bluuebunny/crossref_metadata_2025 huggingface dataset:
Strongly prime near-rings
Authors: Groenewald N. J.
Published: December 2008

Strongly prime rings were introduced by Handelman and Lawrence [5] and in [2] Groenewald and Heyman investigated the upper radical determined by the class of all strongly prime rings. In this paper we extend the concept of strongly prime to near-rings. We show that the class M of distributively generated near-rings is a special class in the sense of Kaarli [6]. We also show that if N is any distributively generated near-ring, then UM(N), UM denotes the upper radical determined by the class M, coincides with the intersection of all the strongly prime ideals of N.
Local endomorphism near-rings
Authors: Lyons Carter G. , Peterson Gary L.
Published: December 2008

The purpose of this paper is to study the consequences of an endomorphism near-ring of a finite group being a local near-ring and the existence of such near-rings. As we shall see in Section 2, an endomorphism near-ring of a finite group being local gives us some information about both the structure of the group (Theorem 2.2) and the automorphisms of the group lying in the near-ring (Theorem 2.3). Existence of local endomorphism near-rings of finite groups is considered in Section 3 where we obtain as our main result that any p-group of automorphisms of a p-group containing the inner automorphisms always generates a local endomorphism near-ring. In particular, we get as a corollary that the endomorphism near-ring of a finite group G generated by the inner automorphisms of G is local if and only if G is a p-group. The third section concludes with a discussion of endomorphism near-rings of dihedral 2-groups and generalized quaternion groups.
Symmetries and conservation laws of 2-dimensional ideal plasticity
Authors: Senashov S. I. , Vinogradov A. M.
Published: December 2008

Symmetry theory is of fundamental importance in studying systems of partial differential equations. At present algebras of classical infinitesimal symmetry transformations are known for many equations of continuum mechanics [1, 2, 4]. Methods foi finding these algebras go back to S. Lie's works written about 100 years ago. Ir particular, knowledge of symmetry algebras makes it possible to construct effectively wide classes of exact solutions for equations under consideration and via Noether's theorem to find conservation laws for Euler–Lagrange equations. The natural development of Lie's theory is the theory of “higher” symmetries and conservation laws [5].
Multiparameter root vectors
Authors: Binding Paul
Published: December 2008

The concept of “root vectors” is investigated for a class of multiparameter eigenvalue problems

where operate in Hilbert spaces Hm and . Previous work on this “uniformly elliptic” class has demonstrated completeness of the decomposable tensors x1 ⊗…⊗ xk in a subspace G of finite codimension in H=H1 ⊗…⊗ Hk, but questions remain about extending this to a basis of H. In this work, bases of elements ym, in general nondecomposable but satisfying recursive equations of the type are constructed for the “root subspaces” corresponding to λ∈ℝk.
Construction of regular semigroups with inverse transversals
Authors: Saito Tatsuhiko
Published: December 2008

Let S be a regular semigroup. An inverse subsemigroup S° of S is an inverse transversal if |V(x)∩S°| = 1 for each x∈S, where V(x) denotes the set of inverses of x. In this case, the unique element of V(x)∩S° is denoted by x°, and x°° denotes (x°)–1. Throughout this paper S denotes a regular semigroup with an inverse transversal S°, and E(S°) = E° denotes the semilattice of idempotents of S°. The sets {e∈S:ee° = e} and {f∈S:f°f=f} are denoted by Is and Λs, respectively, or simply I and Λ. Though each element of these sets is idempotent, they are not necessarily sub-bands of S. When both I and Λ are sub-bands of S, S° is called an S-inverse transversal. An inverse transversal S° is multiplicative if x°xyy°∈E°, and S° is weakly multiplicative if (x°xyy°)°∈E° for every x, y∈S. A band B is left [resp. right] regular if e f e = e f [resp. e f e = f e], and B is left [resp. right] normal if e f g = e g f [resp. e f g = f e g] for every e, f, g∈B. A subset Q of S is a quasi-ideal of S if QSQ ⊆ S.
Linear Hahn–Banach extension operators
Authors: Sims Brailey , Yost David
Published: December 2008

Given any subspace N of a Banach space X, there is a subspace M containing N and of the same density character as N, for which there exists a linear Hahn–Banach extension operator from M* to X*. This result was first proved by Heinrich and Mankiewicz [4, Proposition 3.4] using some of the deeper results of Model Theory. More precisely, they used the Banach space version of the Löwenheim–Skolem theorem due to Stern [11], which in turn relies on the Löwenheim–Skolem and Keisler–Shelah theorems from Model Theory. Previously Lindenstrauss [7], using a finite dimensional lemma and a compactness argument, obtained a version of this for reflexive spaces. We shall show that the same finite dimensional lemma leads directly to the general result, without any appeal to Model Theory.
Distributive elements in the near-rings of polynomials
Authors: Gutierrez Jaime , De Velasco Y Bellas Carlos Ruiz
Published: December 2008

As usual in the theory of polynomial near-rings, we deal with right near-rings. If N = (N, +,·) is a near-ring, the set of distributive elements of N will be denoted by Nd;

It is easy to check that, if N is an abelian near-ring (i.e., r + s = s + r, for all r, s∈N), then Nd is a subring of N.
On the space of matrices of given rank
Authors: Crabb M. C. , Gonçalves D. L.
Published: December 2008

