bluuebunny/crossref_metadata_2025 huggingface dataset:
CSA-groups and separated free constructions
Authors: Gildenhuys D. , Kharlampovich O. , Myasnikov A.
Published: April 2009

A group G is called a CSA-group if all its maximal Abelian subgroups are malnormal; that is, Mx ∩ M = 1 for every maximal Abelian subgroup M and x ∈ G − M. The class of CSA-groups contains all torsion-free hyperbolic groups and all groups freely acting on λ-trees. We describe conditions under which HNN-extensions and amalgamated products of CSA-groups are again CSA. One-relator CSA-groups are characterised as follows: a torsion-free one-relator group is CSA if and only if it does not contain F2 × Z or one of the nonabelian metabelian Baumslag-Solitar groups B1, n = 〈x, y | yxy−1 = xn〉, n ∈ Z ∂ {0, 1}; a one-relator group with torsion is CSA if and only if it does not contain the infinite dihedral group.
Sets of differentials and smoothness of convex functions
Authors: Tang Wee-Kee
Published: April 2009

Approximation by smooth convex functions and questions on the Smooth Variational Principle for a given convex function f on a Banach space are studied in connection with majorising f by C1-smooth functions.
Morita duality and finitely group-graded rings
Authors: Zhang Shenggui
Published: April 2009

We give the relation between the (rigid) graded Morita duality and the Morita duality on a finitely group-graded ring and the relation between a left Morita ring and some of its matrix rings.
On the magnitude of integer points on elliptic curves
Authors: Pintér Ákos
Published: April 2009

The known effective bounds for the magnitude of integer points on elliptic curves are exponential in the “height” of curve. The bound given in this note is polynomial in the height and depends slightly on the discriminant.
Strong barrelledness properties in B(Σ, X)
Authors: Ferrando J.C. , Ruiz L. M. Sánchez
Published: April 2009

In this paper we show that given a σ-algebra Σ of subsets of a set Ω and a normed space X, then the normed space B(Σ, X), endowed with the usual supremum-norm, of the X-valued functions defined on Ω that are the uniform limit of a sequence of σ-simple X-valued functions on Ω is barrelled of class s if and only if X is barrelled of class s. This extends in the normed case the well known result obtained by Mendoza (1982) for barrelled spaces.
Unicity theorems for meromorphic or entire functions II
Authors: Yi Hong-Xun
Published: April 2009

In 1976, Gross posed the question “can one find two (or possibly even one) finite sets Sj (j = 1, 2) such that any two entire functions f and g satisfying Ef(Sj) = Eg(Sj) for j = 1,2 must be identical?”, where Ef(Sj) stands for the inverse image of Sj under f. In this paper, we show that there exists a finite set S with 11 elements such that for any two non-constant meromorphic functions f and g the conditions Ef(S) = Eg(S) and Ef({∞}) = Eg({∞}) imply f ≡ g. As a special case this also answers the question posed by Gross.
Simple modules over the coordinate ring of quantum affine space
Authors: Min Kangju , Oh Sei-Qwon
Published: April 2009

The simple modules of , the coordinate ring of quantum affine space, are classified in the case when q is a root of unity.
On the splitting field of the Alexander polynomial of a periodic knot
Authors: Hillman Jonathan A.
Published: April 2009

We show that the Murasugi conditions for the Alexander polynomial of a cyclically periodic knot imply a modified form of the Burde-Trotter condition.
Finding eisenstein elements in cyclic number fields of odd prime degree
Authors: Acciaro Vincenzo
Published: April 2009

Let L = Q[α] be a cyclic number field of odd prime degree q over the field Q of rationals. In this paper we give an algorithm to compute the discriminant of L/Q, which relies upon a fast method to find Eisenstein elements in L. The algorithm accepts as input the minimal polynomial of α over Q and a complete factorisation of the discriminant of α, and computes, in time polynomial in the size of the input, a list consisting of all the ramified primes with corresponding Eisenstein elements.
An extension of the generalised schur inequality
Authors: Mond B. , Pečarić J.E.
Published: April 2009

The well-known Schur inequality relates the sum of the squares of the absolute values of the eigenvalues of A to the elements of A. This was recently generalised to powers between one and two. Here we show that the inequality holds for powers between zero and two.
Trace functions on inverse semigroup algebras
Authors: Easdown D. , Munn W.D.
Published: April 2009

Let S be an inverse semigroup and let F be a subring of the complex field containing 1 and closed under complex conjugation. This paper concerns the existence of trace functions on F[S], the semigroup algebra of S over F. Necessary and sufficient conditions on S are found for the existence of a trace function on F[S] that takes positive integral values on the idempotents of S. Although F[S] does not always admit a trace function, a weaker form of linear functional is shown to exist for all choices of S. This is used to show that the natural involution on F[S] is special. It also leads to the construction of a trace function on F[S] for the case in which F is the real or complex field and S is completely semisimple of a type that includes countable free inverse semigroups.
On the stable classification of certain 4-manifolds
Authors: Cavicchioli Alberto , Hegenbarth Friedrich , Repovš Dušan
Published: April 2009

We study the s-cobordism type of closed orientable (smooth or PL) 4–manifolds with free or surface fundamental groups. We prove stable classification theorems for these classes of manifolds by using surgery theory.
The determinant of the sum of two matrices
Authors: Li Chi-Kwong , Mathias Roy
Published: April 2009

