Algebraic approximation of analytic sets and mappings

Let {X_n} be a sequence of analytic sets converging to some analytic set X in the sense of holomorphic chains. We introduce a condition which implies that every irreducible component of X is the limit of a sequence of irreducible components of the sets from {X_n}. Next we apply the condition to approximate a holomorphic solution y=f(x) of a system Q(x,y)=0 of Nash equations by Nash solutions. Presented methods allow to construct an algorithm of approximation of the holomorphic solutions.Comment: 23 page

Approximation by piecewise-regular maps

A real algebraic variety W of dimension m is said to be uniformly rational if each of its points has a Zariski open neighborhood which is biregularly isomorphic to a Zariski open subset of R^m. Let l be any nonnegative integer. We prove that every map of class C^l from a compact subset of a real algebraic variety into a uniformly rational real algebraic variety can be approximated in the C^l topology by piecewise-regular maps of class C^k, where k is an arbitrary integer greater than or equal to l. Next we derive consequences regarding algebraization of topological vector bundles.Comment: 19 pages; Sections 1, 2.3 reorganize

Control of contaminants in liquid-metal systems

Contaminant controls and cleaning procedures in SNAP-8 simulation loop of liquid metal