Geodesic
Conditions of separability of weight factors from the sums with members of sequences of two aspects
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2013), pp. 91-100.

Voir la notice de l'article provenant de la source Math-Net.Ru

Representation of conditions of separability of integer weight factors from the sequences organizing a basis of enciphering is described. Two aspects of such sequences are considered: a geometrical progression and sequence with equal powers of natural numbers. These sequences of constant signs and alternating sequences are used when generating the relative summarized residuals, expression of each of which is located in a central part of a double inequality. Definition of conditions of separability involving the residual sequence — a geometrical progression is made with reference to its common ratio, and conditions of separability involving the the residual sequence containing equal powers of natural numbers, are found using the accompanying function introduced with reference to integer arguments of formed values of relative summarized residuals.
Keywords: separability conditions, weight factors, summarized residual, relative summarized residual, an exterior member.
Mots-clés : free multipliers 
@article{VSGTU_2013_2_a10,
     author = {A. I. Nikonov},
     title = {Conditions of separability of weight factors from the sums with members of sequences of two aspects},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {91--100},
     publisher = {mathdoc},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2013_2_a10/}
}
TY  - JOUR
AU  - A. I. Nikonov
TI  - Conditions of separability of weight factors from the sums with members of sequences of two aspects
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2013
SP  - 91
EP  - 100
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2013_2_a10/
LA  - ru
ID  - VSGTU_2013_2_a10
ER  - 
%0 Journal Article
%A A. I. Nikonov
%T Conditions of separability of weight factors from the sums with members of sequences of two aspects
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2013
%P 91-100
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2013_2_a10/
%G ru
%F VSGTU_2013_2_a10
A. I. Nikonov. Conditions of separability of weight factors from the sums with members of sequences of two aspects. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2013), pp. 91-100. http://geodesic.mathdoc.fr/item/VSGTU_2013_2_a10/

[1] A. I. Nikonov, “Enciphering on the basis of the sums with products of weight and free components as summands”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2012, no. 4(29), 199–206 | DOI

[2] J. A. Anderson, Discrete Mathematics with Combinatorics, Prentice Hall, New Jersey, 2000, 799 pp.; Dzh. Anderson, Diskretnaya matematika i kombinatorika, Vilyams, M., 2004, 960 pp.

[3] A. I. Nikonov, “Converting the Sum of Weighted Degrees of Natural Numbers with the Same Parameters”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2010, no. 1(20), 258–262 | DOI

[4] A. I. Nikonov, “Reduction of the sum of the weight equal powers to explicit combinatorial representation”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2012, no. 3(28), 163–169 | DOI | Zbl

[5] S. Banach, Rachunek różniczkowy i całkowy, tom I (Differential and Integral Calculus, vol. 1), Zakład Narodowy im. Ossolińskich, Lwów, 1929, 294 pp.; S. Banakh, Differentsialnoe i integralnoe ischislenie, Nauka, M., 1972, 424 pp.