Effects of Crossing Saddle Coil Conductors: Electric Length X Mutual Inductance

In magnetic resonance imaging (MRI), either on human or animal studies, the main requirements for radiofrequency (RF) coils are to produce a homogeneous RF field while used as a transmitter coil and to have the best signal-to-noise ratio (SNR) while used as a receiver. Besides, they need to be easily frequency adjustable and have input impedance matching 50 Omega to several different load conditions. New theoretical and practical concepts are presented here for considerable enhancing of RF coil homogeneity for MRI experiments on small animals. To optimize field homogeneity, we have performed simulations using Blot and Savart law varying the coil`s window angle, achieving the optimum one. However, when the coil`s dimensions are the same order of the wave length and according to transmission line theory, differences in electrical length and effects of mutual inductances between adjacent strip conductors decrease both field homogeneity and SNR. The problematic interactions between strip conductors by means of mutual inductance were eliminated by inserting crossings at half electrical length, avoiding distortion on current density, thus eliminating sources of field inhomogeneity. Experimental results show that measured field maps and simulations are in good agreement. The new coil design, dubbed double-crossed saddle described here have field homogeneity and SNR superior than the linearly driven 8-rung birdcage coil. One of our major findings was that the effects of mutual inductance are more significant than differences in electrical length for this frequency and coil dimensions. In vitro images of a primate Cebus paela brain were acquired, confirming double-crossed saddle superiority. (C) 2010 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 37B: 193-201, 2010

Bifurcation analysis of a model for biological control

In this paper we study the Lyapunov stability and Hopf bifurcation in a biological system which models the biological control of parasites of orange plantations. (c) 2007 Elsevier Ltd. All rights reserved.

Stability and Hopf bifurcation in an hexagonal governor system

In this paper we study the Lyapunov stability and the Hopf bifurcation in a system coupling an hexagonal centrifugal governor with a steam engine. Here are given sufficient conditions for the stability of the equilibrium state and of the bifurcating periodic orbit. These conditions are expressed in terms of the physical parameters of the system, and hold for parameters outside a variety of codimension two. (C) 2007 Elsevier Ltd. All rights reserved.

ON THE SUPERCRITICALITY OF THE FIRST HOPF BIFURCATION IN A DELAY BOUNDARY PROBLEM

The goal of this paper is to analyze the character of the first Hopf bifurcation (subcritical versus supercritical) that appears in a one-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We showed in the previous work [Arrieta et al., 2010] that if the delay is small, the unique non-negative equilibrium solution is asymptotically stable. We also showed that, as the delay increases and crosses certain critical value, this equilibrium becomes unstable and undergoes a Hopf bifurcation. This bifurcation is the first one of a cascade occurring as the delay goes to infinity. The structure of this cascade will depend on the parameters appearing in the equation. In this paper, we show that the first bifurcation that occurs is supercritical, that is, when the parameter is bigger than the delay bifurcation value, stable periodic orbits branch off from the constant equilibrium.

Twisted conjugacy classes in nilpotent groups

A group is said to have the R(infinity) property if every automorphism has an infinite number of twisted conjugacy classes. We study the question whether G has the R(infinity) property when G is a finitely generated torsion-free nilpotent group. As a consequence, we show that for every positive integer n >= 5, there is a compact nilmanifold of dimension n on which every homeomorphism is isotopic to a fixed point free homeomorphism. As a by-product, we give a purely group theoretic proof that the free group on two generators has the R(infinity) property. The R(infinity) property for virtually abelian and for C-nilpotent groups are also discussed.

COMMUTATIVE FINITE-DIMENSIONAL ALGEBRAS SATISFYING x(x(xy))=0 ARE NILPOTENT

We investigate the structure of commutative non-associative algebras satisfying the identity x(x(xy)) = 0. Recently, Correa and Hentzel proved that every commutative algebra satisfying above identity over a field of characteristic not equal 2 is solvable. We prove that every commutative finite-dimensional algebra u over a field F of characteristic not equal 2, 3 which satisfies the identity x(x(xy)) = 0 is nilpotent. Furthermore, we obtain new identities and properties for this class of algebras.

Locally nilpotent groups of units in tiled rings

We consider locally nilpotent subgroups of units in basic tiled rings A, over local rings O which satisfy a weak commutativity condition. Tiled rings are generalizations of both tiled orders and incidence rings. If, in addition, O is Artinian then we give a complete description of the maximal locally nilpotent subgroups of the unit group of A up to conjugacy. All of them are both nilpotent and maximal Engel. This generalizes our description of such subgroups of upper-triangular matrices over O given in M. Dokuchaev, V. Kirichenko, and C. Polcino Milies (2005) [3]. (C) 2010 Elsevier Inc. All rights reserved.

PERIODIC PERTURBATION of QUADRATIC SYSTEMS WITH TWO INFINITE HETEROCLINIC CYCLES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

HOPF BIFURCATION FROM LINES of EQUILIBRIA WITHOUT PARAMETERS IN MEMRISTOR OSCILLATORS

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Bifurcation analysis of a new Lorenz-like chaotic system

In this paper we study the local codimension one and two bifurcations which occur in a family of three-dimensional vector fields depending on three parameters. An equivalent family, depending on five parameters, was recently proposed as a new chaotic system with a Lorenz-like butterfly shaped attractor and was studied mainly from a numerical point of view, for particular values of the parameters, for which computational evidences of the chaotic attractor was shown. In order to contribute to the understand of this new system we present an analytical study and the bifurcation diagrams of an equivalent three parameter system, showing the qualitative changes in the dynamics of its solutions, for different values of the parameters. (C) 2007 Elsevier Ltd. All rights reserved.

Bifurcation Analysis of a Van der Pol-Duffing Circuit with Parallel Resistor

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Bifurcation of limit cycles from an n-dimensional linear center inside a class of piecewise linear differential systems

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

NONDEGENERATE UMBILICS, THE PATH FORMULATION and GRADIENT BIFURCATION PROBLEMS

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

IN VITRO INCIDENCE of ROOT CANAL BIFURCATION IN MANDIBULAR INCISORS BY RADIOVISIOGRAPHY

Objective: The aim of this study was to verify, in vivo and in vitro, the prevalence of root canal bifurcation in mandibular incisors by digital radiography. Material and Methods: Four hundred teeth were analyzed for the in vivo study. Digital radiographs were taken in an orthoradial direction from the mandibular incisor and canine regions. The digital radiographs of the canine region allowed visualizing the incisors in a distoradial direction using 20 degrees deviation. All individuals agreed to participate by signing an informed consent form. The in vitro study was conducted on 200 mandibular incisors positioned on a model, simulating the mandibular dental arch. Digital radiographs were taken from the mandibular incisors in both buccolingual and mesiodistal directions. Results: The digital radiography showed presence of bifurcation in 20% of teeth evaluated in vitro in the mesiodistal direction. In the buccolingual direction, 17.5% of teeth evaluated in vivo and 15% evaluated in vitro presented bifurcation or characteristics indicating bifurcation. Conclusions: Digital radiography associated with X-ray beam distally allowed detection of a larger number of cases of bifurcated root canals or characteristics of bifurcation.

Geometrical properties of coupled oscillators at synchronization

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)