Let A and B be n × n matrices over the real or complex field. Lower and upper bounds for |det(A + B)| are given in terms of the singular values of A and B. Extension of our techniques to estimate |f(A + B)| for other scalar-valued functions f on matrices is also considered.
Analytic cycles and generically finite holomorphic maps
Authors: Li Yingchen
Published: April 2009

We study the behaviour of analytic cycles under generically finite holomorphic mappings between compact analytic spaces and prove that if two compact and normal complex analytic spaces have the same analytic homology groups, then any generically one to one holomorphic map between them must be a biholomorphic mapping. This generalises an old theorem of Ax and Borel.
A farthest-point characterisation of the relative Chebyshev centre
Authors: Huotari R. , Prophet M.P. , Shi J.
Published: April 2009

We characterise the relative Chebyshev centre of a compact subsetFof a real Banach space in terms of the Gateaux derivative of the distance to farthest points. We present a relative-Chebyshev-centre characterisation of Hilbert space. In Hilbert space we show that the relative Chebyshev centre is in the closed convex hull of the metric projection ofF, and we estimate the relative Chebyshev radius ofF.
On weighted estimates for Stein's maximal function
Authors: Gunawan Hendra
Published: April 2009

Let φ denote the normalised surface measure on the unit sphere Sn−1. We shall be interested in the weighted Lp estimate for Stein's maximal function Mφf, namely

where w is an Ap weight, especially for 1 < p ≤ 2. Using the Mellin transformation approach, we prove that the estimate holds for every weight wδ where w ∈ Ap and 0 ≤ δ < (p(n − 1) − n)/(n(p − 1)), for n ≥ 3 and n/(n − 1) < p ≤ 2.
Higher commutators, ideals and cardinality
Authors: Lanski Charles
Published: April 2009

For an associative ring R, we investigate the relation between the cardinality of the commutator [R, R], or of higher commutators such as [[R, R], [R, R]], the cardinality of the ideal it generates, and the index of the centre of R. For example, when R is a semiprime ring, any finite higher commutator generates a finite ideal, and if R is also 2-torsion free then there is a central ideal of R of finite index in R. With the same assumption on R, any infinite higher commutator T generates an ideal of cardinality at most 2cardT and there is a central ideal of R of index at most 2cardT in R.
Two types of duality in multiobjective fractional programming
Authors: Coladas L. , Li Z. , Wang S.
Published: April 2009

In this paper, we tire concerned with duality of a multiobjective fractional program. Two different dual problems are introduced with respect to the primal multiobjective fractional program. Under a mild assumption, we prove a weak duality theorem and a strong duality theorem for each type of duality. Finally, we explore some relations between these two types of duality.
New Telyakovskii-type estimates via the Boolean sum approach
Authors: Cao Jia-Ding , Gonska Heinz H.
Published: April 2009

In the present note the magnitude of constants in Telyakovskii-type theorems is investigated. Our general approach to construct the linear operators yielding good constants is the one via Boolean sums. Explicit values for the constants in question are given for general convolution-type operators; the classical Fejér-Korovkin kernel is then used as an example for which one obtains rather small values. Furthermore, also an asymptotic assertion is derived which indicates the room left for improvement of the main results. This leads to a natural conjecture concluding this article.
Existence of positive solutions of quasilinear elliptic equations
Authors: Constantin Adrian
Published: April 2009

We prove under quite general assumptions the existence of a positive solution to the equation Δu + f(x, u) + g(x)x.∇u = 0 in exterior domains of Rn (n ≥ 3).
An algorithm for constructing locally optimal min-max triangulation
Authors: Shrivastava M.
Published: April 2009

Several interesting criteria for constructing triangulations associated with a given set of points in a plane have been introduced. In order to obtain optimal triangula-tion with respect to the min-max-angle criterion, it is essential to study the nature of neutral cases with respect to the criterion. Our aim in this paper is to establish precise equations for neutral set curves with respect to the min-max-angle criterion and to develop an algorithm to obtain a locally optimal triangulation with respect to the criterion.
Gap Tauberian theorems
Authors: Connor Jeff
Published: April 2009

In the first section we establish a connection between gap Tauberian conditions and isomorphic copies of Co for perfect coregular conservative BK spaces and in the second we give a characterisation of gap Tauberian conditions for strong summability with respect to a nonnnegative regular summability matrix. These results are used to show that a gap Tauberian condition for strong weighted mean summability is also a gap Tauberian condition for ordinary weighted mean summability. We also make a remark regarding the support set of a matrix and give a Tauberian theorem for a class of conull spaces.
On a weak* drop property
Authors: Moors Warren B.
Published: April 2009

Rolewicz said that the norm of a Banach space (X, ║·║) has the drop property if for every closed set C disjoint from the closed unit ball B(X), there exists an x ∈ C such that co(x, B(X)) ∩ C = {x}. He then showed that if the norm of a Banach space (X, ║·║) has the drop property then it is reflexive. Later, in 1990 Giles, Sims and Yorke showed that the norm of a Banach space (X, ║·║) has the drop property if and only if the duality mapping f → D(f) from the dual sphere S(X*) into subsets of the second dual sphere S(X**) is norm upper semi-continuous and norm compact-valued on S(X*).
Twist orbits for non continuous maps of degree one
Authors: Esquembre Francisco
Published: April 2009

The existence of twist orbits and twist cycles with a given rotation number is considered for discrete dynamical systems generated by iteration of liftings of maps of the circle into itself. The class of maps for which such orbits exist for every number in the interior of the rotation set is extended to contain an important subclass of non-continuous maps.
On relations between Jacobians and resultants of polynomials in two variables
Authors: Sakkalis Takis
Published: April 2009

