Abstract
We derive likelihood ratio tests for the equality of the directional parameters of k bipolar Watson distributions defined on the hypersphere with common concentration parameter. We analyze the power of these tests in the case of two distributions supposing in the alternative hypothesis two directional parameters forming an angle, which varies from 18 degrees to 90 degrees. We also compare the likelihood ratio tests with a high-concentration F-test.

Abstract
As the Watson distribution is frequently used for modeling axial data, it is important to investigate the existence of possible outliers in samples from this distribution. Then, we develop for the bipolar Watson distribution defined on the hypersphere, some tests of discordancy of an outlier or several outliers en bloc based on the likelihood ratio, supposing an alternative model of contamination of slippage type. We evaluate the performance of these tests of discordancy of an outlier and we also compare some tests of discordancy of an outlier available for this distribution.

Abstract
After characterization of preferred conditions for Helicobacter pylori survival in the sessile state, it was observed that the bacterium transforms from spiral to coccoid under mild circumstances, whereas under extreme ones it is unable to undergo shape modification. This strongly supports the view that transformation into the coccoid form is an active, biologically led process, switched on by the bacterium as a protection mechanism.

Abstract
Bread is one of the most consumed staple food by man. However, its high salt level has been while of concern, especially because of the relationship between salt intake and Hipertension development, with high prevalence in Portugal. The purpose of this study was to analyse the sodium content in white bread, the most consumed bread by Portuguese. This study was developed in two different phases, March and May. To quantify the sodium level, flame photometry technique has been used, previously validated for the study. The bread samples were acquired in 80 different bakeries located in 12 different areas of Oporto city. The sodium concentration in bread samples ranged between 344 mg/100g and 718 mg/100g (mean 534 mg/100g, standard deviation 30 mg/100g). There was no significant association between the weight of the bread and its sodium concentration. The principal component decomposition of the studied variables allows the observation of the different characteristics of the evaluated areas of Oporto.

Abstract

Abstract