Décompte dans une conjecture de Lang sur les corps de fonctions : cas des courbes

Let $X$ be a genus $d$ curve with $d\geq 2$ defined over a global function field $K$ of characteristic $p>0$ with $p>2d+1$. Suppose $X$ non-isotrivial. Let $\Gamma$ be a sub-group of $J(K_s)$, where $J$ is the jacobian of $X$ and $K_s$ is a separable closure of $K$, verifying $\Gamma/p \Gamma$ finite. Then one shows that $X\cap \Gamma$ has finite cardinal and one provides an explicit upper bound. This generalizes a result of Buium and Voloch

A New Cubic Equation of State for Predicting Phase Behavior of Hydrocarbons

In this work, a two parameter cubic equation of state is presented. The parameters of the new cubic equation of state are considered temperature dependent. For calculating the thermodynamic properties of a pure hydrocarbon, this equation of state requires the critical temperature, the critical pressure and the acentric factor of hydrocarbon. The proposed equation of state is applied for PVT and VLE calculations of different pure hydrocarbons and fluid mixtures. The results are compared with those obtained by two commonly used cubic equation of state. The comparisons indicate that the new equation of state yields better results