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Roman Cherniha

Marie Curie Research Fellow, Faculty of Science

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Biography

My current activity is mostly focused on

  • Scientific problems described in the project 328563 FP7-PEOPLE-2012-IIF 'Reductions and exact solutions of boundary value problems with moving boundaries by means of symmetry based methods' funded by EU (see http://ec.europa.eu/research/participants/portal/doc/call/fp7/fp7-people-2012-iif/1570123-m-grantagreement-status-30062013_iif_en.pdf)
  • Serving as Guest Editor-in-Chief for special issue `Lie Theory and Its Application` of the SYMMETRY journal ( see details http://www.mdpi.com/journal/symmetry/special_issues/lie_theory )
  • Preparing the monograph 'Nonlinear reaction-diffusion systems: conditional symmetry, exact solutions and their applications' (Dr. Vasyl' Davydovych is the co-author) to be published in 2015 by Springer.

I have a wide range of research interests and am ready for collaboration (either interesting or profitable, preferably both) within the following topics

• Non-linear partial differential equations (PDEs): Lie and conditional symmetries, exact solutions and their properties

• Development of new methods for analytical solving non-linear PDEs

• Application of modern methods for analytical solving nonlinear boundary value problems,

arising in mathematical physics and mathematical biology

•Analytical and numerical solving boundary value problems with free boundaries (including Stefan problems)

• Development of mathematical models describing the specific processes arising in physics, biology and medicine

CURRICULUM VITAE

Educational data

1976-1981 : Kyiv (Kiev) Taras Shevchenko State University, Faculty of Mechanics and Mathematics, majoring in mathematical physics;

1981 : M.Sc. with Honours, Kyiv Taras Shevchenko State University;

1983-1987 : Post-graduate courses, Kyiv Taras Shevchenko State University;

1987 : Ph.D. dissertation. Institute of Mathematics, Academy of Sciences of Ukraine, Kyiv.

Supervisor: Prof. Wilhelm Fushchych.

Research experience

1981-1992 : Research Assistant and Research Associate, Institute of Technical Heat Physics, Academy of Sciences of Ukraine, Kyiv, Ukraine

1992 - 2004: Senior Scientist , Department of Applied Research, Institute of Mathematics, NAS of Ukraine, Kyiv, Ukraine

Oct. - Dec. 2003: Scholar (temporary CNRS position), Laboratoire de Physique des Materiaux, Universite Henri Poincare Nancy I, Nancy, France

From 2004 - till now: Leading Scientist (an equivalent to the professor position at universities in Ukraine), Department of Mathematical Methods in Statistical Mechanics (2004- 2007) and Department of Applied Research ( 2007 - till now), Institute of Mathematics, NAS of Ukraine, Kyiv, Ukraine ( Research and academic achievements (since 2000 year only )

Awards:

July 2003: Dr. Sci. dissertation (habilitation) 'Nonlinear evolution equations: Galilei invariance, exact solutions and their applications'. Institute of Mathematics, NAS of Ukraine, Kyiv;

March 2008: Visiting professor for one month, Departement de Physique de la Matiere et des Materiaux, Institut Jean Lamour, Universite Nancy, Nancy, France.

May- June 2009: Visiting professor for one month, Departement de Physique de la Matiere et des Materiaux, Institut Jean Lamour, Universite Nancy, Nancy, France.

May 2012: Professor in Mathematics (the state title given by the Government of Ukraine for the considerable achievements in both scientific and pedagogical activities)

The project leader/co-leader of the international projects:

2001-2004: The Royal Society International Joint Project 14184 'Symmetries and Solutions of Nonlinear Reaction-Diffusion-Convection Systems ' (together with Prof. JR King);

2003-2005: The project 'Applications of modern mathematical methods for solving nonlinear patterns arising in peritoneal dialysis' (together with Prof. J.Waniewski). The project funded jointly by NAS of Ukraine and Polish Academy of Sciences.

2010: The project 'Mathematical models of fluid and solute transport in normal and pathological tissue' funded by the Mianowski Fund (Warsaw, Poland);

2011-2014: The project 'Mathematical modeling of transport processes in tissue during peritoneal dialysis' (together with Prof. J.Waniewski). The project funded jointly by NAS of Ukraine and Polish Academy of Sciences.

