prof. Vladimir Mityushev

Pedagogical University of Cracow

Books:

Research papers (since 1997):

• Czapla R., Mityushev V., Macroscopic conductivity of curvilinear channels, 2010 :: full text in PDF
• V. Mityushev, Cluster method in composites and its convergence, Applied Mathematics Letters 77 (2018) 44-48 doi.org/10.1016/j.aml.2017.10.001
• E. Pesetskaya, R. Czapla, V. Mityushev, An analytical formula for the effective conductivity of 2D domains with cracks of high density, Applied Mathematical Modelling 53 (2018) 214–222
• P. Drygaś, S. Gluzman, V. Mityushev, W. Nawalaniec, Effective elastic constants of hexagonal array of soft fibers, Computational Materials Science 139 (2017) 395-405. http://dx.doi.org/10.1016/j.commatsci.2017.08.009
• Piotr Drygaś, Vladimir Mityushev, Contrast Expansion Method for Elastic Incompressible Fibrous Composites Advances in Mathematical Physics, Volume 2017 (2017), Article ID 4780928, 11 pages, https://doi.org/10.1155/2017/4780928 :: full text in PDF
• Mityushev V., Optimal and stable random pattern formations, J Theoretical Biology 2017, Volume 422, 7, 12–17 doi.org/10.1016/j.jtbi.2017.04.010
• Semyon Yakubovich, Piotr Drygaś, Vladimir Mityushev, Closed-form evaluation of 2D static lattice sums, Proc Roy. Soc. London A472, 2016, issue 2195. DOI: 10.1098/rspa.2016.0510 :: full text in PDF :: full text in PDF
• V. V. Mityushev · E. Pesetskaya, Solution to the Dirichlet problem for an infinite strip domain with holes, Complex Variables and Elliptic Equations, 62, 2016, 57-65. doi.org/10.1080/17476933.2016.1202937 :: full text in PDF :: full text in PDF
• Conformal Mapping of Circular Multiply Connected Domains Onto Domains with Slits :: full text in PDF
• Functional Equations for Analytic Functions and Their Application to Elastic Composites :: full text in PDF
• Talk at cn2017 :: full text in PDF
• V. Mityushev, Dirichlet problem with prescribed vertices in multiply connected domains, Complex Analysis and Potential Theory with Applications, Eds. T. Aliev Azerogly, A. Goldberg, S.V. Rogosin, Cambridge Sci. Publ., Cambridge, 139-146 2014. :: full text in PDF
• Czapla R., Mityushev V., A criterion of collective behavior of bacteria, Mathematical Biosciences and Engineering, 2017 :: full text in PDF
• Mityushev V., Random 2D Composites and the Generalized Method of Schwarz, Advances in Mathematical Physics, 2015 :: full text in PDF
• Paolo Musolino, Vladimir Mityushev, Asymptotic behavior of the longitudinal permeability of a periodic array of thin cylinders, Electronic Journal of Differential Equations, 2015 :: full text in PDF
• Czapla R., Nawalaniec W., Mityushev V., Effective conductivity of random two-dimensional compositeswith circular non--overlapping inclusions, Computational Materials Science, 2012 :: full text in PDF
• B. Bojarski, V. Mityushev, R-linear problem for multiply connected domains and alternating method of Schwarz, Journal of Mathematical Sciences, 2013 :: full text in PDF
• Mityushev V., Schwarz-Christoffel formula for multiply connected domains, Computational Methods and Function Theory 2012 :: full text in PDF
• Mityushev V., Composites with invisible inclusions: Eigenvalues of R-linear problems, Euro. J. Appl. Math., 2016 :: full text in PDF
• Drygaś P, Mityushev V. Effective elastic properties of random two-dimensional composites, IJSS, 2016 :: full text in PDF
• S. Gluzman, V. Mityushev, W. Nawalaniec, G. Sokal, Random composite: stirred or shaken? Arch. Mech., 68, 3, 229-241, 2016 :: full text in PDF
