bluuebunny/crossref_metadata_2025 huggingface dataset:
Burnside rings of finite representation type
Authors: Raggi-Cárdenas Alberto
Published: April 2009

Let G be a finite group. It is proved that the localised Buinside ring Ωp(G) is of finite representation type if and only if for each p–perfect subgroup H of G, , where means the conjugacy class of K.
Approximation by Boolean sums of linear operators: Telyakovskiǐ-type estimates
Authors: Cao Jia-Ding , Gonska Heinz H.
Published: April 2009

In the present note we study the question: “Under which general conditions do certain Boolean sums of linear operators satisfy Telyakovskiǐ-type estimates?” It is shown, in particular, that any sequence of linear algebraic polynomial operators satisfying a Timan-type inequality can be modified appropriately so as to obtain the corresponding upper bound of the Telyakovskiǐ-type. Several examples are included.
The Stone-Čech compactification and weakly Fréchet spaces
Authors: King Deborah M. , Morris Sidney A.
Published: April 2009

This paper resulted from an attempt to answer questions like: does βP have a subspace homeomorphic to βQ and does βQ have a subspace homeomorphic to P, where P denotes the space of all irrational numbers. These questions are answered in the negative by providing the appropriate machinery which can also be applied to other examples. En route we prove that weakly Fréchet realcompact spaces have homeomorphic Stone-Čech compactifications if and only if they are homeomorphic.
Hermite-Fejér type interpolation and Korovkin's theorem
Authors: Knoop H.-B. , Locher F.
Published: April 2009

In this note we consider Hermite-Fejér interpolation at the zeros of Jacobi polynomials and with additional boundary conditions. For the associated Hermite-Fejér type operators and special values of α, β it was proved by the first author in recent papers that one has uniform convergence on the whole interval [−1,1]. The second author could show by introducing the concept of asymptotic positivity how to get the known convergence results for the classical Hermite-Fejér interpolation operators. In the present paper we show, using a slightly modified Bohman-Korovkin theorem for asymptotically positive functionals, that the Hermite-Fejér type interpolation polynomials , converge pointwise to f for arbitrary α, β > −1. The convergence is uniform on [−1 + δ,1 − δ].
Linear functionals on some weighted Bergman spaces
Authors: Marzuq Maher M.H.
Published: April 2009

The weighted Bergman space Ap, α, 0 < p < 1, a > −1 of analytic functions on the unit disc Δ in C is an F-space. We determine the dual of Ap, α explicitly.
Constante rectangle et biais d'un espace de Banach
Authors: Desbiens Jocelyn
Published: April 2009

We study in this paper the relations existing between Joly's rectangular constant (µ) and the degree of asymmetry of Birkhoff-James's orthogonality relation (β). New bounds on the variation of µ in terms of β and estimation of the values taken by β in the case of uniformly convex Banach spaces are given.
Regularity of locally convex surfaces
Authors: Schulz Friedmar
Published: April 2009

Interior estimates are derived for theC2,µ-Hölder norm of the radius vector X ∈C1, 1(Ω) of a locally convex surface Σ in terms of the first fundamental formIΣ, the Gauss curvatureKand the integral ∫ |H|dσ. HereHis the mean curvature of Σ. The coefficientsgijof IΣare assumed to belong to the Hölder classC2,µ(Ω) for someμ, 0 < μ < 1. A boundary condition is discussed which ensures an estimate for ∫ |H|dσ.
Subdirect product of PS-rings need not be PS
Authors: Xue Weimin
Published: April 2009

An associative ring R with identity is called a PS-ring if soc(RR) is projective. We construct a non- PS-ring R which is a subdirect product of two PS-rings, thus answering a question of Nicholson and Watters in the negative.
Some Banach space embeddings of classical function spaces
Authors: Carothers N.L. , Dilworth S.J.
Published: April 2009

Banach space embeddings of the Orlicz space Lp + Lq and the Lorentz space Lp, q into the Lebesgue-Bochner space Lr(ls) are demonstrated for appropriate ranges of the parameters.
On an angle between two rings
Authors: Rzadkowski Grzegorz
Published: April 2009

Jakóbczak and Mazur found the L2-angle between two concentric rings on the complex plane. In this note we investigate the same case but for spaces of square integrable functions with various weights. Moreover the continuity of the L2-angle for the Fock space is examined.
A factor theorem for locally convex differentiability spaces
Authors: Eyland Roger , Sharp Bernice
Published: April 2009

The main result of this paper is that a continuous convex function with domain in a locally convex space factors through a normed space. In a recent paper by Sharp, topological linear spaces are categorised according to the differentiability properties of their continuous convex functions; we show that under suitable conditions the classification is preserved by linear maps. A technique for deducing results for locally convex spaces from Banach space theory is an immediate consequence. Examples are given and Asplund C(S) spaces are characterised.
New criteria for meromorphic starlike univalent functions
Authors: Uralegaddi B.A. , Somanatha C.
Published: April 2009

This paper establishes new criteria for meromorphic starlike univalent functions of the form

Further property preserving integrals are considered.
A deformation lemma and some critical point theorems
Authors: Du Yihong
Published: April 2009

A new deformation lemma for functions satisfying the Palais-Smale condition on a real Banach space is obtained. This is used to deduce some critical point theorems which are extensions of some well known results.
The smooth variational principle and generic differentiability
Authors: Georgiev Pando Grigorov
Published: April 2009

