bluuebunny/crossref_metadata_2025 huggingface dataset:
Asymptotic expansion of a series of Ramanujan
Authors: Berndt Bruce C. , Evans Ronald J.
Published: December 2008

An asymptotic expansion is given for the series

as x→∞ in the sector |Argx|≦π/2–δ. Here δ, Re(a), and Re(s) are positive and r is a positive integer. In the case a = r = s = 1, this yields the nontrivial result

stated by Ramanujan in his notebooks [6].
Limits of pure states, II
Authors: Archbold R. J. , Zaki A. M.
Published: December 2008

We answer a question raised in an earlier paper concerning the pure state space of a separable C*-algebra.
Distinguishedness of weighted Fréchet spaces of continuous functions
Authors: Bastin Françoise
Published: December 2008

In this paper, we prove that ifis an increasing sequence of strictly positive and continuous functions on a locally compact Hausdorff spaceXsuch thatthen the Fréchet spaceC(X) is distinguished if and only if it satisfies Heinrich's density condition, or equivalently, if and only if the sequencesatisfies condition (H) (cf. e.g.‵[1] for the introduction of (H)). As a consequence, the bidual λ∞(A) of the distinguished Köthe echelon space λ0(A) is distinguished if and only if the space λ1(A) is distinguished. This gives counterexamples to a problem of Grothendieck in the context of Köthe echelon spaces.
On a problem of R. G. D. Richardson
Authors: Binding Paul , Volkmer Hans
Published: December 2008

In 1913 Richardson published necessary and sufficient conditions for a system of three Sturm–Liouville equations, linked by three parameters, to possess eigenfunctions with arbitrarily many zeros. His work contains errors, but we give conditions of his type valid for k self-adjoint equations, with k parameters.
On a non-convex hyperbolic differential inclusion
Authors: Staicu Vasile
Published: December 2008

We prove the existence of a solution u(.,.;α,β) of the Darboux problem uxy∈F(x, y, u), u(x,0) = α(x), u(0, y) = β(y), which is continuous with respect to (α,β). We assume that F is Lipschitzean with respect to u but not necessarily convex valued.
On valuations of K(x)
Authors: Khanduja Sudesh K.
Published: December 2008

For a valued field (K, v), let Kv denote the residue field of v and Gv its value group. One way of extending a valuation v defined on a field K to a simple transcendental extension K(x) is to choose any α in K and any μ in a totally ordered Abelian group containing Gv, and define a valuation w on K[x] by w(Σici(x – α)i) = mini (v(ci) + iμ). Clearly either Gv is a subgroup of finite index in Gw = Gv + ℤμ or Gw/Gv is not a torsion group. It can be easily shown that K(x)w is a simple transcendental extension of Kv in the former case. Conversely it is well known that for an algebraically closed field K with a valuation v, if w is an extension of v to K(x) such that either K(x)w is not algebraic over Kv or Gw/Gv is not a torsion group, then w is of the type described above. The present paper deals with the converse problem for any field K. It determines explicitly all such valuations w together with their residue fields and value groups.
The extraordinary higher tangent spaces of certain quadric intersections
Authors: Dye R. H.
Published: December 2008

Let Cr, be the intersection of n — r quadrics with a common self-polar simplex S in projective n-space [n]. Let Γr be a Cr that can be taken in coordinate form as Every C1 is a Γ1, and its points of hyperosculation have special properties: they are the points of intersection of C1 with the faces of S each counting (n—1)(n — 2)/2 times, and the osculating [s], for s≦n–1, has 2s-point contact. Here we show that if r≧2 and n>2r then every point of Γ, has exceptional higher tangent spaces: the s-tangent space at a point P of an r-dimensional variety V is the intersection of all primes that cut V in a variety having an (s + l)-fold point (at least) at P, and normally has dimension if this is less than n. The s-tangent space to Γ, at a point not in a face of S is an [rs] (provided rs <n). Usually it is the existence of lines on V through P that cause a lower than expected s-tangent dimension. Not so on Γr, since its lines form a subvariety. If n≧5 not every C2 is a Γ2. Take n≧5. We show that C2 is Γ2 if and only if C2 contains a line. Also C2 is a Γ2 if and only if at some one point of C2 off the faces of S the second-tangent space is a [4]. Thus, unexpectedly, we have: if one point of C2 off the faces of S has a [4] for second-tangent space, then so do all such points of C2. We obtain results for points of Γ, in the faces of S.
Trigonometric interpolation
Authors: Goodman T. N. T. , Sharma A.
Published: December 2008

We consider interpolation at 2n equidistant nodes in [0,π) from the space ℱN spanned by sines and cosines of odd multiples of x. This interpolation problem is shown to be correct for an arbitrary sequence of derivatives specified at all the nodes. Explicit expressions for the fundamental polynomials are obtained and it is shown that under mild smoothness assumptions on the function f interpolant from ℱN converges uniformly to f as the node spacing goes to zero.
Homotopy equivariance, strict equivariance and induction theory
Authors: Greenlees J. P. C.
Published: December 2008

An obvious question occurs at the very start of equivariant homotopy theory. What is the relationship between maps equivariant up to homotopy and strictly equivariant maps? This question has been studied by various people, usually away from the group order ([8, 11, 22, 25, 26]). We consider the problem stably and answer it by giving a spectral sequence proceeding from homotopy equivariant to strictly equivariant information. The form of the spectral sequence is not surprising, but there are three distinctive features of our approach: (1) we show that the spectral sequence may be viewed as an Adams spectral sequence based on nonequivariant homotopy, (2) we show how to exploit the product structure, and (3) we give a treatment showing how Dress's algebra of induction theory [13] applies to give non-normal subgroups equal status. As a spinoff from (3) we also obtain spectral sequences for calculating homology and cohomology of universal spaces (3.5).
Residuated regular semigroups
Authors: Blyth T. S. , Pinto G. A.
Published: December 2008

