bluuebunny/crossref_metadata_2025 huggingface dataset:
On lower estimates for linear forms involving certain transcendental numbers
Authors: Väänänen Keijo
Published: April 2009

Let

where λ is rational and not an integer. The author investigates lower estimates for example for

where the αi are distinct rational numbers not 0, and where x1, …, xk, are integers and
Fixed point theorems in uniformly rotund metric spaces
Authors: Staples John
Published: April 2009

In recent years fixed point theorems have been proved for non-expansive and similar mappings on uniformly convex Banach spaces. The only role the linear structure plays in the statement of these results occurs in the definition of uniform convexity. It is therefore natural to ask whether the results depend essentially on the linear structure, or whether an extension of the notion of uniform convexity to metric spaces would allow the hypothesis of linear structure on the underlying space to be removed.
The construction of groups in models of set theory that fail the Axiom of Choice
Authors: Hickman J.L.
Published: April 2009

The purpose of this paper is to show that a well-known method for constructing “queer” sets in models of ZF set theory is also applicable to certain algebraic structures. An infinite set is called “quasi-minimal” if every subset of it is either finite or cofinite. In Section 1 I set out the two systems of set theory to be used in this paper, and illustrate the technique in its most fundamental form by constructing a model of set theory containing a quasi-minimal set. In Section 2 I show that by choosing the parameters appropriately, one can use this technique to obtain models of set theory containing groups whose carriers are quasi-minimal. In the third section various independence results are deduced from the existence of such models: in particular, it is shown that it is possible in ZF set theory to have an infinite group that satisfies both the ascending and descending chain conditions. The quasi-minimal groups constructed in Section 2 were all elementary abelian; in Section 4 it is shown that this was not just chance, but that in fact all quasi-minimal groups must be of this type. Finally in Section 5 permutations and permutation groups on quasi-minimal sets are examined.
Double covers of graphs
Authors: Waller Derek A.
Published: April 2009

A projection morphism ρ: G1 → G2 of finite graphs maps the vertex-set of G1 onto the vertex-set of G2, and preserves adjacency. As an example, if each vertex v of the dodecahedron graph D is identified with its unique antipodal vertex v¯ (which has distance 5 from v) then this induces an identification of antipodal pairs of edges, and gives a (2:1)-projection p: D → P where P is the Petersen graph.

In this paper a category-theoretical approach to graphs is used to define and study such double cover projections. An upper bound is found for the number of distinct double covers ρ: G1 → G2 for a given graph G2. A classification theorem for double cover projections is obtained, and it is shown that the n–dimensional octahedron graph K2,2,…,2 plays the role of universal object.
The comma-free codes with words of length two
Authors: Ball A.H. , Cummings L.J.
Published: April 2009

A code not requiring a distinct symbol to separate words is called comma-free. Two codes are isomorphic if one can be obtained from the other by a permutation of the underlying alphabet. Since subcodes of comma-free codes are comma-free, we investigate only maximal comma-free codes. All isomorphism classes of maximal comma-free codes with words of length 2 are determined and a natural representative of each class is given.
Representations of metabelian groups satisfying the minimal condition for normal subgroups
Authors: Silcock Howard L.
Published: April 2009

A question of John S. Wilson concerning indecomposable representations of metabelian groups satisfying the minimal condition for normal subgroups is answered negatively, by means of an example. It is shown that such representations need not be irreducible, even when the group being represented is an extension of an elementary abelian p–group by a quasicyclic q–group of the type first described by V.S. Čarin, and the characteristic of the field is a prime distinct from both p and q. This implies that certain techniques used in the study of metabelian groups satisfying the minimal condition for normal subgroups are not available for the corresponding class of soluble groups of derived length 3.
On the hamiltonian product of graphs
Authors: Krishnamoorthy V.
Published: April 2009

Let G1 and G2 be graphs and h1, h2 be hamiltonian paths (h-paths) in G1 and G2 respectively. The hamiltonian product (G1, h2)*(G2, h2) was defined by Holton. If a hamiltonian cycle exists in G2, it can give rise to 2nh-paths. Peckham conjectured that (G1, h1)*(G2, h2)≡(G1, h1)*(G2, h3) where h2 and h3 are any two of these 2nh-paths of G2. He has proved the validity of this conjecture for those h2, h3 where h3 is obtainable from h2 by a rotation along the h-cycle of G2. Here we disprove this conjecture for those h2, h3 where one is obtained from the other by a reflection of the h-cycle.
On a problem of Kurt Mahler concerning binomial coefficents
Authors: Williams Ian S.
Published: April 2009

Recently Kurt Mahler asked: for which natural numbers N is the least common multiple of all the binomial coefficients the product of the primes less than or equal to N? We obtain a formula for the least common multiple of all the binomial coefficients of any natural number N and hence show that 2,11, and 23 are the only soultions to Mahler's problem.
On groups with extremal blocks
Authors: Herzog Marcel
Published: April 2009

Let G be a finite group. It is shown that G is 2-closed if and only if

(a) every 2-block of G has full defect, and

(b) every Sylow 2-intersection is centralized by a Sylow 2-subgroup of G.