2013-2016: Marie Curie Individual International Incoming Fellowship Grand (Project number 328563). The project funded by EU within FP7-PEOPLE-2012-IIF.

The project co-leader of several national projects funded by NAS of Ukraine. The current project is 'Symmetry, Super-symmetry and Integrability of Differential Equations' (2011-2015). The state registration number 0110U008615.

Other professional activities (since 2000 only)

International Scientific Visits

Visiting scholar, IBIB of Polish Academy of Sciences, Warszawa (Poland). May and Nov. 2001; Apr.2002; March and Oct. 2003; Oct. 2004.

Visiting scholar, University of Nottingham (England). May-June, 2002; March-May, 2003; March- April, 2004.

Visiting professor, IBIB of Polish Academy of Sciences, Warszawa (Poland). July 2005, June 2006, July 2007, June 2008; Oct. 2009, May-June, 2010 and Oct.2012.

Visiting professor according to the programm `Research in Pairs' , Mathematisches Forschung Institut Oberwolfach, Oberwolfach (Germany). Oct.-Nov., 2006.

Visiting professor. University of Warsaw, Warszawa (Poland). October, 2011.

Visiting professor. Universite P&M Curie, Paris. November, 2011.

Participation in major international conferences

Most recent conferences:

4th, 5th, 6th, 7 and 8th International Conferences "Symmetry in Nonlinear Mathematical Physics" , Kyiv (Kiev) July 2001, June 2003, June 2005, June 2007 and June 2009, respectively.

33rd Symposiums on Mathematical Physics, Torun (Poland), June 2001.

XXIV International Colloquium on Group Theoretical Methods in Physics, Paris, July 2002.

International Conference on Theoretical Physics, UNESCO, Paris, July 2002.

International Conference "Recent Trends in Kinetic Theory and Its Applications", Kyiv, May, 2004.

6th European Conferences on Mathematics Applied to Biology and Medicine, Dresden (Germany), July 2005.

XXV Dynamics Day Europe, Berlin, July 2005.

6th International Congress on Industrial and Applied Mathematics, Zurich, July, 2007.

5th Baltic-Nordic AGMP Workshop: Algebra, Geometry, and Mathematical Physics. Bedlewo (Poland), October, 2009.

XIX International Colloquium Integrable Systems and Quantum Symmetries, Praha (Prague), 17-19 June, 2010.

8th European Conferences on Mathematics Applied to Biology and Medicine, Krakow (Poland), July, 2011.

7th Baltic-Nordic AGMP Workshop: Algebra, Geometry, and Mathematical Physics. Mulhouse (France), October, 2011.

8th Baltic-Nordic AGMP Workshop: Algebra, Geometry, and Mathematical Physics. Brno (Czech Rep.), October, 2012.

More than 100 scientific papers published up to date 31.12.2013.

37 papers are listed in ISI Web of Knowledge data base and 44 papers are listed in Scopus data base.

Refereeing

Acted as the referee for several international scientific journals including: Journal of Mathematical Analysis and Applications, Reports on Mathematical Physics, Journal of Engineering Mathematics, Applied Mathematics Letters, Math.& Comp. Modelling, Phys. Scripta, Com. Nonlin. Sci.& Num.Sim. and J. Phys. A:Math. Teor., Applied Mathematics & Computation, Intl. J. of Heat & Mass Transfer.

Membership in scientific societies

Kyiv Mathematical Society http://www.mathsociety.kiev.ua/ (since 1993 till now)

European Society for Mathematical and Theoretical Biology: http://www.esmtb.org/ (since 1996 till now)

Co-founder and head (in 2006-2007) of All-Ukrainian Association for European Values in Science https://sites.google.com/site/ukrsci/

Languages: Ukrainian (native speaker), English (good), Russian (fluent),

Polish and German (basic communicative skills, reading, translation)

Expertise Summary

Fields of research

• Non-linear PDEs: Lie and conditional symmetries, exact solutions and their properties.

• Development of new methods for analytical solving non-linear partial differential equations (PDEs).

• Application of modern methods for analytical solving nonlinear boundary value problems,

arising in mathematical physics and mathematical biology.

•Analytical and numerical solving boundary value problems with moving boundaries (including Stefan problems)

• Development of mathematical models describing the specific processes arising in physics, biology and medicine.

