Serge Preston,

 

Selected Publications:

 

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

 

 M. Elzanovsky, 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.

 

 Prishepionok, S. "Weyl Groups of Parabolic Subgroups of Real

Semi-Simple Lie Groups", Soviet Math. Dokl.,  vol.24, No. 3, pp.467-471, 1981.

 

 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, “Thermodynamics and the Heisenberg Group”, Appendix (Chapter 11), in E. Binz, S. Pods, “The Geometry of Heisenberg Group in Signal Theory, Optics, and Quantization”, to appear in Springer Verlag.

 

S. Preston, J. Vargo, " Indefinite  metric of R. Mrugala and the geometry of thermodynamical phase space", in “Proceedings of THERMOCONN 2005”, publ. in Atti dell'Accademia Peloritana dei Pericolanti, Messina, It.

 

 

 

 

 Submitted articles

 

D. Fish, S. Preston_, "On the Integrability of Orthogonal Distributions in Poisson Manifolds", see also arXiv: math. SG/0405149, 8 May 2004.

 

S. Preston, Geometrical Theory of Balance Systems and the Entropy Principle, Proceedings of GCM7, Lancaster, UK..

 

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.

 

2.  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.

 

4.  S. Preston, “Multisymplectic Theory of Balance Systems and the Entropy Principle”,

                         arXive math-ph/0611079, Nov.2006.

 

 

Work in progress:

 

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

 

Articles:

 

1. S. Preston, “On the Moduli of the Subalgebra Structures of a Lie Algebra”.

 

2.  S. Preston, M. de Leon, D. M. Diego, “Multisymplectic Elasticity”.

 

3. S. Preston, “On a Degenerate Lagrangian Problem of Material Aging”.

 

4. M. Francaviglia, V. Ciancio, M. Dolfin, S. Preston, “Uniform materials and the multiplicative decomposition of the deformation gradient in finite elasto-plasticity.”

 

 5. S. Preston, R. Thompson, “Polarized Harmonic Mappings and the Optimal G-moving Frames”.