As a consequence it is shown that G is a TI-group if and only if every 2-block of G has either full defect or defect zero and (b) holds. This result and a theorem of Kwok yield complete characterizations of finite groups with certain relations being satisfied by every nonprincipal irreducible character.
A remark on the construction of designs for two-way elimination of heterogeneity
Authors: Sterling Leon S. , Wormald Nicholas
Published: April 2009

A method of construction of designs with parameters v1 = r2 = p2, r1 = v2 = p + 1, b = p(p+1), k = p which may be used for the two-way elimination of heterogeneity is discussed. These designs were first studied in connection with estimating tobacco mosaic virus. Our designs have the advantage that every treatment occurs at most once in a row or column. We give the designs explicitly for p = 3, 4, 5.
Automorphisms of the semigroup of all onto mappings of a set
Authors: Chantip Suchat , Wood G.R.
Published: April 2009

The semigroup of all onto mappings of a set to itself and the semigroup of all one-to-one mappings of a set to itself are shown to have the property that every automorphism is inner.
On the invariance of certain estimators
Authors: Gentle J.E. , Sposito V.A.
Published: April 2009

In this note, Lp estimators for the parameters in the linear model y = Xβ are considered. In particular, it is shown that these estimators are invariant under scale transformations on the dependent variable; that is, if is an Lp estimator for β, then for any nonzero scalar a. It is shown that this result does not extend to more general transformations on y, and the invariance property does not hold for general nonlinear models.
Certain classes of univalent functions with negative coefficients
Authors: Gupta V.P. , Jain P.K.
Published: April 2009

The subclasses S*(α, β) and C*(α, β) of T, the class of analytic and univalent functions of the form have been considered. Sharp results concerning coefficients, distortion of functions belonging to S*(α, β) and C*(α, β) are determined along with a representation formula for the functions in S*(α, β). Furthermore, it is shown that the classes S*(α, β) and C*(α,.β) are closed under arithmetic mean and convex linear combinations.
A note on centralizers of involutions involving simple groups
Authors: Wright Donald
Published: April 2009

If a finite group G has a ‘central’ involution t whose centralizer in G is (t) × H then, under certain conditions on H, G cannot be simple.
Note on rational approximations of the exponential function at rational points
Authors: Durand Alain
Published: April 2009

Let p, q, u, and v be any four positive integers, and let δ be a number in the interval 0 < δ ≤ 2. In one of his papers, Kurt Mahler, Bull. Austral. Math. Soc. 10 (1974), 325–335, proved that if q satisfies the inequalities

then

In this note, by a slightly different treatment of some inequalities in Mahler's paper, we easily obtain the same result with q only restricted by the first condition.
Power and commutator structure of groups
Authors: Shield David
Published: April 2009

The purpose of this paper is to prove a result about the power and commutator structure of groups which generalises some results of Philip Hall. The results presented here are the key to determining the class of a nilpotent wreath product.
Oscillations of a first order functional differential equation
Authors: Tomaras Alexander
Published: April 2009

Oscillation results are obtained for a first order functional differential equation, by transforming it to an equation for which oscillatory information exists in the literature already.
On families of finite sets no two of which intersect in a singleton
Authors: Frankl Peter
Published: April 2009

Let X be a finite set of cardinality n, and let F be a family of k-subsets of X. In this paper we prove the following conjecture of P. Erdös and V.T. Sós.

If n > n0(k), k ≥ 4, then we can find two members F and G in F such that |F ∩ G| = 1.
A note on a theorem on a nonlinear complementarity problem
Authors: Nanda Sudarsan
Published: April 2009

In the paper “A nonlinear complementarity problem for monotone functions”, Bull. Austral. Math. Soc. 20 (1979), 227–231, Nanda and Patel proved that for a monotone function that fixes the origin, the complementarity problem admits a solution. In this note we give a short proof of the same result under weaker assumptions.
A semigroup with an epimorphically embedded subband
Authors: Higgins Peter M.
Published: April 2009

We construct a semigroup S with an epimorphically embedded proper subband U. The band U furnishes an example of a regular semigroup which is not saturated, thus answering a question posed by Hall, Semigroup Forum (to appear).
On a functional differential equation in locally convex spaces
Authors: Yamamuro Sadayuki
Published: April 2009

The notion of accretiveness for multi-valued nonlinear maps is defined in locally convex spaces and it is used to obtain a locally convex space version of a result of M.G. Crandall and J.A. Nohel.
Oscillation of second order linear ordinary differential equations with alternating coefficients
Authors: Philos Ch.G.
Published: April 2009

A new result is obtained for the oscillation of second order linear ordinary differential equations with alternating coefficients. This oscillation result extends a recent oscillation criterion due to Kamenev [.Mat. Zametki 23 (1978), 249–251].
On the asymptotic behaviour of the jackknife for stochastic processes
Authors: Kokic P.N. , Weber N.C.
Published: April 2009

The limiting behaviour of the J∞ jackknife estimator for parameters associated with stochastic processes is shown to depend on the nature of the underlying process through the asymptotic behaviour of the estimator being jackknifed. In particular, the jackknifed versions of certain estimators associated with renewal processes are shown to have an asymptotic normal distribution.
On decoupling of linear recursions
Authors: Mattheij R.M.M.
Published: April 2009

We show how a well known algorithm to compute solutions of a second order recursion which are unstable both in forward and in backward direction, can be related to a number of other methods. They are: order reduction, invariant imbedding and decoupling based on triangularization. It is shown that these methods in this order form an increasingly general approach to solve the problem. In particular this means that the stability of the first three algorithms can be understood from the theory that has been established for the decoupling algorithm. In this way one does not need to investigate the stability of the large sparse system which is often related to the first method.
Some saturated varieties of semigroups
Authors: Khan N.M.
Published: April 2009

