bluuebunny/crossref_metadata_2025 huggingface dataset:
Regression analysis of dependent error models
Authors: McGilchrist C. A.
Published: April 2009

A method of analysing the general linear regression model is described, for the case where the observations are correlated. For many applications the correlations are structured, with neighbouring observations being more strongly correlated than those some distance apart in time or space. Such correlation structures may often be assumed to belong to some class of models indexed by a small number of parameters. Estimation and inference procedures which are able to cope with a wide range of correlation models, are described and the methods are applied to problems which occur in biometry.
The free orthomodular word problem is solvable
Authors: Kalmbach Gudrun
Published: April 2009

It is shown that the free orthomodular word problem is solvable. Since the free orthomodular lattice L0 on countable many generators has, as a partial subalgebra, every finite partial orthomodular lattice P, which is contained in some orthomodular lattice as a partial subalgebra, it is sufficient to prove Evans embedding property for these P only. The construction of the finite orthomodular lattice containing P as a partial subalgebra has and can be done outside of L0. It uses the coatom extension for ortholattices.
A note on periodic solutions of some nonautonomous differential equations
Authors: Grossinho M. R. , Sanchez L.
Published: April 2009

We prove the existence of nontrivial periodic solutions of some nonlinear ordinary differential equations with time-dependent coefficients using variational methods.
On the additive groups of subdirectly irreducible rings
Authors: Hirano Yasuyuki , Mogami Isao
Published: April 2009

In this paper we study the additive group structure of subdirectly irreducible rings and their hearts. We give and example of a torsion-free, non-reduced abelian group which is not the underlying additive group of any associative subdirectly irreducible ring. It is a counterexample to a theorem in Feigelstock's book “Additive Groups of Rings.”
A characterization of chaos
Authors: Janková K. , Smítal J.
Published: April 2009

Consider the continuous mappings f from a compact real interval to itself. We show that when f has a positive topological entropy (or equivalently, when f has a cycle of order ≠ 2n, n = 0, 1, 2, …) then f has a more complex behaviour than chaoticity in the sense of Li and Yorke: something like strong or uniform chaoticity, distinguishable on a certain level ɛ > 0. Recent results of the second author then imply that any continuous map has exactly one of the following properties: It is either strongly chaotic or every trajectory is approximable by cycles. Also some other conditions characterizing chaos are given.
Almost Baire class one multi-functions
Authors: Maritz P.
Published: April 2009

In this paper we employ quasi-continuous multifunctions and introduce almost Baire class 1 multifunctions in order to generalize a theorem of Kuratowski and also to answer a question posed by him concerning Baire class 1 multifunctions. We also show that certain multifunctions can be decomposed into mutually singular multifunctions.
The higher derivations of functions bounded in various senses
Authors: Yamashita Shinji
Published: April 2009

An extension (Theorem 1) of Schwarz and Pick's lemma motivates us to study the analogues for functions which are bounded in the sense of Bloch, normal, or yoshida. A typical result is that, for a function f holomorphic in D = {|z| < 1} and Bloch, that is, , with the expansion f(w) = c0 + cn (w − z)n + … (n ≧ 1) about 2 ε D, we have (1 − |z|2)n|f(n) (z)|/n! ≦ Anα, where An is an absclute constant; the estimate is sharp.
Kleene algebras are almost universal
Authors: Adams M. E. , Priestley H. A.
Published: April 2009

This paper studies endomorphism monoids of Kleene algebras. The main result is that these algebras form an almost universal variety k, from which it follows that for a given monoid M there is a proper class of non-isomorphic Kleene algebras with endomorphism monoid M+ (where M+ denotes the extension of M by a single element that is a right zero in M+). Kleene algebras form a subvariety of de Morgan algebras containing Boolean algebras. Previously it has been shown the latter are uniquely determined by their endomorphisms, while the former constitute a universal variety, containing, in particular, arbitrarily large finite rigid algebras. Non-trivial algebras in K always have non-trivial endomorphisms (so that universality of K is ruled out) and unlike the situation for de Morgan algebras the size of End(L) for a finite Kleene algebra L necessarily increases as |L| does. The paper concludes with results on endomorphism monoids of algebras in subvarieties of the variety of MS-algebras.
Erdös-Turán mean convergence theorem for Lagrange interpolation at Lobatto points
Authors: Smith William E.
Published: April 2009

Let {Qn} denote the orthogonal polynomials associated with the weight function p on [−1, 1] and let denote the zeros of (1−x2) Qn (x). Consider the Lagrange polynomials which interpolate a given continuous function at these points. It is shown that, as n → ∞, the Lagrange polynomial converges to the function in the W weighted mean square sense, where w (x) = ρ(x)\(1−x2), provided that W is integrable. An application to numerical product integration is noted.
Proper embeddability of inverse semigroups
Authors: Shehadah A.
Published: April 2009

Let S be an inverse semigroup. We prove that there is a ring with a proper involution * in which S is *-embeddable. The ring will be a natural one, R[S], the semigroup ring of S over any formally complex ring R; for example ℝ, Ȼ.
On variants of a semigroup
Authors: Hickey J. B.
Published: April 2009

IfSis a (multiplicative) Semigroup anda∈S, the binary operation ∘ defined on the setSbyx∘y=x a yis associative and the resulting semigroup is called a variant ofS. We study the congruenceadefined onSby saying that two elements are α-related if and only if they determine the same variant ofS. Certain quotients of variants are used to provide an arbitrary semigroup with a generalised local structure. The variant formulation of Nambooripad's partial order on a regular semigroup is used to show that the order possesses a certain property (involvingD-equivalence).
A note on n-harmonic majorants
Authors: Kim Hong Oh , Lee Chang Ock
Published: April 2009

Suppose D (υ) is the Dirichlet integral of a function υ defined on the unit disc U in the complex plane. It is well known that if υ is a harmonic function in U with D (υ) < ∞, then for each p, 0 < p < ∞, |υ|p has a harmonic majorant in U.

