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Symmetry in Nonlinear Mathematical Physics '99</h2></center>

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<h2>
Conference Program</h2></center>

<h3>
Tuesday, July 13</h3>
900 - 930&nbsp; Opening Ceremony
Plenary Session Chairperson: G. Goldin
930 - 1015&nbsp;&nbsp; B. Kent
HARRISON (Department of Physics and Astronomy,
Brigham University, USA) Matrix Methods of Searching for Lax Pairs and
a Paper by Estevez
1015 - 1100&nbsp;&nbsp; Mykola
SHKIL' (M. Dragomanov National Pedagogical University,
Kyiv, Ukraine) On Asymptotic Expansions for Solutions of Systems of
Differential Equations in Case of Multiple Roots of Characteristic Equation
1100 - 1130&nbsp; Coffee break
1130 - 1215&nbsp; Anatoly NIKITIN,
Ronald WILTSHIRE (Department of Applied Research,
Institute of Mathematics of the National Academy of Sciences of Ukraine,
Kyiv, Ukraine) Symmetry Analysis of Systems of Diffusion Equations
1215 - 1300&nbsp; Jules BECKERS
(Department of Theoretical and Mathematical Physics, Institute of Physics,
University of Liege, Liege, Belgium) On Nonlinear Deformations of Lie
Algebras and Their Applications in Quantum Physics
1300 - 1500 Lunch
Section A Chairperson: E.Belokolos
1500 - 1525&nbsp; Renat ZHDANOV
(Department of Applied Research, Institute of Mathematics of the National
Academy of Sciences of Ukraine, Kyiv, Ukraine) Higher Order Conditional
Symmetries and Reduction of Initial Value Problems for Evolution Equations
1525 - 1550 Masayosi TAJIRI
(Osaka Prefecture University, Sakai, Osaka, Japan) Periodic Soliton
Solutions to the Davey-Stewartson Equation
1550 - 1615 Alexander KUSYUMOV
(Kazan State Technical University, Aerodynamics Department, Kazan, Russia)
About
Symmetries of Exterior Differential Equations Appropriate to a System of
Quasilinear Differential Equations of the First Order
1615- 1635&nbsp; Coffee break
Chairperson: P. Basarab-Horwath
1635- 1700 Adil CHEIKHI
(LEMTA UMR CNRS, France) (with Sero-Guillaume Olivier) Generalisation
of the Preliminary Classification by Use of Nonclassical Equivalence Transformations
1700- 1725 Leonid BARANNYK
(Institute of Mathematics, Pedagogical University, Slupsk, Poland) On
Exact Solutions of the Nonlinear Heat Conduction Equation with Source
1725-&nbsp; 1750 Vasyl
FEDORCHUK (Pidstryhach Institute of Applied Problems
of Mechanics and Mathematics of the National Ukrainian Academy of Sciences,
Lviv, Ukraine) (with I.M.Fedorchuk, V.I.Fedorchuk) On Symmetry
Reduction of the five-dimensional Dirac Equation
Section B Chairperson: A. Lopatin
1500 - 1525&nbsp; Mina B. ABD-EL-MALEK
(Department of Engineering Mathematics and Physics, Alexandria University,
Alexandria, Egypt) Electrostatic Potential Between Two Conducting Cylinders
via the Group Method Approach
1525 - 1550 Antonino SCIARRINO
(Dipartimento di Scienze Fisiche - Universita' di Napoli "Federico II",
Napoli, Italy) Crystal Basis Model of the Genetic Code: Structure and
Consequences
1550 - 1615 Irina ORLOVA
(Samara State University, Samara, Russia) (with L. Berkovich) Exact
Linearization of Some Classes of Ordinary Differential Equations of Order
n>2
1615- 1635&nbsp; Coffee break
Chairperson: A. Zajtz
1635- 1700 Victor LAHNO
(Pedagogical Institute, Poltava, Ukraine) New Realisation of Poincare
Group for Scalar Field
1700- 1725 Ivan TSYFRA
(Subbotin Institute of Geophysics of the National Academy of Sciences of
Ukraine, Kyiv, Ukraine) Symmetries and Reductions of Nonlinear Differential
Equations.