We show that a semigroup satisfying a heterotypical identity of which at least one side has no repeated variable is saturated and find sufficient conditions on a homotypical identity which is not a permutation identity and of which at least one side has no repeated variable, to ensure that any semigroup satisfying the identity is saturated.
Time delays in n-species competition – I: Global stability in constant environments
Authors: Gopalsamy K. , Ahlip R.A.
Published: April 2009

Sufficient conditions which are verifiable in a finite number of arithmetical steps are derived for the existence and global asymptotic stability of a feasible steady state in an integro-differential system modelling the dynamics of n competing species in a constant environment with delayed interspecific interactions. A novel method involving a nested sequence of “asymptotic” upper and lower bounds is developed.
A boundedness condition for sets with lattice point constraints
Authors: Scott P.R.
Published: April 2009

Let K be a closed convex body in Rn containing a finite number of points of lattice Λ in its interior. We show that K is bounded if K contains a certain suitably large simplex.
Commutative rings whose factors have Artinian rings of quotients
Authors: Blair William D.
Published: April 2009

Let R be a commutative ring with unity. Then every factor ring of R has an Artinian total quotient ring if and only if R is a direct sum of one-dimensional Noetherian domains and local Artinian rings.
Eventually regular semigroups
Authors: Edwards P.M.
Published: April 2009

A semigroup is said to be eventually regular if each of its elements has some power that is regular. Regular and group-bound semigroups are each eventually regular. Idempotent-surjective semigroups are semigroups such that all idempotent congruence classes contain idempotents; eventually regular semigroups are idempotent-surjective. Many results for regular semigroups also hold for eventually regular semigroups or even for idempotent-surjective semigroups and so in particular are also valid for group-bound semigroups. Lallement's lemma is generalized to eventually regular semigroups and the maximum idempotent-separating congruence on such a semigroup is found. Other congruences are considered and the results obtained are applied to yield results on biordered sets.
Inverse limit theorem and expansion theorem for cohomological dimension
Authors: Deo Satya , Muttepawar Subhash
Published: April 2009

For a given ground ringL, let dimL(X) denote the sheaf theoretic cohomological dimension of a spaceX. In this paper we prove an inverse limit theorem for this dimension function. Then we apply this theorem to show that for a large classs of rings the Freudenthal's expansion theorem, expressing a compact metric spaceXof dimL(X) as the inverse limit of an system of compact polyhedraKαof dimL(Kα), is not valid.
Families of partial functions
Authors: Balanda Kevin P.
Published: April 2009

The degree of disjunction, δ(F), of a family F of functions is the least cardinal τ such that every pair of functions in F agree on a set of cardinality less than τ.

Suppose θ, μ, λ, κ are non-zero cardinals with θ ≤ μ ≤ λ. This paper is concerned with functions which map μ-sized subsets of λ into κ. We first show there is always a ‘large’ family F of such functions satisfying δ(F) ≤ θ. Next we determine the cardinalities of families F of such functions that are maximal with respect to δ(F) ≤ θ.
Beurling's ordinary value
Authors: Yamashita Shinji
Published: April 2009

Let n(w, f) be the number of w-points of f meromorphic in D = {|z| < 1}. Beurling defined the quantity and called w an ordinary value of f if < ∞. We shall consider the intermediate quantity ṉ(w, f) in the sense that n(w, f) ≤ ṉ(w, f) , and construct two bounded holo-morphic functions f1 and f2 of finite Dirichlet integrals in D for which

and

.
The difference operators and extended Laguerre polynomials
Authors: Parashar B.P.
Published: April 2009

A new set of polynomials in powers of xh (h > 0) which are related to the Laguerre polynomials , have been defined by a Rodrigues type formula involving the forward difference operator Δh of increment h. Besides obtaining shift operator formulae for , a definition of fractional power of Δh has been given. The definition has been illustrated by establishing known relations of the confluent hypergeometric function.
The power structure of finite p-groups
Authors: Xu Mingyao
Published: April 2009

In this survey article we give an exposition of some work on the power structure of p-groups; especially work of the author's. The titles of the three sections are: Section 1. p-groups which have regular power structure; Section 2. Some weaker power structure properties; Section 3. p-central series of p-groups.
On circulant matrices for certain periodic spline and histospline projections
Authors: Dubeau François , Savoie Jean
Published: April 2009

We present a unified treatment of the band circulant matrices which occur in the periodic spline and histospline projection theory with equispaced knots. Explicit bounds for the norm of these matrices are given.
Common fixed point theorems in complete metric and probabilistic metric spaces
Authors: Stojakovic Mila
Published: April 2009

In this paper several common fixed point theorems for four continuous mappings in Menger and metric spaces are proved. These mappings are assumed to satisfy some generalizations of the contraction condition.
Translation complements of C-planes: (I)
Authors: Narayana Rao M. L. , Kuppuswamy Rao K. , Subba Rao G. V.
Published: April 2009

Narayana Rao, Rodabaugh, Wilke and Zemmer constructed a new class of finite translation planes from exceptional near-fields described by Dickson and Zassenhaus. These planes referred to as C-planes are not coordinatized by the generalized André systems. In this paper we compute the translation complement of the C-plane corresponding to the C-system III–1. It is found that the translation complement is of order 6912 and it divides the set of ideal points into two orbits of lengths 2 and 48.
Semi-homomorphisms of rings
Authors: Huq S. A.
Published: April 2009

