Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue

“Take as your place of worship the place where Abraham stood (to pray).”

In the verse “Take as your place of worship the place where Abraham stood (to pray)” Abraham’s position is an intense discussion among Fariqain commentators. Commentary of this verse as Mosalla of Tawaf prayer and Tawaf area has a practical and jurisprudential role during Hajj and Umrah. On commentary of Abraham’s position and his status, more than six exegetic viewpoints have been proposed fro...

On the Placement of an Obstacle or a Well so as to Optimize the Fundamental Eigenvalue

On the First Eigenvalue of a Fourth Order Steklov Problem

We prove some results about the first Steklov eigenvalue d1 of the biharmonic operator in bounded domains. Firstly, we show that Fichera’s principle of duality [9] may be extended to a wide class of nonsmooth domains. Next, we study the optimization of d1 for varying domains: we disprove a long-standing conjecture, we show some new and unexpected features and we suggest some challenging problem...

The first biharmonic Steklov eigenvalue: positivity preserving and shape optimization

We consider the Steklov problem for the linear biharmonic equation. We survey existing results for the positivity preserving property to hold. These are connected with the first Steklov eigenvalue. We address the problem of minimizing this eigenvalue among suitable classes of domains. We prove the existence of an optimal convex domain of fixed measure. Mathematics Subject Classification (2000)....

from linguistics to literature: a linguistic approach to the study of linguistic deviations in the turkish divan of shahriar

chapter i provides an overview of structural linguistics and touches upon the saussurean dichotomies with the final goal of exploring their relevance to the stylistic studies of literature. to provide evidence for the singificance of the study, chapter ii deals with the controversial issue of linguistics and literature, and presents opposing views which, at the same time, have been central to t...