The relativistic quantum Boltzmann equation (or the Uehling-Uhlenbeck equation) describes dynamics of single-species fast-moving particles. With recent development mechanics, has been widely used in physics and engineering such as collision experiments simulations electrons graphene. In spite importance, there no mathematical theory on existence solutions for to best authors' knowledge. this pa...

this study proposed a new discharge estimation method using a mean velocity formula derived from chiu’s 2d velocity formula of probabilistic entropy concept and the river bed shear stress of channel. in particular, we could calculate the mean velocity, which is hardly measurable in flooding natural rivers, in consideration of several factors reflecting basic hydraulic characteristics such as ri...

a difference in salt concentration in two solutions separated by a membrane leads to an electrical potential difference across the membrane, also without applied current. a literature study is presented on proposed theories for the origin of this membrane potential (ϕm). the most well-known theoretical description is teorell-meyer-sievers (tms) theory, which we analyze and extend. experimental ...

we consider the bifurcation of periodic solutions from an equilibrium point of the given equation: x =f(x,?) , where x ? r , ? is a vector of real parameters ? , ? , ... , ? and f:r x r ->r has at least second continuous derivations in variables

A non-ideal osmotic equilibrium equation is proposed as a replacement for the Boyle van't Hoff equation to describe the equilibrium volume of a living cell as a function of external osmolality. Contrary to common understanding, the Boyle van't Hoff equation is only thermodynamically correct for ideal, dilute solutions. However, the Boyle van't Hoff equation is commonly used to determine the osm...

The Kelvin equation, the Gibbs equation and the Gibbs-Thomson equation are compared. It is shown that the Kelvin equation (on equilibrium vapor pressure above nano-droplets) can be derived if the inner pressure due to the curvature (from the Laplace equation) is substituted incorrectly into the external pressure term of the Gibbs equation. Thus, the Kelvin equation is excluded in its present fo...