.
Bounded Pointwise Approximation of Solutions of Elliptic Equations
Authors: Bonilla A. , Trujillo-González  
Published: December 2010

AbstractWe characterize open subsets U of ℝN in which the bounded solutions of certain elliptic equations can be approximated pointwise by uniformly bounded solutions that are continuous in Ū. This result is established in terms of certain capacities. For closed subsets X, this characterization allows us to approximate bounded solutions in X° uniformly on relatively closed subsets of X° by solutions continuous on certain subsets of the boundary of X.
Generators of Ideals Defining Certain Surfaces in Projective Space
Authors: Holay Sandeep H. 
Published: December 2010

AbstractWe consider the surface obtained from the projective plane by blowing up the points of intersection of two plane curves meeting transversely. We find minimal generating sets of the defining ideals of these surfaces embedded in projective space by the sections of a very ample divisor class. All of the results are proven over an algebraically closed field of arbitrary characteristic.
Rings With Finite Maximal Invariant Subrings
Authors: Lanski Charles 
Published: December 2010

AbstractWe prove that if φ is an (anti-) automorphism of a ringRwith finite orbits onR, or integral over the integers, and ifRcontains a finite maximal φ-invariant subring, thenRmust be finite. Special cases are when φ has finite order or is an involution. Two corollaries are thatRmust be finite whenRcontains only finitely many φ-invariant subrings or has both ascending and descending chain conditions on φ invariant subrings. These generalize results in the literature for the special case when φ = idR.
Reconstruction of Entire Functions From Irregularly Spaced Sample Points
Authors: Grozev Georgi R. , Rahman Qazi I. 
Published: December 2010

AbstractLet where {λn}n ∈ Ζ is a sequence of real numbers such that |λn — n| ≤ Δ for some Δ > 0 and all n ∈ ℤ . Extending an obvious property of sin πz to which the function G reduces when Δ = 0 we show that is bounded by a constant independent of n. The result is then applied to a problem concerning derivative sampling in one and several variables.
Positive-Defininte Functions on Free Semigroups
Authors: Popescu Gelu 
Published: December 2010

AbstractAn extension of the Naimark dilation theorem [N], [SzF2] to positive-definite functions on free semigroups is given. This is used to extend the operatorial trigonometric moment problem [A] to a non-commutative setting and to characterize the classes 𝐶ρ (ρ > 0) of all n-tuples of operators that have a p-isometric dilation (see [SzF2] for the case n = 1). It is also shown that 𝐶ρ ⊂ 𝐶ρ′ and 𝐶ρ ≠ 𝐶ρ′ for 0 < ρ < ρ′ < ∞.The von Neumann inequality [vN], [Po2] is extended to the classes 𝐶p. This is used to prove that any element in 𝐶ρ is simultaneously similar to an element in 𝐶1.
Homological Duality and Quasi-Heredity
Authors: Ágoston István , Dlab Vlastimil , Lukács Erzsébet 
Published: December 2010

AbstractThis paper represents a general study of the (Yoneda) Ext-algebra A* of a finite dimensional K-algebra A. Our motivation lies in the problem of establishing conditions under which (i) the species of A* coincides with the dual species of A and (ii) the quasi-heredity of A (or A*) yields the quasi-heredity of A* (or A, respectively). These questions are closely related to the Kazhdan—Lusztig Theory as presented by [CPS2]. The main results include introducing the concept of a solid algebra and the relevant Theorem 4.5 as well as a rather complete description of the situation in the case of monomial algebras in Section 5.
Nonabelian Fully-Ramified Sections
Authors: Lewis Mark L. 
Published: December 2010

AbstractLet G be a finite group and let K and L be normal subgroups of G such that |K : L| and |G : K| are relatively prime, and assume that |K : L| is odd. Let H be a subgroup of G such that G = HK and H ∩ K = L. Let φ be an irreducible character of L that is invariant under the action of L and is fully ramified with respect to K/L. If χ ∈ Irr(G) is a constituent of φG, then we prove that χH has a unique irreducible constituent having odd multiplicity.
The Modular Group Algebra Problem for Small p-Groups Of Maximal Class
Authors: Salim Mohamed A. M. , Sandling Robert 
Published: December 2010

AbstractWe show that p-groups of maximal class and order p5 are determined by their group algebras over the field of p elements. The most important information requisite for the proof is obtained from a detailed study of the unit group of a quotient algebra of the group algebra, larger than the small group algebra.
Sweeping Out Properties of Operator Sequences
Authors: Akcoglu Mustafa A. , Ha Dzung M. , Jones Roger L. 
Published: December 2010

AbstractLet Lp = Lp(X, μ), 1 ≤ p ≤ ∞, be the usual Banach Spaces of real valued functions on a complete non-atomic probability space. Let (T1, . . . ,TK) be L2-contractions. Let 0 < ε < δ ≤ 1. Call a function f a δ-spanning function if ‖f‖2 = 1 and if ‖Tkf - Qk-1Tkf‖2 ≥ δ for each k = 1, . . . ,K, where Q0 = 0 and Qk is the orthogonal projection on the subspace spanned by (T1f , . . . ,Tkf). Call a function h a (δ, ε) -sweeping function if ‖h‖∞ ≤ 1, ‖h‖1 < ε, and if max1≤k≤K|Tkh| > δ-ε on a set of measure greater than 1 - ε. The following is the main technical result, which is obtained by elementary estimates. There is an integer K = K(δ, ε) ≥ 1 such that if f is a δ-spanning function, and if the joint distribution of (f , T1f , . . . ,TKf) is normal, then h = ((fΛM)Ꮩ(-M)/M is a (δ, ε)-sweeping function, for some M > 0. Furthermore, if Tks are the averages of operators induced by the iterates of ameasure preserving ergodic transformation, then a similar result is true without requiring that the joint distribution is normal. This gives the following theorem on a sequence (Ti) of these averages.Assume that for each K ≤ 1 there is a subsequence (Ti1 , . . . ,Tik) of length K, and a δ-spanning function fK for this subsequence. Then for each ε > 0 there is a function h, 0 ≥ h ≥ 1, ‖h‖1 < ε, such that lim supi Tih ≤ δ a.e.. Another application of the main result gives a refinement of a part of Bourgain’s “Entropy Theorem”, resulting in a different, self contained proof of that theorem.