• Mityushev V. Pattern formations and optimal packing, Mathematical Biosciences, 2016 :: full text in PDF
• Mityushev V. On the solutions of the R-linear boundary value problem (Markushevich's problem) on the torus and cylinder. Izv. vuzov. Math. Preprint N 7546-B87, VINITI, 1987 :: full text in PDF
• S. D. Ryan, V. Mityushev, V. Vinokur, L. Berlyand, Rayleigh approximation to ground state of the Bose and Coulomb glasses, Scientific Reports, Nature, 2015, 5, 7821 doi:10.1038/srep07821 :: full text in PDF
• Mityushev V., ℝ-linear and Riemann–Hilbert Problems for Multiply Connected Domains, S.V. Rogosin and A.A. Koroleva (eds.), Advances in Applied Analysis, Birkhäuser, Basel 2012, 147-176 :: full text in PDF
• V. Mityushev, Random composites and the generalized method of Schwarz I. Conductivity problems. Arx 2015 :: full text in PDF
• Mityushev V., Schwarz-Christoffel formula for multiply connected domains, Computational Methods and Function Theory, 12, N 2, 2012, 449-463 :: full text in PDF
• Mityushev V., Poincare ℝ-series for classical Schottky groups and its applications, Milovanović, Gradimir V., Rassias, Michael Th. (Eds.). Analytic Number Theory, Approximation Theory, and Special Functions, Springer, 827-852, 2014 :: full text in PDF
• Mityushev V., Rylko N., A fast algorithm for computing the flux around non-overlapping disks on the plane, Mathematical and Computer Modelling 57 (2013) 1350-1359 :: full text in PDF
• B. Bojarski, V. Mityushev, R-linear problem for multiply connected domains and alternating method of Schwarz, Journal of Mathematical Sciences, Vol. 189, No. 1, 68-77, 2013. :: full text in PDF
• Mityushev V. On construction of Abelian differentials on the closed Riemannian surface, Slupskie Prace Mat.-Przyr. 11a, 213-228, 1997 :: full text in PDF
• Mityushev V. , Rylko N. Boundary value problems, the Poincare series, the method of Schwarz and composite materials, 1997, Int. Congres IMACS 97, Berlin, v.1, 165-170 :: full text in PDF
• Mityushev V. Transport properties of two-dimensional composite materials with circular inclusions, Proc. Royal Society. London A, A455, 2513-2528, 1999 :: full text in PDF
• Berlyand L., Mityushev V. Generalized Clausius-Mossotti formula for random composite with circular fibers, J Statist. Phys. v.102, N 1/2, 2001, 115-145
• Mityushev V. Transport properties of doubly periodic arrays of circular cylinders and optimal design problems, Appl.Math. & Optimization, 2001, v.44, 17-31 :: full text in PDF
• Mityushev V., Zhorovina T.N., Effective conductivity of the layer-fibre composite materials, Proc. IUTAM. Kluwer Publ., 2001, 159-168 :: full text in PDF
• Berlyand L., Mityushev V. Increase and Decrease of the Effective Conductivity of Two Phase Composites due to Polydispersity, J Statist. Phys., v. 118, N 3-4, 481 - 509, 2005
• Mityushev V. Representative cell in mechanics of composites and generalized Eisenstein-Rayleigh sums (Complex Variables) :: full text in PDF
• P.M. Adler, V. Mityushev, Boundary value problems of porous media mechanics, Analytical Methods of Analysis and Differential Equations, v. 6, 7-12, 2000 :: full text in PDF
• Malevich A.E., Mityushev V., Adler P., Macroscopic diffusion on surfaces, 3rd International ISAAC Congress August 20-25, 2001 Freie Universitaet Berlin, Germany :: full text in PDF
• Mityushev V., Adler P.M., Longitudial permeability of a doubly periodic rectangular array of circular cylinders, I, ZAMM, 82, N 5, 2002, 335-345 :: full text in PDF
