Abstract Palmitoleic acid (C16:1n7, POA), a 16-carbon ω-7 monounsaturated functional fatty acid, has been demonstrated a variety of beneficial properties to human health and a wide range of applications in nutrition, medical and chemical industries. Lipozyme® RM IM (Rhizomucor Miehei lipase), a Sn-1,3 specific lipase, was used to catalyze the hydrolysis of seabuckthorn fruit oil and produce monoglycates rich in palmitoleic acid. The fruit oil of seabuckthorn was used as the research object, the dosage of enzyme taking 10% wt.% oil, the influence of water/oil ratio, pH value and reaction temperature to hydrolysis rate were investigated, and then the response surface methodology was applied for optimizing the process conditions. Further, the relationship between the hydrolysis rate and the content of monoacylglycerol was studied under the optimal hydrolysis conditions. The result indicated that the optimal combined condition is as follows: the reaction temperature is 55°C, the pH is 7, the water-oil quality ratio is 1:1. The hydrolysis rate achieved 79.59% within 12 h in the condition above. Under the optimal conditions, the hydrolysis rate was positively correlated with the content of monoester, and the correlation coefficient was 0.999 within the first 10 h of the reaction. The hydrolysis rate was 66.76% at 10 h, and the content of monoglyceride reached the highest of 61.11%. Hereafter, the hydrolysis of monoglyceride began if the reaction continued. The content of palmitoleic acid increased from 27.11% to 40.84%, and that of linoleic acid increased from 4.51% to 33.34%, so the total amount of the two functional fatty acids reached 74.18%. Enzymatic hydrolysis can be an effective way to improve the function of seabuckthorn fruit oil.

Assumindo que a matriz Variância-Covariância das observações foi obtida, a análise dos resíduos obtidos pelos mínimos quadrados não corresponde ao teste w de Baarda. Geralmente, esta consideração não é aceita na comunidade. Em casos especiais, onde os graus de liberdade são igual a 1 (um), todos os 3 (três) tipos de testes estatísticos, incluindo o teste de normalidade de Gauss, o teste t-Students e o teste Tau-Pope, não podem ser aplicados para detecção de outliers: (1) todos os quadrados do teste de normalidade de Gauss, coincidem com o teste estatístico global, mesmo para observações correlacionadas. Assim, a falha do teste global implica em observações classificadas como outliers e, então, o teste de normalidade de Gauss é inconclusivo para a detecção de outliers; (2) os valores absolutos do teste Tau são exatamente iguais a um, não importando se as observações estão eivadas de erros. Portanto, nesta situação, o teste Tau não é eficiente para detecção de outliers, e (3) as estatísticas do teste t-Student são indefinidas.

Under the assumption of that the variance-covariance matrix is fully populated, Baarda's w-test is turn out to be completely different from the standardized least-squares residual. Unfortunately, this is not generally recognized. In the limiting case of only one degree of freedom, all the three types of test statistics, including Gaussian normal test, Student's t-test and Pope's Tau-test, will be invalid for identification of outliers: (1) all the squares of the Gaussian normal test statistic coincide with the goodness-of-fit (global) test statistic, even for correlated observations. Hence, the failure of the global test implies that all the observations will be flagged as outliers, and thus the Gaussian normal test is inconclusive for localization of outliers; (2) the absolute values of the Tau-test statistic are all exactly equal to one, no matter whether the observations are contaminated. Therefore, the Tau-test cannot work for outlier detection in this situation; and (3) Student's t-test statistics are undefined.

A técnica de mínimos quadrados iterativa com reponderação dos pesos tem sido amplamente usada na literatura geodésica e geofísica. As medidas confiáveis são instrumentos diagnósticos importantes para inferir a força da validação do modelo. Um método analítico exato é adaptado para obter a compreensão do quanto a reponderação iterativa dos pesos pode afetar os indicadores de qualidade dos resultados. Análises teóricas e numéricas mostram que, quando o procedimento de diminuição dos pesos é feita: 1) a precisão métrica e a tendência mínima detectável, aumenta; 2) As tendências da variação média do ruído estarão envolvidas e; 3) Todos os resultados coincidirão com aqueles obtidos com o método de aproximação de primeira ordem.

The iteratively reweighted least-squares (IRLS) technique has been widely employed in geodetic and geophysical literature. The reliability measures are important diagnostic tools for inferring the strength of the model validation. An exact analytical method is adopted to obtain insights on how much iterative reweighting can affect the quality indicators. Theoretical analyses and numerical results show that, when the downweighting procedure is performed, (1) the precision, all kinds of dilution of precision (DOP) metrics and the minimal detectable bias (MDB) will become larger; (2) the variations of the bias-to-noise ratio (BNR) are involved, and (3) all these results coincide with those obtained by the first-order approximation method.