A modified version of the smooth variational principle of Borwein and Preiss is proved. By its help it is shown that in a Banach space with uniformly Gâteaux differentiable norm every continuous function, which is directionally differentiable on a dense Gδ subset of the space, is Gâteaux differentiable on a dense Gδ subset of the space.
A generalised exchange theorem for matroid bases
Authors: Donald John , Tobey Malcolm
Published: April 2009

Let b and c be bases of a matroid. Then for any integer r, there exists an injection σ from r−subsets I of b to r-subsets σ(I) of c such that b – I + σ(I) is a base for all I. This result has implications for the structure of matroid base graphs.
On moment conditions for supremum of normed sums of martingale differences
Authors: Ahn Wi Chong , Choi Bong Dae , Sung Soo Hak
Published: April 2009

Let {Sn, n ≥ 1} denote the partial sum of sequence (Xn) of identically distributed martingale differences. It is shown that E|X1|q (lg |X1|)r < ∞ implies E(sup((lg n)pr/q/npr/q)|Sn|p) < ∞, where 1 < p < 2, p < q, r ∈ R and lg x = max{1, log+x} For the independent identically distributed case, the converse of the above statement holds.
An identity involving Nörlund polynomials
Authors: Özlük A.E. , Snyder C.
Published: April 2009

We prove an identity involving Nörlund polynomials, the proof of which is elementary and involves the enumeration of lattice points. The identity is slightly stronger than an identity of Carlitz which he obtained by using Apostol's transformation formula for Lambert series.
Corrigendum: How complete are categories of algebras
Authors: Adámek Jiří
Published: April 2009

Proposition 1.6 states that the category Alg(P*) is hypercomplete but non-compact. This is true, but the argument for non-compactness must be corrected as follows.

Let A be the category of algebras (X, x′, x″) where x′, x″: P*X → X are operations with x′(φ) = x″(φ), and homomorphisms are mappings which are P*-homomorphisms with respect to both operations. The embedding E: Alg(P*) → A with E(X, x) = (X, x, x) preserves colimits, although it is not a left adjoint. In fact, the preservation of colimits C = colim D is obvious in case C is finite, and for the infinite case the original argument presented in the paper is correct (namely, one of the colimit maps is onto). E is not a left adjoint because given A = (X, x′, x″) in A with X infinite and x′(M) ≠ x″(M) for any M ≠ φ, then there is no universal arrow into A with respect to E.
On quasicaustics and their logarithmic vector fields
Authors: Janeczko S.
Published: April 2009

Suppose F: (Cn+1 × Cp, 0) → (C, 0) is a germ of a holomorphic function, and (S, 0) ⊂ (Cn+1, 0) is a germ of some hypersurface in (Cn+1, 0). The quasicaustic Q(F) of F is defined as Q(F) = {a ∈ Cp; F(•, a) has a critical point on S}. We investigate the structure of quasicaustics corresponding to boundary singularities. The procedure for calculating the modules of logarithmic vector fields is given. The minimal set of generators for the Whitney's cross-cap singular variety is explicitly calculated.
Characterisation of drop and weak drop properties for closed bounded convex sets
Authors: Giles J.R. , Kutzarova Denka N.
Published: April 2009

Modifying the concept underlying Daneš' drop theorem, Rolewicz introduced the notion of the drop property of a norm which was later generalised to the weak drop property of a norm. Kutzarova extended the discussion to consider the drop property for closed bounded convex sets. Here we characterise the drop and weak drop properties for such sets by upper semi-continuous and compact valued subdifferential mappings.
On holomorphic differentials of some algebraic function field of one variable over C
Authors: Koo Ja Kyung
Published: April 2009

We give holomorphic differentials of some algebraic function field K of complex dimension one which is a generalisation of a hyperelliptic field.
Commutativity theorems for rings with polynomial constraints on certain subsets
Authors: Komatsu Hiroaki , Tominaga Hisao
Published: April 2009

We prove several commutativity theorems for unital rings with polynomial constraints on certain subsets, which improve and generalise the recent results of Grosen, and Ashraf and Quadri.
Discrete Wirtinger and isoperimetric type inequalities
Authors: Tang Dingyi
Published: April 2009

In this paper we give some new types of inequalities which can be regarded as discrete forms of the Wirtinger inequality and several new isoperimetric-type inequalities.
On the relative behaviour of moduli of smoothness
Authors: Zhou S.P.
Published: April 2009

Some general theorems concerning the relative behaviour of moduli of smoothness are established. In particular an open problem raised by Dickmeis, Nessel and van Wickeren is negated.
On the Cesàro-Perron integral
Authors: Bose M.K. , Ghosh B.
Published: April 2009

In the present paper a simple proof of a theorem of Sargent on CλP-integral of Burkill is given.
The Attouch-Wets topology and a characterisation of normable linear spaces
Authors: Holá Ľubica
Published: April 2009

Let X and Y be metric spaces and C(X, Y) be the space of all continuous functions from X to Y. If X is a locally connected space, the compact-open topology on C(X, Y) is weaker than the Attouch-Wets topology on C(X, Y). The result is applied on the space of continuous linear functions. Let X be a locally convex topological linear space metrisable with an invariant metric and X* be a continuous dual. X is normable if and only if the strong topology on X* and the Attouch-Wets topology coincide.
Commutativity conditions on rings
Authors: Misso Paola
Published: April 2009