We define the “iterated” Dirichlet integral Dn (υ) for a function υ on the polydisc Un of Cn and prove the polydisc version of the well known fact above:

If υ is an n-harmonic function in Un with Dn (υ) < ∞, then for each p, 0 < p < ∞, |υ|p has an n-harmonic majorant in Un.
Linear monads
Authors: Day B. J.
Published: April 2009

A monad T = (T, μ, η) on a category C is said to be linear with respect to a dense functor N: A → C if the operator T is the epimorphic image of a certain colimit of its values on A. The main aim of the article is to relate the concept of a linear monad to that of a monad with rank. A comparison is then made between linear monads and algebraic theories.
Isomorphic queues
Authors: Ghosal A.
Published: April 2009

Two systems of queues are said to be isomorphic in the restricted sense if at least one of their output elements, for example waiting time, queue size, idle time, inter-departure time, and so on, has exactly or approximately the same probability distribution function, irrespective of differences in their input elements, for example, inter-arrival time, service time, and so on. This property has been used in deriving approximate solutions to systems which do not have exact solutions. The paper highlights the systems approach in queueing problems and its practical usefulness.
A monadicity theorem
Authors: Borceux Francis , Day B. J.
Published: April 2009

A monadicity theorem is established, for functors which satisfy the conditions of the “first isomorphism theorem” (following Linton's terminology). An application is made to the characterisation of certain types of algebraic categories generated by linear monads.
A class of replacement systems with simple optimality theory
Authors: Staples John
Published: April 2009

A class of replacement systems is studied which satisfies a “subcommutativity” condition. Examples of systems satisfying this condition are many of the systems of graph-like expressions which have recently been studied in connection with the efficient evaluation of recursive definitions. An optimality theory of subcommutative systems is developed and is used to give conditions which are sufficient to ensure that an evaluation (reduction) procedure is optimal. The optimality theory is also applied to develop conditions under which a given subcommutative system speeds up, in a natural sense, another replacement system.
A diagonal dominance criterion for exponential dichotomy
Authors: Palmer Kenneth J.
Published: April 2009

Roughly speaking, a system of linear differential equations has an exponential dichotomy if it has a subspace of solutions shrinking exponentially and a complementary subspace of solutions growing exponentially. In the case of constant coefficients, this happens if and only if the eigenvalues of the coefficient matrix have nonzero real parts. In the general case, Lazer has shown that if the coefficient matrix function is bounded and satisfies a diagonal dominance condition (which, in the constant case, is a sufficient but not necessary condition that the eigenvalues have nonzero real parts) then the system has an exponential dichotomy. In this paper we prove the same result with a weaker diagonal dominance condition, thus generalizing a theorem of Nakajima.
A note on injectors in finite soluble groups
Authors: Cossey John
Published: April 2009

Groups of nilpotent length four containing a subgroup which covers and avoids the same chief factors as an -injector for some Fitting class but which is not itself an -injector have been constructed by F.P. Lockett (in his PhD thesis) and T.R. Berger and John Cossey (in preparation). Graham A. Chambers (J. Algebra 16 (1970), 442–455) has shown that such a subgroup cannot exist in a group of p–length one for all primes p. The main result of this paper closes the small gap remaining: it includes Chambers' result and establishes also that such a subgroup cannot exist in a group of nilpotent length three.
On the stability of impulsively perturbed differential systems
Authors: Pandit S.G.
Published: April 2009

This paper deals with the study of uniform asymptotic stability of the measure differential systemDx=F(t, x) +G(t, x)Du, where the symbolDstands for the derivative in the sense of distributions. The system is viewed as a perturbed system of the ordinary differential systemx'=F(t, x), where the perturbation termG(t, x)Duis impulsive and the state of the system changes suddenly at the points of discontinuity ofu. It is shown, under certain conditions, that the uniform asymptotic stability property of the unperturbed system is shared by the perturbed system. To do this, the well-known Gronwall integral inequality is generalized so as to be applicable to Lebesgue-Stieltjes integrals.
Colimits of algebras revisited
Authors: Adámek Jiří
Published: April 2009

It has “been open for some time whether, given an algebraic theory (triple, monad) Π in a cocomplete category K, also the category KΠ of Π-algebras must be cocomplete. We solve this in the negative by exhibiting a free algebraic theory Π in the category Gra of graphs such that GraΠ is not cocomplete. Further, we improve somewhat the well-known colimit theorem of Barr and Linton by showing that the base category need not be complete.
Moons, bridges, birds … and nonexpansive mappings in Hilbert space
Authors: Goebel Kasimierz , Schöneberg Rainald
Published: April 2009