1725-&nbsp; 1750 Luis
Miguel&nbsp; POZO CORONADO (Departamento de Geometria
y Topologia, Universidad Complutense de Madrid, Madrid, Spain) (with
Prof. Jaime Munoz Masque) Hamiltonian Formulation and Order Reduction
for Nonlinear Splines in the Euclidean 3-Space
Section C Chairperson: K. Shima
1500 - 1525 Kazuyuki FUJII
(Department of Mathematical Sciences, Yokohama City University, Yokohama,
Japan) Nonlinear Integrable Models with Higher d'Alembertian Operator
in Any Dimension
1525 - 1550 Arthur SERGYEYEV
(Department of Applied Research, Institute of Mathematics of the National
Academy of Sciences of Ukraine, Kyiv, Ukraine) On Local Time-Dependent
Symmetries of Integrable Evolution Equations
1550 - 1615 Taras SKRYPNYK
(Bogolyubov Institute for Theoretical Physics of the National Academy of
Sciences of Ukraine, Kyiv, Ukraine) Quantum Integrable Systems and New
Commutative Subalgebras in the Universal Enveloping Algebras
1615- 1635&nbsp; Coffee break
Chairperson: V.Ostrovskii
1635- 1700 I.M. BURBAN
(Bogolyubov Institute for Theoretical Physics of the National Academy of
Sciences of Ukraine, Kyiv, Ukraine) Some Problems of Quantum Group Gauge
Theories
1700- 1725 Olexander GAVRILIK
(Bogolyubov Institute for Theoretical Physics of the National Academy of
Sciences of Ukraine, Kyiv, Ukraine) The Use of Quantum Algebras in Quantum
Gravity
1725- 1735&nbsp; Coffee break
1735-&nbsp; 1800 Olexander
GAVRILIK, N. IORGOV (Bogolyubov Institute
for Theoretical Physics of the National Academy of Sciences of Ukraine,
Kyiv, Ukraine) On the Casimir Elements of q-Algebras U'q(son)
and Their Eigenvalues
1800 - 1825 A. PAVLENKO,A. PIRYATINSKAYA
(Institute of Mathematics of the National Academy of Sciences of Ukraine,
Kyiv, Ukraine) On Representations of Generalized Cuntz Algebras Ona
<h3>
Wednesday, July 14</h3>
Plenary Session Chairperson: J. Beckers
930 - 1015 Gerald GOLDIN
(Department of Mathematics and Physics, Rutgers University, USA) Generalized
Gauge Invariants for Certain Nonlinear Schroedinger Equations
1015 - 1100 Christiane QUESNE
(Universite Libre de Bruxelles, Physique Nucleaire Theorique et Physique
Mathematique, Brussels, Belgium) Cl -extended
Oscillator Algebras: Theory and Applications to (Variants of) Supersymmetric
Quantum Mechanics
1100 - 1130&nbsp; Coffee break
1130 - 1215 Remi LEANDRE
(Departement de Mathematiques, Universite de Nancy I, Vandoeuvre-les-Nancy,
France) A Stochastic Approach to Some Objects of Conformal Field Theory
1215 - 1300 Anatoly MESHKOV
(Oryol State University, Oryol, Russia) Computer Package for Investigation
of the Complete Integrability
<h3>
Poster Session</h3>
Posters should be placed at 930. Authors are asked
to be at their posters during coffee breaks.
