Random regression models to estimate genetic parameters for milk production of Guzerat cows using orthogonal Legendre polynomials

The objective of this work was to compare random regression models for the estimation of genetic parameters for Guzerat milk production, using orthogonal Legendre polynomials. Records (20,524) of test-day milk yield (TDMY) from 2,816 first-lactation Guzerat cows were used. TDMY grouped into 10-monthly classes were analyzed for additive genetic effect and for environmental and residual permanent effects (random effects), whereas the contemporary group, calving age (linear and quadratic effects) and mean lactation curve were analized as fixed effects. Trajectories for the additive genetic and permanent environmental effects were modeled by means of a covariance function employing orthogonal Legendre polynomials ranging from the second to the fifth order. Residual variances were considered in one, four, six, or ten variance classes. The best model had six residual variance classes. The heritability estimates for the TDMY records varied from 0.19 to 0.32. The random regression model that used a second-order Legendre polynomial for the additive genetic effect, and a fifth-order polynomial for the permanent environmental effect is adequate for comparison by the main employed criteria. The model with a second-order Legendre polynomial for the additive genetic effect, and that with a fourth-order for the permanent environmental effect could also be employed in these analyses.

Remarks on an algebraic semantics for paraconsistent Nelson's logic

In the paper Busaniche and Cignoli (2009) we presented a quasivariety of commutative residuated lattices, called NPc-lattices, that serves as an algebraic semantics for paraconsistent Nelson's logic. In the present paper we show that NPc-lattices form a subvariety of the variety of commutative residuated lattices, we study congruences of NPc-lattices and some subvarieties of NPc-lattices.

O regime de chuvas em Pesqueira

The authors studied the rainfall in Pesqueira (Pernambuco, Brasil) in a period of 48 years (1910 through 1957) by the method of orthogonal polynomials, degrees up to the fourth having been tried. None of them was significant, so that it seems that no trend is present. The mean observed was 679.00 mm., with standard error of the mean 205.5 mm., and a 30.3% coefficient of variation. The 95% level of probability would include annual rainfall from 263.9 up to 1094.1mm.

Estudo sôbre as temperaturas médias em Campinas

This paper deals with the study by orthogonal polynomials of trends in the mean annual and mean monthly temperatures (in degrees Centigrade) in Campinas (State of São Paulo, Brasil), from 1890 up to 1956. Only 4 months were studied (January, April, July and October) taken as typical of their respective season. For the annual averages both linear and quadratic components were significant, the regression equation being y = 19.95 - 0.0219 x + 0.00057 x², where y is the temperature (in degrees Centigrade) and x is the number of years after 1889. Thus 1890 corresponds to x = 1, 1891, to x = 2, etc. The equation shows a minimum for the year 1908, with a calculated mean y = 19.74. The expected means by the regression equation are given below. Anual temperature means for Campinas (SP, Brasil) calculated by the regression equation Year Annual mean (Degrees Centigrade) 1890 19.93 1900 10.78 1908 19.74 (minimum) 1010 19.75 1920 19.82 1930 20.01 1940 20.32 1950 20.74 1956 21.05 The mean for 67 years was 20.08°C with standard error of the mean 0.08°G. For January the regression equation was y = 23.08 - 0.0661 x + 0.00122 x², with a minimum of 22.19°C for 1916. The average for 67 years was 22.70°C, with standard error 0.12°C. For April no component of regression was significant. The average was 20.42°C, with standard error 0.13°C. For July the regression equation was of first degree, y = 16.01 + 0.0140X. The average for 67 years was 16.49°C, with standard error of the mean 0.14°C. Finally, for October the regression equation was y = 20.55 - 0.0362x + 0.00078x², with a minimum of 20.13°C for 1912. The average was 20.52°C, with standard error of the mean equal to 0.14°C.

