Equivalence of the Duffin-Kemmer-Petiau and Klein-Gordon-Fock equations

A strict proof of the equivalence of the Duffin-Kemmer-Petiau and Klein-Gordon Fock theories is presented for physical S-matrix elements in the case of charged scalar particles minimally interacting with an external or quantized electromagnetic field. The Hamiltonian canonical approach to the Duffin - Kemmer Petiau theory is first developed in both the component and the matrix form. The theory is then quantized through the construction of the generating functional for the Green's functions, and the physical matrix elements of the S-matrix are proved to be relativistic invariants. The equivalence of the two theories is then proved for the matrix elements of the scattered scalar particles using the reduction formulas of Lehmann, Symanzik, and Zimmermann and for the many-photon Green's functions.

Lamé differential equations and electrostatics

The problem of existence and uniqueness of polynomial solutions of the Lamé differential equation A(x)y″ + 2B(x)y′ + C(x)y = 0, where A(x),B(x) and C(x) are polynomials of degree p + 1,p and p - 1, is under discussion. We concentrate on the case when A(x) has only real zeros aj and, in contrast to a classical result of Heine and Stieltjes which concerns the case of positive coefficients rj in the partial fraction decomposition B(x)/A(x) = ∑j p=0 rj/(x - aj), we allow the presence of both positive and negative coefficients rj. The corresponding electrostatic interpretation of the zeros of the solution y(x) as points of equilibrium in an electrostatic field generated by charges rj at aj is given. As an application we prove that the zeros of the Gegenbauer-Laurent polynomials are the points of unique equilibrium in a field generated by two positive and two negative charges. © 2000 American Mathematical Society.

Galilean covariance and non-relativistic Bhabha equations

We apply a five-dimensional formulation of Galilean covariance to construct non-relativistic Bhabha first-order wave equations which, depending on the representation, correspond either to the well known Dirac equation (for particles with spin 1/2) or the Duffin-Kemmer-Petiau equation (for spinless and spin 1 particles). Here the irreducible representations belong to the Lie algebra of the 'de Sitter group' in 4 + 1 dimensions, SO(5, 1). Using this approach, the non-relativistic limits of the corresponding equations are obtained directly, without taking any low-velocity approximation. As a simple illustration, we discuss the harmonic oscillator.

Embryo recovery and pregnancy rates after the delay of ovulation and fixed time insemination in superstimulated beef cows

The aim of this study was to evaluate the effect of delaying ovulation subsequent to superstimulation of follicular growth in beef cows (Bos indicus) on embryo recovery rates and the capacity of embryos to establish pregnancies. Ovulation was delayed by three treatments using either progesterone (CIDR-B®) or a GnRH agonist (deslorelin). Multiparous Nelore cows (n = 24) received three of four superstimulation treatments in an incomplete block design (n = 18 per group). Cows in Groups CTRL, P48 and P60 were treated with a CIDR-B device plus estradiol benzoate (EB, 4 mg, i.m.) on Day-5, while cows in Group D60 were implanted with deslorelin on Day-7. Cows were superstimulated with FSH (Folltropin-V® 200 mg), from Day 0 to 3, using twice daily injections in decreasing amounts. All cows were treated with a luteolytic dose of prostaglandin on Day 2 (08:00 h). CIDR-B devices were removed as follows: Group CTRL, Day 2 (20:00 h); Group P48, Day 4 (08:00 h); Group P60, Day 4 (20:00 h). Cows in Group CTRL were inseminated at 10, 20 and 30 h after first detected estrus. Ovulation was induced for cows in Group P48 (Day 4, 08:00 h) and Groups P60 and D60 (Day 4, 20:00 h) by injection of LH (Lutropin®, 25 mg, i.m.), and these cows were inseminated 10 and 20 h after treatment with LH. Embryos were recovered on Days 11 or 12, graded and transferred to synchronized recipients. Pregnancies were determined by ultrasonography around Day 100. Data were analyzed by mixed procedure, Kruskal-Wallis and Chi-square tests. The number of ova/embryos, transferable embryos (mean ± S.E.M.) and pregnancy rates (%) were as follows, respectively: Group CTRL (10.8 ± 1.8, 6.1 ± 1.3, 51.5), P48 (12.6 ± 1.9, 7.1 ± 1.0, 52.3), P60 (10.5 ± 1.6, 5.7 ± 1.3, 40.0) and D60 (10.3 ± 1.7, 5.0 ± 1.2, 50.0). There were no significant differences among the groups (P > 0.05). It was concluded that fixed time AI in association with induced ovulation did not influence embryo recovery. Furthermore, pregnancy rates in embryos recovered from cows with delayed ovulation were similar to those in embryos obtained from cows treated with a conventional superstimulation protocol. © 2002 Elsevier B.V. All rights reserved.