1300 - 1500 Lunch
Section A Chairperson: K. Fujii
1500 - 1525 Iryna YEHORCHENKO
(Department of Applied Research, Institute of Mathematics of the National
Academy of Sciences of Ukraine, Kyiv, Ukraine) On Symmetry Of a Class
of First-Order PDEs
1525 - 1550 Xing-Biao HU
(Institute of Computational Mathematics and Scientific Engineering Computing,
Academia Sinica, Beijing, China) Nonlocal Symmetries via Darboux Transformations
1550 - 1615 Anatoly BARANNYK
(Institute of Mathematics, Pedagogical University, Slupsk, Poland), Ivan
I. YURYK (Ukrainian State University of Food Technologies, Kyiv, Ukraine)
The
Separation of Variables and the Construction of Exact Solutions of Nonlinear
Wave Equations
1615- 1635&nbsp; Coffee break
Chairperson: R. Zhdanov
1635- 1700 Vassil VASSILEV
(Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria)
Symmetry
Groups and Conservation Laws in Structural Mechanics
1700- 1725&nbsp; Michal MARVAN
(Institute of Mathematics, Silesian Univ. at Opava, Opava, Czech Republic)
On
the Horizontal Gauge Cohomology
1725- 1750 Olexander ZHALIY
(Department of Applied Research, Institute of Mathematics of the National
Academy of Sciences of Ukraine, Kyiv, Ukraine) Separation of Variables
in Three-Dimensional Fokker- Planck Equation
Section B Chairperson: M. Tajiri
1500 - 1525 Igor V. KULEMIN
(Oryol State University, Oryol, Russia) (with A.G.Meshkov, M. Ju Balakhnev)New
Evolution Completely Integrable System.
1525 - 1550 A. KOROSTIL
(Institute of Magnetism of the National Academy of Science of Ukraine,
Kyiv, Ukraine) On Hyperelliptic Solutions of the Spectral Problem for
the Two-Dimensional Schrodinger Operator
1550 - 1615 Rajkumar ROYCHOUDHURY
(Indian Statistical Institute, Calcutta, India) Quasipotential Approach
to Solitary Wave Solutions in Nonlinear Plasma Physics.
1615- 1635&nbsp; Coffee break
Chairperson: W. Schempp
1635- 1700 Orest BATSULA
(Bogolyubov Institute for Theoretical Physics of the National Academy of
Sciences of Ukraine, Kyiv, Ukraine) Principle of Spontaneous Symmetry
Breaking, Hidden Symmetry and Algebraic Geometry
1700- 1725 Askold DUVIRYAK
(Institute for Condensed Matter Physics, Lviv, Ukraine) Classical Mechanics
of Relativistic Particles with Colour
1725-&nbsp; 1750 V.I.
KUCHERYAVY (Bogolyubov Institute for Theoretical
Physics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine)
Symmetries
Their Breaking and Anomalies in the Self-Consistent Renormalization. Discrete
Symmetry Shadow in Chiral Anomalies
Section C Chairperson T. Guhr
1500 - 1525 Ziemowit POPOWICZ
(Institute of Theoretcal Physics, University of Wroclaw, Wroclaw, Poland)
Computer
Algebra, Supersymmetry and Solitons
1525 - 1550&nbsp; Olexander GALKIN
(Department of Applied Research, Institute of Mathematics of the National
Academy of Sciences of Ukraine, Kyiv, Ukraine) Poincare Parasuperalgebra
with Central Charges
1550 - 1615 A. PAVLYUK
(Bogolyubov Institute for Theoretical Physics of the National Academy of
Sciences of Ukraine, Kyiv, Ukraine) First-Order Equations of Motion
in the N = 2 Supersymmetric Yang-Mills Theory
1615- 1635&nbsp; Coffee break
Chairperson: Y.Ohnuki
1635- 1700 Violetta BUCHYNCHYK
(Department of Applied Research, Institute of Mathematics of the National
Academy of Sciences of Ukraine, Kyiv, Ukraine) On Exact Foldy - Wouthuysen
Transformations for Bosons
1700- 1725 Roman MATSYUK
(Pidstryhach Institute of Applied Problems in Mechanics and Mathematics
of the National Academy of Sciences of Ukraine, Lviv, Ukraine) Vector-Valued
versus Scalar Differential Forms Description of the Symmetries of Euler-Poisson
Equations
1725- 1750 Volodymyr PELYKH
(Pidstryhach Institute of Applied Problems in Mechanics and Mathematics
of the National Academy of Sciences of Ukraine, Lviv, Ukraine) Including
Theorem for Solutions of the Rarita-Schwinger and Generalized Sen-Witten
Equations on a Distribution in a Curved Space-Time
<h2>
1800&nbsp; Concert</h2>

<h3>
Thursday, July 15</h3>
Plenary Session Chaiperson:
Ch.