This paper investigates some of the connections between the zeros of a polynomial vector field F = (f, g): ℂ2 ← ℂ2 and the Jacobian determinant J(f, g) of f and g. As a consequence, sufficient conditions are given for F to have no zeros. In addition, in the case where F has an inverse F−1, it is proven that F−1 is also polynomial.
Strictly real Banach algebras
Authors: Miller John Boris
Published: April 2009

A complex Banach algebra is a complexification of a real Banach algebra if and only if it carries a conjugation operator. We prove a uniqueness theorem concerning strictly real selfconjugate subalgebras of a given complex algebra. An example is given of a complex Banach algebra carrying two distinct but commuting conjugations, whose selfconjugate subalgebras are both strictly real. The class of strictly real Banach algebras is shown to be a variety, and the manner of their generation by suitable elements is proved. A corollary describes some strictly real subalgebras in Hermitian Banach star algebras, including C* algebras.
Inequalities with weights for powers of generalised inverses
Authors: Mond B. , Pečarić J.E.
Published: April 2009

Recently the authors extended to positive semi-definite matrices converses of matrix inequalities corresponding to ratios and differences of means and of Hölder's inequality. Here, further generalisations are given to the case of several vectors with appropriate weights.
Enlargeable Banach-Lie algebras and free topological groups
Authors: Pestov Vladimir G.
Published: April 2009

We characterise in terms of free topological groups those Banach-Lie algebras with finite-dimensional centre coming from Lie groups.
Combined two stabilities imply Axiom A for vector fields
Authors: Wen Lan
Published: April 2009

It is proved in this paper that if a vector field is both C structurally stable and topologically stable, then it satisfies Axiom A.
Existence and dimensionality of simple weight modules for quantum enveloping algebras
Authors: Shi Zhiyong
Published: April 2009

We give sufficient and necessary conditions for simple modules of the quantum group or the quantum enveloping algebraUq(g) to have weight space decompositions, where g is a semisimple Lie algebra andqis a nonzero complex number. We show that

(i) ifqis a root of unity, any simple module ofUq(g) is finite dimensional, and hence is a weight module;

(ii) ifqis generic, that is, not a root of unity, then there are simple modules ofUq(g) which do not have weight space decompositions.

Also the group of units ofUq(g) is found.
On the width of a planar convex set containing zero or one lattice points
Authors: Scott Paul R.
Published: April 2009

We generalise to a rectangular lattice a known result about the maximal width of a planar compact convex set containing no points of the integral lattice. As a corollary we give a new short proof that the planar compact convex set of greatest width which contains just one point of the triangular lattice is an equilateral triangle.
A note on bounds of cardinal functions in the closed preimage
Authors: Miller Edward S.
Published: April 2009

Let X and Y be T1 spaces and f: X → Y be a closed and onto mapping. If a fiber of the mapping f is defined to be the inverse image of a singleton in the range, then a bound for the tightness of the domain is the product of the tightness of the range and the supremum of the tightness of the fibers of f. Similar bounds can also be shown for the Lindelöf degree and the extent of X. Examples are provided to demonstrate that such results are not possible for open maps. Cellularity and spread are discussed briefly.
On semigroups with involution
Authors: Easdown D. , Munn W.D.
Published: April 2009

A semigroup S with an involution * is called a special involution semigroup if and only if, for every finite nonempty subset T of S,

.

It is shown that a semigroup is inverse if and only if it is a special involution semigroup in which every element invariant under the involution is periodic. Other examples of special involution semigroups are discussed; these include free semigroups, totally ordered cancellative commutative semigroups and certain semigroups of matrices. Some properties of the semigroup algebras of special involution semigroups are also derived. In particular, it is shown that their real and complex semigroup algebras are semiprimitive.
Two graph-colouring games
Authors: Harary Frank , Tuza Zsolt
Published: April 2009

We introduce two graph-colouring 2-person games, and analyse who has a winning strategy on some specific graphs such as the Petersen graph, and paths and cycles of given length.
Polynomial density of commutative semigroups
Authors: Kisielewicz Andrzej , Newrly Norbert
Published: April 2009

An algebra is said to be polynomially n−dense if all equational theories extending the equational theory of the algebra with constants have a relative base consisting of equations in no more than n variables. In this paper, we investigate polynomial density of commutative semigroups. In particular, we prove that, for n > 1, a commutative semigroup is (n − 1)-dense if and only if its subsemigroup consisting of all n−factor-products is either a monoid or a union of groups of a bounded order. Moreover, a commutative semigroup is 0-dense if and only if it is a bounded semilattice. For semilattices, we give a full description of the corresponding lattices of equational theories.
On joint spectra of non-commuting normal operators
Authors: Pryde Alan J. , Sołtysiak Andrzej
Published: April 2009

The purpose of the paper is to show that the Harte spectrum and the bicommutant spectrum of an arbitrary n−tuple of normal Hilbert space operators can be obtained from the spectral set γ introduced by McIntosh and Pryde. It is also proved that many commonly used joint spectra of an n−tuple of normal m by m matrices are equal. These results are non-commutative variants of some theorems proved by McIntosh, Pryde, and Ricker for commuting sets of operators.
Asymptotic-norming and Mazur intersection properties in Bochner function spaces
Authors: Hu Zhibao , Lin Bor-Luh
Published: April 2009

