We consider the minimal conformal model describing the tricritical Ising model on the disk and on the upper half plane. Using the coulomb-gas formalism we determine its consistents boundary states as well as its 1-point and 2-point correlation functions.

In this paper, we introduce a time-changed geometric Brownian motion and investigate the corresponding martingale properties and fractional Fokker-Planck type equation. As an application, we prove that the market model considered is arbitrage-free and gives pricing formulae for the prices of European call options when the underlying asset price follows the time-changed geometric Brownian motion.

The heat transfer equation is used to determine the heat flow by conduction through a composite material along the real axis. An analytical dimensionless analysis is implemented in the framework of a separation of variables method (SVM). This approach leads to an Eigenvalues problem that is solved by the Newton's method. Two types of dynamics are found: An unsteady condition (in the form of jumps or drops in temperatures depending on the considered case), and a permanent equilibrium (tending to the ambient temperature). The validity and effectiveness of the proposed approach for any number of adjacent layers is also discussed. It is shown that, as expected, the diffusion of the temperature is linked to the ratio of the thermo-physical properties of the considered layers and their number.