Incompressible Flow Around a Small Obstacle and the Vanishing Viscosity Limit

In this article we consider viscous flow in the exterior of an obstacle satisfying the standard no-slip boundary condition at the surface of the obstacle. We seek conditions under which solutions of the Navier-Stokes system in the exterior domain converge to solutions of the Euler system in the full space when both viscosity and the size of the obstacle vanish. We prove that this convergence is true assuming two hypotheses: first, that the initial exterior domain velocity converges strongly in L ² to the full-space initial velocity and second, that the diameter of the obstacle is smaller than a suitable constant times viscosity, or, in other words, that the obstacle is sufficiently small. The convergence holds as long as the solution to the limit problem is known to exist and stays sufficiently smooth. This work complements the study of incompressible flow around small obstacles, which has been carried out in [4–6].     

Geochemical analysis of Minho Estuary sedimentary record and its contribution to palaeoenvironmental evolution

Two sediment cores (~30 m long) were retrieved at the mouth of the Minho Estuary to assess its palaeoenvironmental evolution for the last millennia. Samples were characterized by Energy-Dispersive X-Ray Fluorescence Spectrometry and Instrumental Neutron Activation Analysis, complemented by sedimentological analyses. Provenance of major and trace element contents (lithogenic or biogenic, continental or marine) is assessed. The influence of grain size effect on total element concentration is discussed. Most of the samples present a negative Eu anomaly. Sedimentological and geochemical parameters allow differentiating four geological units––fluvial, marine, estuarine and sand barrier––which reflects the temporal evolution of the Minho Estuary.     

Evaluation of Cashew Apple Juice for Surfactin Production by Bacillus subtilis LAMI008

Bacillus subtilis LAMI008 strain isolated from the tank of Chlorination at the Wastewater Treatment Plant on Campus do Pici in Federal University of Ceará, Brazil has been screened for surfactin production in mineral medium containing clarified cashew apple juice (MM-CAJC). Results were compared with the ones obtained using mineral medium with glucose PA as carbon source. The influence on growth and surfactin production of culture medium supplementation with yeast extract was also studied. The substrate concentration analysis indicated that B. subtilis LAMI008 was able to degrade all carbon sources studied and produce biosurfactant. The highest reduction in surface tension was achieved with the fermentation of MM-CAJC, supplemented with yeast extract, which decreased from 58.95?±?0.10 to 38.10?±?0.81 dyn cm^?1. The biosurfactant produced was capable of emulsifying kerosene, achieving an emulsification index of 65%. Surfactin concentration of 3.5 mg L^?1 was obtained when MM-CAJC, supplemented with yeast extract, was used, thus indicating that it is feasible to produce surfactin from clarified cashew apple juice, a renewable and low-cost carbon source.     

Analysis of Biogenic Amines Using Immunoassays,HPLC, and a Newly Developed IC-MS/MS Technique in Fish Products—A Comparative Study

In this study, comparative analyses were carried out with ion chromatography mass-spectrometry (IC-MS/MS) which has no derivatization step, high-performance liquid chromatography (HPLC) technique, as well as two quantitative and two semi-quantitative immunoassays. The results demonstrated that HPLC and quantitative immunoassay methods were well-correlated with IC-MS/MS in determining histamine in various types of fish products. The best correlation was observed with the HistaSure ELISA Fast Track kit (R² = 0.9903). More than half of the values (68%) obtained by two methods were also statistically similar. The results of semi-quantitative test kits also supported histamine values estimated by quantitative methods, with some exceptions. The best results were found for HistaSure Lateral Flow in supporting the quantitative techniques. Therefore, these methods are found suitable for monitoring histamine in fish products in terms of food safety. Good correlations were also observed HPLC and IC-MS/MS in determining cadaverine, putrescine, and tyramine with the highest value observed for tyramine as R² = 0.9785. However, no correlation was observed for other biogenic amines, and the majority of the results were significantly different from each other for these amines (p < 0.05). The differences may be caused by the drawbacks reported previously for HPLC. However, further studies are required to confirm the possible effects. This study provides a comparative evaluation of several methods in terms of their suitability in determining biogenic amines in fish products for both monitoring and regulatory purposes.     

