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Mathematical Notes - 相似文献
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M. A. Tuzhilin 《Doklady Mathematics》2016,93(2):186-189
A relationship between invariants of four-dimensional singularities of integrable Hamiltonian systems (with two degrees of freedom) and invariants of two-dimensional foliations on three-dimensional manifolds being the “boundaries” of these four-dimensional singularities is discovered. Nonequivalent singularities which, nevertheless, have equal three-dimensional invariants are found. 相似文献
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M.A. Tuzhilin 《Moscow University Mathematics Bulletin》2016,71(5):185-190
Four-dimensional momentum mapping singularities of integrable Hamiltonian systems with two degrees of freedom are considered. An infinite series of pairs of 4-dimensional saddle–saddle singularities is constructed so that 4-singularities from each pair are not Liouville equivalent, but 2-foliations on their 3-boundaries are Liouville equivalent. 相似文献
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A.YA. Dorofeev L.S. Kazarin V.M. Sidelnikov M.E. Tuzhilin 《Designs, Codes and Cryptography》2005,37(3):391-404
We consider a finite matrix group
with 34· 216 elements, which is a subgroup of the infinite group
, where
is the regular representation of the quaternion group and C is a matrix that transforms the regular representation Q to its cellwise-diagonal form. There is a number of ways to define the matrix C. Our aim is to make the group
similar in a certain sense to a finite group. The eventual choice of an appropriate matrix C done heuristically.
We study the structure of the group
and use this group to construct spherical orbit codes on the unit Euclidean sphere in R8. These codes have code distance less than 1. One of them has 32· 28 = 2304 elements and its squared Euclidean code distance is 0.293.
Communicated by: V. A. Zinoviev 相似文献
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The first part of this work deals with the investigation and modeling of foliations generated by dynamic systems on their phase spaces and configuration spaces. In the second part, we speak in greater detail about curves and surfaces in three-dimensional space and their geometrical characteristics that can be useful for modeling polymer conformation. 相似文献
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We single out the class of so-called quasiregular Lagrangians, which have singularities on the zero section of the cotangent bundle to the manifold on which extremal networks are considered. A criterion for a network to be extremal is proved for such Lagrangians: the Euler--Lagrange equations must be satisfied on each edge, and some matching conditions must be valid at the vertices. 相似文献
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The aim of this paper is to get an effective restriction on the topologies of minimal 2-trees in terms of twisting numbers of the trees and the convexity levels number of the trees boundaries. 相似文献
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The Steiner ratio characterizes the greatest possible deviation of the length of a minimal spanning tree from the length of the minimal Steiner tree. In this paper, estimates of the Steiner ratio on Riemannian manifolds are obtained. As a corollary, the Steiner ratio for flat tori, flat Klein bottles, and projective plane of constant positive curvature are computed. 相似文献
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