Russian Journal of Mathematical Research. Series A

3-9

Authors: Samuel Bonaya Buya

In this research proof of Legendre conjecture is presented. The proof is based on a property possessed exclusively by all prime numbers. That is, the positive square-root of any prime number is an irrational number that always lies between two consecutive positive integers. This property excludes the number one from the set of prime numbers. Not all composite numbers possess this sure property possessed by all prime numbers. It is this special property of prime numbers special property of prime numbers that makes Legendre conjecture a sure law for all prime numbers. In the process of seeking to prove Legendre’s conjecture the prime gap problem is resolved and Riemann hypothesis reviewed in the light of these findings.

16-25

Authors: Rafik A. Khachatryan

In the paper the question of the existence of a differential inclusion under the initial condition is considered. It is assumed that a multivalued mapping a continuous and the sets are almost convex.

3-14

Authors: Sergei A. Aivazian, Mikhail Y. Afanasiev, Alexander V. Kudrov

The methodological basis is developed and tested for building indicators which shows the main directions of economic development of regions of the Russian Federation. The novelty of the results is determined by the fact that these indicators are built on the basis of a common vector basis. Two groups of indicators that characterize the different directions of the economic development: "production of products and services" and "material welfare" are highlighted in the structure of the main indicators of social and economic development. Two indicators are constructed based on the vector basis, each of which is maximally correlated with the indicator formed on the basis of corresponding group indicators. It is shown that for the considered direction of regional development the vector basis provides a higher consistency of the indexes and ranks of regions than the first major components.

19-22

Authors: Samuel Bonaya Buya

In this research Riemann hypothesis is investigated for a proof. A functional extension of the Riemann zeta function is proposed for which non trivial zeroes can be generated. It found that non trivial zeroes can also be generated outside the critical strip. Thus it is found that the Riemann hypothesis is found to be incomplete.

31-37

Authors: Irina L. Makarova, Viktor I. Samarin

Examples of solving by the simplex method some linear programming problems in which it is possible to improve the algorithm for reducing computations are considered.

36-48

Authors: Viktor I. Samarin, Irina L. Makarova, Natalya F. Yakunina

The range of admissible values of the real roots of a quadratic equation with fuzzy parameters, taking into account the requirements for satisfying the formulas of Viet's theorem, is analyzed. The formulas for the boundary values of the fuzzy real roots of the quadratic equation are given. On the example of the solution of fuzzy cooperative game, a method is proposed for finding the roots of a quadratic equation with zero discriminant.

62-66

Authors: Nikolay V. Shipov

Steinhaus theorem about uniformly equiconverged Fourier series argues that the difference between the partial sums uniformly tends to zero when for any summable function and the function which satisfies the Lipchitz conditions of first order. In the present work it is proved that this theorem remains fair, if the function belongs to the , and the function satisfies the Lipchitz condition of order . The results obtained can be used when examining the conditions of convergence of Fourier series in a fixed location, as well as in examining the conditions of uniform convergence (or absolute convergence in some cases) of these series.

4-9

Authors: Stanislav V. Gordienko

The application of technological solutions in the processes of reproduction of the regional tourist products increases the efficiency. Measuring effectiveness helps assess the feasibility of a project. The proposed methods of graphical representation and mathematical definition various types of efficiency: economic, non-economic and integrated. Methods can be used for single and multiple entities as part of the regional tourism products.

15-28

Authors: Viktor I. Samarin

The most widespread algorithms for formation the maximum flow on the network are given. The algorithm for this task solution that provides the greater visibility and transparency of the initial network digraph transformation due to its stepwise simplification is offered. There are investigated the cases when at the last step of the algorithm it is necessary to use fictitious throughputs of the digraph arcs in the direction opposite to the main flow.

46-55

Authors: Naseem Ahmad, Ravins

A closed form solution to the unsteady boundary layer flow of visco-elastic fluid (Walter’s Liquid B Model) past a stretching plate has been obtained. Using the obtained velocity components and , the heat transfer problem has been studied. The behaviour of velocity components and temperature field has been studied though the graphs drawn for various randomly chosen values of time duration and visco-elasticity. Boundary layer thickness, skin friction and the Nusselt number have also been obtained and studied through graphs.

64-70

Authors: Seyran P. Stepanyan

We consider the axisymmetric bending problem of orthotropic circular plate resting, with the whole area, on an elastic foundation. The plate edge is simply supported. On the basis of the Fuss-Winkler hypothesis, within the framework of the Hambartsumyan revised theory that takes into account the effect of transverse shear and compression, the differential equations of the problem are obtained. On the basis of the numerical analysis of the dimensionless results of the problem solution certain qualitative conclusions are made.

77-84

Authors: Vahagn K. Vardanyan

A set of knots is called -independent if for arbitrary data at those knots, there is a (not necessary unique) polynomial of total degree at most that matches the given information. For an arbitrary -independent knot set in we are interested with -fundamental polynomials which have simplest possible form. In the present paper we bring necessary and sufficient conditions for the set of cardinality not exceeding , such that all its knots have -fundamental polynomials in form of products of linear factors We bring also necessary and sufficient conditions for -independence of non-coplanar knot sets in of the mentioned cardinality

93-105

Authors: Irina A. Zemlyakova

In this paper we will find the solution of quantile hedging problem using the duality theory of linear programming. This problem is relevant because market of financial options is just beginning its development. It is necessary to determine the capital, portfolio and the initial capital value as the value of the option for which current payment obligation is performed. So, was built hedging strategy, that maximizes the probability of a successful hedging, given the restriction on the required cost. These solutions have been applied in practice for CRR-model (case of complete market) and trinomial model (case of incomplete market).