Vertex operator representation of some quantum tori Lie algebras

We are defining the trigonometric Lie subalgebras in which are the natural generalization of the well known Sin-Lie algebra. The embedding formulas into are introduced. These algebras can be considered as some Lie algebras of quantum tori. An irreducible representation ofA, B series of trigonometric Lie algebras is constructed. Special cases of the trigonometric Lie factor algebras, which can be considered as a quantum (preserving Lie algebra structure) deformation of the Kac-Moody algebras are considered.     

Laser fluorescence-absorption analysis of iodine-129 and nitrogen dioxide impurities in a special atmosphere

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 56, No. 1, pp. 116–121, January, 1992.     

Black holes and everyday physics

Black holes have piqued much curiosity. But thus far they have been important only in remote subjects like astrophysics and quantum gravity. We show that the situation can be improved. By a judicious application of black hole physics, one can obtain new results in everyday physics. For example, black holes yield a quantum universal upper bound on the entropy-to-energy ratio for ordinary thermodynamical systems which was unknown earlier. It can be checked, albeit with much labor, by ordinary statistical methods. Black holes set a limitation on the number of species of elementary particles-quarks, leptons, neutrinos-which may exist. And black holes lead to a fundamental limitation on the rate at which information can be transferred for given message energy by any communication system.This Essay received the first award from the Gravity Research Foundation for the year 1981-Ed.     

An experiment to measure the one-way velocity of propagation of electromagnetic radiation

In this paper we describe a propagation experiment to measure the one-way velocity of electromagnetic radiation. The experiment utilizes the rotation of the earth to interchange the positions of two rubidium vapor frequency standards over12 h, thereby canceling initial clock phase differences. It is demonstrated that although the drift characteristics of modern rubidium atomic clocks may be large for long-term absolute timing requirements, the short-term random fluctuations are small. It is found that over a24-h period, the long-term drift can be accurately parameterized in retrospect and removed, thereby permitting the detection of temporal variations less than1 nsec in magnitude. With coherent summing techniques this value may be significantly reduced, and it becomes realistic to consider an experiment where the clocks are separated by distances of the order of several hundreds of meters in order to detect velocities of the order of that of the solar system with respect to the center of the galaxy(10 ⁵ m sec ^–1 ), thus ensuring that the rotational motion of the earth has a negligible effect in altering the relative inertial characteristics of the reference frames of each clock. It is demonstrated that under such conditions the measurement of the one-way speed of propagation of electromagnetic radiation is not only meaningful, but can be simply implemented with commercially available instrumentation.This study was supported at Utah State University by a grant from the USU Vice President for Research, and by NASA Grant NAGW-119.     

The microwave spectrum of thioformaldehyde,CD2S,and CH2S: Average structure,dipole moments,and 33S quadrupole coupling

Microwave transitions up to J = 53 in the ground vibrational state of deuterothioformaldehyde, CD₂S, were studied between 8 and 40 GHz. A detailed centrifugal distortion analysis yields accurate constants for comparison with force field values. The isotopic species ¹³CH₂S, CH₂³⁴S, CH₂³³S, ¹³CD₂S, CD₂³⁴S, and CD₂³³S were studied in natural abundance. Accurate average zero-point structures were determined for both CD₂S and CH₂S:

$\text{CH}{}_2\text{S}\text{CS}\text{=1.6138(4)}\text{CH}\text{= 1.0962(6)}\text{A}\text{?}\text{∠}\text{HCH}\text{=116° 16(6)′,}\text{CD}{}_2\text{S}\text{CS}\text{=1.6136(4)}\text{CD}\text{= 1.0931(4)}\text{A}\text{?}\text{∠}\text{DCD}\text{=116° 25(5)′}$

Changes in the zero-point geometry for deuterium substitution were established. Quadrupole fine structure arising from the ³³S nucleus has been measured in CH₂³³S and CD₂³³S. Analysis gives the following coupling constants (for both molecules) as χ_aa = ?11.7 and χ_bb - χ_cc = 88.1 MHz. The dipole moment of CD₂S was measured to be 1.6588(8)D and an accurate comparison with CH₂S was made; the ratio of dipole moments $\text{CD}{}_2\text{S}\text{CH}{}_2\text{S}$ was found to be 1.0062(4). The spectroscopic and bonding properties of CH₂S will be compared with formaldehyde and other molecules.     

Dynamic birefringence and conformation of molecules of aromatic polyamide-hydrazide in solutions

Flow birefringence (FB) in solutions has been investigated for a number of samples of polyamide-hydrazide (PPAH) in dimethylsulphoxide; intrinsic viscosities [η] of the same solutions have been measured. Characteristic values of FB, [η], and orientation angles [χ/g] of the solutions were determined. Molecular weights of the PPAH samples were calculated from values of [χ/g] and [η]. The use of characteristic values of [n] and [η] and the theory of optical anisotropy of persistent chains gives quantitative data on the equilibrium rigidity of PPAH molecules. It was shown that the length of the statistical segment of the PPAH chain is 800 Å. The possible reasons for the fact that the equilibrium flexibility of PPAH molecules is greater than that of poly-p-phenylene terephthalamide molecules have been discussed.     

Fluorine-containing carbocations. II. Polyfluorinated benzyl cations

When dissolved in SbF₅, polyfluorinated trifluoromethylbenzenes produce polyfluorinated α,α-difluorobenzyl ions. The ¹⁹F chemicals shifts and spin-spin coupling constants J(FF) have been analysed in terms of the resonance structures which contribute to the overall positive charge distribution. The influence of halogen atoms situated at position 4 on the downfield signal shift of α-fluorines follows the sequence F > Cl > Br which is opposite to that observed for 4-XC₆H₄CF₂⁺ ions.     

Spectrophotometric determination of thallium as thallium tetriodide

Iodide ions react with thallic ions at pH 2–8 to form a complex iodide, which is suitable for the spectrophotometric determination of thallium. The reaction has a sensitivity of 0.05 μg Tl per cm² for log $\text{I}{}_0\text{I}$ = 0.001 and obeys Beer's law up to 40 p.p.m. Optimum conditions for the reaction have been established. The standard deviation is 0.6%. The effects of temperature and pH, the ratio of thallium to reagent, stability of the complex, its conformity to Beer's law, and the rate of color formation were studied. The effect of many diverse ions was examined.     

Synthesis of poly(N-vinylpyrrolidone) and N-vinylpyrrolidone-methyl methacrylate copolymers in the presence of C-phenyl-N-tert-butylnitrone

The free-radical polymerization of N-vinylpyrrolidone and its copolymerization with methyl methacrylate have been studied at 60°C in the presence of C-phenyl-N-tert-butylnitrone as a chain-growth regulator. It has been shown that the above additive makes it possible to synthesize poly(N-vinylpyrrolidone) and its copolymers without any gel effect and to control molecular-mass characteristics of homo-and (co)polymers.