Mean time exit and isoperimetric inequalities for minimal submanifolds of NxR

Based on Markvorsen and Palmer's work on mean time exit andisoperimetric inequalities, we establish a slightly better isoperimetricinequality and mean time exit estimates for minimal submanifoldsof N x when N is non-positively curved. We prove isoperimetricinequalities for submanifolds with tamed second fundamentalform in Hadamard spaces with bounded sectional curvature. Weuse mean time exit functions to show that spherically symmetricmanifolds with geodesic spheres with exponential volume growthhave a positive first eigenvalue.     

The mean curvature of cylindrically bounded submanifolds

We give an estimate of the mean curvature of a complete submanifold lying inside a closed cylinder in a product Riemannian manifold . It follows that a complete hypersurface of given constant mean curvature lying inside a closed circular cylinder in Euclidean space cannot be proper if the circular base is of sufficiently small radius. In particular, any possible counterexample to a conjecture of Calabi on complete minimal hypersurfaces cannot be proper. As another application of our method, we derive a result about the stochastic incompleteness of submanifolds with sufficiently small mean curvature. Dedicated to Professor Manfredo P. do Carmo on the occasion of his 80th birthday.     

Comparison of two gas–liquid chromatograph columns for the analysis of fatty acids in ruminant meat

Two gas–liquid chromatograph capillary columns for the analysis of fatty acids (FA) in ruminant fat are compared. Those columns are the CP-Sil 88 of 100 m long with a highly polar stationary phase and the Omegawax 250 of 30 m long with a stationary phase of intermediate polarity. Fatty acid methyl ester (FAME) patterns of branched-chain, cis and trans octadecenoate isomers, as well as conjugated and non-conjugated 18:2 and 18:3 isomers are fairly different between columns, even though most of the FAME could be separated on either column. However, the CP-Sil 88 showed better resolution of 18:1 isomers than Omegawax 250. The analysis of 96 samples of ruminant meat fat in both chromatographic systems showed that averages obtained for total FA content and for most of the individual FA did not differ between columns. Moreover, regression analysis of Omegawax and CP-Sil 88 data is highly correlated. Quantitative differences between chromatographic systems were detected for samples containing more than 66 mg fatty acids per gram of muscle dry matter.     

Riemannian Submersions with Discrete Spectrum

We prove some estimates on the spectrum of the Laplacian of the total space of a Riemannian submersion in terms of the spectrum of the Laplacian of the base and the geometry of the fibers. When the fibers of the submersions are compact and minimal, we prove that the spectrum of the Laplacian of the total space is discrete if and only if the spectrum of the Laplacian of the base is discrete. When the fibers are not minimal, we prove a discreteness criterion for the total space in terms of the relative growth of the mean curvature of the fibers and the mean curvature of the geodesic spheres in the base. We discuss in particular the case of warped products.     

Solvatochromic relationship: Prediction of distribution of ionic solutes in aqueous two-phase systems

Partition ratios of several ionic compounds in 20 different polymer/polymer aqueous two-phase systems (ATPS) containing 0.15 M NaCl in 0.01 M phosphate buffer, pH 7.4, were determined. The differences between the electrostatic properties of the phases in all the ATPS were estimated from partitioning of the homologous series of dinitrophenylated-amino acids. Also the solvatochromic solvent parameters characterizing the solvent dipolarity/polarizability (π*), solvent hydrogen-bond donor acidity (α), and solvent hydrogen-bond acceptor basicity (β) of aqueous media were measured in the coexisting phases of the ATPS. The solute-specific coefficients for the compounds examined were determined by the multiple linear regression analysis using the modified linear solvation energy relationship equation. The minimal number of ATPS necessary for determination of the coefficients was established and 10 ATPS were selected as a reference ATPS set. The solute-specific coefficients values obtained with this reference set of ATPS were used to predict the partition ratios for the compounds in 10 ATPS not included in the reference set. The predicted partition ratios values were compared to those determined experimentally and found to be in good agreement. It is concluded that the presented model of solute–solvent interactions as the driving force for solute partitioning in polymer/polymer ATPS describes experimental observations with 90–95% accuracy.     

Natural radionuclides content and radon exhalation rate from Brazilian phosphogypsum piles

Phosphogypsum is a waste of the wet-acid process for producing phosphoric acid from phosphate rock. For every ton of phosphoric acid obtained, from the reaction of phosphate rock with sulphuric acid, about four tons of phosphogypsum are produced. The level of radioactivity present in the phosphogypsum, among other impurities, prevents its reuse for a variety of purposes. Large quantities of phosphogypsum have been produced worldwide. In 2006, the annual production was estimated to be about 170 million tons. Brazilian annual production of phosphogypsum reaches 5.5 million tons. Brazil, like other countries that produce phosphate fertilizer, tries to find solutions for the safe applications of phosphogypsum, in order to minimize the impact caused by its disposal. Most of the worldwide phosphogypsum is stockpiled, posing environmental concerns. The monitoring of air and groundwater pollution, radon exhalation rate and direct exposure to gamma radiation for workers should be considered. The aim of this study is to evaluate the natural radionuclides content and the radon exhalation rate from phosphogypsum piles from Ultrafertil and Fosfertil fertilizer industries. Samples of this material were analyzed by gamma ray spectrometry for their radionuclide content. Radon exhalation rate was measured by the activated charcoal collector method. A theoretical model for radon exhalation calculation, suggested by UNSCEAR, was applied in order to corroborate the experimental results.