We prove the following result: let R be an arbitrary ring with centre Z such that for every x, y ∈ R, there exists a positive integer n = n(x, y) ≥ 1 such that (xy)n − ynxn ∈ Z and (yx)n − xnyn ∈ Z; then, if R has no non-zero nil ideals, R is commutative. We also prove a result on commutativity of general rings: if R is r!-torsion free and for all x, y ∈ R, [xr, ys] = 0 for fixed integers r ≥ s ≥ 1, then R is commutative. As a corollary we obtain that if R is (n + 1)!-torsion free and there exists a fixed n ≥ 1 such that (xy)n − ynxn = (yx)n − xnyn ∈ Z for all x, y ∈ R, then R is commutative.
Positive solutions of a class of biological models in a heterogeneous environment
Authors: Ghoreishi Afshin , Logan Roger
Published: April 2009

In this paper we discuss existence of positive solutions to a general nonlinear elliptic system of reaction-diffusion equations representing a predator-prey or competition model of interaction between two species, in a heterogeneous environment. We also consider homogeneous Dirichlet and/or Robin boundary conditions. In the predator-prey case we give necessary and sufficient conditions for the existence of positive solutions, while in the competition case we give sufficient conditions. We use index theory in a positive cone to attack our problem and characterise our results by the sign of the first eigenvalues of certain Schrodinger type operators.
Relative normal-convexity and amalgamations
Authors: Brick Stephen G.
Published: April 2009

The notion of relative normal-convexity is introduced and its connection to equations over groups is studied. We study the effect on relative normal-convexity by free products, amalgamations, and HNN extensions.
Perturbations of a Hamiltonian family of cubic vector fields
Authors: Urbina A.M. , Cañas M. , de la Barra G. León , de la Barra M. León
Published: April 2009

This paper is related with the configurations of limit cycles for cubic polynomial vector fields in two variables (χ3).

It is an open question to decide whether every limit cycle configuration in χ3 can be obtained by perturbation of a corresponding Hamiltonian configuration of centres and graphs.

In this work, by considering perturbations of the Hamiltonian vector field XH = (Hy, − Hx), where H(x, y) = [a(x + h)2 + by2 − 1] [a(x − h)2 + by2 − 1], we make a global analysis of the possible cases.

The vector field XH has three centres (C−, C+ and the origin) and two saddles. By means of quadratic perturbations the centres become fine foci where C−and C+ have the same type of stability but opposed to that one of the origin and infinity. Further introducing cubic perturbations changes the stability of C−, C+ and the cycle at infinity and generates limit cycles. Lastly extra linear terms change the stability of the origin and generate another limit cycle.

Finally, we analyse the rupture of saddle connection of the Hamiltonian field under perturbation, via Melnikov's integral, in order to complete the study of the global phase portrait and to consider the possibility of new limit cycles emerging from the Hamiltonian graph.
An estimate of Ramanujan related to the greatest integer function
Authors: Bhargava S. , Adiga Chandrashekar , Somashekara D.D.
Published: April 2009

If a and n are positive integers and if ⌊⌋ is the greatest integer function we obtain upper and lower estimates for stated by Ramanujan in his notebooks.
Modules with the quasi-summand intersection property
Authors: Albrecht Ulrich , Hausen Jutta
Published: April 2009

Given a torsion-free abelian group G, a subgroup A of G is said to be a quasi-summand of G if nG ≤ A ⊕ B ≤ G for some subgroup B of G and some positive integer n. If the intersection of any two quasi-summands of G is a quasi-summand, then G is said to have the quasi-summand intersection property. This is a generalisation of the summand intersection property of L. Fuchs. In this note, we give a complete characterisation of the torsion-free abelian groups (in fact, torsion-free modules over torsion-free rings) with the quasi-summand intersection property. It is shown that such a characterisation cannot be given via endomorphism rings alone but must involve the way in which the endomorphism ring acts on the underlying group. For torsion-free groups G of finite rank without proper fully invariant quasi-summands however, the structure of its quasi-endomorphism ring QE(G) suffices: G has the quasi-summand intersection property if and only if the ring QE(G) is simple or else G is strongly indecomposable.
On rings generating atoms of lattices of special and supernilpotent radicals
Authors: France-Jackson Halina
Published: April 2009

This note is to indicate a nonsemiprime ring R such that the smallest supernilpotent (respectively special) radical containing the ring R is an atom of the lattice of all supernilpotent (respectively special) radicals. This gives a positive answer to Puczylowski's and Roszkowska's question.
On the Gauss map of minimal surfaces with finite total curvature
Authors: Ru Min
Published: April 2009

We prove that if a nonflat complete regular minimal surface immersed in Rn is of finite total curvature, then its Gauss map can omit at most (n – 1)(n + 2)/2 hyperplanes in general position in Pn–1 (ℂ).
A class of one-relator groups with centre
Authors: McCool James
Published: April 2009

Let the group H have presentation where m ≥ 3, pi ≥ 2 and (pi, pj) = 1 if i ≠ j. We show that H is a one-relator group precisely if H can be obtained from a suitable group 〈a, b; ap = bp〉 by repeated applications of a (two-stage) procedure consisting of applying central Nielsen transformations followed by adjoining a root of a generator. We conjecture that any one-relator group G with non-trivial centre and G/G′ not free abelian of rank two can be obtained in the same way from a suitable group 〈a, b; ap = bp〉.
Decompositions of dual discriminator varieties
Authors: Bignall R.J.
Published: April 2009

A necessary and sufficient condition for a dual discriminator variety to be the product of a discriminator variety and a dual discriminator variety is given, along with an example of such a variety.
Nonexistence of stable currents in submanifolds of a product of two spheres
Authors: Zhang Xue-shan
Published: April 2009