• Mityushev V., Adler P.M., Longitudial permeability of a doubly periodic rectangular arrays of circular cylinders, II, ZAMP, 53, 2002, 486-517 :: full text in PDF
• Adler P., Malevich A.E., Mityushev V., Macroscopic diffusion on a class of surfaces, Physical Review E, 69, 011607, 2004 :: full text in PDF
• Malevich A.E., Mityushev V., Adler P., Navier-Stokes equations in channel with wavy walls, 5th International ISAAC Congress July 25-30, 2005 Department of Mathematics and Informatics, University of Catania Catania, Italy :: full text in PDF
• Malevich A.E., Mityushev V., Adler P., Stokes flow through a curvilinear channel Acta Mechanica, 2006, 182, 151-182 :: full text in PDF
• Mityushev V., Adler P., Darcy flow around a two--dimensional lense, J Phys A: Math. Gen. 39, 2006, 3545-3560 :: full text in PDF
• Mityushev V., Representative Cell in Mechanics of Composites and Generalized Eisenstein-Rayleigh Sums, Complex Variables and Elliptic Equations, v.51, N 8-11, 1033-1045, 2006 :: full text in PDF
• Mityushev V., The P-function of Weierstrass is not topologically conjugated to exponent, Proc. Int. Conf. "Education, science and economics at universities. Integration to international educational area", Płock, Poland 2006 :: full text in PDF
• Mityushev V., Exact solution of the R-linear problem for a disk in a class of doubly periodic functions. J. Appl. Funct. Anal. 2, No. 2, 115-127, 2007 :: full text in PDF
• Makaruk S. F., Mityushev V., Rogosin S. V., An optimal design problem for two-dimensional composite materials with circular inclusions. A constructive approach. Proc. AMADE 2003. Cambridge University Press, 2007
• Malevich A.E., Mityushev V., Adler P., Couette flow in a channel with wavy walls. Acta Mechanica 0001-5970 (Print) 1619-6937 (Online), 2007 :: full text in PDF
• Moonja Jeong, Mityushev V., The Bergman kernel for circular multiply connected domains. Pacific J. Math. 233 (2007), no. 1, 145-157
• Mityushev V. Exponent in one of the variables. Pr. Nauk. Akad. Jana Dlugosza Czest. Mat. 12 (2007), 77-79 :: full text in PDF
• Mityushev V. Boundary value problem and functional equations for overlapping disks. Ann. Acad. Paedagog. Crac., Stud. Math. 45 (6), 131-136 (2007)
• Mityushev V., Pesetskaya E., Rogosin S. Chapter Analytical Methods for Heat Conduction in Composites and Porous Media in Cellular and Porous Materials Ochsner A., Murch G, de Lemos M. (eds.) Wiley-VCH, Weinheim 2008 :: full text in PDF
• Mityushev V., Rogosin S. V., On Riemann-Hilbert problem with a piecewise constant matrix, ZAA (Journal of Analysis and its Applications), 27, 53-66, 2008 :: full text in PDF
• Mityushev, V. Constructive solution to an inverse R-linear problem. Analytic methods of analysis and differential equations: AMADE 2006, 245-249, Camb. Sci. Publ., Cambridge, 2008
• Adler P., Mityushev V., Resurgence flows in porous media, Physical Review E 79, 026310, 2009 :: full text in PDF
• Mityushev V., Rogosin S. V., The Weierstrass P-function is not topologically elementary, p. 1243-1246 Proc. 5th International ISAAC Congress edited by H. G. W. Begehr & F. Nicolosi. New Trends in Mathematical Physics, New Jersy etc 2009
• Mityushev V., Conductivity of a two-dimensional composite containing elliptical inclusions, Proc. Roy. Soc. London A, 2009 465: 2991-3010 :: full text in PDF
• Mityushev V., Ryłko N. Application of the first digit method to economic processes, Congress IMEM 2009, Ruzomberok, 2009, 85-89