In recent years some fixed point theorems have been proved for nonexpansive mappings in Hilbert space, which have non-convex domains. The purpose of this paper is to present a simple but very useful new result of that kind and to indicate some of its consequences.
Continuous convergence and the Hahn-Banach problem
Authors: Beattie Ronald
Published: April 2009

In this note, a positive solution is given to the Hahn-Banach problem for an important class of convergence vector spaces. As well, a topological vector space characterization is obtained for fully complete and Br-complete spaces.
The inverse of a certain block matrix
Authors: Singh V.N.
Published: April 2009

A simple formula for the inverse of a block matrix with non-zero blocks in the principal diagonal and the first sub-diagonal only is proved. The matrix had arisen in an investigation of a difference equation.
Fixed point theorems for nonexpansive mappings in a locally convex space
Authors: Srivastava P. , Srivastava S.C.
Published: April 2009

Several fixed point theorems for nonexpansive self mappings in metric spaces and in uniform spaces are known. In this context the concept of orbital diameters in a metric space was introduced by Belluce and Kirk. The concept of normal structure was utilized earlier by Brodskiĭ and Mil'man. In the present paper, both these concepts have been extended to obtain definitions of β-orbital diameter and β-normal structure in a uniform space having β as base for the uniformity. The closed symmetric neighbourhoods of zero in a locally convex space determine a base β of a compatible uniformity. For 3-nonexpansive self mappings of a locally convex space, fixed point theorems have been obtained using the concepts of β-orbital diameter and β-normal structure. These theorems generalise certain theorems of Belluce and Kirk.
A theorem in Banach algebras and its applications
Authors: Srinivasan V.K. , Shaing Hu
Published: April 2009

IfAis a complex Banach algebra which is also a Bezout domain, it is shown that for any primepand a non-negative integern,pnis not a topological divisor of zero. Using the above result it is shown that a complex Banach algebra which is a principal ideal domain is isomorphic to the complex field.
Weak star separability
Authors: Dancer E.N. , Sims Brailey
Published: April 2009

For a Banach space X, Susumu Okada raised the question of whether the unit hall of the dual space X* is weak* separable if X* is weak* separable. The problem occurred in the theory of manifolds modelled on locally convex spaces. We answer the question in the negative but show that it is true for particular types of spaces.
The lower radical construction for non-associative rings: Examples and counterexamples
Authors: Gardner B.J.
Published: April 2009

Some sufficient conditions are presented for the lower radical construction in a variety of algebras to terminate at the step corresponding to the first infinite ordinal. An example is also presented, in a variety satisfying some non-trivial identities, of a lower radical construction terminating in four steps.
The Cauchy problem for a second-order nonlinear hyperbolic equation with initial data on a line of parabolicity
Authors: Rassias John M.S.
Published: April 2009

In this paper we study the Cauchy problem for the second order nonlinear hyperbolic partial differential equation

with initial conditions

where

and |u|, |ux|, |uy| < ∞, y ≥ 0, r = r(x) ∈ C4(·), ν = ν(x) ∈ C4(·).

These conditions on k, H, f, r, and ν are assumed to be satisfied in some sufficiently small neighborhood of the segment I, y = 0, in the upper half-plane y > 0

This paper generalizes the results obtained by N.A. Lar'kin (Differencial'nye Uravnenija 8 (1972), 76–84), who has treated the special case H = H(x, y, u); that is, the quasi-linear hyperbolic equation (*).
On the representation of metric spaces
Authors: Logan G.J.
Published: April 2009

A closure algebra is a set X with a closure operator C defined on it. It is possible to construct a topology τ on MX, the family of maximal, proper, closed subsets of X, and then to examine the relationship between the algebraic structure of (X, C) and the topological structure of the dual space (MX τ) This paper describes the algebraic conditions which are necessary and sufficient for the dual space to be separable metric and metric respectively.
A duality theorem for a nondifferentiable nonlinear fractional programming problem
Authors: Mond B. , Craven B.D.
Published: April 2009

A duality theorem, and a converse duality theorem, are proved for a nonlinear fractional program, where the numerator of the objective function involves a concave function, not necessarily differentiable, and also the support function of a convex set, and the denominator involves a convex function, and the support function of a convex set. Various known results are deduced as special cases.
Topological dynamics and algebras with an involution
Authors: Yang J.S.
Published: April 2009

I this paper we extend such dynamical concepts as weak almost periodicity and simple equicontinuity of topological dynamics to the context of groups of *-automorphisms on a C*-algebra with unit. If (A, G) is a C* flow and if S(A) is the state space of A, we show that (A, G) is weakly almost periodic if and only if (S(A), G) is weakly almost periodic, and that, if A is a von Neumann algebra, then A is G-finite if and only if G is simple equicontinuous on the unit ball of A with respect to the weak *-topology.
Further inequalities for convex sets with lattice point constraints in the plane
Authors: Scott P.R.
Published: April 2009

Let K be a bounded closed convex set in the plane containing no points of the integral lattice in its interior and having width w, area A, perimeter p and circumradius R. The following best possible inequalities are established:
Integral inequalities and applications
Authors: Reddy K. Narsimha
Published: April 2009

In this paper some nonlinear analogues of Gronwall's integral inequality are established and an application to differential equations is given.
A commutativity theorem for division rings
Authors: Abu-Khuzam Hazar , Yaqub Adil
Published: April 2009

