On stability of differential equations with piecewise constant argument and the associated discrete equations using dichotomic map

Dichotomic maps are considered by means of the stability of the null solution of a class of differential equations with piecewise constant argument via associated discrete equations. Copyright © 2008 Watam Press.

Degenerate hope bifurcations in Chua's system

In this paper we study the local codimension one, two and three Hopf bifurcations which occur in the classical Chua's differential equations with cubic nonlinearity. A detailed analytical description of the regions in the parameter space for which multiple small periodic solutions bifurcate from the equilibria of the system is obtained. As a consequence, a complete answer for the challenge proposed in [Moiola & Chua, 1999] is provided. © 2009 World Scientific Publishing Company.

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.

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.

Voltammetric Study of a Cubic Silsesquioxane Organically Modified with Imidazole and their Subsequent Reaction with Cadmium and Hexacyanoferrate (III)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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.

Tilings induced by a class of cubic Rauzy fractals

We study aperiodic and periodic tilings induced by the Rauzy fractal and its subtiles associated with beta-substitutions related to the polynomial x3-ax2-bx-1 for a≥b≥1. In particular, we compute the corresponding boundary graphs, describing the adjacencies in the tilings. These graphs are a valuable tool for more advanced studies of the topological properties of the Rauzy fractals. As an example, we show that the Rauzy fractals are not homeomorphic to a closed disc as soon as a≤2b-4. The methods presented in this paper may be used to obtain similar results for other classes of substitutions.© 2012 Elsevier B.V. All rights reserved.

A new hybrid polyhedral cubic silsesquioxane chemically modified with 4-amino-5-(4-pyridyl)-4H-1,2,4-triazole-3-thiol (APTT) and copper hexacyanoferrate(III) for voltammetric determination of nitrite

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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.

A cubic silsesquioxane modified with purpald®: Preparation, characterization and a voltammetric application for determination of sulfite

A novel composite formed by interaction of a octa(3-chloropropyl)octasilsesquioxane modified with Purpald®, and its subsequent reaction with silver and hexacyanoferrate (III) (AgHSP), was synthesized and initially characterized by Fourier transform infrared spectra (FTIR) and cyclic voltammetry. The cyclic voltammogram of the modified graphite paste electrode with AgHSP, showed one redox couple with formal potential Eθ'=0.64V (vs Ag/AgCl, KNO3, 1.0 mol L-1; v = 20 mV s-1), attributed to the Fe2+(CN)6/ Fe3+(CN)6 process. The redox couple presents an electrocatalytic response for determination of sulfite. The modified electrode showed a linear response from 7.0×10-5 to 1.0×10-3 mol L-1 with the corresponding equation Y(μA) = 18.05 + 29.983×103 [sulfite], and a correlation coefficient of r=0.999. The method showed a detection limit of 0.115×10-4 mol L-1 with a relative standard deviation of ± 4% (n = 3) and amperometric sensitivity of 29.983×10-3A mol L-1. The modified electrode showed a excellent stability and good reproducibility during experiments. © 2013 by ESG.

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.

Determination of copper in different ethanolic matrices using a chloropropyl silica gel modified with a nanostructured cubic octa(3-aminopropyl)octasilsesquioxane

The chloropropyl silica gel was modified with octa(3-aminopropyl) octasilsesquioxane and characterized by Fourier transform infrared (FTIR) spectroscopy, nuclear magnetic resonance (NMR), spectroscopies, and surface and area porosity. The specific sorption capacity of metallic ions (Cu2+ and Ni2+) increases in the following solvent order: water < ethanol 42% < ethanol < ketone. The high values of the constant (K) in the order of 103 L mol-1 suggested the high adsorbent capacity of the modified silica (SGAPC) for Cu2+ and Ni2+. SGAPC was applied to a separation column and shows recoveries of around 100% of copper in samples of sugar cane spirit, vodka, ginger brandy, and ethanol fuel. © 2013 Devaney Ribeiro Do Carmo et al.