• An operator approach to Vlasov scaling for some models of spatial ecology 

  Finkelshtein, D.; Kondratiev, Yu.; Kutoviy, O. (2013)

  We consider Vlasov-type scaling for Markov evolution of birth-and-death type in continuum, which is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related ...
• Darboux transformation of generalized Jacobi matrices 

  Kovalyov, Ivan (2014)

  Let J be a monic generalized Jacobi matrix, i.e. a three-diagonal block matrix of special form, introduced by M. Derevyagin and V. Derkach in 2004. We find conditions for a monic generalized Jacobi matrix J to admit a ...
• On a class of generalized Stieltjes continued fractions 

  Derkach, Vladimir; Kovalyov, Ivan (2015)

  With each sequence of real numbers s = {sj}∞j=0 two kinds of continued fractions are associated, — the so-called P-fraction and a generalized Stieltjes fraction that, in the case when s = {sj}∞j=0 is a sequence of moments ...
• Fractional contact model in the continuum 

  Kochubei, Anatoly N.; Kondratiev, Yuri G. (2015)

  We consider the evolution of correlation functions in a non-Markov version of the contact model in the continuum. The memory effects are introduced by assuming the fractional evolution equation for the statistical dynamics. ...
• Around Ovsyannikov's method 

  Finkelshtein, Dmitri (2015)

  We study existence, uniqueness, and a limiting behavior of solutions to an abstract linear evolution equation in a scale of Banach spaces. The generator of the equation is a perturbation of the operator which satisfies the ...
• Smooth functions on 2-torus whose Kronrod-Reeb graph contains a cycle 

  Maksymenko, Sergiy; Feshchenko, Bohdan (2015)

  Let f : M → R be a Morse function on a connected compact surface M, and S(f) and O(f) be respectively the stabilizer and the orbit of f with respect to the right action of the group of diffeomorphisms D(M). In a series of ...
• Foliations with all non-closed leaves on non-compact surfaces 

  Maksymenko, Sergiy; Polulyakh, Eugene (2016)

  Let X be a connected non-compact 2-dimensional manifold possibly with boundary and Δ be a foliation on X such that each leaf ω ∈ Δ is homeomorphic to and has a trivially foliated neighborhood. Such foliations on the plane ...
• Actions of finite groups and smooth functions on surfaces 

  Feshchenko, Bohdan (2016)

  Abstract. Let f : M → be a Morse function on a smooth closed surface, V be a connected component of some critical level of f, and EV be its atom. Let also S(f) be a stabilizer of the function f under the right action of ...
• Fractional statistical dynamics and fractional kinetics 

  Silva, José Luís da; Kochubei, Anatoly N.; Kondratiev, Yuri (2016)

  We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum in terms of solutions to Vlasov-type hierarchies. As a by-product we obtain the evolution of the density of particles ...
• Level sets of asymptotic mean of digits function for 4 -adic representation of real number 

  Pratsiovytyi, M. V.; Klymchuk, S. O.; Makarchuk, O. P. (2016)

  We study topological, metric and fractal properties of the level sets Sθ = {x : r(x) = θ} of the function r of asymptotic mean of digits of a number x ∈ [0; 1] in its 4-adic representation, r(x) = lim n→∞ 1 n Xn i=1 αi(x) ...
• Automorphisms generated by umbral calculus on a nuclear space of entire test functions 

  Jamil, Ferdinand; Kondratiev, Yuri; Menchavez, Sheila; Streit, Ludwig (2018)

  In this paper we show that Sheffer operators, mapping monomials to certain Sheffer polynomial sequences, such as falling and rising factorials, Charlier, and Hermite polynomials extend to continuous automorphisms on the ...
• Fractional kinetics in a spatial ecology model 

  Silva, José Luís da; Kondratiev, Yuri; Tkachov, Pasha (2018)

  In this paper we study the effect of subordination to the solution of a model of spatial ecology in terms of the evolution density. The asymptotic behavior of the subordinated solution for different rates of spatial ...
• Weak-coupling limit for ergodic environments 

  Friesen, Martin; Kondratiev, Yuri (2019)

  The main aim of this work is to establish an averaging principle for a wide class of interacting particle systems in the continuum. This principle is an important step in the analysis of Markov evolutions and is usually ...
• Representations of the Infinite-Dimensional Affine Group 

  Kondratiev, Yuri (2020)

  We introdu e an in nite-dimensional a ne group and onstru t its irredu ible unitary representation. Our approa h follows the one used by Vershik, Gelfand and Graev for the di eomorphism group, but with modi ations made ...
• On the Hausdorff dimension faithfulness and the Cantor series expansion 

  Albeverio, S.; Ivanenko, Ganna; Lebid, Mykola; Torbin, Grygoriy (2020)

  We study families \Phi of coverings which are faithful for the Hausdorff dimension calculation on a given set E (i. e., special relatively narrow families of coverings leading to the classical Hausdorff dimension of an ...
• Green measures for Markov processes 

  Kondratiev, Yuri; Silva, José L. da (2020)

  In this paper we study Green measures of certain classes of Markov processes. In particular Brownian motion and processes with jump generators with different tails. The Green measures are represented as a sum of a singular ...
• Automorphisms of Kronrod-Reeb graphs of Morse functions on 2-torus 

  Kravchenko, Anna; Feshchenko, Bohdan (2020)

  This paper is devoted to a study of special subgroups of automorphism groups of Kronrod-Reeb graphs of Morse functions on 2-torus T2 which arise from actions of diffeomorphisms preserving a given Morse function on T2 . ...
• Full indefinite Stieltjes moment problem and Padé approximants 

  Derkach, Volodymyr; Kovalyov, Ivan (2020)

  Full indefinite Stieltjes moment problem is studied via the step-by-step Schur algorithm. Naturally associated with indefinite Stieltjes moment problem are generalized Stieltjes continued fraction and a system of difference ...
• α − regular indefinite Stieltjes moment problem and Darboux transformation 

  Kovalyov, Ivan; Lebedeva, Elena; Stakhova, Olena (2021)

  A sequence of the real numbers s = \{ si\}\ell i=0 is associated with the some indefinite Stieltjes moment problem and generalized Jacobi matrices. The relation between the \alpha - regular indefinite Stieltjes moment ...
• Green Measures for Time Changed Markov Processes 

  Kondratiev, Yuri; Silva, José Luís da (2021)

  In this paper we study Green measures for certain classes of random time change Markov processes where the random time change are inverse subordinators. We show the existence of the Green measure for these processes under ...

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