9,352 research outputs found
For the Jubilee of Vladimir Mikhailovich Chernov
On April 25, 2019, Vladimir Chernov celebrated his 70th birthday, Doctor of Physics and Mathematics, Chief Researcher at the Laboratory of Mathematical Methods of Image Processing of the Image Processing Systems Institute of the Russian Academy of Sciences (IPSI RAS), a branch of the Federal Science Research Center "Crystallography and Photonics RAS and part-Time Professor at the Department of Geoinformatics and Information Security of the Samara National Research University named after academician S.P. Korolev (Samara University). The article briefly describes the scientific and pedagogical achievements of the hero of the day. © Published under licence by IOP Publishing Ltd
Construction of Doubly Periodic Solutions via the Poincare-Lindstedt Method in the case of Massless Phi^4 Theory
Doubly periodic (periodic both in time and in space) solutions for the
Lagrange-Euler equation of the (1+1)-dimensional scalar Phi^4 theory are
considered. The nonlinear term is assumed to be small, and the
Poincare-Lindstedt method is used to find asymptotic solutions in the standing
wave form. The principal resonance problem, which arises for zero mass, is
solved if the leading-order term is taken in the form of a Jacobi elliptic
function. It have been proved that the choice of elliptic cosine with fixed
value of module k (k=0.451075598811) as the leading-order term puts the
principal resonance to zero and allows us constructed (with accuracy to third
order of small parameter) the asymptotic solution in the standing wave form. To
obtain this leading-order term the computer algebra system REDUCE have been
used. We have appended the REDUCE program to this paper.Comment: 16 pages, LaTeX 2.09. This paper have been published in the
Electronic Proceedings of the Fourth International IMACS Conference on
Applications of Computer Algebra (ACA'98) {Prague (Czech Republic)} at
http://math.unm.edu/ACA/1998/sessions/dynamical/verno
Bases for qudits from a nonstandard approach to SU(2)
Bases of finite-dimensional Hilbert spaces (in dimension d) of relevance for
quantum information and quantum computation are constructed from angular
momentum theory and su(2) Lie algebraic methods. We report on a formula for
deriving in one step the (1+p)p qupits (i.e., qudits with d = p a prime
integer) of a complete set of 1+p mutually unbiased bases in C^p. Repeated
application of the formula can be used for generating mutually unbiased bases
in C^d with d = p^e (e > or = 2) a power of a prime integer. A connection
between mutually unbiased bases and the unitary group SU(d) is briefly
discussed in the case d = p^e.Comment: From a talk presented at the 13th International Conference on
Symmetry Methods in Physics (Dubna, Russia, 6-9 July 2009) organized in
memory of Prof. Yurii Fedorovich Smirnov by the Bogoliubov Laboratory of
Theoretical Physics of the JINR and the ICAS at Yerevan State University
Forgotten Motives: the Varieties of Scientific Experience
Personal recollections about Alexandre Grothendieck and early days of his
theory of motivesComment: 10 pages. Small corrections inserted. Published in: "Alexandre
Grothendieck: A Mathematical Portrait." Ed. by Leila Schneps, International
Press of Boston, 2014, 307 p
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