Improvement of Etalon-fringe Immunity in Diode-laser Derivative Spectroscopy

In a sensitive spectrometry with lead-salt diode lasers, etalon-fringe phenomena often intervene in the measured absorption spectrum. Derivative methods are employed for the purpose of high resolution where the pertaining wavelength is modulated. This paper presents results of mathematical examination on a possible improvement of immunity from the etalon-fringes by choosing the profile of the wavelength modulation

Harmonic transplantation and its applications to Sobolev embeddings, functional inequalities and PDEs (Women in Mathematics)

The harmonic transplantaion is proposed by Hersch in 1969. It is a generalization of the conformal transplantation and is a powerful tool for the construction of comparison functions or approximate solutions f variational problems. In this talk, I give different kinds of applications of the harmonic transplantation. Also, I report on my recent results about the embedding, the variational problem and the PDE via the harmonic transplantation

Two limits on Hardy and Sobolev inequalities (Geometric aspects of solutions to partial differential equations)

It is known that classical Hardy and Sobolev inequalities hold when the exponent p and the dimension N satisfy p < N < ∞. In this note, we consider two limits of Hardy and Sobolev inequalities as p ↗ N and N ↗ ∞ in some sense

Fast Spectrometry System with Using Tunable Laser Diode

Basic prohlems are discussed about a local, realtime and very sensitive air-pollution monitoring using a laser diode. The method employs the second derivative spectrometry replacing the incoherent light source and mechanical choppers in a traditional method with the laser diode and a newly developed electronic system. Etalon fringes at this system becomes the dominant noise source and its statistic and dynamical features are to be understood. Numerical examination was done for the optimal width of optical frequency modulation. A very fast measurement of weak absorption spectra became possible by the development of lock-in-amplifiers with finite integration time instead of a low-pass filter. Spectra of methane in 7.6 μm region and a time-dependent spectrum of the etaIon fringe are shown