Quesne
930 - 1015 Petro BASARAB-HORWATH
(Department of Mathematics, Linkoeping University, Linkoeping, Sweden)
Aspects
of Conformal Symmetry
1015 - 1100 Thomas GUHR
(Max Planck Institut fuer Kernphysik, Heidelberg, Germany) Supersymmetry
and Supergroups in Stochastic Quantum Physics
1100 - 1130&nbsp; Coffee break
1130 - 1215 Lev BERKOVICH
(Samara State University, Samara, Russia) Transformations of Ordinary
Differential Equations: Local and Nonlocal Symmetries
1215 - 1300 Anatoly KLIMYK
(Bogolyubov Institute for Theoretical Physics of the National Academy of
Sciences of Ukraine, Kyiv, Ukraine) (with M. Havlicek, S.Posta)The
q-deformed Algebras U'q(so3) U'q(so2,1)
and Their Representations
1300 - 1500 Lunch
<h2>
1600&nbsp; River Cruise</h2>

<h3>
Friday, July 16</h3>
Plenary Session Chairperson:
B.
Klink
930 - 1015 Walter SCHEMPP
(Lehrstuhl fuer Mathematik I University of Siegen, Siegen, Germany) A
Clifford Dual Approach to the Quantum Hall Effect
1015 - 1100 Kazunari SHIMA
(Saitama Institute of Technology, Okabe-machi, Saitama, Japan) Nonlinear
Symmetry and Unity of Spacetime and Matter
1100 - 1130&nbsp; Coffee break
1130 - 1215 Hendrik GRUNDLING
(Department of Pure Mathematics, University of New South Wales, Sydney,
Australia) Dynamics Constraining in Quantum Mechanics
1215 - 1300 Roman GIELERAK
(Institute of Theoretical Physics, University of Wroclaw, Wroclaw, Poland)
From
Stochastic Partial Differential Equations to Local Quantum Field Theories
1300 - 1500 Lunch
Section A Chairperson: A.Gavrilik
1500 - 1525 Yoshio OHNUKI
(Nagoya Women's University, Takamiya Tempaku, Nagoya, Japan) Irreducible
Representations of the Dirac Algebra for a System Constrained on a Manifold
Diffeomorphic to SD
1525 - 1550 Andrij NAZARENKO
(Institute for Condensed Matter Physics of the National Academy of Sciences
of Ukraine, Lviv, Ukraine) The Canonical Realization of the Poincare
Algebra for a Relativistic System of Charged Particles plus Electromagnetic
Field
1550 - 1615 Tetyana KUZMENKO
(Bogolyubov Institute for Theoretical Physics of the National Academy of
Sciences of Ukraine, Kyiv, Ukraine) Quantum Mechanism of Generation
of the SU(N) Gauge Fields
1615- 1635&nbsp; Coffee break
Chairperson: H. Grundling
1635- 1700 Volodymyr SHPYTKO
(Institute for Condensed Matter Physics of the National Academy of Sciences
of Ukraine, Lviv, Ukraine) N-particle Canonical Realization of the Poincare
Algebra in the Two-Dimensional Space-Time and Weyl-type Quantization Rules
1700- 1725 T. MAISTRENKO,S. POPOVYCH
(Institute of Mathematics of the National Academy of Sciences of Ukraine,
Kyiv, Ukraine) Stability of Isomorphism Classes of C*-Algebras Associated
with Quadratic Map
1725- 1735&nbsp; Coffee break
1735- 1800&nbsp; Yarema PRYKARPATSKY,
Anatoly SAMOILENKO (Institute of Mathematics of
the National Academy of Sciences of Ukraine, Kyiv, Ukraine) A Method
of Investigating Imbedding Mappings for Integral Submanifolds
1800- 1825&nbsp;&nbsp; Petro
HOLOD, Taras SKRYPNYK (Bogolyubov Institute for
Theoretical Physics of the National Academy of Sciences of Ukraine, Kyiv,
Ukraine) Duality for the Nonlinear Integrable Hierarchies in Finite-Gap
Sector
Section B Chairperson: A.Prykarpatsky
1500 - 1525 Alexey K. LOPATIN
(Institute of Mathematics of the National Academy of Sciences of Ukraine,
Kyiv, Ukraine) Group-Theoretical Methods in the Problem of Study of
