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 Armenian Journal of MathematicsNumber of Followers: 0     Open Access journal ISSN (Online) 1829-1163 Published by National Academy of Sciences of the Republic of Armenia  [1 journal]
• Normal Automorphisms of Free Burnside Groups of Period 3

• Authors: Varujan Atabekyan, H.T. Aslanyan, A. E. Grigoryan
Pages: 60 - 67
Abstract: 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 $m\ge3$.
PubDate: 2017-12-26
Issue No: Vol. 9, No. 2 (2017)

• On a Convergence of Rational Approximations by the Modified Fourier Basis

• Authors: Tigran Bakaryan
Pages: 68 - 83
Abstract: 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.
PubDate: 2017-12-26
Issue No: Vol. 9, No. 2 (2017)

• Black-Scholes Formula for Asian Option with Several Futures

Pages: 84 - 92
Abstract: 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.
PubDate: 2017-12-26
Issue No: Vol. 9, No. 2 (2017)

• On Characteristic Function of a Contraction, Its Model and Function of
Strauss

Pages: 93 - 101
Abstract: 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.
PubDate: 2017-12-26
Issue No: Vol. 9, No. 2 (2017)

• The Newton Polyhedron, Spaces of Differentiable Functions and General
Theory of Differential Equations

• Authors: Haik Ghazaryan
Pages: 102 - 145
Abstract:  In the paper we investigate the role of the  Newton polyhedron $\Re,$ which generates a multianisotropic  Sobolev space  $W_{p}^{\Re}$ and   Gevrey space $G^{\Re},$   and the role of the  Newton polyhedron $\Re ( P)$ of a polynomial $P(\xi)$  ( of a linear differential operator  $P ( D)$) in the behaviour of  $P(\xi)$ at infinity and in the smoothness of solutions of the equation $P ( D)u = f.$
PubDate: 2017-12-26
Issue No: Vol. 9, No. 2 (2017)

• Hyperidentities and Related Concepts, I

• Authors: Yuri Movsisyan
Pages: 146 - 222
Abstract: This survey article illustrates many important current trends and
perspectives for the field including classification of
hyperidentities, characterizations of algebras with
hyperidentities, functional representations of free algebras,
structure results for bigroups, categorical questions and
applications. However, the paper contains new results, too.
PubDate: 2017-12-26
Issue No: Vol. 9, No. 2 (2017)

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