Some Examples of the Use of Simulation in U.S. and Canadian Agriculture

Mathematical simulation is a technique widely used by agricultural engineers to determine systems interactions, to evaluate technical feasibility, to determine economic feasibility, to design complex structures and to help with managing production. In the past, simulation has been used one level removed from the farmers who manage operation on a day-to-day basis. This is changing.Three completely different types of simulations are presented: (1) a static and deterministic simulation of on-farm ethanol production that models the conversion process and determines economic feasibility; (2) a dynamic and deterministic simulation of maize production, including harvest and drying that is weather dependent; (3) a static and stochastic simulation that uses Monte Carlo techniques to obtain information about strength and performance of glued-laminated beams.We believe that inexpensive computing capability will tremendously increase the use of simulation models, such as the three described, that will help farmers better manage their production systems.     

High yield selective 3′-silylation of ribonucleosides

Procedures have been developed which permit the highly selective silylation of the 3′-hydroxyl of ribonucleosides to produce 3′,5′-diprotected derivatives in high yields.     

Analytic matrix elements of the dipole moment and Herman-Wallis coefficients

Perturbation theory proves to be a powerful approach to obtain in analytic form both vibration-rotational energies and matrix elements of the dipole moment of diatomic molecules in terms of the expansion parameter = 2B _e/gw_e,B _e and _e being, respectively, the equilibrium rotational and harmonic vibrational spectral parameters. A systematic and efficient algorithm has been developed to execute such calculations with sufficient accuracy for most physical applications when the potential-energy function is accurately represented in the Dunham form. The method also provides analytic expressions of the Herman-Wallis coefficientsC _v ^v andD _v ^v for the vibration-rotational overtone bandsv ¹v for diatomic molecules in¹ electronic states.     

Harmonic force fields and mean amplitudes of vibration for some molecules containing nitrogen: methanal azine

A harmonic force field was developed for methanal azine. The force constants were used to calculate mean amplitudes of vibration, perpendicular amplitude correction coefficients and Coriolis coupling coefficients.     

Radial Functions of Diatomic Lithium Halides X 1Σ+ From Vibration-Rotational Spectra

The radial functions for potential energy and adiabatic and nonadiabatic effects in the forms of polynomials with coefficients c_j, h_j ^Li, h_j ^X, g_j ^Li and g_j ^X of the reduced variable for internuclear distance z=2.(R-R_e)/(R+R_e) to various non-negative powers have been determined for the family of diatomic molecules of the lithium halides, LiF, LiCl, LiBr and LiI, with the corresponding results of LiH included for purposes of comparison. Trends are evident in the coefficients of lower order, but those of higher order are susceptible not only to the influence of the extent and quality of the data but also to the truncation of the power series in the representations. The various radial functions are valid with the specified ranges of internuclear distance depending on the maximum extent of vibrational excitation of the spectra.     

Does He2 Exist?

For the electronic ground state X ¹Σ⁺_g, the potential-energy function of He₂ reported by Aziz et al. has been transformed into the form V(z), containing only eight parameters, which is more suitable for the investigation of the existence of states of discrete energy. We found no evidence that a bound vibration-rotational state of the stable diatomic molecule ³He₂ or ⁴He₂, even if rotating, can exist in the electronic ground state.