Let V and W be finite dimensional real vector spaces, k≧0 an integer. We write L(V, W) for the space of all linear maps V→W and Lk(V, W) for the subspace of maps with kernel of dimension k; in particular, L0(V, W) is the open subspace of injective linear maps. Thus Lk(ℝn, ℝn) is the space of n × n-matrices of rank n – k in the title. We also need the notation Gk(V) for the Grassmann manifold of K-dimensional subspaces of V.
Group rings which are v-HC orders and Krull orders
Authors: Brown K. A. , Marubayashi H. , Smith P. F.
Published: December 2008

Let R be a ring and G a polycyclic-by-finite group. In this paper, it is determined, in terms of properties of R and G, when the group ring R[G] is a prime Krull order and when it is a price v-HC order. The key ingredient in obtaining both characterizations is the first author's earlier study of height one prime ideals in the ring R[G[.
Prime essential rings
Authors: Gardner B. J. , Stewart P. N.
Published: December 2008

A ring R is prime essential if R is semiprime and for each prime ideal P of R, P ∩ I ≠0 whenever I is a nonzero two-sided ideal of R. Examples of prime essential rings include rings of continuous functions and infinite products modulo infinite sums. We show that the class of prime essential rings is closed under many familiar operations; in particular, we consider polynomial rings, matix rings, fixed rings and skew group rings. Also, we explore the relationship between prime essential rings and special radical classes, and we demonstrate how prime essential rings can be used to construct radical classes which are not special.
On bounding the Stückrad-Vogel multiplicity
Authors: O'Carroll L.
Published: December 2008

Using a classical result of Nagata, Achilles, Huneke and Vogel gave a criterion for the Stückrad-Vogel multiplicity to take the value one. We use Huneke's extension of Nagata's theorem to give a necessary condition for the Stückrad-Vogel multiplicity to have an arbitrary preassigned bound, under certain conditions. A usable criterion of multiplicity n results (given mild hypotheses). We also revisit some basic results in the Stückrad-Vogel theory in the light of the behaviour of tensor products of affine primary rings, and also revisit some arguments of Achilles, Huneke and Vogel from the point of view of fibre rings.
Embeddings into finite idempotent-generated semigroups: some arithmetical results
Authors: Giraldes Emilia , Howie John M.
Published: December 2008

A semiband is defined as a semigroup generated by idempotents. It is known that every finite semigroup is embeddable in a finite semiband. For a class C of semigroups and an integer n≧2, the number σC (n) is defined as the smallest k with the property that every semigroup of order n in the class C is embeddable in a semiband of order not exceeding k. It is shown that for the class Gp of groups σGp(n) = nq(ρGp(n)), where

and

Estimates are known (and are quoted) for the function q. Estimates are considered for the function pC for various C

It is shown also that if C0S, CS denote respectively the classes of completely 0-simple and completely simple semigroups, then
Hilbert spaces of tempered distributions, Hermite expansions and sequence spaces
Authors: Picard Rainer H.
Published: December 2008

Although it is well-known that tempered distributions on ℝn can be expanded into series of Herrnite functions, it does not seem to be known, however, that expansions of this type are accessible through the elementary concept of orthonorma! expansions in Hilbert space. This approach is developed here complementing previous work on a Hilbert space approach to distributions. The basis of the development is the observation that the Hermite functions are a complete orthogonal set in each space of a certain scale of Sobolev type Hilbert spaces associated with the family of differential operators defined by

Here Ф denotes a smooth function with compact support. The setting is first developed in the one-dimensional case. By use of the usual multi-index notation this can be extended to the higher-dimensional case. As applications various imbedding results are derived. The paper concludes with a characterization of tempered distributions by convergent Hermite expansions.
On a problem of Barnes and Duncan
Authors: McLean R. G.
Published: December 2008

Consider the free monoid on a non-empty set P, and let R be the quotient monoid determined by the relations:

Let R have its natural involution * in which each element of P is Hermitian. We show that the Banach *-algebra ℓ1(R) has a separating family of finite dimensional *-representations and consequently is *-semisimple. This generalizes a result of B. A. Barnes and J. Duncan (J. Funct. Anal.18 (1975), 96–113.) dealing with the case where P has two elements.
A family of crystallographic groups with 2-torsion in K0 of the rational group algebra
Authors: Kropholler P. H. , Moselle B.
Published: December 2008

We calculate K0 of the rational group algebra of a certain crystallographic group, showing that it contains an element of order 2. We show that this element is the Euler class, and use our calculation to produce a whole family of groups with Euler class of order 2.
Radially symmetric solutions of a class of singular elliptic equations
Authors: Gatica Juan A. , Hernandez Gaston E. , Waltman P.
Published: December 2008

The boundary value problem

is studied with a view to obtaining the existence of positive solutions in C1([0, 1])∩C2((0, 1)). The function f is assumed to be singular in the second variable, with the singularity modeled after the special case f(x, y) = a(x)y−p, p>0.

This boundary value problem arises in the search of positive radially symmetric solutions to

where Ω is the open unit ball in ℝN, centered at the origin, Γ is its boundary and |x| is the Euclidean norm of x.
On pseudo-Anosov maps which extend over two handlebodies
Authors: Long D. D.
Published: December 2008

We show that there is a pair of handlebodies H1 and H2 with common boundary F with the properties:

(a) There is no essential simple closed curve in F bounding a disc in both H1 and H2.

(b) Given any positive number, there are essential simple curves Cii = 1, 2 on F, bounding discs in Hi whose distance apart in the Hausdorff topology on F is less than this positive number.