A Banach space X has the asymptotic-norming property if and only if the Lebesgue-Bochner function space Lp (μ, X) has the asumptotic-norming property for p with 1 < p < ∞. It follows that a Banach space X is Hahn-Banach smooth if and only if Lp (μ, X) is Hahn-Banach smooth for p with 1 < p < ∞. We also show that for p with 1 < p < ∞, (1) if X has the compact Mazur intersection property then so does Lp(μ, X); (2) if the measure μ is not purely atomic, then the space Lp(μ, X) has the Mazur intersection property if and only if X is an Asplund space and has the Mazur intersection property.
On some p−estimates for Banach spaces
Authors: Kutzarova D. , Maluta E. , Prus S.
Published: April 2009

Relations between lp-type estimates of Khamsi and a uniform version of the Kadec-Klee property are studied. Khamsi's result on normal structure is strengthened.
Stability for some equations of mathematical biology and monotone flows
Authors: Fomenko Igor V.
Published: April 2009

The theory of monotone flows and operators is applied to study stable equilibria of autonomous cooperative systems and stable periodic solutions of periodic perturbations of these systems. The connection between analyticity and the property of asymptotic stability is established.
On co-FPF modules
Authors: Van Thuyet Le
Published: April 2009

A ring R is called right co-FPF if every finitely generated cofaithful right R-module is a generator in mod-R. This definition can be carried over from rings to modules. We say that a finitely generated projective distinguished right R-module P is a co-FPF module (quasi-co-FPF module) if every P-finitely generated module, which finitely cogenerates P, generates σ[P] (P, respectively). We shall prove a result about the relationship between a co-FPF module and its endomorphism ring, and apply it to study some co-FPF rings.
The Dunford-Pettis property on vector-valued continuous and bounded functions
Authors: Aguayo Jose , Sanchez Jose
Published: April 2009

Let X be a completely regular space, E a Banach space, Cb(X, E) the space of all continuous, bounded and E-valued functions defined on X, M(X, L(E, F)) the space of all L(E, F)-valued measures defined on the algebra generated by zero subsets of X. Weakly compact and β0-continuous operators defined from Cb(X, E) into a Banach space F are represented by integrals with respect to L(E, F)-valued measures. The strict Dunford-Pettis and the Dunford-Pettis properties are established on (Cb(X, E), βi), where βi denotes one of the strict topologies β0, β or β1, when E is a Schur space; the same properties are established on (Cb(X, E), β0), when E is an AM-space or an AL-space.
The invariants of orthogonal group actions
Authors: Chiang Li , Hung Yu-Ching
Published: April 2009

Let Fq be the finite field of order q, an odd number, Q a non-degenerate quadratic form on , O(n, Q) the orthogonal group defined by Q. Regard O(n, Q) as a linear group of Fq -automorphisms acting linearly on the rational function field Fq(x1, …, xn). We shall prove that the invariant subfield Fq(x1,…, xn)O(n, Q) is a purely transcendental extension over Fq for n = 5 by giving a set of generators for it.
Commutativity of (2 × 2) selfadjoint matrices
Authors: Ricker W.J.
Published: April 2009

An elementary proof is given of the fact that an n–tuple A = (A1, …, An) of self-adjoint matrices in a 2-dimensional Hilbert space consists of mutually commuting matrices Aj, 1 ≤ j ≤ n, if and only if γ(A) is non-empty. Here γ(A) ⊆ ℝn is the joint spectrum of A (in the sense of McIntosh and Pryde) consisting of those points β ∈ ℝn for which the matrix is not invertible.
Taylor expansions for continuous Stieltjes differential equations
Authors: Kloeden P.E. , Panadiwal J.
Published: April 2009

The general structure of Taylor expansions of functions of solutions of continuous Stieltjes differential equations is established. A compact formalism involving hierarchical sets of multi-indices and their associated remainder sets is used. The corresponding multiple Riemann-Stieltjes integrals of time and of the driving functions in the Stieltjes terms of the differential equations, necessarily of bounded variation and continuous here, appear in the expansions and their remainders.
On spanning surfaces of links
Authors: Hudson J.F.P.
Published: April 2009

In his paper on knot cobordism groups in codimension 2, Levine develops conditions for a knotted Sn in Sn+2 to bound a disc in Bn+3 In this paper some of his methods are extended to introduce a necessary condition for a classical link in S3 to bound a surface of specified genus in B4. In particular, this answers a question of Zeemann's about some links related to the ‘Mazur link’.
The centre and the depth of the centre of a tree map
Authors: Ye Xiangdong
Published: April 2009

Let X be a tree and f be a continuous map from X into itself. Denote by P(f) and R(f) the set of periodic points and the set of recurrent points of f respectively. We show in this note that the centre is and the depth of the centre is at most 3. Furthermore we have .
Linear mappings preserving square-zero matrices
Authors: Šemrl Peter
Published: April 2009

Let sln denote the set of all n × n complex matrices with trace zero. Suppose that ø: sln → sln is a bijective linear mapping preserving square-zero matrices. Then ø is either of the form ø(A) = cUAU-1 or ø(A) = cUAtU-1 where U is an invertible n × n matrix and c is a nonzero complex number. The same result holds if we assume that ø is a linear mapping preserving square-zero matrices in both directions. Applying this result we prove that a linear mapping ø defined on the algebra of all n × n matrices is an automorphism if and only if it preserves zero products in both directions and satisfies ø(I) = I. An extension of this last result to the infinite-dimensional case is considered.
Equivalents of Ekeland's principle
Authors: Oettli W. , Théra M.
Published: April 2009

