Theory of Valuations on Manifolds: A Survey

This is a non-technical survey of a recent theory of valuations on manifolds constructed in [A10], [A11], [AF] and [A12], and actually a guide to this series of articles. We also review some recent related results obtained by a number of people. Received: February 2006, Revision: June 2006, Accepted: June 2006     

Sol-Gel Particulate Float Process to Make Vitreous Silica Bodies

Particulate sol-gel technology uses larger particles than that of alkoxide-derived gels and provides larger pore sizes in the gelled object. This allows relatively rapid drying and fabrication of large rods or tubular shapes. However, the formation of more complex or flat shapes, which require extensive surface contact with a mold, is more difficult. The shrinkage during drying, with the significantly greater stress of surface friction due to adhesion, frequently leads to cracking.We have demonstrated a solution to this problem by floating the gel on the surface of a dense liquid. Dry silica panels up to 28 × 40 × 0.7 cm³ were prepared in this way. The use of patterning molds allowed the fabrication of more sophisticated shapes. These bodies were sintered to transparent vitreous silica articles of near net dimensions.     

Thermodynamics of condensation of phthalonitrile with m-phenylenediamine

Conclusions The reaction of phthalonitrile condensation with m-phenylenediamine is thermodynamically allowed at temperatures from 250° to 500°K, and its equilibrium is almost completely shifted toward the formation of the macroheterocycle.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 4, pp. 779–787, April, 1984.     

Direct measurements of long-range surface forces in gas and liquid media

A modified set-up was applied to carry out direct measurements of the forces of molecular attraction of gold spheres and crossed quartz filaments in air within the region of distances from 10 to 100 nm. Some quantitative deviations from Lifshitz's theory for gold may be attributed to an insufficient reliability of the spectral data used in the calculations. The DLVO theory adequately describes the interaction of glass threads in KCl (10^?3 ÷ 10^?5 N) solutions within the region of 5 to 100 nm. At a distance smaller than 5 nm, the deviations from DLVO theory are attributable to the influence of structural forces.When the contact between crossed hydrophobized quartz threads in water is broken, the attraction forces (which exceed the molecular forces by several orders of magnitude) at a distance of up to 300 nm are detected.     

Syntheses and structures of methyltris(pyrazolyl)silane complexes of the group 6 metals

The methyltris(3,5-dimethylpyrazolyl)silane ligand, TpsMe2, was readily prepared by the metathesis reaction of methyltrichlorosilane with 3 equiv of lithium 3,5-dimethylpyrazolate. The octahedral tricarbonyl complexes (TpsMe2)M(CO)3 were synthesized either by ligand exchange with the labile nitrile adducts M(CO)3(NCR)3 (M = Cr, Mo, R = Me; M = W, R = Et) or thermally by direct substitution on the hexacarbonyls M(CO)6 (M = Cr, Mo). The three new complexes were characterized by a combination of analytical and spectroscopic techniques, including electrospray ionization mass spectrometry and single-crystal X-ray diffraction. They are all isostructural and display in the solid state the expected distorted octahedral geometries with facially coordinated tris(pyrazolyl)silane ligands. Crystallographic data were used to calculate the ligand cone angles (251-264 degrees) in (TpsMe2)M(CO)3 and also to estimate a value of 1.59 A for the covalent radius of octahedral W(0).     

Overview: Synchronization and patterns in complex systems

The theory of complex systems, such as neural assemblies or lattices of chaotic oscillators has generated many new problems including the synchronization or regularization of the cooperative behavior of systems consisting of chaotic elements, regular spatial patterns in "chaotic" lattices, and so on. A number of these problems were discussed at the International School in Nonlinear Science-95 (Nizhniy Novgorod, Russia). In this overview we try to formulate some of the most interesting problems that were discussed at that meeting. (c) 1996 American Institute of Physics.