On stability of differential equations with piecewise constant argument using dichotomic maps

This paper deals with the study of the basic theory of existence, uniqueness and continuation of solutions of di®erential equations with piecewise constant argument. Results about asymptotic stability of the equation x(t) =-bx(t) + f(x([t])) with argu- ment [t], where [t] designates the greatest integer function, are established by means of dichotomic maps. Other example is given to illustrate the application of the method. Copyright © 2011 Watam Press.

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

We consider a charged Brownian gas under the influence of external and non-uniform electric, magnetic and mechanical fields, immersed in a non-uniform bath temperature. With the collision time as an expansion parameter, we study the solution to the associated Kramers equation, including a linear reactive term. To the first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle density, a Smoluchowski- reactive like equation; for the particle's momentum density, a generalized Ohm's-like equation; and for the particle's energy density, a MaxwellCattaneo-like equation. Defining a nonequilibrium temperature as the mean kinetic energy density, and introducing Boltzmann's entropy density via the one particle distribution function, we present a complete thermohydrodynamical picture for a charged Brownian gas. We probe the validity of the local equilibrium approximation, Onsager relations, variational principles associated to the entropy production, and apply our results to: carrier transport in semiconductors, hot carriers and Brownian motors. Finally, we outline a method to incorporate non-linear reactive kinetics and a mean field approach to interacting Brownian particles. © 2011 Elsevier B.V. All rights reserved.

A generalized Riemann- Stieltjes integral on time scales and discontinuous dynamical equations

This paper is concerned with a generalization of the Riemann- Stieltjes integral on time scales for deal with some aspects of discontinuous dynamic equations in which Riemann-Stieltjes integral does not works. © 2011 Academic Publications.

State Dependent Riccati Equation (SDRE) control method applied in cancellation of a parametric resonance in a magnetically levitated body

Here, a simplified dynamical model of a magnetically levitated body is considered. The origin of an inertial Cartesian reference frame is set at the pivot point of the pendulum on the levitated body in its static equilibrium state (ie, the gap between the magnet on the base and the magnet on the body, in this state). The governing equations of motion has been derived and the characteristic feature of the strategy is the exploitation of the nonlinear effect of the inertial force associated, with the motion of a pendulum-type vibration absorber driven, by an appropriate control torque [4]. In the present paper, we analyzed the nonlinear dynamics of problem, discussed the energy transfer between the main system and the pendulum in time, and developed State Dependent Riccati Equation (SDRE) control design to reducing the unstable oscillatory movement of the magnetically levitated body to a stable fixed point. The simulations results showed the effectiveness of the (SDRE) control design. Copyright © 2011 by ASME.

A set of linear equations to calculate the steady-state operation of an electrical distribution system

In this paper, the calculation of the steady-state operation of a radial/meshed electrical distribution system (EDS) through solving a system of linear equations (non-iterative load flow) is presented. The constant power type demand of the EDS is modeled through linear approximations in terms of real and imaginary parts of the voltage taking into account the typical operating conditions of the EDS's. To illustrate the use of the proposed set of linear equations, a linear model for the optimal power flow with distributed generator is presented. Results using some test and real systems show the excellent performance of the proposed methodology when is compared with conventional methods. © 2011 IEEE.

On the periodic solutions of a class of duffing differential equations

In this work we study the periodic solutions, their stability and bifurcation for the class of Duffing differential equation mathematical equation represented where C > 0, ε > 0 and Λ are real parameter, A(t), b(t) and h(t) are continuous T periodic functions and ε is sufficiently small. Our results are proved using the averaging method of first order.

DBI equations and holographic dc conductivity

We provide a simple method for writing the Dirac-Born-Infeld equations of a Dp-brane in an arbitrary static background whose metric depends only on the holographic radial coordinate z. Using this method we revisit the Karch-O'Bannon procedure to calculate the dc conductivity in the presence of constant electric and magnetic fields for backgrounds where the boundary is four- or three-dimensional and satisfies homogeneity and isotropy. We find a frame-independent expression for the dc conductivity tensor. For particular backgrounds we recover previous results on holographic metals and strange metals. © 2013 American Physical Society.

