bluuebunny/crossref_metadata_2025_split huggingface dataset:
On a problem of Barnes and Duncan
Authors: McLean R. G. 
Published: December 2008

Consider the free monoid on a non-empty set P, and let R be the quotient monoid determined by the relations:Let R have its natural involution * in which each element of P is Hermitian. We show that the Banach *-algebra ℓ1(R) has a separating family of finite dimensional *-representations and consequently is *-semisimple. This generalizes a result of B. A. Barnes and J. Duncan (J. Funct. Anal.18 (1975), 96–113.) dealing with the case where P has two elements.
Radially symmetric solutions of a class of singular elliptic equations
Authors: Gatica Juan A. , Hernandez Gaston E. , Waltman P. 
Published: December 2008

The boundary value problemis studied with a view to obtaining the existence of positive solutions in C1([0, 1])∩C2((0, 1)). The function f is assumed to be singular in the second variable, with the singularity modeled after the special case f(x, y) = a(x)y−p, p>0.This boundary value problem arises in the search of positive radially symmetric solutions towhere Ω is the open unit ball in ℝN, centered at the origin, Γ is its boundary and |x| is the Euclidean norm of x.
On pseudo-Anosov maps which extend over two handlebodies
Authors: Long D. D. 
Published: December 2008

We show that there is a pair of handlebodies H1 and H2 with common boundary F with the properties:(a) There is no essential simple closed curve in F bounding a disc in both H1 and H2.(b) Given any positive number, there are essential simple curves Cii = 1, 2 on F, bounding discs in Hi whose distance apart in the Hausdorff topology on F is less than this positive number.Such an example has consequences for Heegaard splittings and recognising the 3-sphere.
On the characters of affine Kac–Moody groups
Authors: Slebarski Stephen 
Published: December 2008

Let G be an affine Kac–Moody group over ℂ, and V∞ an integrable simple quotient of a Verma module for g. Let Gmin be the subgroup of G generated by the maximal algebraic torus T, and the real root subgroups.It is shown that (the least positive imaginary root) gives a character δ∈Hom(G, ℂ*) such that the pointwise character χ∞ of V∞ may be defined on Gmin ∩ G>1.
Sturm–Liouville problems with eigenparameter dependent boundary conditions
Authors: Binding P. A. , Browne P. J. , Seddighi K. 
Published: December 2008

Sturm theory is extended to the equationfor 1/p, q, r∈L1 [0, 1] with p, r > 0, subject to boundary conditionsandOscillation and comparison results are given, and asymptotic estimates are developed. Interlacing of eigenvalues with those of a standard Sturm–Liouville problem where the boundary conditions are ajy(j) = cj(py′)(j), j=0, 1, forms a key tool.
Explicit evaluation of Euler sums
Authors: Borwein David , Borwein Jonathan M. , Girgensohn Roland 
Published: December 2008

In response to a letter from Goldbach, Euler considered sums of the formwhere s and t are positive integers.As Euler discovered by a process of extrapolation (from s + t ≦ 13), σh(s, t) can be evaluated in terms of Riemann ζ-functions when s + t is odd. We provide a rigorous proof of Euler's discovery and then give analogous evaluations with proofs for corresponding alternating sums. Relatedly we give a formula for the seriesThis evaluation involves ζ-functions and σh(2, m).
Hypoelliptic differential operators with generalized constant coefficients
Authors: Nedeljkov M. , Pilipović S. 
Published: December 2008

The space of Colombeau generalized functions is used as a frame for the study of hypoellipticity of a family of differential operators whose coefficients depend on a small parameter ε.There are given necessary and sufficient conditions for the hypoellipticity of a family of differential operators with constant coefficients which depend on ε and behave like powers of ε as ε→0. The solutions of such family of equations should also satisfy the power order estimate with respect to ε.
Closed ideals in the Banach algebra ℓ1(ω) when ω is ∈-star shaped
Authors: Thomas Marc P. 
Published: December 2008