In this note we present a new result which is equivalent to the celebrated Ekeland's variational principle, and a set of implications which includes a new non-convex minimisation principle due to Takahashi.
Local integral metrics and Daniell-Loomis integrals
Authors: Carrillo M. Diaz , Günzler H.
Published: April 2009

Recently Guerrero and the first author (Diaz Carrillo) proved an anologue to Daniell's extension process which works for arbitrary nonnegative linear functionals, without any continuity conditions. With the aid of Schäfke's local integral metrics we generalise this extension process and prove convergence theorems using a suitable local mean convergence, which can be traced back to Loomis.
On a resonance problem with nonlinearities of arbitrary polynomial growth
Authors: Ha Chung-Wei , Song Wen-Bing
Published: April 2009

We prove some existence theorems for solutions of a semilinear two point boundary value problem at resonance in which the nonlinear terms can have arbitrary polynomial growth in one of the directions ∞ or –∞, and are bounded in the other. The results are based on degree theoretic arguments and the Borsuk odd mapping theorem.
The minimal size of a square which includes a digital convex 2K–gon
Authors: Acketa Dragan M. , Žunić Joviša D.
Published: April 2009

This paper presents a construction of a digital convex 2k–gon (for a given natural number k), which can be inscribed into a square grid of the minimal possible size F(2k). An explicit expression for the function F(2k) is also given.
Landau-Kolmogorov inequality on a finite interval
Authors: Chen W.
Published: April 2009

A sharp Landau-Kolmogorov inequality on a finite interval is proved. The proof yields the known Landau-Kolmogorov inequality onRas a limiting case, and thus provides a new proof for that result.
Maximal elements and equilibria for u-majorised preferences
Authors: Tan Kok-Keong , Yuan Xian-Zhi
Published: April 2009

The purpose of this note is to give a general existence theorem for maximal elements for a new type of preference correspondences which are u-majorised. As an application, an existence theorem of equilibria for a qualitative game is obtained in which the preferences are u-majorised with an arbitrary (countable or uncountable) set of players and without compactness assumption on their domains in Hausdorff locally convex topological vector spaces.
When are dense subgroups of LCA groups closed under intersections?
Authors: Khan M.A.
Published: April 2009

Let G be a nondiscrete locally compact Hausdorff abelian group. It is shown that if G contains an open torsion subgroup, then every proper dense subgroup of G is contained in a maximal subgroup; while if G has no open torsion subgroup, then it has a dense subgroup D such that G/D is algebraically isomorphic to R, the additive group of reals. With each G, containing an open torsion subgroup, we associate the least positive integer n such that the nth multiple of every discontinuous character of G is continuous. The following are proved equivalent for a nondiscrete locally compact abelian group G:

(1) The intersection of any two dense subgroups of G is dense in G.

(2) The intersection of all dense subgroups of G is dense in G.

(3) G contains an open torsion subgroup, and for each prime p dividing the positive integer associated with G, pG is either open or a proper dense subgroup of G.

Finally, we construct a locally compact abelian group G with infinitely many dense subgroups satisfying the three equivalent conditions stated above.
Oscillation and nonoscillation of a delay differential equation
Authors: Kou Chunhai , Yan Weiping , Yan Jurang
Published: April 2009

In this paper, some necessary and sufficient conditions for oscillation of a first order delay differential equation with oscillating coefficients of the form

are established. Several applications of our results improve and generalise some of the known results in the literature.
On the divergence of Hermite-Fejér type interpolation with equidistant nodes
Authors: Mills T.M. , Smith Simon J.
Published: April 2009

If f(x) is defined on [−1, 1], let H¯1 n(f, x) denote the Lagrange interpolation polynomial of degree n (or less) for f which agrees with f at the n+1 equally spaced points xk, n = −1 + (2k)/n (0 ≤ k ≤ n). A famous example due to S. Bernstein shows that even for the simple function h(x) = │x│, the sequence H¯1 n (h, x) diverges as n → ∞ for each x in 0 < │x│ < 1. A generalisation of Lagrange interpolation is the Hermite-Fejér interpolation polynomial H¯mn (f, x), which is the unique polynomial of degree no greater than m(n + 1) – 1 which satisfies (f, Xk, n) = δo, pf(xk, n) (0 ≤ p ≤ m − 1, 0 ≤ k ≤ n). In general terms, if m is an even number, the polynomials H¯mn(f, x) seem to possess better convergence properties than the H¯1 n (f, x). Nevertheless, D.L. Berman was able to show that for g(x) ≡ x, the sequence H¯2n(g, x) diverges as n → ∞ for each x in 0 < │x│. In this paper we extend Berman's result by showing that for any even m, H¯mn(g, x) diverges as n → ∞ for each x in 0 < │x│ < 1. Further, we are able to obtain an estimate for the error │H¯mn(g, x) – g(x)│.
A note on Fréchet and approximate subdifferentials of composite functions
Authors: Jourani A. , Thibault L.
Published: April 2009

The aim of this note is to present in the reflexive Banach space setting a natural and simple proof of the formula of the approximate subdifferential of a composite function.
On connected transversals to Abelian subgroups
Authors: Niemenmaa Markku , Kepka Tomas
Published: April 2009

In this paper we investigate the situation where a group G has an abelian subgroup H with connected transversals. We show that if H is finite then G is solvable. We also investigate some special cases where the structure of H is very close to the structure of a cyclic group. Finally we apply our results to loop theory and we show that if the inner mapping group of a finite loop Q is abelian then Q is centrally nilpotent.
On weakly SI-modules
Authors: Van Sanh Nguyen
Published: April 2009

