Predicting the death rate around the world due to Covid-19 using regression analysis

Nowadays, COVID-19 is considered to be the biggest disaster that the world is facing. It has created a lot of destruction in the whole world. Due to this COVID-19, analysis has been done to predict the death rate and infected rate from the total population. To perform the analysis on COVID-19, regression analysis has been implemented by applying the differential equation and ordinary differential equation (ODE) on the parameters. The parameters taken for analysis are the number of susceptible individuals, the number of Infected Individuals, and the number of Recovered Individuals. This work will predict the total cases, death cases, and infected cases in the near future based on different reproductive rate values. This work has shown the comparison based on 4 different productive rates i.e. 2.45, 2.55, 2.65, and 2.75. The analysis is done on two different datasets; the first dataset is related to China, and the second dataset is associated with the world's data. The work has predicted that by 2020-08-12: 59,450,123 new cases and 432,499,003 total cases and 10,928,383 deaths.

Semi-discrete optimal transport methods for the semi-geostrophic equations

We give a new and constructive proof of the existence of global-in-time weak solutions of the 3-dimensional incompressible semi-geostrophic equations (SG) in geostrophic coordinates, for arbitrary initial measures with compact support. This new proof, based on semi-discrete optimal transport techniques, works by characterising discrete solutions of SG in geostrophic coordinates in terms of trajectories satisfying an ordinary differential equation. It is advantageous in its simplicity and its explicit relation to Eulerian coordinates through the use of Laguerre tessellations. Using our method, we obtain improved time-regularity for a large class of discrete initial measures, and we compute explicitly two discrete solutions. The method naturally gives rise to an efficient numerical method, which we illustrate by presenting simulations of a 2-dimensional semi-geostrophic flow in geostrophic coordinates generated using a numerical solver for the semi-discrete optimal transport problem coupled with an ordinary differential equation solver.

Scalar-Torsion Theories in Four Dimensional Static Spacetimes

In this paper, we consider a class of static spacetimes scalar-torsion theories in four dimensioanal static spacetimes with the scalar potential turned on. We discover that the 2-dimensional submanifold must admit constant triplet structures, one of which is the torsion scalar. This indicates that these equations of motion can be reduced to a single highly non-linear ordinary differential equation known as the master equation. Then, we show that there are no exact solution of the scalar-torsion theory in four dimensions considering the Sinh-Gordon potential.

The simplest amplitude-period formula for non-conservative oscillators

The simplest frequency formulation for conservative oscillators was proposed in 2019 (Results Phys 2019;15:102546). However, it becomes invalid for non-conservative oscillators. This work suggests the simplest amplitude-period formulation for non-conservative oscillators. The existence of a periodic solution of a second-order ordinary differential equation is given, and the periodic orbits are easily obtained. To the best of the authors’ knowledge, such a powerful result is not available in the literature, providing a tool to determining periodic orbits/limit cycles in the most general scenario.

Mathematical modeling of the demographic dividend (DD) capture applied in economy.

The purpose of this work is to develop tools and techniques for modeling the capture of the Demographic Dividend. We presented the ordinary differential equation (ODE) system modeling the variation of economically dependent and economically non dependent populations. The system uses natality, natural mortality, infant mortality, migration (incoming and outgoing), and transfers. The mathematical study of this ODE system shows the existence of an equilibrium point whose stability depends on a certain number of system parameters. Numerical simulations of the resulting model were performed using scenarios approach.

A New Special 15-Step Block Method for Solving General Fourth Order Ordinary Differential Equations

A new higher-implicit block method for the direct numerical solution of fourth order ordinary differential equation is derived in this research paper. The formulation of the new formula which is 15-step, is achieved through interpolation and collocation techniques. The basic numerical properties of the method such as zero-stability, consistency and A-stability have been examined. Investigation showed that the new method is zero stable, consistent and A-stable, hence convergent. Test examples from recent literature have been used to confirm the accuracy of the new method.

Mixed boundary value problem for an ordinary differential equation with fractional derivatives with different origins

Решается смешанная краевая задача для обыкновенного дифференциального уравнения, содержащего композицию лево- и правосторонних операторов дробного дифференцирования Римана-Лиувилля и Капуто. Задача эквивалентно редуцирована к интегральному уравнению Фредгольма второго рода, для которого найдено достаточное условие однозначной разрешимости. В качестве следствия,для исследуемой задачи доказано неравенство Ляпунова A mixed boundary value problem is solved for an ordinary differential equation containing a composition of left- and right-sided Riemann-Liouville and Caputo fractional differentiation operators. The problem is equivalently reduced to a Fredholm integral equation of the second kind, for which a sufficient condition for unique solvability is found. As a consequence, the Lyapunov inequality is proved for the problem under study.