Effective gravitational equations for f(R) braneworld models

The viability of achieving gravitational consistent braneworld models in the framework of a f(R) theory of gravity is investigated. After a careful generalization of the usual junction conditions encompassing the embedding of the 3-brane into a f(R) bulk, we provide a prescription giving the necessary constraints in order to implement the projected second-order effective field equations on the brane. © 2013 American Physical Society.

Conformally and gauge invariant spin-2 field equations

Using an approach based on the Casimir operators of the de Sitter group, conformally invariant equations for a fundamental spin-2 field are obtained, and their consistency is discussed. It is shown that only when the spin-2 field is interpreted as a 1-form assuming values in the Lie algebra of the translation group, rather than a symmetric second-rank tensor, the field equation is both conformally and gauge invariant. © 2013 Pleiades Publishing, Ltd.

Development of equations to estimate microbial contamination in ruminal incubation residues of forage produced under tropical conditions using 15N as a label1

The objective of this study was to use 15N to label microbial cells to allow development of equations for estimating the microbial contamination in ruminal in situ incubation residues of forage produced under tropical conditions. A total of 24 tropical forages were ruminal incubated in 3 steers at 3 separate times. To determine microbial contamination of the incubated residues, ruminal bacteria were labeled with 15N by continuous intraruminal infusion 60 h before the first incubation and continued until the last day of incubation. Ruminal digesta was collected for the isolation of bacteria before the first infusion of 15N on adaptation period and after the infusion of 15N on collection period. To determine the microbial contamination of CP fractions, restricted models were compared with the full model using the model identity test. A value of the corrected fraction A was estimated from the corresponding noncorrected fraction by this equation: Corrected A fraction (ACPC) = 1.99286 + 0.98256 × A fraction without correction (ACPWC). The corrected fraction B was estimated from the corresponding noncorrected fraction and from CP, NDF, neutral detergent insoluble protein (NDIP), and indigestible NDF (iNDF) using the equation corrected B fraction (BCPC) = -17.2181 - 0.0344 × fraction B without correction (BCPWC) + 0.65433 × CP + 1.03787 × NDF + 2.66010 × NDIP - 0.85979 × iNDF. The corrected degradation rate of B fraction (kd)was estimated using the equation corrected degradation rate of B fraction (kdCPC) = 0.04667 + 0.35139 × degradation rate of B fraction without correction (kdCPWC) + 0.0020 × CP - 0.00055839 × NDF - 0.00336 × NDIP + 0.00075089 × iNDF. This equation was obtained to estimate the contamination using CP of the feeds: %C = 79.21 × (1 - e-0.0555t) × e-0.0874CP. It was concluded that A and B fractions and kd of CP could be highly biased by microbial CP contamination, and therefore these corrected values could be obtained mathematically, replacing the use of microbial markers. The percentage of contamination and the corrected apparent degradability of CP could be obtained from values of CP and time of incubation for each feed, which could reduce cost and labor involved when using 15N. © 2013 American Society of Animal Science. All rights reserved.

Study of the threshold line between macroscopic and bulk behaviors for homogeneous type II superconductors

In this work we solved the time dependent Ginzburg-Landau equations to simulate homogeneous superconducting samples with square geometry for several lateral sizes. As a result of such simulations we notice that in the Meissner state, when the vortices do not penetrate the superconductor, the response of small samples are not coincident with that expected for the bulk ones, i.e., 4. πM=. -. H. Thus, we focused our analyzes on the way which the M(. H) curves approximate from the characteristic curve of bulk superconductors. With such study, we built a diagram of the size of the sample as a function of the temperature which indicates a threshold line between macroscopic and bulk behaviors. © 2013 Elsevier B.V.

On the regularity of the pressure field of relaxed solutions to Euler equations with variable density

In this paper we improve the regularity in time of the gradient of the pressure field in the solution of relaxed version of variational formulation proposed by V. I. Arnold and by Y. Brenier, for the incompressible Euler equations with variable density. We obtain that the pressure field is not only a measure, but a function in Lloc2((0,T);BVloc(D)) as an extension of the work of Ambrosio and Figalli (2008) in [1] to the variable density case. © 2013 Elsevier Ltd.

Integração de Redes GNSS locais ao SIRGAS

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Um modelo de linha de transmissão bifásica desenvolvido diretamente no domínio das fases

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Modelagem matemática da doença do caranguejo letárgico via ondas viajantes

Pós-graduação em Biometria - IBB