bluuebunny/crossref_metadata_2025 huggingface dataset:
Diagrammatically reducible complexes and Haken manifolds
Authors: Corson J. M , Trace B.
Published: April 2009

We show that diagrammatically reducible two-complexes are characterized by the property: every finity subconmplex of the universal cover collapses to a one-complex. We use this to show that a compact orientable three-manifold with nonempty boundary is Haken if and only if it has a diagrammatically reducible spine. We also formulate an nanlogue of diagrammatic reducibility for higher dimensional complexes. Like Haken three-manifolds, we observe that ifn≥ 4 andMis compact connectedn-dimensional manifold with a traingulation, or a spine, satisfying this property, then the interior of the universal cover ofMis homeomorphic to Euclideann-space.
About the zeros of some entire functions and their derivatives
Authors: Stoyanov Todor
Published: April 2009

In this article we localize the zeros of some polynomials and the derivatives of some entire functions of finite genus. If we put m = 1 in the condition of Theorem 1 we obtain the famous Obreshkoff Theorem which can be regarded as a ‘complex version’ of a well-known theorem due to Laguerre. The nonreal zeros of the derivative of the real entire funtion of Theorem 3 must belong to circles Vk which are similar to the Jen circles for polynomials.
Ergodic behaviour of extreme values
Authors: Cheng S. , Peng L. , Qi Y.
Published: April 2009

Let {Xn, n ≥ 1} be independent identically distributed random variables with a common non-degenerate distribution function F. For each n ≥ 1, denote Mn = max {X1,…, Xn}. Under certain conditions on F, there exist constants an > 0 and bn ∈ R such that . In this paper, we shall show that {(Mn – bn)/an} exhibits ergodic behaviour under additional conditions of F.
Spectral and asymptotic properties of resolvent-dominated operators
Authors: Räbiger Frank , Wolff Manfred P. H.
Published: April 2009

Let A and B be (not necessarily bounded) linear operators on a Banach lattice E such that |(s – B)-1x|≤ (s – A)-1|x| for all x in E and sufficiently large s ∈ R. The main purpose of this paper is to investigate the relation between the spectra σ(B) and σ(A) of B and A, respectively. We apply our results to study asymptotic properties of dominated C0-semigroups.
Pseudo differential operators on local Hardy spaces on chébli-teimèche hypergroups
Authors: Bloom Walter R. , Xu Zengfu
Published: April 2009

In this paper we consider pseudo differential operators on local Hardy spaces hp (0 < p ≤ 1) on Chébli-Trimèche hypergroups of exponential growth.
Sharkovskii's order and the stability of periodic points of maps of the interval
Authors: Zhang Guang Yuan , Li Qing Zhong
Published: April 2009

Let f be a Cr (r ≥ 0) map from the interval [0, 1] into itself and m be a positive integer. This paper gives a sufficient and necessary condition under which the set of periodic points of period m disappears after a certain small Cr-perturbation.
Loomis-sikorski theorem for σ-complete MV-algebras and ℓ-groups
Authors: Dvurečenskij Anatolij
Published: April 2009

We show that every σ-complete MV-algebra is an MV-σ-homomorphic image of some σ-complete MV- algebra of fuzzy sets, called a tribe, which is a system of fuzzy sets of a crisp set Ω containing 1Ωand closed under fuzzy complementation and formation of min {∑nfn, 1}. Since a tribe is a direct generalization of a σ-algebra of crisp subsets, the representation theorem is an analogue of the Loomis-Sikorski theorem for MV-algebras. In addition, this result will be extended also for Dedekind σ-complete ℓ-groups with strong unit.
A solution of a problem of Plotkin and Vovsi and an application to varieties of groups
Authors: Gupta C. K. , Krasil'nikov A. N.
Published: April 2009

Let K be an arbitrary field of characteristic 2, F a free group of countably infinite rank. We construct a finitely generated fully invariant subgroup U in F such that the relatively free group F/U satisfies the maximal condition on fully invariant subgroups but the group algebra K (F/U) does not satisfy the maximal condition on fully invariant ideals. This solves a problem posed by Plotkin and Vovsi. Using the developed techniques we also construct the first example of a non-finitely based (nilpotent of class 2)-by-(nilpotent of class 2) variety whose Abelian-by-(nilpotent of class at most 2) groups form a hereditarily finitely based subvariety.
Infinite time interval BSDEs and the convergence of g-martingales
Authors: Chen Zengjing , Wang Bo
Published: April 2009

In this paper, we first give a sufficient condition on the coefficients of a class of infinite time interval backward stochastic differential equations (BSDEs) under which the infinite time interval BSDEs have a unique solution for any given square integrable terminal value, and then, using the infinite time interval BSDEs, we study the convergence of g-martingales introduced by Peng via a kind of BSDEs. Finally, we study the applications of g-expectations and g-martingales in both finance and economics.
Self θ-congruent minimal surfaces in ℝ3
Authors: Chen Weihuan , Fang Yi
Published: April 2009

A minimal surface is a surface with vanishing mean curvature. In this paper we study self θ -congruent minimal surfaces, that is, surfaces which are congruent to their θ-associates under rigid motions in R3 for 0 ≤ θ < 2π. We give necessary and sufficient conditions in terms of its Weierstrass pair for a surface to be self θ-congruent. We also construct some examples and give an application.
The embeddability of ring and semigroup amalgams is undecidable
Authors: Jackson Marcel
Published: April 2009

