The modified method of simplest equation is applied to the extended Korteweg de Vries equation and to generalized Camassa Holm equation. Exact traveling wave solutions of these two nonlinear partial differential equations are obtained. The equations of Bernoulli, Riccati and the extended tanh equation are used as simplest equations. Some of the obtained solutions correspond to surface water wav...

Analytical relations between the critical buckling load of a functionally graded material (FGM) Timoshenko beam and that of the corresponding homogeneous Euler–Bernoulli beam subjected to axial compressive load have been derived for clamped–clamped (C–C), simply supported–simply supported (S–S) and clamped–free (C–F) edges. However, no such relation is found for clamped–simply supported (C–S) b...

The Bernoulli risk equation has long been used within HIV transmission models to calculate population-level incidence rates [1–3]. In an article in this issue, Fox et al. [4] use the Bernoulli risk equation to quantify the degree to which an uninfected individual in a discordant couple has been exposed to HIV, based on their past sexual practices. Consequently, Fox et al. describe the Bernoulli...

We study the stability of an interconnected system of Euler−Bernoulli beam and heat equation with boundary coupling, where the boundary temperature of the heat equation is fed as the boundary moment of the Euler−Bernoulli beam and, in turn, the boundary angular velocity of the Euler−Bernoulli beam is fed into the boundary heat flux of the heat equation. We show that the spectrum of the closed-l...

The paper is concerned with the accuracy in total variation of the approximation of the distribution of a sum of independent Bernoulli distributed random d–vectors by the product distribution with Poisson marginals which has the same mean. The best results, obtained using generating function methods, are those of Roos (1998, 1999). Stein’s method has so far yielded somewhat weaker bounds. We de...

The Erdős–Moser equation is a Diophantine equation proposed more than 60 years ago which remains unresolved to this day. In this paper, we consider the problem in terms of divisibility of power sums and in terms of certain Egyptian fraction equations. As a consequence, we show that solutions must satisfy strong divisibility properties and a restrictive Egyptian fraction equation. Our studies le...

-260 Archimedes mathematically works out the principle of the lever and discovers the principle of buoyancy 60 Hero of Alexandria writes Metrica, Mechanics, and Pneumatics 1490 Leonardo da Vinci describes capillary action 1581 Galileo Galilei notices the timekeeping property of the pendulum 1589 Galileo Galilei uses balls rolling on inclined planes to show that di erent weights fall with the sa...

We consider the Cauchy problem for the Euler-Bernoulli equation of the vibrating beam and solve it in Gevrey classes under appropriate Levi conditions on the lower order terms.