Analysis of light scattering by a particle inside a layer by the method of discrete sources
Analysis of light scattering by a particle inside a layer by the method of discrete sources
E.Yu. Eremina, A.G. Sveshnikov
A mathematical model of the problem of light scattering by a particle residing inside a layer on a substrate is analyzed on the basis of the method of discrete sources. A computational algorithm has been constructed. Computation results have been presented for light scattering by particles of various materials.
Show AbstractOn conditionally well-posed inverse problems
On conditionally well-posed inverse problems
V.B. Glasko, Yu.V. Glasko, D.G. Polyanin, S. V. Rodionov
The possibilities of a natural conditional well-posed statement and algorithmization of two problems of immunology and seismology are discussed. The results of a mathematical experiment on estimating the modulus of continuity have been presented.
Show AbstractRenormalization along the lines: normal and anomalous Ward identities in the Yang-Mills model
Renormalization along the lines: normal and anomalous Ward identities in the Yang-Mills model
D.A. Slavnov
A generating equation for normal and anomalous Ward identities in the Yang-Mills model has been obtained in the framework of the dimensional renormalization along the lines. It has been confirmed that only one-loop diagrams are responsible for the chiral anomalies.
Show AbstractSurprises of quantum measurements
Surprises of quantum measurements
Yu.I. Vorontsov
Formal analysis of the state of an object after measuring its coordinate shows that the conditional variance of the momentum may depend on the result of coordinate measurement and be smaller than the momentum variance in the initial state even if there is no correlation between the momentum and the momentum squared with the coordinate. This fact cannot be interpreted on the basis of ordinary statistics, exemplifying still another nonclassical consequence of the quantum theory.
Show AbstractDirac fermion in strong coulomb field in 2+1 dimensions
Dirac fermion in strong coulomb field in 2+1 dimensions
V.R. Khalilov
The effect of charged fermion pair production hy a strong external Coulomb field in two spatial dimensions is studied. Exact solutions to the Dirac equation have been found for a Coulomb field in 2+1 dimensions. It is shown that the behavior of the lower energy levels of an electron in a strong Coulomb field differs significantly in the cases of two and three spatial dimensions. An equation has been obtained for the critical charge and solved numerically for a simple model. The critical charge in 2+1 dimensions is much smaller than its value for the same model in 3+1 dimensions.
Show AbstractGlobal synchronization in a chain of parametrically coupled quadratic mappings
Global synchronization in a chain of parametrically coupled quadratic mappings
A.Yu. Loskutov, S.D. Rybalko
A chain of parametrically linearly coupled quadratic mappings was analytically shown to have global synchronization, i.e., that the system tends to a trivial equilibrium state.
Show AbstractDetermination of electromagnetic form factors of nucleon resonances from data on $\gamma p\to \Delta^{++}\pi^-$ and $\gamma p\to p\rho^0$ reaction cross sections
Determination of electromagnetic form factors of nucleon resonances from data on $\gamma p\to \Delta^{++}\pi^-$ and $\gamma p\to p\rho^0$ reaction cross sections
E.N. Golovach$^1$, V.S. Zamiralov$^1$, B.S. Ishkhanov$^1$, V.I. Mokeev$^1$, G. Rico$^2$, M. Ripani$^2$, D.A. Rodionov$^1$
A method for extracting form factors $N^*$ from the experimental data on cross sections of exclusive reactions $\gamma_{r,v} p \rightarrow \Delta^{++} \pi^{-} $ and $\gamma_{r,v} p \rightarrow p \rho^0$ has been developed. It is shown that the method ensures stable calculation of form factors with an inaccuracy of about 10% if the errors in measuring cross sections of said quasi-two-particle reactions do not exceed 3%.
Show AbstractImproving the sensitivity of radiometric systems by signal postdetector digital processing
Improving the sensitivity of radiometric systems by signal postdetector digital processing
V.V. Gladun, A.I. Dubina, Yu.A. Pirogov
A digital method is described for processing the postdetector signal that makes it possible to maximize the sensitivity of radiometric systems. The method also allows for adapting radiometric systems to operation in microwave imaging devices using phased antenna arrays in scanning the scenes observed in real time.
Show AbstractAcoustooptic light modulation in an isotropic medium in the case of strong acoustooptic interaction
Acoustooptic light modulation in an isotropic medium in the case of strong acoustooptic interaction
V.I. Balakshy, I.A. Nagaeva
The results are presented of theoretical studies into the diffraction of light by an amplitude-modulated acoustic wave in conditions of strong acoustooptic interaction. The diffraction efficiency is calculated for a Bragg-type modulator. It is demonstrated that where the modulation frequency is high enough, the symmetry of the acoustooptic coupling is disturbed so that the diffraction efficiency may be as high as 94% even for a focused light beam.
Show AbstractCalculation of associated mass tensor in the problem of the Earth's hard core motion
Calculation of associated mass tensor in the problem of the Earth's hard core motion
S.L. Pasynok
We have calculated the associated mass tensor for harmonic oscillations of the Earth's hard core. The consideration of this tensor causes free oscillation periods of the Earth's inner core to increase by approximately an hour. For some values of the core density, the periods of oscillation are close to the experimental ones obtained by D. E. Smylie. The splitting of experimental frequencies can well be interpreted as the splitting of the equatorial mode of free oscillations of the inner core in the gravity field of the asymmetric shell, provided that the latter possesses a corresponding quadrupole moment.
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