RITZ ANALYSIS OF THE FOURIER SPECTRUM OF CH3OH BETWEEN 350 AND 950 CM(-1)

A new ''Ritz'' program has been used for revising and expanding the assignment of the Fourier transform infrared and far-infrared spectrum of CH3OH. This program evaluates the energy levels involved in the assigned transitions by the Rydberg-Ritz combination principle and can tackle such perturbations as Fermi-type resonances or Coriolis interactions. Up to now this program has evaluated the energies of 2768 levels belonging to A-type symmetry and 4133 levels belonging to E-type symmetry of CH3OH. Here we present the assignment of almost 9600 lines between 350 and 950 cm(-1). The Taylor expansion coefficients for evaluating the energies of the levels involved in the transitions are also given. All of the lines presented in this paper correspond to transitions involving torsionally excited levels within the ground vibrational state. (C) 1995 Academic Press, Inc.

Systematic analysis of the Fourier transform spectrum of (CH3OH)-C-13 between 400 and 950 cm(-1)

We have investigated a high-resolution Fourier transform (FT) absorption spectrum of the (CH3OH)-C-13 isotopomer of methanol from 400 to 950 cm(-1) with the Ritz program. We present the assignments of 7160 transitions, 3021 of which belong to Asymmetry, and 4139 to E-symmetry. These transitions occur between states labeled by K quantum numbers up to 14, and by torsional quantum numbers n up to 4. The Ritz program evaluated the energies of the 4684 involved levels with an accuracy of the order of 10(-4) cm(-1). All of the assigned lines correspond to transitions involving torsionally excited levels within the ground small-amplitude vibrational state. (c) 2005 Elsevier B.V. All rights reserved.

Landau and Kolmogoroff type polynomial inequalities

Let 0

LARGE-ORDER PERTURBATION EXPANSIONS FOR THE CHARGED HARMONIC-OSCILLATOR

The charged oscillator, defined by the Hamiltonian H = -d2/dr2+ r2 + lambda/r in the domain [0, infinity], is a particular case of the family of spiked oscillators, which does not behave as a supersingular Hamiltonian. This problem is analysed around the three regions lambda --> infinity, lambda --> 0 and lambda --> -infinity by using Rayleigh-Ritz large-order perturbative expansions. A path is found to connect the large lambda regions with the small lambda region by means of the renormalization of the series expansions in lambda. Finally, the Riccati-Pade method is used to construct an implicit expansion around lambda --> 0 which extends to very large values of Absolute value of lambda.

Assignments of FIR laser lines from optically pumped (CH3OH)-C-13

We have revisited the assignments of the far-infrared laser lines emitted by (CH3OH)-C-13 by comparing the laser systems to a high resolution Fourier transform absorption spectrum of (CH3OH)-C-13. The absorption spectrum was analyzed by means of the ''Ritz'' program, which calculates the energy level values directly from the Rydberg-Ritz combination principle. We report new assignments for 11 FIR laser transitions, 17 frequency predictions for new possible laser lines, and we confirm 11 previous assignments. (C) 1996 Academic Press, Inc.

Investigation of C-O stretching band of CD3OH: Assignments of far-infrared laser lines

We have investigated the high-resolution Fourier transform spectrum of the C-O stretching fundamental band of CD3OH in order to assign far-infrared (FIR) laser transitions. The absorption spectrum was analyzed by means of the ''Ritz'' program, which calculates the energy level values directly from the Rydberg-Ritz combination principle. We have also used the ''LaseRitz'' program to facilitate the assignment of the FIR laser lines. As a consequence we could determine 12 new assignments, confirming 4 previously proposed ones and predicting new FIR laser emissions. (C) 1997 Academic Press.

Methanol laser line assignments: evidence of four-level laser systems

The Ritz computer program, developed for facilitating the assignment of molecular Fourier transform absorption spectra and described in a previous work, determines the energy level values involved in the assigned transitions by the Rydberg-Ritz combination principle. Combining the data obtained from the analyses of high-resolution infrared (IR) and far-infrared (FIR) spectra, it is possible to predict possible FIR laser emissions of molecules. In the present work we have applied this method to the common isotopomer methanol, 12CH3 16OH, and obtained 14 proposed assignments for previously unassigned FIR laser lines. We also predict 15 possible new FIR laser emissions. For the first time, an assignment involving a four-level laser system with collisional population transfer to a slightly higher energy level is reported. © 1998 Academic Press.

Modal Analysis of a Beam with a Tip Rotor by Using a Fundamental Response

The shape modes of a damped-free beam model with a tip rotor are determined by using a dynamical basis that is generated by a fundamental spatial free response. This is a non-classical distributed model for the displacements in the transverse directions of the beam which turns out to be coupled through boundary conditions due to rotation. Numerical calculations are performed by using the Ritz-Rayleigh method with several approximating basis.

Landau and Kolmogoroff type polynomial inequalities II

Let 0 < j < m ≤ n. Kolmogoroff type inequalities of the form ∥f(j)∥2 ≤ A∥f(m)∥ 2 + B∥f∥2 which hold for algebraic polynomials of degree n are established. Here the norm is defined by ∫ f2(x)dμ(x), where dμ(x) is any distribution associated with the Jacobi, Laguerre or Bessel orthogonal polynomials. In particular we characterize completely the positive constants A and B, for which the Landau weighted polynomial inequalities ∥f′∥ 2 ≤ A∥f″∥2 + B∥f∥ 2 hold. © Dynamic Publishers, Inc.

A classificação das disciplinas matemáticas e a Mathesis Universalis nos séculos XVI e XVII: um estudo do pensamento de Adriaan van Roomen

Pós-graduação em Educação Matemática - IGCE

Ambiente web de suporte à transcrição fonética automática de lemas em verbetes de dicionários do português do Brasil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)