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<h2>
The Proceedings of SNMP'99</h2>
are published as Part 1 (pages 1-264) and Part 2 (pages 265-552) of Volume
30 of Proceedings of Institute of Mathematics
<br>NAS of Ukraine, Editors <a href="http://www.imath.kiev.ua/~nikitin/">A.G.
Nikitin</a> and <a href="http://www.imath.kiev.ua/~boyko/">V.M. Boyko</a>,
Kyiv, Institute of Mathematics, 2000.
<p>ISBN 966-02-1444-8 (general)
<br>ISBN 966-02-1401-4&nbsp; (for Part 1)
<br>ISBN 966-02-1402-2&nbsp; (for Part 2)
<p>&nbsp;&nbsp;&nbsp;&nbsp; You can download the contents of both parts
in PostScript and PDF formats:
<dir>
<li>
<a href="http://www.imath.kiev.ua/~appmath/cont.ps">PostScript File</a></li>

<li>
<a href="http://www.imath.kiev.ua/~appmath/cont.pdf">PDF File</a></li>
</dir>

<hr WIDTH="100%">
<p>These Proceedings are papers of the third conference in the series "<a href="http://www.imath.kiev.ua/~appmath/conf.html">Symmetry
in Nonlinear Mathematical Physics</a>"
<p>
<hr WIDTH="100%">
<p><b><font color="#FF0000"><font size=+2>!!!!!</font></font></b> You can
download both parts of Proceedings: <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/symmetry1999.pdf">pdf</a>
(8,56 Mb) or <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/symmetry1999.djvu">djvu</a>
(4,1 Mb)
<p>
<hr WIDTH="100%">
<p>We present the full list of articles, which are published in Proceedings
of Third International Conference "Symmetry in
<br>Nonlinear Mathematical Physics" (in PDF format). Please contact us
if you have any difficulties with downloading the files (<a href="mailto:appmath@imath.kiev.ua">appmath@imath.kiev.ua</a>).
<p><b><font size=+1>Part 1</font></b>
<p>NIKITIN A.G., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/preface.pdf">Preface</a>
(pages 5-5)
<p><a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/participants.pdf">List
of Participants</a> (pages 8-11)
<p><b>Symmetry of Differential Equations</b>
<p>HARRISON B.K., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art1.pdf">Matrix
Methods of Searching for Lax Pairs and a Paper by Estevez</a> (pages 17-24)
<p>BERKOVICH L.M., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art2.pdf">Transformations
of Ordinary Differential Equations: Local and Nonlocal Symmetries</a> (pages
25-34)
<p>MESHKOV A.G., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art3.pdf">Computer
Package for Investigation of the Complete Integrability</a> (pages 35-46)
<p>NIKITIN A.G., WILTSHIRE R.J., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art4.pdf">Symmetries
of Systems of Nonlinear Reaction-Diffusion Equations</a> (pages 47-59)
<p>ABD-EL-MALEK M.B., EL-AWADI I.A. and&nbsp; EL-MANSI S.M.A., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art5.pdf">Electro-Static
Potential Between Two Conducting Cylinders via the Group Method Approach</a>
(pages 60-67)
<p>BALAKHNEV M.Ju., KULEMIN I.V. and MESHKOV A.G., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art6.pdf">New
Evolution Completely Integrable System</a> (pages 68-72)
<p>BARANNYK A.F. and YURYK I.I, <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art7.pdf">Separation
of Variables and Construction of Exact Solutions of Nonlinear Wave</a>
<br><a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art7.pdf">Equations</a>
(pages 73-82)
<p>BARANNYK L.F., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art8.pdf">On
Exact Solutions of the Nonlinear Heat Conduction Equation with Source</a>
(pages 83-89)
<p>BERKOVICH L.M. and ORLOVA I.S., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art9.pdf">The
Exact Linearization of Some Classes of Ordinary Differential Equations
for Order $n> 2$</a> (pages 90-98)
<p>BOYKO V., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art10.pdf">On
the Galilei&nbsp; Invariance of the Continuity Equation</a> (pages 99-102)
<p>FEDORCHUK V.M., FEDORCHUK I.M. and FEDORCHUK V.I., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art11.pdf">On
Symmetry Reduction of the Five-Dimensional Dirac Equation</a> (pages 103-108)
<p>FEDORCHUK V.M. and LEIBOV O., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art12.pdf">On
Symmetry Reduction and Some Exact Solutions of the Multidimensional</a>
<br><a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art12.pdf">Born--Infeld
Equation</a> (pages 109-115)
<p>FUJII K., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art13.pdf">Nonlinear
