Our goal for this lecture is to prove that morphisms of projective varieties are closed maps. In fact we will prove something stronger, that projective varieties are complete, a property that plays a role comparable to compactness in topology. For varieties, compactness as a topological space does not mean much because the Zariski topology is so coarse. Indeed, every subset of An (and hence of ...

We establish some properties of the bilateral Riemann–Liouville fractional derivative Ds. set notation, and study associated Sobolev spaces order s, denoted by Ws,1(a,b), bounded variation BVs(a,b). Examples, embeddings compactness related to these are addressed, aiming a functional framework suitable for variational models image analysis.

In this talk we investigate the compactness theorem (as a property) in non-classical logics. We focus on the following problems: (a) What kind of semantics make a logic having compactnesss theorem? (b) What is the relationship between the compactness theorem and the classical model existence theorem (CME)/model existence theorem?

Lascar described EKP as a composition of EL and the topological closure of EL ([1]). We generalize this result to some other pairs of equivalence relations. Motivated by an attempt to construct a new example of a non-G-compact theory, we consider the following example. Assume G is a group definable in a structure M. We define a structure M′ consisting of M and X as two sorts, where X is an affi...

in this work, cofe2o4 nanoparticles have been prepared by co-precipitation technique. the synthesized cofe2o4 nanoparticles were applied in the preparation of cofe2o4/polyacrylonitrile fiber nanocomposites by the electrospinning process. the prepared nanoparticles and nanofibers were characterized using the scanning electron microscopy (sem) and x-ray diffraction methods. the results manifested...