We prove that there is no algorithm to determine when an amalgam of finite rings (or semigroups) can be embedded in the class of rings or in the class of finite rings (respectively, in the class of semigroups or in the class of finite semigroups). These results are in marked contrast with the corresponding problems for groups where every amalgam of finite groups can be embedded in a finite group.
Transference on certain multilinear multiplier operators
Authors: Fan Dashan , Sato Shuichi
Published: April 2009

We study DeLeeuw type theorems for certain multilinear operators on the Lebesgue spaces and on the Hardy spaces. As applications, on the torus we obtain an analog of Lacey—Thiele's theorem on the bilinear Hilbert transform, as well as analogies of some recent theorems on multilinear singular integrals by Kenig—Stein and by Grafakos—Torres.
A note on amalgams of inverse semigroups
Authors: steinberg Benjamin
Published: April 2009

This note gives a necessary condition, in terms of graded actions, for an inverse semigroup to be a full amalgam. Under a mild additional hypothesis, the condition becomes sufficient.
Non-linear differential equations with transcendental meromorphic solutions
Authors: Ishizaki Katsuya , Wang Yuefei
Published: April 2009

In this paper we treat two non-linear differential equations which come from complex dynamics theory. We give a complete classification of the equations when they possess transcendental meromorphic solutions.
Character sums and the series L(1, χ)
Authors: Leu Ming-Guang
Published: April 2009

In this paper we derive a relation between character sums and partial sums of Dirichlet series.
Sharp starlikeness conditions for analytic functions with bounded derivative
Authors: Rønning Frode , Ruscheweyh Stephan , Samaris Nikolas
Published: April 2009

We develop sharp conditions for various types of starlikeness for functions analytic in the unit disk with bounded derivatives. We also describe the precise range {zf′(z)/f(z): z ∈ D, f ∈ }, where f ∈ means f (0) = 0, f′(0) = 1, and |f′(z) - 1 |< ≦ λ in the unit disc D, and draw some cnoslusions from that.
A uniqueness theorem for properly embedded minimal surfaces bounded by straight lines
Authors: Lopez Francisco J. , Martin Francisco
Published: April 2009

In this paper we prove a uniqueness theorem for minimal discs in R3 spanning a polygonal boundary.
Semidistributive inverse semigroups
Authors: Johnston-Thom Katherine G. , Jones Peter R.
Published: April 2009

An inverse semigroupSis said to be meet (join) semidistributive if its lattice(S) of full inverse subsemigroups is meet (join) semidistributive. We show that every meet (join) semidistributive inverse semigroup is in fact distributive.
Remarks on converse Carleman and Krein criteria for the classical moment problem
Authors: Pakes Anthony G.
Published: April 2009

The key theme is converse forms of criteria for deciding determinateness in the classical moment problem. A method of proof due to Koosis is streamlined and generalized giving a convexity condition under which moments satisfying implies that c a positive constant. A contrapositive version is proved under a rapid variation condition on f (x), generalizing a result of Lin. These results are used to obtain converses of the Stieltjes versions of the Carleman and Krein criteria. Hamburger versions are obtained which relax the symmetry assumption of Koosis and Lin, respectively. A sufficient condition for Stieltjes determinateness of a discrete law is given in terms of its mass function. These criteria are illustrated through several examples.
A problem of expressibility in some amalgamated products of groups
Authors: Faiziev Valerii
Published: April 2009

Let S be a subset of a group G such that S−1 = S. Denote by gr (S) the subgroup of G generated by S, and by ls(g) the length of an element g ∈ gr(S) relative to the set S. Suppose that V is a finite subset of a free group F of countable rank such that the verbal subgroup V (F) is a proper subgroup of F. For an arbitrary group G, denote by (G) the set of values in G of all the words from the set V. In the present paper, for amalgamated products G = A *HB such that A ≠ H and the number of double cosets of B by H is at least three, the infiniteness of the set {ls(g) | g ∈ gr(S)}, where S = (G) ∪ (G)−1, is estabilished.
The characterisation of scoring functions
Authors: Deakin Michael A. B.
Published: April 2009

The literature on subjective probabilities contains a number of functions that have been proposed as ‘scoring functions’. The principal requirement is that, with several events that may occur in the future and to which subjective ‘probabilities’ are assigned, the expected score given by these ‘probabilities’ will be extremised if the values assigned equal the ‘true probabilities’ of the various outcomes. This article discusses the question of what other scoring functions might be used (beyond those so far proposed).
On the probability of generating a minimal d-generated group
Authors: Volta F. Dalla , Lucchini A. , Morini F.
Published: April 2009

We consider finite groups with the property that any proper factor can be generated by a smaller number of elements than the group itself. We study some problems related with the probability of generating these groups with a given number of elements.
Modules over infinite nilpotent groups
Authors: Groves J. R. J.
Published: April 2009

The paper discusses modules over free nilpotent groups and demonstrates that faithful modules are more restricted than might appear at first glance. Some discussion is also made of applying the techniques more generally.
On a family of cyclically-presented fundamental groups
Authors: Newman M. F.
Published: April 2009

Bounds are obtained for the minimum number of generators for the fundamental groups of a family of closed 3-dimensional manifolds. A significant role has been played by the use of computers.
Multiplicity-free quotient tensor algebras
Authors: Wall G. E.
Published: April 2009