Provided that the weight function ω satisfies certain submultiplicative and decay conditions, the discrete convolution algebra ℓ1(ω) becomes a commutative radical Banach algebra with identity adjoined. There are obvious closed ideals in ℓ1(ω) and these are denoted standard ideals. Earlier results of Thomas, strengthened by Yakubovich and Domar, showed that if the weight ω is star-shaped then all closed ideals are standard. Consequently, the closed ideal generated by any element f in ℓ1(ω) must be standard.The requirement that ω be star-shaped (essentially that ω(n)1/n must decrease to zero) is somewhat restrictive in that no local maxima of ω(n)1/n are allowed. We generalize this previous result to apply to the larger class of ε-star shaped weights (0 < ε ≤ 1) which allow such local maxima. If f is a non-zero element on ℓ1(ω) we let the integer α(f) = k0 denote the index of its first non-zero term. We introduce the concept of an ε-peak point for k0. If ε = 1 then ω is star-shaped in the usual sense and there are an infinite number of 1-peak points for any k0. Although this latter fact may fail if 0 < ε < 1, if ω(n)1/n tends to zero sufficiently quickly (dependent on k0 and ε) there will always be an infinite number of ε-peak points for k0.Our main result is that if ω is an ε-star shaped weight, if f is an non-zero element of ℓ1(ω), if α(f) = k0, and if the number of ε-peak points for k0 is infinite, then the closed ideal generated by f is standard.
Positive solutions and eigenvalues of conjugate boundary value problems
Authors: Agarwal Ravi P. , Bohner Martin , Wong Patricia J. Y. 
Published: December 2008

We consider the following boundary value problemwhere λ > 0 and 1 ≤ p ≤ n – 1 is fixed. The values of λ are characterized so that the boundary value problem has a positive solution. Further, for the case λ = 1 we offer criteria for the existence of two positive solutions of the boundary value problem. Upper and lower bounds for these positive solutions are also established for special cases. Several examples are included to dwell upon the importance of the results obtained.
On realization of splitting obstructions in Browder-Livesay groups for closed manifold pairs
Authors: Akhmetiev P. M. , Cavicchioli A. , Repovš D. 
Published: December 2008

AbstractWe consider some new types of realization problem for obstructions in the Browder-Livesay groups by homotopy equivalences of closed manifold pairs. We give several examples of calculations. We also consider relations with classical surgery problems.
Triangularizing semigroups of positive operators on an atomic normed Riesz Space
Authors: Drnovšek Roman 
Published: December 2008

AbstractIn the first part of the paper we prove several results on the existence of invariant closed ideals for semigroups of bounded operators on a normed Riesz space (of dimension greater than 1) possessing an atom. For instance, if S is a multiplicative semigroup of positive operators on such space that are locally quasinilpotent at the same atom, then S has a non-trivial invariant closed ideal. Furthermore, if T is a non-zero positive operator that is quasinilpotent at an atom and if S is a multiplicative semigroup of positive operators such that TS ≤ ST for all S ∈ S, then S and T have a common non-trivial invariant closed ideal. We also give a simple example of a quasinilpotent compact positive operator on the Banach lattice l∞ with no non-trivial invariant band.The second part is devoted to the triangularizability of collections of operators on an atomic normed Riesz space L. For a semigroup S of quasinilpotent, order continuous, positive, bounded operators on L we determine a chain of invariant closed bands. If, in addition, L has order continuous norm, then this chain is maximal in the lattice of all closed subspaces of L.
Hilbert-Samuel function and Grothendieck group
Authors: Nishida Koji 
Published: December 2008

AbstractLet (A, m) be a Noetherian local ring such that the residue field A/m is infinite. Let I be arbitrary ideal in A, and M a finitely generated A-module. We denote by ℓ(I, M) the Krull dimension of the graded module ⊕n≥0InM/mInM over the associated graded ring of I. Notice that ℓ(I, A) is just the analytic spread of I. In this paper, we define, for 0 ≤ i ≤ ℓ = ℓ(I, M), certain elements ei(I, M) in the Grothendieck group K0(A/I) that suitably generalize the notion of the coefficients of Hilbert polynomial for m-primary ideals. In particular, we show that the top term eℓ (I, M), which is denoted by eI(M), enjoys the same properties as the ordinary multiplicity of M with respect to an m-primary ideal.
The dynamics of linearized polynomials
Authors: Cohen Stephen D. , Hachenberger Dirk 
Published: December 2008

