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## Lp-estimates for scalar products of vector fields and their application to electromagnetic theory problems

Mathematical Methods in the Applied Sciences. 2018. No. № № 18. V. 41. P. 9283-9292.

Tyukhtina A. A., Kalinin A.

Language:
English

Gusein-Zade S., Алгебра и анализ 2021 Т. 33 № 3 С. 73-84

Indices of singular points of a vector field or of a 1-form on a smooth manifold are closely related with the Euler characteristic through the classical Poincar\'e--Hopf theorem. Generalized Euler characteristics (additive topological invariants of spaces with some additional structures) are sometimes related with corresponding analogues of indices of singular points. Earlier, there was defined ...

Added: May 2, 2021

Glutsyuk A., Rybnikov L. G., Nonlinearity 2017 Vol. 30 No. 1 P. 61-72

We consider two-parametric families of non-autonomous ordinary differential equations on the two-torus with coordinates (x, t) of the type x'=v(x)+A+Bf(t). We study its rotation number as a function of the parameters (A, B). The phase-lock areas are those level sets of the rotation number function that have non-empty interiors. Buchstaber, Karpov and Tertychnyi studied the ...

Added: February 15, 2017

Springer, 2015

This book gathers a selection of invited and contributed lectures from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) held in Lausanne, Switzerland, August 26-30, 2013. It provides an overview of recent developments in numerical analysis, computational mathematics and applications from leading experts in the field. New results on finite element methods, multiscale ...

Added: October 10, 2014

191574970, Sbornik Mathematics 1994 Vol. 185 No. 11 P. 3-22

Added: September 23, 2016

Tikhonov E., Sneps-Sneppe M., International Journal of Open Information Technologies 2020 Vol. 8 No. 6 P. 51-42

Data transmission using orthogonal functions means combining base carrier signals (scaled by numbers of useful information) into one sent signal. Processing the mixed signal after receiving allows dividing it back into carriers and restoring useful numbers.
What is the most compact set of complex sine waves for this? How will the random components of the spectrum ...

Added: April 9, 2022

E. Yakovlev, Lerman L., Journal of Geometry and Physics 2019 Vol. 135 P. 70-79

A mathematically correct description is presented on the interrelations between the dynamics of divergence free vector fields on an oriented 3-dimensional manifold M and the dynamics of Hamiltonian systems. It is shown that for a given divergence free vector field Xwith a global cross-section there exist some 4-dimensional symplectic manifold M̃⊃M and a smooth Hamilton function H:M̃→R such that for some c∈R one gets M={H=c}and ...

Added: October 22, 2018

Ilyashenko Y., , in : Mathematical Sciences with Multidisciplinary Applications. In Honor of Professor Christiane Rousseau. And In Recognition of the Mathematics for Planet Earth Initiative. Vol. 157.: NY : Springer, 2016. Ch. 13. P. 269-299.

This is an outline of a theory to be created, as it was seen in April 2015. An addendnum to the proofs at the end of the chapter describes the recent developments. ...

Added: December 15, 2016