Main research results

  • All two-component systems of quasilinear parabolic equations invariant under the Galilei algebra and its standard extensions (including the Schroedinger algebra) are constructed and new exact solutions of several physically (biologically) motivated Galilei-invariant systems are found (the results published in papers .
  • New classes of strongly non-linear second-order PDEs and systems (conditionally) invariant under conformal Galilei algebra, exotic conformal Galilei algebra and some infinity-dimensional extensions of Galilei algebra are constructed .
  • A modification of the well-known Ovsiannikov method for solving group classification problems based on using additional equivalence transformations, is proposed. Using this modified method, a complete description of Lie symmetries of the general reaction-diffusion-convection equation (involving arbitrary functions in diffusion, convection and reaction terms) is obtained. The same problem is solved also for two-component systems of multidimensional reaction-diffusion equations (involving arbitrary functions in the diffusion and reaction terms) and for the generalized thin film equation (involving three arbitrary functions).
  • New algorithm, called the method of additional generating conditions, for construction exact solutions of nonlinear PDEs with trivial Lie symmetry is worked out. Using this algorithm, new exact solutions of several physically (biologically) motivated non-linear PDEs and systems were found.
  • A complete description of Q-conditional (i.e. non-classical) symmetries for the most common subcases of the general reaction-diffusion-convection equation is obtained. The results are successfully applied for constructing new exact solutions for nonlinear PDEs arising in modeling of some real world processes.
  • New definitions of Q-conditional symmetry for systems of PDEs are presented, which generalize the standard notation of non-classical symmetry. It is shown that different types of Q-conditional symmetry of a system generate a hierarchy of conditional symmetry operators. Two-component systems of reaction-diffusion equations (including the classical Lotka-Volterra system) were examined to demonstrate the applicability of the definitions for finding new symmetries and constructing exact solutions with physical and biological interpretation.
  • New definitions of invariance of BVP with a wide range of boundary conditions (including those on non-regular manifolds and moving surfaces) is formulated and an algorithm of the group classification for the given class of BVPs is worked out .
  • New mathematical models to describe fluid transport in peritoneal dialysis is developed, exact and numerical solutions of the models are constructed under some biologically motivated assumptions.

More than 100 scientific papers published up to date 31.12.2013.

37 papers are listed in ISI Web of Knowledge data base and 44 papers are listed in Scopus data base.

According to the WEB of Science data base (http://thomsonreuters.com/web-of-science/) my papers were cited approximately 470 times in 180 scientific works (WEB of Science counts citations only in those papers and books, which are included to this data base) and Hirsch index is h=12. My most cited paper is [5], while [27] is the most cited paper per year.

Papers published in major international journals with impact-factor

(ISI Web of Knowledge http://thomsonreuters.com/web-of-science/ )

