bluuebunny/crossref_metadata_2025 huggingface dataset:
On realization of splitting obstructions in Browder-Livesay groups for closed manifold pairs
Authors: Akhmetiev P. M. , Cavicchioli A. , Repovš D.
Published: December 2008

We 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

In 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

Let (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

Let 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

A 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

We 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

This 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

The 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

We 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.
Limiting behaviours of non-oscillatory solutions of a pair of coupled nonlinear differential equations
Authors: Li Wan-Tong , Cheng Sui Sun
Published: December 2008

A pair of coupled nonlinear differential equations is studied and asymptotic properties of its non-oscillatory solutions are obtained. In particular, we provide classification schemes for these solutions which are justified by existence criteria.
Higher-order estimates for fully nonlinear difference equations. I
Authors: Holtby Derek W.
Published: December 2008

The 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

We 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

For 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

We 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

In this paper we consider the following semilinear elliptic equation

where 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

This 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

In 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
On the inner automorphisms of finite transformation semigroups
Authors: Levi Inessa
Published: December 2008

If the group of inner automorphisms of a semigroup S of transformations of a finite n-element set contains an isomorphic copy of the alternating group Altn, then S is an Sn-normal semigroup and all the automorphisms of S are inner.
A note on the product of F-subgroups in a finite group
Authors: Carocca Angel
Published: December 2008

Saturated formations are closed under the product of subgroups which are connected by certain permutability properties.
Foldings and monomorphisms
Authors: Goldstein R. Z.
Published: December 2008

In this paper we generalize the folding process initiated by Stallings for graphs to a class of generalized covering spaces. These spaces are called pinched coverings or pinched cores, depending on the particular situation. We then apply our generalized folding process to manipulate these spaces into actual coverings. By using elementary homotopy arguments, we can calculate the fundamental groups of these spaces. As a corollary to our main result we obtain a generalization of a result due to Gersten concerning monomorphisms between free products of groups.
A simplistic approach to inverse transversals
Authors: Blyth T. S. , Santos M. H. Almeida
Published: December 2008

An inverse transversal of a regular semigroup S is an inverse subsemigroup that contains precisely one inverse of each element of S. In the literature there are three known types of inverse transversal, namely those that are multiplicative, those that are weakly multiplicative, and those that form quasi-ideals. Here, by considering natural ways in which certain words can be simplified, we reveal four new types of inverse transversal. All of these can be illustrated nicely in examples that are based on 2 × 2 matrices.
Asymptotic spectrum of multiparameter eigenvalue problems
Authors: Volkmer Hans
Published: December 2008

Results are given for the asymptotic spectrum of a multiparameter eigenvalue problem in Hilbert space. They are based on estimates for eigenvalues derived from the minim un-maximum principle. As an application, a multiparameter Sturm-Liouville problem is considered.
On an existence result for nonlinear evolution inclusions
Authors: Migórski Stanislaw
Published: December 2008

In this paper we present an existence result for a class of nonlinear evolutions inclusions. A result on the compactness of the solution set for a differential inclusion is also established.
Multipliers for semigroups
Authors: Blower G.
Published: December 2008

Let L be a positive invertible self-adjoint operator in L2(X;C). Using transference methods for locally bounded groups of operators we obtain multipliers for the group of complex powers Liu on vector-valued Lebesgue spaces. Using a Mellin inversion formula, we derive a sufficient condition for a function to be a multiplier of the semigroup e-tL on Lp(X;E) where E is a UMD Banach space and 1<p<∞.
Direct finiteness of certain monoid algebras II
Authors: Munn W. D.
Published: December 2008

Let S be a nontrivial monoid with zero and let F be a field. A sufficient condition, on the 0-simple principal factors of S and the characteristic of F, is given for the contracted monoid algebra of S over F to be directly finite.
Enlargements of regular semigroups
Authors: Lawson M. V.
Published: December 2008