Such an example has consequences for Heegaard splittings and recognising the 3-sphere.
Some dual aspects of the Poisson kernel
Authors: Bonsall F. F.
Published: December 2008

The Poisson kernel is defined for z in the open unit disc D and ζ in the unit circle ∂D. As usually employed, it is integrated with respect to the second variable and a measure on ∂D to yield a harmonic function on D. Here, we fix a σ-finite positive Borel measure m on D and integrate the Poisson kernel with respect to the first variable against a function φ in L1(m) to obtain a function Tmφ on ∂D. We ask for what measures m the range of Tm is L1(∂D), for what m the kernel of Tm is non-zero, and for what m every positive continuous function on ∂D is of the form Tmφ with φ non-negative. When m is the counting measure of a countably infinite subset {ak:k∈ℕ} of D, the function (Tmφ)(ζ) is of the form with . The main results generalize results previously obtained for sums of this form. A related mapping from Lp(m) into Lp(∂D) with 1 <p<∞ is briefly considered.
On the index of tricyclic Hamiltonian graphs
Authors: Bell F. K. , Rowlinson P.
Published: December 2008

Among the tricyclic Hamiltonian graphs with a prescribed number of vertices, the unique graph with maximal index is determined. Some subsidiary results are also included.
Cardinal interpolation by symmetric exponential box splines on a three-direction mesh
Authors: Goodman T. N. T. , Taani A. A.
Published: December 2008

We consider certain exponential box splines E on a three-direction mesh whose exponents satisfy a symmetry condition. It is shown, in particular, that given bounded data on the integer lattice in R2, there is a unique bounded combination of integer translates of E that interpolates the data. When all exponents are zero, this reduces to a result of de Boor, Höllig and Riemenschneider in [2]. Unlike the proof in [2] we use only elementary analysis and do not employ any computer calculations.
On the zeros of second order linear differential polynomials
Authors: Langley J. K.
Published: December 2008

We determine all functions f(z) meromorphic in the plane such that f′(z)/f(z) has finite order and f(z) and F(z) have only finitely many zeros, where F(z) = f″(z) + Af(z) for some constant A.
Finitely presented ordered groups
Authors: Glass A. M. W.
Published: December 2008

Theorem. There exist non-Abelian finitely presented lattice-ordered groups which are totally ordered. This disproves a previous conjecture of the author [5]
When is the spectrum of a convolution operator on Lp independent of p?
Authors: Barnes Bruce A.
Published: December 2008

In this paper conditions are given that imply that a convolution operator has the same spectrum on all of the spaces Lp(G), 1≦p≦∞.
On the characters of affine Kac–Moody groups
Authors: Slebarski Stephen
Published: December 2008

Let G be an affine Kac–Moody group over ℂ, and V∞ an integrable simple quotient of a Verma module for g. Let Gmin be the subgroup of G generated by the maximal algebraic torus T, and the real root subgroups.

It is shown that (the least positive imaginary root) gives a character δ∈Hom(G, ℂ*) such that the pointwise character χ∞ of V∞ may be defined on Gmin ∩ G>1.
Soluble groups with a finite rewriting system
Authors: Groves J. R. J. , Smith G. C.
Published: December 2008

We describe a class of soluble groups with a finite complete rewriting system which includes all the soluble groups known to have such a system. It is an open question, related to deep questions in the theory of groups, whether it includes all soluble groups with such a system.
Coverings and embeddings of inverse semigroups
Authors: Lawson Mark V.
Published: December 2008

A correspondence is established between a class of coverings of an inverse semigroupSand a class of embeddings ofS, generalising results of McAlister and Reilly onE-unitary covers of inverse semigroups.
On the complex oscillation theory of f(k) + Af = F
Authors: Zong-Xuan Chen
Published: December 2008

In this paper, we investigate the complex oscillation theory of

where A, F≢0 are entire functions, and obtain general estimates of the exponent of convergence of the zero-sequence and of the order of growth of solutions for the above equation.
A bicombing that implies a sub-exponential isoperimetric inequality
Authors: Huck Günther , Rosebrock Stephan
Published: December 2008

The idea of applying isoperimetric functions to group theory is due to M. Gromov [8]. We introduce the concept of a “bicombing of narrow shape” which generalizes the usual notion of bicombing as defined for example in [5], [2], and [10]. Our bicombing is related to but different from the combings defined by M. Bridson [4]. If they Cayley graph of a group with respect to a given set of generators admits a bicombing of narrow shape then the group is finitely presented and satisfies a sub-exponential isoperimetric inequality, as well as a polynomial isodiametric inequality. We give an infinite class of examples which are not bicombable in the usual sense but admit bicombings of narrow shape.
The closure of convergence sets for continued fractions are convergence sets
Authors: Lorentzen Lisa
Published: December 2008

We prove that if Ω is a simple convergence set for continued fractions K(an/bn), then the closure of Ω is also such a convergence set. Actually, we prove more: every continued fraction K(an/bn) has a “neighbourhood” where rn>0 and sn>0, with the following property: Every continued fraction from {n} converges if and only if K(an/bn) converges.
An example of a non-exposed extreme function in the unit ball of H1
Authors: Inoue Jyunji
Published: December 2008

We construct a non-exposed extreme function f of the unit ball of H1, the classical Hardy space on the unit disc of the plane, which has the property: f(z)/(1−q(z))2 ∉ H1 for any nonconstant inner function q(z). This function constitutes a counterexample to a conjecture in D. Sarason [7].
A note on the Wiman–Valiron method
Authors: Fenton P. C.
Published: December 2008