  1. Fushchych W.I and Cherniha R.M The Galilean relativistic principle and nonlinear partial differential equations. J.Phys.A.:Math. and Gen.--1985.-v.18, N 18.--P.3491―3503.
  2. Cherniha R. and Cherniha N. Exact solution of a class of nonlinear boundary value problems with moving boundaries. J.Phys.A.:Math. and Gen. 1993.-v.26, N 18.--P. L935-940.
  3. Fushchych W.I and Cherniha R.M. Galilei-invariant systems of nonlinear systems of evolution equations. J.Phys.A: Math.Gen. -1995. -vol. 28, P.5569-5579.
  1. Cherniha R. A constructive method for obtaining new exact solutions of nonlinear evolution equations. Rept. Math. Phys.-1996.- vol. 38, P.301-312.
  2. Cherniha R. and Serov M. Symmetries, Ansaetze and Exact Solutions of Nonlinear Second-order Evolution Equations with Convection Terms. European J. of Appl. Math.--1998. - vol. 9, No 5, P.527-542.
  3. Cherniha R. New Non-Lie Ansaetze and Exact Solutions of Nonlinear Reaction-Diffusion-Convection Equations. J. Phys. A: Math.Gen. -- 1998.-vol. 31, No 40, P.8179-8198.
  4. Cherniha R. and Fehribach J. New exact solutions for a free boundary system. J.Phys. A: Math. and Gen. ― 1998. -- vol. 31, No 16, P.3815-3829.
  5. Cherniha R. New Exact Solutions of Nonlinear Reaction-Diffusion Equations. Rept. Math. Phys. ―1998.―V.41, No 2, P. 333-349.
  6. Cherniha R. and King J. R. Lie symmetries of nonlinear multidimensional reaction-diffusion systems: I. J. Phys. A: Math. and Gen. -- 2000.-- V.33, No 2-- P.267-282.
  7. Cherniha R. and King J. R. Addendum. Lie symmetries of nonlinear multidimensional reaction-diffusion systems: I. J. Phys. A: Math. and Gen.-- 2000.-- V.33, No 43-- P.7839-41.
  8. Cherniha R. Lie Symmetries of Nonlinear Two-dimensional Reaction-Diffusion Systems. Rept. Math. Phys.--2000. ―v.46. ―P. 63-76.
  9. Cherniha R. and Dutka V. Exact and Numerical Solutions of the Generalized Fisher Equation. Rept. Math. Phys.--2001.-v.47.--P. 393-411.
  10. Cherniha R. M. Nonlinear Galilei-invariant PDEs with infinite-dimensional Lie symmetry. J.Math.Anal.Appl.--2001.-v.253.-- P.126-141.
  11. Cherniha R and Serov M. Nonlinear Systems of the Burgers-type Equations: Lie and Q-condi-tional Symmetries, Ansaetze and Solutions. J.Math. Anal. Appl.--2003.-v.282.--P.305-328.
  12. Cherniha R. and King J. R. Lie symmetries of nonlinear multidimensional reaction-diffusion systems. II. J. Phys. A: Math. and Gen.--- 2003.-- vol.36. -- P.~405―425.
  13. Cherniha R. and Henkel M On nonlinear partial differential equations with an infinite-dimensional conditional symmetry. J.Math.Anal.Appl.--2004.-v.298.-- P.487--500.
  14. Cherniha R. and King J. R. Nonlinear Reaction-Diffusion Systems with Variable Diffusivities: Lie Symmetries, Ansaetze and Exact Solution. J.Math.Anal.Appl.--2005.-v.308.-- P.11--35.
  15. Cherniha R. and King J. R. Lie Symmetries and Conservation Laws of Nonlinear Multidimensional Reaction-Diffusion Systems with Variable Diffusivities. IMA J. Appl. Math. 2006 -vol.71 - P.391-408.
  16. Cherniha R. and Serov M. Symmetries, Ansaetze and Exact Solutions of Nonlinear Second-order Evolution Equations with Convection Terms, II. European J. of Appl. Math. -2006.-v.17.―597-605.
  17. R. Cherniha, V.Dutka, J.Stachowska-Pietka and J.Waniewski. Fluid transport in peritoneal dialysis: a mathematical model and numerical solutions. In:Mathematical Modeling of Biological Systems, Vоl..I. Ed. by A.Deutsch et al., Birkhaeuser, P.291-298, 2007
  18. Cherniha R. New Q-conditional symmetries end exact solutions reaction-diffusion-convection eduations arising in mathematical biology. J.Math.Anal.Appl. .--2007.-v.326.-- P.783―799.
  19. Cherniha R. and Pliukhin O. New conditional symmetries and exact solutions of nonlinear -reaction-diffusion-convection equations. J. Phys. A: Math. and Theor.--- 2007.-- vol.40. -- P.~10049―10070.
  20. Cherniha R., Serov M. and Rassokha I. Lie Symmetries and Form-preserving Transformations of Reaction-Diffusion-Convection Equations. J.Math.Anal.Appl. .--2008.-v.342.-- P.1363―1379.
  21. Cherniha R. and Pliukhin O. New conditional symmetries and exact solutions of reaction-diffusion systems with power diffusivities. J. Phys. A: Math. and Theor.--- 2008.-- vol.41, 185208 (14pp).
  22. Cherniha R. and Myroniuk L. New exact solutions of a nonlinear cross-diffusion system. J. Phys. A: Math. and Theor.--- 2008.-- vol.41, 395204 (15pp).
  23. Cherniha R. and Kovalenko S. Exact solutions of nonlinear boundary value problems of the Stefan type. J. Phys. A: Math. and Theor.--- 2009.-- vol.42, 355202 (14pp).
  24. Cherniha R. and Henkel M The exotic conformal Galilei algebra and nonlinear partial differential equations. J.Math.Anal.Appl.--2010.-v.369.-- P.120--132.
  25. Cherniha R. Conditional symmetries for systems of PDEs: new definitions and their application for reaction-diffusion systems. J. Phys. A: Math. and Theor.--- 2010.-- vol.43, 405207 (13pp).
  26. Cherniha R. and Kovalenko S. Lie symmetries and reductions of multidimensional boundary value problems of the Stefan type. J. Phys. A : Math. Theor. --2011.--Vol. 44.,485202 (25 pp).
  27. Cherniha R. and Davydovych V. Conditional symmetries and exact solutions of the diffusive Lotka-Volterra system. Math. Comp. Model.-2011.-vol.54, 1238-1251.
  28. Cherniha R. and Kovalenko S. Lie symmetries of nonlinear boundary value problems. Commun. Nonlinear Sci. Numer. Simul.--2012.--Vol. 17. P. 71-84.
  29. Cherniha R. and Davydovych V. Conditional symmetries and exact solutions of nonlinear reaction-diffusion systems with non-constant diffusivities. Commun. Nonlinear Sci. Numer. Simul.--2012.--Vol. 17. P. 3177-88.
  30. Cherniha R. and Davydovych V. Lie and conditional symmetries of the three-component diffusive Lotka-Volterra system. J. Phys. A: Math. and Theor.--- 2013.-- vol.46, 185204 (14pp).
  31. Cherniha R. and Pliukhin O. New conditional symmetries and exact solutions of reaction-diffusion-convection equations with exponential nonlinearities. J.Math.Anal.Appl.--2013.-vol.403.-- P.23--37.
  32. Cherniha R. and Didovych M. Exact solutions of the simplified Keller-Segel model. Commun. Nonlinear Sci. Numer. Simul.--2013.--Vol. 18. P. 2960-297.
  33. Cherniha R. Conditional symmetries for boundary value problems: new definition and its application for nonlinear problems. Miskolc Math. Notes --2013.--Vol. 14. P. 637-646.
  34. R. Cherniha, J. Stachowska-Pietka and J. Waniewski. A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis. Int. J. Appl. Math. Comp. Sci., 2014, vol.24, P.837-851.