The following theorem is proved: Let D be a division ring such that for all x, y in D there exists a positive integer n = n(x, y) for which (xy)n − (yx)n is in the center of D. Then D is commutative. This theorem also holds for semisimple rings.
On the spectrum of Stein quasigroups
Authors: Bennett F.E. , Mendelsohn N.S.
Published: April 2009

In this paper we investigate the spectrum of a variety of quasigroups satisfying the 2-variable identity x(xy) = yx, called Stein quasigroups. Stein quasigroups are known to be self-orthogonal and have been given a considerable amount of attention because of this property. It is known that there are no Stein quasigroups of order 2, 3, 6, 7, 8, 10, 12, 14. The object of this paper is to show that for all but 36 values of n ≥ 15 there exists a Stein quasigroup of order n. In particular, the spectrum of Stein quasigroups contains all n ≥ 191.
Extension with larger norm and separation with double support in normed linear spaces
Authors: Singer Ivan
Published: April 2009

We prove, in normed linear spaces, the existence of extensions of continuous linear functionals from linear subspaces to the whole space, with arbitrarily prescribed larger norm. Also, we prove that under an additional boundedness assumption, in the known separation theorems for convex sets, there exist hyperplanes which separate and support both sets.
Applications of convergence spaces
Authors: Richardson Gary D.
Published: April 2009

Convergence notions are used extensively in the areas of probability and statistics. Many times proofs can be simplified by considering an appropriate convergence structure on the space and using well-known results from the theory of convergence spaces; for example, compactness arguments are sometimes simplified by using a generalized Ascoli theorem in the convergence space setting. The theory of convergence spaces is also used to generalize some results in probability and statistics.
Non-compact composition operators
Authors: Singh R.K. , Sharma S.D.
Published: April 2009

In this note sufficient conditions for non-compactness of composition operators on two different functional Hilbert spaces have been obtained.
On approximation of continuously differentiable functions by positive linear operators
Authors: Gonska Heinz H.
Published: April 2009

The aim of this note is to prove a theorem on the pointwise degree of approximation of continuously differentiable functions by positive linear operators. As can be seen from the applications to Bernstein and Hermite-Fejér operators, our inequality yields better constants and sometimes even a higher degree of approximation than the known general results.
On an optimal control problem involving second order hyperbolic systems with boundary controls
Authors: Choo K.G. , Teo K.L. , Wu Z.S.
Published: April 2009

In this paper, we consider an optimal control problem involving second-order hyperbolic systems with boundary controls. Necessary and sufficient conditions are derived and a result on the existence of optimal controls is obtained. Also, a computational algorithm which generated minimizing sequences of controls is devised and the convergence properties of the algorithm are investigated.
Polar locally convex topologies and Attouch-Wets convergence
Authors: Beer Gerald
Published: April 2009

Let X be a Hausdorff locally convex space. We show that convergence of a net of continuous linear functionals on X with respect to a given polar topology on its continuous dual X′ can be explained in terms of the convergence of the corresponding net of its graphs in X × R, and the corresponding net of level sets at a fixed height in X, with respect to a natural generalisation of Attouch-Wets convergence in normable spaces.
Invex optimisation problems
Authors: Luc D.T. , Malivert C.
Published: April 2009

In this paper we extend the concept of invexity to set-valued maps and study vector optimisation problems with invex set-valued data. Necessary and sufficient optimality conditions are established in terms of contingent derivatives. Wolfe type dual problems are constructed via two recently developed approaches which guarantee the zero-gap duality property.
Functions of bounded kth variation and absolutely kth continuous functions
Authors: Mukhopadhyay S.K. , Mukhopadhyay S.N.
Published: April 2009

Functions of bounded kth variation and absolutely kth continuous functions are considered on sets and various properties are studied.
Characterisations for analytic functions of bounded mean oscillation
Authors: Miao Jie
Published: April 2009

Let α > 0 and let f[α](z) be the αth fractional derivative of an analytic function f on the unit disc D. In this paper we show that f ∈ BMOA if and only if |f[α](z)|2 (l - |z|2)2α−1dA(z) is a Carleson measure and f ∈ VMOA if and only if |f[α](z)|2 (1 − |z|2)2α−1dA(z) is a vanishing Carleson measure, where A denotes the normalised Lebesgue measure on D. Hence a significant extension of familiar characterisations for analytic functions of bounded and vanishing mean oscillation is obtained.
A certain fixed point theorem and its applications to integral-functional equations
Authors: Zima M.
Published: April 2009

In this paper a variant of Banach's contraction principle is established. By using the properties of the spectral radius of a bounded linear operatorAdefined in a suitable Banach space, we conclude that another operatorAhas exactly one fixed point in this space. In the second part of this paper some applications are given.
A remark on Gelfand duality
Authors: Sun Shu-Hao
Published: April 2009

In this paper, we prove a Gelfand-Mulvey type of duality for a certain class of rings which includes the Gelfand rings. We also show that the Maximal Ideal Theorem (MIT) can be replaced by the Prime Ideal Theorem (PIT) in the original Gelfand-Mulvey duality.
Points fixes dans les espaces des operateurs nucleaires
Authors: Besbes Mourad
Published: April 2009

We prove that some metric inequalities imply weak or weak-star normal structure. In particular, we prove that every ω*-compact convex set in the space C1(lp, lq) of nuclear operators from lp into lq, (1 < p, q < ∞, 1/p + 1/q = 1) has the weak* normal structure. This generalises a recent result of C. Lennard.
Cylindrical representations of some infinite dimensional nuclear Lie groups
Authors: Marion Jean
Published: April 2009

