Armenian Journal of Mathematics http://armjmath.sci.am/index.php/ajm Armenian Journal of Mathematics Armen.J.Math., original research papers, survey articles, areas of mathematics, theoretical mathematics, applications, review articles, short communications, conference proceedings, algorithms, Ph.D and doctoral thesis’s. National Academy of Sciences of Armenia en-US Armenian Journal of Mathematics 1829-1163 Normal Automorphisms of Free Burnside Groups of Period 3 http://armjmath.sci.am/index.php/ajm/article/view/157 <p>If any normal subgroup of a group $G$ is $\phi$-invariant for some automorphism $\phi$ of $G$, then $\phi$ is called a normal automorphism. Each inner automorphism of a group is normal, but converse is not true in the general case. We prove that any normal automorphism of free Burnside group $B(m,3)$ of period 3 is inner for all rank $m\ge3$.</p> Varujan Atabekyan H.T. Aslanyan A. E. Grigoryan ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2017-12-26 2017-12-26 9 2 60 67 On a Convergence of Rational Approximations by the Modified Fourier Basis http://armjmath.sci.am/index.php/ajm/article/view/166 <p>We continue investigations of the modified-trigonometric-rational approximations that arise while accelerating the convergence of the modified Fourier expansions by means of rational corrections. Previously, we investigated the pointwise convergence of the rational approximations away from the endpoints and the $L_2$-convergence on the entire interval. Here, we study the convergence at the endpoints and derive the exact constants for the main terms of asymptotic errors. We show that the Fourier-Pade approximations are much more accurate in all frameworks than the modified expansions for sufficiently smooth functions. Moreover, we consider a simplified version of the rational approximations and explore the optimal values of parameters that lead to better accuracy in the framework of the $L_2$-error. Numerical experiments perform comparisons of the rational approximations with the modified Fourier expansions.</p> Tigran Bakaryan ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2017-12-26 2017-12-26 9 2 68 83 Black-Scholes Formula for Asian Option with Several Futures http://armjmath.sci.am/index.php/ajm/article/view/164 <p>The paper suggests the Black-Scholes type formulas for some options. The Asian options for several futures with depending components and uniform time steps are investigated.</p> Mohammad Ebrahim Alaei ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2017-12-26 2017-12-26 9 2 84 92 On Characteristic Function of a Contraction, Its Model and Function of Strauss http://armjmath.sci.am/index.php/ajm/article/view/151 <p>It is shown that Nagy-Foias characteristic function of a completely nonunitary contraction and a variant of its functional model can be presented by means of projection-valued analytic operator function, arising in the presentation theory of A.V.~Strauss.</p> Perch MelikAdamyan ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2017-12-26 2017-12-26 9 2 93 101 The Newton Polyhedron, Spaces of Differentiable Functions and General Theory of Differential Equations http://armjmath.sci.am/index.php/ajm/article/view/132 <p>&nbsp;In the paper we investigate the role of the &nbsp;Newton polyhedron $\Re,$ which generates a multianisotropic &nbsp;Sobolev space &nbsp;$W_{p}^{\Re}$ and &nbsp; Gevrey space $G^{\Re},$ &nbsp; and the role of the &nbsp;Newton polyhedron $\Re ( P)$ of a polynomial $P(\xi)$ &nbsp;( of a linear differential operator &nbsp;$P ( D)$) in the behaviour of &nbsp;$P(\xi)$ at infinity and in the smoothness of solutions of the equation $&nbsp;P ( D)u = f.$</p> Haik Ghazaryan ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2017-12-26 2017-12-26 9 2 102 145 Hyperidentities and Related Concepts, I http://armjmath.sci.am/index.php/ajm/article/view/143 <p>This survey article illustrates many important current trends and<br>perspectives for the field including classification of<br>hyperidentities, characterizations of algebras with<br>hyperidentities, functional representations of free algebras,<br>structure results for bigroups, categorical questions and<br>applications. However, the paper contains new results, too.</p> Yuri Movsisyan ##submission.copyrightStatement## http://creativecommons.org/licenses/by/4.0 2017-12-26 2017-12-26 9 2 146 222