We introduce a class of regular extensions of regular semigroups, called enlargements; a regular semigroup T is said to be an enlargement of a regular subsemigroup S if S = STS and T = TST. We show that S and T have many properties in common, and that enlargements may be used to analyse a number of questions in regular semigroup theory.
Invariants for automorphisms of certain iterated skew polynomial rings
Authors: Jordan David A. , Wells Imogen E.
Published: December 2008

Rings of invariants are identified for some automorphisms θ of certain iterated skew polynomial rings R, including the enveloping algebra of sl2(k), the Weyl algebra A1 and their quantizations. We investigate how finite-dimensional simple R-modules split over the ring of invariants Rθ and how finite-dimensional simple Rθ-modules extend to R.
The radial oscillation of solutions to ode's in the complex domain
Authors: Rossi John , Wang Shupei
Published: December 2008

We prove three results concerning the oscillation near a ray of solutions to (*)w″ + Aw = 0, where A is an entire function. The first result assumes that A is a polynomial and gives an upper bound on the number of its real zeros if (*) admits a solution with only real zeros and infinitely many. The second result proves that for A of finite order a solution w to (*) has “few” zeros “near” a ray if and only if the same is true for w′. The third result involves the density of the zeros of a solution to (*) “away” from a finite set of rays.
Principal congruences on distributive double p-algebras
Authors: De Carvalho Júlia Vaz
Published: December 2008

We use Priestley's duality to characterize, via their dual space, the distributive double p-algebras on which all congruences are principal.
Factorizations of outer functions and extremal problems
Authors: Nakazi Takahiko
Published: December 2008

The author has proved that an outer function in the Hardy space H1 can be factored into a product in which one factor is strongly outer and the other is the sum of two inner functions. In an endeavor to understand better the latter factor, we introduce a class of functions containing sums of inner functions as a special case. Using it, we describe the solutions of extremal problems in the Hardy spaces Hp for 1≦p<∞.
Local spectrum and subharmonicity
Authors: Aupetit B. , Drissi D.
Published: December 2008

Introducing the technique of subharmonic functions, we prove that the local spectrum Spu(λ)(T) is almost constant if u is an analytic family of vectors and if the spectrum of T is thin, a result which is similar to the finite-dimensional situation. We apply this result to improve a former result of C. Foiaş [7] on generalized scalar operators and results of C. Foiaş and F. -H. Vasilescu [8] on generalized commutators.
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, and

satisfyx/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.
Weighted spaces of harmonic and holomorphic functions: sequence space representations and protective descriptions
Authors: Mattila Päivi , Saksman Eero , Taskinen Jari
Published: December 2008

We study the structure of inductive limits of weighted spaces of harmonic and holomorphic functions defined on the open unit disk of ℂ, and of the associated weighted locally convex spaces. Using a result of Lusky we prove, for certain radial weights on the open unit disk D of ℂ, that the spaces of harmonic and holomorphic functions are isomorphic to complemented subspaces of the corresponding Köthe sequence spaces. We also study the spaces of harmonic functions for certain non-radial weights on D. We show, under a natural sufficient condition for the weights, that the spaces of harmonic functions on D are isomorphic to corresponding spaces of continuous or bounded functions on ∂D.
Classifications of 2-complexes whose finite fundamental group is that of a 3-manifold
Authors: Beyl F. Rudolf , Latiolais M. Paul , Waller Nancy
Published: December 2008

We consider spines of spherical space forms; i.e., spines of closed oriented 3-manifolds whose universal cover is the 3-sphere. We give sufficient conditions for such spines to be homotopy or simple homotopy equivalent to 2-complexes with the same fundamental groupGand minimal Euler characteristic 1. If the group ring ℤGsatisfies stably-free cancellation, then any such 2-complex is homotopy equivalent to a spine of a 3-manifold. IfK1(ℤG) is represented by units andKis homotopy equivalent to a spineX, thenKandXare simple homotopy equivalent. We exhibit several infinite families of non-abelian groupsGfor which these conditions apply.
Space sextic curves with six bitangents, and some geometry of the diagonal cubic surface
Authors: Dye R. H.
Published: December 2008