Let Γ.𝒜 be the semi-direct product group of a nuclear Lie group Γ with the additive group 𝒜 of a real nuclear vector space. We give an explicit description of all the continuous representations of Γ.𝒜 the restriction of which to 𝒜 is a cyclic unitary representation, and a necessary and sufficient condition for the unitarity of such cylindrical representations is stated. This general result is successfully used to obtain irreducible unitary representations of the nuclear Lie groups of Riemannian motions, and, in the setting of the theory of multiplicative distributions initiated by I.M. Gelfand, it is proved that for any connected real finite dimensional Lie groupGand for any strictly positive integerkthere exist non located and non trivially decomposable representations of orderkof the nuclear Lie group(M;G) of all theG-valued test-functions on a given paracompact manifoldM.
A note on regular metabelian groups of prime-power order
Authors: Newman M.F. , Xu Ming-Yao
Published: April 2009

Let p be a prime and d, e positive integers. We prove that a regular d-generator metabelian p-group whose commutator subgroup has exponent pe has nilpotency class at most e(p – 2) + 1 unless e = 1, d > 2, p > 2 when the class can be p and these bounds are best possible.
Stability of weak normal structure in James quasi reflexive space
Authors: Jiménez-Melado A.
Published: April 2009

We introduce a coefficient on general Banach spaces which allows us to derive the weak normal structure for those Banach spaces whose Banach-Mazur distance to James quasi reflexive space is less than .
Oscillations of certain partial differential equations with deviating arguments
Authors: Lalli B.S. , Yu Y.H. , Cui B.T.
Published: April 2009

Sufficient conditions are established for the oscillation of solutions of hyperbolic equations of neutral type of the form

where R+ = {0, ∞), Ω is a bounded domain in Rn with a piecewise smooth boundary ∂Ω.
The stability of solutions in an initial-boundary reaction-diffusion system
Authors: Tuma E. , Blázquez C.M.
Published: April 2009

We study the asymptotic behaviour as t → ∞ of solutions of the initial-boundary value problem vt = G(u, v), ut = uxx + F(u, v), and t > 0, x ∈ ℝ or x ∈ ℝ+ for a wide class of initial and boundary values, where F and G are smooth functions so that the system has three rest points.
The number of lattice rules having given invariants
Authors: Joe Stephen , Hunt David C.
Published: April 2009

A lattice rule is a quadrature rule used for the approximation of integrals over the s-dimensional unit cube. Every lattice rule may be characterised by an integer r called the rank of the rule and a set of r positive integers called the invariants. By exploiting the group-theoretic structure of lattice rules we determine the number of distinct lattice rules having given invariants. Some numerical results supporting the theoretical results are included. These numerical results are obtained by calculating the Smith normal form of certain integer matrices.
An internal characterisation of strongly regular rings
Authors: Huang Luosheng , Xue Weimin
Published: April 2009

We show that a right duo ring R is strongly regular if and only if for each ideal I of R, the coset product of I in the factor ring R/I is the same as their set product.
On minimax inequalities on spaces having certain contractible subsets
Authors: Park Sehie
Published: April 2009

The concept of a convex space is extended to an H-space; that is, a space having certain family of contractible subsets. For such spaces the KKM type theorems, the Fan-Browder fixed point theorem, the Ky Fan type matching theorem, and minimax inequalities are given. Moreover, applications to a von Neumann-Sion type minimax theorem, a saddle point theorem, a quasi-variational inequality, and a Kakutani type fixed point theorem are obtained.
A direct ellipsoid method for linear programming
Authors: Wu Shiquan , Wu Fang
Published: April 2009

This paper indicates how to apply the ellipsoid method directly to Linear Programming problems and proves that this kind of version of the ellipsoid method is almost as good as Karmarkar's type method in the theoretical sense.
Critical point theorems with relaxed boundary condition and applications
Authors: Du Yihong
Published: April 2009

This paper is a sequel to a recent paper by the author in this journal. We prove some -variants of the min-max type critical point theorems with relaxed boundary condition and then apply the abstract results to a semilinear elliptic boundary value problem.
Power roots of polynomials
Authors: Miller John Boris
Published: April 2009

Sufficient conditions are given for the existence of an mth power root of one polynomial modulo another, over the complexes or the reals. Examples show the non-necessity of the conditions. In particular cases there can exist infinitely many square roots.
Axioms for convexity
Authors: Coppel W.A.
Published: April 2009

The basic elementary results about convex sets are derived successively from various properties of segments. The complete set of properties is shown to form a natural set of axioms characterising the convex sets in a real vector space.
Pure subgroups of LCA groups
Authors: Wu Sheng L.
Published: April 2009

This paper originated with our interest in the open question “If every pure subgroup of an LCA groupGis closed, mustGbe discrete ?” that was raised by Armacost. The answer was surprisingly easy, but led to some interesting questions. We attempted to characterise those LCA groups that contain a proper pure dense subgroup, and found that every non-discrete torsion-free LCA group contains a proper pure dense subgroup; so does every non-discrete infinite self-dual torsion LCA group. We also give a necessary and sufficient condition for a torsion LCA group to contain a proper pure dense subgroup.
A characterisation of compact minimal hypersurfaces in a unit sphere
Authors: Cheng Qing-Ming
Published: April 2009