In this note, following Kaplanasky's study of semi-automorphisms of rings and Herstein's study of semi-homomorphisms of groups, we present a general study of semi-homomorphisms of rings.
A note on groups with separable finitely generated subgroups
Authors: Burns R. G. , Karrass A. , Solitar D.
Published: April 2009

An example is given of an infinite cyclic extension of a free group of finite rank in which not every finitely generated subgroup is finitely separable. This answers negatively the question of Peter Scott as to whether in all finitely generated 3-manifold groups the finitely generated subgroups are finitely separable. In the positive direction it is shown that in knot groups and one-relator groups with centre, the finitely generated normal subgroups are finitely separable.
The circle group
Authors: Morris Sidney A.
Published: April 2009

We prove the following theorem: if G is a locally compact Hausdorff group such that each of its proper closed subgroups has only a finite number of closed subgroups, then G is topologically isomorphic to the circle group.
The closed graph theorem without category
Authors: Swartz Charles
Published: April 2009

We show that a diagonal theorem of P. Antosik can be used to give a proof of the Closed Graph Theorem for normed spaces which does not depend upon the Baire Category Theorem.
Rings in which every element is the sum of two idempotents
Authors: Hirano Yasuyuki , Tominaga Hisao
Published: April 2009

Let R be a ring with prime radical P. The main theorems of this paper are (1) The following conditions are equivalent.: 1) R is a commutative ring in which every element is the sum of two idempotents; 2) R is a ring in which every element is the sum of two commuting idempotents; 3) R satisfies the identity x3 = x. (2) If R is a PI-ring in which every element is the sum of two idempotents, then R/P satisfies the identity x3 = x. (3) Let R be a semi-perfect ring in which every element is the sum of two idempotents. If RRR is quasi-projective, then R is a finite direct sum of copies of GF(2) and/or GF(3).
On the generalised dominated convergence theorem
Authors: Seng Chew Tuan
Published: April 2009

In this paper we give another version of the generalised dominated convergence theorem, which is better than other convergence theorems for Perron integrals in the sense that it can be applied more easily.
Structure presque-transverse intégrable
Authors: Duc Tong Van
Published: April 2009

We find conditions for which a manifold endowed with an integrable almost transversal structure is the total space of a vector bundle isomorphic to the transversal bundle of a foliation.
Smoothness in spaces of compact operators
Authors: Sersouri A.
Published: April 2009

We prove that if X and Y are two (real) Banach spaces such that dim X ≥ 2 and dim Y ≥ 2, then the space K(X, Y) contains a convex compact subset C with dim C ≥ 2 (in the affine sense) which fails to be an intersection of balls. This improves two results of Ruess and Stegall.
Locally homogeneous S-structures
Authors: Ledger A.J. , Vanhecke L.
Published: April 2009

We prove a characterisation of locally s-regular manifolds using the theory of homogeneous structures.
Phelps spaces and finite dimensional decompositions
Authors: Deville R. , Godefroy G. , Hare D.E.G. , Zizler V.
Published: April 2009

We show that if X is a separable Banach space such that X* fails the weak* convex point-of-continuity property (C*PCP), then there is a subspace Y of X such that both Y* and (X/Y)* fail C*PCP and both Y and X/Y have finite dimensional Schauder decompositions.
P-adic interpolation of dedekind sums
Authors: Snyder C.
Published: April 2009

In this article we give an explicit representation of p-adic Dedekind sums and their reciprocity laws by using p-adic measure theory. We then study the consequences of the p-adic reciprocity law for particular positive integer values in which case we can recover a reciprocity law for Dedekind sums attached to particular Dirichlet characters. This gives a proof different from that of Nagasaka.
A linear complementarity problem involving a subgradient
Authors: Parida J. , Sen A. , Kumar A.
Published: April 2009

A linear complementarity problem, involving a given square matrix and vector, is generalised by including an element of the subdifferential of a convex function. The existence of a solution to this nonlinear complementarity problem is shown, under various conditions on the matrix. An application to convex nonlinear nondifferentiable programs is presented.
Integrally closed factor domains
Authors: Barucci Valentina , Dobbs David E. , Mulay S.B.
Published: April 2009

This paper characterises the integral domains R with the property that R/P is integrally closed for each prime ideal P of R. It is shown that Dedekind domains are the only Noetherian domains with this property. On the other hand, each integrally closed going-down domain has this property. Related properties and examples are also studied.
The Dirichlet problem for degenerate elliptic 2-dimensional Monge-Ampère equation
Authors: Amano Kazuo
Published: April 2009

We study the following Dirichlet problem for the degenerate elliptic Monge-Ampère equation: Given , f ≥ 0 and , find a solution , t ≥ 2, satisfying in Ω and u = g on ∂Ω. Since f is nonnegative, we cannot apply any standard elliptic methods. In this paper, we use an iteration scheme of Nash-Moser type and a priori estimates for degenerate elliptic operators, and solve the Dirichlet problem for a certain class of f and g.
Quasi-continuity with respect to semi-regularisation topology
Authors: Psyk Stanislaw
Published: April 2009

This paper gives some sufficient conditions under which upper, lower or both upper and lower quasi-continuity of multifunction in the process of semi-regularisation of a topological space are preserved. Analogous results for continuous maps are true.
On uniformly strongly prime gamma rings
Authors: Booth G.L. , Groenwald N.J.
Published: April 2009

