A Blow-Up Criterion for Classical Solutions to the Compressible Navier-Stokes Equations

In this paper, we obtain a blow up criterion for classical solutions to the 3-D compressible Naiver-Stokes equations just in terms of the gradient of the velocity, similar to the Beal-Kato-Majda criterion for the ideal incompressible flow. In addition, initial vacuum is allowed in our case.Comment: 25 page

Diffusion MRI in early cancer therapeutic response assessment

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/136261/1/nbm3458_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136261/2/nbm3458.pd

Electrodynamics of Media

Contains research objectives, summary of research and reports on one research project.Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DAAB07-71-C-0300U.S. Air Force Cambridge Research Laboratories Contract F19628-70-C-0064M.I.T. Sloan Fund for Basic Research(Grant 616)M.I.T. Lincoln Laboratory Purchase Order A-627

Nonlocalized modulation of periodic reaction diffusion waves: The Whitham equation

In a companion paper, we established nonlinear stability with detailed diffusive rates of decay of spectrally stable periodic traveling-wave solutions of reaction diffusion systems under small perturbations consisting of a nonlocalized modulation plus a localized perturbation. Here, we determine time-asymptotic behavior under such perturbations, showing that solutions consist to leading order of a modulation whose parameter evolution is governed by an associated Whitham averaged equation

Geotecnologias e aprendizagem espacial em ambiente educacional: o mapeamento de nascentes utilizando técnicas de geoprocessamento por meio de softwares livres.

The headwaters of streams are extremely important to maintain the water sources and contribute to the permanent preservation areas (PPA) and hence with the ecosystems of any region. Thus this aspect were investigated by mapping using GIS techniques by free software. The data were validated by field research conducted by students of the 1st year of high school ? Escola Estadual de Ensino Médio Pedro Migliorini, located in the municipality of Monte Belo do Sul, Brazil. The objective of the study was to allow students to assess quantitatively and qualitatively the headwaters of the city, analyzing water usage, as well as the situation of the same as the environmental laws. Students were divided into work areas, conducted interviews with landowners in order to research on the consumption and use of water and what methods are used for the preservation of the spring on the property. To assess if the sources informed the owners comply with current legislation, GIS tools were employed and was generated a buffer of 50 meters (area corresponding to PPA) around the source. At the end of the study were located 427 points with the following observations: 1) 95 are used for human consumption, 2) 107 for animal consumption, 3) 145 have some protection; 4) 23 are in accordance with current legislation . 37 springs were not informed about the use