In this note, we show that the totally geodesic sphere, Clifford torus and Cartan hypersurface are the only compact minimal hypersurfaces in S4(1) with constant scalar curvature if the Ricci curvature is not less than −1.
On optimal symmetric orthogonalisation and square roots of a normal matrix
Authors: Sherif Nagwa
Published: April 2009

It is well known that the factors in the polar decomposition of a full rank real m × n matrix, m ≥ n possess best approximation properties. We propose an iterative technique to compute the polar factors based on these best approximation properties. For normal matrices, the polar decomposition is useful. It is applied to compute the principal square roots of real and complex normal matrices.
On prime essential rings
Authors: France-Jackson Halina
Published: April 2009

A ring A is prime essential if A is semiprime and every prime ideal of A has a nonzero intersection with each nonzero ideal of A. We prove that any radical (other than the Baer's lower radical) whose semisimple class contains all prime essential rings is not special. This yields non-speciality of certain known radicals and answers some open questions.
On skew-commuting mappings of rings
Authors: Brešar Matej
Published: April 2009

A mapping f of a ring R into itself is called skew-commuting on a subset S of R if f(s)s + sf(s) = 0 for all s ∈ S. We prove two theorems which show that under rather mild assumptions a nonzero additive mapping cannot have this property. The first theorem asserts that if R is a prime ring of characteristic not 2, and f: R → R is an additive mapping which is skew-commuting on an ideal I of R, then f(I) = 0. The second theorem states that zero is the only additive mapping which is skew-commuting on a 2-torsion free semiprime ring.
On union-closed sets and Conway's sequence
Authors: Renaud J-C. , Fitina L.F.
Published: April 2009

In 1991 Renaud defined a boundary function φ(n) for union-closed sets, and evaluated it to n = 17. Also in 1991, Mallows examined a sequence a(n) defined recursively by Conway in 1988.

Investigation of some properties of strictly reduced ordered power sets, a class of union-closed sets, leads to the conclusion that a(n + 1) is an upper bound for φ(n), and the union-closed sets conjecture holds if the conjecture φ(n) = a(n + 1) is valid.
Distance transitive graphs with symmetric or alternating automorphism group
Authors: Liebeck Martin W. , Praeger Cheryl E. , Saxl Jan
Published: April 2009

The paper classifies all distance transitive graphs Γ such thatAn≤ Aut Γ ≤ AutAnfor some alternating groupAn, and Aut Γ acts primitively on the vertices of Γ. This result forms part of our programme for determining all finite primitive distance transitive graphs.
Lower bounds for tau coefficients and operator norms using composite matrix norms
Authors: Tan Choon Peng
Published: April 2009

Lower bounds for the tau coefficients and operator norms are derived by using composite matrix norms. For a special class of matrices B, our bounds on ‖B‖p (the operator norm of B induced by the ℓp norm) improve upon a general class of Maitre (1967) bounds for p ≥ 2.
Regular topological distributively generated near-rings
Authors: Tharmaratnam V.
Published: April 2009

In this paper we introduce regular topological distributively generated (d.g.) near-rings (distinct from d.g. regular near-rings) as the d.g. near-ring analogue of regular rings and develop a structure theory for this class of near-rings.
Metric spaces with nice closed balls and distance functions for closed sets
Authors: Beer Gerald
Published: April 2009

A metric space 〈X,d〉 is said to have nice closed balls if each closed ball in X is either compact or the entire space. This class of spaces includes the metric spaces in which closed and bounded sets are compact and those for which the distance function is the zero-one metric. We show that these are the spaces in which the relation F = Lim Fn for sequences of closed sets is equivalent to the pointwise convergence of 〈d (.,Fn)〉 to d (.,F). We also reconcile these modes of convergence with three other closely related ones.
A note on convex cones in topological vector spaces
Authors: Sterna-Karwat Alicia
Published: April 2009

The aim of the present note is an independent study of a class of convex cones, which is the largest possible with regard to existence of cone-maximal points in abstract vector optimization problems.
N-th root rings
Authors: Heatherly Henry , Blanchet Altha
Published: April 2009

A ring for which there is a fixed integern≥ 2 such that every element in the ring has ann-th in the ring is called ann-th root ring. This paper gives numerous examples of diverse types ofn-th root rings, some via general construction procedures. It is shown that every commutative ring can be embedded in a commutativen-th root ring with unity. The structure ofn-th root rings with chain conditions is developed and finiten-th root rings are completely classified. Subdirect product representations are given for several classes ofn-th root rings.
Growth of polynomials whose zeros are within or outside a circle
Authors: Aziz Abdul
Published: April 2009

Let P (z) be a polynomial of degree n which does not vanish in the disk |z| < K. For K = 1, it is known that

In this paper we consider the two cases K ≥ 1 and K < 1, and present certain generalizations of these results.
Mazur's intersection property of balls for compact convex sets
Authors: Whitfield J. H. M. , Zizler V.
Published: April 2009

We show that every compact convex set in a Banach space X is an intersection of balls provided the cone generated by the set of all extreme points of the dual unit ball of X* is dense in X* in the topology of uniform convergence on compact sets in X. This allows us to renorm every Banach space with transfinite Schauder basis by a norm which shares the mentioned intersection property.
Extreme positive linear maps between Jordan Banach algebras
Authors: Chu Cho-Ho , Jefferies Nigel P. H.
Published: April 2009