We prove that in a residuated regular semigroup the elements of the form and are idempotents, and derive some consequences of this fact. In particular, we show how the maximality of such idempotents is related to the semigroup being naturally ordered, and obtain from this a characterisation of the boot-lace semigroup of [2].
Lp-equivalence of a linear and a nonlinear impulsive differential equation in a Banach space
Authors: Bainov D. D. , Kostadinov S. I. , Zabreiko P. P.
Published: December 2008

In the present paper by means of the Schauder-Tychonoff principle sufficient conditions are obtained for Lp-equivalence of a linear and a nonlinear impulsive differential equations.
The asymptotic distribution of the eigenvalues of right definite multiparameter Sturm-Liouville systems
Authors: Rynne Bryan P.
Published: December 2008

This paper studies the asymptotic distribution of the multiparameter eigenvalues of a right definite multiparameter Sturm–Liouville eigenvalue problem. A uniform asymptotic analysis of the oscillation number of solutions of a single Sturm–Liouville type equation with potential depending on a general parameter is given; these results are then applied to the system of multiparameter Sturm–Liouville equations to give the asymptotic eigenvalue distribution for the system as a function of a “multi-index” oscillation number.
On semigroup presentations
Authors: Robertson Edmund F. , Ünlü Yusuf
Published: December 2008

Semigroup presentations have been studied over a long period, usually as a means of providing examples of semigroups. In 1967 B. H. Neumann introduced an enumeration method for finitely presented semigroups analogous to the Todd–Coxeter coset enumeration process for groups. A proof of Neumann's enumeration method was given by Jura in 1978.

In Section 3 of this paper we describe a machine implementation of a semigroup enumeration algorithm based on that of Neumann. In Section 2 we examine certain semigroup presentations, motivated by the fact that the corresponding group presentation has yielded interesting groups. The theorems, although proved algebraically, were suggested by the semigroup enumeration program.
On minimal thinness, reduced functions and Green potentials
Authors: Essén Matts
Published: December 2008

Let Ω be an open connected subset of the unit disc U, let E = U\Ω and let {Ωk} be a Whitney decomposition of U. If z(Q) is the centre of the “square” Q, if T is the unit circle and t = dist.(Q, T), we consider

where Ek = E ∩ Qk and c(Ek) is the capacity of Ek. We prove that the set E is minimally thin at τ ∈ T in U if and only if W(τ)< ∞. We study functions of type W and discuss the relation between certain results of Naim on minimal thinness [15], a minimum principle of Beurling [3], related results due to Dahlberg [7] and Sjögren [16] and recent work of Hayman-Lyons [15] (cf. also Bonsall [4]) and Volberg [19]. For simplicity, we discuss our problems in the unit disc U in the plane. However, the same techniques work for analogous problems in higher dimensions and in more complicated regions.
Classification of limits of triangular matrix algebras
Authors: Hopenwasser A. , Power S. C.
Published: December 2008

Let Tn be the operator algebra of upper triangular n × n complex matrices. Three families of limit algebras of the form lim (Tnk) are classified up to isometric algebra isomorphism: (i) the limit algebras arising when the embeddings Tnk→Tnk+1, are alternately of standard and refinement type; (ii) limit algebras associated with refinement embeddings with a single column twist; (iii) limit algebras determined by certain homogeneous embeddings. The last family is related to certain fractal like subsets of the unit square.
The squareroot of an ambiguous form in the principal genus
Authors: Hardy Kenneth , Williams Kenneth S.
Published: December 2008

A squareroot of an ambiguous form in the principal genus of primitive integral binary quadratic forms of fixed discriminant is given explicitly in terms of a solution of a certain Legendre equation.
Lp-convergence of a certain class of product martingales
Authors: Koumandos Stamatis
Published: December 2008

We establish the Kakutani dichotomy property for two generalized Rademacher–Riesz product measures μ, ν that either μ, ν are equivalent measures or they are mutually singular according as a certain series converges or diverges. We further give sufficient conditions so that in the equivalence case the Radon–Nikodym derivative dμ/dν belongs to Lp(v) for all positive real numbers p, by proving that a certain product martingale converges in Lp(v) for p ≧ 1.
On rooted properties of complex analytic systems
Authors: Zhao Xiao-Qiang
Published: December 2008

This paper is devoted to the study of rooted properties of phase surfaces defined by complex analytic systems. We first obtain the Rooted Theorem of Analytic Systems. Then we prove the Generalized Strong Rooted Theorem of (m ≧ 2), which implying the Strong Rooted Theorem of a Class of .
The asymptotic distribution of the eigenvalues of multiparameter Sturm–Liouville systems II
Authors: Rynne Bryan P.
Published: December 2008

In a previous paper we studied the asymptotic distribution of the multiparameter eigenvalues of uniformly right definite multiparameter Sturm–Liouville eigenvalue problems. In this paper we extend the analysis to deal with multiparameter Sturm–Liouville problems satisfying uniform left definiteness, and non-uniform left and right definiteness.
Unions of Cockcroft two-complexes
Authors: Bogley W. A.
Published: December 2008