Bound state solutions of schrödinger equation for a more general exponential screened coulomb potential via Nikiforov-Uvarov method

The arbitrary angular momentum solutions of the Schrödinger equation for a diatomic molecule with the general exponential screened coulomb potential of the form V(r) = (- a / r){1+ (1+ b )e-2b } has been presented. The energy eigenvalues and the corresponding eigenfunctions are calculated analytically by the use of Nikiforov-Uvarov (NU) method which is related to the solutions in terms of Jacobi polynomials. The bounded state eigenvalues are calculated numerically for the 1s state of N2 CO and NO

BEM/FEM non-linear model applied to transient analysis with viscous damping

In this article a two-dimensional transient boundary element formulation based on the mass matrix approach is discussed. The implicit formulation of the method to deal with elastoplastic analysis is considered, as well as the way to deal with viscous damping effects. The time integration processes are based on the Newmark rhoand Houbolt methods, while the domain integrals for mass, elastoplastic and damping effects are carried out by the well known cell approximation technique. The boundary element algebraic relations are also coupled with finite element frame relations to solve stiffened domains. Some examples to illustrate the accuracy and efficiency of the proposed formulation are also presented.

A temperature predicting model for manufacturing processes requiring coiling

A model for predicting temperature evolution for automatic controling systems in manufacturing processes requiring the coiling of bars in the transfer table is presented. Although the method is of a general nature, the presentation in this work refers to the manufacturing of steel plates in hot rolling mills. The predicting strategy is based on a mathematical model of the evolution of temperature in a coiling and uncoiling bar and is presented in the form of a parabolic partial differential equation for a shape changing domain. The mathematical model is solved numerically by a space discretization via geometrically adaptive finite elements which accomodate the change in shape of the domain, using a computationally novel treatment of the resulting thermal contact problem due to coiling. Time is discretized according to a Crank-Nicolson scheme. Since the actual physical process takes less time than the time required by the process controlling computer to solve the full mathematical model, a special predictive device was developed, in the form of a set of least squares polynomials, based on the off-line numerical solution of the mathematical model.

An experimental/numerical study of the turbulent boundary layer development along a surface with a sudden change in roughness

A theory for the description of turbulent boundary layer flows over surfaces with a sudden change in roughness is considered. The theory resorts to the concept of displacement in origin to specify a wall function boundary condition for a kappa-epsilon model. An approximate algebraic expression for the displacement in origin is obtained from the experimental data by using the chart method of Perry and Joubert(J.F.M., vol. 17, pp. 193-122, 1963). This expression is subsequently included in the near wall logarithmic velocity profile, which is then adopted as a boundary condition for a kappa-epsilon modelling of the external flow. The results are compared with the lower atmospheric observations made by Bradley(Q. J. Roy. Meteo. Soc., vol. 94, pp. 361-379, 1968) as well as with velocity profiles extracted from a set of wind tunnel experiments carried out by Avelino et al.( 7th ENCIT, 1998). The measurements are found to be in good agreement with the theoretical computations. The skin-friction coefficient was calculated according to the chart method of Perry and Joubert(J.F.M., vol. 17, pp. 193-122, 1963) and to a balance of the integral momentum equation. In particular, the growth of the internal boundary layer thickness obtained from the numerical simulation is compared with predictions of the experimental data calculated by two methods, the "knee" point method and the "merge" point method.

Application of a non isotropic turbulence model to stable atmospheric flows and dispersion over 3D topography

A non isotropic turbulence model is extended and applied to three dimensional stably stratified flows and dispersion calculations. The model is derived from the algebraic stress model (including wall proximity effects), but it retains the simplicity of the "eddy viscosity" concept of first order models. The "modified k-epsilon" is implemented in a three dimensional numerical code. Once the flow is resolved, the predicted velocity and turbulence fields are interpolated into a second grid and used to solve the concentration equation. To evaluate the model, various steady state numerical solutions are compared with small scale dispersion experiments which were conducted at the wind tunnel of Mitsubishi Heavy Industries, in Japan. Stably stratified flows and plume dispersion over three distinct idealized complex topographies (flat and hilly terrain) are studied. Vertical profiles of velocity and pollutant concentration are shown and discussed. Also, comparisons are made against the results obtained with the standard k-epsilon model.