A general space curve has only a finite number of quadrisecants, and it is rare for these to be bitangents. We show that there are irreducible rational space sextics whose six quadrisecants are all bitangents. All such sextics are projectively equivalent, and they lie by pairs on diagonal cubic surfaces. The bitangents of such a related pair are the halves of the distinguished double-six of the diagonal cubic surface. No space sextic curve has more than six bitangents, and the only other types with six bitangents are certain (4,2) curves on quadrics. In the course of the argument we see that space sextics with at least six quadrisecants are either (4,2) or (5,1) quadric curves with infinitely many, or are curves which each lie on a unique, and non-singular, cubic surface and have one half of a double-six for quadrisecants.
Modularity* in Lie algebras
Authors: Bowman K. , Varea V. R.
Published: December 2008

A subalgebra U of a Lie algebra L over a field F is called modular* in L if U satisfies the dual of the modular identities in the lattice of subalgebras of L. Our aim is the study of the influence of the modular* identities in the structure of the algebra. First we prove that if the modular* conditions are imposed on an ideal of L then every element of L acts as an scalar on this ideal and if they are imposed on a non-ideal subalgebra U of L then the largest ideal of L contained in U also satisfies the modular* identities. We determine Lie algebras having a subalgebra which satisfies both the modular and modular* identities, provided that either L is solvable or char(F)≠ 2,3. As immediate consequences of this result we obtain that the existence of a co-atom satisfying the modular* identities in the lattice L(L) forces that the lattice L(L) is modular and that the modular* identities on any subalgebra U forces that U is quasi-abelian. In the case when L is supersolvable we obtain that the modular* conditions on any non-ideal of L are enough to guarantee that L(L) is modular. For arbitrary fields and any Lie algebra L, we prove that the modular* conditions on every co-atom of the lattice L(L) guarantee that L(L) is modular.
A note on function spaces generated by Rademacher series
Authors: Curbera Guillermo P.
Published: December 2008

Let X be a rearrangement invariant function space on [0,1] in which the Rademacher functions (rn) generate a subspace isomorphic to ℓ2. We consider the space Λ(R, X) of measurable functions f such that fg∈X for every function g=∑bnrn where (bn)∈ℓ2. We show that if X satisfies certain conditions on the fundamental function and on certain interpolation indices then the space Λ(R, X) is not order isomorphic to a rearrangement invariant space. The result includes the spaces Lp, q and certain classes of Orlicz and Lorentz spaces. We also study the cases X = Lexp and X = Lψ2 for ψ2) = exp(t2) – 1.
Weakly compact multilinear mappings
Authors: Aron Richard M. , Galindo Pablo
Published: December 2008

The notion of Arens regularity of a bilinear form on a Banach space E is extended to continuous m-linear forms, in such a way that the natural associated linear mappings, E→L (m−1E) and (m – l)-linear mappings E × … × E → E', are all weakly compact. Among other applications, polynomials whose first derivative is weakly compact are characterized.
Factorization of triangular operators and ideals through the diagonal
Authors: Orr John Lindsay , Pitts David R.
Published: December 2008

We give a necessary and sufficient condition to determine when an operator in the nest algebra of doubly infinite block upper triangular operators factors through a diagonal projection. An example shows that this condition does not extend to more general nest algebras, but a similar criterion yields a description of the ideals of nest algebras generated by diagonal projections.
Spectral mapping theorem for representations of measure algebras
Authors: Seferoǧlu H.
Published: December 2008