In this note we characterise finitely generated self-projectiveR-modulesMsatisfying the property that every non-zeroM-singular.R-module contains a non-zeroM-injective submodule.
Quantum double finite group algebras and link polynomials
Authors: Tsohantjis I. , Gould M.D.
Published: April 2009

Unitary representations of the braid group and corresponding link polynomials are constructed corresponding to each irreducible representation of a quantum double finite group algebra. Moreover the diagonal form of the braid generator is derived from which a general closed formula is obtained for link polynomials. As an example, link polynomials corresponding to certain induced representations of the symmetric group and its subgroups are determined explicitly.
Classification de Mahler et distances locales
Authors: Philippon Patrice
Published: April 2009

We consider the classifying set, denoted ℂ/˜ below, introduced by Mahler and we show that it can be endowed with non-discrete, Hausdorff topologies (even local distances) based on diophantine approximation properties of (complex) numbers. We then establish several results on the pointed topological space obtained, which could be dubbed Mahler's space (of first degree). We recover an analogue of Mahler's original classification by considering local distances to the special point (that is the class of all algebraic numbers). The main ingredients used here are diophantine properties in dimension zero over ℚ and non-standard analysis.
Minimax inequalities and generalisations of the Gale-Nikaido-Debreu Lemma
Authors: Tan Kok-Keong , Yu Jian
Published: April 2009

Some minimax inequalities are first proved both in the compact case and in the non-compact case using the concept of escaping sequences introduced by Border. Applications are given to deduce a generalisation of the Gale-Nikaido-Debreu Lemma due to Mehta and Tarafdar and to obtain a new generalisation of the Gale-Nikaido-Debreu Lemma from which the corresponding generalisation due to Grandmont is derived.
A geometrical representation theory for orthogonal arrays
Authors: Glynn David G.
Published: April 2009

Every orthogonal array of strength s and of prime-power (or perhaps infinite) order q, has a well-defined collection of ranks r. Having rank r means that it can be constructed as a cone cut by qs hyperplanes in projective space of dimension r over a field of order q.
Integrability and L-convergence of multiple trigonometric series
Authors: Chen Chang-Pao
Published: April 2009

It is proved that under the following condition, the sum f of the double trigonometric series with coefficients cjk is integrable and the rectangular partial sums smn(f, x, y) converge to f in L1 norm:

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On ring extensions of FSG rings
Authors: Van Thuyet Le
Published: April 2009

A ring R is called right FSG if every finitely generated right R-subgenerator is a generator. In this note we consider the question of when a ring extension of a given right FSG ring is right FSG and the converse. As a consequence we obtain some results about right FSG group rings.
Ideals generated by powers of elements
Authors: Anderson D.D. , Knopp Kent R. , Lewin Rebecca L.
Published: April 2009

For an ideal I in a commutative ring R we consider the ideal In = ({in | i ∈I}). We show that if n! is a unit in R, then In = In. We give an example of a doubly generated ideal I with Is not finitely generated.
Global dimension of factor rings
Authors: Hirano Yasuyuki , Park Jae Keol , Roggenkamp Klaus W.
Published: April 2009

Let R be a right Noetherian ring with right global dimension bounded by 2, which is integral over its centre, and let a be a regular non-unit element in R. Then R/a; R is right hereditary if and only if a; is not in the square of any maximal ideal of R. More generally, we compare for a right Noetherian ring R which is integral over its center, the global dimension of R with the global dimension of R/(a1R + a2R + … + arR) for a regular R-sequence {ai}, which will allow us to give a considerable extension of a result of Hillman.
On some geometry associated with a generalised Toda lattice
Authors: Vassiliou P.J.
Published: April 2009

We define the notion of Darboux integrability for linear second order partial differential operators,

.

We then build on certain geometric results of E. Vessiot related to the theory of Monge characteristics to show that the Darboux integrable operators L can be used to obtain a solution of the A2 Toda field theory. This solution is parametrised by four arbitrary functions. The approach presented in this paper thereby represents an alternative means of linearising the A2 Toda equations and may be contrasted with the known linearisation via the Lax pair.
Representation of finite groups as short products of subsets
Authors: Jia Xingde
Published: April 2009

Let M be a finite quasigroup of order n. For any integer k ≥ 2, let H(k, M) be the smallest positive integer h such that there exist h subsets Ai (i = 1, 2, …, h) such that Ai … Ah = M and |Ai| = k for every i = 1, 2, …, h. Define H(k, n) = max H(k, M). It is proved in this paper that

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Repelling invariant curves in planar discrete dynamical systems
Authors: Esquembre Francisco
Published: April 2009

Constructive, simple proofs for the existence, regularity, continuous dependence and dynamical properties of a repelling invariant curve for a discrete dynamical system of the plane with an attracting fixed point with real eigenvalues are given. These proofs can be used to generate a numerical algorithm to find these curves and to compute explicitly the dependence of the curve with respect to the system.
Ordered compactifications with countable remainders
Authors: Kent D.C. , Richmond T.A.
Published: April 2009

It is shown that if a partially-ordered topological space X admits a finite-point T2-ordered compactification, then it admits a countable T2-ordered compactification if and only if it admits n−point T2-ordered compactifications for all n beyond some integer m.
On completely principally injective rings
Authors: Nicholson W.K. , Yousif M.F.
Published: April 2009

