Conditionally positive definite kernels on Euclidean domains

AbstractThis paper characterizes several classes of conditionally positive definite kernels on a domain Ω of either Rl or Cl. Among the classes is that composed of strictly conditionally positive definite kernels. These kernels are known to be useful in the solution of variational interpolation problems on Ω. Our study covers the case in which Ω is the sphere Sl−1 of Rl or a similar manifold. Among other things, our results imply that the characterization of (strict) conditional positive definiteness on Ω can be obtained from a characterization of (strict) positive definiteness on Ω. The bi-zonal strictly conditionally positive definite kernels on Sl−1, l⩾3, are described

Positive Definite Functions on Complex Spheres and their Walks through Dimensions

We provide walks through dimensions for isotropic positive definite functions defined over complex spheres. We show that the analogues of Montée and Descente operators as proposed by Beatson and zu Castell [J. Approx. Theory 221 (2017), 22-37] on the basis of the original Matheron operator [Les variables régionalisées et leur estimation, Masson, Paris, 1965], allow for similar walks through dimensions. We show that the Montée operators also preserve, up to a constant, strict positive definiteness. For the Descente operators, we show that strict positive definiteness is preserved under some additional conditions, but we provide counterexamples showing that this is not true in general. We also provide a list of parametric families of (strictly) positive definite functions over complex spheres, which are important for several applications

Órgãos internos e trato gastrintestinal de novilhos de gerações avançadas do cruzamento rotativo entre as raças Charolês e Nelore terminados em confinamento Internal organs and gastrointestinal tract of feedlot finished steers of advanced generations of rotational crossbreeding between Charolais and Nellore

Foram avaliados os efeitos de heterose e de grupo genético nos órgãos internos e no trato gastrintestinal de novilhos puros (Charolês - C e Nelore - N) e cruzados da segunda (G2) (3/4C 1/4N e 3/4N 1/4C), terceira (G3) (5/8C 3/8N e 5/8N 3/8C) e quarta (G4) (11/16C 5/16N e 11/16N 5/16C) gerações de cruzamento terminados em confinamento e abatidos com 23 meses de idade. Os animais cruzados da G2, G3 e G4 foram, respectivamente, 14,95; 17,25 e 18,46% superiores aos puros quanto ao peso de corpo vazio (PCVZ). A heterose para o rendimento de carcaça fria em relação ao PCVZ (RCFCVZ) foi positiva em todas as gerações. Os mestiços apresentaram menor peso relativo (ao PCVZ) de coração, pulmões e rins, de modo que a heterose foi significativa para peso de coração (-18,29%) e rins (-14,29%) na G3 e para pulmões (-13,45%) na G4. Novilhos mestiços apresentaram valores inferiores à média dos puros para todos os componentes do trato gastrintestinal quando o peso destes componentes foi expresso em relação a 100 kg de PCVZ ou de peso vivo ao abate (PVA), com exceção do rúmen na G2. A heterose retida foi positiva e significativa para PCVZ, RCFCVZ e para peso absoluto do fígado. Entretanto, foi negativa para a quantidade de sangue para os pesos de coração, intestino delgado + grosso e trato gastrintestinal quando expressos em relação a 100 kg de PCVZ e de PVA. Entre os animais puros, os novilhos Nelore tiveram maior RCFCVZ (57,09 vs 61,64%). O peso absoluto de rúmen, abomaso, intestino delgado + grosso e o trato gastrintestinal foram maiores nos novilhos Charolês em relação aos Nelore, o que também foi observado quando estes componentes foram expressos em relação ao PCVZ e PVA, com exceção para o intestino grosso + delgado. Estas diferenças explicam, em parte, o maior rendimento de carcaça dos novilhos Nelore.<br>The objective of this trial was to investigate the effect of heterosis and genetic group on the yield and weight of internal organs and gastrointestinal tract (GIT) of feedlot purebred (Charolais C and Nellore N) and crossbred steers from second (G2) (¾C ¼N and ¾N ¼C), third (G3) (5/8C 3/8N and 5/8N 3/8C) and fourth (G4) (11/16C 5/16N and 11/16N 5/16C) generations of rotational crossbreeding slaughtered at 23 month of age. Crossbred steers from G2, G3 and G4 had, respectively, 14.95, 17.25 and 18.46% higher empty body weight (EBW) than that from purebred animals. A positive heterosis for cold carcass yield expressed as a proportion of EBW (CCYEBW) was observed in G2, G3, and G4. Weights of heart, lungs, and kidneys adjusted for EBW were lower on crossbred compared to purebred steers; the heterosis was significant for the weights of heart (-18.29%) and kidneys (-14.29%) in G3 and for that of lungs (-13.45%) in G4. Weights of all organs of the GIT either expressed as 100 kg of EBW or as proportion of slaughter body weight (SBW) were lower on crossbred than on purebred steers with the exception of rumen weight in G2. Retained heterosis was positive and significant for EBW, CCYEBW and liver weight. However, it was negative for amount of blood and weights of heart and small plus large intestines when expressed as 100 kg of EBW and SBW. Within purebred animals, N showed greater CCYEBW (61.64%) than C (57.09). Conversely, weights of rumen, abomasum, small plus large intestine, and GIT were all higher on C than N steers; excepting for small plus large intestine, the same was observed when weights of the remaining GIT components were expressed as proportion of EBW and SB. These differences partially explain the increased carcass yield on N steers