LetVbe an infinite-dimensional vector space ovre a field of characteristic 0. It is well known that the tensor algebraTonVis a completely reducible module for the general linear groupGonV. This paper is concerned with those quotient algebrasAofTthat are at the same time modules forG. A partial solution is given to the problem of determinig thoseAin which no irreducible constitutent has multiplicity greater thatn 1.
Orbit sizes, local subgroups and chains of p-groups
Authors: Isaacs I. M.
Published: April 2009

Let G be a finite group that acts on a finite group V, and let p be a prime that does not divide the order of V. Then the p-parts of the orbit sizes are the same in the actions of G on the sets of conjugacy classes and irreducible characters of V. This result is derived as a consequence of some general theory relating orbits and chains of p-subgroups of a group.
A note on multipliers of Lp(G, A)
Authors: Öztop Serap
Published: April 2009

Let G be a locally compact abelian group, 1 < p < ∞, and A be a commutative Banach algebra. In this paper we study the space of multipliers on Lp (G, A) and characterize it as the space of multipliers of certain banach algebra. We also study the multipliers space on L1 (G, A) ∩ Lp (G, A).
Manifolds that fail to be co-dimension 2 fibrators necessarily cover themselves
Authors: Im Young Ho , Kim Yongkunk
Published: April 2009

LetNbe a closeds-Hopfiann-manifold with residually finite, torsion free π1(N) and finiteH1(N). Suppose that either πk(N) is finitely generated for allk≥ 2, or πk(N) ≅ 0 for 1 <k<n– 1, orn≤ 4. We show that ifNfails to be a co-dimension 2 fibrator, thenNcyclically covers itself, up to homotopy type.
Generalized quasilinear hyperbolic equations and Yosida approximations
Authors: Park Jong Yeoul , Jung Il Hyo , Kang Yong Han
Published: April 2009

We will show the existence, uniqueness and regularity of global solutions for the Cauchy problem for nonlinear evolution equations with the damping term.

As an application of our results, we give the global solvability and regularity of the mixed problem with Dirichiet boundary conditions:
Naturally reductive homogeneous real hypersurfaces in quaternionic space forms
Authors: Nagai Setsuo
Published: April 2009

We determine the naturally reductive homogeneous real hypersurfaces in the family of curvature-adapted real hypersurfaces in quaternionic projective space HPn(n ≥ 3). We conclude that the naturally reductive curvature-adapted real hypersurfaces in HPn are Q-quasiumbilical and vice-versa. Further, we study the same problem in quaternionic hyperbolic space HHn(n ≥ 3).
Biseparating linear maps between continuous vector-valued function spaces
Authors: Gau Haw-Long , Jeang Jyh-Shyang , Wong Nagi-Ching
Published: April 2009

Let X, Y be compact Hausdorff spaces and E, F be Banach spaces. A linear map T: C(X, E) → C(Y, F) is separating if Tf, Tg have disjoint cozeroes whenever f, g have disjoint cozeroes. We prove that a biseparating linear bijection T (that is, T and T-1 are separating) is a weighted composition operator Tf = h · f o ϕ. Here, h is a function from Y into the set of invertible linear operators from E onto F, and ϕ, is a homeomorphism from Y onto X. We also show that T is bounded if and only if h(y) is a bounded operator from E onto F for all y in Y. In this case, h is continuous with respect to the strong operator topology.
Daisy structure in Desarguesian projective planes
Authors: Pardo M. Gabriela Araujo
Published: April 2009

We distribute the points and lines ofPG(2, 2n+1) according to a special structure that we call the daisy structure. This distribution is intimately related to a special block design which turns out to be isomorphic toPG(n, 2).

We show a blocking set of 3qpoints inPG(2, 2n+1)that intersects each line in at least two points and we apply this to find a lower bound for the heterochromatic number of the projective plane.
Betti numbers of fixed point sets and multiplicities of indecomposable summands
Authors: Kaptanoglu Semra Öztürk
Published: April 2009

Let G be a finite group of even order, k be a field of characteristic 2, and M be a finitely generated kG-module. If M is realized by a compact G-Moore space X, then the Betti numbers of the fixed point set XCn and the multiplicities of indecomposable summands of M considered as a kCn-module are related via a localization theorem in equivariant cohomology, where Cn is a cyclic subgroup of G of order n. Explicit formulas are given for n = 2 and n = 4.
Joint continuity of injective tensor products of vector measures in Banach lattices
Authors: Kawabe Jun
Published: April 2009

It is shown that the injective tensor product of positive vector measures in certain Banach lattices is jointly continuous with respect to the weak convergence of vector measures. This result is obtained by a diagonal convergence theorem for injective tensor integrals. Our approach to this problem is based on Bartle's bilinear integration theory.
On -hyperexcentric modules for Lie algebras
Authors: Barnes Donald W.
Published: April 2009

Let be a saturated formation of soluble Lie algebras over the field F, and let L ∈ . Let V and W be -hypercentral and -hyperexcentric L-modules respectively. Then V ⊗FW and HomF(V, W) are -hyperexcentric and Hn(L, W) = 0 for all n.
Strange permutation representations of free groups
Authors: Bhattacharjee Meenaxi , MacPherson Dugald
Published: April 2009

Certain permutation representations of free groups are constructed by finite approximation. The first is a construction of a cofinitary group with special properties, answering a question of Tim Wall published by Cameron. The second yields, via a method of Kepert and Willis, a totally disconnected locally compact group which is compactly generated and uniscalar but has no compact open normal subgroup. Finally, an oligomorphic group of automorphisms of the random graph is built, all of whose non-trivial subgroups have just finitely many orbits.
On permutation groups with constant movement
Authors: Alaeiyan(Khayaty) Mehdi
Published: April 2009