Without prior assumptions about growth, fundamental inequalities for the Taylor series of an entire function are obtained, valid outside a certain exceptional set. The results are vacuous or not depending on the estimate for the exceptional set. Only then does the growth of the function enter.
Sturm–Liouville problems with eigenparameter dependent boundary conditions
Authors: Binding P. A. , Browne P. J. , Seddighi K.
Published: December 2008

Sturm theory is extended to the equation

for 1/p, q, r∈L1 [0, 1] with p, r > 0, subject to boundary conditions

and

Oscillation and comparison results are given, and asymptotic estimates are developed. Interlacing of eigenvalues with those of a standard Sturm–Liouville problem where the boundary conditions are ajy(j) = cj(py′)(j), j=0, 1, forms a key tool.
On weakly multiplicative inverse transversals
Authors: Blyth T. S. , Santos M. H. Almeida
Published: December 2008

We show that an inverse transversal of a regular semigroup is multiplicative if and only if it is both weakly multiplicative and a quasi-ideal. Examples of quasi-ideal inverse transversals that are not multiplicative are known. Here we give an example of a weakly multiplicative inverse transversal that is not multiplicative. An interesting feature of this example is that it also serves to show that, in an ordered regular semigroup in which every element x has a biggest inverse x0, the mapping x↦x00 is not in general a closure; nor is x↦x** in a principally ordered regular semigroup.
Topologically free actions and ideals in discrete C*-dynamical systems
Authors: Archbold R. J. , Spielberg J. S.
Published: December 2008

A C*-dynamical system is called topologically free if the action satisfies a certain natural condition weaker than freeness. It is shown that if a discrete system is topologically free then the ideal structure of the crossed product algebra is related to that of the original algebra. One consequence is that a minimal topologically free discrete system has a simple reduced crossed product. Sharper results are obtained when the algebra is abelian.
Invertible disjointness preserving operators
Authors: Huijsmans C. B. , De Pagter B.
Published: December 2008

It is shown that an invertible disjointness preserving operator from a uniformly complete vector lattice onto a normed vector lattice has a disjointness preserving inverse and is necessarily order bounded.
A convergence problem for Kergin interpolation
Authors: Calvi Jean Paul
Published: December 2008

Let E, F, G be three compact sets in ℂn. We say that (E, F, G) holds if for any choice of an interpolating array in F and of an analytic function ℂ on G, the Kergjn interpolation polynomial of ℂ exists and converges to ℂ on E. Given two of the three sets, we study how to construct the third in order that (E, F, G) holds.
Cancellation in the Stone–Čech compactification of a discrete semigroup
Authors: Hindman Neil , Strauss Dona
Published: December 2008

We investigate both left and right cancellation in the Stone–Čech compactification βSof a discrete semigroupS, obtaining several results for arbitrary semigroupsSand others for more restricted semigroups. In particular, ifSis the semigroup of injective functions from a set to itself we determine precisely which pairsx, yandShave somep∈βSwithpx=py. We also obtain several new results about right cancellation in (βℕ, +).
Differential properties of some dense subalgebras of C*-algebras
Authors: Kissin E. , Shulman V. S.
Published: December 2008

The paper studies some classes of dense *-subalgebras B of C*-algebras A whose properties are close to the properties of the algebras of differentiable functions. In terms of a set of norms on B it defines -subalgebras of A and establishes that they are locally normal Q*-subalgebras. If x = x* ∈ B and f(t) is a function on Sp(x), some sufficient conditions are given for f(x) to belong to B. For p = 1, in particular, it is shown that -subalgebras are closed under C∞-calculus. If δ is a closed derivation of A, the algebras D(δp) are -subalgebras of A. In the case when δ is a generator of a one-parameter semigroup of automorphisms of A, it is proved that, in fact, D(δp) are -subalgebras. The paper also characterizes those Banach *-algebras which are isomorphic to subalgebras of C*-algebras.
Minimal 4-manifolds for groups of cohomological dimension 2
Authors: Hillman Jonathan A.
Published: December 2008

We show that if π is a group with a finite 2-dimensional Eilenberg-Mac Lane complex then the minimum of the Euler characteristics of closed 4-manifolds with fundamental group π is 2χ(K(π, 1)). If moreoverMis such a manifold realizing this minimum then π2(M) ≅Similarly, if π is a PD3-group andw1(M) is the canonical orientation character of π then χ(M)≧l and π2(M) is stably isomorphic to the augmentation ideal ofZ[π].
Inequalities in l1 and lp and applications to group algebras
Authors: Wood Geoffrey V.
Published: December 2008

In this note, we show that, if (an) in l1 with Σ|an| < 2 and Σ|an|2 = 1, then max {|ai| + |aj|:i ≠ j} ≧ 1, but that the corresponding theorem for sequences in lp(1<p<2) fails—but only just! Applications to group algebras are given, when it is shown that elements in l1(G) with powers bounded by ½(1+ ) are bounded away from the identity e of G, but that the corresponding result for lp (G) is false.
A specific form of Grothendieck's inequality for the two-dimensional case, with applications to C*-algebras
Authors: Jameson G. J. O.
Published: December 2008

We characterize bilinear forms V on such that V(e, e) = ‖V‖ = 1 in terms of their matrices. For such V we prove that |V(x, y)|2≦φ(|x|2)ψ(|y|2) for all x, y, where φ(x)= V(x, e), ψ(y) = V(e, y). Some other properties of such forms are given.
The topology of graph products of groups
Authors: Meier John
Published: December 2008

