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 The second students competition
10.11.2004
In 2005 the second All-Russia competition of student’s abstracts on a theme
“Hypercomplex numbers and their relation with the geometry of linear Finsler Spaces”
appears.
The purpose and conditions of competition:
1. The purpose of competition is attraction of Russians universities and high schools students attention to the geometry of linear Finsler spaces closely connected with commutative and associative hypercomplex numbers.
2. The founder of competition is Dr. Pavlov Dmitry Gennadievich, chairman of Board of directors of the group of enterprises " ANTARES ".
3.The organizer of competition is the Joint Physical Society of the Russian Federation.
4.Students of all Russians universities and specialized physical and mathematical high schools can take part in competition.
5.On competition the works written in Russian and sent by mail before May, 30th, 2005 by e-mail are accepted: geom2004@mail.ru.
6.The sent works are not reviewed, and information carriers do not come back.
7.Work should represent the abstract in volume not less than 10 pages, written on materials [1-6] on a theme of one of nondegenerated commutative and associative algebra of dimension three or four from positions of Finsler geometry.
8.Each work should contain sections:
–The basic concepts of linear metric spaces;
–The law of multiplication of chosen algebra in a minimum in two characteristic bases;
–The development of number exponential representation formula;
–The geometrical sense of number and the basic operations of the chosen algebra from the point of view of corresponding Finsler spaces;
–The enumeration of transversal (the generalized orthogonal) directions, characteristic for vectors of considered space;
–The description of isotropic subspaces;
–Examples of the elementary nonlinear subspaces (unit quasisphere, a surface consisting of points, equidistant from two fixed points, etc.) and the illustrations of the given manifold executed by means of a computer in affine coordinates;
–Ideas on a theme of possible application of geometry, connected with commutative and associative hypercomplex numbers. Presence and the content of other sections are not regulated.
9. Summarizing of competition will pass in the correspondence form which results will be published on a site http: // www.hypercomplex.ru till 15.06.05.
10. For winners three premiums are provided. The first - the annual grant at a rate of 5000 rubls/month, the Second - 3000 rubls/month and the Third – 2000 rubls/month. It will be offered to winners and authors of the best works to visit in the summer of 2005 Moscow with the purpose to get acquainted with leading experts in the field of Finsler geometry, with payment of road and three-day residing.
References
[1] Кантор И.Л., Солодовников А.С. Гиперкомплексные числа. М., "Наука", 1973.
[2] Лаврентьев М.А., Шабат Б.О. Проблемы гидродинамики и их математические модели. М., "Наука", 1977.
[3] Olariu S. Complex Numbers in n Dimensions. http://xxx.lanl.gov/abs/math.CV/0011044.
[4] Рашевский П.К. Геометрическая тория уравнений с частными производными. Изд. 2-е, стереотипное. М., "Едиториал УРСС", 2003. Глава 1. Глава 10.
[5] Павлов Д.Г. Гиперкомплексные числа и связанные с ними пространства. www.hypercomplex.ru.
[6] Journal "Hypercomplex Numbers in Geometry and Physics". №1, 2004.
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