Let G be a locally compact abelian group, M0(G) be a closed regular subalgebra of the convolution measure algebra M(G) which contains the group algebra L1(G) and ω: M0(G) → B be a continuous homomorphism of M0(G) into the unital Banach algebra B (possibly noncommutative) such that ω(L1(G)) is without order with respect to B in the sense that if for all b ∈ B, b.ω(L1(G)) = {0} implies b = 0. We prove that if sp(ω) is a synthesis set for L1(G) then the equality holds for each μ ∈ M0(G), where sp(ω) denotes the Arveson spectrum of ω, σB(.) the usual spectrum in B, the Fourier-Stieltjes transform of μ.
Embeddings into efficient groups
Authors: Harlander Jens
Published: December 2008

A finite presentation F/N of a group G is called efficient if dF(N) = d(H2(G)) + d(F) – r(H1(G)). A finitely presented group is called efficient if it admits an efficient presentation. We show that a finitely presented group embeds into an efficient group.
Reducing the classical multipliers ℓ∞, C0 and bv0
Authors: Saxon Stephen A. , Ruckle William H.
Published: December 2008

For R ∈ {bv0, c0, ℓ∞} a multiplier of FK spaces, the classical sectional convergence theorems permit the reduction of R to any of its dense barrelled subspaces as a simple consequence of the Closed Graph Theorem. (Cf. the Bachelis/Rosenthal reduction of R = ℓ∞ to its dense barrelled subspace m0.) A natural modern setting permits the reduction of R to any of the larger class of dense βφ subspaces. Bennett and Kalton's FK setting remarkably reduced R = ℓ∞ to any of its dense subspaces. This extreme reduction also obtains in the modern βφ setting since, surprisingly, every dense subspace of ℓ∞ is a βφ subspace. Moreover, the standard results, including the Bennett/Kalton reduction, easily follow from their βφ versions and the Closed Graph Theorem. Our two supporting papers find relevant “Non-barrelled dense βφ subspaces” and study “Generalized sectional convergence and multipliers”. Here we specialize the βφ approach to ordinary, particularly unconditional, sectional convergence.
Boolean algebras of projections and resolutions of the identity of scalar-type spectral operators
Authors: de Pagter B. , Ricker W. J.
Published: December 2008

Let Μ be a Bade complete (or σ-complete) Boolean algebra of projections in a Banach space X. This paper is concerned with the following questions: When is Μ equal to the resolution of the identity (or the strong operator closure of the resolution of the identity) of some scalar-type spectral operator T (with σ(T) ⊆ ℝ) in X? It is shown that if X is separable, then Μ always coincides with such a resolution of the identity. For certain restrictions on Μ some positive results are established in non-separable spaces X. An example is given for which Μ is neither a resolution of the identity nor the strong operator closure of a resolution of the identity.
Test words of a free product of two finite cyclic groups
Authors: Voce Daniel A.
Published: December 2008

We characterize the test words of ℤm * ℤn. They are those elements not contained in a proper retract.
Asymptotic behaviours of a class of integral transforms in complex domains
Authors: Pathak R. S. , Mishra S. K.
Published: December 2008

Zemanian [17] obtained abelian theorems for the Hankel and K-transforms of functions and then extended his results to the corresponding transforms of distributions in the sense of Schwartz [11]. Jones [6] has discussed at length asymptotic behaviours of transforms generalized in his sense. Following the technique of Zemanian many authors have obtained abelian theorems for more general transforms of functions and distributions in the sense of Schwartz. Mention may be made of the works of Joshi and Saxena [7], Lavoine and Misra [8] and Pathak [10]. However, these authors were confined to the transforms of real variables only.
Maps of Stiefel manifolds and a Borsuk–Ulam theorem
Authors: Jaworowski Jan
Published: December 2008

We are concerned with the following classical version of the Borsuk–Ulam theorem: Let f:Sn→Rk be a map and let Af = {x∈Sn|fx= f(−x)}. Then, if k≦n, Af≠φ. In fact, theorems due to Yang [17] give an estimation of the size of Af in terms of the cohomology index. This classical theorem concerns the antipodal action of the group G=ℤ2 on Sn. It has been generalized and extended in many ways (see a comprehensive expository article by Steinlein [16]). This author ([9, 10)] and Nakaoka [14] proved “continuous” or “parameterized” versions of the theorem. Analogous theorems for actions of the groups G=S1 or S3 have been proved in [11], and [12]; compare also [4, 5, 6].
A moduli space of exotic ℝ4'S
Authors: Gompf Robert E.
Published: December 2008