By using techniques of the calculus of variations in geometric measure theory, we investigate the nonexistence of stable integral currents in Sn1 × Sn2 and its immersed submanifolds. Several vanishing theorems concerning the homology group of these manifolds are established.
On strongly right bounded finite rings
Authors: Xue Weimin
Published: April 2009

An associative ring is called strongly right (left) bounded if every nonzero right (left) ideal contains a nonzero ideal. We prove that if R is a strongly right bounded finite ring with unity and the order |R| of R has no factors of the form p5, then R is strongly left bounded. This answers a question of Birkenmeier and Tucci.
A commutativity theorem for rings
Authors: Komatsu Hiroaki , Nishinaka Tsunekazu , Tominaga Hisao
Published: April 2009

We prove the following theorem: Let R be a ring, l a positive integer, and n a non-negative integer. If for each x, y ∈ R, either xy = yx or xy = xn f(y)x1 for some f(X) ∈ X2Z[X], then R is commutative.
Finite type pseudo-umbilical submanifolds in a hypersphere
Authors: Li Shi-Jie
Published: April 2009

The notion of finite type submanifolds was introduced by B.Y. Chen. In this article we study 2- and 3-type pseudo-umbilical submanifolds in a hypersphere. Two theorems in this respect are obtained.
Local minima of the Gauss curvature of a minimal surface
Authors: Yamashita Shinji
Published: April 2009

Let D be a domain in the complex ω-plane and let x: D → R3 be a regular minimal surface. Let M(K) be the set of points ω0 ∈ D where the Gauss curvature K attains local minima: K(ω0) ≤ K(ω) for |ω – ω0| < δ(ω0), δ(ω0) < 0. The components of M(K) are of three types: isolated points; simple analytic arcs terminating nowhere in D; analytic Jordan curves in D. Components of the third type are related to the Gauss map.
Minimal partial clones
Authors: Börner F. , Haddad L. , Pöschel R.
Published: April 2009

LetAbe a finite set. A partial clone on A is a composition closed set of operations containing all projections. It is well known that the partial clones on A, ordered by inclusion, form a lattice. We show that the minimal partial clones onAare:

(a) minimal clones of full operations or

(b) generated by partial projections defined on a totally reflexive and totally symmetric domain.
Extensions of certain results in Walsh-type equiconvergence
Authors: Bokhari M.A.
Published: April 2009

Two sequences of rational functions are constructed from different expansions of (tqn − 1)−1 and extensions of certain known results in the theory of Walsh-type equiconvergence are sought.
Holomorphic curves in the orthogonal twistor space
Authors: Talmadge Andy , Yang Kichoon
Published: April 2009

A complete description of holomorphic curves in the Hermitian symmetric space SO(6)/U(3) is given in terms of orthogonal differential invariants.
Duality in nonconvex vector minimum problems
Authors: Gulati T.R. , Talaat Nadia
Published: April 2009

A nonlinear vector minimum problem is considered. Duality theorems are proved for Mond-Weir type dual and their application to a certain nonlinear fractional vector minimum problem is discussed.
Oscillation of neutral delay differential equations
Authors: Yu Jianshe , Wang Zhicheng , Qian Chuanxi
Published: April 2009

Consider the following neutral delay differential equation

whereP∈ ℝ,T∈ (0, ∞), σ ∈ (0, ∞) andQ∈C[(t0, ∞), [0, ∞)]. We obtain a sufficient condition for the oscillation of all solutions of Equation (*) withP= −1, which does not require that

But, for the cases −1 <P< 0 andP< −1, we show that (**) is a necessary condition for the oscillation of all solutions of Equation (*). These new results solve some open problems in the literature.
On the additivity of unbounded set functions
Authors: Jefferies Brian
Published: April 2009

The set functions associated with Schrödinger's equation are known to be unbounded on the algebra of cylinder sets. However, there do exist examples of scalar valued set functions which are unbounded, yet σ-additive on the underlying algebra of sets. The purpose of this note is to show that the set functions associated with Schrödinger's equation are not σ-additive on cylinder sets. In the course of the proof, general conditions implying the non-σ-additivity of unbounded set functions are given.
A note on bounds on the minimum area of convex lattice polygons
Authors: Colbourn Charles J. , Simpson R.J.
Published: April 2009

The minimum area a(v) of a v–sided convex lattice polygon is known to satisfy . We conjecture that a(v) = cv3 + o(v3), for c a constant; we prove that , and that for some positive constant c, .
The moment spaces of normed linear spaces
Authors: Sejeeni Fowzi Ahmad , Badri Matooq Ahmad
Published: April 2009

For a linearly independent sequence in a normed linear space the moment space is defined. Basic properties of moment spaces are discussed as well as a necessary and sufficient condition for the moment space to be a closed subspace of l∞.
On normal covers of locally compact spaces
Authors: Yajima Yukinobu
Published: April 2009

In this paper, we deal with the following question: What kind of open covers are normal if they have cushioned open refinements? For this, we prove that an open cover consisting of members with compact closure is a desired one.
The gap between subspaces and perturbation of non-semi-Fredholm operators
Authors: Alvarez Jose A. , Alvarez Teresa , Gonzalez Manuel
Published: April 2009

We study a concept of stability under the gap of isomorphic properties of Banach spaces and apply it to obtain some results of stability under compact or small norm perturbation for non-semi-Fredholm operators with closed range.
Haar measure and compact right topological groups
Authors: Milnes Paul
Published: April 2009

