Hypercomplex geometric derivative from a Cauchy-like integral formula

The derivation and integration of hipercomplex functions have been investigated along the years, see [7], [11], [14]. The main purpose of this brief article is to give a geometrical interpretation for quaternionic derivatives, based on a recent determination of a Cauchy-like formula for quaternions, see [3]. © 2011 Academic Publications.

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 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.

The fractional-nonlinear robotic manipulator: Modeling and dynamic simulations

In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional-order nonlinear dynamics equations of a two link robotic manipulator. The aformentioned equations have been simulated for several cases involving: integer and non-integer order analysis, with and without external forcing acting and some different initial conditions. The fractional nonlinear governing equations of motion are coupled and the time evolution of the angular positions and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the dynamics equations of a two link robotic manipulator have been modeled with the fractional Euler-Lagrange dynamics approach. The results reveal that the fractional-nonlinear robotic manipulator can exhibit different and curious behavior from those obtained with the standard dynamical system and can be useful for a better understanding and control of such nonlinear systems. © 2012 American Institute of Physics.

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.

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.

Teorema de Riemann-Roch e aplicações

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

Universalidade em matrizes aleatórias via problemas de Riemann-Hilbert

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

Semigrupos de operadores lineares aplicados às equações diferenciais parciais

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

Existência de solução de equações integrais não lineares em escalas temporais sobre espaços de Banach

Pós-graduação em Matemática - IBILCE

Soluções auto-similares das equações de Navier-Stokes em Lp-Fraco

Pós-graduação em Matemática - IBILCE