Serge Preston,

 

Publications:

 

S. Preston, “Variational Bicomplex and the Balance Systems”,  SIGMA, issue for S4 Symposium, SIGMA 7 (2011), 063, 18 pages.

 

M. Dolfin, M. Francaviglia,S. Preston, L. Restuccia, “Material Point Model and Geometry of Entropy Form”,  IJGMMP, v7, N6  (September), 2010, pp. 1021-1042.

 

S. Preston, “Variational theory of balance systems", International Journal of Geometrical Methods of Modern Physics, v7 N5 (August), 2010,  pp 745-795.

S. Preston, M. Elzanowski, “Material Uniformity and the Concept of the Stress Space in “Continuous Media with Microstructure” Proceedings,  in honor of  Prof. Dr. Krzysztof  Wilmanski , Soringer, 2010.

D. Fish, S. Preston, "On the Integrability of Orthogonal Distributions in Poisson Manifolds",   Balkan Journal of the Geometry and Applications, Volume 15 (2010), No. 2, pp.49-60.

 

S. Preston, Noncommuting variations in the Lagrangian field theory and the dissipation, IL NUOVO CIMENTO Vol. 32 C, N. 1 Gennaio-Febbraio 2009, pp. 159-172.

 

 S. Preston, “Thermodynamics, Geometry and the Heisenberg Group”,   Appendix A, in the book E. Binz, S. Pods, “The Geometry of Heisenberg Group in Signal Theory, Optics, and Quantization”,   AMS, Providence,  2008.

 

M. Francaviglia, V. Ciancio, M. Dolfin, S. Preston, “Uniform materials and the multiplicative decomposition of the deformation gradient in finite Elasto-Plasticity,” Journal of Non Equilibrium Thermodynamics, v.33, 2008.

 

 S. Preston, “Variational Theory of Balance Systems”, in “Differential Geometry and its Applications”, Proceedings. Conf., in Honour of Leonhard Euler,”,  Olomouc, August 2007,   World Scientific, pp. 675–688, 2008.

 

S. Preston, J. Vargo, "Indefinite  metric of R. Mrugala and the geometry of thermodynamical phase space", in “Proceedings of THERMOCONN 2005”,   Atti dell’Accademia Peloritana dei Pericolanti, Messibna, It., Classe di Scienze Fisiche, Matematiche e Naturali Vol. LXXXVI, C1S0801019 (2008) - Suppl. 1-12.

 

 M.Elzanowski, S.Preston, “A Model of the Self-Driven Evolution of a Defective Continuum”, Mathematics and Mechanics of Solids, Vol.12, N.4, 450-465, 2007.

 

S. Preston, Geometrical Theory of Balance Systems and the Entropy Principle, Proceedings of GCM7, Lancaster, UK, Journal of Physics: Conference Series, vol.62, pp.1-52, 2007.

 

A. Chudnovsky, S. Preston, “4D Geometrical Modeling of A Material Aging”,  International Journal of Geometric Methods in Modern Physics,  v.3, N8 (2006), pp.1-30,   extended version see at  arXive, math-ph/0604034, April 16,2006.

 

 D. Cao, D. Liu, S. Preston, R. Tucker, “Evolutionary Systems for Slender Thermomechanical Structures,” in Proceedings of   “Global Integrability of Field Theories, Nov. 1-3, ed. By J.Calmet, W.Seiler, R.Tucker, Universitatsverlag, Karlsruhe, 2006.

 

M. Elzanowski, S. Preston, "On the torsion evolution of 2-dim uniform materials", “Mathematics and Mechanics of Solids”, April 7, 2006.

 

  M. Elzanowski, S. Preston, "Modeling the Evolution of Inhomogeneities", in. Yongqi Wang, K.Hutter, “Trends in Applications of   Mathematcs to Mechanics”,  Shaker Verlag, Aachen, 2005, 391-398.

 

 B. Botvinnik, S. Preston, “Conformal Laplacian and Conical Singularities", in  Proceeding of the School on High-Dimensional Manifold Topology, ICTP, Trieste, Italy, World Scientific, 2003., also  arXiv: math. DG/0201058 v.2 8 Jan 2002.

 

S.Preston, I. Kunin, J.Gliklikh, G.Chernukh,  “On the geometrical characteristics of chaotic dynamics,I”, International Journal of Engineering Science, 41 (2003),495-506.

 

A. Chudnovsky, S. Preston,_”Configurational mechanics of Necking Phenomena” in Engineering Thermoplastics, Mechanics Research Communications, 29 (2002), 465-475.

 

 A. Chudnovsky, S. Preston, “Variational Formulation of a Material Ageing Model”,  in “Configurational Mechanics of Materials”, ed. G.Maugin, R. Kienzler, Springer, Wien, 2001, pp.273-306.

 

  A. Chudnovsky, S.Preston, “Geometrical Modeling of Material Aging”, Extracta  Mathematicae 11(1) (1996) 1-15.

 

  M. Elzanowski., S. Preston, “On Non-Holonomic Second-Order Connections with  Applications to Continua with Microstructure”, Extracta Mathematicae 11(1) (1996) 51-58.

 

 S. Preston, I. Kunin, "G-moving Frames and their Applications in Dynamics", "Int. J. of Engineering Science", v.33, n.15, pp.  2261-2275, 1995.

 

  M. Elzanowski, S. Prishepionok, "Connections on Higher Order Frame Bundles” in: Tamassy and J.Szenthe (eds),   New Developments in Differential Geometry, Debrecin, 1994, pp. 131-142., Kluver Acad. Publishers, 1996.