Given a finite (connected) simplicial graph with groups assigned to the vertices, the graph product of the vertex groups is the free product modulo the relation that adjacent groups commute. The graph product of finitely presented infinite groups is both semistable at infinity and quasi-simply filtrated. Explicit bounds for the isoperimetric inequality and isodiametric inequality for graph products is given, based on isoperimetric and isodiametric inequalities for the vertex groups.
On the finiteness and uniqueness of certain 2-tame N-groups
Authors: Scott S. D.
Published: December 2008

Unlike ring modules certain faithful N-groups are unique. The main theorem is that if N is a 2-tame ring-free near-ring where N/J(N) has DCCR, then all faithful 2-tame N-groups are finite and N-isomorphic. The finiteness of such an N-group follows easily from the fact it has a composition series. It is then shown that the length of a composition series depends only on N. This fact is used at key points in the proof. The situations where the N-group has or has not a minimal submodule require different analysis. The first case makes use of other interesting results and the second makes strong use of the inductive assumption.
Product formulas for Steenrod operations
Authors: Li Zaiqing
Published: December 2008

A star operation is defined and studied for the Steenrod algebra. Numerous product formulas of Steenrod operations are presented.
Interpolation of compact operators by the methods of Calderón and Gustavsson–Peetre
Authors: Cwikel M. , Kalton N. J.
Published: December 2008

Let X = (X0, X1) and Y = (Y0, Y1) be Banach couples and suppose T:X→Y is a linear operator such that T:X0→Y0 is compact. We consider the question whether the operator T:[X0, X1]θ→[Y0, Y1]θ is compact and show a positive answer under a variety of conditions. For example it suffices that X0 be a UMD-space or that X0 is reflexive and there is a Banach space so that X0 = [W, X1]α, for some 0<α<1.
Explicit evaluation of Euler sums
Authors: Borwein David , Borwein Jonathan M. , Girgensohn Roland
Published: December 2008

In response to a letter from Goldbach, Euler considered sums of the form

where s and t are positive integers.

As Euler discovered by a process of extrapolation (from s + t ≦ 13), σh(s, t) can be evaluated in terms of Riemann ζ-functions when s + t is odd. We provide a rigorous proof of Euler's discovery and then give analogous evaluations with proofs for corresponding alternating sums. Relatedly we give a formula for the series

This evaluation involves ζ-functions and σh(2, m).
On reduction exponents of ideals with Gorenstein formring
Authors: Herrmann M. , Huneke C. , Ribbe J.
Published: December 2008

This paper studies questions connected with when the Rees algebra of an ideal or the formring of an ideal is Gorenstein. The main results are for ideals of small analytic deviation, and for m-primary ideals of a regular local ring (R, m). The general point proved is that the Gorenstein property forces (and is sometimes equivalent to) lowering the reduction number of the ideal by one from the value predicted if one only assumes the Rees algebra or formring is Cohen–Macaulay.
Homotopy groups and H-maps
Authors: Jeanneret Alain
Published: December 2008

The first nonvanishing homotopy group of a finite H-space X whose mod 2 homology ring is associative occurs in degrees 1, 3 or 7. Generators of these groups can be represented by maps α:Sn→X for n = 1, 3 or 7. In this note we prove that under some hypothesis on X there exists an H-structure on Sn, n = 1, 3 or 7 such that α is an H-map.
Tesselations ofS2and equations over torsion-free groups
Authors: Clifford A. , Goldstein R. Z.
Published: December 2008

LetGbe a torsion free group,Fthe free group generated byt. The equationr(t) = 1 is said to have a solution overGif there is a solution in some group that containsG. In this paper we generalize a result due to Klyachko who established the solution when the exponent sum oftis one.
Schunck classes and projectors in a class of locally finite groups
Authors: Tomkinson M. J.
Published: December 2008

We introduce a definition of a Schunck class of periodic abelian-by-finite soluble groups using major subgroups in place of the maximal subgroups used in Finite groups. This allows us to develop the theory as in the finite case proving the existence and conjugacy of projectors. Saturated formations are examples of Schunck classes and we are also able to obtain an infinite version of Gaschütz Ω-subgroups.
The mean lattice point discrepancy
Authors: Huxley M. N.
Published: December 2008

Consider a sufficiently smooth simple closed convex plane curve enclosing the origin, expanding linearly with time. The root mean square of the discrepancy (number of lattice points minus area) from time t = M to t = M + 1 is almost as small as the root mean square discrepancy from time t = 0 to t = M, so the discrepancy has no memory.
Radial functions on compact support
Authors: Buhmann M. D.
Published: December 2008

In this paper, radial basis functions that are compactly supported and give rise to positive definite interpolation matrices for scattered data are discussed. They are related to the well-known thin plate spline radial functions which are highly useful in applications for gridfree approximation methods. Also, encouraging approximation results for the compactly supported radial functions are shown.
Hypoelliptic differential operators with generalized constant coefficients
Authors: Nedeljkov M. , Pilipović S.
Published: December 2008

The space of Colombeau generalized functions is used as a frame for the study of hypoellipticity of a family of differential operators whose coefficients depend on a small parameter ε.

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

Provided that the weight function ω satisfies certain submultiplicative and decay conditions, the discrete convolution algebra ℓ1(ω) becomes a commutative radical Banach algebra with identity adjoined. There are obvious closed ideals in ℓ1(ω) and these are denoted standard ideals. Earlier results of Thomas, strengthened by Yakubovich and Domar, showed that if the weight ω is star-shaped then all closed ideals are standard. Consequently, the closed ideal generated by any element f in ℓ1(ω) must be standard.

