Millimeter-wave Hilbert-transform spectrum analyzer based on Josephson junction

Conclusions A prototype of the Hilbert-transform spectrum analyzer based on the Josephson junctions is described and first spectral measurements are demonstrated in millimeter-wave band. The measurements in the whole millimeter-wave band may be carried out by this spectrum analyzer with resolution as low as 2 GHz and during a time interval as low as a few milliseconds. According to this set of parameters, this Josephson-effect spectrum analyzer may be used for microwave diagnostics of the thermonuclear plasma.     

Syntheses and crystal structures of ferrocenyl derivatives of biphenyl

Arylation of ferrocene with substituted biphenyldiazonium tetrafluoroborates afforded 4-bromo-, 4-nitro-, and 4-cyano-4"-ferrocenylbiphenyls. 4-Nitro- and 4-cyano-4"-ferrocenylbiphenyls were studied by X-ray diffraction analysis. In the crystals of 4-nitro-4"-ferrocenylbiphenyl, the molecules are linked via stacking - interactions.     

Rapid route to 3,4-substituted indoles via a directed ortho metalation-retro-Mannich sequence

[reaction: see text] In the presence of NXS (X = Br, I, Cl), gramine derivatives 1, derived by combined directed ortho metalation (DoM)-cross-coupling sequences, rapidly undergo retro-Mannich fragmentation (2) to afford 3-halo indoles 3 in 37-88% yields. A conceptually new methodology to diverse 3,4-substituted indoles (10, 11, 13) is thereby introduced.     

Laser photonics application in prosthetic dentistry for denture design optimization

The aim of this work is to demonstrate that holographic and speckle interferometry—laser photonics methods are compatible and useful for prosthetic stomatology. These methods allow to study the deformation of the mandible after insertion of mini-implants of various forms, and to give the practical medical recommendations.     

Modified KdV equation with a source term in a bounded domain

A mixed problem for the modified KdV equation in Q = (0,1) × (0,∞) (1) where a(t)>0, is considered. No restriction on the sign of d(t) is imposed. We prove the existence and uniqueness of strong and weak global solutions as well as the exponential decay of solutions as t→+∞. Copyright © 2006 John Wiley & Sons, Ltd.     

Root finding by divided differences

Summary A recursive method is presented for computing a simple zero of an analytic functionf from information contained in a table of divided differences of its reciprocalh=1/f. A good deal of flexibility is permitted in the choice of ordinate and derivative values, and in the choice of the number of previous points upon which to base the next estimate of the required zero.The method is shown to be equivalent to a process of fitting rational functions with linear numerators to data sampled fromf. Asymptotic and regional convergence properties of such a process have already been studied; in particular, asymptotically quadratic convergence is easily obtained, at the expense of only one function evaluation and a moderate amount of overhead computation per step. In these respects the method is comparable with the Newton form of iterated polynomial inverse interpolation, while its regional convergence characteristics may be superior in certain circum-stances.It is also shown that the method is not unduly sensitive to round-off errors.     

Synthesis and mass spectrometric study of α,ω-diallylpermethyloligosilanes

Representatives of the homologous series of α,ω-diallylpermethyloligosilanes were synthesized for the first time by the reaction of α,ω-dichloropermethyloligosilanes Cl(Me₂Si)_nCl (n = 2–6) with allylmagnesium chloride. Fragmentation of α,ω-diallylpermethyloligosilanes under electron impact ionization was studied by mass spectrometry.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2129–2132, October, 2004.