One Dimensional Models with a Singular Potential of the Type −<Emphasis Type="Italic">αδ</Emphasis>(<Emphasis Type="Italic">x</Emphasis>)+<Emphasis Type="Italic">βδ</Emphasis>′(<Emphasis Type="Italic">x</Emphasis>)

We study a one-dimensional singular potential plus two types of regular interactions: constant electric field and harmonic oscillator. In order to search for the bound state energies, we shall use the Lippman-Schwinger Green function technique. Another direct method will be mentioned for the harmonic oscillator. In the electric field case the unique bound state coincides with that found in an earlier study as the field is switched off. For non-zero field the ground state is shifted and positive energy “quasibound states” appear. The harmonic oscillator demonstrates the general result that for a symmetric potential the odd states are not altered whereas the even states energies are lowered or raised accordingly as the delta perturbation is attractive or repulsive. No states are created or annihilated.     

An adaptive pneumatic suspension based on the estimation of the excitation frequency

A pneumatic suspension that can adapt itself to the incoming vibration is presented in this paper. A switching control strategy between two different configurations is proposed and studied. The objective is to avoid undesirable resonant frequencies. The control procedure is based on the pre-knowledge of the incoming vibration frequency, and when this frequency is unknown, a very efficient prediction technique is used. The results show that the adaptable suspension has improved performance as compared to any of its passive counterparts. The transient response when switching typically takes less than three cycles and does not hinder the suspension performance.     

A metric space to study differences between polynucleotides

We introduce a new metric in the space of fuzzy polynucleotides.     

Crystallizability of ethylene homopolymers by crystallization analysis fractionation

The effect of molecular weight and long‐chain branching on the crystallization analysis fractionation (CRYSTAF) of ethylene homopolymers was investigated. Several ethylene homopolymers were prepared with different molecular weights and levels of long‐chain branching to isolate these effects from the dominant effect of comonomer content on crystallizability measured by CRYSTAF. Molecular weight effects might be significant for samples with number‐average molecular weights below 5000, but this effect can be corrected if terminal methyl groups are taken into account. Long‐chain branching has only a very small effect on the CRYSTAF profile of the samples investigated in this study. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1616–1628, 2001     

Symmetries of the heat equation on the lattice

Discrete versions of the heat equation on two-dimensional uniform lattices are shown to possess the same symmetry algebra as their continuum limits. Solutions with definite symmetry properties are presented.     

Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations

We prove some fixed point theorems in partially ordered sets, providing an extension of the Banach contractive mapping theorem. Having studied previously the nondecreasing case, we consider in this paper nonincreasing mappings as well as non monotone mappings. We also present some applications to first–order ordinary differential equations with periodic boundary conditions, proving the existence of a unique solution admitting the existence of a lower solution. Research partially supported by Ministerio de Educación y Ciencia and FEDER, Project MTM2004-06652-C03-01, and by Xunta de Galicia and FEDER, Projects PGIDIT02PXIC20703PN and PGIDIT05PXIC20702PN     

Extremal solutions of second order nonlinear periodic boundary value problems

We study a periodic boundary value problem for a nonlinear ordinary differential equation of second order when the nonlinearity is given by a Carathéodory function. We generalize the monotone iterative method to cover the fully nonlinear case.