Let k be a field of characteristic zero, n any positive integer and let δn be the derivation n i=1 Xi ∂ ∂Y i of the polynomial ring k[X1,. .. , Xn, Y1,. .. , Yn] in 2n variables over k. A Conjecture of Nowicki (Conjecture 6.9.10 in (8)) states the following ker δn = k[X1,. .. , Xn, XiYj − XjYi; 1 ≤ i < j ≤ n] in which case we say that δn is standard. In this paper, we use the elimination theory of Groebner bases to prove that Nowicki's conjecture holds in the more general case of the derivation D = n i=1 X t i i ∂ ∂Y i , ti ∈ Z ≥0. In (6), H. Kojima and M. Miyanishi argued that D is standard in the case where ti = t (i = 1,. .. n) for some t ≥ 3. Although the result is true, we show in Section 4 of this paper that the proof presented in (6) is not complete.
Inheritance of fruit-related traits was studied in a population generated by crossing two heirloom pepper (Capsicum annuum) cultivars, Round of Hungary and Bulgarian carrot. Inheritance of corrugated pericarp phenotype of ‘Round of Hungary’ behaved as a recessive trait controlled by two genes while round fruit shape behaved as a single gene. Pungent cultivar Bulgarian carrot had significantly higher total soluble solids, titratable acidity, antioxidant activities, and significantly thinner pericarp than fruit of Round of Hungary. Pericarp thickness was related to differences in both cell number and cell size. Analyses of F2 fruit indicated that fruit weight was positively correlated (P < 0.01) to fruit width and pericarp thickness. Fruit width was negatively correlated (P < 0.01) to fruit length and total soluble solids and positively correlated (P < 0.01) to pericarp thickness. Yellow color was negatively correlated (P < 0.05) to total soluble solids. Fruit length showed high inbreeding depression and transgressive segregation. Color measurements showed that yellow was correlated to lightness, and the relationships between red and yellow color spaces and carotenoid composition were complex.
O conhecimento do limite de estabilidade de tratores é fundamental à segurança das operações agrícolas. O objetivo deste trabalho foi desenvolver um modelo matemático para previsão da perda da estabilidade de tratores agrícolas. No modelo foram utilizadas as características geométricas e ponderais do trator e de sua condição numa pista de ensaio. Análises de balanço de forças e de momentos foram realizadas para determinar as equações que regem o comportamento estático e dinâmico do trator em superfície inclinada. Com base nos resultados da comparação entre os valores dos ângulos-limite de tombamento simulados e experimentais, conclui-se que o modelo matemático desenvolvido é capaz de prever a perda da estabilidade de trator 4x2 satisfatoriamente.
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