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.

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.

Depression of Serotonin Synaptic Transmission by the Dopamine Precursor L-DOPA

Imbalance between the dopamine and serotonin (5-HT) neurotransmitter systems has been implicated in the comorbidity of Parkinson's disease (PD) and psychiatric disorders. L-DOPA, the leading treatment of PD, facilitates the production and release of dopamine. This study assessed the action of L-DOPA on monoamine synaptic transmission in mouse brain slices. Application of L-DOPA augmented the D2-receptor-mediated inhibitory postsynaptic current (IPSC) in dopamine neurons of the substantia nigra. This augmentation was largely due to dopamine release from 5-HT terminals. Selective optogenetic stimulation of 5-HT terminals evoked dopamine release, producing D2-receptor-mediated IPSCs following treatment with L-DOPA. In the dorsal raphe, L-DOPA produced a long-lasting depression of the 5-HT1A-receptor-mediated IPSC in 5-HT neurons. When D2 receptors were expressed in the dorsal raphe, application of L-DOPA resulted in a D2-receptor-mediated IPSC. Thus, treatment with L-DOPA caused ectopic dopamine release from 5-HT terminals and a loss of 5-HT-mediated synaptic transmission.

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.