Influence of Rayleigh-Doppler broadening on the selection of H2O dial system parameters

Computer simulations have enabled the performance of a H2O Differential Absorption Lidar (DIAL) system to be studied by spectrally analyzing the forward propagating and backscattered laser energy. The simulations were done for a high altitude (21 km) DIAL system operating in a nadir-viewing mode. The influence of Rayleigh Doppler broadening on DIAL measurement accuracies were evaluated and show that the Rayleigh broadening influence, which can be corrected to first order in regions free of large aerosol gradients, reduces the sensitivity of DIAL H2O measurement errors in the upper tropospheric region. The ability to correct the Rayleigh broadening and the selection of H2O DIAL parameters when all the systematic effects are combined, were discussed

Tur\'an type inequalities for Tricomi confluent hypergeometric functions

Some sharp two-sided Tur\'an type inequalities for parabolic cylinder functions and Tricomi confluent hypergeometric functions are deduced. The proofs are based on integral representations for quotients of parabolic cylinder functions and Tricomi confluent hypergeometric functions, which arise in the study of the infinite divisibility of the Fisher-Snedecor F distribution. Moroever, some complete monotonicity results are given concerning Tur\'an determinants of Tricomi confluent hypergeometric functions. These complement and improve some of the results of Ismail and Laforgia [23].Comment: 20 page

Spectral Analysis of Certain Schr\"odinger Operators

The $J$-matrix method is extended to difference and $q$-difference operators and is applied to several explicit differential, difference, $q$-difference and second order Askey-Wilson type operators. The spectrum and the spectral measures are discussed in each case and the corresponding eigenfunction expansion is written down explicitly in most cases. In some cases we encounter new orthogonal polynomials with explicit three term recurrence relations where nothing is known about their explicit representations or orthogonality measures. Each model we analyze is a discrete quantum mechanical model in the sense of Odake and Sasaki [J. Phys. A: Math. Theor. 44 (2011), 353001, 47 pages]