Highly Conjugated Bis(benzo[b]phosphole)-P-oxides: Synthesis and Electrochemical,Optical, and Computational Studies

The first examples of a π-conjugated benzo[b]phosphole P-oxide in which two phosphole P-oxide units are connected by a carbon-carbon double bond are described. The molecules are synthesized as E isomers with respect to the carbon-carbon double bond and exist as stable cis and trans isomers (chiral and meso one respectively) relatively to the two stereogenic P atoms. The optical and electrochemical properties of both isomers have been investigated by experiment and computations.     

The Cu- and Zn-complex-catalyzed methanolysis of the chemical warfare nerve agents soman,sarin, and VX

The catalytic methanolysis of the chemical warfare nerve agents soman, sarin, and VX was investigated by using Cu or Zn complexes. Although VX withstood decontamination, the decomposition yield being around 96%, the soman and sarin deposited on different surfaces were almost fully destroyed under ambient conditions. The catalytic tests performed on a wide range of contaminated surfaces confirm the activity of the investigated catalytic systems, these complexes being suitable, from an economical point of view, for use in the formulation of a possible decomposition kit with military or civilian applicability.     

Collision and escape orbits in a generalized Hénon–Heiles model

The motion of a material point of unit mass in a field determined by a generalized Hénon–Heiles potential $U=A{q}_1^2+B{q}_2^2+C{q}_1^2{q}_2+D{q}_2^3$, with $(q_1,q_2)=$ standard Cartesian coordinates and $(A,B,C,D)\in {(0,\infty )}^2\times R^2$, is addressed for two limit situations: collision and escape. Using McGehee-type transformations, the corresponding collision and infinity boundary manifolds pasted on the phase space are determined. These are fictitious manifolds, but, due to the continuity with respect to initial data, their flow determines the near by orbit behaviour.The dynamics on the collision and infinity manifolds is fully described. The topology of the flow on the collision manifold is independent of the parameters. In the full phase space, while spiraling collision orbits are present, most of the orbits avoid collision. The topology of the flow on the infinity manifold changes as the ratio between $C$ and $D$ varies. More precisely, there are two symmetric pitchfork bifurcations along the line $2C?3D=0$, due to the reshaping of the potential along the bifurcation line. Besides rectilinear and spiraling orbits, the near-escape dynamics includes oscillatory orbits, for which angular momentum alternates sign.     

Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces

In this paper we introduce the concept of a tripled coincidence point for a pair of nonlinear contractive mappings F : X³ → X and g : X → X. The obtained results extend recent coincidence theorems due to ?iri? and Lakshmikantham [V. Lakshmikantham, L. ?iri?, L., Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009) 4341-4349].     

A common fixed point theorem for compatible quasi contractive self mappings in metric spaces

A common fixed point theorem for weakly commuting quasi contractive self mappings with contracting orbital diameters in metric spaces [V. Berinde, A common fixed point theorem for quasi contractive type mappings, Ann. Univ. Sci. Budapest. 46 (2003) 81-90] is extended to the more general class of compatible quasi contractive self mappings. Our result does extend and generalize numerous related results in literature.     

Exponential Stability in Mean Square for a General Class of Discrete-Time Linear Stochastic Systems

Abstract

The problem of the mean square exponential stability for a class of discrete-time linear stochastic systems subject to independent random perturbations and Markovian switching is investigated. The case of the linear systems whose coefficients depend both to present state and the previous state of the Markov chain is considered. Three different definitions of the concept of exponential stability in mean square are introduced and it is shown that they are not always equivalent. One definition of the concept of mean square exponential stability is done in terms of the exponential stability of the evolution defined by a sequence of linear positive operators on an ordered Hilbert space. The other two definitions are given in terms of different types of exponential behavior of the trajectories of the considered system. In our approach the Markov chain is not prefixed. The only available information about the Markov chain is the sequence of probability transition matrices and the set of its states. In this way one obtains that if the system is affected by Markovian jumping the property of exponential stability is independent of the initial distribution of the Markov chain.

The definition expressed in terms of exponential stability of the evolution generated by a sequence of linear positive operators, allows us to characterize the mean square exponential stability based on the existence of some quadratic Lyapunov functions.

The results developed in this article may be used to derive some procedures for designing stabilizing controllers for the considered class of discrete-time linear stochastic systems in the presence of a delay in the transmission of the data.     

Full Nuclear Cones and a Relation Between Strong Optimization and Pareto Efficiency

In this paper we present some new and pertinent connections between the Strong Optimization and the Approximate Pareto type Efficiency, in particular, with the usual Vector Optimization, at first in the Ordered Vector Spaces by the natural Convex Cones and, afterwards, in the Ordered Hausdorff Locally Convex Spaces. The main result is obtained considering the notion of full nuclear cone. Our results, is related to an appropriate scalarization method Mathematics Subject Classification (2000). 90C29     

A bivariate non-homogeneous birth and death model for predator–prey interactions

We propose a bivariate non-homogeneous birth and death process as a model for predator–prey interactions. Its expectation is periodic, as it is a solution to the classical Lotka–Volterra system. Moreover, the mean age at extinction, as defined in Kendall (1948), is infinite.     

Multiple nontrivial solutions for nonlinear periodic problems with the p-Laplacian

We consider a nonlinear periodic problem driven by the scalar p-Laplacian with a nonsmooth potential (hemivariational inequality). Using the degree theory for multivalued perturbations of (S)₊-operators and the spectrum of a class of weighted eigenvalue problems for the scalar p-Laplacian, we prove the existence of at least three distinct nontrivial solutions, two of which have constant sign.