A combinatorial hypothesis is presented that serves as a necessary and sufficient condition for a union of connected Cockcroft two-complexes to be Cockcroft. This combinatorial hypothesis has a component that can be expressed in terms of the second homology of groups. The hypothesis is applied to the study of the third homology of groups.
Oscillation results on y″ + Ay = 0 in the complex domain with transcendental entire coefficients which have extremal deficiencies
Authors: Chiang Y. M.
Published: December 2008

Let A(z) be a transcendental entire function and f1, f2 be linearly independent solutions of

We prove that if A(z) has Nevanlinna deficiency δ(0, A) = 1, then the exponent of convergence of E: = flf2 is infinite. The theorems that we prove here are similar to those in Bank, Laine and Langley [3].
Asymptotic tracts of harmonic functions II
Authors: Barth K. F. , Brannan D. A.
Published: December 2008

An asymptotic tract of a real function u harmonic and non-constant in ℂ is a component of the set {z:u(z)≠c}, for some real number c; a quasi-tractT(≠ℂ) is an unbounded simply-connected domain in ℂ such that there exists a function u that is positive, unbounded and harmonic in T such that, for each point ζ∈∂T∩ℂ,

and a ℱ-tract is an unbounded simply-connected domain T in ℂ whose every prime end that contains ∞ in its impression is of the first kind.

The authors study the growth of a harmonic function in one of its asymptotic tracts, and the question of whether a quasi-tract is an asymptotic tract. The branching of either type of tract is also taken into consideration.
Fronts, domain walls and pulses in a generalized Ginzburg-Landau equation
Authors: Duan Jinqiao , Holmes Philip
Published: December 2008

We discuss the existence and non-existence of front, domain wall and pulse type traveling wave solutions of a Ginzburg-Landau equation with cubic terms containing spatial derivatives and a fifth order term, in both subcritical and supercritical cases. Our results appear to be the first rigorous existence and non-existence proofs for the full equation with all possible terms derived from second order perturbation theory present.
Idempotent endomorphisms of an independence algebra of finite rank
Authors: Gomes Gracinda M. S. , Howie John M.
Published: December 2008

The result of Ballantine [1] to the effect that a singular matrix A is a product of k idempotent matrices if and only if the rank of I – A does not exceed k times the nullity of A is generalized to endomorphisms of a class of independence algebras.
Functional calculi and decomposability of unbounded multiplier operators in LP(ℝN)
Authors: Albrecht Ernst , Ricker Werner J.
Published: December 2008

It is known, for each 1<p<∞, p≠2, that there exist differential operators in LP(ℝN) which are not (unbounded) decomposable operators in the sense of C. Foiaş. In this note we exhibit large classes of differential (and unbounded multiplier operators which are decomposable in LP(ℝN) and hence have good spectral mapping properties; the arguments are based on the existence of a sufficiently rich functional calculus. The basic idea is to take advantage of existing classical results on p-multipliers and use them to generate appropriate functional calculi.
A simple construction of exponential bases in L2 of the union of several intervals
Authors: Seip Kristian
Published: December 2008

It is proved that every space L2 (I1, ∪ I2), where I1 and I2 are finite intervals, has a Riesz basis of complex exponentials , {λk} a sequence of real numbers. A partial result for the corresponding problem for n≧3 finite intervals is also obtained.
Projective resolutions for graph products
Authors: Cohen Daniel E.
Published: December 2008

Let Γ be a finite graph together with a group Gv at each vertex v. The graph productG(Γ) is obtained from the free product of all Gv by factoring out by the normal subgroup generated by for all adjacent v, w.

In this note we construct a projective resolution for G(Γ) given projective resolutions for each Gv, and obtain some applications.
Multiparameter spectral theory of singular differential operators
Authors: Rynne B. P.
Published: December 2008

In this paper we investigate certain aspects of the multiparameter spectral theory of systems of singular ordinary differential operators. Such systems arise in various contexts. For instance, separation of variables for a partial differential equation on an unbounded domain leads to a multiparameter system of ordinary differential equations, some of which are defined on unbounded intervals. The spectral theory of systems of regular differential operators has been studied in many recent papers, e.g. [1, 3, 6, 9, 19, 21], but the singular case has not received so much attention. Some references for the singular case are [7, 8, 10, 13, 14, 18, 20], in addition general multiparameter spectral theory for self adjoint operators is discussed in [3, 9, 19].
On the automorphisms of the group ring of a finitely generated free abelian group
Authors: Parmenter M. M.
Published: December 2008

Let R be an associative ring with 1 and G a finitely generated torsion-free abelian group. In this note, we classify all R-automorphisms of the group ring RG. The special case where G is infinite cyclic was previously settled in [8], and our interest in this problem was rekindled by the recent paper of Mehrvarz and Wallace [7], who carried out the classification in the case where R contains a nilpotent prime ideal.
Hyperbolic travelling fronts
Authors: Hadeler K. P.
Published: December 2008

Since the work of R. A. Fisher [2] and Kolmogorov, Petrovskij and Piskunov [7] (see [6] for further references) the problem of travelling fronts in reaction–diffusion equations has been extensively studied. For the equation

with F(0) = F(1) = 0 a travelling front is a solution

where the function of one variable φ is decreasing and satisfies φ(−∞) = 1, φ(+∞) = 0. The function φ describes the shape of the front and the constant c is the speed of propagation. There are two main types of the problem. In the all-positive case, where the function F satisfies

there is a half-line [c0, ∞), c0>0, of speeds. For each c∈[c0, ∞) there is, up to translation, a unique travelling front. Fronts for different c can be distinguished by the rate of decay towards +∞. In the threshold case, where F has the property, for some λ∈(0, 1),

there is a unique speed c0 with a travelling front, which is unique up to translation. In this case the sign of c0 is determined by the sign of the integral
An algorithm for solving generalized algebraic Lyapunov equations in Hilbert space, applications to boundary value problems
Authors: Jódar Lucas
Published: December 2008