The concept of uniformly strongly prime (usp) is introduced for Γ-ring, and a usp radical τ(M) is defined for a Γ-ring M. If M has left and right unities, then τ(L)+ = τ(M) = τ(R)*, where L and R denote, respectively, the left and right operator rings of M, and τ(·) denotes the usp radical of a ring. If m, n are positive integers, then τ(Mmn) = (τ(M))mn, where Mmn is the matrix Γnm-ring. τ is shown to be a special radical in the variety of Γ-rings. τ1 is the upper radical determined by the class of usp Γ-rings of bound 1. τ ⊆ τ1, but the reverse inclusion does not hold in general. The place of τ and τ1 in the hierarchy of radicals for Γ-rings is shown.
On the integral cohomology of the seven-connective cover of BO
Authors: Ng Tze Beng
Published: April 2009

Let BO, BSO and BSpin be the classifying spaces for the infinite orthogonal, infinite special orthogonal and infinite spinor groups respectively. It is well known that their integral cohomology rings have torsion only of order 2. In this paper we present an elementary proof that for the 7-connective cover of BO, BO〈8〉, the integral cohomology ring H* (BO〈8〉; Z) too has torsion only of order 2. The method follows that of Borel and Hirzebruch and a result of Wu concerning the Steenrod reduced mod p operation for an odd prime p on the Pontrjagin classes.
Characterising complete boolean algebras in terms of pure essentialness
Authors: Bhutani Kiran R.
Published: April 2009

We discuss purity and pure essentialness of abelian groups in a topos of sheaves on a locale and show that purity is not a local property. We prove that is divisible if and only if it is pure in every extension, and give an example of a category in winch absolutely pure does not imply divisible. We discuss uniform abelian groups and show that each AU uniform in Ab does not imply that A is uniform in

Banaschewski showed that the pure subgroups of are exactly of the type for the different . We show that is essential in if and only if U is dense in , Finally, we characterise as complete boolean algebras the locales for which the only pure and essential subgroup of is .
Stability and J-depth of expansions
Authors: Birget Jean-Camille
Published: April 2009

In this paper I prove that if a semigroup S is stable then ∧L(S) and ∧R(S) (the Rhodes expansions), and ∧+(SA) (the iteration of those expansions) are also stable. I also prove that if S is stable and has a J-depth function then these expansions also have a J-depth functon. More generally, if X →→ S is a J*-surmorphism and if S is stable and has a J-depth function then X has a J-depth function. All these results are needed for the structure theory of semigroups which are stable and have a J-depth function.

The techniques used were originally developed by the author to prove that ∧+(SA) is finite if S is finite (later Rhodes found a much more direct proof of that result).
A note on annihilator Banach algebras
Authors: Wong Pak-Ken
Published: April 2009

LetAbe a semisimple Banach algebra with ‖ · ‖, which is a dense subalgebra of a semisimple Banach algebraBwith | · | such that ‖ · ‖ majorises | · | onA. The purpose of this paper is to investigate the annihilator property between the algebrasAandB.
Approximation by fourier stieltjes series
Authors: Mazhar S.M.
Published: April 2009

In this paper certain estimates of the rate of convergence of triangular matrix means of the Fourier Stieltjes series and its conjugate series are obtained.
The uniform structure of boundedly compact spaces
Authors: Potter M.D.
Published: April 2009

A uniform space can be given a boundedly compact compatible psuedometric if and only if it is uniformly locally compact and second countable and has a countable base for its entourages.
Unimodal expanding maps of the interval
Authors: Du Bau-Sen
Published: April 2009

Let I = [0, 1] and let f be an unimodal expanding map in C0(I, I). If f has an expanding constant for some integers m ≧ 0 and n ≧ 1, where λn is the unique positive zero of the polynomial x2n+1 − 2x2n−1 −1, then we show that f has a periodic point of period 2m(2n + 1). The converse of the above result is trivially false. The condition in the above result is the best possible in the sense that we cannot have the same conclusion if the number λn is replaced by any smaller positive number and the generalisation of the above result to arbitrary piecewise monotonic expanding maps in C0(I, I) is not possible.
On Newton's method and nondiscrete mathematical induction
Authors: Argyros Ioannis K.
Published: April 2009

The method of nondiscrete mathematical induction is used to find sharp error bounds for Newton's method. We assume only that the operator has Hölder continuous derivatives. In the case when the Fréchet-derivative of the operator satisfies a Lipschitz condition, our results reduce to the ones obtained by Ptak and Potra in 1972.
On conjugacy classes in finite loops
Authors: Kepka T. , Niemenmaa M.
Published: April 2009

The rôle of the conjugacy relation is certainly important in the structure theory of groups. Here we study this relation in a considerably more general setting, namely in the theory of loops. We first recall some basic facts about quasigroups, their multiplication groups, their inner mapping groups and the conjugacy relation. After this we estimate the size and the number of the conjugacy classes and we study the structure of loops having only two conjugacy classes. Finally, the values of the centraliser function are discussed.
Commutativity results for rings
Authors: Abu-Khuzam Hazar
Published: April 2009

Let R be an associative ring. We prove that if for each finite subset F of R there exists a positive integer n = n(F) such that (xy)n − yn xn is in the centre of R for every x, y in F, then the commutator ideal of R is nil. We also prove that if n is a fixed positive integer and R is an n(n + 1)-torsion-free ring with identity such that (xy)n − ynxn = (yx)n xnyn is in the centre of R for all x, y in R, then R is commutative.
On a theorem of Li-Banghe and Peterson on immersions of manifolds
Authors: Ng Tze-Beng
Published: April 2009