A ring R is called right principally injective (right P-injective) if every R-linear map from a principal right ideal of R can be extended to R. If every ring homomorphic image of R is right P-injective, R is called completely right P-injective (right CP-injective). In this paper we characterise completely quasi-Frobenius rings in terms of CP-injectivity.
An abstract common fixed point principle and its applications
Authors: Jachymski Jacek R.
Published: April 2009

We establish a common fixed point principle for a commutative family of self-maps on an abstract set. This principle easily yields the Markoff-Kakutani theorem for affine maps, Kirk's theorem for nonexpansive maps and Cano's theorem for maps on the unit interval. As another application we obtain a new common fixed point theorem for a commutative family of maps on an arbitrary interval, which generalises an earlier result of Mitchell.
Generalised hessian, max function and weak convexity
Authors: Yang X. Q.
Published: April 2009

In this paper, a second-order characterisation of η-convex C1, 1 functions is derived in a Hilbert space using a generalised second-order directional derivative. Using this result it is then shown that every C1, 1 function is locally weakly convex, that is, every C1, 1 real-valued function f can be represented as f (x) = h (x) − η‖x‖2 on a neighbourhood of x where h is a convex function and η > 0. Moreover, a characterisation of the generalised second-order directional derivative for max functions is given.
On the Bellman equations with varying control
Authors: Koike Shigeaki
Published: April 2009

The value function is presented by minimisation of a cost functional over admissible controls. The associated first order Bellman equations with varying control are treated. It turns out that the value function is a viscosity solution of the Bellman equation and the comparison principle holds, which is an essential tool in obtaining the uniqueness of the viscosity solutions.
Unicity theorems for meromorphic or entire functions III
Authors: Yi Hong-Xun
Published: April 2009

This paper studies the unique range set of meromorphic functions and shows that the set S = {w | w13 + w11 + 1 = 0} is unique range set of meromorphic functions with 13 elements.
M-harmonic functions with M-harmonic square
Authors: Kim Hong Oh
Published: April 2009

ℳ-harmonic functions with ℳ-harmonic square are proved to be either holomorphic or antiholomorphic in the unit ball of complex n-space under certain additional conditions. For example, if u and u2 are ℳ-harmonic in the unit ball of ℂ2 and if u is continuously differentiable up to the boundary then u is either holomorphic or antiholomorphic.
Generalised discriminants
Authors: Woodcock C. F. , Graves-Morris P. R.
Published: April 2009

In this paper, we establish the generalized discriminant theorem governing uniqueness of symmetric polynomials in n variables of least total degree dn, k which vanish when any k + 1 of the variables are equal.
Degree of pointedness of a convex function
Authors: Seeger Alberto
Published: April 2009

A convex function f is said to be pointed if its epigraph has a recession cone which is pointed. Partial pointedness of f refers to the case in which such a recession cone is only partially pointed. In this note we show that the degree of pointedness of f is related to the “thickness” of the effective domain of the conjugate function f*.
The existence of bounded harmonic functions on C-H manifolds
Authors: Ding Qing , Zhou Detang
Published: April 2009

Let M be a Cartan-Hadamard manifold of dimension n (n ≥ 2). Suppose that M satisfies for every x > M outside a compact set an inequality:

where b, A are positive constants and A > 4. Then M admits a wealth of bounded harmonic functions, more precisely, the Dirichlet problem of the Laplacian of M at infinity can be solved for any continuous boundary data on Sn−1(∞).
A note on Hall closure of metanilpotent fitting classes
Authors: Menth Martin
Published: April 2009

Metanilpotent Lockett classes are Hall closed. There is an example of a supersoluble, not Hall closed Fitting class.
Essential covers and complements of radicals
Authors: Birkenmeier Gary F. , Wiegandt Richard
Published: April 2009

We show that a radical has a semisimple essential cover if and only if it is hereditary and has a complement in the lattice of hereditary radicals. In 1971 Snider gave a full description of supernilpotent radicals which have a complement. Recently Beidar, Fong, Ke, and Shum have determined radicals with semisimple essential covers. Using their results, we are able to provide a lower radical representation of complemented subidempotent radicals. This completes Snider's description of hereditary complemented radicals.
A note on strong geometric isolation in 3-orbitfolds
Authors: Calegari Danny
Published: April 2009

Neuman and Reid describe a 2-cusped hyperbolic 3-orbifold in which the cusps are geometrically isolated. Based on numerical evidence provided by Jeff Weeks' “SnapPea” program, they conjecture that the cusps are strongly geometrically isolated, a fact which we establish here. We also give a parameterisation of the Dehn Surgery Space of this orbifold which has amusing properties.
Global asymptotic stability of a periodic system of delay logistic equations
Authors: Ahlip R.A. , King R.R.
Published: April 2009

Sufficient conditions are obtained for the existence and global asymptotic stability of a periodic solution in Volterra's population system of integrodifferential equations with periodic coefficients. It is shown that if (i) the intraspecific negative feedbacks are instantaneous and dominate the interspecific effects (ii) the minimum possible growth rates are stronger than the maximum interspecific effects weighted with the respective sizes of all species, when they are near their potential maximum sizes, then the system of integrodifferential equations has a unique componentwise periodic solution which is globally asymptotically stable.
Duality map characterisations for Opial conditions
Authors: Dalby Tim , Sims Brailey
Published: April 2009