The requirement that ω be star-shaped (essentially that ω(n)1/n must decrease to zero) is somewhat restrictive in that no local maxima of ω(n)1/n are allowed. We generalize this previous result to apply to the larger class of ε-star shaped weights (0 < ε ≤ 1) which allow such local maxima. If f is a non-zero element on ℓ1(ω) we let the integer α(f) = k0 denote the index of its first non-zero term. We introduce the concept of an ε-peak point for k0. If ε = 1 then ω is star-shaped in the usual sense and there are an infinite number of 1-peak points for any k0. Although this latter fact may fail if 0 < ε < 1, if ω(n)1/n tends to zero sufficiently quickly (dependent on k0 and ε) there will always be an infinite number of ε-peak points for k0.

Our main result is that if ω is an ε-star shaped weight, if f is an non-zero element of ℓ1(ω), if α(f) = k0, and if the number of ε-peak points for k0 is infinite, then the closed ideal generated by f is standard.
On the Goldie dimension of injective modules
Authors: Pardo José L. Gómez , Asensio Pedro A. Guil
Published: December 2008

Let M be an essentially finitely generated injective (or, more generally, quasi-continuous) module. It is shown that if M satisfies a mild uniqueness condition on essential closures of certain submodules, then the existence of an infinite independent set of submodules of M implies the existence of a larger independent set on some quotient of M modulo a directed union of direct summands. This provides new characterisations of injective (or quasi-continuous) modules of finite Goldie dimension. These results are then applied to the study of indecomposable decompositions of quasi-continuous modules and nonsingular CS modules.
Tame automorphisms of finitely generated abelian groups
Authors: Turner Edward C. , Voce Daniel A.
Published: December 2008

We characterize tame automorphisms of finitely generated abelian groups via a simple determinant condition.
Comparison of graded and ungraded Cousin complexes
Authors: Petzl Henrike , Sharp Rodney Y.
Published: December 2008

Let R = ⊕n∈zRn be a ℤ-graded commutative Noetherian ring and let M be a ℤ-graded R-module. S. Goto and K. Watanabe introduced the graded Cousin complex *C(M)* for M, a complex of graded R-modules. Also one can ignore the grading on M and construct the Cousin complex C(M)* for M, discussed in earlier papers by the second author. The main results in this paper are that *C(M)* can be considered as a subcomplex of C(M)* and that the resulting quotient complex is always exact. This sheds new light on the known facts that, when M is non-zero and finitely generated, C(M)* is exact if and only if *C(M)* is (and this is the case precisely when M is Cohen-Macaulay).
Generic affine differential geometry of plane curves
Authors: Izumiya Shyuichi , Sano Takasi
Published: December 2008

We study affine invariants of plane curves from the view point of the singularity theory of smooth functions
A dendrological proof of the Scott conjecture for automorphisms of free groups
Authors: Gaboriau D. , Levitt G. , Lustig M.
Published: December 2008

Let α be an automorphism of a free group of rank n. The Scott conjecture, proved by Bestvina-Handel, asserts that the fixed subgroup of α has rank at most n. We give a short alternative proof of this result using R-trees.
A–∞-interpolation in the ball
Authors: Massaneda Xavier
Published: December 2008

We give a necessary and sufficient condition for a sequence {ak}k in the unit ball of ℂn to be interpolating for the class A–∞ of holomorphic functions with polynomial growth. The condition, which goes along the lines of the ones given by Berenstein and Li for some weighted spaces of entire functions and by Amar for H∞ functions in the ball, is given in terms of the derivatives of m ≥ n functions F1, …,Fm ∈ A–∞ vanishing on {ak}k.
On periodic groups having almost regular 2-elements
Authors: Rocco N. R. , Shumyatsky P.
Published: December 2008

We show that if a periodic residually-finite group G has a 2-element with finite centralizer then G is locally finite.
Products of derivations
Authors: Creedon T.
Published: December 2008

We prove that if the product of two derivations on an algebra is a derivation, then the product maps the algebra into its nilradical. As a consequence we obtain a characterisation of when the product of two derivations on a semiprime algebra is a derivation. We also give a condition on two derivations on a Banach algebra which implies that their product has range contained in the Jacobson radical.
Algebraic orders and chordal limit algebras
Authors: Donsig Allan P.
Published: December 2008

We develop an isomorphism invariant for limit algebras: an extension of Power's strong algebraic order on the scale of theK0-group (Power,J. Operator Theory27 (1992), 87–106). This invariant is complete for a certain family of limit algebras: inductive limits of digraph algebras (a.k.a. finite dimensional CSL algebras) satisfying two conditions: (1) the inclusions of the digraph algebras respect the order-preserving normalisers, and (2) the digraph algebras have chordal digraphs. The first condition is also used to show that the invariant depends only on the limit algebra and not the direct system. We give an intrinsic characterisation of the limit algebra and not the direct system. We give an intrinsic characterisation of the limit algebras satisfying both (1) and (2).
Monoid gradings on algebras and the cartan determinant conjecture
Authors: Saorín Manuel
Published: December 2008