Let G be a permutation group on a set Ω with no fixed point in Ω. If for each subset Г of Ω the size |Гg - Г| is bounded, for g ∈ G, we define the movement of g as the max|Гg − Г| over all subsets Г of Ω. In particular, if all non-identity elements of G have the same movement, then we say that G has constant movement. In this paper we will first give some families of groups with constant movement. We then classify all transitive permutation groups with a given constant movement m on a set of maximum size.
The Wielandt Subalgebra of a Lie Algebra
Authors: Barnes Donald W. , Groves Daniel
Published: April 2009

Following the analogy with group theory, we define the Wielandt subalgebra of a finite-dimensional Lie algebra to be the intersection of the normalisers of the subnormal subalgebras. In a non-zero algebra, this is a non-zero ideal if the ground field has characteristic 0 or if the derived algebra is nilpotent, allowing the definition of the Wielandt series. For a Lie algebra with nilpotent derived algebra, we obtain a bound for the derived length in terms of the Wielandt length and show this bound to be best possible. We also characterise the Lie algebras with nilpotent derived algebra and Wielandt length 2.
An Embedding Construction for Ordered Groups
Authors: Mikaelian Vahagn H.
Published: April 2009

Generalizing and strengthening some well-known results of Higman, B. Neumann, Hanna Neumann and Dark on embeddings into two-generator groups, we introduce a construction of subnormal verbal embedding of an arbitrary (soluble, fully ordered or torsion free) ordered countable group into a twogenerator ordered group with these properties. Further, we establish subnormal verbal embedding of defect two of an arbitrary (soluble, fully ordered or torsion free) ordered group G into a group with these properties and of the same cardinality as G, and show in connection with a problem of Heineken that the defect of such an embedding cannot be made smaller, that is, such verbal embeddings of ordered groups cannot in general be normal.
Transferring Optimal Dualities: Theory and Practice
Authors: Davey B. A. , Haviar M.
Published: April 2009

Consider the quasi-variety generated by a finite algebra and assume that yields a natural duality on based on which is optimal modulo endomorphisms. We shoe that, provided satisfies certain minimality conditions, we can transfer this duality to a natural duality on based on , which is also optimal modulo endormorphisms, for any finite algebra in that has a subalgebra isomorphic to .
On Products in Lattice-ordered Algebras
Authors: Boulabiar Karim
Published: April 2009

Let A be a uniformly complete vector sublattice of an Archimedean semiprime f-algebra B and p ∈ {1, 2,…}. It is shown that the set ΠBp (A) = {f1 … fp: fk ∈ A, k = 1, …, p } is a uniformly complete vector sublattice of B. Moreover, if A is provided with an almost f-algebra multiplication * then there exists a positive operator Tp, from ΠBp(A) into A such that fi *…* fp = Tp(f1 …fp) for all f1…fp ∈ A.

As application, being given a uniformly complete almost f-algebra (A, *) and a natural number p ≧ 3, the set Π*p(A) = {f1 *… *fp: fk ∈ A, k = 1…p} is a uniformly complete semiprime f-algebra under the ordering and the multiplication inherited from A.
The Direct Decomposition of l-algebras into Products of Subdirectly Irreducible Factors
Authors: Radeleczki Sándor
Published: April 2009

Generalizing earlier results of Katriňák, El-Assar and the present author we prove new structure theorems for l-algebras. We obtain necessary and sufficient conditions for the decomposition of an arbitrary bounded lattice into a direct product of (finitely) subdirectly irreducible lattices.
Banach-Dieudonné Theorem Revisited
Authors: Bruguera Montserrat , Martín-Peinador Elena
Published: April 2009

We prove that in the character group of an abelian topological group, the topology associated (in a standard way) to the continuous convergence structure is the finest of all those which induce the topology of simple convergence on the corresponding equicontinuous subsets. If the starting group is furthermore metrizable (or even almost metrizable), we obtain that such a topology coincides with the compact-open topology. This result constitutes a generalization of the theorem of Banach-Dieudonné, which is well known in the theory of locally convex spaces.

We also characterize completeness, in the class of locally quasi-convex metrizable groups, by means of a property which we have calledthe quasi-convex compactness property, or brieflyqcp(Section 3).
Extreme Point Methods and Banach-Stone Theorems
Authors: Al-Halees Hasan , Fleming Richard J.
Published: April 2009

An operator is said to be nice if its conjugate maps extreme points of the dual unit ball to extreme points. The classical Banach-Stone Theorem says that an isometry from a space of continuous functions on a compact Hausdorff space onto another such space is a weighted composition operator. One common proof of this result uses the fact that an isometry is a nice operator. We use extreme point methods and the notion of centralizer to characterize nice operators as operator weighted compositions on subspaces of spaces of continuous functions with values in a Banach space. Previous characterizations of isometries from a subspace M of C0( Q, X) into C0(K, Y) require Y to be strictly convex, but we are able to obtain some results without that assumption. Important use is made of a vector-valued version of the Choquet Boundary. We also characterize nice operators from one function module to another.
Connectedness of graphs generated by a randomd-process
Authors: Ruciński A. , Wormald N. C.
Published: April 2009

