Quantization of Forms on the Cotangent Bundle

We consider the following construction of quantization. For a Riemannian manifold $M$ the space of forms on T ^{⋆ M} is made into a space of (full) symbols of operators acting on forms on M. This gives rise to the composition of symbols, which is a deformation of the (“super”)commutative multiplication of forms. The symbol calculus is exact for differential operators and the symbols that are polynomial in momenta. We calculate the symbols of natural Laplacians. (Some nice Weitzenb?ck like identities appear here.) Formulae for the traces corresponding to natural gradings of Ω (T ^{⋆ M} ) are established. Using these formulae, we give a simple direct proof of the Gauss–Bonnet–Chern Theorem. We discuss these results in connection with a general question of the quantization of forms on a Poisson manifold. Received: 12 November 1998 / Accepted: 1 March 1999     

An effective way to stabilize colloidal particles dispersed in polar and nonpolar media

This article offers a new approach to building up self-adjustable invertible polymer coatings at solid surfaces. The approach is based on a two-step process. In the first step, the surface of dispersed TiO2 has been functionalized with the aid of toluene diisocyanate (TDI) as a coupling agent. In the second step, the chains of amphiphilic oligoester have been covalently grafted to the titanium dioxide surface functionalized with isocyanate groups. It is shown that the titania modified in this way can form stable suspensions in both polar (water) and nonpolar (toluene) media. Multiple redispersion cycles show the ability of the modified titanium dioxide particles, after their removal from one type of dispersion and consequent drying, to be redispersed in dispersing media strongly differing by polarity from the previous.     

Frequency-lock system for microwave local oscillators using molecular absorption lines

We describe the frequency-lock (FL) system for local oscillators in receivers in the 130 to 360 GHz range, using the resonance lines of molecules with a known absorption spectrum. The functions of a frequency discriminator, a diplexer, and a noise rejector are performed by a Mach-Zehnder interferometer with a gas cell. Deceased Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 11, pp. 1399–1404, November, 1998.     

Specific features of the ferroelastic phase transition in CsLiS1−z CrzO4 solid solutions

Single crystals of the CsLiS_1?z Cr_zO₄ solid solutions (z = 0, 0.1, 0.4, 0.5, 0.9, 1.0) are grown, optical polarization studies are performed, and the birefringence and the angle of rotation of the optical indicatrix φ(T) are measured. A (z?T) phase diagram is constructed in the temperature range from 77 to ～550 K. It is established that substitution of chromium for sulfur has practically no effect on the shape of the optical indicatrix in the initial phase with Pmcn symmetry but produces strong distortions in the monoclinic phase with P112₁/n symmetry. The unusual shape of the curve φ(T) for compositions with z ≈ 1 is accounted for by the interaction of the polarization-constant tensor components a _ij. No radical differences in the patterns of the ferroelastic phase transition between CsLiSO₄ and CsLiCrO₄ are revealed (the critical exponent for the transition parameter is β = 0.33 ± 0.01). These crystals differ only in the magnitudes of the anomalies, which is associated with the large difference between the ionic radii of sulfur and chromium.     

New O-acyl derivatives of lariciresinol

Summary In an investigation of the composition of the extractive substance of the wood ofAbies sibirica Ledeb. andA. nephrolepis Maxim., new O-acylated lignans, previously unknown in nature, have been isolated. The structures of the two new compounds have been established by physicochemical methods and by independent synthesis: they are lariciresinol coumarate and ferulate.The PMR spectra of laricyl coumarate and laricyl ferulate were taken by G. A. Kalabin.Irkutsk Institute of Organic Chemistry, Siberian Branch of the Academy of Sciences of the USSR. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 162–166, March–April, 1976.     

Damage to extreme-ultraviolet Sc/Si multilayer mirrors exposed to intense 46.9-nm laser pulses

The damage threshold and damage mechanism of extreme-ultraviolet Sc/Si multilayer mirror coatings are investigated with focused nanosecond pulses at 46.9-nm radiation from a compact capillary-discharge laser. Damage threshold fluences of approximately 0.08 J/cm2 are measured for coatings deposited on both borosilicate glass and Si substrates. The use of scanning and transmission electron microscopy and small-angle x-ray diffraction techniques reveals the thermal nature of the damage mechanism. The results are relevant to the use of newly developed high-flux extreme-ultraviolet sources in applications.     

Bragg solitons in quantum-well structures

Soliton pulse propagation in a periodic quantum-well structure with a period close to one-half the light wavelength corresponding to the exciton resonance frequency was studied. The various kinds of exciton nonlinearity characteristic of a quantum well (P³-and EP²-type nonlinearities, biexciton nonlinearity) were included. The characteristic features of the soliton were studied in each of the cases considered. The effect of refractive index mismatch between the barrier and quantum-well materials on the soliton parameters was analyzed. Soliton solutions to the Maxwell-Bloch nonlinear equations are compared with their plane-wave solutions.     

Anharmonic properties of the double giant dipole resonance

A systematic microscopic study of the anharmonic properties of the double giant dipole resonance (DGDR) has been carried out, for the first time, for nuclei with mass number A spanning the whole mass table. It is concluded that the corrections of the energy centroid of the Jpi = 0(+) and 2(+) components of the DGDR from its harmonic limit are negative, have a value of the order of a few hundred keV, and follow an A-1 dependence.