AbstractLet F = GF(q). To any polynomial G ∈ F[x] there is associated a mapping Ĝ on the set IF of monic irreducible polynomials over F. We present a natural and effective theory of the dynamics of Ĝ for the case in which G is a monic q-linearized polynomial. The main outcome is the following theorem.Assume that G is not of the form , where l ≥ 0 (in which event the dynamics is trivial). Then, for every integer n ≥ 1 and for every integer k ≥ 0, there exist infinitely many μ ∈ IF. having preperiod k and primitive period n with respect to Ĝ.Previously, Morton, by somewhat different means, had studied the primitive periods of Ĝ when G = xq – ax, α a non-zero element of F. Our theorem extends and generalizes Morton's result. Moreover, it establishes a conjecture of Morton for the class of q-linearized polynomials.
On the Weiss conjecture for finite locally primitive graphs
Authors: Conder Marston D. , Li Cai Heng , Praeger Cheryl E. 
Published: December 2008

AbstractA graph Γ is said to be locally primitive if, for each vertex α, the stabilizer in Aut Γ of α induces a primitive permutation group on the set of vertices adjacent to α. In 1978, Richard Weiss conjectured that for a finite vertex-transitive locally primitive graph Γ, the number of automorphisms fixing a given vertex is bounded above by some function of the valency of Γ. In this paper we prove that the conjecture is true for finite non-bipartite graphsprovided that it is true in the case in which Aut Γ contains a locally primitive subgroup that is almost simple.
On δ-Lie supertriple systems associated with (ε, δ)-Freudenthal-Kantor supertriple systems
Authors: Kamiya Noriaki , Okubo Susumu 
Published: December 2008

AbstractWe will present an investigation of (ε, δ)-Freudenthal–Kantor supertriple systems that are intimately related to Lie supertriple systems and Lie superalgebras. We can also introduce a super analogue of Nijenhuis tensor and almost-complex structure in differential geometry.
Exact and analytic-numerical solutions of strongly coupled mixed diffusion problems
Authors: Jódar L. , Navarro E. , Martin J. A. 
Published: December 2008

AbstractThis paper deals with the construction of exact and analytical-numerical solutions with a priori error bounds for systems of the type ut = Auxx, A1u(0, t) + B1ux (0, t) = 0, A2u (1, t) + B2ux (1, t) = 0, 0 < x < 1, t > 0, u(x, 0) = f(x), where A1, A2, B1 and B2 are matrices for which no simultaneous diagonalizable hypothesis is assumed, and A is a positive stable matrix. Given an admissible error ε and a bounded subdomain D, an approximate solution whose error with respect to an exact series solution is less than ε uniformly in D is constructed.
The Dirichlet problem for the two-dimensional Laplace equation in a multiply connected domain with cuts
Authors: Krutitskii P. A. 
Published: December 2008

AbstractThe Dirichlet problem for the Laplace equation in a connected-plane region with cuts is studied. The existence of a classical solution is proved by potential theory. The problem is reduced to a Fredholm equation of the second kind, which is uniquely solvable.
Primitive inverse congruences on categorical semigroups
Authors: Fountain John , Gomes Gracinda M. S. 
Published: December 2008

AbstractWe give an abstract description of the kernel of a proper primitive inverse congruence on a categorical semigroup. More specifically, we show that it is a *-reflexive, *-unitary, *-dense subsemigroup, and that on a given categorical semigroup there is a one–one correspondence between such subsemigroups and the proper primitive inverse congruences. Our results allow us to give a description of the minimum proper primitive inverse semigroup congruence on a stronglyE*-dense categorical semigroup.
Higher-order estimates for fully nonlinear difference equations. I
Authors: Holtby Derek W. 
Published: December 2008

AbstractThe purpose of this work is to establish a priori C2, α estimates for mesh function solutions of nonlinear positive difference equations in fully nonlinear form on a uniform mesh, where the fully nonlinear finite-difference operator ℱh is concave in the second-order variables. The estimate is an analogue of the corresponding estimate for solutions of concave fully nonlinear elliptic partial differential equations. We deal here with the special case that the operator does not depend explicitly upon the independent variables. We do this by discretizing the approach of Evans for fully nonlinear elliptic partial differential equations using the discrete linear theory of Kuo and Trudinger. The result in this special case forms the basis for a more general result in part II. We also derive the discrete interpolation inequalities needed to obtain estimates for the interior C2, α semi-norm in terms of the C0 norm.
On the limit cycles of polynomial differential systems with homogeneous nonlinearities
Authors: Li Chengzhi , Li Weigu , Llibre Jaume , Zhang Zhifen 
Published: December 2008