Let Mn and N2n−2 be smooth, connected manifolds of dimension n and 2n − 2 respectively with n ≡ 2 mod 4 and 6 ≤ n ≤ 26. Let f: Mn → N2n−2 be a continuous map. Under certain suitable conditions on the stable normal bundle of f, we give a direct and simpler proof that f is homotopic to an immersion. For the case 6 ≤ n ≤ 26 and n ≠ 18, the result was proved by Li-Banghe and Peterson by using non-stable obstruction theory and their earlier result.
Automorphisms of certain p-groups (p odd).
Authors: Curran M.J.
Published: April 2009

This paper shows that amongst the p-groups of order p5, where p denotes an odd prime, there is only one group whose automorphism group is again a p-group. This automorphism group has order p6 and it is shown that this is the smallest order a p-group may have when it occurs as an automorphism group. The paper also shows that all groups of order p5 have an automorphism of order 2 apart from the group above and three other related groups.
Point at infinity
Authors: Shell Niel
Published: April 2009

We adjoin a point at infinity to a field with a ring topology and extend the topology by taking complements of bounded sets as neighbourhoods of infinity. We note some elementary relations between the topology on the field and the topology on the field with infinity adjoined.
Stability of linear neutral delay-differential systems
Authors: Li Li-Ming
Published: April 2009

Sufficient conditions are obtained for the stability of linear neutral delay-differential systems by using a delay-differential inequality.
A Discrete calculus of variations algorithm
Authors: Tan H.H. , Potts R.B.
Published: April 2009

An algorithm which has been developed to solve the problem of determining an optimal path of the hand of a robot is applied to various classical problems in the calculus of variations.
Contracted primes of the complete ring of quotients
Authors: Call Frederick W.
Published: April 2009

The generic closure of the set of primes contracted from the complete ring of quotients of a reduced commutative ring is shown to be just the set of those primes not containing a finitely generated dense ideal. It is also the smallest generically closed, quasi-compact set containing the minimal primes.
Characterisation of a multivariate stochastic ordering
Authors: O'Cinneide Colm Art
Published: April 2009

The multivariate stochastic ordering induced by the convex nondecreasing functions compares a combination of size and variability of random vectors. Closely following methods developed by Strassen, we show that two probability measures are ordered in this way if and only if they are the marginals of some submartingale. The implications of this in majorisation theory are discussed.
A note on compact sets in spaces of subsets
Authors: Diamond Phil , Kloeden Peter
Published: April 2009

A simple characterisation is given of compact sets of the space K(X), of nonempty compact subsets of a complete metric space X, with the Hausdorff metric dH. It is used to give a new proof of the Blaschke selection theorem for compact starshaped sets.
On the p-norm of the truncated Hilbert transform
Authors: McLean W. , Elliott D.
Published: April 2009

The p-norm of the Hilbert transform is the same as the p-norm of its truncation to any Lebesgue measurable set with strictly positive measure. This fact follows from two symmetry properties, the joint presence of which is essentially unique to the Hilbert transform. Our result applies, in particular, to the finite Hilbert transform taken over (−1, 1), and to the one-sided Hilbert transform taken over (0, ∞). A related weaker property holds for integral operators with Hardy kernels.
Upper middle annihilators
Authors: Stewart Patrick N.
Published: April 2009

Each ring contains a unique smallest ideal which when factored out yields a ring with zero middle annihilator. Various results concerning this ideal are obtained including theorems about how it behaves in connection with normalising extensions and smash products.
Strongly right FBN rings
Authors: Lee Heakyung
Published: April 2009

The annihilator of a finite generated β-critical module is called a β-coprimative ideal. A prime ideal P is called β-prime if the Krull dimension of R/P is β. This paper is concerned with the relationship between the set of β-prime ideals and the set of minimal β-coprimitive ideals over a strongly right FBN ring. it is shown that there exists a one-to-one correspondence between the set of β-prime ideals and the set on minimal β-coprimitive ideals over a strongly right FBN ring R for −1 < β ≤ α, where α is the Krull dimension of R.
Minimising quadratic functionals over closed convex cones
Authors: Gowda M. Seetharama
Published: April 2009

In this article we show that, under suitable conditions a quadratic functional attains its minimum on a closed convex cone (in a finite dimensional real Hilbert space) whenever it is bounded below on the cone. As an application, we solve Generalised Linear Complementarity Problems over closed convex cones.
Neighbourhood lattices – a poset approach to topological spaces
Authors: Prokop Frank P.
Published: April 2009

In this paper neighbourhood lattices are developed as a generalisation of topological spaces in order to examine to what extent the concepts of “openness”, “closedness”, and “continuity” defined in topological spaces depend on the lattice structure of P(X), the power set of X.

A general pre-neighbourhood system, which satisfies the poset analogues of the neighbourhood system of points in a topological space, is defined on an ∧-semi-lattice, and is used to define open elements. Neighbourhood systems, which satisfy the poset analogues of the neighbourhood system of sets in a topological space, are introduced and it is shown that it is the conditionally complete atomistic structure of P(X) which determines the extension of pre-neighbourhoods of points to the neighbourhoods of sets.

