A solution to the problem of clustered objects compact partitioning

The urgency of the study consists in the fact that an object arrangement topology of a distributed system is often nonuniform. Objects can be placed at different distances from each other, thus forming clusters. That is why solving the problem of compact partitioning into sets containing thousands of objects requires the most effective way to a better use of natural structuring of objects that form clusters. The aim of the study is the development of methods of compact partitioning of sets of objects presented as clusters. The research methods are based on applied theories of sets, theory of compact sets and compact partitions, and linear programming methods with Boolean variables. As a result, the paper offers the method necessary to analyze composition and content of clusters. It also evaluates cluster compactness, which results in the decision to include clusters into the sets of partitions. It addresses the problem of optimizing the rearrangement of objects between compact sets that form clusters, which is based on the criteria of maximizing the total compactness of sets. The problem is formulated in the class of objectives of linear programming methods with Boolean variables. It introduces the example of object rearrangement

Physico-chemical Modification of the Fibrous Filter Nozzles for Purification Processes of Water and Air

A set of experiments to study physical and chemical modification of the surface of fibers is conducted to expand the area of their application for purification of water, gas and air (including that in conditions of space). The possibility of modification of filter nozzles in the process of fiber formation by particles of coal of BAU type, copper sulfide and silver chloride is experimentally shown. The fraction of the copper sulfide powder less than 50 microns in size was crushed in a spherical mill; it was deposited on fiber at air temperature of 50° C and powder consumption of 0.5 g/l of air. The resulting material contained 6–18 CuS particles per 1 cm of the fiber length. An effective bactericidal fibrous material can be produced using rather cheap material – CuS and relatively cheap natural compounds of sulphides and oxides of heavy metals