Suppose that a graph process begins withnisolated vertices, to which edges are added randomly one by one so that the maximum degree of the induced graph is always at mostd. In a previous article, the authors showed that asn→ ∞, with probability tending to 1, the result of this process is a d-regular graph. This graph is shown to be connected with probability asymptotic to 1.
On transcendental meromorphic functions which are geometrically finite
Authors: Zheng Jian-Hua
Published: April 2009

In this paper we give the definition of a meromorphic function which is geometrically finite and investigate some properties of geometrically finite meromorphic functions and the Lebesgue measure of their Julia sets.
The zeros of linear combinations of translates of polynomials
Authors: Walker Peter
Published: April 2009

We investigate the location and separation of zeros of certain three-term linear combination of translates of polynomials. In particular, we find an interval of the formI= [−1, 1 +h],h> 0 such that for a polynomialf, all of whose zeros are real, and λ ∈I, all zeros off(x+ 2ic) + 2λf(x) +f(x– 2ic) are also real.
On the distribution of harmonic measure on simply connected planar domains
Authors: Betsakos Dimitrios , Solynin Alexander Yu.
Published: April 2009

For a simply connected planar domain D with 0 ∈ D and dist(0, ∂D) = 1, let hD(r) be the harmonic measure of ∂ D ∩{|Z| ≤ r} evaluated at 0. The function hD(r) is the distribution of harmonic measure. It has been studied by B. L. Walden and L. A. Ward. We continue their study and answer some questions raised by them by constructing domains with pre-specified distribution.
Projective descriptions of the (LF)-spaces of type LB(λp(A), F)
Authors: Albanese Angela A.
Published: April 2009

Let 1 < p < + ∞ or p = 0 and let A = (an)n be an increasing sequence of strictly positive weights on I. Let F be a Fréchet space. It is proved that if λp(A) satisfies the density condition of Heinrich and a certain condition (Ct) holds, then the (LF)-space LBi(λp(A), F) is a topological subspace of Lb(λp(A), F). It is also proved that these conditions are necessary provided F = λq(A) or F contains a complemented copy of Iq with 1 < p ≤ q < +∞.
A new approach to thek(GV)-problem
Authors: Keller Thomas Michael
Published: April 2009

This paper is concerned with the well-known and long-standingk(G V)-problem: If the finite groupGacts faithfully and irreducibly on the finiteGF(p)-moduleVandpdoes not divide the order ofG, is the numberk(GV) of conjugacy classes of the semidirect productGVbounded above by the order ofV? Over the past two decades, through the work of numerous people, by using deep character theoretic arguments this question has been answered in the affirmative except for ρ = 5 for which it is still open. In this paper we suggest a new approach to thek(G V)-problem which is independent of most of the previous work on the problem and which is mainly group theoretical. To demonstrate the potential of the new line of attack we use it to solve thek(G V)-problem for solvableGand large ρ.
Correspondences of the Gelfand invariants in reductive dual pairs
Authors: Itoh Minoru
Published: April 2009

For each complex reductive dual pair introduced by R. Howe, this paper presents a formula for the central elements of the universal enveloping algebras given by I. M. Gelfand. This formula provides an explicit description of the correspondence between the ‘centers’ of the two universal enveloping algebras.
Bilinear integration with positive vector measures
Authors: Jefferies Brian , Rothnie Paul
Published: April 2009

The integration of vector (and operator) valued functions with respect to vector (and operator) valued measures can be simplified by assuming that the measures involved take values in the positive elements of a Banach lattice.
Mono-unary algebras are strongly dualizable
Authors: Hyndman Jennifer
Published: April 2009

We show that mono-unary algebras have rank at most two and are thus strongly dualizable. We provide an example of a strong duality for a mono-unary algebra using an alter ego with (partial) operations of arity at most two. This mono-unary algebra has rank two and generates the same quasivariety as an injective, hence rank one, mono-unary algebra.
Some irreducible free group representations in which a linear combination of the generators has an eigenvalue
Authors: Paschke William L.
Published: April 2009

We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the eigenvalue is specified, we conjecture that there is only one such representation. The representation we have found is described explicitly (modulo inversion of a certain rational map on Euclidean space) in terms of a positive definite function, and also by means of a quasi-invariant probability measure on the combinatorial boundary of the group.
Perspective simplexes
Authors: Mandan Sahib Ram
Published: April 2009

The main purpose of this paper is to prove the proposition: “A set of r mutually perspective (m.p.) (s—1)-simplexes have the same [s−2] (say x) of perspectivity, if and only if their centres of perspectivity (c.p.) lie in an [r−2] (say y); there then arises another such set of s m.p. (r—1)-simplexes, having the same rs vertices, which have y as their common [r−2] of perspectivity such that their c.p. lie in x.” The proposition is true in any [k] for k = s−1, s,…, r+s−2 (r ≦ s). The configuration of the proposition in [r+s−2] arises from the incidences of any r+s arbitrary primes therein and is therefore invariant under the symmetric group of permutations of r+s objects, and that in [r+s−3] is self-dual and therefore self- polar for a quadric therein. Some special cases of some interest for r = s are deduced. The treatment is an illustration of the elegance of the Möbius Barycentric Calculus ([15], pp. 136–143; [1], p. 71).
Propagation of elastic waves
Authors: Cooper G. J. , Craggs J. W.
Published: April 2009

The behaviour of waves in elastic solids with linear stress strain curves is expressed, for plane strain, by a pair of simultaneous partial differential equations of hyperbolic type. Detailed behaviour of the waves is examined by solving these equations numerically.
Supports and singular supports of pseudomeasures
Authors: Edwards R. E.
Published: April 2009