Main publications (in English) published in other scientific journals/books

38. Fushchich W. and Cherniga R.. Galilei-invariant nonlinear equations of Schroedinger-type and their exact solutions I. Ukrainian Math.J. -1989.- vol.41, P. 1161-67 .

39. Fushchich W. and Cherniga R.. Galilei-invariant nonlinear equations of Schroedinger-type and their exact solutions II. Ukrainian Math.J. -1989.- vol.41, P.1456-63.

40. Cherniga R.M. and Odnorozhenko I.G. Studies of the processes of melting and evaporation of metals under the action of laser radiation pulses. Promyshlennaya Teplotekhnika-1991-vol.13- No-4, P.51-59 (English translation in: Heat Transfer Research, USA).

41. Cherniha R. Galilei-invariant non-linear PDEs and their exact solutions. J. Nonlinear Math. Phys. --1995.- vol. 2- No 3-4, p.374-383.

42. Fushchych W.I., Cherniha R. and Chopyk V. On unique symmetry of two nonlinear generalizations of the Schroedinger equation. J. Nonlinear Math. Phys. -1996.-vol.3, N 3-4, P.296-301.

43. Cherniha R. and Wilhelmsson H. Symmetry and exact solution of heat-mass transfer equations in thermonuclear plasma. Ukrainian Math. J. 1996.- vol. 48-- No 9, P.1434--1449

44. Cherniha R. New spherycally symmetryc solutions of nonlinear Schroedinger equations. J. Nonlin. Math. Phys.-1997.- Vol.4, No.1-2.P.107--113.

45. Cherniha R. Application of a constructive method for obtaining non-Lie solutions of nonlinear evolution equations. Ukrainian Math. J. - 1997.- vol. 49-- No 6, P.910--924

46. Cherniha R. New Exact Solutions of a Nonlinear Reaction-Diffusion Equation Arising in Mathematical Biology and Their Properties. Ukrainian Math. J. 2001.- vol.53-- No 10, P.1712--1727.

47. Cherniha R. and Dutka V. A. A diffusive Lotka-Volterra system: Lie symmetries, exact and numerical solutions. Ukrainian Math. J. 2004.- vol.56-- No 10, P.1665-1675.