Quasi-Greedy Triangulations Approximating the Minimum Weight Triangulation

This article settles the following two longstanding open problems:

• What is the worst case approximation ratio between the greedy triangulation and the minimum weight triangulation?

• Is there a polynomial time algorithm that always produces a triangulation whose length is within a constant factor from the minimum?

The answer to the first question is that the known lower bound is tight. The second question is answered in the affirmative by using a slight modification of anO(n log n) algorithm for the greedy triangulation. We also derive some other interesting results. For example, we show that a constant-factor approximation of the minimum weight convex partition can be obtained within the same time bounds.     

Nonlinear shoaling of shallow water waves: perspective in terms of the inverse scattering transform

Summary We study nonlinear interactions in measured surface wave trains obtained in the Northern Adriatic Sea about 16 kilometres from Venice, Italy.Nonlinear Fourier analysis is discussed in terms of the exact spectral solution to the Korteweg-deVries (KdV) equation as given by theinverse scattering transform (IST). For the periodic and/or quasi-periodic boundary conditions assumed herein, the approach may be viewed as a nonlinear, broad-banded generalization of the ordinary, linear Fourier transform. In particular, we study solition interactions, their properties and the nonlinear dynamics of the radiation (or oscillation) modes as found from the inverse scattering transform analysis. We also conduct a number of computer experiments in which measured wave trains are numerically propagated forward in time toward shallow water and backward in time into deep water in order to assess how the nonlinear wave dynamics are influenced by propagation over variable bathymetry. On this basis we develop a scenario for the evolution of nonlinear wave trains, initially far offshore in deep water, as they propagate into shallow water regions. The deep-water waves have a small Ursell number and are hence not very nonlinear; as they propagate toward shallow water, the Ursell number gradually increases in the numerical experiments by about an order of magnitude. A useful parameterization of nonlinearity in these studies is the ?spectral modulus,? a number between 0 and 1, which is associated with each IST spectral frequency. Small values of the modulus mean that a particular spectral component is linear (a sine wave); large values of the modulus (≈1) indicate that the component is nonlinear (a soliton). There is a systematic increase of the modulus as the waves propagate into shallow water where nonlinear effects predominate; we describe how the modulus varies as a function of spectral frequency during this shoaling process. The results suggest that the effect of increasing nonlinearity ?saturates? the IST spectrum (i.e. the modulus ≈1 for all frequencies) to that virtually all spectral components become solitons in sufficiently shallow water.     

Graph theory and molecular orbitals

A simple algorithm for the determination of the number of zeros in the molecular graphs of alternant cata-condensed conjugated hydrocarbons is derived. For non-branched hydrocarbons it is shown that, from the topological point of view, only four types of ring systems exist. The given algorithm enables the derivation of a number of general regularities relating the structural features of the molecule with its stability.     

一个太阳活动区的频谱

本文得出了活动区AR 2490的射电频谱,波长范围从0.8cm到20cm.在λ≥2.8cm,活动区呈现双重结构.在λ=6cm时出现的回旋共振吸收是该活动区悬浮在黑子上空不透明度的主要源,它在与H_α谱斑相协的射电源中也起着重要的作用.     

Phase relations in the system Bi2O3CdO

Phase relations in the system Bi₂O₃CdO were studied in the composition range from 90-30 mole% Bi₂O₃. A new phase, Bi₂O₃ · CdO, was found to exist up to 925 K. At this temperature it decomposes to form CdO and the 5Bi₂O₃ · 3CdO phase. The 5Bi₂O₃ · 3CdO phase is stable between 925 and 963 K and melts incongruently. Below 925 K it decomposes to Bi₂O₃ · CdO and 6Bi₂O₃ · CdO. The phase 5Bi₂O₃ · 3CdO has cubic symmetry. The Sillenite-type bcc phase 6Bi₂O₃ · CdO forms above 897 K from oxide mixtures in the solid state or from fused oxide mixtures, but the compound could never be prepared as a single phase.