The consideration of compact right topological groups goes back at least to a paper of Ellis in 1958, where it is shown that a flow is distal if and only if the enveloping semigroup of the flow is such a group (now called the Ellis group of the distal flow). Later Ellis, and also Namioka, proved that a compact right topological group admits a left invariant probability measure. As well, Namioka proved that there is a strong structure theorem for compact right topological groups. More recently, John Pym and the author strengthened this structure theorem enough to be able to establish the existence of Haar measure on a compact right topological group, a probability measure that is invariant under all continuous left and right translations, and is unique as such. Examples of compact right topological groups have been considered earlier. In the present paper, we give concrete representations of several Ellis groups coming from low dimensional nilpotent Lie groups. We study these compact right topological groups, and two others, in some detail, paying attention in particular to the structure theorem and Haar measure, and to the question: is Haar measure uniquely determined by left invariance alone? (It is uniquely determined by right invariance alone.) To assist in answering this question, we develop some sufficient conditions for a positive answer. We suspect that one of the examples, a compact right topological group coming from the Euclidean group of the plane, does not satisfy these conditions; we don't know if the question has a positive answer for this group.
Sharp error bounds for Newton-like methods under weak smoothness assumptions
Authors: Argyros Ioannis K.
Published: April 2009

We provide sufficient convergence conditions as well as sharp error bounds for Newton-like iterations which generalise a wide class of known methods for solving nonlinear equations in Banach space.
Positive solutions for a class of semilinear two-point boundary value problems
Authors: Sanchez Luis
Published: April 2009

We study the existence of positive solutions of the periodic, Neumann or Dirichlet problem for the semilinear equation u″ + f(t, u) = 0, 0 ≤ t ≤ T, where f is a Carathéodory function. Our assumptions in each case are such that the problem possesses a lower solution or an upper solution.
On polygonal products of finitely generated abelian groups
Authors: Kim Goansu
Published: April 2009

We prove that a polygonal product of polycyclic-by-finite groups amalgamating subgroups, with trivial intersections, is cyclic subgroup separable (hence, it is residually finite) if the amalgamated subgroups are contained in the centres of the vertex groups containing them. Hence a polygonal product of finitely generated abelian groups, amalgamating any subgroups with trivial intersections, is cyclic subgroup separable. Unlike this result, most polygonal products of four finitely generated abelian groups, with trivial intersections, are not subgroup separable (LERF). We find necessary and sufficient conditions for certain polygonal products of four groups to be subgroup separable.
Groups with a quotient that contains the original group as a direct factor
Authors: Hirshon Ron , Meier David
Published: April 2009

We prove that given a finitely generated group G with a homomorphism of G onto G × H, H non-trivial, or a finitely generated group G with a homomorphism of G onto G × G, we can always find normal subgroups N ≠ G such that G/N ≅ G/N × H or G/N ≅ G/N × G/N respectively. We also show that given a finitely presented non-Hopfian group U and a homomorphism φ of U onto U, which is not an isomorphism, we can always find a finitely presented group H ⊇ U and a finitely generated free group F such that φ induces a homomorphism of U * F onto (U * F) × H. Together with the results above this allows the construction of many examples of finitely generated groups G with G ≅ G × H where H is finitely presented. A finitely presented group G with a homomorphism of G onto G × G was first constructed by Baumslag and Miller. We use a slight generalisation of their method to obtain more examples of such groups.
Braid representations of periodic links
Authors: Lee Sang Youl , Park Chan-Young
Published: April 2009

In this paper, we study periodic braid representations of periodic links. It is shown that no 2-bridge non-fibred knot has a periodic braid representation and conditions under which periodic links are fibred are given. We give a construction of all periodic links over a fixed factor link.
Collections of sequences having the Ramsey property only for few colours
Authors: Landman Bruce M. , Wysocka Beata
Published: April 2009

A family 𝑐 of sequences has the r-Ramsey property if for every positive integer k, there exists a least positive integer g(r)(k) such that for every r-colouring of {1, 2, …, g(r)(k)} there is a monochromatic k-term member of 𝑐. For fixed integers m > 1 and 0 ≤ a < m, define a k-term a (mod m)-sequence to be an increasing sequence of positive integers {x1, …, xk} such that xi − xi−1 ≡ a (mod m) for i = 2, …, k. Define an m-a.p. to be an arithmetic progression where the difference between successive terms is m. Let be the collection of sequences that are either a(mod m)-sequences or m-a.p.'s. Landman and Long showed that for all m ≥ 2 and 1 ≤ a < m, has the 2-Ramsey property, and that the 2-Ramsey function , corresponding to k-term a(mod m)-sequences or n-term m-a.p.'s, has order of magnitude mkn. We show that does not have the 4-Ramsey property and that, unless m/a = 2, it does not have the 3-Ramsey property. In the case where m/a = 2, we give an exact formula for . We show that if a ≠ 0, there exist 4-colourings or 6-colourings (depending on m and a) of the positive integers which avoid 2-term monochromatic members of , but that there never exist such 3-colourings. We also give an exact formula for .
Tree sign pattern matrices that require zero eigenvalues
Authors: Chen Wei-Hsu , Chien Mao-Ting
Published: April 2009

We characterise tree sign pattern matrices that require at least k zero eigenvalues, and exactly k zero eigenvalues.
Quasi reflexivity and the sup of linear functionals
Authors: Jain P.K. , Arora K.K. , Sinha D.P.
Published: April 2009

Quasi reflexive Banach spaces are characterised among the weakly countably determined Asplund spaces, in terms of the cardinality of the sets of linearly independent bounded linear functionals each of which does not attain its supremum on the unit sphere.
Quadratic approximation of solutions for ordinary differential equations
Authors: Nieto Juan J.
Published: April 2009