Let L(H) be the algebra of all bounded linear operators on a separable complex Hubert space H. In a recent paper [7], explicit expressions for solutions of a boundary value problem in the Hubert space H, of the type

are given in terms of solutions of an algebraic operator equation
Boundary value problem for a singularly perturbed system of linear differential equations with impulses
Authors: Bainov D. D. , Hekimova M. A. , Veliov V. M.
Published: December 2008

In connection with the analysis of mathematical models of real processes undergoing short time perturbations, in the last years the interest in the differential equations with impulses remarkably increased. Going back to the papers of Mil'man and Myshkis [4, 5] the investigations of this subject are now extended to different directions concerning applications in physics, biology, electronics, automatic control etc.
Multiparameter spectral theory and Taylor's joint spectrum in Hilbert space
Authors: Rynne B. P.
Published: December 2008

Let n≧1 be an integer and suppose that for each i= 1,…,n, we have a Hilbert space Hi and a set of bounded linear operators Ti, Vij:Hi→Hi, j=1,…,n. We define the system of operators

where λ=(λ1,…,λn)∈ℂn. Coupled systems of the form (1.1) are called multiparameter systems and the spectral theory of such systems has been studied in many recent papers. Most of the literature on multiparameter theory deals with the case where the operators Ti and Vij are self-adjoint (see [14]). The non self-adjoint case, which has received relatively little attention, is discussed in [12] and [13].
Covering lemmas revisited
Authors: Carbery Anthony
Published: December 2008

In this note we intend to discuss the method of A. Córdoba and R. Fefferman of using covering lemmas to control maximal functions, and make some simplifications which allow us to obtain alternative proofs of some of their results.
Asymptotic equivalence of a linear and nonlinear system with impulse effect
Authors: Simeonov P. S. , Bainov D. D.
Published: December 2008

The present paper deals with the problem of asymptotic equivalence of the system with impulse effect

and

where x, y:I→Rn; g:I→Rn; f:I × Rn→Rn; bk:Rn→Rn; I = [0, ∞); Rn is the n-dimensional Euclidean space with a norm |·|; A and B are constant matrices; the moments {tk} constitute an increasing sequence 0 < t1 < … < tk < …, limk→∞tk = ∞.
Aronszajn's theorem for some nonlinear Dirichlet problems with unbounded nonlinearities
Authors: Nieto Juan J.
Published: December 2008

We consider the Dirichlet problem

where g is continuous and h ∈ L2(0, π).
Differentiability of solutions of systems with impulse effect with respect to initial data and parameter
Authors: Simeonov P. S. , Bainov D. D.
Published: December 2008

It is characteristic for the development of many processes that in certain moments they change their state in jumps. Systems with impulse effect provide an adequate mathematical model of such processes. The investigation of these systems begins with the paper of Millman and Myshkis [7] and afterwards the number of publications dedicated to this problem rapidly increases.
Semisimple radical classes of involution algebras
Authors: Loi N. V.
Published: December 2008

J. Wichman has asked about semisimple radical classes of involution algebras. In the present paper we describe the semisimple radical classes of involution algebras over a field K* with involution *. If K* is infinite, then there are only trivial semisimple radical classes. If K* is finite then these classes are subdirect closures of strongly hereditary finite sets of finite idempotent algebras. In proving this result we determine the structure of certain simple involution algebras. We prove that the variety of symmetric involution algebras over Z(2) does not have attainable identities, answering a problem posed by Gardner [2]. Most of the results are valid also for involution rings (over the integers).
Rings that are FGC relative to filters of ideals
Authors: Barbut Erol , Brandal Willy
Published: December 2008

All our rings will be commutative with identity not equal to zero. Also R will always denote a ring. is a filter of ideals of R if is a nonempty set of ideals of R satisfying: I∈ and J is an ideal of R with I⊂J, then J∈, and if I, J∈ then I∩J∈. A Gabriel topology of R is a filter of ideals of R satisfying: if J∈ and I is an ideal of R with (I:x)∈ for all x∈J, then I∈. See the B. Stenström text [6]. We say that a ring R is an FGC ring if every finitely generated R-module is a direct sum of cyclic R-modules. Use mspec R for the set of all maximal ideals of R.
Notes on a radical of Divinsky
Authors: Sands A. D.
Published: December 2008

In his book [1] Divinsky refers to eight radicals as classical. In [6] radicals were considered such that the radical of each one-sided ideal of a ring may be expressed as the intersection of a left ideal and a right ideal of the ring. From results obtained there it was deduced that seven of these eight radicals have this property. The purpose of this note is to give a proof that this property also holds for the remaining one of these classical radicals.
Naturally ordered regular semigroups with maximum inverses
Authors: Saito Tatsuhiko
Published: December 2008

Let S be a regular semigroup. An inverse subsemigroup S° of S is called an inverse transversal if S° contains a unique inverse of each element of S. An inverse transversal S° of S is called multiplicative if x°xyy° is an idempotent of S° for every x, y∈S, where x° denotes the unique inverse of x∈S in S°. In Section 1, we obtain a necessary and sufficient condition in order for inverse transversals to be multiplicative.
Differential inclusions with state constraints
Authors: Papageorgiou Nikolaos S.
Published: December 2008