• Drygas P., Mityushev V., Effective conductivity of arrays of unidirectional cylinders with interfacial resistance, Quart J Appl Math Mech, 2009
• Nawalaniec W., Mityushev V., Application of conformal mappings to grid generation in finite element methods, 2010
• Mityushev V., Ryłko N., Mathematical model of electrokinetic phenomena in two-dimensional channels, Nanomaterials, Int. Conf. E&E, ed. L. Jaworska, Kraków, 2010, 5-20
• Adler P., Mityushev V., Resurgence flows in three-dimensional periodic porous media, Physical Review E 82, 016317, 2010
• Malevich A.E., Adler P., Mityushev V., Electrokinetic phenomena in wavy channels, J Col Int Sci, 345, 72-87, 2010 :: full text in PDF
• Mityushev V., Riemann-Hilbert problems for multiply connected domains and circular slit maps, Computational Methods and Function Theory, 11, N 2, 2011, 575-590 :: full text in PDF
• Jarczyk P., Mityushev V., Neutral coated inclusions of finite conductivity, Proc. Roy. Soc. London A , 2011 Published online doi:10.1098/rspa.2011.0230 :: full text in PDF
• Mityushev V., Scalar Riemann-Hilbert Problem for Multiply Connected Domains, Th.M. Rassias and J. Brzdęk (eds.), Functional Equations in Mathematical Analysis, Springer Optimization and Its Applications 52, DOI 10.1007/978-1-4614-0055-4 38, Springer Scien
• Mityushev V. Convergence of the Poincare series for classical Schottky groups, Procedings Amer. Math. Soc., 126, 8, 2399-2406, 1998 :: full text in PDF
• Mityushev V., Rylko N., Optimal distribution of the non-overlapping conducting disks, Multiscale Model. Simul. 10, 2012, 180-190 :: full text in PDF
• Mityushev V. Exact solution of the R-linear problem for a disk in a class of doubly periodic functions (Proc. Workshop on Complex Analysis, submitted) Other version: Effective conductivity of square array of cylinders :: full text in PDF
• Mityushev V. V., Rogosin S.V., Constructive methods for boundary value problems for analytic functions. Progress in analysis, Vol. 2, 769-777, World Sci. Publishing, River Edge, NJ, 2003 :: full text in PDF
• Mityushev V.V. New boundary value problems and their applications to invisible materials // Analytic Methods of Analysis and Differential Equations: AMADE-2011: materials of the 6th International Conference, dedicated to the memory of prof. A.A.Kilbas (Ed. by S.V.Rogosin). - Minsk, Publishing House of BSU, 2012, p. 141-146 :: full text in PDF
• Mityushev V., Riemann-Hilbert problem for multiply connected domains and its applications to porous media and composites, Workshop on RecenTrendsin Applied Complex Analysis June 1-5, 2004 Middle East Technical University Ankara, Turkey :: full text in PDF
• Mityushev V., R-linear problem on torus and its application to composites, Complex Variables, v. 50, N 7-10, 621-630, 2005 :: full text in PDF
• Barannyk L.F., Kloskowska B., Mityushev V. Invariant solutions of the multidimensional Boussinesq equation, Proc. Conf. Symmetry in Nonlinear Physics. Kiev. July 1997, v.1, pp. 62-69, 1997 :: full text in PDF
• Mityushev V., Transport properties of a regular array of coated inclusions. IUTAM Symposium 99/4, pp.48-49. January 1999. Sydney, Australia :: full text in PDF

Talks, Papers and Books

Talks:

• Effective properties of composites with unidirectional cylindrical fibers :: see details in PDF
• Riemann-Hilbert problem for multiply connected domains :: see details in PDF
• Zagadnienia mechaniki materiałów kompozytowych (Polish) :: see details in PDF