The duals of pre-neighbourhood systems are used to generate closed elements in an arbitrary lattice, independently of closure operators or complementation. These dual systems then form the backdrop for a brief discussion of the relationship between preneighbourhood systems, topological closure operators, algebraic closure operators, and Čech closure operators.

Continuity is defined for functions between neighbourhood lattices, and it is proved that a function f: X → Y between topological spaces is continuous if and only if corresponding direct image function between the neighbourhood lattices P(X) and P(Y) is continuous in the neighbourhood sense. Further, it is shown that the algebraic character of continuity, that is, the non-convergence aspects, depends only on the properites of pre-neighbourhood systems. This observation leads to a discussion of the continuity properties of residuated mappings. Finally, the topological properties of normality and regularity are characterised in terms of the continuity properties of the closure operator on a topological space.
Oscillation of second order neutral differential equations
Authors: Erbe L.H. , Zhang B.G.
Published: April 2009

Some new sufficient conditions are obtained for the oscillation of the neutral differential equation

wherer(t)> 0, 0 <c< 1,p(t)≥ 0, σ(t) > τ > 0 and α = 1 or 0 < α < 1.
On the twistor space of the six-sphere
Authors: Musso Emilio
Published: April 2009

The set of all complex lines of the right-handed Dirac spinor bundle of a standard six-sphere is the total space of the twistor fibration. The twistor space, endowed with its natural Kähler structure, is recognised to be a six-dimensional complex quadric. The relevant group is Spin(7), which acts transitively on the six-quadric, as a group of fiber-preserving isometries. We use a result due to Berard-Bérgery and Matsuzawa to show the existence of a non-Kähler, non symmetric, Hermitian-Einstein metric on the six-quadric, which is Spin(7)-invariant.
Higher order schemes and Richardson extrapolation for singular perturbation problems
Authors: Herceg Dragoslav , Vulanović Relja , Petrović Nenad
Published: April 2009

Semilinear singular perturbation problems are solved numerically by using finite–difference schemes on non-equidistant meshes which are dense in the layers. The fourth order uniform accuracy of the Hermitian approximation is improved by the Richardson extrapolation.
Radial growth and boundedness for Bloch functions
Authors: Bonilla A. , Gonzalez F. Perez
Published: April 2009

Let B be the Bloch space of all those functions f holomorphic in the open unit disc D of the complex plane satisfying . We establish sufficient conditions for the boundedness of functions f belonging to B satisfying a certain uniform radial boundedness condition, and, by introducing a wide class of subsets E of ∂D, which we call negligible sets for boundedness, we show that if f ∈ B and there is a constant K > 0 such that , then f is bounded in D. Hence a significant extension of a theorem of Goolsby is obtained.
The duality between flow charts and circuits
Authors: Kasangian S. , Walters R.F.C.
Published: April 2009

This paper contains a precise description of the duality between the formal evolutions of flow charts and of circuits. In addition, it contains a new description of the free category-with-products on a multigraph as a familially representable construction.
Certain conditions under which near-rings are rings
Authors: Quadri Murtaza A. , Ashraf M. , Ali Asma
Published: April 2009

In 1969, Ligh proved that distributively generated (d-g) Boolean near-rings are rings, and hinted that some of the more complicated polynomial identities implying commutativity in rings may turn d-g near-rings into rings. In the present paper we investigate the following conditions: (1) xy = (xy)n(x, y); (2) xy = (yz)n (xy); (3) xy = ym (x, y)xn (x, y); (4) xy = xy n(x, y)x; (5) xy = xn(x, y)ym (x, y); finally prove that under appropriate additional hypotheses a d-g near-ring must be a commutative ring. Indeed the theorem proved here is a wide generalisation of many recently established results.
The normal structure of James quasi reflexive space
Authors: Tingley Daryl
Published: April 2009

It is shown that weakly compact sets of James quasi reflexive space have normal structure.
Semilinear fourth order boundary value problems
Authors: Metzen Gerhard
Published: April 2009

We study a certain linear fourth order differential operator and show the existence of solutions to corresponding nonlinear problems. It will be shown that a maximum principle holds and that under certain conditions the linear operator has a positive principal eigenvalue with corresponding positive eigenfunction.
More properties of the product of two derivations of a C*-algebra
Authors: Mathieu Martin
Published: April 2009

It is proved that the product of two non-zero derivations of a prime C*-algebra is bounded only if both of them are bounded.
Disproof of a coefficient estimate related to Bazilevic functions
Authors: Jahangiri Massoud
Published: April 2009

A coefficient estimate for powers of a class of Bazilevic functions obtained by M.M. Elhosh, is disproved and some sharp bounds are given.
Rings whose additive endomorphisms are ring endomorphisms
Authors: Birkenmeier Gary , Heatherly Henry
Published: April 2009

A ring R is said to be an AE-ring if every additive endomorphism is a ring endomorphism. In this paper further steps are made toward solving Sullivan's Problem of characterising these rings. The classification of AE-rings with. R3 ≠ 0 is completed. Complete characterisations are given for AE-rings which are either: (i) subdirectly irreducible, (ii) algebras over fields, or (iii) additively indecomposable. Substantial progress is made in classifying AE-rings which are mixed – the last open case – by imposing various finiteness conditions (chain conditions on special ideals, height restricting conditions). Several open questions are posed.
Multiplicativity of the uniform norm and independent functions
Authors: Robertson A. Guyan
Published: April 2009