Integrable Models with Higher d'Alembertian Operator in Any Dimension</a>
(pages 116-119)
<p>HU X.-B. and LOU S.-Y., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art14.pdf">Nonlocal
Symmetries of Nonlinear Integrable Models</a> (pages 120-126)
<p>KHOMCHENKO L.V., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art15.pdf">Oscillation
of Solutions of Ordinary Differential Equations Systems Generated by Finite-Dimensional</a>
<br><a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art15.pdf">Group
Algebra</a> (pages 127-130)
<p>KUSYUMOV A., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art16.pdf">About
Symmetries of Exterior Differential Equations, Appropriated to a System
of Quasilinear Differential Equations of the First Order</a> (pages 131-136)
<p>KUZMENKO A., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art17.pdf">Construction
of Invariants&nbsp; for a System of Differential Equations in the $n+2m$-Dimensional
Space</a> (pages 137-140)
<p>LAHNO V. and ONYSHCHENKO A., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art18.pdf">The
Ovsjannikov's Theorem on Group Classification&nbsp; of a Linear Hyperbolic
Type Partial Differential Equation Revisited</a> (pages 141-145)
<p>LAHNO V. and ZHDANOV R.Z., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art19.pdf">Towards
a Classification of Realizations of the Euclid Algebra $e(3)$</a> (pages
146-150)
<p>LUTFULLIN M., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art20.pdf">Realizations
of the Euclidean&nbsp; Algebra within the Class of Complex Lie Vector Fields</a>
(pages 151-156)
<p>LEHENKYI V., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art21.pdf">The
Integrability of Some Underdetermined Systems</a> (pages 157-164)
<p>MAGDA O., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art22.pdf">The
Group Classification&nbsp; of Nonlinear Wave Equations Invariant under
Two-Dimensional Lie Algebras</a> (pages 165-169)
<p>MU\~NOZ MASQU\'E J. and POZO CORONADO L.M., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art23.pdf">Hamiltonian
Formulation and Order Reduction&nbsp; for Nonlinear Splines in the Euclidean
3-Space</a> (pages 170-176)
<p>PANCHAK O., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art24.pdf">A
Class of Non-Lie Solutions&nbsp; for a Non-linear d'Alembert&nbsp; Equation</a>
(pages 177-179)
<p>POPOVYCH H.V., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art25.pdf">On
$SO(3)$-Partially Invariant Solutions of&nbsp; the Euler Equations</a>
(pages 180-183)
<p>POPOVYCH R.O., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art26.pdf">Equivalence
of $Q$-Conditional Symmetries Under Group of Local Transformation</a> (pages
184-189)
<p>POPOVYCH V.O., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art27.pdf">Lie
Submodels of Rank 1 for the MHD Equations</a> (pages 190-195)
<p>SERGYEYEV A., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art28.pdf">On
Local Time-Dependent Symmetries of Integrable Evolution Equations</a> (pages
196-203)
<p>SPICHAK S. and STOGNII V., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art29.pdf">One-Dimensional
Fokker--Planck Equation Invariant under Four- and Six-Parametrical</a>
<br><a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art29.pdf">Group</a>
(pages 204-209)
<p>TAJIRI M. and ARAI T., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art30.pdf">Periodic
Soliton Solutions to the Davey--Stewartson Equation</a> (pages 210-217)
<p>TSYFRA I., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art31.pdf">Symmetries
and Reductions of Partial Differential Equations</a> (pages 218-222)
<p>VASSILEV V.M. and DJONDJOROV P.A., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art32.pdf">Symmetry
Groups and Conservation Laws in Structural Mechanics</a> (pages 223-231)
<p>VLADIMIROV V.A., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art33.pdf">Modelling
System for Relaxing Media. Symmetry, Restrictions and Attractive Features
of Invariant</a>
<br><a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art33.pdf">Solutions</a>
(pages 232-238)
<p>VLADIMIROV V.A. and SKURATIVSKY S.I., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art34.pdf">On
Invariant Wave Patterns in Non-Local Model of Structured Media</a> (pages&nbsp;
239-244)
<p>YEHORCHENKO I., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art35.pdf">On
