Sentence examples for discovered equation from inspiring English sources

When Rosenau [1] was concerned with the problem of how to describe the dynamics of a dense lattice, he discovered Equation (1.1) by a continuum method.

Two integrable Camassa-Holm-type equations with cubic nonlinearity have been discovered, Equation (1.1) and the Novikov equation [36] m_{t}+u^{2}m_{x}+3uu_{x}m =0, quad m=u-u_{xx}, (1.4) which was recently discovered by Novikov in a symmetry classification of nonlocal PDEs with quadratic or cubic nonlinearity [36].

Evolution in a different direction began when the French mathematicians Alexis Clairaut in 1740 and d'Alembert in 1752 discovered equations for fluid flow.

The novel theoretical approach is to rewrite the method in the framework of discontinuous Petrov Galerkin (DPG) method, and then show numerical stability by using a key equation discovered by Gopalakrishnan and Qiu (2014).

Johann Jakob Balmer, a Swiss mathematician and secondary school teacher, in 1885 discovered an equation for representing the wavelengths of hydrogen spectral lines, of which nine had been observed in the laboratory and of which five more were photographed in the spectrum of the star Sirius.

In her Ph.D. thesis (published as Stellar Atmospheres [1925]), Payne used the spectral lines of many different elements and the work of Indian astrophysicist Meghnad Saha, who had discovered an equation relating the ionization states of an element in a star to the temperature to definitively establish that the spectral sequence did correspond to quantifiable stellar temperatures.

In this audio clip, Lightman recounts two experiences from his past when he discovered that equations aren't the entire story.

The key idea for our algorithm is quite similar: whenever two objects (actually, two blocks of pixels) of the reference KFs have estimated trajectories both passing near the current position, we take into account the object depth, instead of simply selecting the trajectory closer to the current position, as DISCOVER would do (see Equation 1).

After solving this equation, we discovered that these differential equations are known in the mathematical literature.

Schrödinger discovered a wave equation for these matter waves.

And he discovered that simple equation that describes our complex interconnected world.