A Coboundary Morphism For The Grothendieck Spectral Sequence

Given an abelian category $\mathcal{A}$ with enough injectives we show that a short exact sequence of chain complexes of objects in $\mathcal{A}$ gives rise to a short exact sequence of Cartan-Eilenberg resolutions. Using this we construct coboundary morphisms between Grothendieck spectral sequences associated to objects in a short exact sequence. We show that the coboundary preserves the filtrations associated with the spectral sequences and give an application of these result to filtrations in sheaf cohomology.Comment: 18 page

The Influence of Melt State on Atomization Process and Quality of Powders on Iron and Nickel Base

The analysis of the results of physical and chemical properties and structure investigation in liquid multicomponent steels and alloys indicates that after melting their state is generally not in equilibrium. Heating to the critical temperatures helps the system to transform into the equilibrium state or the state close to it. Melt preparing before atomization affects the process of liquid metal dispersion and helps to improve the structure and properties of the powder. The optimum melt preparing technology before atomization leads to formation the dispersion dendritic structure, optimum morphology, quantity and size of primary and eutectic phases in the powders particles and increase in properties. © 2008 IOP Publishing Ltd