We characterise Opial's condition, the non-strict Opial condition, and the uniform Opial condition for a Banach space X in terms of properties of the duality mapping from X into X*.
Single identities for Mendelsohn and Steiner 3-quasigroups
Authors: Stojaković Zoran
Published: April 2009

We prove that varieties of algebras equivalent to Mendelsohn and Steiner quadruple systems can be defined by single identities.
Almost fixed point and best approximations theorems in H-spaces
Authors: Hadžić O.
Published: April 2009

Using the methods of KKM theory, almost fixed point and best approximations theorems in H-spaces are proved.
A characterisation of reflexive modules
Authors: Pardo José L. Gómez , Asensio Pedro A. Guil
Published: April 2009

We characterise reflexive modules over the rings R such that each finitely generated submodule of E(RR) is torsionless (left QF-3″ rings) by means of a suitable linear compactness condition relative to the Lambek torsion theory.
Remarks on bounded solutions of linear systems
Authors: Topuzu Elena , Topuzu Paul
Published: April 2009

In the case of continuous time systems with bounded operators (coefficients) the following result, of Perron type is well known: “The linear differential system ẋ = Ax + f(t) has, for every function f continuous and bounded on ℝ, a unique bounded solution on ℝ, if and only if the spectrum of the operator A has no points on the imaginary axis”.
Width-diameter relations for planar convex sets with lattice point constraints
Authors: Awyong Poh W. , Scott Paul R.
Published: April 2009

We obtain an inequality concerning the width and diameter of a planar convex set with interior containing no point of the rectangular lattice. We then use the result to obtain a corresponding inequality for a planar convex set with interior containing exactly two points of the integral lattice.
Oblique derivative problem for quasilinear elliptic equations with VMO coefficients
Authors: Di Fazio Guiseppe , Palagachev Dian K.
Published: April 2009

Strong solvability and uniqueness in the Sobolev space W2, q(Ω), q > n, are proved for the oblique derivative problem

assuming the coefficients of the quasilinear elliptic operator to be Carathéodory functions, aij ∈ VMO∩L∞ with respect to x, and b to grow at most quadratically with respect to the gradient.
Different methods of complex interpolation
Authors: Servidei Laura
Published: April 2009

We prove that the classic interpolation spaces of Calderón can be defined using spaces of functions that satisfy weaket conditions. For Calderón's second space we use a space of functions defined by Cwickel and Janson; we then modify their definition to find another space of functions which defines Calderón's first space.
Locally dyadic topological groups
Authors: Cleary Joan , Morris Sidney A.
Published: April 2009

A topological space is said to be locally dyadic if every neighbourhood of a point contains a dyadic neighbourhood of that point. It is proved here that every locally compact Hausdorff topological group is locally dyadic.
On an extension of a theorem of Sato
Authors: Yang Lian-Zhong
Published: April 2009

Let f(z) be a n-valued algebroid function of order λ(0 ≤ λ ≤ 1), Sato obtained an elliptic theorem for f(z) with a condition. In this paper, we prove that Sato's theorem is true without conditions and give a generalisation.
Calculus of variations in mean and convex Lagrangians, II
Authors: Blot Joël
Published: April 2009

We prove the Legendre Necessary Condition of the Calculus of Variations in Mean an arbitrary finite dimension. When the Lagrangian is convex, we establish that if the Euler-Lagrange equation possesses an almost periodic solution then it possesses periodic and constant solutions. We deduce from this fact various consequences on the structure of the set of almost periodic solutions.
A note on semi-homomorphisms of rings
Authors: Fong Y. , van Wyk L.
Published: April 2009

Huq presented a general study of semi-homomorphisms of rings, following, amongst others, Kaplansky's study of semi-automorphisnis of rings and Herstein's study of semi-homomorphisms of groups. Huq gave several “sufficient” conditions for a semi-homomorphism and a semi-monomorphism of rings to be a homomorphism and a monomorphism respectively. In this note we introduce semi-subgroups of groups, provide counterexamples to four of Huq's assertions and show how a minor, albeit forced, change to one of the conditions of the fourth assertion turns it into a special case of another theorem of Huq's.
A modified projection method for equations of the second kind: corrigendum and addendum
Authors: Nair M. Teamban
Published: April 2009

The author would like to correct an error in the statement of a result ‘in Bull. Aust. Math. Soc. 36 (1987) 485–492’ and also to incorporate an additional result.
An analogue of Kolmogorov's law of the iterated logarithm for arrays
Authors: Sung Soo Hak
Published: April 2009

This paper is concerned with the almost sure convergence for arrays of independent, but not necessarily identically distributed, random variables. We show that Kolmogorov's law of the iterated logarithm does not hold for arrays and obtain an analogue of Kolmogorov's law.
Measure convergent sequences in Lebesgue spaces and Fatou's lemma
Authors: Klei Heinz-Albrecht
Published: April 2009

Let (fn) be a sequence of positive P-integrable functions such that (∫ fndP)n converges. We prove that (fn) converges in measure to if and only if equality holds in the generalised Fatou's lemma. Let f∞ be an integrable function such that (∥fn − f∞∥1)n converges. We present in terms of the modulus of uniform integrability of (fn) necessary and sufficient conditions for (fn) to converge in measure to f∞.
Homogeneous Poisson structures
Authors: Malek F. , Abad A. Shafei Deh
Published: April 2009

In this paper we provide an algebraic definition for the Schouten product and give a decomposition for homogeneous Poisson structures in any n-dimensional vector space. A large class of n-homogeneous Poisson structures in ℝk is also characterised.