We generalize a beautiful method of Blasius and Ramakrishnan, that in order to exhibit particular instances of the Langlands functorial correspondence, it is enough to show that the correspondence holds in the semistable case, provided the arithmetic data we are considering is closed with respect to cyclic base change and descent.

We show that the p-adic Galois representations attached to Hilbert modular forms of motivic weight are potentially semistable at all places above p and are compatible with the local Langlands correspondence at these places, proving this for those forms not covered by the previous works of T. Saito and of D. Blasius and J. Rogawski. 2000 Mathematics Subject Classification: 11F80, 11F41

As the number of applications of micro electro mechanical systems, or MEMS, increase, the variety of flow geometries that must be analyzed at the micro-scale is also increasing. To date, most of the work on MEMS scale fluid mechanics has focused on internal flow geometries, such as microchannels. As applications such as micro-scale flyers are considered, it is becoming necessary to consider ext...

In this paper, we have defined the free boundary formulation for two extended Blasius problems. These problems are of interest in layer theory and deduced from governing partial differential equations by using appropriate similarity variables. The computed results, so-called missing initial condition, favorably compared with recent results available literature.