Abstract We make rigorous and old idea of using mean curvature flow to prove a theorem Richard Hamilton on the compactness proper hypersurfaces with pinched, bounded curvature.

In this paper, we study the existence of solution to integro-differential equations in space Lebesgue-integrable on un-bounded interval after transformed nonlinear integral functional equation, used tool is fixed point theorem due Schauder with weak measure non compactness, De-Blasi. addition, give an example which satisfies conditions our theorem.

in this paper, countable compactness and the lindel¨of propertyare defined for l-fuzzy sets, where l is a complete de morgan algebra. theydon’t rely on the structure of the basis lattice l and no distributivity is requiredin l. a fuzzy compact l-set is countably compact and has the lindel¨ofproperty. an l-set having the lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

We establish a new Easton theorem for the least supercompact cardinal κ that is consistent with the level by level equivalence between strong compactness and supercompactness. This theorem is true in any model of ZFC containing at least one supercompact cardinal, regardless if level by level equivalence holds. Unlike previous Easton theorems for supercompactness, there are no limits on the East...