377 research outputs found
Harmonic analysis on local fields and adelic spaces I
We develop a harmonic analysis on objects of some category of
infinite-dimensional filtered vector spaces over a finite field. It includes
two-dimensional local fields and adelic spaces of algebraic surfaces defined
over a finite field. The main result is the theory of the Fourier transform on
these objects and two-dimensional Poisson formulas.Comment: 69 pages; corrected typos and inserted some changes into the last
sectio
Harmonic analysis and the Riemann-Roch theorem
This paper is a continuation of papers: arXiv:0707.1766 [math.AG] and
arXiv:0912.1577 [math.AG]. Using the two-dimensional Poisson formulas from
these papers and two-dimensional adelic theory we obtain the Riemann-Roch
formula on a projective smooth algebraic surface over a finite field.Comment: 7 pages; to appear in Doklady Mathematic
Effect of a Magnetic Field on the Dipole Echo in Glasses with Nuclear Quadrupole Moments
The effect of a magnetic field on the dipole echo amplitude in glasses at
temperatures of about 10 mK caused by nonspherical nuclei with electric
quadrupole moments has been studied theoretically. It has been shown that in
this case, the two-level systems (TLS's) that determine the glass properties at
low temperatures are transformed into more complicated multilevel systems.
These systems have new properties as compared to usual TLS's and, in
particular, exhibit oscillations of electric dipole echo amplitude in magnetic
field. A general formula that describes the echo amplitude in an arbitrary
split TLS has been derived with perturbation theory. Detailed analytic and
numerical analysis of the formula has been performed. The theory agrees
qualitatively and quantitatively well with experimental data.Comment: 5 pages, 3 figure
Maximum propagation speed and Cherenkov effect in optical phonon transport through periodic molecular chains
Optical phonons serve as the fast and efficient carriers of energy across
periodic polymers due to their delocalization, large group velocity because of
covalent bonding and large energy quantum compared to that for acoustic
phonons, as it was observed in a number of recent measurements in different
oligomers. However, this transport is dramatically sensitive to anharmonic
interactions, including the unavoidable interaction with acoustic phonons
responsible for the transport decoherence, suppressing ballistic transport at
long distances. Here we show that this decoherence is substantially suppressed
if the group velocity of optical phonons is less than the sound velocity of
acoustic phonons; otherwise ballistic transport is substantially suppressed by
a Cherenkov's like emission of acoustic phonons. This conclusion is justified
considering energy and momentum conservation during phonon absorption or
emission and supported by the numerical evaluation of lifetimes of the optical
phonons. It is also consistent with the recent experimental investigations of
ballistic optical phonon transport in oligomers with minor exception of
relatively short oligophenylenes.Comment: 35 pages, 16 figures, to appear in Journal of Chemical Physic
Innovative manufacturing techniques of the profiled drawing tool
In this article, the new technique of fast production of the tool of irregular shape for profiling of variable thickness wall tubes is described. The specific technological sequence is given, recommendations about computer modeling are made, and the explaining illustration for one of characteristic cases of chosen tube type profiling is given. There is an introduction defining relevance of the solved problem, and recommendations about its solution are made. © 2019 Published under licence by IOP Publishing Ltd.The reported study was funded by the state budget themes “Theoretical foundations for the development of new processes and machines for improving the competitiveness of manufactured products”, “Developing the theoretical foundations of technologies and equipment for producing new types of metal products”
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