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  • On a Recently Introduced Fifth-Order Bi-Hamiltonian Equation and Trivially Related Hamiltonian Operators 
    Talati, D.; Turhan, R. (Symmetry, Integrability and Geometry: Methods and Applications, 2011)
    We show that a recently introduced fifth-order bi-Hamiltonian equation with a differentially constrained arbitrary function by A. de Sole, V.G. Kac and M. Wakimoto is not a new one but a higher symmetry of a third-order ...
  • On a Regular Hypersimplex Inscribed into the Multidimensional Cube 
    Medianik, A.I. (Журнал математической физики, анализа, геометрии, 2006)
    It is proved the existence of a regular hypersimplex inscribed into the (4n - 1)-dimensional cube under the vanishing condition of the resultant of some system of 4n - 1 algebraic equations with 4n - 1 unknown quantities.
  • On a relation between memory effects by Maxwell - Boltzmann and Kelvin - Voigt in linear viscoelastic theory 
    Matarazzo, G. (Нелінійні коливання, 1999)
    We study the smoothness properties of relaxation function such that a linear viscoelastic material system by Maxwell Boltzmann can be considered of Kelvin Voigt type; assuming that the relaxation function and its derivative ...
  • On arrangement of subgroups in groups and related topics: some recent developments 
    Subbotin, I.Ya. (Algebra and Discrete Mathematics, 2009)
    Investigation of groups satisfying certain conditions, related to the subgroup arrangement, enabled algebraists to introduce and describe many important classes of groups. The roots of such investigations lie in the works ...
  • On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point 
    Chuchman, I. (Algebra and Discrete Mathematics, 2011)
    In this paper we study the semigroup IC(I,[a]) (IO(I,[a])) of closed (open) connected partial homeomorphisms of the unit interval I with a fixed point a∈I. We describe left and right ideals of IC(I,[0]) and the Green's ...
  • On a Seminal Paper by Karlin and McGregor 
    Castro, M.M.; Grünbaum, F.A. (Symmetry, Integrability and Geometry: Methods and Applications, 2013)
    The use of spectral methods to study birth-and-death processes was pioneered by S. Karlin and J. McGregor. Their expression for the transition probabilities was made explicit by them in a few cases. Here we complete their ...
  • On a semitopological polycyclic monoid 
    Bardyla, S.; Gutik, O. (Algebra and Discrete Mathematics, 2016)
    We study algebraic structure of the λ-polycyclic monoid Pλ and its topologizations. We show that the λ-polycyclic monoid for an infinite cardinal λ≥2 has similar algebraic properties so has the polycyclic monoid Pn with ...
  • On a simple model of the photonic or phononic crystal 
    Kosevich, A.M. (Вопросы атомной науки и техники, 2001)
    A model is proposed for a one-dimensional dielectric or elastic superlattice (SL) that relatively simply describes the frequency spectrum of electromagnetic or acoustic waves. The band frequency spectrum is reduced to ...
  • On a spherical code in the space of spherical harmonics 
    Bondarenko, A.V. (Український математичний журнал, 2010)
    We propose a new method for the construction of new “nice” configurations of vectors on the unit sphere S d with the use of spaces of spherical harmonics.
  • On associative algebras satisfying the identity x⁵=0 
    Shestakov, I.; Zhukavets, N. (Algebra and Discrete Mathematics, 2004)
    We study Kuzmin’s conjecture on the index of nilpotency for the variety N il₅ of associative nil-algebras of degree 5. Due to Vaughan-Lee [11] the problem is reduced to that for k-generator N il₅-superalgebras, where k ...
  • On asymptotic behaviour of probabilities of small deviations for compound Cox processes 
    Frolov, A.N. (2008)
    We derive logarithmic asymtotics for probabilities of small deviations for compound Cox processes in the space of trajectories. We find conditions under which these asymptotics are the same as those for sums of independent ...
  • On asymptotic decompositions of o-solutions in the theory of quasilinear systems of difference equations 
    Kostin, A.V.; Skripnik, I.V. (Український математичний журнал, 1997)
    We consider a quasilinear system of difference equations with certain conditions. We prove that there exists a formal partial o-solution of this system in the form of functional series of special type. We also prove a ...
  • On asymptotic information integral inequalities 
    Veretennikov, A. (2007)
    Asymptotical versions of Bayesian Cramer – Rao inequalities are discussed.
  • On Asymptotic Regimes of Orthogonal Polynomials with Complex Varying Quartic Exponential Weight 
    Bertola, M.; Tovbis, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2016)
    We study the asymptotics of recurrence coefficients for monic orthogonal polynomials πn(z) with the quartic exponential weight exp[−N(1/2z²+1/4tz⁴)], where t∈C and N∈N, N→∞. Our goal is to describe these asymptotic behaviors ...
  • On a Theoretical Study of the Properties of Solutions of the Limit Problem for a Magnetically Noninsulated Diode 
    Dulov, E.V.; Sinitsyn, A.V. (Український математичний журнал, 2005)
    In this paper, we study the lower and upper bounds for solutions of the limit problem for the plane vacuum diode in the magnetic field in the statement by N. Ben Abdallah, P. Degond, and F. Mehats. This problem was finally ...
  • On a Trivial Family of Noncommutative Integrable Systems 
    Tsiganov, A.V. (Symmetry, Integrability and Geometry: Methods and Applications, 2013)
    We discuss trivial deformations of the canonical Poisson brackets associated with the Toda lattices, relativistic Toda lattices, Henon-Heiles, rational Calogero-Moser and Ruijsenaars-Schneider systems and apply one of these ...
  • On automorphism groups of some modules 
    Dashkova, O.Yu. (Algebra and Discrete Mathematics, 2006)
    In this paper we investigated ZG-module A, where G is either nilpotent or soluble group of infinite special rank. It is described the construction of these modules in the case, if for any proper subgroup H of infinite ...
  • On autotopies and automorphisms of n-ary linear quasigroups 
    Marini, A.; Shcherbacov, V. (Algebra and Discrete Mathematics, 2004)
    In this article we study structure of autotopies, automorphisms, autotopy groups and automorphism groups of nary linear quasigroups. We find a connection between automorphism groups of some special kinds of n-ary ...
  • On averaging difference equations on an infinite interval 
    Stanzhitskyi, O.M.; Ateiwi, A.M. (Нелінійні коливання, 2003)
    The averaging method on the semi-axis is justified for systems of difference equations. A theorem on closeness of the corresponding solutions of the exact and averaged systems on the semi-axis is proved. This theorem is ...
  • On a Whitham-Type Equation 
    Sakovich, S. (Symmetry, Integrability and Geometry: Methods and Applications, 2009)
    The Hunter-Saxton equation and the Gurevich-Zybin system are considered as two mutually non-equivalent representations of one and the same Whitham-type equation, and all their common solutions are obtained exactly.