In 1982, the first exotic ℝ4 was discovered—a smooth manifold homeomorphic to ℝ4, but not diffeomorphic to it. The object shocked topologists by its open defiance of the rules of high-dimensional smoothing theory. The exotic ℝ4 was constructed by connecting the two powerful machines of Freedman [4] and Donaldson [2] to earlier work of Casson [1].
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 spaces

where 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).
Rees matrix semigroups
Authors: Lawson Mark V.
Published: December 2008

In this paper we provide a new, abstract characterisation of classical Rees matrix semigroups over monoids with zero. The corresponding abstract class of semigroups is obtained by abstracting a number of algebraic properties from completely 0-simple semigroups: in particular, the relationship between arbitrary elements and idempotents.
Pro-C completions of crossed modules
Authors: Korkes F. J. , Porter T.
Published: December 2008

Crossed modules occur in the theory of group presentations, in group cohomology and in providing algebraic models for certain homotopy types. There are profinite analogues of each of these contexts. In this paper, we examine the problem of extending the profinite completion functor on groups to one on crossed modules thus providing a method for comparing the information contained in profinite and abstract crossed modules in each of these situations.
A class of factorable topological algebras
Authors: Ansari-Piri E.
Published: December 2008

The famous Cohen factorization theorem, which says that every Banach algebra with bounded approximate identity factors, has already been generalized to locally convex algebras with what may be termed “uniformly bounded approximate identities”. Here we introduce a new notion, that of fundamentality generalizing both local boundedness and local convexity, and we show that a fundamental Fréchet algebra with uniformly bounded approximate identity factors. Fundamentality is a topological vector space property rather than an algebra property. We exhibit some non-fundamental topological vector space and give a necessary condition for Orlicz space to be fundamental.
Existence and uniqueness of solutions for a nonlinear second order differential equation in Hilbert space
Authors: Hai Dang Dinh
Published: December 2008

This paper is concerned with the existence and uniqueness of solutions for the Picard boundary value problem

in a real Hilbert space. Our theorems improve corresponding results of Mawhin for |k| large.
Some matrix groups over finite-dimensional division algebras
Authors: Wehrfritz B. A. F.
Published: December 2008

Let n be a positive integer and D a division algebra of finite dimension m over its centre. We describe in detail the structure of a soluble subgroup G of GL(n,D). (More generally we consider subgroups of GL{n,D) with no free subgroup of rank 2.) Of course G is isomorphic to a linear group of degree mn and hence linear theory describes G, but the object here is to reduce as far as possible the dependence of the description on m. The results are particularly sharp if n=l. They will be used in later papers to study matrix groups over certain types of infinite-dimensional division algebra. This present paper was very much inspired by A. I. Lichtman's work: Free subgroups in linear groups over some skew fields, J. Algebra105 (1987), 1–28.
Nevanlinna-type characterizations for the Bloch space and related spaces
Authors: Stroethoff Karel
Published: December 2008

We give a characterisation of the Bloch space in terms of an area version of the Nevanlinna characteristic, analogous to Baernstein's description of the space BMOA in terms of the usual Nevanlinna characteristic. We prove analogous results for the little Bloch space and the space VMOA, and give value distribution characterizations for all these spaces. Finally we give valence conditions on a Bloch or little Bloch function for containment in BMOA or VMOA.
More On the countability index and the density index of S(X)
Authors: Magill K. D.
Published: December 2008