In “Viability Theory”, we select trajectories which are viable in the sense that they always satisfy a given constraint. Since the fundamental work of Nagumo [26], we know that in order to guarantee existence of viable trajectories, we need to satisfy certain tangential conditions. In the case of differential inclusions and using the modern terminology and notation of tangent cones, this condition takes the formF(t,x) ∩TK#φ, whereF(.,.) is the orientor field involved in the differential inclusion,Kis the viability (constraint) set andTK(x) is the tangent cone toKatx. Results on the existence of viable solutions for differential inclusions can be found in Aubin–Cellina [2] and Papageorgiou [30,32].
A version of Runge's theorem for the Helmholtz equation with applications to scattering theory
Authors: Ochs R. L.
Published: December 2008

Let D be a bounded, simply connected domain in the plane R2 that is starlike with respect to the origin and has C2, α boundary, ∂D, described by the equation in polar coordinates

where C2, α denotes the space of twice Hölder continuously differentiable functions of index α. In this paper, it is shown that any solution of the Helmholtz equation

in D can be approximated in the space by an entire Herglotz wave function

with kernel g ∈ L2[0,2π] having support in an interval [0, η] with η chosen arbitrarily in 0 > η < 2π.
An elementary approach to the matricial Nevanlinna–Pick interpolation criterion
Authors: Power S. C.
Published: December 2008

The matricial Nevanlinna–Pick interpolation criterion determines when there is an analytic matrix contraction valued function on the complex unit disc which assumes preassigned n × n matrix values w1,…,wm at preassigned interpolation points z1,…,zm. Taking ∥wi∥ < 1, for i = 1,…,m, the necessary and sufficient condition is the positivity of the nm × nm matricial Pick matrix,
On the non-vanishing of Poincaré series
Authors: Mozzochi C. J.
Published: December 2008

R. A. Rankin [2] and J. Lehner [1] considered the non-vanishing of Poincaré series for the classical modular matrix group and for an arbitrary fuchsian group, respectively.

In this paper we consider the non-vanishing of Poincaré series for the congruence group
Hermitian forms over odd dimensional algebras
Authors: Lewis D. W.
Published: December 2008

Let L be an odd degree extension field of the field K, char K ≠ 2. Let U* denote the natural extension map from W(K) to W(L) where W(K), resp. W(L) denotes the Witt group of quadratic forms over K, resp. L. It is well-known that U* is injective [4, p. 198]. In fact Springer [10] proved a stronger theorem, namely that if φ is anisotropic over K then it remains anisotropic on extension to L. Rosenberg and Ware [8] proved that if L is a Galois extension then the image of U* is precisely the subgroup of W(L) fixed by the Galois group of L over K, this Galois group having a natural action on W(L). See [4, p. 214] and [3] for a quick proof. See also Dress [1] who extended these results to equivariant forms. In this article we investigate the corresponding map U* when we replace the field L by a central simple K-algebra of odd degree and indeed more generally by any finite dimensional K-algebra which becomes odd-dimensional on factoring out by the radical. Our algebras are equipped with an involution of the second kind, i.e. one which is non-trivial on the centre, and we replace quadratic forms by hermitian forms with respect to the involution. We show that U* is injective for all the algebras mentioned above and that a weaker version of Springer's theorem holds for central simple algebras of odd degree provided we make a suitable restriction on the nature of the involution. We show that the analogue of the Rosenberg-Ware result is valid for hermitian forms over odd-dimensional Galois field extensions but that for central simple algebras of odd degree a result as nice as the Rosenberg–Ware one cannot hold. Indeed the group of all K-automorphisms of such an algebra which commute with the involution fixes all of the Witt group. However the map U* is not surjective in general even for division algebras of odd degree.
The 2-primitive ideals of structural matrix near-rings
Authors: Van Wyk L.
Published: December 2008

An isomorphism (as groups) is established between an arbitrary connected module over a structural matrix near-ring and a direct sum of appropriate modules over the base near-ring. This isomorphism leads to a characterization of the 2-primitive ideals of a structural matrix near-ring.
On central automorphisms of finite-by-nilpotent groups
Authors: Franciosi Silvana , de Giovanni Francesco
Published: December 2008

The effect of imposing a certain finiteness condition on the group of central automorphisms of a finite-by-nilpotent group is investigated. In particular it is shown that, if each central automorphism of a finite-by-nilpotent group G has finite order, then the factor group G/Z(G) has finite exponent.
On the lower radical construction of Tangeman and Kreiling
Authors: Sands A. D.
Published: December 2008

It is shown that the lower radical construction of Tangeman and Kreiling need not terminate at any ordinal.
An upper bound for λ1 for Γ(q) and Γ0(q)
Authors: Mozzochi C. J.
Published: December 2008

Under the assumption of the Selberg conjecture I establish by means of the Selberg trace formula the following:

Theorem. Let Γ denote Γ(q) or Γ0(q), q square-free. Let Δq denote the Laplace operator on L2(Γ\H), and let Σq denote its discrete spectrum. Then there exists an absolute positive constant A such that for q≧A
Monoids over which all weakly flat acts are flat
Authors: Bulman-Fleming Sydney , McDowell Kenneth
Published: December 2008

If R is a ring with identity and M is a left R-module then it is well known that the following statements are equivalent:

(1) M is flat.

(2) The functor −⊗M preserves embeddings of right ideals into R.