48. Cherniha R. and Waniewski J. Exact solutions of a mathematical model for fluid transport in peritoneal dialysis. Ukrainian Math. J. - 2005.- vol. 57. P.1112--1119.

49. J.Waniewski, V.Dutka, J.Stachowska-Pietka, R. Cherniha. Distributed Modeling of Glucose-Induced Osmotic Flow. Advances in Peritoneal Dialysis―2007―vol.23 (part 1)―P.2―6.

50. Cherniha R. and Pliukhin O. Symmetries and solutions of reaction-diffusion-convection equations with power diffusivities. PAMM Proc. Math.Mech.-- 2007-vol.7, P.2040065-6.

51. Cherniha R. and Myroniuk L. Lie Symmetries and Exact Solutions of a Class of Thin Film Equations. Journal of Physical Mathematics - 2010-- Vol: 2 P. 1-19.

52. Cherniha R. and Kovalenko S. Lie symmetry of a class of nonlinear boundary value

problems with free boundaries. Banach Center Publ. --2011. --Vol. 93. P. 95-104

53. Cherniha R. and Pliukhin O. Nonlinear evolution equations with exponential

nonlinearities: conditional symmetries and exact solutions. Banach Center Publ. --2011. --Vol. 93. P. 105-115.

54. Cherniha R and Davydovych V Reaction-diffusion systems with constant diffusivities: conditional symmetries and form-preserving transformations in: Algebra, Geomerty and Mathematical Physics, Springer Proc. in Mathematics \& Statistics, 2014, vol.85, 533-553.

Teaching Summary

Courses of lectures:

  • Mathematical Analysis: for undergraduate students with specialization 'applied mathematics' ( 2004 -2009);
  • Complex Analysis: for undergraduate students with specialization 'applied mathematics' ( 2005-2008; 2012);
  • Equations of Mathematical Physics: for undergraduate students with specialization 'applied mathematics' ( 2005 -- 2012)
  • Mathematical Biology: for graduate and undergraduate students with specialization 'mathematics' and 'applied mathematics' ( 2006 --2013)
  • Nonlinear Differential Equations: for graduate students with specialization 'applied mathematics' ( 2012-2013)

The textbook: Cherniha R.M. Equations of Mathematical Physics. - Kyiv: Publishing house 'Kyiv-Mohyla Academy', 2012 (In Ukrainian, Summary in English, ISBN 978-966-2410-14-3)

Research Summary

My current activity is mostly focused on

  • Scientific problems described in the project 328563 FP7-PEOPLE-2012-IIF 'Reductions and exact solutions of boundary value problems with moving boundaries by means of symmetry based methods' funded by EU (see http://ec.europa.eu/research/participants/portal/doc/call/fp7/fp7-people-2012-iif/1570123-m-grantagreement-status-30062013_iif_en.pdf)
  • Serving as Guest Editor-in-Chief for special issue `Lie Theory and Its Application` of the SYMMETRY journal ( see details http://www.mdpi.com/journal/symmetry/special_issues/lie_theory )
  • Preparing the monograph 'Nonlinear reaction-diffusion systems: conditional symmetry, exact solutions and their applications' (Dr. Vasyl' Davydovych is the co-author) to be published in 2015 by Springer.

I have a wide range of research interests and am ready for collaboration (either interesting or profitable, preferably both) within the following topics

• Non-linear partial differential equations (PDEs): Lie and conditional symmetries, exact solutions and their properties

• Development of new methods for analytical solving non-linear (PDEs)

• Application of modern methods for analytical solving nonlinear boundary value problems,

arising in mathematical physics and mathematical biology

•Analytical and numerical solving boundary value problems with free boundaries (including Stefan problems)

• Development of mathematical models describing the specific processes arising in physics, biology and medicine

I am mostly working with Professor JR King. I am also working with Prof. J Waniewski (IBIB of PAS, Warsaw), Prof. M Henkel (University Nancy) and my PhD students in past Dr. V. Davydovych, Dr. S. Kovalenko & Dr. O. Pliukhin.

More than 100 scientific papers published up to date 31.12.2014

An extended list of main papers can be found in Expertise Summary, while the most recent papers are listed in Publications.

Recent Publications

Past Research

see my CV & list of my publications

School of Mathematical Sciences

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telephone: +44 (0) 115 951 4949
fax: +44 (0) 115 951 4951
email: maths-enquiries@nottingham.ac.uk