The countability index, C(S), of a semigroup S is the smallest integer n, if it exists, such that every countable subset of S is contained in a subsemigroup with n generators. If no such integer exists, define C(S) = ∞. The density index, D(S), of a topological semigroup S is the smallest integer n, if it exists, such that S contains a dense subsemigroup with n generators. If no such integer exists, define D(S) = ∞. S(X) is the topological semigroup of all continuous selfmaps of the locally compact Hausdorff space X where S(X) is given the compact-open topology. Various results are obtained about C(S(X)) and D(S(X)). For example, if X consists of a finite number (< 1) of components, each of which is a compact N-dimensional subspace of Euclidean Nspace and has the internal extension property and X is not the two point discrete space. Then C(S(X)) exceeds two but is finite. There are additional results for C(S(X)) and similar results for D(S(X)).
Language modernization and planning in comparison with other types of national modernization and planning
Authors: Fishman Joshua A.
Published: December 2008

The 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

The 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

Three 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

This 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)
Decreolization?
Authors: Bailey Guy , Maynor Natalie
Published: December 2008

As scholars have begun to reach a consensus on the Black English Vernacular (BEV) over the last decade, three important assumptions about that variety have emerged: (a) the grammars of children and adults are essentially alike, (b) BEV is decreolizing, and (c) most differences between BEV and white speech are the result of the persistence of creole features. However, these assumptions are largely based on comparisons of the speech of North American black children to that of Caribbean creole speakers, with no real attempt to establish the direction of grammatical change in BEV. Our work with black children and elderly adults in Texas tries to determine the direction of grammatical change in black English. This work suggests that all three of the assumptions listed above are unwarranted. The grammars of elderly adults and children are structurally, not just quantitatively different. The differences between the two varieties indicate that BEV is not decreolizing but is actually diverging from white speech. Finally, the differences suggest that differences between black and white speech are sometimes the result of contemporary developments rather than of the persistence of creole features. (Black English, decreolization, divergence, language change, reanalysis, sociolinguistics)
An account of social usages of Americanized argot in modern Russia
Authors: Korovkin Michael A.
Published: December 2008

This article reports the emergence of a new “Americanized” argot in post-Stalinist Russia. It attempts to qualify the type of communicative code characteristic of the argot and to illuminate the link between the code and the communicative competence of argot-speaking groups. The article examines the pattern of recruitment into argot-speaking groups. It speculates on the set of relationships between this pattern and the process of socialization in the wider social milieu at school and in the families of different socioeconomic classes. (Sociolinguistics, symbolic anthropology, social change, Slavonic and Soviet studies, social boundaries and “primary groups,” revitalization movements)
“Something on the order of around forty to forty-four”: Imprecise numerical expressions in biomedical slide talks
Authors: Dubois Betty Lou
Published: December 2008

To investigate forms and functions of imprecise numerical expressions in biomedical slide talks, tokens were extracted from fifty-two talks presented at the 1979 annual meeting of the Federation of American Societies for Experimental Biology. Imprecise expressions include rounding, extreme rounding (to multiples of five or ten), ranges (both explicit and implicit), common fractions, and common multiples, all of which can be hedged, either simply or multiply. Imprecision can be occasioned by factors such as preliminary nature of results, small number of experimental animals, questionably applicable technique or apparatus, and inability to measure all members of a class. Rhetorically, imprecision foregrounds other, more precise quantities which the experimenter considers important, and thus, it can be seen as modality. Imprecision marks the talks as preinformation in Ziman's model of the social production of science and also as simultaneous popularization and peer communication. (Biomedical slide talks, imprecise numerical expressions, scientific rhetoric, modality, Zimanian social production of science)
Rules of address in secondary schools in Catania: Linguistic variation and its social/cultural value
Authors: Consoli Eleonora
Published: December 2008