This paper investigates situations in which the analogous statements are equivalent in the context of S-sets over a monoid S.
The Baker–Pym theorem and multipliers
Authors: Takahasi Sin-Ei
Published: December 2008

A new interpretation of the Baker–Pym theorem is given in terms of operators and applies to a characterization of multipliers on a Banach algebra.
On normal subgroups of direct products
Authors: Johnson F. E. A.
Published: December 2008

We investigate the equivalence classes of normal subdirect products of a product of free groups Fn1 × … × Fnk under the simultaneous equivalence relations of commensurability and conjugacy under the full automorphism group. By abelianisation, the problem is reduced to one in the representation theory of quivers of free abelian groups. We show there are infinitely many such classes when k≧3, and list the finite number of classes when k = 2.
Differential algebra of the “even order Korteweg–De Vries equations”
Authors: Verosky John M.
Published: December 2008

In the quotient ring of differential polynomials modulo cubic terms the usual odd order hierarchy of Korteweg–de Vries equations can be supplemented by an even order hierarchy. The full (even and odd) sequence is generated by an Olver recursion operator of order one and any pair has zero bracket in the quotient ring. The even order equations do not possess a Hamiltonian structure and thus their related Rosencrans densities are considered.
Generalized spectrum and commuting compact perturbations
Authors: Rakočević Vladimir
Published: December 2008

Let X be an infinite-dimensional complex Banach space and denote the set of bounded (compact) linear operators on X by B(X) (K(X)). Let N(A) and R(A) denote, respectively, the null space and the range space of an element A of B(X). Set R(A∞)=∩nR(An) and k(A)=dim N(A)/(N(A)∩R(A∞)). Let σg(A) = ℂ\{λ∈ℂ:R(A−λ) is closed and k(A−λ)=0} denote the generalized (regular) spectrum of A. In this paper we study the subset σgb(A) of σg(A) defined by σgb(A) = ℂ\{λ∈ℂ:R(A−λ) is closed and k(A−λ)<∞}. Among other things, we prove that if f is a function analytic in a neighborhood of σ(A), then σgb(f(A)) = f(σgb(A)).
Injectively immersed tori in branched covers over the figure eight knot
Authors: Jones Kerry N.
Published: December 2008

An algorithm is given for determining presence or absence of injectively (at the fundamental group level) immersed tori (and constructing them, if present) in a branched cover of S3, branched over the figure eight knot, with all branching indices greater than 2. Such tori are important for understanding the topology of 3-manifolds in light of (for example) the Jaco-Shalen–Johannson torus decomposition theorem and the fact that the figure eight knot is universal, i.e., that all 3-manifolds are representable as branched covers of S3, branched over the figure eight knot.

The algorithm is principally geometric in its derivation and graph-theoretic in its operation. It is applied to two examples, one of which has an incompressible torus and the other of which is atoroidal.
On the lifting of bounded sets in Fréchet spaces
Authors: Bonet José , Dierolf Susanne
Published: December 2008

This paper considers the behaviour of a quotient map between Fréchet spaces concerning the lifting of bounded sets. The main result shows that a quotient map between Fréchet spaces that lifts bounded sets with closure (or equivalently such that its strong transpose is a topological isomorphism) must also lift bounded sets without closure.
The p-Huppert-subgroup and the set of p-quasi-superfluous elements in a finite group
Authors: Carocca Angel , Maier Rudolf
Published: December 2008

Based on the theory of p-supersoluble and supersoluble groups, a prime-number parametrized family of canonical characteristic subgroups Γp(G) and their intersection Γ(G) is introduced in every finite group G and some of its properties are studied. Special interest is dedicated to an elementwise description of the largest p-nilpotent normal subgroup of Γp(G) and of the Fitting subgroup of Γ(G).
Prime ideals in skew Laurent polynomial rings
Authors: Mackenzie K. W.
Published: December 2008

Let R be a commutative ring and {σ1,…,σn} a set of commuting automorphisms of R. Let T = be the skew Laurent polynomial ring in n indeterminates over R and let be the Laurent polynomial ring in n central indeterminates over R. There is an isomorphism φ of right R-modules between T and S given by φ(θj) = xj. We will show that the map φ induces a bijection between the prime ideals of T and the Γ-prime ideals of S, where Γ is a certain set of endomorphisms of the ℤ-module S. We can study the structure of the lattice of Γ-prime ideals of the ring S by using commutative algebra, and this allows us to deduce results about the prime ideal structure of the ring T. As an example, if R is a Cohen-Macaulay ℂ-algebra and the action of the σj on R is locally finite-dimensional, we will show that the ring T is catenary.
Spectral convergence of multiquadric interpolation
Authors: Buhmann Martin , Dyn Nira
Published: December 2008

In this paper, we consider interpolants onh·ℤnfrom the closure of the space spanned by translates of the function (‖·‖2+ 1)β/2(β>−nand not an even nonnegative integer) alongh·ℤn. We show that these interpolants approximate a function, whose Fourier transform satisfies certain asymptotic conditions, up to an error of orderhp, on any compact domain in ℝn, wherepis only restricted by the smoothness of the function.
A note on skew-symmetric determinants
Authors: Ledermann Walter
Published: December 2008

A short proof, based on the Schur complement, is given of the classical result that the determinant of a skew-symmetric matrix of even order is the square of a polynomial in its coefficients.
Non-isomorphic rings with isomorphic matrix rings
Authors: Chatters A. W.
Published: December 2008

We construct an uncountable family of pairwise non-isomorphic rings Si, such that the corresponding full 2 by 2 matrix rings M2(Si) are all isomorphic to each other. The rings Si are Noetherian integral domains which are finitely-generated as modules over their centres.
On the closure of the prime radical of a Banach algebra
Authors: Somerset D. W. B. , Willis G. A.
Published: December 2008