On the numerical integration of rigid body nonlinear dynamics in presence of parameters singularities

One of the main complexities in the simulation of the nonlinear dynamics of rigid bodies consists in describing properly the finite rotations that they may undergo. It is well known that, to avoid singularities in the representation of the SO(3) rotation group, at least four parameters must be used. However, it is computationally expensive to use a four-parameters representation since, as only three of the parameters are independent, one needs to introduce constraint equations in the model, leading to differential-algebraic equations instead of ordinary differential ones. Three-parameter representations are numerically more efficient. Therefore, the objective of this paper is to evaluate numerically the influence of the parametrization and its singularities on the simulation of the dynamics of a rigid body. This is done through the analysis of a heavy top with a fixed point, using two three-parameter systems, Euler's angles and rotation vector. Theoretical results were used to guide the numerical simulation and to assure that all possible cases were analyzed. The two parametrizations were compared using several integrators. The results show that Euler's angles lead to faster integration compared to the rotation vector. An Euler's angles singular case, where representation approaches a theoretical singular point, was analyzed in detail. It is shown that on the contrary of what may be expected, 1) the numerical integration is very efficient, even more than for any other case, and 2) in spite of the uncertainty on the Euler's angles themselves, the body motion is well represented.

Substitution-Newton-Raphson method applied to the modeling of a vapour compression refrigeration system using different representations of the thermodynamic properties of R-134a

This paper gives a detailed presentation of the Substitution-Newton-Raphson method, suitable for large sparse non-linear systems. It combines the Successive Substitution method and the Newton-Raphson method in such way as to take the best advantages of both, keeping the convergence features of the Newton-Raphson with the low requirements of memory and time of the Successive Substitution schemes. The large system is solved employing few effective variables, using the greatest possible part of the model equations in substitution fashion to fix the remaining variables, but maintaining the convergence characteristics of the Newton-Raphson. The methodology is exemplified through a simple algebraic system, and applied to a simple thermodynamic, mechanical and heat transfer modeling of a single-stage vapor compression refrigeration system. Three distinct approaches for reproducing the thermodynamic properties of the refrigerant R-134a are compared: the linear interpolation from tabulated data, the use of polynomial fitted curves and the use of functions derived from the Helmholtz free energy.

Optimal design of 3R manipulators by using classical techniques and simulated annealin

In this paper, the optimum design of 3R manipulators is formulated and solved by using an algebraic formulation of workspace boundary. A manipulator design can be approached as a problem of optimization, in which the objective functions are the size of the manipulator and workspace volume; and the constrains can be given as a prescribed workspace volume. The numerical solution of the optimization problem is investigated by using two different numerical techniques, namely, sequential quadratic programming and simulated annealing. Numerical examples illustrate a design procedure and show the efficiency of the proposed algorithms.

Measuring higher order optical aberrations of the human eye: techniques and applications

In the present paper we discuss the development of "wave-front", an instrument for determining the lower and higher optical aberrations of the human eye. We also discuss the advantages that such instrumentation and techniques might bring to the ophthalmology professional of the 21st century. By shining a small light spot on the retina of subjects and observing the light that is reflected back from within the eye, we are able to quantitatively determine the amount of lower order aberrations (astigmatism, myopia, hyperopia) and higher order aberrations (coma, spherical aberration, etc.). We have measured artificial eyes with calibrated ametropia ranging from +5 to -5 D, with and without 2 D astigmatism with axis at 45º and 90º. We used a device known as the Hartmann-Shack (HS) sensor, originally developed for measuring the optical aberrations of optical instruments and general refracting surfaces in astronomical telescopes. The HS sensor sends information to a computer software for decomposition of wave-front aberrations into a set of Zernike polynomials. These polynomials have special mathematical properties and are more suitable in this case than the traditional Seidel polynomials. We have demonstrated that this technique is more precise than conventional autorefraction, with a root mean square error (RMSE) of less than 0.1 µm for a 4-mm diameter pupil. In terms of dioptric power this represents an RMSE error of less than 0.04 D and 5º for the axis. This precision is sufficient for customized corneal ablations, among other applications.