On radicals of Novikov algebras

We show that in a prime nonassociative Novikov algebra every nonzero ideal is non-associative. We prove that Baer (and Andrunakievich) radical and left quasiregular radical coincide in finite dimensional Novikov algebras over a field of characteristic 0 or algebraically closed field of odd characteristic. We show non-existence of right quasiregular radical in finite dimensional Novikov algebras.Comment: 9 page

Semiprime Novikov Algebras

We study prime and semiprime Novikov algebras. We prove that prime nonassociative Novikov algebra has zero nucleus and center. It is well known that an ideal of an alternative (semi)prime algebra is (semi)prime algebra. We proved this statement for Novikov algebras. It implies that a Baer radical exists in a class of Novikov algebras. Also, we proved that a minimal ideal of Novikov algebra is either trivial, or a simple algebra.Comment: 11 page

Multiscale modeling of light absorption in tissues: limitations of classical homogenization approach.

International audienceIn biophotonics, the light absorption in a tissue is usually modeled by the Helmholtz equation with two constant parameters, the scattering coefficient and the absorption coefficient. This classic approximation of "haemoglobin diluted everywhere" (constant absorption coefficient) corresponds to the classical homogenization approach. The paper discusses the limitations of this approach. The scattering coefficient is supposed to be constant (equal to one) while the absorption coefficient is equal to zero everywhere except for a periodic set of thin parallel strips simulating the blood vessels, where it is a large parameter ω. The problem contains two other parameters which are small: ε, the ratio of the distance between the axes of vessels to the characteristic macroscopic size, and δ, the ratio of the thickness of thin vessels and the period. We construct asymptotic expansion in two cases: ε --> 0, ω --> ∞, δ --> 0, ωδ --> ∞, ε2ωδ --> 0 and ε --> 0, ω --> ∞, δ --> 0, ε2ωδ --> ∞, and and prove that in the first case the classical homogenization (averaging) of the differential equation is true while in the second case it is wrong. This result may be applied in the biomedical optics, for instance, in the modeling of the skin and cosmetics

On Determinants of Euro-Dollar Rates : An Empirical Study by DOLS

© 2015 Springer Science+Business Media New York. Characteristics of the wave disturbances of the ionospheric electron number density were measured using the Kharkov incoherent scatter radar. The disturbance generation accompanied the SURA heating of the near-Earth plasma by high-power periodic radiation. The distance between the heater and the radar was about 960 km. The possibility of generating ionospheric wave disturbances with a period of 20 to 30 min in the internal gravity wave range was confirmed. The disturbance propagation velocity was near 320–400 m/s, and the relative amplitude of the electron density variation was 1–10%. The wave disturbances appeared in the altitude range 145–235 km. Aperiodic bursts of the electron number density with a relative amplitude of up to 5–10% were detected after the first switch-ons of periodic radiation in the 30-min heating — 30-min pause regime at altitudes of 145 to 310 km. The observation results generally conform to the synchronous observation data obtained using the Kharkov vertical-sounding Doppler radar and a network of ionosondes