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New England Reporter
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Rotational-temperature Determination in Flowing Nitrogen Using an Electron Beam
The measurement of rotational temperature by the electron-beam fluorescence technique is investigated for temperatures between 78 K and 300 K by using the 0-0 band of the nitrogen first negative system. Existing methods for calculating the rotational temperature from electron-beam spectra result in values which are higher than the true temperature and the error increases with density and electron-beam current. The errors are believed to arise through neglect of the effects of secondary electrons. Excitation by low-energy secondary electrons can increase the population of the sparsely populated rotational ground states at the expense of the abundantly populated states. This secondary excitation is proposed as the cause of the error in the calculated rotational temperature and a theoretical study determines that the density and beam current govern the excitation rate. Rotational-temperature measurements are made in a flowing stream of nitrogen at a known temperature for a range of densities and beam currents.
A First Course in Fractional Sobolev Spaces
This book provides a gentle introduction to fractional Sobolev spaces which play a central role in the calculus of variations, partial differential equations, and harmonic analysis. The first part deals with fractional Sobolev spaces of one variable. It covers the definition, standard properties, extensions, embeddings, Hardy inequalities, and interpolation inequalities. The second part deals with fractional Sobolev spaces of several variables. The author studies completeness, density, homogeneous fractional Sobolev spaces, embeddings, necessary and sufficient conditions for extensions, Gagliardo-Nirenberg type interpolation inequalities, and trace theory. The third part explores some applic...
