Chains of Infinite Order, Chains with Memory of Variable Length, and Maps of the Interval

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we characterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval.

Enhancement of Nematic Order and Global Phase Diagram of a Lattice Model for Coupled Nematic Systems

We use an infinite-range Maier-Saupe model, with two sets of local quadrupolar variables and restricted orientations, to investigate the global phase diagram of a coupled system of two nematic subsystems. The free energy and the equations of state are exactly calculated by standard techniques of statistical mechanics. The nematic-isotropic transition temperature of system A increases with both the interaction energy among mesogens of system B, and the two-subsystem coupling J. This enhancement of the nematic phase is manifested in a global phase diagram in terms of the interaction parameters and the temperature T. We make some comments on the connections of these results with experimental findings for a system of diluted ferroelectric nanoparticles embedded in a nematic liquid-crystalline environment.

On abstract differential equations with nonlocal conditions involving the temporal derivative of the solution

In this paper we discuss the existence of solutions for a class of abstract differential equations with nonlocal conditions for which the nonlocal term involves the temporal derivative of the solution. Some concrete applications to parabolic differential equations with nonlocal conditions are considered. (C) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

IDM - A New Parallel Methodology to Calculate the Determinant of Matrices of the Order n, with Computational Complexity O(n)

This paper presents a new parallel methodology for calculating the determinant of matrices of the order n, with computational complexity O(n), using the Gauss-Jordan Elimination Method and Chio's Rule as references. We intend to present our step-by-step methodology using clear mathematical language, where we will demonstrate how to calculate the determinant of a matrix of the order n in an analytical format. We will also present a computational model with one sequential algorithm and one parallel algorithm using a pseudo-code.

On the generalized canonical equations of Hamilton for a time-dependent mass particle

Fundamental principles of mechanics were primarily conceived for constant mass systems. Since the pioneering works of Meshcherskii (see historical review in Mikhailov (Mech. Solids 10(5):32-40, 1975), efforts have been made in order to elaborate an adequate mathematical formalism for variable mass systems. This is a current research field in theoretical mechanics. In this paper, attention is focused on the derivation of the so-called 'generalized canonical equations of Hamilton' for a variable mass particle. The applied technique consists in the consideration of the mass variation process as a dissipative phenomenon. Kozlov's (Stek. Inst. Math 223:178-184, 1998) method, originally devoted to the derivation of the generalized canonical equations of Hamilton for dissipative systems, is accordingly extended to the scenario of variable mass systems. This is done by conveniently writing the flux of kinetic energy from or into the variable mass particle as a 'Rayleigh-like dissipation function'. Cayley (Proc. R Soc. Lond. 8:506-511, 1857) was the first scholar to propose such an analogy. A deeper discussion on this particular subject will be left for a future paper.

Analysis of elastic functionally graded materials under large displacements via high-order tetrahedral elements

The purpose of this study is to present a position based tetrahedral finite element method of any order to accurately predict the mechanical behavior of solids constituted by functionally graded elastic materials and subjected to large displacements. The application of high-order elements makes it possible to overcome the volumetric and shear locking that appears in usual homogeneous isotropic situations or even in non-homogeneous cases developing small or large displacements. The use of parallel processing to improve the computational efficiency, allows employing high-order elements instead of low-order ones with reduced integration techniques or strain enhancements. The Green-Lagrange strain is adopted and the constitutive relation is the functionally graded Saint Venant-Kirchhoff law. The equilibrium is achieved by the minimum total potential energy principle. Examples of large displacement problems are presented and results confirm the locking free behavior of high-order elements for non-homogeneous materials. (C) 2011 Elsevier B.V. All rights reserved.

EFFECT OF HEAD GROUP AND CURVATURE ON BINDING OF THE ANTIMICROBIAL PEPTIDE TRITRPTICIN TO LIPID MEMBRANES

In this work we examine the interaction between the 13-residue cationic antimicrobial peptide (AMP) tritrpticin (VRRFPWWWPFLRR, TRP3) and model membranes of variable lipid composition. The effect on peptide conformational properties was investigated by means of CD (circular dichroism) and fluorescence spectroscopies. Based on the hypothesis that the antibiotic acts through a mechanism involving toroidal pore formation, and taking into account that models of toroidal pores imply the formation of positive curvature, we used large unilamellar vesicles (LUV) to mimic the initial step of peptide-lipid interaction, when the peptide binds to the bilayer membrane, and micelles to mimic the topology of the pore itself, since these aggregates display positive curvature. In order to more faithfully assess the role of curvature, micelles were prepared with lysophospholipids containing (qualitatively and quantitatively) head groups identical to those of bilayer phospholipids. CD and fluorescence spectra showed that, while TRP3 binds to bilayers only when they carry negatively charged phospholipids. binding to micelles occurs irrespective of surface charge, indicating that electrostatic interactions play a less predominant role in the latter case. Moreover, the conformations acquired by the peptide were independent of lipid composition in both bilayers and micelles. However, the conformations were different in bilayers and in micelles, suggesting that curvature has an influence on the secondary structure acquired by the peptide. Fluorescence data pointed to an interfacial location of TRP3 in both types of aggregates. Nevertheless, experiments with a water soluble fluorescence quencher suggested that the tryptophan residues are more accessible to the quencher in micelles than in bilayers. Thus, we propose that bilayers and micelles can be used as models for the two steps of toroidal pore formation. (C) 2011 Elsevier Ireland Ltd. All rights reserved.

Previous illumination of a water soluble chlorine photosensitizer increases its cytotoxicity

Photodithazine (PDZ) is an N-methyl-D-glucosamine derivative of chlorine e6 that is water soluble and has an intense absorption in the range of 650-680 nm. PDZ photobleaching and photoproduct formation were induced by illumination with laser at two wavelengths: 514 nm (ion argon laser) as well as in 630 nm (dye laser). The time constants of PDZ photobleaching were: 18 min for 630 nm irradiation and 50 min for 514 nm irradiation, suggesting that degradation after irradiation with red light is faster than with green light. Photoproducts formation was evidenced by the appearance of a new absorption band at 668 nm with slight broaden of the Soret band, suggesting that there was no break of the macrocycle. The cytotoxicity of the photodegradated PDZ was investigated and showed to be lower in the dark and higher than non irradiated PDZ. These results may have important clinical implications for PDT such as the possibility to use the previously irradiated PDZ just before clinical application in order to get increased efficiency.

The tangential variation of a localized flux-type eigenvalue problem

In this work the differentiability of the principal eigenvalue lambda = lambda(1)(Gamma) to the localized Steklov problem -Delta u + qu = 0 in Omega, partial derivative u/partial derivative nu = lambda chi(Gamma)(x)u on partial derivative Omega, where Gamma subset of partial derivative Omega is a smooth subdomain of partial derivative Omega and chi(Gamma) is its characteristic function relative to partial derivative Omega, is shown. As a key point, the flux subdomain Gamma is regarded here as the variable with respect to which such differentiation is performed. An explicit formula for the derivative of lambda(1) (Gamma) with respect to Gamma is obtained. The lack of regularity up to the boundary of the first derivative of the principal eigenfunctions is a further intrinsic feature of the problem. Therefore, the whole analysis must be done in the weak sense of H(1)(Omega). The study is of interest in mathematical models in morphogenesis. (C) 2011 Elsevier Inc. All rights reserved.