AbstractWe consider three classes of polynomial differential equations of the form ẋ = y + establish Pn (x, y), ẏ = x + Qn (x, y), where establish Pn and Qn are homogeneous polynomials of degree n, having a non-Hamiltonian centre at the origin. By using a method different from the classical ones, we study the limit cycles that bifurcate from the periodic orbits of such centres when we perturb them inside the class of all polynomial differential systems of the above form. A more detailed study is made for the particular cases of degree n = 2 and n = 3.
Elliptic problems in ℝN with discontinuous nonlinearities
Authors: Bonanno Gabriele , Marano Salvatore A. 
Published: December 2008

AbstractFor a class of elliptic equations in the entire space and with nonlinear terms having a possibly uncountable (but of Lebesgue measure zero) set of discontinuities, the existence of strong solutions is established. Two simple applications are then developed. The approach taken is strictly based on set-valued analysis and fixed-points arguments.
Extremal solutions and strong relaxation for nonlinear periodic evolution inclusions
Authors: Papageorgiou Nikolaos S. , Yannakakis Nikolaos 
Published: December 2008

AbstractWe study the existence of extremal periodic solutions for nonlinear evolution inclusions defined on an evolution triple of spaces and with the nonlinear operator establish A being time-dependent and pseudomonotone. Using techniques of multivalued analysis and a surjectivity result for L-generalized pseudomonotone operators, we prove the existence of extremal periodic solutions. Subsequently, by assuming that A(t, ·) is monotone, we prove a strong relaxation theorem for the periodic problem. Two examples of nonlinear distributed parameter systems illustrate the applicability of our results.
On the blow-up and positive entire solutions of semilinear elliptic equations
Authors: Chern Jann-Long 
Published: December 2008

AbstractIn this paper we consider the following semilinear elliptic equationwhere n ≥ 3, and β ≥ 0, γ ≥ 0, q > p ≥ 1, μ and ν are real constants. We note that if γ = 0, β > 0 and ν ≥ 2, then the equation above is called the Matukuma-type equation. If β = 0, γ > 0 and ν > 2, then the complete classification of all possible positive solutions had been conducted by Cheng and Ni. If β > 0, γ > 0 and μ ≥ ν ≥ 2, then some results about the maximal solution and positive solution structures can be found in Chern. The purpose of this paper is to discuss and investigate the blow-up and positive entire solutions of the equation above for the μ ≥ 2 ≥ ν case.
An algorithm for constructing multidimensional biorthogonal periodic multiwavelets
Authors: Goh Say Song , Teo K. M. 
Published: December 2008

AbstractThis paper deals with the problem of constructing multidimensional biorthogonal periodic multiwavelets from a given pair of biorthogonal periodic multiresolutions. Biorthogonal polyphase splines introduced to reduce the problem to a matrix extension problem, and an algorithm for solving the matrix extension problem is derived. Sufficient conditions for collections of periodic multiwavelets to form a pair of biorthogonal Riesz bases of the entire function space are also obtained.
Infinite metacyclic groups and their non-abelian tensor squares
Authors: Beuerle James R. , Kappe Luise-Charlotte 
Published: December 2008

AbstractIn this paper we classify all infinite metacyclic groups up to isomorphism and determine their non-abelian tensor squares. As an application we compute various other functors, among them are the exterior square, the symmetric product, and the second homology group for these groups. We show that an infinite non-abelian metacyclic group is capable if and only if it is isomorphic to the infinite dihedral group
Two more representation problems
Authors: Bremner Andrew , Guy Richard K. 
Published: December 2008

We discuss the problem of finding those integers which may be represented by (x+y+z)3/xyz, and also those which may be represented byx/y+y/z+z/x, wherex, y, zare integers. For example,satisfy (x+y+z)3/(xyz) = -47, andsatisfyx/y+y/z+z/x= -86.
Groups generated by elements with rational fixed points
Authors: Mason A. W. 
Published: December 2008

Let R be a commutative integral domain and let S be its quotient field. The group GL2(R) acts on Ŝ = S ∪ {∞} as a group of linear fractional transformations in the usual way. Let F2(R, z) be the stabilizer of z ∈ Ŝ in GL2(R) and let F2(R) be the subgroup generated by all F2(R, z). Among the subgroups contained in F2(R) are U2(R), the subgroup generated by all unipotent matrices, and NE2(R), the normal subgroup generated by all elementary matrices.We prove a structure theorem for F2(R, z), when R is a Krull domain. A more precise version holds when R is a Dedekind domain. For a large class of arithmetic Dedekind domains it is known that the groups NE2(R),U2(R) and SL2(R) coincide. An example is given for which all these subgroups are distinct.
Completely bounded isomorphisms of injective von Neumann algebras
Authors: Christensen Erik , Sinclair Allan M. 
Published: December 2008