Solutions for a class of integro-differential equations with time periodic coefficients

In this work, a series solution is found for the integro-differential equation y″ (t) = -(ω2 c + ω2 f sin2 ωpt)y(t) + ωf (sin ωpt) z′ (0) + ω2 fωp sin ωpt ∫t 0 (cos ωps) y(s)ds, which describes the charged particle motion for certain configurations of oscillating magnetic fields. As an interesting feature, the terms of the solution are related to distinct sequences of prime numbers.

PI Stabilization of a Class of Time Delay Systems

In this paper we use the Hermite-Biehler theorem to establish results for the design of proportional plus integral (PI) controllers for a class of time delay systems. We extend results of the polynomial case to quasipolynomials using the property of interlacing in high frequencies of the class of time delay systems considered. A signature for the quasipolynomials in this class is derived and used in the proposed approach which yields the complete set of the stabilizing PI controllers.

A FEM approach to the equations of magneto-aerodynamics

In this work, a Finite Element Method treatment is outlined for the equations of Magnetoaerodynamics. In order to provide a good basis for numerical treatment of Magneto-aerodynamics, a full version of the complete equations is presented and FEM contribution matrices are deduced, as well as further terms of stabilization for the compressible flow case.

Supersymmetry and the KdV equations for integrable hierarchies with a half-integer gradation

Supersymmetry is formulated for integrable models based on the sl(2 1) loop algebra endowed with a principal gradation. The symmetry transformations which have half-integer grades generate supersymmetry. The sl(2 1) loop algebra leads to N=2 supersymmetric mKdV and sinh-Gordon equations. The corresponding N=1 mKdV and sinh-Gordon equations are obtained via reduction induced by twisted automorphism. Our method allows for a description of a non-local symmetry structure of supersymmetric integrable models. © 2003 Elsevier B.V. All rights reserved.

A dynamical gluon mass solution in a coupled system of the Schwinger-Dyson equations

We study numerically the Schwinger-Dyson equations for the coupled system of gluon and ghost propagators in the Landau gauge and in the case of pure gauge QCD. We show that a dynamical mass for the gluon propagator arises as a solution while the ghost propagator develops an enhanced behavior in the infrared regime of QCD. Simple analytical expressions are proposed for the propagators, and the mass dependency on the ΛQCD scale and its perturbative scaling are studied. We discuss the implications of our results for the infrared behavior of the coupling constant, which, according to fits for the propagators infrared behavior, seems to indicate that α s(q2) → 0 as q2 → 0. © SISSA/ISAS 2004.

Schwinger-dyson equations and dynamical gluon mass generation

We discuss the solutions obtained for the gluon propagador in Landau gauge within two distinct approximations for the Schwinger-Dyson equations (SDE). The first, named Mandelstam's approximation, consist in neglecting all contributions that come from fermions and ghosts fields while in the second, the ghosts fields are taken into account leading to a coupled system of integral equations. In both cases we show that a dynamical mass for the gluon propagator can arise as a solution. © 2005 American Institute of Physics.

PID stabilization of a class of time delay systems

In this paper we use the Hermite-Biehler theorem to establish results for the design of proportional plus integral plus derivative (PID) controllers concerning a class of time delay systems. Using the property of interlacing at high frequencies of the class of systems considered and linear programming we obtain the set of all stabilizing PID controllers. © 2005 IEEE.

Discrete-time sliding mode control of input-delay systems applied on a power generation system

This paper presents two discrete sliding mode control (SMC) design. The first one is a discrete-time SMC design that doesn't take into account the time-delay. The second one is a discrete-time SMC design, which takes in consideration the time-delay. The proposed techniques aim at the accomplishment simplicity and robustness for an uncertainty class. Simulations results are shown and the effectiveness of the used techniques is analyzed. © 2006 IEEE.

Substitution-newton-Raphson method for the solution of electric network equations

The power flow problem, in transmission networks, has been well solved, for most cases, using Newton-Raphson method (NR) and its decoupled versions. Generally speaking, the solution of a non-linear system of equations refers to two methods: NR and Successive Substitution. The proposal of this paper is to evaluate the potential of the Substitution-Newton-Raphson Method (SNR), which combines both methods, on the solution of the power flow problem. Simulations were performed using a two-bus test network in order to observe the characteristics of these methods. It was verified that the NR is faster than SNR, in terms of convergence, considering non-stressed scenarios. For those cases where the power flow in the network is closed to the limits (stressed system), the SNR converges faster. This paper presents the power flow formulation of the SNR and describes its potential for its application in special cases such as stressed scenarios. © 2006 IEEE.

Effect of mating delay in the ovary of Apis mellifera L. (Hymenoptera, Apidae) queens: Histological aspects

This paper reports the effect of mating delay on the queen Apis mellifera ovaries based on a light microscopy analysis. Soon after a queen emerges from the brood cell, oocytes start to differentiate in the ovaries, but if mating does not occur at the correct age (about 6 days after emergence) cell degeneration begins. Ovaries of 15-day-old virgin queens show extensive disorganization with cell death affecting all types of ovariole cells. Types of cell death and the possible causes are discussed.

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.