In this work we tackle the Cartan determinant conjecture for finite-dimensional algebras through monoid gradings. Given an adequate ∑-grading on the left Artinian ring A, where ∑ is a monoid, we construct a generalized Cartan matrix with entries in ℤ∑, which is right invertitale whenever gl.dim A < ∞. That gives a positive answer to the conjecture when A admits a strongly adequate grading by an aperiodic commutative monoid. We then show that, even though this does not give a definite answer to the conjecture, it strictly widens the class of known graded algebras for which it is true.
Maximal operators and B.M.O. for Banach lattices
Authors: García-Cuerva J. , Macías R. A. , Torrea J. L.
Published: December 2008

We investigate the behaviour of the classical (non-smooth) Hardy-Littlewood maximal operator in the context of Banach lattices. We are mainly concerned with end-point results for p = ∞. Naturally, the main role is played by the space BMO. We analyze the range of the maximal operator in BMOx. This turns out to depend strongly on the convexity of the Banach lattice . We apply these results to study the behaviour of the commutators associated to the maximal operator. We also consider the parallel results for the maximal fractional integral operator.
On additive polynomials over a finite field
Authors: Odoni R. W. K.
Published: December 2008

This paper is based on the interpretation of the ring of additive polynomials in one variable over a finite field Fq, as a maximal R-order inside a certain skew-field D, R being a principal ideal domain isomorphic to Fp[T]. The classical (1930's) structure theory of maximal orders in global fields is used to solve enumeration questions involving the iteration of members of Pages from .
Reflexivity of the group of surjective isometries on some Banach spaces
Authors: Molnár Lajos , Zalar Borut
Published: December 2008

In this paper we study the problem of algebraic reflexivity of the isometry group of some important Banach spaces. Because of the previous work in similar topics, our main interest lies in the von Neumann – Schatten p-classes of compact operators. The ideas developed there can be used in ℓp-spaces, Banach spaces of continuous functions and spin factors as well. Moreover, we attempt to attract the attention to this problem from general Banach spaces geometry view-point. This study, we believe, would provide nice geometrical results.
An algorithm for stem products and one-relator groups
Authors: Metaftsis V.
Published: December 2008

We give an algorithm which for a given set of generators can decide whether a stem product of infinite cyclic groups is a one-relator group. We also generalize this to the case of one-relator products of groups.
The semicentre of a group algebra
Authors: Wauters Paul
Published: December 2008

We study the semicentre of a group algebra K[G] where K is a field of characteristic zero and G is a polycyclic-by-finite group suchthat Δ(G) is torsion-free abelian. Several properties about the structure of this ring are proved, in particular as to when is the semicentre a UFD. Examples are constructed when this is not the case. We also prove necessary and sufficient conditions for every normal element of K[G] which belongs to K[Δ(G)] to be the product of a unit and a semi-invariant.
Some undecidable embedding problems for finite semigroups
Authors: Jackson Marcel
Published: December 2008

Let S be a finite semigroup, A be a given subset of S and L, R, H, D and J be Green's equivalence relations. The problem of determining whether there exists a supersemigroup T of S from the class of all semigroups or from the class of finite semigroups, such that A lies in an L or R-class of T has a simple and well known solution (see for example [7], [8] or [3]). The analogous problem for J or D relations is trivial if T is of arbitrary size, but undecidable if T is required to be finite [4] (even if we restrict ourselves to the case |A| = 2 [6]). We show that for the relation H, the corresponding problem is undecidable in both the class of finite semigroups (answering Problem 1 of [9]) and in the class of all semigroups, extending related results obtained by M. V. Sapir in [9]. An infinite semigroup with a subset never lying in a H-class of any embedding semigroup is known and, in [9], the existence of a finite semigroup with this property is established. We present two eight element examples of such semigroups as well as other examples satisfying related properties.
The minimal operator module of a Banach module
Authors: Magajna Bojan
Published: December 2008

Banach modules over C*-algebras (von Neumann algebras) that can be represented isometrically as operator modules (normal operator modules, respectively) are characterised.
Optimal functions for a periodic uncertainty principle and multiresolution analysis
Authors: Prestin Jürgen , Quak Ewald
Published: December 2008

In this paper, it is shown that certain Theta functions are asymptotically optimal for the periodic time frequency uncertainty principle described by Breitenberger in [3]. These extremal functions give rise to a periodic multiresolution analysis where the corresponding wavelets also show similar localization properties.
Interpolation restricted to decreasing functions and Lorentz spaces
Authors: Cerdà Joan , Martín Joaquim
Published: December 2008

For the real interpolation method, we identify the interpolated spaces of couples of classical Lorentz spaces through interpolation of the corresponding weighted Lp-spaces restricted to decreasing functions.
Computing eigenvalues of Sturm-Liouville systems of Bessel type
Authors: Boumenir A. , Chanane B.
Published: December 2008

In this paper we shall develop a new method for the computation of eigenvalues of singular Sturm-Liouville problems of the Bessel type. This new method is based on the interpolation of a boundary function in Paley-Wiener spaces. Numerical results are provided to illustrate the method.
A Bernstein-Gabber-Joseph theorem for affine algebras
Authors: Bavula V. V. , Lenagan T. H.
Published: December 2008

Bernstein's famous result, that any non-zero module M over the n-th Weyl algebra An satisfies GKdim(M)≥GKdim(An)/2, does not carry over to arbitrary simple affine algebras, as is shown by an example of McConnell. Bavula introduced the notion of filter dimension of simple algebra to explain this failure. Here, we introduce the faithful dimension of a module, a variant of the filter dimension, to investigate this phenomenon further and to study a revised definition of holonomic modules. We compute the faithful dimension for certain modules over a variant of the McConnell example to illustrate the utility of this new dimension.
Positive solutions and eigenvalues of conjugate boundary value problems
Authors: Agarwal Ravi P. , Bohner Martin , Wong Patricia J. Y.
Published: December 2008

