On ω-limit Sets of Triangular Maps on the Unit Cube

We consider Sturm–Liouville eigenvalue problems of second order with arbitary seperated boundary conditions and perform a suitabl discretization of them. The obtained discrete Sturm–Liouville eigenvalue problems are examined and the asymptotic behavior of their eigenvalue as the norm of the partition tends to zero is investigated.     

Decomposition of pseudo-radioactive chemical products with a mathematical approach

The aim of this paper is to study the decomposition of pseudo–radioactive products that follow a dynamics determined by a trigonometric factor. In particular for maps of the form $e^{\cos (\pi t)}$ is proved that an asymptotic sampling recomposition property, generalizing the classical Shannon–Whittaker–Kotel’nikov Theorem, works.     

On the Lefschetz periodic point free continuous self-maps on connected compact manifolds

We characterize the Lefschetz periodic point free self-continuous maps on the following connected compact manifolds: CPn the n-dimensional complex projective space, HPn the n-dimensional quaternion projective space, Sn the n-dimensional sphere and Sp×Sq the product space of the p-dimensional with the q-dimensional spheres.     

A Toughness Condition for Fractional (k,m)-deleted Graphs Revisited

In computer networks, toughness is an important parameter which is used to measure the vulnerability of the network. Zhou et al. obtains a toughness condition for a graph to be fractional (k, m)-deleted and presents an example to show the sharpness of the toughness bound. In this paper, we remark that the previous example does not work and inspired by this fact, we present a new toughness condition for fractional (k, m)-deleted graphs improving the existing one. Finally, we state an open problem.     

Schauder Bases under Uniform Renormings

Let X be a separable superreflexive Banach space with a Schauder basis. We prove the existence of an equivalent uniformly smooth (resp. uniformly rotund) renorming under which the given basis is monotone. First author supported by the grants MTM2005-08379 of MECD (Spain), 00690/PI/04 of Fundación Séneca (CARM, Spain) and AP2003-4453 of MECD (Spain), Second author supported by AV0Z10190503 and A100190502.     

Nonwandering set of points of skew-product maps with base having closed set of periodic points

The aim of the present paper is to study the structure of the nonwandering set of points Ω() for the skew-product maps of the unit square , (x,y)→(f(x),g(x,y)), with base f having closed set of periodic points. For every and every point (x,y) with x periodic of period p_x by f and y not chain recurrent of F^p_x|_Ix, where , we prove that (x,y)Ω(F). On the other hand we construct a map with an isolated fixed point x₀ of f and y₀Ω(F|_Ix0) such that (x₀,y₀)Ω(F₀).     

Ranges of operators and derivatives

We show a unified method of proving the existence of C¹-Fréchet smooth and Lipschitz mappings which are surjective or whose range of the derivative contains the whole dual unit ball. As an application, under Martin's Maximum axiom, we obtain a complete result for those spaces with density character ω₁.     

A Bishop–Phelps–Bollobás type theorem for uniform algebras

This paper is devoted to showing that Asplund operators with range in a uniform Banach algebra have the Bishop–Phelps–Bollobás property, i.e., they are approximated by norm attaining Asplund operators at the same time that a point where the approximated operator almost attains its norm is approximated by a point at which the approximating operator attains it. To prove this result we use the weak^∗${}^{\ast }$-to-norm fragmentability of weak^∗${}^{\ast }$-compact subsets of the dual of Asplund spaces and we need to observe a Urysohn type result producing peak complex-valued functions in uniform algebras that are small outside a given open set and whose image is inside a Stolz region.