3,160 research outputs found
Counting solutions without zeros or repetitions of a linear congruence and rarefaction in b-multiplicative sequences
Consider a strongly -multiplicative sequence and a prime . Studying its
-rarefaction consists in characterizing the asymptotic behaviour of the sums
of the first terms indexed by the multiples of . The integer values of the
"norm" -variate polynomial
where is a primitive -th root of unity, and
determine this asymptotic behaviour. It will
be shown that a combinatorial method can be applied to The method enables deducing functional relations
between the coefficients as well as various properties of the coefficients of
, in particular for
This method provides relations between binomial coefficients. It gives new
proofs of the two identities
and (the
-th Lucas number). The sign and the residue modulo of the symmetric
polynomials of can also be obtained. An algorithm for
computation of coefficients of is
developed.Comment: 31 pages, 2 figures. Published in Journal de Theorie des Nombres de
Bordeau
On the Intermediate Orbits of the Earth's Artificial Satellites
Intermediate orbits of artificial earth satellit
Magnetic non-collinear neutron wave resonator
Equations for the neutron reflection amplitude from a magnetic non-collinear
wave resonator (NWR) are obtained. It is shown that resonances of the same
reflection order of neutrons experiencing spin-flip (spin-flip neutrons) appear
in pairs. Conditions under which in the resonator square enhancement of the
spin-flip neutron reflection intensity with respect to growth of the portion of
scattered and absorbed neutrons takes place, are determined.Comment: Submitted to the journal "Nuclear Instruments and Methods in Physics
Research Section A". Variant 2 is after referee's revision. Corresponding
author is Yu.V. Nikitenko ([email protected]). The manuscript contains 11
pages, 7 figures and 1 table. Keywords: Polarized neutron reflectometry;
Layered structures; Neutron resonance
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