We consider the following boundary value problem

where λ > 0 and 1 ≤ p ≤ n – 1 is fixed. The values of λ are characterized so that the boundary value problem has a positive solution. Further, for the case λ = 1 we offer criteria for the existence of two positive solutions of the boundary value problem. Upper and lower bounds for these positive solutions are also established for special cases. Several examples are included to dwell upon the importance of the results obtained.
The cover associated to a (1,3)-polarized bielliptic abelian surface and its branch locus
Authors: Casnati Gianfranco
Published: December 2008

Let A be an abelian surface and let |D| be a polarization of type (1,3) on A. If (A,|D|) is not a product of elliptic curves, such a polarization induces a finite morphism Q: A →p2C of degree 6. In this paper we describe the branch locus of Q when A is bielliptic in thesense of K. Hulek and S. H. Weintraub (see [13]), generalizing the results proved by Ch. Birkenhake and H. Lange in [4].
Asymptotic behaviour of solutions to the Becker-Döring equations
Authors: Carr J. , Dunwell R. M.
Published: December 2008

The asymptotics behaviour of solutions of the Becker-Döring cluster equations is determined for cases in which coagulation dominates fragmentation. We show that all non-zero solutions tend weak* to zero.
Linear combinations of harmonic measures and quadrature domains of signed measures with small supports
Authors: Sakai Makoto
Published: December 2008

In this paper we discuss the shape of the quadrature domain of a signed measure for harmonic functions. It is known that the quadrature domain of a positive measure with small support is like a ball if the total measure is large enough. We show that, on the contrary, if the measure is not positive then the quadrature domain can be close to an arbitrary domain. This follows from a lemma concerning linear combinations of harmonic measures.
Generalized Hensel's lemma
Authors: Khanduja Sudesh K. , Saha Jayanti
Published: December 2008

Let (K, v) be a complete, rank-1 valued field with valuation ring Rv, and residue field kv. Let vx be the Gaussian extension of the valuation v to a simple transcendental extension K(x) defined by The classical Hensel's lemma asserts that if polynomials F(x), G0(x), H0(x) in Rv[x] are such that (i) vx(F(x) – G0(x)H0(x)) > 0, (ii) the leading coefficient of G0(x) has v-valuation zero, (iii) there are polynomials A(x), B(x) belonging to the valuation ring of vx satisfying vx(A(x)G0(x) + B(x)H0(x) – 1) > 0, then there exist G(x), H(x) in K[x] such that (a) F(x) = G(x)H(x), (b) deg G(x) = deg G0(x), (c) vx(G(x)–G0(x)) > 0, vx(H(x) – H0(x)) > 0. In this paper, our goal is to prove an analogous result when vx is replaced by any prolongation w of v to K(x), with the residue field of wa transcendental extension of kv.
Generators and relations of Rees matrix semigroups
Authors: Ayik H. , Ruškuc N.
Published: December 2008

In this paper we consider finite generation and finite presentability of Rees matrix semigroups (with or without zero) over arbitrary semigroups. The main result states that a Rees matrix semigroupM[S; I, J; P]is finitely generated (respectively, finitely presented) if and only ifSis finitely generated (respectively, finitely presented), and the setsI, J and S\Uare finite, whereUis the ideal ofSgenerated by the entries ofP.
Lower semimodular Lie algebras
Authors: Varea V. R.
Published: December 2008

This paper is concerned with the relationship between the properties of the subalgebra lattice ℒ(L) of a Lie algebra L and the structure of L. If the lattice ℒ(L) is lower semimodular, then the Lie algebra L is said to be lower semimodular. If a subalgebra S of L is a modular element in the lattice ℒ(L), then S is called a modular subalgebra of L. The easiest condition to ensure that L is lower semimodular is that dim A/B = 1 whenever B < A ≤ L and B is maximal in A (Lie algebras satisfying this condition are called sχ-algebras). Our aim is to characterize lower semimodular Lie algebras and sχ-algebras, over any field of characteristic greater than three. Also, we obtain results about the influence of two solvable modularmaximal subalgebras on the structure of the Lie algebra and some results on the structure of Lie algebras all of whose maximal subalgebras are modular.
Random spanning trees of Cayley graphs and an associated compactification of semigroups
Authors: Evans Steven N.
Published: December 2008

A sequential construction of a random spanning tree for the Cayley graph of a finitely generated, countably infinite subsemigroup V of a group G is considered. At stage n, the spanning tree T isapproximated by a finite tree Tn rooted at the identity.The approximation Tn+1 is obtained by connecting edges to the points of V that are not already vertices of Tn but can be obtained from vertices of Tn via multiplication by a random walk step taking values in the generating set of V. This construction leads to a compactification of the semigroup V inwhich a sequence of elements of V that is not eventually constant is convergent if the random geodesic through the spanning tree T that joins the identity to the nth element of the sequence converges in distribution as n→∞. The compactification is identified in a number of examples. Also, it is shown that if h(Tn) and #(Tn) denote, respectively, the height and size of the approximating tree Tn, then there are constants 0<ch≤1 and 0≥c# ≤log2 such that limn→∞ n–1 h(Tn)= ch and limn→∞n–1 log# (Tn)= c# almost surely.