Let A and B be unital JB-algebras. We study the extremal structure of the convex set S (A,B) of all identity preserving positive linear maps from A to B. We show that every unital Jordan homomorphism from A to B is an extreme point of S (A,B). An extreme point of S (A,B) need not be a homomorphism and we show that, given A, every extreme point of S (A,B) is a homomorphism for any B if, and only if, dim A ≤ 2. We also determine when S (A,B) is a simplex.
Semigroups of composition operators in Bergman spaces
Authors: Siskakis Aristomenis G.
Published: April 2009

Semigroups consisting of composition operators are considered on weighted Bergman spaces. They are strongly continuous, and their infinitesimal generators are identified. One specific semigroup is used to obtain information on an averaging operator.
Homomorphisms of distributive p-algebras with countably many minimal prime ideals
Authors: Adams M. E. , Koubek V. , Sichler J.
Published: April 2009

According to a result of Lee, varieties of pseudocomplemented distributive lattices form an ω+1 chain in which is the trivial variety and is the variety of Boolean algebras. In the present paper it is shown that the variety contains an almost universal subcategory B in which the members of Hom(B,B') associated with minimal prime ideals of B form a countably infinite set for any B,B' ∈ B. In particular, B3contains arbitrarily large algebras whose nontrivial endomorphisms form the countably infinite right zero semigroup. Our earlier results concerning categorical properties of varieties of pseudocomplemented distributive lattices show that no further reduction of the right zero count is possible.
A note on a space Hp, a of holomorphic functions
Authors: Kim H. O. , Kim S. M. , Kwon E. G.
Published: April 2009

For 0 < p < ∞ and 0 ≤a; ≤ 1, we define a space Hp, a of holomorphic functions on the unit disc of the complex plane, for which Hp, 0 = H∞, the space of all bounded holomorphic functions, and Hp, 1 = Hp, the usual Hardy space. We introduce a weak type operator whose boundedness extends the well-known Hardy-Littlewood embedding theorem to Hp, a, give some results on the Taylor coefficients of the functions of Hp, a and show by an example that the inner factor cannot be divisible in Hp, a.
Free Lie algebra and lambda-ring structure
Authors: Ronco Maria
Published: April 2009

Let R be a graded λ-ring. We extend a well-known formula in the universal ring of Witt vectors by replacing the power operations by the Adams operations. Our method provides us an easy way to compute the inverse image by the symmetric power operators of certain elements of R. As a corollary we get identities, found by Klyachko and Hanlon, in the rings 1 + ℤ[[t]]+ and 1 + Rˆ[[t]]+, where R is the representation ring of the symmetric groups.
Well-posedness of determining the source term of an elliptic equation
Authors: Yu Wenhuan
Published: April 2009

In this paper the inverse problem for determining the source term of a linear, uniformly elliptic equation is investigated. The uniqueness of the inverse problem is proved under mild assumptions by use of the orthogonality method and an elimination method. The existence of the inverse problem is proved by means of the theory of solvable operators between Banach spaces, moreover, the continuous dependence of the solution to the inverse problem on measurement is also obtained.
Existence of entire solutions for some elliptic systems
Authors: Yanheng Ding , Shujie Li
Published: April 2009

We establish the existence of solutions for the elliptic systems on ℝN:such thatu, v∈W1, 2(ℝN), wherewithq(x)→∞ as |x| → ∞ and(x, u, v) being superlinear or sublinear as.
Optimality conditions for multiobjecttve and nonsmooth minimisation in abstract spaces
Authors: Coladas L. , Li Z. , Wang S.
Published: April 2009

In this paper we study optimality conditions for an efficient solution in various senses of a general multiobjective optimisation problem in abstract spaces. We utilise properties of the Clarke's generalised differential and properties of a conesubconvexlike function to derive a few necessary and/or sufficient conditions for a feasible solution to be a weak minimum (a minimum, a strong minimum or a proper minimum) of the vector optimisation problem. The results in this paper are extensions and refinements of some known results in vector optimisation.
On strong convergence of arrays
Authors: Qi Yong-Cheng
Published: April 2009

In this paper we study almost sure convergence for arrays of independent and identically distributed random variables. We obtain a condition under which Marcinkiewicz's strong law holds and get a rate analogous to the law of the iterated logarithm under a condition weaker than Hu and Weber's.
An application of Jacobi type polynomials to irrationality measures
Authors: Heimonen Ari , Matala-Aho Tapani , Väänänen Keijo
Published: April 2009

The paper provides irrationality measures for certain values of binomial functions and definite integrals of some rational functions. The results are obtained using Jacobi type polynomials and divisibility considerations of their coefficients.
Twists of matrix algebras and some subgroups of Brauer groups II
Authors: Chi Wenchen
Published: April 2009

We consider some subgroups of Brauer groups arising from twists of matrix algebras by some continuous characters. Explicit descriptions of these subgroups are given in terms of Gauss sums of Dirichlet characters.
Méthodes fonctionnelles pour la transcendance en caractéristique finie
Authors: Denis Laurent
Published: April 2009