It has long been known that there is a close connection between stochastic independence of continuous functions on an interval and space-filling curves [9]. In fact any two nonconstant continuous functions on [0, 1] which are independent relative to Lebesgue measure are the coordinate functions of a space filling curve. (The results of Steinhaus [9] have apparently been overlooked in more recent work in this area [3, 5, 6].)
On convergence of the conjugate Fourier series of a function of Wiener's class: Corrigendum
Authors: Siddiqi Rafat N.
Published: April 2009

In the statement of the main theorem (top p.337) published by the author in Bull. Austral. Math. Soc. Vol. 39 (1989) pp.335–338, the phrase, “for which f̄(x) exists” should be replaced by “for which f(x) is continuous and f̄(x) exists”.
Sums of deficiencies of algebroid functions
Authors: Yang Lian-Zhong
Published: April 2009

Let f(z) be an n–Valued algebroid function of finite lower order. In the present paper, we give a spread relation of f(z) and some applications of the spread relation.
On local equivalence for vector field systems
Authors: Vassiliou P.J.
Published: April 2009

We give sufficient conditions for C∞ vector field systems on Rn with genus g = 1 to be diffeomorphic to a contact structure. The diffeomorphism is explicitly constructed and used to give the most general integral submanifolds for the systems. Finally the implications of these results for integrable hyperbolic partial differential equations in the plane is discussed.
Frattini classes of saturated formations of finite groups
Authors: Förster Peter
Published: April 2009

We study the following question: given any local formation of finite groups, do there exist maximal local subformations? An answer is given by providing a local definition of the intersection of all maximal local subformations.
On the conformal deformation of Riemannian structures
Authors: Jung Yoon-Tae
Published: April 2009

In this paper, we study a nonlinear partial differential equation on a compact manifold;

where a > 1 is a constant, r is a positive constant, and H is a prescribed smooth function.

Kazdan and Warner showed that if λ1(g) < 0 and < 0, where is the mean of H, then there is a constant 0 < r0(H) ≤ ∞ such that one can solve this equation for 0 < r < r0(H), but not for r > r0(H). They also proved that if r0(H) = ∞, then H(x) ≤ 0 (≢0) for all x ∈ M. They conjectured that this necessary condition might be sufficient.

I show that this conjecture is right; that is, if H(x) ≤ 0 (≠ 0) for all x ∈ M, then r0(H) = ∞.
The C*-algebras of some inverse semigroups
Authors: Hancock Rachel , Raeburn Iain
Published: April 2009

We discuss the structure of some inverse semigroups and the associated C* algebras. In particular, we study the bicyclic semigroup and the free monogenic inverse semigroup, following earlier work of Conway, Duncan and Paterson. We then associate to each zero-one matrix A an inverse semigroup CA, and show that the C*-algebra OA of Cuntz and Krieger is closely related to the semigroup algebra C*(CA).
Convex lattice polygons of minimum area
Authors: Simpson R.J.
Published: April 2009

A convex lattice polygon is a polygon whose vertices are points on the integer lattice and whose interior angles are strictly less than π radians. We define a(2n) to be the least possible area of a convex lattice polygon with 2n vertices. A method for constructing convex lattice polygons with area a(2n) is described, and values of a(2n) for low n are obtained.
Analyticity and quasi-Banach valued functions
Authors: Bernal Antonio , Cerdà Joan
Published: April 2009

We compare the definitions of analyticity of vector-valued functions and their connections with the topological tensor products of non-locally convex spaces.
On variation of equicontinuity in dynamical systems
Authors: Elaydi S. , Farran H.R.
Published: April 2009

In this paper we investigate the relationships among the notions of minimality, characteristic 0, equicontinuity, Lipschitz stability and isometry in dynamical systems. Examples are provided to show that the results obtained are sharp.
Nonsmooth invexity
Authors: Reiland Thomas W.
Published: April 2009

The concept of invexity is extended to nondifferentiable functions. Characterisations of nonsmooth invexity are derived as well as results in unconstrained and constrained optimisation and duality. The principal analytic tool is the generalised gradient of Clarke for Lipschitz functions.
Ruled surfaces of finite type
Authors: Chen Bang-Yen , Dillen Franki , Verstraelen Leopold , Vrancken Luc
Published: April 2009

We show that a ruled surface of finite type in a Euclidean space is a cylinder on a curve of finite type or a helicoid in Euclidean 3-space.
Nonoscillation criteria for Emden-Fowler systems
Authors: Erbe Lynn H. , Liu Xinzhi
Published: April 2009

A number of nonoscillation criteria for the Emden-Fowler system

where a(t), b(t) > 0, r1, r2 > 0 and b(t)/a(t) is locally of bounded variation, are established employing energy function techniques. The results obtained here include many known nonoscillation theorems for the classical Emden-Fowler equations as special cases. We illustrate the results obtained with several examples.
The Wielandt subgroup of metacyclic p-groups
Authors: Ormerod Elizabeth A.
Published: April 2009

The Wielandt subgroup is the intersection of the normalisers of all the subnormal subgroups of a group. For a finite group it is a non-trivial characteristic subgroup, and this makes it possible to define an ascending normal series terminating at the group. This series is called the Wielandt series and its length determines the Wielandt length of the group. In this paper the Wielandt subgroup of a metacyclic p–group is identified, and using this information it is shown that if a metacyclic p–group has Wielandt length n, its nilpotency class is n or n + 1.