Narrowband, tunable, frequency-doubled, erbium-doped fiber-amplifed transmitter

We report on the development of a fiber-based laser transmitter designed for active remote sensing spectroscopy. The transmitter uses a master oscillator power amplifier (MOPA) configuration with a distributed feedback diode-laser master oscillator and an erbium-doped fiber amplifier. The output from the MOPA is frequency-doubled with a periodically poled potassium titanium oxide phosphate crystal. With 35 W of single-frequency peak optical pump power, 8 W of frequency-doubled peak power was achieved. The utility of this single-frequency, wavelength tunable, power scalable laser was then demonstrated in a spectroscopic measurement of diatomic oxygen A band.     

Laguerre polynomial expansions in indefinite inner product spaces

When ?j ? 1 < α < ?j, where j is a positive integer, the Laguerre polynomials {L_n^(α)}_{n = 0}^∞ form a complete orthogonal set in a nondegenerate inner product space H which is defined by employing an appropriate regularized linear functional on H^(j)[[0, ∞); x^{α + j}e^?x]. Expansions in terms of these Laguerre polynomials are exhibited. The Laguerre differential operator is shown to be self-adjoint with real, discrete, integer eigenvalues. Its spectral resolution and resolvent are exhibited and discussed.     

Nonlinear Schrödinger equations and simple Lie algebras

We associate a system of integrable, generalised nonlinear Schrödinger (NLS) equations with each Hermitian symmetric space. These NLS equations are considered as reductions of more general systems, this time associated with a reductive homogeneous space. The nonlinear terms are related to the curvature and torsion tensors of the appropriate geometrical space. The Hamiltonian structure is investigated using “r-matrix” techniques and shown to be “canonical” for all these equations. Throughout the reduction procedure this Hamiltonian structure does not degenerate. Each of the above systems of equations is gauge equivalent to a generalised ferromagnet. Reductions of the latter are discussed in terms of the corresponding NLS type equations.     

Isoperimetric constants of manifolds with small handles

Mathematische Zeitschrift -     

Chemical shifts in ESCA and NMR

A detailed examination of the relationship between chemical shifts in ESCA and NMR is presented. It is demonstrated that even in series of closely related compounds a linear correlation between ESCA and NMR shifts cannot be expected. Included is a discussion of reorganization effects on electron binding energies. The close relation between chemical shifts of ESCA and NMR and the spin—rotation constants of molecules is pointed out.     

estimates for overdetermined Radon transforms

We prove several variations on the results of F. Ricci and G. Travaglini (2001), concerning bounds for convolution with all rotations of arc length measure on a fixed convex curve in . Estimates are obtained for averages over higher-dimensional convex (nonsmooth) hypersurfaces, smooth -dimensional surfaces, and nontranslation-invariant families of surfaces. We compare Ricci and Travaglini's approach, based on average decay of the Fourier transform, with an approach based on boundedness of Fourier integral operators, and show that essentially the same geometric condition arises in proofs using the two techniques.