Qualitative Behaviour of Solutions of Differential Equations
1525 - 1550 Andrei ANDREYTSEV
(Kherson State Technical University, Kherson, Ukraine) On Some Evolution
Equations Admitting Condtitional Lie-Backlung Symmetries
1550 - 1615 Mykola SHKIL', Petro
SAMUSENKO (M. Dragomanov National Pedagogical
University, Kyiv, Ukraine) On Asymptotic Formulas for Solutions of Systems
of Differential Equations with Summable Coefficients
1615- 1635&nbsp; Coffee break
Chairperson: V. Vladimirov
1635- 1700 Vasyl L. OSTROVSKII
(Institute of Mathematics of the National Academy of Sciences of Ukraine,
Kyiv, Ukraine) (with O.Bratteli and P.E.T.Jorgensen) KMS-States
and Type III Factor Representations of Cuntz Algebras
1700- 1725&nbsp; Roman POPOVYCH
(Department of Applied Research, Institute of Mathematics of the National
Academy of Sciences of Ukraine, Kyiv, Ukraine) Equivalence of Q-Conditional
Symmetries Under Local Transformations
1725- 1750 Svitlana V. KONDACOVA
(The National Pedagogical M. Dragomanov University, Kyiv, Ukraine) Asymptotic
Integration of Systems of Differential Equations
Section C Chairperson: A. Meshkov
1500 - 1525 Vsevolod VLADIMIROV
(Subbotin Institute of Geophysics of the National Academy of Sciences of
Ukraine, Kyiv, Ukraine) Modelling System for Relaxing Media. Symmetry
and Intermediate Asymptotics
1525 - 1550 Victor LEHENKYI
(Airforce Scientific Center, Kyiv, Ukraine) The Integrability of Some
Underdetermined Systems
1550 - 1615&nbsp; Stanislav SPICHAK,Valerii
STOGNII (Department of Applied Research, Institute
of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine)
Q-Conditional
Symmetry of the One-Dimensional Fokker - Planck Equation
1615- 1635&nbsp; Coffee break
Chairperson: R.Leandre
1635- 1700 Yurij YAREMKO
(Institute for Condensed Matter Physics of the National Academy of Sciences
of Ukraine, Lviv, Ukraine) Tangent Groups of a Lie Group and Gauge Invariance
in Lagrangian Dynamics
1700- 1725 Larissa SVIRINA
(Institute of Physics NASB, Minsk, Belarus) Symmetry-Breaking Bifurcations
in a Single-Mode Class - a Gas Laser.
1725- 1750 Volodymyr TRETYAK
(Institute for Condensed Matter Physics of the National Academy of Sciences
of Ukraine, Lviv, Ukraine) Lie-Backlund Symmetries in Classical Relativistic
Dynamics of Interacting Particle Systems
 &nbsp;
 &nbsp;
<h3>
Saturday, July 17</h3>

Plenary 5 Chairperson: K. Harrison
930 - 1015 Andrzej ZAJTZ
(Pedagogical University, Krakow, Poland) On Global Conjugacy of Smooth
Dynamical Systems
1015 - 1100&nbsp; Evgenii BELOKOLOS
(Institute of Magnetism of the National Academy of Sciences of Ukraine,
Kyiv, Ukraine) Algebraically Integrable Hamiltonian Systems, Their Symmetry
Reduction and Averaging
1100 - 1130&nbsp; Coffee break
1130 - 1215 William KLINK
(Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa,
USA) Relativistic Quantum Mechanics and Discrete Subgroups of the Poincare
Group
1215 - 1300 Anatoly PRYKARPATSKY
(Dept.of Applied Mathematics at the AGH, Krakow, Poland, and Dept. of Nonlin.
Mathem. Analysis at the IPPMM of the National Academy of Sciences of Ukraine,
Lviv, Ukraine) Non-Abelian Liouville-Arnold Theorem on Integrability
by Quadratures -- a Symplectic Theory Approach
1300 - 1330 Closing Ceremony
<h2>
1400&nbsp;&nbsp; Farewell Banquet</h2>

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