Milutin's Theorem states that if X and Y are uncountable metrizable compact Hausdorff spaces, then C(X) and C(Y) are isomorphic as Banach spaces [15, p. 379]. Thus there is only one isomorphism class of such Banach spaces. There is also an extensive theory of the Banach–Mazur distance between various classes of classical Banach spaces with the deepest results depending on probabilistic and asymptotic estimates [18]. Lindenstrauss, Haagerup and possibly others know that as Banach spaceswhere H is the infinite dimensional separable Hilbert space, R is the injective II 1-factor on H, and ≈ denotes Banach space isomorphism. Haagerup informed us of this result, and suggested considering completely bounded isomorphisms; it is a pleasure to acknowledge his suggestion. We replace Banach space isomorphisms by completely bounded isomorphisms that preserve the linear structure and involution, but not the product. One of the two theorems of this paper is a strengthened version of the above result: if N is an injective von Neumann algebra with separable predual and not finite type I of bounded degree, then N is completely boundedly isomorphic to B(H). The methods used are similar to those in Banach space theory with complete boundedness needing a little care at various points in the argument. Extensive use is made of the conditional expectation available for injective algebras, and the methods do not apply to the interesting problems of completely bounded isomorphisms of non-injective von Neumann algebras (see [4] for a study of the completely bounded approximation property).
Language modernization and planning in comparison with other types of national modernization and planning
Authors: Fishman Joshua A. 
Published: December 2008

ABSTRACTThe purpose of this review is two-fold. First of all, to move toward greater clarity with respect to a number of basic terms revealing less consensus in the language planning literature (e.g. planning, traditional, development, modernization, Westernization) than in the social sciences more generally. Secondly, but more importantly, to introduce into the language planning field a large number of concepts, questions and dimensions which have not yet found their way there from planning theory and planning research in other-than-language fields. In many (but not all) respects it would seem, on logical and impressionistic grounds, that language planning and other- than-language planning face similar burdens and benefit from related social and organizational circumstances.
Verbal and nonverbal deixis: the pointed lip gesture among the San Blas Cuna
Authors: Sherzer Joel 
Published: December 2008

ABSTRACTThe pointed lip gesture is a facial gesture in use among the Cuna Indians of San Blas, Panama. It occurs in various contexts with meanings which at first appear to be unrelated. An analysis of the contexts reveals, however, that the meaning ‘pointing’ is always present and that further meanings are derived from the discourse structures in which the pointed lip gesture is found.
Historical and linguistic evidence in favour of the relexification theory in the formation of creoles
Authors: Voorhoeve Jan 
Published: December 2008

ABSTRACTThree different Creoles spoken in Surinam are examined for their Creole origins. Saramaccan (SM) and Sranan (SN) are compared on basic vocabulary and other linguistic features and analyzed in conjunction with historical evidence. It is suggested that SN and SM speakers came to Surinam plantations with a basic knowledge of Portuguese-Creole. SN completely relexified in the direction of English, whereas SM only partly relexified toward English. Evidence suggests that Ndjuka (ND) is not a product of relexification, but developed from an eighteenth-century English pidgin. It is concluded that both ‘normal’ genetic developments and relexification may have similar results and that comparative evidence alone is not a sufficient basis for historical conclusions (comparative linguistics, creoles, relexification).
Language contact, language loyalty, and language prejudice on the Mexican border
Authors: Hidalgo Margarita 
Published: December 2008

ABSTRACTThis paper documents attitudes toward English, Spanish, and Spanish-English Code-switching in Juarez, Mexico, the oldest and largest city along the Mexican–U.S. border. It refutes the finding of related work which has shown two distinct orientations – integrative and instrumental – toward English as a foreign and as a second language, but supports various assumptions regarding the relationship between attitudes and use and the impact of the local milieu on language attitudes. It also explores attitudes toward correctness and sentiments of language loyalty, and highlights the influence of language loyalty on perceptions of Spanish-English Code-switching. Eighty-five Juarez residents were interviewed. (Language attitudes, so-ciolinguistics, Hispanic linguistics, border studies, ethnic studies, Latin American studies)