Let G denote a Hausdorff locally compact Abelian group which is nondiscrete and second countable. The main results (Theorems (2.2) and (2.3)) assert that, for any closed subset E of G there exists a pseudomeasure s on G whose singular support is E; and that if no portion of E is a Helson set, then such an s may be chosen having its support equal to E. There follow (Corollaries (2.2.4) and (2.3.2)) sufficient conditions for the relations to hold for some pseudomeasure s, E and F being given closed subsets of G. These results are analogues and refinements of a theorem of Pollard [4] for the case G = R, which asserts the existence of a function in L∞(R) whose spectrum coincides with any preassigned closed subset of R.
Algorithms for generalized stability numbers of tree graphs
Authors: Daykin D. E. , Ng C. P.
Published: April 2009

In this paper we give some algorithms for determining αw(T) and βw(T), the generalized internal and external stability numbers respectively, of a finite directed tree graph T whose nodes are weighted by a function w. We define αw(T) and βw in section 2. When w gives every node of T the weight 1 then αw(T) = α(T) and βw(T) = β(T) where α(T) and β(T) are the usual stability numbers.
The iterated equation of generalized axially symmetric potential theory. I. Particular solutions
Authors: Burns J. C.
Published: April 2009

The iterated equation of generalized axially symmetric potential theory (GASPT) [1] is defined by the relations (1) where (2) and Particular cases of this equation occur in many physical problems. In classical hydrodynamics, for example, the case n = 1 appears in the study of the irrotational motion of an incompressible fluid where, in two-dimensional flow, both the velocity potential φ and the stream function Ψ satisfy Laplace's equation, L0(f) = 0; and, in axially symmetric flow, φ and satisfy the equations L1 (φ) = 0, L-1 (ψ) = 0. The case n = 2 occurs in the study of the Stokes flow of a viscous fluid where the stream function satisfies the equation L2k(ψ) = 0 with k = 0 in two-dimensional flow and k = −1 in axially symmetric flow.
Certain homomorphisms of a compact semigroup onto a thread
Authors: Hunter R. P. , Anderson L. W.
Published: April 2009

Let S be a compact semigroup and f a continuous homomorphism of S onto the (compact) semigroup T. What can be said concerning the relations among S, f, and T? It is to one special aspect of this problem which we shall address ourselves. In particular, our primary considerations will be directed toward the case in which T is a standard thread. A standard thread is a compact semigroup which is topologically an arc, one endpoint being an identity element, the other being a zero element. The structure of standard threads is rather completely determined e.g. see [20]. Among the standard threads there are three which have a rather special rôle. These are as follows: A unit thread is a standard thread with only two idempotents and no nilpotent element. A unit thread is isomorphic to the usual unit interval [14]. A nil thread again has only two idempotents but has a non-zero nilpotent element. A nil thread is isomorphic with the interval [½, 1], the multiplication being the maximum of ½ and the usual product — or, what is the same thing, the Rees quotient of the usual [0, 1] by the ideal [0,½ ]. Finally there is the idempotent thread, the multiplication being x o y = mm (x, y). These three standard threads can often be considered separately and, in this paper, we reserve the symbols I1I2 and I3 to denote the unit, nil and idempotent threads respectively. Also, throughout this paper, by a homomorphism we mean a continuous homomorphism.
Linear operators which commute with translations. Part II: Applications of the representation theorems
Authors: Brainerd B. , Edwards R. E.
Published: April 2009

This paper comprises a number of applications of the results of Part I. We use essentially the same notation as in Part I with a few additions necessary for the problems at hand.
Some local limit results in fluctuation theory
Authors: Heyde C. C.
Published: April 2009

Let Xi, ι = 1, 2, 3,… be a sequence of independent and identically distributed random variables and write S0 = 0, Sn = ∑ni=1Xi, n ≧ 1. Nn is the number of positive terms in the sequence S0, S1, S2,…, Snn ≧ 0.
Trivial knots with arbitrary projection
Authors: Smythe N.
Published: April 2009

Let k be a polygonal knot in Euclidean 3-space, p a projection onto a plane. If p;/k is 1:1 except at a finite number of points, which are not vertices of k and at which p/k is 2:1, then p(k) is said to be a regular projection of k this means that p(k) is closed curve with a finite number of double points (“crossings”) which are not points of tangency. Clearly for every polygonal knot there is a plane onto which it can be projected regularly. At each crossing of p(k), the knot k assigns an overcrossing arc and an undercrossing arc of the projection; conversely, if at each crossing we say which arc is an overcrossing, then there is a knot, uniquely determined up to homeomorphism, with this regular projection with the assigned overcrossings.
Semigroup structures for families of functions, III
Authors: Magill Kenneth D.
Published: April 2009

Let Fx and Fy denote families of subsets of the nonempty sets X and Y respectively and let be a function mapping Y onto X with the property that [H] ∈ Fx for each H∈Fy. Then the family l of all functions mapping X into Y such that [H] ∈Fy for each H ∈Fx is a semigroup if the product g of two such functions and g is defined by g = o o g (i.e., (Fg)(x) = (f(g(x))) for each x in X). With some restrictions on the families Fx and Fy and the function , these are the semigroups mentioned in the title and are the objects of investigation in this paper. The restrictions on fxfy and are sufficiently mild so that the semigroups considered here include such semigroups of functions on topological spaces as semi- groups of closed functions, semigroups of connected functions, etc.
The approximation of continuous functions by Riesz typical means of their Fourier series
Authors: Kwee B.
Published: April 2009