Symmetry of a Class of First Order PDEs Equations</a> (pages 245-248)
<p>ZHALIJ A., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art36.pdf">On
Some New Classes of Separable Fokker--Planck Equations</a> (pages 249-254)
<p>ZHDANOV R.Z., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art37.pdf">Higher
Conditional Symmetries&nbsp; and Reduction of Initial Value Problems&nbsp;
for Nonlinear Evolution Equations</a> (pages 255-263)
<br>&nbsp;
<p><b><font size=+1>Part 2</font></b>
<p><b>q-Algebras and Quantum Groups</b>
<p>BECKERS J., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art38.pdf">On
Nonlinear Deformations of Lie Algebras and their Applications in Quantum
Physics</a> (pages 275-279)
<p>HAVL\'{I}\v CEK M., PO\v STA~S. and&nbsp; KLIMYK A.U., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art39.pdf">Representations
of the $q$-Deformed Algebra ${\mathrm{so}}_{q}(2,1)$</a> (pages 280-287)
<p>QUESNE C. and VANSTEENKISTE N., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art40.pdf">$C_\lambda$-Extended
Oscillator Algebras: Theory and Applications to (Variants of) Supersymmetric
Quantum Mechanics</a> (pages 288-297)
<p>BURBAN I.M., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art41.pdf">Some
Problems of Quantum Group Gauge Field Theory</a> (pages 298-303)
<p>GAVRILIK A.M., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art42.pdf">The
Use of Quantum Algebras in&nbsp; Quantum Gravity</a> (pages 304-309)
<p>GAVRILIK A.M. and IORGOV N.Z., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art43.pdf">On
the Casimir Elements of $q$-Algebras ${U'_q({\rm so}_n)}$ and Their Eigenvalues
in Representations</a> (pages 310-314)
<p><b>Algebras and Groups: Developments and Applications</b>
<p>KLINK W.H., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art44.pdf">Discrete
Subgroups of the Poincar\'{e} Group</a> (pages 317-323)
<p>ABRAMENKO A., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art45.pdf">Matrix
Realizations of Four-Dimensional Lie Algebras and Corresponding Invariant
Spases</a> (pages 324-329)
<p>BONDARENKO V.M., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art46.pdf">Operators
on $(A,\ast)$-Spaces and Linear Classification Problems</a> (pages 330-332)
<p>GALKIN A.V., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art47.pdf">Poincar\'e
Parasuperalgebra with Central Charges</a> (pages 333-340)
<p>KALUTSKII S.,&nbsp; <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art48.pdf">On
$*$-Wild Algebras</a> (pages 341-342)
<p>NAZARENKO A., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art49.pdf">Canonical
Realization of the Poincar\'e Algebra for a Relativistic System of Charged
Particles Plus Electromagnetic Field</a> (pages 343-349)
<p>OHNUKI Y., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art50.pdf">Irreducible
Representations of the Dirac Algebra for a System Constrained on a Manifold
Diffeomorphic to&nbsp; $S^{D}$</a> (pages 350-356)
<p>PAVLENKO H. and PIRYATINSKA A., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art51.pdf">On
Generalization of the Cuntz&nbsp; Algebras</a> (pages 357-363)
<p>POPOVYCH S.V. and MAISTRENKO T.Yu., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art52.pdf">$C^*$-Algebras
Associated with&nbsp; Quadratic Dynamical System</a> (pages 364-370)
<p><b>Related Problems of Mathematical Physics</b>
<p>SHKIL M.I., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art53.pdf">On
Asymptotic Decompositions for Solutions of Systems of Differential Equations
in the Case of Multiple</a>
<br><a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art53.pdf">Roots
of the Characteristic Equation</a> (pages 373-381)
<p>SHKIL M.I. and SAMUSENKO P.F., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art54.pdf">On
Asymptotic Formulae for Solutions of Differential Equations with Summable</a>
<br><a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art54.pdf">Coefficients</a>
(pages 382-386)
<p>FILCHAKOVA V.P., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art55.pdf">PP-Test
for Integrability of Some Evolution Differential Equations</a> (pages 387-391)
<p>KONDAKOVA S., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art56.pdf">Asymptotic
Integration of System of the Differential Equations of Third Order</a>
(pages 392-400)
<p>KOROSTIL A.M., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art57.pdf">On
