Two problems of sub-Lorentzian geometry on the Martinet distribution are studied. For the first one, the reachable set has a nontrivial intersection with the Martinet plane, while a trivial intersection occurs for the second problem. Reachable sets, optimal trajectories, and sub-Lorentzian distances and spheres are described.
A closed system of equations for describing turbulent flows is obtained. Additional equations for the cross pulsation moments (rho overline {Delta {{u}_{i}}Delta {{u}_{k}}} ) are derived using a balanced kinetic equation, which was previously used to obtain a quasi-gasdynamic system of equations. Numerical results for the problem of a two-dimensional mixing layer between two flows are presented.
Using the recoupling theory, we define a representation of the pure braid group and show that it is not trivial.
New cases of integrable seventh-order dynamical systems that are homogeneous with respect to some of the variables are presented, in which a system on the tangent bundle of a three-dimensional manifold can be distinguished. In this case, the force field is divided into an internal (conservative) and an external component, which has dissipation of different signs. The external field is introduced using some unimodular transformation and generalizes previously considered fields. Complete sets of both first integrals and invariant differential forms are given.
We prove that for any (varepsilon > 0) and ({{n}^{{ - frac{{e - 2}}{{3e - 2}} + varepsilon }}} leqslant p = o(1)) the maximum size of an induced subtree of the binomial random graph (G(n,p)) is concentrated asymptotically almost surely at two consecutive points.
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：