Let p be a prime number. In this article we present a theorem, suggested by Peter Scholze, which states that Gal(Qp/Qp) is the étale fundamental group of a certain object Z which is defined over an algebraically closed field. This object is the quotient of the “punctured perfectoid open disk” by an action of the group Qp . The proof of this fact combines two themes: the tilting equivalence for ...

The use of Geometric Logic as the foundation of a speciication language called GeoZ is proposed elsewhere 4]. In this note we explore GeoZ from the perspective of practitioners, who are familiar with the existing Z notation, by explaining the issues that arise and the essential role of schema entailment in the GeoZ reformulation of Z's mathematical toolkit.

Let $p$ be an analytic function defined on the open unit disc $mathbb{D}$ with $p(0)=1.$ The conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{C}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ ...

I here propose an index that links the number of papers a researcher has published with impact factors (IFs) of the journals that publish these papers. A researcher is said to have an index z if totally z of his/her papers are published in journals with IFs of at least z/2. The z-index, not meant to evaluate, compare and rank scientists, is a number that hopefully conveniently summarizes the nu...

one studies the $hx$-hypergroups, corresponding to the chinese hypergroups associated with the direct products of some ${bf z}/n {bf z},$ calculating their fuzzy grades.

in this paper, a new topology for boost z-source inverterbased on switched-inductor cell is proposed. the operating modes of the proposed inverter are analyzed and also a suitable control method to generate the trigger signals of the inverter is presented. having a common earth between the input source and inverter and capability to generate a higher voltage gain by using lower amounts of the d...