A new approximation of mean-time trends for the second wave of COVID-19 pandemic evolving in key six countries

We have presented in the current analytic research the generating formulae and results of direct mathematical modelling of non-classical trends for COVID-19’s evolution in world which, nevertheless, can be divided into two types: (1) the general trends for European countries such as Germany presented by the curve of modified sigmoid-type with up-inclination of the upper limit of saturation (at the end of first wave of pandemic) as well as for other cases of key countries that suffered from pandemic such as USA, India, Brazil, Russia (we conclude that the same type of coronavirus pandemic is valid for most of the countries in world with similar scenarios of the same type for general trends); (2) non-classical general trends for Middle East countries (such as Iran), with the appropriate bulge on graphical plots at the beginning of first wave of pandemic. We expect that the second wave of pandemic will pass its peak at the end of December 2020 for various countries. Moreover, the second wave of pandemic will have come to end at first decade of January 2021 in Germany and Iran (but at the end of January 2021 in India as well), so we should restrict ourselves in modelling the first and second waves of pandemic within this time period for these countries. Thus, the model of first approximation is considered here which allows to understand the mean-time trends of COVID-19 evolution for the first + second waves of pandemic for USA, Brazil and Russia, or predict the approximated time period of the upcoming third wave of pandemic in cases of India, Germany and Iran. © 2021, The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature

On a new type of solving procedure for Euler–Poisson equations (rigid body rotation over the fixed point)

In this paper, we proceed to develop a new approach which was formulated first in Ershkov (Acta Mech 228(7):2719–2723, 2017) for solving Poisson equations: a new type of the solving procedure for Euler–Poisson equations (rigid body rotation over the fixed point) is suggested in the current research. Meanwhile, the Euler–Poisson system of equations has been successfully explored for the existence of analytical solutions. As the main result, a new ansatz is suggested for solving Euler–Poisson equations: the Euler–Poisson equations are reduced to a system of three nonlinear ordinary differential equations of first order in regard to three functions Ω i (i= 1 , 2 , 3); the proper elegant approximate solution has been obtained as a set of quasi-periodic cycles via re-inversing the proper elliptical integral. So the system of Euler–Poisson equations is proved to have analytical solutions (in quadratures) only in classical simplifying cases: (1) Lagrange’s case, or (2) Kovalevskaya’s case or (3) Euler’s case or other well-known but particular cases. © 2018, Springer-Verlag GmbH Austria, part of Springer Nature

On a new type of solving procedure for Laplace tidal equation

In this paper, we present a new approach for solving Laplace tidal equations (LTE) which was formulated first by S. V. Ershkov ["A Riccati-type solution of Euler-Poisson equations of rigid body rotation over the fixed point," Acta Mech. 228(7), 2719 (2017)] for solving Poisson equations: a new type of the solving procedure for Euler-Poisson equations (rigid body rotation over the fixed point) is implemented here for solving the momentum equation of LTE, Laplace tidal equations. Meanwhile, the system of Laplace tidal equations (including continuity equation) has been successfully explored with respect to the existence of an analytical way for presentation of the solution. As the main result, a new ansatz is suggested here for solving LTE: solving the momentum equation is reduced to solving a system of 3 nonlinear ordinary differential equations of 1st order with regards to 3 components of the flow velocity (depending on time t), along with the continuity equation which determines the spatial part of solution. Nevertheless, a proper elegant partial solution has been obtained due to invariant dependence between temporary components of the solution. In addition to this, it is proved here that the system of Laplace tidal equations does not have the analytical presentation of a solution (in quadratures) in the case of the nonzero fluid pressure in the oceans, as well as nonzero total gravitational potential and the centrifugal potential (due to planetary rotation). © 2018 Author(s)