The present research was carried out in Catania, a town of 600,000 inhabitants on the eastern coast of Sicily, and was motivated by the observation of cases of nonreciprocity of address to female teachers in secondary schools. While male teachers were always addressed with their academic, professional titles, which have great, overt prestige in southern Italy, women, on the contrary, were often addressed as signora or signorina ‘Mrs./Miss’ in the vocative form. The main objectives of the research were to find out (a) which schools were involved in this case of nonreciprocity; (b) how many female teachers considered it a sign of respect or an act of discrimination; (c) if the linguistic imbalance reflected a social one; and (d) what were its psychological causes. (Linguistic imbalance, nonreciprocity of titles, asymmetrical address, social imbalance, Italian)
Cross cultural factors in phonological change
Authors: Lomax Alan
Published: December 2008

ABSTRACTS

Analysis of the vowel/consonant patterns in a world sample of folk songs indicates that some speech sounds vary regularly with certain aspects of social structure. Consonant frequencies shift in relation to technological level: mid stops, fricatives and laterals increase in relative frequency along a scale of productive range. Alteration in the vowel map, on the other hand, seems to be related to cross-cultural differences in sex role. Thus changes in phonology, familiar to the linguist, may be symbolic of and explained by familiar societal phenomena. These suppositions are, it is true, based on the analysis of sung languages and remain to be confirmed for speech. However, the power of expressive style as a general diagnostic of the layout of culture implies that they will be so confirmed, since expressive patterns often turn out to be a sort of heightened and extra-redundant version of everyday behavior. Moreover, collections of recorded song performances provide a world-wide resource of ‘unselfconscious’ and culturally validated language data that is simply unavailable for other kinds of speech activity. (Phonology; variation; expressive (stylistic) function; song style; mode of production and se role; cross-cultural sample.)
Haya metaphors for speech
Authors: Seitel Peter
Published: December 2008

Metaphorical statements about speech are shown to embody implicitly certain indigenously named semantic dimensions. Hayas use these dimensions to conceive of and evaluate their own speech behavior. The dimensions are specified first through indigenous literal statements about speech, then through one-word metaphors applied to speech, and finally through ten proverbs about speech interactions that link metaphorically a named category of speech act with the alimentary act of expelling a flatus. (Metaphor, humor, componential analysis, folklore, proverbs, speech acts, ethnography of communication.)
On the structure of speaker–auditor interaction during speaking turns
Authors: Duncan Starkey
Published: December 2008

The structure of speaker–auditor interaction during speaking turns was explored, using detailed transcriptions of language, paralanguage, and body-motion behaviors displayed by both participants in dyadic, face-to-face conversations. On the basis of certain observed regularities in these behaviors, three signals were hypothesized: (a) a speaker within-turn signal, (b) an auditor back-channel signal, and (c) a speaker continuation signal. These signals were composed of various behaviors in language and in body motion. It was further hypothesized that the display of appropriate ordered sequences of these signals by both participants, served to mark ‘units of interaction’ during speaking turns. (Conversational analysis; speaking turns; back-channel behaviors; interrelations of verbal and nonverbal behavior; American English (Chicago)).
Error correction as an interactional resource
Authors: Jefferson Gail
Published: December 2008

This paper considers some small errors which occur in natural talk, treating them as matters of competence, both in the production of coherent speech and the conduct of meaningful interaction.

Focusing on a rule-governed occurrence of the interjection ‘uh’, a format is described by which one can display that one is correcting an error one almost, but did not, produce. It is argued that there are systematic ways in which someone who hears such talk can find that an error was almost made and what that error would have been.

Two broad classes of error are considered, both of which can be announced by and extracted from the occurrence of an error correction format. These are ‘production’ errors; i.e. a range of troubles one encounters in the attempt to produce coherent, grammatically correct speech, and ‘interactional’ errors; i.e. mistakes one might make in the attempt to speak appropriately to some co-participant(s) and/or within some situation.

Focusing on interactional errors, it is proposed that the error correction format (and other formats for events other than error) can be used to invoke alternatives to some current formulation of self and other(s), situation and relationship, and thereby serve as a resource for negotiating and perhaps reformulating a current set of identities. (Conversational analysis, discourse devices (metalinguistic, attitudinal markers), U.S. English.)