The relationship between the prime ideals and the primal ideals of a Banach algebra is investigated. It is shown that the closure of the prime radical of a Banach algebra may be properly contained in the intersection of the closed primal ideals of the algebra.
Notes on questions of W. Vogel concerning the converse to Bézout's theorem
Authors: Pruschke Thilo
Published: December 2008

Lazarsfeld proved a bound for the excess dimension of an intersection of irreducible and reduced schemes. Flenner and Vogel gave another approach for reduced, non-degenerate schemes which are connected in codimension one, using the intersection algorithm of Stückrad and Vogel and defining a new multiplicityk. Renschuch and Vogel considered a condition to ensure that there is no degeneration for more than two schemes. We define an integer which enables us to unify these methods. This allows us to generalize the result of Flenner and Vogel to non-reduced schemes by comparing the multiplicitiesjandk. Using this point of view we give applications to converses of Bézout's theorem; in particular we investigate the Cohen-Macaulay case.
Generators for locally compact groups
Authors: Cleary Joan , Morris Sidney A.
Published: December 2008

It is proved that if G is any compact connected Hausdorff group with weight w(G)≦c, ℝ is the topological group of all real numbers and n is a positive integer, then the topological group G × ℝn can be topologically generated by n + 1 elements, and no fewer elements will suffice.
Residue fields of valued function fields of conics
Authors: Khanduja Sudesh K. , Garg Usha
Published: December 2008

Suppose that K is a function field of a conic over a subfield K0. Let v0 be a valuation of K0 with residue field k0 of characteristic ≠2. Let v be an extension of v0 to K having residue field k. It has been proved that either k is an algebraic extension of k0 or k is a regular function field of a conic over a finite extension of k0. This result can also be deduced from the genus inequality of Matignon (cf. [On valued function fields I, Manuscripta Math. 65 (1989), 357–376]) which has been proved using results about vector space defect and methods of rigid analytic geometry. The proof given here is more or less self-contained requiring only elementary valuation theory.
Closed incompressible surfaces in 2-generator hyperbolic 3-manifolds with a single cusp
Authors: Long D. D. , Reid A. W.
Published: December 2008

A knot K is said to have tunnel number 1 if there is an embedded arc A in S3, with endpoints on K, whose interior is disjoint from K and such that the complement of a regular neighbourhood of K ∪ A is a genus 2 handlebody. In particular the fundamental group of the complement of a tunnel number one knot is 2-generator. There has been some interest in the question as to whether there exists a hyperbolic tunnel number one knot whose complement contains a closed essential surface. The aim of this paper is to prove the existence of infinitely many 2-generator hyperbolic 3-manifolds with a single cusp which contain a closed essential surface. One such example is a knot complement in RP3. The methods used are of interest as they include the possibility that one of our examples is a knot complement in S3.
Some theorems on Stirling-type pairs
Authors: Hsu Leetsch C.
Published: December 2008

It is shown that an extended Schlömilch formula for Stirling-type pairs of numbers and the inversion formula of Lagrange are implied by each other. Also proved are some congruence relations modulo a prime numberp(>2) associated with generalized Stirling numbers. The third result is concerned with the asymptotic expansions of Stirling-type pairs involving large parameters.
Existence of solutions in a singular biharmonic nonlinear problem
Authors: Hernandez Gaston L. , Choi Y.
Published: December 2008

In this work we prove the existence and uniqueness of positive solutions of the nonlinear singular boundary value problem

where 0<σ<1.

Extensions of the above results to the case of Δ2u−f(x, u) = 0 with appropriate singularity built into f are also given.
Modular Jordan nilalgebras
Authors: Anquela Jose Angel
Published: December 2008

In this paper we give a classification up to isomorphism of Jordan nilalgebras whose lattices of subalgebras are modular when the ground field is algebraically closed.
A uniqueness problem in simple transcendental extensions of valued fields
Authors: Khanduja Sudesh K.
Published: December 2008

Let υ0 be a valuation of a field K0 with value group G0 and υ be an extension of υ0 to a simple transcendental extension K0(x) having value group G such that G/G0 is not a torsion group. In this paper we investigate whether there exists t∈K0(x)/K0 with υ(t) non-torsion mod G0 such that υ is the unique extension to K0(x) of its restriction to the subfield K0(t). It is proved that the answer to this question is “yes” if υ0 is henselian or if υ0 is of rank 1 with G0 a cofinal subset of the value group of υ in the latter case, and that it is “no” in general. It is also shown that the affirmative answer to this problem is equivalent to a fundamental equality which relates some important numerical invariants of the extension (K, υ)/(K0, υ0).
The congruence lattice of a combinatorial strict inverse semigroup
Authors: Auinger Karl
Published: December 2008

The congruence lattice of a combinatorial strict inverse semigroup is shown to be isomorphic to a complete subdirect product of congruence lattices of semilattices preserving pseudocomplements.
Radial growth and exceptional sets for Cauchy–Stieltjes integrals
Authors: Hallenbeck D. J. , MacGregor T. H.
Published: December 2008

This paper considers the radial and nontangential growth of a function f given by

where α>0 and μ is a complex-valued Borel measure on the unit circle. The main theorem shows how certain local conditions on μ near eiθ affect the growth of f(z) as z→eiθ in Stolz angles. This result leads to estimates on the nontangential growth of f where exceptional sets occur having zero β-capacity.
A diffusion equation with localized chemical reactions
Authors: Chadam John M. , Yin Hong-Ming
Published: December 2008

