We first extend the Arens-Royden theorem to unital, commutative Frechet algebras under certain conditions. Then, we show that if A is a uniform Frechet algebra on X=MA, where MA is the continuous character space of A, then A does not have dense invertible group, if we impose some conditions on X. On the other hand, if A has dense invertible group, then it is shown that A=C (X), with certain conditions on X. Thus, the results of Dawson and Feinstein on denseness of the invertible group in Banach algebras are extended to uniform Frechet algebras.

In this paper the effect of corrugations on mechanical sensitivity of diaphragm for MEMS capacitive microphone is investigated. Analytical analyses have been carried out to derive mathematic expression for mechanical sensitivity and displacement of corrugated diaphragm with residual stress. It is shown that the mechanical sensitivity and displacement of diaphragm can be modeled using thin plate theory.The mechanical stress of corrugated diaphragm is calculated using mathematical model and its relationship with residual stress is expressed. The analytical results show that the mechanical sensitivity of diaphragm can be increased using corrugations, because of reducing the effect of residual stress in corrugated diaphragm.