We present a generalisation of the quasilinearisation method to obtain a monotone sequence of approximate solutions that converges quadratically to a solution of a nonlinear ordinary differential equation of order n ≥ 1.
A characterisation of Helices and Cornu spirals in real space forms
Authors: Arroyo J. , Barros M. , Garay O.J.
Published: April 2009

We classify unit speed curves contained in a real space form of arbitrary dimension Nm(c), whose mean curvature vector is proper for the Laplacian. Then we use these results to classify Hopf cylinders of S3 and semi-Riemannian Hopf cylinders of with proper mean curvature function.
Convexity at infinity and bounded harmonic functions
Authors: Borbély Albert
Published: April 2009

It is shown that a complete simply connected negatively curved manifold supports nontrivial bounded harmonic functions if the singular set of the ideal boundary is disconnected.
An action of the Klein four-group on the irrational rotation C*-algebra
Authors: Stacey P.J.
Published: April 2009

Explicit automorphisms of the irrational rotation algebra are constructed which are associated with the two 2 × 2 diagonal integer matrices of determinant −1. The fixed point algebra of the product of these two automorphisms is shown to be isomorphic to the fixed point algebra of the flip.
Equality algebras
Authors: Fearnley-Sander Desmond , Stokes Tim
Published: April 2009

As part of an attempt to capture abstractly the most fundamental properties of algebraic reasoning involving equality, we introduce the notion of an equality algebra. It is a universal algebra A endowed with a binary function =iA × A → L, where L is a meet-semilattice with top element 1, called internalised equality, and satisfying, for all x, y ∈ A,

1. (x =ix) = 1; and

2. (x =iy)f(x) = (x =iy)f(y), where f is any function A → L derived from the Operations on A, the semilattice operations, and = i.

We charecterise internalised equalities in terms of finetly many identities, give examples, and show that all are equivalent to internalised equalities defined in terms of congruences on the underlying algebra. In the special case in which A is an Abelian group or ring, the internalised equality is shown to be equivalent to the dual of a norm-like mapping taking values in semilattice.
On continuity of derivations and epimorphisms on some vector-valued group algebras
Authors: Garimella Ramesh V.
Published: April 2009

For a locally compact Abelian group G and a commutative Banach algebra B, let L1(G, B) be the Banach algebra of all Bochner integrable functions. We show that if G is compact and B is a nonunital Banach algebra without nontrivial zero divisors, then (i) all derivations on L1(G, B) are continuous if and only if all derivations on B are continuous, and (ii) each epimorphism from a Banach algebra X onto L1(G, B) is continuous provided every epimorphism from X onto B is continuous. If G is noncompact then every derivation on L1(G, B) and every epimorphism from a commutative Banach algebra onto L1(G, B) are continuous. Our results extend the results of Neumann and Velasco for nonunital Banach algebras.
The computational complexity of torsion-freeness of finitely presented groups
Authors: Lempp Steffen
Published: April 2009

We determine the complexity of torsion-freeness of finitely presented groups in Kleene's arithmetical hierarchy as -complete. This implies in particular that there is no effective listing of all torsion-free finitely presented groups, or of all non-torsion-free finitely presented groups.
Expansion of analytic functions of an operator in series of Faber polynomials
Authors: Hasson Maurice
Published: April 2009

Let T: B → B be a bounded linear operator on the complex Banach space B and let f(z) be analytic on a domain D containing the spectrum Sp(T) of T. Then f(T) is defined by

where C is a contour surrounding SP(T) and contained in D.
On the Biadjoint of Riesz-like homomorphisms on partially ordered vector spaces
Authors: Buskes Gerard , Summerville Jamie
Published: April 2009

We generalise to partially ordered vector spaces, with a new technique, Arendt's approach to Kim's characterisation of Riesz homomorphisms.
Distance for Bézier curves and degree reduction
Authors: Lee Byung-Gook , Park Yunbeom
Published: April 2009

An algorithmic approach to degree reduction of Bézier curves is presented. The algorithm is based on the matrix representations of the degree elevation and degree reduction processes. The control points of the approximation are obtained by the generalised least squares method. The computations are carried out by minimising the L2 and discrete l2 distance between the two curves.
An example of rank two symmetric Osserman space
Authors: Rakić Zoran
Published: April 2009

Recently, Blažić, Bokan and Rakić, obtained some classes of 4-dimensional Osserman pseudo-Riemannian manifolds. One of these is the class of rank 2 locally symmetric space endowed with an integrable para-quaternionic structure. In this paper we give an explicit construction of an example of a space of that kind.
Perturbed generalised Hamiltonian systems and some advection models
Authors: Li Jibin , Christie J.R. , Gopalsamy K.
Published: April 2009

In this paper, it is shown that the theory of perturbed generalised Hamiltonian systems provides an effective method for understanding the description of flow patterns of some three-dimensional flows. Firstly, theorems for the persistence of periodic solutions of three-dimensional generalised Hamiltonian systems under perturbation are given by developing Melnikov's method. Then, three different systems of three-dimensional steady fluid flows are discussed and the existence or non-existence of periodic solutions of these systems is proved.
Weighted diameters of complete sets of conjugate algebraic integers
Authors: Grandcolas Michel
Published: April 2009

In this work, we generalise the study of Favard's Problems to the weighted diameters of a complete set of conjugate algebraic integers, that is, the roots of an irreducible monic polynomial with coefficients in ℤ.
Remarks on James's distortion theorems
Authors: Dowling Patrick N. , Randrianantoanina Narcisse , Turett Barry
Published: April 2009