Let (x) be a continuous function with period 2π. It is well known that the Fourier series of (x) is summable Riesz of any positive order to (x). The aim of this paper is the proof of the following theorem.
On radical extensions of rings
Authors: Armendariz Efraim P.
Published: April 2009

A ring K is a radical extension of a subring B if for each x ∈ K there is aninteger n = n(x) > 0 such that xn ∈ B. In [2] and [3], C. Faith considered radical extensions in connection with commutativity questions, as well as the generation of rings. In this paper additional commutativity theorems are established, and rings with right minimum condition are examined. The main tool is Theorem 1.1 which relates the Jacobson radical of K to that of B, and is of independent interest in itself. The author is indebted to the referee for his helpful suggestions, in particular for the strengthening of Theorem 2.1.
A third-Engel 5-group
Authors: Macdonald I. D. , Neumann B. H.
Published: April 2009

In this paper a certain group with the third-Engel condition, that is a member of the variety defined by1 will be presented. Reasons for which its properties may be of interest are advanced in the present section.
The relativistic incompressible sphere
Authors: Buchdahl H. A. , Land W. J.
Published: April 2009

The Schwarzschild Interior Solution represents a static sphere the proper density of which has the same value throughout. Though it is sometimes referred to as an “incompressible” sphere it is physically unacceptable since (formally) the speed of sound within it is infinite. Perhaps the most natural analogue of the classical incompressible sphere is therefore a sphere such that the speed of sound is everywhere just equal to the speed of light. This paper investigates spheres of this kind in some detail.
A sufficient condition for an extreme covering of n-space by spheres
Authors: Dickson T. J.
Published: April 2009

The problem of finding the most economical coverings of n-dimensional Euclidean space by equal spheres whose centres form a lattice, which is equivalent to a problem concerning the inhomogeneous minima of positive definite quadratic forms, has been discussed recently by Barnes and Dickson [1]. The reader is referred to [1] for a complete background on the problem. Terms and notations used will be as in that paper.
Statistics of fragments from enzyme-induced breakup of co-polymer chains
Authors: Blatt John M.
Published: April 2009

A number of studies [1] have concerned themselves with properties of artificial poly-peptide chains, which differ from naturally occurring poly-peptides in two ways: There is only one kind of amino-acid in each polymer chain, but that acid occurs both in its right-handed and in its left-handed (D and L) forms, with some random order of L and D constituents.
A note on compactifications and semi-normal spaces
Authors: Alo R. A. , Shapiro H. L.
Published: April 2009

Recently Orrin Frink (see [2]) gave a neat internal characterization of Tychonoff or completely regular T spaces. This characterization was given in terms of the notion of a normal base for the closed sets of a space X. A normal base for the closed sets of a space X is a base which is a disjunctive ring of sets, disjoint members of which may be separated by disjoint complements of members of . In a normal space the ring of closed sets is a normal base.
Reversible topological spaces
Authors: Rajagopalan M. , Wilansky A.
Published: April 2009

We propose to study a topological property which is not new, but seems not to have been systematically investigated.
An extreme covering of 4-space by spheres
Authors: Dickson T. J.
Published: April 2009

Let Λ be a lattice in n-dimensional Euclidean space En. For any lattice there is a unique minimal positive number μ such that if spheres of radius μ are placed at the points of the lattice then the entire space is covered, i.e. every point in En lies in at least one of the spheres. The density of this covering is defined to be θn(Λ) = Jnμn/d(Λ), where Jn is the volume of an n-dimensional unit sphere and d(Λ) is the determinant of the lattice.
Power-associative regular real normed algebras
Authors: Strzelecki Emanuel
Published: April 2009

Definition 1. A real algebra A is a real vector space in which an operation of multiplication is defined satisfying the following conditions: for arbitrary x, y, z ∈ A and any real number α.
A Queueing system with general moving average input and negative exponential service time
Authors: Pearce C.
Published: April 2009

If we think of the input to a queueing system as arising from some process and depending on the history of that process, we might well expect the duration of inter-arrival intervals to depend mostly on the recent history and to a much smaller extent on that which is more remote.
On critical groups
Authors: Kovács L. G. , Newman M. F.
Published: April 2009

The concept of critical group was introduced by D. C. Cross (as reported byG. Higman in [5]): a finite group is calledcriticalif it is not contained in the variety generated by its proper factors. (Thefactorsof a groupGare the groups H/K where KH ≦G, and H/K is aproper factorofGunlessH = GandK=1). Some investigations concerning finite groups and varieties depend on the investigator's ability to decide whether a given group is critical or not. (For instance, one of the crucial points in the important paper [9] of Sheila Oates and M. B. Powell is a necessary condition of criticality: their Lemma 2.4.2.) An obvious necessary condition is that the group should have only one minimal normal subgroup: the group is then calledmonolithic, and the minimal normal subgroup itsmonolith. This is, however, far from being a sufficient condition, and it is the purpose of the present paper to give some sufficient conditions for the criticality of monolithic groups. (We consider the trivial group neither monolithic nor critical.) The basis of our results is an analysis of the following situation.
A convolution semigroup of modular functions
Authors: Lin Y.-F.
Published: April 2009

