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Regular version of the site
Of all publications in the section: 283
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Article
В.А.Васильев Математические заметки. 1996. Т. 60. № 5. С. 670-680.
Added: May 28, 2010
Article
Михайлович А. В., Кочергин В. В. Математические заметки. 2019. Т. 105. № 1. С. 32-41.

A problem of complexity of Boolean functions realization over in􏰅finite complete bases of special type is studied. These bases contain all monotone functions with zero weight and fi􏰅nite number of non-monotone functions with unit weight. Exhaustive description of Boolean realization over basis that consists of all monotone functions and one non-monotone function negation has been obtained by Markov. The minimal su􏰆fficient number of negations for arbitrary Boolean function realization (i.e. inversion complexity of the function f) equals ⌈log2(d(f)+1)⌉, where d(f) is the maximal number of function value changes from 1 to 0 over all increasing chains of tuples of variables values. In this paper the result above is generalized to the arbitrary basis of this type. It is shown that the minimal su􏰆cient for arbitrary Boolean function f realization number of non-monotone functions equals ⌈log2(d(f)/D(B) + 1)⌉. Here D(B) is the maximum d(ω) over all non-monotone functions ω from the basis B

Added: Sep 28, 2017
Article
Вьюгин И. В. Математические заметки. 2009. Т. 85. № 6. С. 817-825.
Added: Feb 27, 2013
Article
Ни Минь К., Дмитриев М. Г., Васильева А. Математические заметки. 2006. № 1. С. 120-126.
Added: Oct 3, 2011
Article
Гринес В. З., Гуревич Е. Я., Починка О. В. Математические заметки. 2014. Т. 96. № 6. С. 856-863.

For gradient-like flows without heteroclinic intersections of the stable and unstable manifolds of saddle periodic points all

of whose saddle equilibrium states have Morse index 1 or n − 1, the notion of consistent equivalence of energy functions

is introduced. It is shown that the consistent equivalence of energy functions is necessary and sufficient for topological

equivalence.

Added: Sep 29, 2014
Article
Романов А. В. Математические заметки. 2019. Т. 106. № 2. С. 295-306.
Added: Jan 30, 2019