Degree of multicollinearity and variables involved in linear dependence in additive-dominant models

The objective of this work was to assess the degree of multicollinearity and to identify the variables involved in linear dependence relations in additive-dominant models. Data of birth weight (n=141,567), yearling weight (n=58,124), and scrotal circumference (n=20,371) of Montana Tropical composite cattle were used. Diagnosis of multicollinearity was based on the variance inflation factor (VIF) and on the evaluation of the condition indexes and eigenvalues from the correlation matrix among explanatory variables. The first model studied (RM) included the fixed effect of dam age class at calving and the covariates associated to the direct and maternal additive and non-additive effects. The second model (R) included all the effects of the RM model except the maternal additive effects. Multicollinearity was detected in both models for all traits considered, with VIF values of 1.03 - 70.20 for RM and 1.03 - 60.70 for R. Collinearity increased with the increase of variables in the model and the decrease in the number of observations, and it was classified as weak, with condition index values between 10.00 and 26.77. In general, the variables associated with additive and non-additive effects were involved in multicollinearity, partially due to the natural connection between these covariables as fractions of the biological types in breed composition.

Selection of the most informative morphoagronomic descriptors for cassava germplasm

The objective of this work was to select the most informative morphoagronomic descriptors for cassava (Manihot esculenta) germplasm and to evaluate the ability of different methods to select the descriptors. Ninety-five accessions were characterized using 51 morphoagronomic descriptors. Data were subjected to a multiple correspondence analysis (MCA), whose information was used in the following four methods of descriptor selection: reverse order of the descriptor for the pth factorial axis of the MCA (Jolliffe); sequential, multiple correspondence analysis (SMCA); mean of the contribution orders of the descriptor in the first three factorial axes (C3PA); and C3PA method weighted by the respective eigenvalues of the full analysis (C3PAWeig). The correlations between the dissimilarity matrix with all descriptors and the most informative descriptors were high and significant (0.75, 0.77, 0.83, and 0.84 for C3PAWeig, C3PA, SMCA, and Jolliffe, respectively). The less informative descriptors were discarded, considering those common among the selection methods and relevant for the breeding interests. Therefore, 32 morphoagronomic descriptors with correlation between the dissimilarity matrices (r=0.81) were selected, due to their high capacity to discriminate cassava germplasm and to their ability to maintain some preliminary agronomic traits, useful for the initial characterization of the germplasm.

Uma introdução à espectroscopia atômica: o átomo de hidrogênio

The Balmer equation is obtained from the hydrogen spectrum in an empirical way, using a graphic method; from this equation the energy level terms are derived. Emphasis is given to concepts in order to make clear the meaning of quantum numbers, eigenvalues and eigenfunctions in the Schrödinger equation.

Uma introdução à espectroscopia atômica: II - o espectro do sódio

The present article is devoted to Chemistry or Physics undergraduate students, given their difficulty to understand fundamental concepts and technical language used in atomic spectroscopy and quantum mechanics. An easy approach is shown in the treatment of the emission spectrum of the sodium atom without any involved calculations. In a previous article, the hydrogen spectrum was considered and the energy degeneracy of the angular momentum quantum number was observed. For the sodium spectrum, due to the valence electron penetration into internal shells, a breakdown of this degeneracy occurs and a dependence of this penetration on the angular momentum quantum number is observed. The eigenvalues are determined introducing the quantum defect correction (Rydberg correction) in the denominator of the Balmer equation, and the energy diagram is obtained. The intensity ratio for the observed doublets is explained by introducing new wave functions, containing the magnetic quantum number of the total angular momentum.

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