Roman Pukhtaievych

• Doctor of Philosophy
• Researcher at National Academy of Sciences of Ukraine

In this survey, we present some results on the behavior of effective properties in presence of perturbations of the geometric and physical parameters. We first consider the case of a Newtonian fluid flowing at low Reynolds numbers around a periodic array of cylinders. We show the results of [43], where it is proven that the average longitudinal flo...

We prove that the periodic layer potentials for the Laplace operator depend real analytically on the density function, on the supporting hypersurface, and on the periodicity parameters.

In the paper we consider a certain analog of the Cauchy type integral taking values in a three-dimensional commutative algebra over the field of complex numbers with one-dimensional radical. We have established sufficient conditions for the existence of limiting values for such an integral. It is also shown that analogues of Sokhotskii–Plemelj form...

We study the behavior of the longitudinal flow along a periodic array of cylinders upon perturbations of the shape of the cross section of the cylinders and the periodicity structure, when a Newtonian fluid is flowing at low Reynolds numbers around the cylinders. The periodicity cell is a rectangle of sides of length l and 1/l, where l is a positiv...

We study the asymptotic behavior of the effective thermal conductivity of a periodic two-phase dilute composite obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material, each of them of size proportional to a positive parameter ?. We assume that the normal component of the heat flux is continu...

We study the asymptotic behavior of the effective thermal conductivity of a periodic two-phase dilute composite obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material, each of them of size proportional to a positive parameter \(\epsilon \). We assume a perfect thermal contact at constituent...

We consider monogenic functions taking values in a three-dimensional commutative algebra A 2 over the field of complex numbers with one- dimensional radical. We calculate the logarithmic residues of monogenic functions acting from a three-dimensional real subspace of A 2 into A 2 . It is shown that the logarithmic residue depends not only on zeros...

This paper is devoted to the study of the asymptotic behavior of the solutions of singularly perturbed transmission problems in a periodically perforated domain. The domain is obtained by making in a periodic set of holes, each of them of size proportional to a positive parameter ε. We first consider an ideal transmission problem and investigate th...

Одержано конструктивний опис моногенних функцiй, що набувають значень в скiнченновимiрнiй напiвпростiй комутативнiй алгебрi, за допомогою аналiтичних функцiй комплексної змiнної. Доведено, що такi моногеннi функцiї мають похiднi Гато усiх порядкiв.

We obtained a constructive description of monogenic functions taking values in a finite-dimensional semi-simple commutative algebra by means of analytic functions of the complex variable. We proved that the mentioned monogenic functions have the Gateaux derivatives of all orders. We have proved analogs of classical integral theorems of the theory o...

We obtained a constructive description of monogenic functions taking values in a three-dimensional commutative harmonic semi-simple algebra and of monogenic functions taking values in a three-dimensional harmonic algebra with the one-dimensional radical by means of holomorphic functions of the complex variable. We proved that the mentioned monogeni...

We present a constructive description of monogenic functions that take values in a three-dimensional commutative harmonic algebra with one-dimensional radical by using analytic functions of complex variable. It is shown that monogenic functions have the Gâteaux derivatives of all orders.

We obtain a constructive description of monogenic functions taking values in the three-dimensional commutative harmonic semi-simple algebra by means of holomorphic functions of a complex variable. We prove that the mentioned monogenic functions have Gateaux derivatives of all orders.

В тривимiрнiй гармонiчнiй алгебрi з одновимірним радикалом одержано тейлорiвськi та лоранiвськi розклади моногенних функцiй, класифiковано їх особливостi та встановлено мономорфізм між алгебрами моногенних функцій при переході від одного гармонічного базиса до іншого. Taylor’s and Laurent’s expansions of monogenic functions taking values in a thre...