Kernel estimates for nonautonomous Kolmogorov equations with potential term

Using time dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernels of some nonautonomous Kolmogorov operators with possibly unbounded drift and diffusion coefficients and a possibly unbounded potential term

Croissance de fibres polycristallines de composition eutectique AI2_2O3_3/Y3_3AI5_5O12{12} pour renforcement de composite

Eutectic fiber belongs to the Y$_2$O$_3$Al$_2$O$_3$ system were grown using Laser Heated Pedestal growth technique. We have controlled the fiber and diameter shape during the growth process. The interface of the melting zone was been plane. The fibers length was about few centimetre and are cracks and defects free. The eutectic fibers have high temperature strength properties, it was 577 MPa at 1500°C