We have obtained an expression for retarded potential of electromagnetic field for arbitrary moving point charged particle having a magnetic moment (corresponding terms are added to Lienard-Wiechert ...potential). The radiation reaction (recoil) force corresponding to radiation part of this field is calculated as well.
Nonimprovable, in general, estimates of the number of necessary and sufficient conditions for two Hermitian operators to be unitarily equaivalent in a unitary space are obtained when the ...multiplicities of eigenvalues of operators can be more than 1. The explicit form of these conditions is given. In the Appendix the concept of conditionally functionally independent functions is given and the corresponding necessary and sufficient conditions are presented.
A multiple Vandermonde matrix which, besides the powers of variables, also contains their derivatives is introduced and an explicit expression of its determinant is obtained. For the case of ...arbitrary real powers, when the variables are positive, it is proved that such generalized multiple Vandermonde matrix is positive definite for appropriate enumerations of rows and columns. As an application of these results, some relations are obtained which in the one-dimensional case give the well-known formula for the Euler beta-function.
Relativistic rotation and classic electrodynamics validity limit Lomidze, I.; Karkashadze, D.; Javakhishvili, J.
Proceedings of Xth International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory,
2005
Conference Proceeding
As it is known the limit of applicability of classical electrodynamics (ED) is limited with so called electron's classical radius Rcl/spl sim/elmc/sup 2/. This estimation appears in the several ...totally different approaches to the problem with one common assumption, that electron has a finite size. It is necessary to specify that there is no consecutive and strict account of the relativistic rotational movement's contribution into the calculation of energy and angular momentum of the researched objects. Such omission is that the contribution in cross section of EM waves scattering on the magnetic moment of electron can be neglected, while it is not correct for relativistic velocities. In this paper it is shown that the removal of such omission (in the context of strict relativistic description) leads to the possibility of obtaining the correct limit of applicability of classic Rcl/spl sim/h/mc.
Earlier interaction of indole-3-carbinols with L-ascorbic acid and chemical and biological properties of formed 2-skatylderivatives of L-ascorbic acid (ascorbigens) were discussed. In this ...presentation the properties and stereochemistry of products of interaction of polyfunctional biologically important indole-3-carbinols (indoleglycerol analogs and beta-hydroxytryptamine derivatives) with L-ascorbic acid are investigated. Biological significance of this reaction is discussed.
Research on the character of Georgian verse started in 1731. Since that time, some researchers have described Georgian verse as syllabic, while others have said that it is syllabotonic. The dispute ...about the character of Georgian verse became particularly acute in the 20th century. The main text the participants in the dispute analysed was a prominent piece of Georgian poetry of the 12th century – The Knight in the Panther’s Skin by Shota Rustaveli. It consists of 16-syllable monorhymical quatrains that have a special name in Georgian – shairi. There are two varieties of shairi – the so-called high shairi (4 4 4 4) and low shairi (5 3 5 3). The high shairi was the main issue of the dispute. The researchers who regarded Georgian verse as belonging to the syllabotonic system divided high shairi into trochaic feet, while the supporters of the syllabic theory denied the presence of metric trochaic stress in high shairi, believing that the penultimate syllables can be stressed only in two-syllable words but not in words with multiple syllables (due to the dactylic accentuation typical in the modern Georgian language).
Since natural dactylic stress (found in low shairi) reflects the accentuation norms of the language of the later period (including those of modern Georgian), we assume that metric stress in high shairi, which is no longer found in modern Georgian speech, could be a reflection of the natural accentuation of the comparatively earlier period in the development of the Georgian language. Checking this hypothesis by relying on relevant linguistic literature, we reconstructed the archaic movable and phonologically relevant stress in the rhymed words in The Knight in the Panther’s Skin. We found that metric stresses of both high and low shairi in this epic poem are actually archaic linguistic stresses. This conclusion differs from the views expressed in concepts developed earlier. It enables us to take a fresh look at the metrics and rhymes of The Knight in the Panther’s Skin as well as the main principles and specific features of Georgian verse in general.
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