In this article, we study the obstructions to local-global principle for homogeneous spaces with connected or abelian stabilizers over finite extensions of field $\mathbb{C}((x,y))$ Laurent series in two variables complex numbers and function fields curves $\mathbb{C}((t))$. We give examples that prove usual Brauer-Manin obstruction is not enough explain failure principle, then construct a vari...

Applying two definitions of the union of IF-events, P. Grzegorzewski gave two generalizations of the inclusion-exclusion principle for IF-events.In this paper we prove an inclusion-exclusion principle for IF-states based on a method which can also be used to prove Grzegorzewski's inclusion-exclusion principle for probabilities on IF-events.Finally, we give some applications of this principle by...

The equivalence principle, which states the local equivalence between acceleration and gravity, requires that a free falling observer must result in a co-moving local Minkowski space. On the other hand, covariance principle assumes any Gaussian system to be valid as a space-time coordinate system. Given the mathematical existence of the co-moving local Minkowski space along a time-like geodesic...

We discuss the length Lc,n of longest cycle in a sparse random graph Gn,p, p=c/n, c constant. show that for large there exists function f(c) such Lc,n/n?f(c) a.s. The f(c)=1??k=1?pk(c)e?kc where pk(c) is polynomial c. are only able to explicitly give values p1,p2, although we could principle compute any pk. see immediately path also asymptotic f(c)n w.h.p.

Two regions of mtDNA, cytochrome b and cytochrome c oxidase subunit 1, were sequenced in nine species of Bathyraja from the Southern Ocean and New Zealand. Based on sequence divergence, the species that has been referred to as Bathyraja eatonii from the Antarctic continental shelf and slope is a species distinct from B. eatonii from the Kerguelen Plateau (the type locality) and is a new and und...