Vol. 9 No. 2 (2017)

Published: 2017-12-26

Articles

  • Articles

    Normal Automorphisms of Free Burnside Groups of Period 3

    Varujan Atabekyan, H.T. Aslanyan, A. E. Grigoryan
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    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 $m\ge3$.

    References
  • Articles

    On a Convergence of Rational Approximations by the Modified Fourier Basis

    Tigran Bakaryan
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    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.

    References
  • Articles

    Black-Scholes Formula for Asian Option with Several Futures

    Mohammad Ebrahim Alaei
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    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.

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  • Articles

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

    Perch MelikAdamyan
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    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.

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  • Articles

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

    Haik Ghazaryan
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    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. $

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  • Articles

    Hyperidentities and Related Concepts, I

    Yuri Movsisyan
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    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.

    References