Volume 46, Issue 8

The development of gauge theories is reviewed beginning with Weyl's theory of 1918 and with the changes introduced by London in the context of quantum mechanics. After a discussion of the Yang-Mills theory and Utiyama's work in the fifties the translation to the modern geometric formulation of gauge theories in terms of fiber bundles is presented

The geodesic problem is studied for a Riemannian structure, which is generated by an SO(4) trivializable gauge field. The topological and elliptic geometric defects of such a structure act as attractors for the geodesic curves

The eigenvalue problem of the Stokes operator is solved for an incompressible fluid contained between two coaxial cylinders of infinite height. Flow field patterns and spectra of the eigenmodes ("Stokes modes") are offered. Furthermore, in finite dimensional subspaces generated by these Stokes modes, the eigenproblem for the Navier-Stokes operator linearized about the laminar Taylor-Couette flow is studied. Although the spectrum's qualitative features are still correct, we quantitatively obtain wrong results. We trace this back to a Gibbs like phenomenon of higher order derivatives of the flow field as probable source, since the Stokes modes do not reflect the discontinuity arising from different velocities at both cylinders

The Planck aether substratum model explains Dirac spinors as excitons made up from vortex resonances of the positive and negative mass substratum. In the framework of this model it is conjectured that the higher particle families arise from excited states due to radial oscillations. The characteristic feature of quantum mechanics involving negative masses leads to a finite number of such excited states. Without the knowledge of the mass distribution in the excitons, a maximum number of four families can be predicted from the known mass spectrum of the leptons. Finally, it is conjectured that the small neutrino-electron mass ratio results from a compensating gravimagnetic effect, leading to a value for this ratio equal to (m(GUT)/m (Planck)) 2

We consider the adiabatic approximation as it is applied to a familiar class of infinite-dimensional equations. We show how this approximation may be directly invalidated by analyzing a statistical form of the eigenvalue equation before and after the adiabatic approximation is made. We introduce a statistical quantity which can be used to predict the existence of periodic windows in the chaotic regime

Using 2 H NMR, the dynamics of the cation in phenethylammonium bromide were studied in the two solid phases. Line shape and spin-lattice relaxation rate studies of the ammonium headgroups and the adajacent methylene groups indicate the onset of alkyl-chain motion prior to the first order phase transition. In the low-temperature phase the line shape and the spin-lattice relaxation rates of the -ND 3 groups are consistent with C 3 jumps and an activation energy of 54±4 kJ mol -1 . However, in the high-temperature phase the spin-lattice relaxation studies indicate the presence of small-angle diffusion of the -ND 3 groups around the C 3 symmetry axis. In this phase the -CD 2 - groups show line shapes typical of large-amplitude two-site jumps occurring at a rate > 10 7 s -1 . In the low-temperature phase, at temperatures below 295 K, the -CD 2 - 2 H NMR line shapes indicate that the C - D bonds are essentially static

The water proton spin-lattice relaxation time and recovery function of exchangeable water was measured in tricalcium silicate (C 3 S) gels. The measurements were carried out as a function of the hydration time and grain size. Results show that the hydration of (C 3 S) is a two stage process. A model is developped

A sensitivity modulation method was employed to measure the fluorescence spectra and quantum yields of weakly fluorescent 2-substituted (NH 2 , O, OCH 3 , CI, Br) 3-methylquinoxalines in n-hexane and methanol at room temperature. A strong decrease in the quantum yield with increasing atomic weight of the substituents was observed in n-hexane. In polar solvents, the CI substituent is the strongest quencher although its atomic weight is 2.254 times smaller than that of Br

The ion-solvent interactions involving zinc(II) salts viz. iodate, fluoride and benzoate in waterpyridine mixtures have been investigated by solubility and solvent transport number measurements. The standard Gibbs transfer energies of the salts (Δ G t º), determined from their saturation solubilities in the solvent mixtures, decrease up to x py = 0.1 for zinc(II) iodate, but up to X py = 0.4 for zinc(II) benzoate, and subsequently increase with the addition of pyridine. For zinc(II) fluoride, however, a continuous increase of ΔG t º with the addition of pyridine is observed. The transfer energy of Zn 2 + is negative and that of anions is positive with the former decreasing and the latter increasing continuously with the addition of pyridine. The solvent transport number of pyridine (<Δ py ) is positive and passes through a maximum for all the salts in the range x py = 0.25 to 0.55. These results indicate a heteroselective solvation of the salts with Zn 2 + being preferentially solvated by pyridine and the anions by water

Fluorescence quenching of anthracene and perylene has been studied in deoxygenated and nondeoxygenated two-component mixtures of CCl 4 with cyclohexane, benzene and acetonitrile. It was indicate that the dissolved oxygen only reduces the fluorescence lifetimes of the hydrocarbons, thus suppressing the efficiency of quenching

The pure rotational spectrum of sulfur trioxide has been observed for the first time. A total of 25 high-J transitions could be assigned. The rotational constants, two quartic centrifugal distortion constants, and three sextic centrifugal distortion constants were determined as: B= 10 449.0667(23) MHz, C = 5216.0330(12) MHz, D J = 9.2651 (18) kHz, D JK = -16.3922(18) kHz, H J , = -8.8(34) • 10 -3 Hz, H JK = -15.8(73) • 10 -3 Hz, and H KJ = 34.2(73) • 10 -3 Hz. An r 0 - and an r e -structure are presented: r 0 = 1.4198(7) Å (calculated from B), r 0 = 1.4210(7) Å (calculated from C), and r e = 1.4175 Å

The high-field linear and quadratic Zeeman effect has been observed in nitroethylene. The spectrum is complicated by the presence of 14 N nuclear quadrupole coupling which was reanalyzed from low-J zero-field transitions observed under high resolution. Our 14 N quadrupole coupling constants are X aa = -0.8887(18) MHz, X bb = +0.0429(29) MHz, X cc = +0.8458(29) MHz (c-axis perpendicular to the molecular plane). Our g-values and magnetic susceptibility anisotropics, fitted to the observed high-field Zeeman multiplets, are g aa = -0.15 985(39), -0.07197(31), g cc = -0.01080(32), 2ξ aa -ξ bb -ξ cc = + 19.07(43) * 10 -6 erg * G -2 * mole -1 and 2ξ bb - ξ cc - ξ aa = + 29.67(53) -10 -6 erg * G -2 * mole -1 . From them, the anisotropics in the second moments of the electronic charge distribution and the components of the molecular electric quadrupole moment with respect to the principal inertia axes system follow as <a 2 > -<b 2 > = +36.55(7)Å 2 , <b 2 > - <c 2 >= +23.58(9) Å 2 , <c2>-<a2> = -60.14(8) Å 2 , Q aa = -0.59(29) D * Å, Q bb = +0.07(36) D * Å, and Q cc = +0.52(46) D * Å. The 14 N quadrupole coupling constants, the anisotropics in the second electronic moments and the quadrupole moments are compared to the corresponding Hartree-Fock SCF values calculated with the Gaussian 88 program. The discrepancy between the experimental values and the ab initio values is considerably larger than found earlier in a similar investigation of a group of imines

Closed 1/N-energy-formulae for relativistic two-boson (m 1 ≠ m 2 ) systems with a vector exponential potential have been written down to first 1/N-order. Numerical estimates and structural properties are presented