Search results for "Sixth order"
showing 4 items of 4 documents
2nu3 band of 12CF4 and its simultaneous analysis with nu3
1995
Abstract A nearly Doppler-limited spectrum of the 2ν 3 band of the 12 CF 4 molecule between 2536.0 and 2599.8 cm −1 was recorded at T = 77 K using difference-frequency laser spectroscopy. The simultaneous analysis of the ground (G.S.), ν 3 = 1, and ν 3 = 2 states was performed using an isolated band model to sixth order in the tetrahedral formalism. Fourteen hundred seventy-five transitions were assigned through J = 35 to the F 2 and E vibrational components of the ν 3 = 2 level. A total of 1864 transition frequencies were fit simultaneously (1000 2ν 3 - G.S. newly assigned transitions together with 575 ν 3 - G.S. and 289 ν 3 - ν 3 transitions already reported in the literature). The ground…
A sequence of positive solutions for sixth-order ordinary nonlinear differential problems
2021
Infinitely many solutions for a nonlinear sixth-order differential equation are obtained. The variational methods are adopted and an oscillating behaviour on the nonlinear term is required, avoiding any symmetry assumption.
Moment Generating Functions and Central Moments
2018
This section deals with the moment generating functions (m.g.f.) up to sixth order of some discretely defined operators. We mention the m.g.f. and express them in expanded form to obtain moments, which are important in the theory of approximation relevant to problems of convergence.
Aminoacid zwitterions in solution : Geometric, energetic, and vibrational analysis using density functional theory-continuum model calculations
1998
Glycine and alanine aminoacids chemistry in solution is explored using a hybrid three parameters density functional (B3PW91) together with a continuum model. Geometries, energies, and vibrational spectra of glycine and alanine zwitterions are studied at the B3PW91/6-31+G∗∗ level and the results compared with those obtained at the HF and MP2/6-31+G∗∗ levels. Solvents effects are incorporated by means of an ellipsoidal cavity model with a multipolar expansion (up to sixth order) of the solute’s electrostatic potential. Our results confirm the validity of the B3PW91 functional for studying aminoacid chemistry in solution. Taking into account the more favorable scaling behavior of density funct…