Black Holes, Cosmological Solutions, Future Singularities, and Their Thermodynamical Properties in Modified Gravity Theorie

54 p.

The Slow Search for Solutions: Lessons from Historical Energy Transitions by Sector and Service

28 p.

The propagation of nerve pulses: From the Hodgkin-Huxley model to the soliton theory

The present project aims to describe and study the nature and transmission of nerve pulses. First we review a classical model by Hodgkin-Huxley which describes the nerve pulse as a pure electric signal which propagates due to the opening of some time- and voltage-dependent ion channels. Although this model was quite successful when introduced, it fails to provide a satisfactory explanation to other phenomena that occur in the transmission of nerve pulses, therefore a new theory seems to be necessary. The soliton theory is one such theory, which we explain after introducing two topics that are important for its understanding: (i) the lipid melting of membranes, which are found to display nonlinearity and dispersion during the melting transition, and (ii) the discovery and the conditions required for the existence of solitons. In the soliton theory, the pulse is presented as an electromechanical soliton which forces the membrane through the transition while propagating. The action of anesthesia is also explained in the new framework by the melting point depression caused by anesthetics. Finally, we present a comparison between the two models.

Solutions for New Terrestrial Broadcasting Systems Offering Simultaneously Stationary and Mobile Services

221 p.

The role of H-bonds on the structure and dynamics of very concentrated polymer solutions

153 p.

Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial condition. The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points t(i) is an element of [t(0), t(J)] for i = 0, 1, . . . , J of the solution. Two examples are provided.

On Nonnegative Solutions of Fractional q-Linear Time-Varying Dynamic Systems with Delayed Dynamics

This paper is devoted to the investigation of nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic linear time-varying systems involving delayed dynamics with delays. The dynamic systems are described based on q-calculus and Caputo fractional derivatives on any order.

Distribution theory and fundamental solutions of differential operators

The objective of this dissertation is to study the theory of distributions and some of its applications. Certain concepts which we would include in the theory of distributions nowadays have been widely used in several fields of mathematics and physics. It was Dirac who first introduced the delta function as we know it, in an attempt to keep a convenient notation in his works in quantum mechanics. Their work contributed to open a new path in mathematics, as new objects, similar to functions but not of their same nature, were being used systematically. Distributions are believed to have been first formally introduced by the Soviet mathematician Sergei Sobolev and by Laurent Schwartz. The aim of this project is to show how distribution theory can be used to obtain what we call fundamental solutions of partial differential equations.