We give a simple proof of the Faber-Krahn inequality for the first eigenvalue of the p-Laplace operator with Robin boundary conditions. The techniques introduced allow to work with much less regular domains by using test function arguments. We substantially simplify earlier proofs, and establish the sharpness of the inequality for a larger class of domains at the same time.

‎consider an estimation problem in a one-parameter non-regular distribution when both endpoints of the support depend on a single parameter‎. ‎in this paper‎, ‎we give sufficient conditions for a generalized bayes estimator of a parametric function to be admissible‎. ‎some examples are given‎. ‎

We devise variants of classical nonconforming methods for symmetric elliptic problems. These variants differ from the original ones only by transforming discrete test functions into conforming functions before applying the load functional. We derive and discuss conditions on these transformations implying that the ensuing method is quasi-optimal and that its quasioptimality constant coincides w...

In this study, two-dimensional finite element modeling was used to study the simultaneous effect of the cell shape and regular cell distribution on the anisotropy of the elastic properties of 316L stainless steel foam. In this way, the uniaxial compressive stress-strain curve was predicted using a geometric model and fully solid 316L stainless steel. The results showed that the elastic tangent ...

r is called commuting regular ring (resp. semigroup) if for each x,y $in$ r thereexists a $in$ r such that xy = yxayx. in this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.