Hyperelliptic Solutions of Spectral Problem for the Two-Dimensional Schr\"odinger
Equation</a> (pages 401-405)
<p>SAMOYLENKO V.Hr., SIDORENKO Yu.M., BUONANNO L. and&nbsp; MATARAZZO G.,
<a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art58.pdf">Explicit
Solutions of Nonlinear Evolution Equations via Nonlocal Reductions Approach</a>
(pages 406-410)
<p>ZHUKOVSKY A.N. and KARAGODOV V.P., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art59.pdf">Exact
Solutions of the Inhomogeneous Problems for Polyparabolic Operator</a>
<br>(pages 411-416)
<p><b>Symmetry in Physics and Other Natural Sciences</b>
<p>BINZ E. and SCHEMPP W., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art60.pdf">A
Unitary Parallel Filter Bank Approach to Magnetic Resonance Tomography</a>
(pages 419-428)
<p>GIELERAK~R. and&nbsp;&nbsp; \L UGIEWICZ P.,&nbsp; <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art61.pdf">Models
of Covariant Quantum Theories of Extended Objects from Generalized Random
Fields</a> (pages 429-439)
<p>GOLDIN G.A., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art62.pdf">Generalized
Gauge Invariants for Certain Nonlinear Schr\"odinger Equations</a> (pages
440-446)
<p>GUHR T., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art63.pdf">Supersymmetry
and Supergroups in Stochastic Quantum Physics</a> (pages 447-455)
<p>SHIMA K., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art64.pdf">Nonlinear
Symmetry and Unity of Spacetime and Matter</a> (pages 456-464)
<p>ZAJTZ A., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art65.pdf">On
the Global Conjugacy of Smooth Flows</a> (pages 465-472)
<p>DUVIRYAK A., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art66.pdf">Classical
Mechanics of Relativistic Particle with Colour</a> (pages 473-480)
<p>FRAPPAT L., SCIARRINO A. and SORBA P., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art67.pdf">Crystal
Basis Model of the Genetic Code: Structure and Consequences</a> (pages
481-488)
<p>GOLOVNIA R.M., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art68.pdf">On
a Class of Equations for Paticles with Arbitrary Spin</a> (pages 489-492)
<p>KUCHERYAVY V.I., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art69.pdf">Symmetries,
their Breaking and Anomalies in the Self-Consistent Renormalization. Discrete
Symmetry Shadow in Chiral Anamalies</a> (pages 493-500)
<p>KUZMENKO T.Yu., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art70.pdf">Quantum
Mechanism of Generation of the&nbsp; $SU(N)$ Gauge Fields</a> (pages 501-506)
<p>PAVLYUK A., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art71.pdf">Symmetric
Properties of First-Order Equations of Motion for $N=2$ Super Yang--Mills
Theory</a> (pages 507-509)
<p>ROYCHOUDHURY R., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art72.pdf">Quasipotential
Approach to Solitary Wave Solutions in Nonlinear Plasma</a> (pages 510-515)
<p>SHPYTKO V., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art73.pdf">Weyl-Type
Quantization Rules and&nbsp; $N$-Particle Canonical Realization of the
Poincar\'e Algebra in the Two-Dimensional Space-Time</a> (pages 516-523)
<p>SKRYPNYK T., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art74.pdf">Quantum
Integrability of the Generalized Eulers Top with Symmetries</a> (pages
524-529)
<p>SVIRINA L.P., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art75.pdf">Symmetry-Breaking&nbsp;
Bifurcations in a Single-Mode Class-A Gas Laser</a> (pages 530-536)
<p>TRETYNYK V., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art76.pdf">On
Exact Foldy--Wouthuysen Transformation of Bozons in an&nbsp; Electromagnetic
Field and Reduction</a>
<br><a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art76.pdf">of
Kemmer--Duffin--Petiau Equation</a> (pages 537-543)
<p>YAREMKO Yu., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/art77.pdf">The
Tangent Groups of a Lie Group and Gauge Invariance in Lagrangian Dynamics</a>
(pages 544-550)
<p>NIKITIN A.G., <a href="http://www.imath.kiev.ua/~symmetry/Symmetry99/conclusion.pdf">Conclusion</a>
(pages 551-551)
<br>&nbsp;
<p>A limited number of hard copies of the Proceedings is still available.
I you wish to purchase a copy, you are kindly requested to contact us via
e-mail: <a href="mailto: appmath@imath.kiev.ua">appmath@imath.kiev.ua</a>
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