In some chemical reaction–diffusion processes, the reaction takes place only at some local sites, due to the presence of a catalyst. In this paper we study the well-posedness of a model problem of this type. Sufficient conditions are found to ensure global existence and finite time blowup. The blowup rate and the blowup set are also investigated in the case of special nonlinearity.
On locally soluble periodic groups with Chernikov centralizer of a four-subgroup
Authors: Shumyatsky Pavel
Published: December 2008

Let G be a locally soluble periodic group having a four-subgroup V. We show that if CG(V) is Chernikov then G is hyperabelian-by-Chernikov, if CG(V) is finite then G is hyperabelian.
The Arens irregularity of an extremal algebra
Authors: Crabb M. J. , McGregor C. M.
Published: December 2008

A class of extremal Banach algebras has Arens irregular multiplication.
The action of a maximal parabolic subgroup on the transpositions of the Baby Monster
Authors: Wilson Robert A.
Published: December 2008

We prove a technical result required by Ivanov and Shpectorov in their construction of a non-split extension of 34371 by the Baby Monster simple group.
Nilpotents in semigroups of partial order-preserving transformations
Authors: Garba G. U.
Published: December 2008

In this paper we extend the results of Garba [1] on IOn, the semigroup of all partial one-one order-preserving maps on Xn = {1,…, n}, to POn, the semigroup of all partial order-preserving maps on Xn, A description of the subsemigroup of POn generated by the set N of all its nilpotent elements is given. The set {α∈POn:lim α/≦r and |Xn /dom α|≧r} is shown to be contained in 〈N〉 if and only if r≦½n. The depth of 〈N〉, which is the unique k for which 〈N〉 = N ∪ N2 ∪…∪ Nk and 〈N〉 ≠ N ∪ N2 ∪…∪Nk−1 is shown to be equal to 3 for all n≧3. The rank of the subsemigroup {α∈POπ|imα|≦/n − 2 and α∈〈N〉} is shown to be equal to 6(n − 2), and its nilpotent rank to be equal to 7n−15.
Properly discontinuous actions on Λ-trees
Authors: Chiswell I. M.
Published: December 2008

The main result is a theorem giving several possibilities for the action of a 2-generator group acting on a Λ-tree, generalising the result that, if the action is free then the group is either free or free abelian. This involves investigation of several cases in which the action is shown to be properly discontinuous. This leads to a generalisation of results of Culler and Morgan, characterising abelian, dihedral and irreducible actions on ℝ-trees, to arbitrary Λ-trees.
On value groups and residue fields of some valued function fields
Authors: Khanduja Sudesh K.
Published: December 2008

Let K = K0(x, y) be a function field of transcendence degree one over a field K0 with x, y satisfying y2 = F(x), F(x) being any polynomial over K0. Let υ0 be a valuation of K0 having a residue field k0 and υ be a prolongation of υ to K with residue field k. In the present paper, it is proved that if G0⊆G are the value groups of υ0 and υ, then either G/G0 is a torsion group or there exists an (explicitly constructible) subgroup G1 of G containing G0 with [G1:G0]<∞ together with an element γ of G such that G is the direct sum of G1 and the cyclic group ℤγ. As regards the residue fields, a method of explicitly determining k has been described in case k/k0 is a non-algebraic extension and char k0≠2. The description leads to an inequality relating the genus of K/K0 with that of k/k0: this inequality is slightly stronger than the one implied by the well-known genus inequality (cf. [Manuscripta Math.65 (1989), 357–376’, [Manuscripta Math.58 (1987), 179–214]).
Chern characters, reduced ranks and -modules on the flag variety
Authors: Hodges T. J. , Holland M. P.
Published: December 2008

Let D be the factor of the enveloping algebra of a semisimple Lie algebra by its minimal primitive ideal with trival central character. We give a geometric description of the Chern character ch: K0(D)→HC0(D) and the state (of the maximal ideal m) s: K0(D)→K0(D/m) = ℤ in terms of the Euler characteristic χ:K0()→ℤ, where is the associated flag variety.
Nilpotency indices of the radicals of p-group algebras
Authors: Ninomiya Yasushi
Published: December 2008

Let k be a field of characteristic p>0. We classify all finite p-groups G satisfying the inequality p−2|G|≦t(G) < p−1|G|, where t(G) is the nilpotency index of the Jacobson radical of k[G].
Corrigendum et addendum: the Frattini subalgebra of a Bernstein algebra
Authors: Laliena Jesús
Published: December 2008

In a previous paper it is supposed that if A is a Bernstein algebra, every maximal subalgebra, M, verifies that dim M = dim A − 1. This is not true in general. Therefore Proposition 2 in this paper is not correct. However other results there, where this assertion was used, are correct but their proofs need some modifications now.
Local spectral properties of commutators
Authors: Laursen Kjeld B. , Miller Vivien G. , Neumann Michael M.
Published: December 2008

For a pair of continuous linear operatorsTandSon complex Banach spacesXandY, respectively, this paper studies the local spectral properties of the commutatorC(S, T) given byC(S, T)(A): =SA−ATfor allA∈L(X, Y). Under suitable conditions onTandS, the main results provide the single valued extension property, a description of the local spectrum, and a characterization of the spectral subspaces ofC(S, T), which encompasses the closedness of these subspaces. The strongest results are obtained for quotients and restrictions of decomposable operators. The theory is based on the recent characterization of such operators by Albrecht and Eschmeier and extends the classical results for decomposable operators due to Colojoară, Foiaş, and Vasilescu to considerably larger classes of operators. Counterexamples from the theory of semishifts are included to illustrate that the assumptions are appropriate. Finally, it is shown that the commutator of two super-decomposable operators is decomposable.