Metrical properties of the set of bent functions in view of duality

In the paper, we give a review of metrical properties of the entire set of bent functions and its significant subclasses of self-dual and anti-self-dual bent functions. We present results for iterative construction of bent functions in n + 2 variables based on the concatenation of four bent functions and consider related open problem proposed by one of the authors. Criterion of self-duality of such functions is discussed. It is explored that the pair of sets of bent functions and affine functions as well as a pair of sets of self-dual and anti-self-dual bent functions in n > 4 variables is a pair of mutually maximally distant sets that implies metrical duality. Groups of automorphisms of the sets of bent functions and (anti-)self-dual bent functions are discussed. The solution to the problem of preserving bentness and the Hamming distance between bent function and its dual within automorphisms of the set of all Boolean functions in n variables is considered

Relativistic Model of Detonation Transition from Neutron to Strange Matter

We study the conversion of neutron matter into strange matter as a detonation wave. The detonation is assumed to originate from a central region in a spherically symmetric background of neutrons with a varying radial density distribution. We present self-similar solutions for the propagation of detonation in static and collapsing backgrounds of neutron matter. The solutions are obtained in the framework of general relativistic hydrodynamics, and are relevant for the possible transition of neutron into strange stars. Conditions for the formation of either bare or crusted strange stars are discussed.Comment: 16 pages, 4 figures. Submitted to IJMP

Mathematical methods in solutions of the problems from the Third International Students' Olympiad in Cryptography

The mathematical problems and their solutions of the Third International Students' Olympiad in Cryptography NSUCRYPTO'2016 are presented. We consider mathematical problems related to the construction of algebraic immune vectorial Boolean functions and big Fermat numbers, problems about secrete sharing schemes and pseudorandom binary sequences, biometric cryptosystems and the blockchain technology, etc. Two open problems in mathematical cryptography are also discussed and a solution for one of them proposed by a participant during the Olympiad is described. It was the first time in the Olympiad history

Fitness in the education system

The authors consider the questions of the deliberate introduction fitness technologies in the system of physical education, physical culture for the development and education of children and teenagers, the youth, the recovery of the populationАвторы рассматривают вопросы целенаправленного внедрения фитнес-технологий в систему физкультурного образования, в занятия физической культурой для развития и воспитания детей и подростков, учащейся молодежи, оздоровления населени