There are essentially two ways to obtain transcendence results in finite characteristic. The first, historically, is to use Ore's lemma and to prove that a series whose coefficients satisfy well-behaved divisibility properties cannot be a zero of an additive polynomial. This method is of the same kind as the method of p–automata. The second one is to try to imitate the usual methods in characteristic zero and to do transcendence theory with t–modules analogously to what we can do with algebraic groups. We want to show here that transcendence results over Fq(T) can also be obtained with the help of the variable T. If ec(z) is the Carlitz exponential function and e = ec(1), we obtain, in particular, that 1, e, …, e(p–2) (the P–2 first derivative of e with respect to T) are linearly independent over the algebraic closure of Fq(T). A corollary is that for every non-zero element α in Fq((1/T)), αpe and αec(e1/p) are transcendental over Fq(T). By changing the variable and using older results we also obtain the transcendence of ec(ω) for all ω ∈ Fq((1/T)) such that ω(T) and ω(Ti) are not zero and linearly dependent over Fq (Ti) (q > 2i + 1). Such u appear to be transcendental by the method of Mahler if i is not a power of p.
On prime right alternative rings with commutators in the left nucleus
Authors: Kleinfeld Erwin , Smith Harry F.
Published: April 2009

A ring is called s–prime if the 2-sided annihilator of a nonzero ideal must be zero. In particular, any simple ring or prime (—1, 1) ring is s–prime. Also, a nonzero s–prime right alternative ring, with characteristic ≠ 2, cannot be right nilpotent. Let R be a right alternative ring with commutators in the left nucleus. Then R is associative in the following cases: (1) R is prime, with characteristic ≠ 2, and has an idempotent e ≠ 1 such that (e, e, R) = 0. (2) R is an algebra over a commutative-associative ring with 1/6, and R is either s–prime, or R is prime and locally (—1,1).
Power roots of polynomials over arbitrary fields
Authors: Acciaro Vincenzo
Published: April 2009

Let F be an arbitrary field, and f(x) a polynomial in one variable over F of degree ≥ 1. Given a polynomial g(x) ≠ 0 over F and an integer m > 1 we give necessary and sufficient conditions for the existence of a polynomial z(x) ∈ F[x] such that z(x)m ≡ g(x) (mod f(x)). We show how our results can be specialised to ℝ, ℂ and to finite fields. Since our proofs are constructive it is possible to translate them into an effective algorithm when F is a computable field (for example, a finite field or an algebraic number field).
A note on graphs with a prescribed adjacency property
Authors: Ananchuen W. , Caccetta L.
Published: April 2009

Let m and n be nonnegative integers and k be a positive integer. A graph G is said to have property P(m, n, k) if for any set of m + n distinct vertices of G there are at least k other vertices, each of which is adjacent to the first m vertices of the set but not adjacent to any of the latter n vertices. The problem that arises is that of characterising graphs having property P(m, n, k). This problem has been considered by several authors and a number of results have been obtained. In this paper, we establish a lower bound on the order of a graph having property P(m, n, k). Further, we show that all sufficiently large Paley graphs satisfy properties P(1, n, k) and P(n, 1, k).
Cable knots and infinite necklaces of knots
Authors: Moran Siegfried
Published: April 2009

The group of an arbitrary companion knot is determined using the theory of braids. This seems to be a new result as far as the resulting group is concerned. The latter part of the paper considers infinite necklaces of knots, their groups and in special cases their Alexander power series.
Bistable vector fields are axiom A
Authors: Hurley Mike
Published: April 2009

Recently L. Wen showed that if a C1 vector field (on a smooth compact manifold without boundary) is both structurally stable and topologically stable then it will satisfy Axiom A. The purpose of this note is to indicate how results from an earlier paper can be used to simplify somewhat Wen's argument.
Dual problems of quasiconvex maximisation
Authors: Rubinov Alexander M. , Şimşek Belgin
Published: April 2009

A conjugacy operation is introduced on the set Q(X) of all quasiconvex lower semicontinuous nonnegative functions vanishing at zero. This operation is used in order to introduce and study a dual problem with respect to a maximisation problem where both constraint and objective functions belong to Q(X).
Estimating Mahler's measure
Authors: Everest G.R.
Published: April 2009

In 1962, Mahler defined a measure for integer polynomials in several variables as the logarithmic integral over the torus. Many results exist about the values taken by the measure but many unsolved problems remain. In one variable, it is possible to express the measure as an effective limit of Riemann sums. We show that the same is true in several variables, using a non-obvious parametrisation of the torus together with Baker's Theorem on linear forms in logarithms of algebraic numbers.
Regularity for Hamilton-Jacobi equations via approximation
Authors: Hong Bum Il
Published: April 2009

We prove new regularity results for solutions of first-order partial differential equations of Hamilton-Jacobi type posed as initial value problems on the real line. We show that certain spaces determined by quasinorms related to the solution's approximation properties in C(ℝ) by continuous, piecewise quadratic polynomial functions are invariant under the action of the differential equation. As a result, we show that solutions of Hamilton-Jacobi equations have enough regularity to be approximated well in C(ℝ) by moving-grid finite element methods. The preceding results depend on a new stability theorem for Hamilton-Jacobi equations in any number of spatial dimensions.
Attracting invariant curves in planar discrete dynamical systems
Authors: Esquembre Francisco
Published: April 2009

We study the properties of an invariant attracting curve passing through an attracting fixed point of a planar discrete dynamical system. We compare these properties to the corresponding properties of the invariant repelling curve studied in [3] in order to determine the dynamic behaviour of the system near the fixed point.