If a Banach space X contains a complemented subspace isomorphic to c0 (respectively, ℓ1), then X contains complemented almost isometric copies of c0 (respectively, ℓ1). If a Banach space X is such that X* contains a subspace isomorphic to L1[0, 1] (respectively, ℓ∞), then X* contains almost isometric copies of L1[0, 1] (respectively, ℓ∞).
Compact quantum groups and their corepresentations
Authors: Bui Huu Hung
Published: April 2009

A compact quantum group is defined to be a unital Hopf C*–algebra generated by the matrix elements of a family of invertible corepresentations. We present a version of the Tannaka–Krein duality theorem for compact quantum groups in the context of abstract categories; this result encompasses the result of Woronowicz and the classical Tannaka-Krein duality theorem. We construct the orthogonality relations (similar to the case of compact groups). The Plancherel theorem is then established.
Uniform property (K) and its related properties
Authors: Xu Hong-Kun , Marino Giuseppe
Published: April 2009

A Banach space X is said to have uniform property (K) if there exists a constant (k ∈ [0,1) such that whenever xn ⇀ 0, ∥xn∥ → 1, and we have lim sup ∥ym∥ ≤ k. This property is the uniform version of property (K) recently introduced by B. Sims (Bull. Austral. Math. Soc. 50(1994), 523–528). Sufficient conditions for uniform property (K) are given. Some examples are presented to separate various Banach space properties. Applications to nonlinear operators are also included.
Semi-symmetric ball-homogeneous spaces and a volume conjecture
Authors: Calvaruso G. , Vanhecke L.
Published: April 2009

We prove that semi-symmetric ball-homogeneous spaces are locally symmetric and we use this result to prove that a semi-symmetric Riemannian manifold such that the volume of each sufficiently small geodesic ball is the same as in a Euclidean space, is locally flat.
Approximating common fixed points of two nonexpansive mappings in Banach spaces
Authors: Atsushiba Sachiko , Takahashi Wataru
Published: April 2009

Let C be a nonempty closed convex subset of a real Banach space E and let S, T be nonexpansive mappings of C into itself. In this paper, we consider the following iteration procedure of Mann's type for approximating common fixed points of two mappings S and T:

where {αn is a sequence in [0,1]. Using some ideas in the nonlinear ergodic theory, we prove that the iterates converge weakly to a common fixed point of the nonexpansive mappings T and S in a uniformly convex Banach space which satisfies Opial's condition or whose norm is Fréchet differentiable.
Hausdorffness in varieties of topological groups
Authors: McPhail Carolyn E.
Published: April 2009

A variety of topological groupsis a class of (not necessarily Hausdorff) topological groups closed under the operations of forming subgroups, quotient groups and arbitrary products. It is well known that the class of groups underlying the topological groups contained in any variety of topological groups is a variety of groups. Much work on topological groups is restricted to Hausdorff topological groups and so it is relevant to know if the class of groups underlying Hausdorff topological groups inis a variety of groups. It is shown that this is not always the case. Indeed it is proved that this is not the case for an important proper class of varieties of topological groups.
On Godement's characterisation of amenability
Authors: Valette Alain
Published: April 2009

Motivated by a question related to the construction of the Baum-Connes analytical assembly map for locally compact groups, we refine a criterion of Godement for amenability: for a unimodular group G, our criterion says that G is amenable if and only if every compactly supported, positive-definite function has non-negative integral over G.
From real to complex sign pattern matrices
Authors: Eschenbach Carolyn A. , Hall Frank J. , Li Zhongshan
Published: April 2009

This paper extends some fundamental concepts of qualitative matrix analysis from sign pattern classes of real matrices to sign pattern classes of complex matrices. A complex sign pattern and its corresponding sign pattern class are defined in such a way that they generalize the definitions of a (real) sign pattern and its corresponding sign pattern class. A survey of several qualitative results on complex sign patterns is presented. In particular, sign nonsingular complex patterns are investigated. The type of region in the complex plane representing the distribution of the determinants of the matrices in the sign pattern class of a sign nonsingular complex pattern is identified. Cyclically nonnegative complex patterns and complex patterns that are signature similar to nonnegative patterns are characterized. Extensions of sign stable and sign semistable patterns from the real to the complex case are given. Results on ray patterns are also obtained. Finally, many open questions are mentioned.
A closed simplicial model category for proper homotopy and shape theories
Authors: García-Calcines J.M. , Garcia-Pinillos M. , Hernández-Paricio L.J.
Published: April 2009

In this paper, we introduce the notion of exterior space and give a full embedding of the category P of spaces and proper maps into the category E of exterior spaces. We show that the category E admits the structure of a closed simplicial model category. This technique solves the problem of using homotopy constructions available in the localised category HoE and in the “homotopy category” π0E, which can not be developed in the proper homotopy category.

On the other hand, for compact metrisable spaces we have formulated sets of shape morphisms, discrete shape morphisms and strong shape morphisms in terms of sets of exterior homotopy classes and for the case of finite covering dimension in terms of homomorphism sets in the localised category.

