Study of a Microwave Radar Signal Backscattered at Small Incidence Angles: In-Situ Measurements

We present the results of data processing of the field experiment devoted to a study of a microwave signal backscattered by a rough water surface and compare them with the theoretical estimates. The measurements were conducted sequentially using a radar with parabolic and knife-beam antennas. The radar was mounted on the Molitovsky bridge at a height of 40 m across the Oka river in Nizhny Novgorod, Russia. For the radar with knife-shaped antenna pattern, we examined the reflected-signal power and the shift and width of the Doppler spectrum as functions of the azimuthal angle for the nadir sounding. For the parabolic antenna, we studied the reflected-signal power as a function of the incidence angle. Comparison with the experimental data shows that the developed theoretical model of a Doppler spectrum is in good agreement with the observations. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 8, pp. 661–673, August 2005.     

Functional analysis proofs of Abel's theorems

We give alternative proofs to the classical theorems of Abel, using the concept of Berezin symbol.

     

Spectral characteristics of a microwave radar signal backscattered by the sea surface at small incidence angles

We present a theoretical analysis of the Doppler-spectrum properties of a microwave radar signal scattered by the sea surface at small incidence angles. The dependences of Doppler-spectrum width and shift on the wind velocity and wave development stage and their azimuthal dependence are analyzed. The case of mixed sea (wind wave plus swell) is also considered. The JONSWAP spectrum model is used to describe sea waves. The study shows that Doppler-spectrum parameters are sensitive to variation of sea-surface state; for example, for the case of developed sea waves, an increase in wind velocity by 1 m/sec leads to increases in the Doppler-spectrum width and shift by 15 Hz and 3 Hz, respectively. It is shown that for the case of a moving radar the Doppler spectrum remains sensitive to variation of sea- surface state with a sufficiently narrow radar directivity pattern. Estimates show that in the case of a single sea- wave system on the surface, using Doppler-spectrum parameters we can, in principle, determine wave type (developing wind wave, developed wind wave, or swell), dominant wavelength, wave propagation direction, and wave height; wind velocity, direction, and acceleration distance can be determined for wind waves.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 5, pp. 517–526, May, 1996.This paper was supported by the Russian Foundation for Fundamental Research (project 93-02-15892).     

Muonium adduct radicals from vinyl-aromatic compounds

During irradiation of liquid samples of 1-vinylimidazole, 2-vinylnaphthalene, 2-vinylpyridine, 4-vinylpyridine and 1,1-diphenylethene with positive muons, radicals of the type MuCH₂ĊHAr (Ar=the appropriate aromatic group), and the MuCH₂ĊPh₂ radical were observed by transverse field μSR; the muon hyperfine couplings are considered in the context of the effectiveness of the aryl groups in delocalising the unpaired electron.     

Three-pencil lattices on triangulations

In this paper, three-pencil lattices on triangulations are studied. The explicit representation of a lattice, based upon barycentric coordinates, enables us to construct lattice points in a simple and numerically stable way. Further, this representation carries over to triangulations in a natural way. The construction is based upon group action of S ₃ on triangle vertices, and it is shown that the number of degrees of freedom is equal to the number of vertices of the triangulation.      

Multiscale Finite Element Modeling of Arc Dynamics in a DC Plasma Torch

The dynamics of the electric arc inside a direct current non-transferred arc plasma torch are simulated using a three-dimensional, transient, equilibrium model. The fluid and electromagnetic equations are solved numerically in a fully coupled approach by a multiscale finite element method. Simulations of a torch operating with argon and argon–hydrogen under different operating conditions are presented. The model is able to predict the operation of the torch in steady and takeover modes without any further assumption on the reattachment process except for the use of an artificially high electrical conductivity near the electrodes, needed because of the equilibrium assumption. The results obtained indicate that the reattachment process in these operating modes may be driven by the movement of the arc rather than by a breakdown-like process. It is also found that, for a torch operating in these modes and using straight gas injection, the arc will tend to re-attach to the opposite side of its original attachment. This phenomenon seems to be produced by a net angular momentum on the arc due to the imbalance between magnetic and fluid drag forces.     

Equivalence of regularity for the Bergman projection and the\bar \partial-neumann operator

A necessary and sufficient condition for regularity of the -Neumann operator on (0,q)-forms in a smooth bounded pseudoconvex domain in Cⁿ is that the orthogonal projections onto -closed forms of degrees (0,q−1), (0,q), and (0,q+1) all be regular. The first author partially supported by NSF Grant DMS-8701038     

Spectral multiplicity of certain contractions

One computes the spectral multiplicity of the direct sum of operators of the following form: a unitary operator U=U_aU_s, a contraction T of class C₀, a one-sided shift S, and its conjugate S*. Theorem: where _mo=1 if m=0 and _mo=0 it m>0.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 157, pp. 23–29, 1987.