Let S be a compact topological semigroup, and let be the collection of all normalized non-negative Borel measures on S. It is well-known that , under convolution and the topology induced by the weak-star topology on the dual of the Benach space C(S) of all complex valued continuous functions on S, forms a compact topological semigroup which is known as the convolution semigroup of measures (see for instance, Glicksberg [3], Collins [1], Schwarz [5] and the author [4]). [1], Schwarz [5] and the author [4]). Professor A. D. Wallace asked if the process of forming the convolution semigroup of measures might be generalized to a more general class of set functions, the so-called “modular functions.” The purpose of the present note is to settle this question in the affirmative under a slight restriction. Before we are able to state the Wallace problem precisely, some preliminaries are necessary.
On the Stability of Linear Canonical Systems with Periodic Coefficients
Authors: Coppel W. A. , Howe A.
Published: April 2009

Journal of the Australian Mathematical Society 5 (1965), 169–195

Theorem 9 (p. 183) should read: The indices of any closed curve inD have the form

n+ = hp/s, n− = hq/s

for some integer h, where s (1 ≦ s ≦ n) is the largest number of identical blocks into which the signature σ can be partitioned. Moreover, for any integer h there exists a closed curve in d with these indices.
Forced motion of a charged particle in a magnetic field
Authors: Gleeson L. J.
Published: April 2009

We consider the motion of a particle of mass m and electrical charge e, moving in a constant magnetic field Bk, where k is a unit vector, and acted upon by a force mf(t). The position vector r(t) of this particle is governed by the differential equation where .
Generalization of a theorem of P. D. Finch's on integration of set-functions
Authors: Cunningham F.
Published: April 2009

Let Mbe a σ-field of subsets of a space X. A partition of Xmeans a countable partition Π of Xinto sets belonging to M; the set of partitions is directed by refinement. A. Kolmogoroff in 1930 [1] discussed an integral (Moore-Smith limit as Π gets finer) for set-functions F defined on M. When it exists, IF is σ-additive, and if by chance F is already σ-additive, then IF = F
A converse to Lebesgue's dominated convergence theorem
Authors: Goodner Dwight B.
Published: April 2009

Let (X, B, m) be a measure space and let f(x) be a real-valued or complex-valued measurable function on X. A non-negative measurable function s(x) will be said to dominate f(x) provided |f(x)| ≦ s(x) for almost all x in X. The function s(x) will be said to dominate the sequence {f(x)}n∈N, N = {1, 2,…}, provided it dominates each fn(x) in the sequence. Unless otherwise specified, each integral will be over X with respect to m.
On a theorem of Behrend
Authors: Erdös P. , Sárközy A. , Szemerédi E.
Published: April 2009

A sequence of integers 0 <a1 < a2 <… no term of which divides any other will be called a primitive sequence. Throughout this paper c1, c2,… will denote suitable positive absolute constants. Behrend [1] proved that for every primitive sequence
Geometry of a simplex inscribed in a normal rational curve
Authors: Mandan Sahib Ram
Published: April 2009

In 1959, Professor N. A. Court [2] generated synthetically a twisted cubic C circumscribing a tetrahedron T as the poles for T of the planes of a coaxal family whose axis is called the Lemoine axis of C for T. Here is an analytic attempt to relate a normal rational curve rn of order n, whose natural home is an n-space [n], with its Lemoine [n—2] L such that the first polars of points in L for a simplex S inscribed to rn pass through rn anf the last polars of points on rn for S pass through L. Incidently we come across a pair of mutually inscribed or Moebius simplexes but as a privilege of odd spaces only. In contrast, what happens in even spaces also presents a case, not less interesting, as considered here.
Linear recurrences of order two
Authors: Laxton R. R.
Published: April 2009

Let {f(n)} be a linear recurrence of order two, i.e.

for all positive integers n.
Kinematic geometry; an axiomatic system for Minkowski space-time
Authors: Szekeres G.
Published: April 2009

The aim of this paper is, briefly, an axiomatization of relativistic kinematics. Before stating the aims in more precise terms, a few words about the origins of the paper will be necessary. The idea of a revision of the axiomatic foundations of relativistic kinematics came up in discussions with the late M. L. Urquhart at the 1963 (3rd) Summer Research Institute of the Australian Mathematical Society, and it was a suggestion by Urquhart which started off the present investigation. Following his suggestion I prepared a preliminary draft containing the outlines of an axiomatic system for Minkowski space-time and passed it on to him. Shortly before his death Urquhart asked Professor D. Elliott to send the manuscript back to me and it was this manuscript which formed the nucleus of the present paper.
Certain topological semirings in R1
Authors: Pearson K. R.
Published: April 2009

If we consider any particular topological semigroup S it may seem reasonable to ask for a characterization of all additions on S which make it a topological semiring. We are interested here in this problem when

(i) S is an (I)-semigroup;

(ii) S is [0, ∞) and the multiplication on S is such that 0 and 1 are Zero and identity respectively.
Transcendental entire functions mapping every algebraic number field into itself
Authors: Van Der Poorten A. J.
Published: April 2009

T. Schneider [1] has shown that a transcendental function with a limited rate of growth cannot assume algebraic values at too many algebraic points. It is not clear however whether a transcendental function may assume algebraic values at all algebraic points in an open set in its domain of analyticity. We show, using a method of B. H. Neumann and R. Rado [2] that this can be the case. Indeed we construct transcendental entire functions which, together with all their derivatives, assume, at every point in every algebraic number field, values in that field.