Invariant polytopes of linear systems

Stable linear systems possess invariant sets which have hyperellipsoidalregions associated with their Lyapunov function. In real systems,however, state and control variables are often confined in boundedpolyhedral regions(polytopes) so that a set of linear inequalitieshas to be satisfied. In this paper, necessary and sufficientconditions for the existence of positively invariant polytopesfor both discrete-time and continuous-time linear systems aregiven in terms of their spectral properties.     

A correlation between the order parameters of rigid solutes dissolved in two nematic solvents and in a mixture of them

The orientational data of four rigid solutes dissolved in the nematic solvents ZLI1132, EBBA and in a 55wt% ZLI1132 + EBBA mixture have been obtained from proton NMR spectra at different temperatures and used to find a relationship between the solute order in the two nematics and in their mixture. A crossed comparison of the data shows that a simple linear relation, where the normalized weights of the combination are coincident with the molar fractions of ZLI1132 and EBBA in the mixture, gives excellent agreement independently of the solutes and temperatures. Consideration is given to the possibility of a generalization of the results to any mixture of two nematics.     

Density functional theory calculations of nuclear quadrupole coupling constants with calibrated 14N quadrupole moments

Density functional calculations of the electric field gradient tensor at the nitrogen nucleus in 13 test molecules, containing 14 nitrogen sites, have been performed using the linear combination of Gaussian-type orbital Kohn-Sham density functional theory (LCGTO-KSDFT) approach. Local and gradient corrected functionals were used for all-electron calculations. All the molecular structures were optimized at their respective levels of theory with extended basis sets. Calibrated ¹⁴N nuclear quadrupole moments were obtained through a fitting procedure between calculated electric field gradients and experimental nuclear quadrupole coupling constants of the test set of molecules for each basis set and functional considered. With these calibrated ¹⁴N nuclear quadrupole moments, the nuclear quadrupole coupling constants of the following selected systems were determined: fluoromethylisonitrile, pyridine, pyrrole, imadazole, pyrazole, 1,8-bis(dimethyl-amino)naphthalene, cyclotetramethylenetetranitramine, cocaine and heroin.     

FTIR spectroscopy of the 2v3 overtone band for different BrCN isotopomers: an improved evaluation of the anharmonic force field of cyanogen bromide

The 2v₃ overtone band of six different isotopomers of cyanogen bromide has been recorded in the range from 4200 to 4400 cm^?1 with a resolution of 0.02 cm^?1 using a Fourier transform infrared (FTIR) spectrometer. This allowed us to achieve complete knowledge of the energies for all levels corresponding to double vibrational excitation. An improved evaluation of the quartic force field of cyanogen bromide has been performed using the new data obtained together with those already known from previous works. Theoretical values derived from a recent ab initio calculation have been used to constrain the potential terms which cannot be determined with sufficient precision by the least-squares analysis of the available experimental data.     

Investigation of internal and external potentials acting on benzyl halides dissolved in different nematic solvents

(Molecular Physics, 1994, 83, 309–326)     

On a problem of Pillai with Fibonacci numbers and powers of 2

In this paper, we find all integers c having at least two representations as a difference between a Fibonacci number and a power of 2.     

Body-Fitted Adjoint Formulation of the Euler Equations

The shape optimization problem governed by the Euler equations is posed in a fixed reference plane. The boundary control is exerted by a parametric mapping from the physical plane to the reference fixed plane. The adjoint equations are derived in such fixed plane. By using this approach remeshing is unnecessary; furthermore, as in many practical applications the parametric mapping can be easily differentiated, the computation of mesh sensitivities is avoided.     

The anharmonic force field of cis-1-chloro-2-fluoroethylene

A comprehensive anharmonic vibrational analysis of cis-1-chloro-2-fluoroethylene and its isotopomers has been performed on the basis of a complete ab initio quartic force field constructed by means of second-order Møller-Plesset perturbation theory (MP2) and the coupled-cluster singles and doubles approach, augmented for structural optimization and harmonic force field by a contribution of connected triple excitations (CCSD(T)). The theoretical force field was scaled by global least-squares fitting to all spectroscopic data and parameters experimentally determined for this molecule. This final force field, employing standard perturbation theory, yields a complete set of spectroscopic molecular constants providing a critical assessment of experimental rotational and centrifugal distortion constants, fundamentals, overtones, and combination bands determined over many years. Effects of Fermi and Darling-Dennison resonances were included by matrix diagonalization.     

Millimetre-wave and diode laser spectroscopy of IC 15N: anharmonic force field of cyanogen iodide from spectroscopic data and ab initio calculations

(Molecular Physics, 1998, 93, 95–106)     

THE INFLUENCE OF CYLINDER LUBRICATION ON PISTON SLAP

A model has been developed for determining the time history of piston slap impact force. This model takes into account the influence of the oil film on the impact behaviour, which was found to be an important factor. However, it was also found that entrapped gas bubbles in the oil are equally significant. Three test rigs were designed and built to study these effects on the impact phenomenon and extensive tests were carried out. The impact force time history has been determined using Reynolds' theory. Results have shown that Reynolds' theory for fluid film squeezing can be applied for oil film damping determination. However, the experimental results have also shown that when gas is entrapped during the impact, this theory considerably overpredicts the magnitude of the impact. An eight-degree-of-freedom lumped parameter model was developed through the dynamic analysis of each component of an internal combustion engine's reciprocating system. The effective damping factor derived from this model was found to be inversely proportional to the oil film thickness cubed, as expected from Reynolds' theory. A dynamic model has been proposed, where the oil film mixed with bubbles is considered to be analogous to a serial spring and damping system. By incorporating a spring in series with this damper, the effect of the bubbles can also be predicted.