As applications, we give a new version of the Whitehead Theorem for proper homotopy and an exact sequence that generalises Quigley's exact sequence and contains the shape version of Edwards-Hastings' Comparison Theorem.
On a question of Gross concerning uniqueness of entire functions
Authors: Yi Hong-Xun
Published: April 2009

In this paper, we prove that there exist two finite sets S1 (with 1 element) and S2 (with 3 elements) such that any two entire functions f and g satisfying Ef(Sj) = Eg(Sj) for j = 1, 2 must be identical. This answers a question posed by Gross. Examples are provided to show that this result is sharp.
Curves with continuous Curvatures in Euclidean spaces
Authors: Ushakov Vitaly
Published: April 2009

A class of curves of minimal smoothness for which one can build the Frenet frame, Frenet's formulae and osculating planes is described.
Structural implications of norms with Hölder right-hand derivatives.
Authors: Bartlett Michael O. , Giles John R. , Vanderwerff Jon D.
Published: April 2009

We study a nonsmooth extension of Gateaux differentiability satisfying a directional Hölder condition. In particular, we show that a Banach space is an Asplund space if it has an equivalent norm with a directionally Hölder right-hand derivative at each point of its sphere.
On the conjecture of Jesmanowicz concerning Pythagorean triples
Authors: Deng Moujie , Cohen G.L.
Published: April 2009

Let a, b, c be relatively prime positive integers such that a2 + b2 = c2. Jeśmanowicz conjectured in 1956 that for any given positive integer n the only solution of (an)x + (bn)y = (en)z in positive integers is x = y = z = 2. Building on the work of earlier writers for the case when n = 1 and c = b + 1, we prove the conjecture when n > 1, c = b + 1 and certain further divisibility conditions are satisfied. This leads to the proof of the full conjecture for the five triples (a, b, c) = (3, 4, 5), (5, 12, 13), (7, 24, 25), (9, 40, 41) and (11, 60, 61).
Integral points on elliptic curves over function fields of positive characteristic
Authors: Pacheco Amílcar
Published: April 2009

Let K be a one variable function field of genus g defined over an algebraically closed field k of characteristic p > 0. Let E/K be a non-constant elliptic curve. Denote by MK the set of places of K and let S ⊂ MK be a non-empty finite subset.

Mason in his paper “Diophantine equations over function fields” Chapter VI, Theorem 14 and Voloch in “Explicit p-descent for elliptic curves in characteristic p” Theorem 5.3 proved that the number of S-integral points of a Weiertrass equation of E/K defined over RS is finite. However, no explicit upper bound for this number was given. In this note, under the extra hypotheses that E/K is semi-stable and p > 3, we obtain an explicit upper bound for this number for a certain class of Weierstrass equations called S-minimal.
Time averages for continuous functions on distal flows
Authors: Núñez Carmen
Published: April 2009

We study the time averages of continuous functions along the trajectories of the distal projective flow induced by an ergodic family of Schrödinger equations. General conditions guaranteeing that the set of nonconvergence points is a residual subset are found. Applications to the study of the ergodic structure of the projective flow are given.
Elementary equivalence for finitely generated nilpotent groups and multilinear maps
Authors: Oger Francis
Published: April 2009

We show that two finitely generated finite-by-nilpotent groups are elementarily equivalent if and only if they satisfy the same sentences with two alternations of quantifiers. For each integer n ≥ 2, we prove the same result for the following classes of structures:

(1) the (n + 2)-tuples (A1, …, An+1, f), where A1, …, An+1 are disjoint finitely generated Abelian groups and f: A1 × … × An → An+1 is a n-linear map;

(2) the triples (A, B, f), where A, B are disjoint finitely generated Abelian groups and f: An → B is a n-linear map;

(3) the pairs (A, f), where A is a finitely generated Abelian group and f: An → A is a n-linear map.

In the proof, we use some properties of commutative rings associated to multilinear maps.
Polynomial equations for matrices over finite fields
Authors: Hua Jiuzhao
Published: April 2009

Let E(x) be a monic polynomial over the finite field q of q elements. A formula for the number of n × n matrices θ over q, satisfying E(θ) = 0 is obtained by counting the representations of the algebra q[x]/(E(x)) of degree n. This simplifies a formula of Hodges.
Two amalgams related to the alternating group on six letters
Authors: Papadopoulos Panagiotis
Published: April 2009

A characterisation is given of some of the parabolics found in Co3, and SP4 (9) using the amalgam method.
Some applications of Wedderburn's factorisation theorem
Authors: Segev Yoav
Published: April 2009

The structure of finite quotients of “large” subgroups of the multiplicative group of a finite dimensional division algebra is interesting and is related to the Margulis-Platonov conjecture. We develop machinery to handle such quotients and we conjecture that finite quotients of the multiplicative group of a finite dimensional division algebra are solvable. The proofs rely on Wedderburn's Factorisation Theorem.
Some results on coincidence points
Authors: Latif Abdul , Tweddle Ian
Published: April 2009

In this paper we prove some coincidence point theorems for nonself single-valued and multivalued maps satisfying a nonexpansive condition. These extend fixed point theorems for multivalued maps of a number of authors.
Chain recurrent points of a tree map
Authors: Li Tao , Ye Xiangdong
Published: April 2009

We generalise a result of Hosaka and Kato by proving that if the set of periodic points of a continuous map of a tree is closed then each chain recurrent point is a periodic one. We also show that the topological entropy of a tree map is zero if and only if thew-limit set of each chain recurrent point (which is not periodic) contains no periodic points.
Uniformly convexifying operators in classical Banach spaces
Authors: Basallote Manuela , Contreras Manuel D. , Díaz-Madrigal Santiago
Published: April 2009

We obtain a new characterisation of finite representability of operators and present new results about uniformly convexifying, Rademacher cotype and Rademacher type operators on some classical Banach spaces, including JB* -triples and spaces of analytic functions.