 

S. Prishepionok, M. Elzanowski,_  "Higher Grade Material Structures”, pp.63-68,  in D.Parker, A.England (eds), IUTAM Symposium on Anisotropy, Inhomogeneity  and Nonlinearity, Kluver Acad.Publishes,1995.

 

I.Kunin, S. Prishepionok, F. Houssain, X.Zhou, "Moving frames in continuous  and discrete systems", in "Matherials Sciences  Forum", vol.123-125 (1993),  pp. 175-184.

 

. S. Prishepionok., M. Elzanowski., "On homogeneous configurations of Uniform Elastic Bodies, in "Matherials Sciences Forum", vol.123-125 (1993), p.155-164.

 

  M. Elzanowski, S. Prishepionok, Locally Homogeneous configurations of Uniform Elastic Bodies, Rep. on Math. Physics, v. 31, 1992, p.229-240.

 

  S.Prishepionok, I. Kunin, F. Hussain, X. Zhou, "Centroidal Frames in  Dynamical Systems, parts I, Proc. Roy. Soc.,   London, A(1992) 439,  pp. 441-463.

 

 Prishepionok, S. The Bertrand Problem", Siberian Mathematical Journal,v. 27,  No. 3,pp.450-454, 1986.

 

 Prishepionok, S., "Abel Transformations and Harmonic Analysis, I", Siberian Mathematical Journal, v.26, No. 5,    pp. 736-749, 1985.

 

Abikof, U. \cyr Veshchestvenno analiticheskaya teoriya prostranstva Teĭkhmyullera. (Russian) [The real analytic theory of Teichmüller space]

 Translated from the English by S. Yu. Prishchepionok. Translation edited and with a preface and notes by S. L. Krushkalʹ.

 \cyr Matematika: Novoe v Zarubezhnoĭ Nauke [Mathematics: Recent Publications in Foreign Science], 38. ``Mir'', Moscow, 1985. 119 pp

 

Prishchepionok, S. Yu. The decomposition $K=MK^* M$K=MK*M for semisimple Lie groups of $R$R-rank one. (Russian)  Sibirsk. Mat. Zh. 25 (1984), no. 6, 136–140.

 

 Prishepionok, S. "Weyl Groups of Parabolic Subgroups of Real Semi-Simple Lie Groups", Soviet Math. Dokl.,  vol.24, No. 3, pp.467-471, 1981.

 

Duvaut, Georges; Lions, Jacques-Louis \cyr Neravenstva v mekhanike i fizike. (Russian) [Inequalities in mechanics and physics] Translated from the French by

 S. Yu. Prishchepionok and T. N. Rozhkovskaya. ``Nauka'', Moscow, 1980. 384 pp.

 

 Prishepionok, S. Topologie naturelle pour les representations lineaires des  algebres de Lie semi-simples",  I.C.R.,Ac. Sci.Paris,   t.286, Ser.A. 20 mars 1978,  pp. 499-502; II.C.R.,Ac. Sci. Paris,t.288, Ser.A. 8 janvier  1979, pp. 9-12.

 

 Prishepionok, S. "On the Harish-Chandra component of Regular Representation of  SL(2,R)",  Functional Analysis and Appl.,  v.10,  No.1, pp. 76-77, 1976.

 

  Prishepionok, S. "On a sl(2)-module", Atti della Academia Nazionale dei  Linchei, v. LVII, No. 5, pp. 308-310, 1974.

 

 

To appear:

 

S. Preston, "Supplementary balance laws for Cattaneo heat propagation system", submitted to  Atti dell’Accademia Peloritana dei Pericolanti, Messina, It.

.

S. Preston,  ”Forms of Lepage type and the balance systems”,  To appear in the Proceedings of the DGA 2010, Brno, Czech Rep., Aug. 2010.

 

 

Submitted articles:

.

 M. Dolfin, S. Preston, L. Restuccia, “ENTROPY FORM AND THE CONTACT GEOMETRY OF THE  MATERIAL  POINT MODEL”, submitted to Reports on Mathematical Physics.

 

.

 

 

Recent preprints:

 

     1.     S. Preston, M. Santoro, Curvature of the Weinhold Metrics of  Thermodynamical Systems with

                                          2 Degrees of Freedom", arXive: math-ph/0505010m,  May 2005.

 

  1.  S. Preston, J. Vargo, "Indefinite  metric of R. Mrugala and the geometry of thermodynamical phase space",

                                       arXiv.math. DG/0509267, 12 Sept. 2005.

 

      3.   A. Chudnovsky, S. Preston, Aging Rod I. Homogeneous case, pp.1-104, PSU, 2005.

 

  1. S. Preston, Multisymplectic Theory of Balance Systems, I, arXiv.math.: math-ph/0611079 , November 2006.

 

      5.   S.Preston,  Variational Theory of Balance Systems, arXiv.math.: math-ph    June 2008.

 

       6.  M. Dolfin, S. Preston, L. Restuccia, “Material Point Model and Geometry of Entropy Form ,  arXiv:. math-ph/08112411 , November 2008.

 

 

 

Work in progress:

 

Book:  S.Preston, A. Chudnovsky, “4-D Geometric Modeling of Aging Phenomena”,

 

Articles:

 

1 .S. Preston, “Entropy Principle and the Supplementary Balance Laws in Continuum Thermodynamics. ”.

 

2. A. Chudnovsky, S. Preston, “Porous media relaxation. Material and physical space-time representations”.

 

4. S. Preston, “On the algebra and geometry of the balance equations”.

 

5. M. Dolfin, M. Francaviglia, S. Preston, L. Restuccia, “Entropy forms and the balance systems, III”.