Tvorba regresného modelu na základe experimentálnych skúšok
Regression model creation based on experimental tests of conveyor belts against belt rips resistance Conveyor belt impairing by belt rip can lead to its sequential destruction so that economical costs for operation of belts are rising. Adjusting basic parameters of conveyor belt properties is necessary to assure great belt rip resistance. The paper describes shortly methodology that should be used with experimental tests of conveyor belts regarding to its belt rip resistance. In the paper there is mathematical mentioned model creation describing the forces acting to the belt by falling-down a material. At the end of the paper there are described ways to optimize methodology of measuring process to make costs (financial or time) much lower even in the phase of belt designing.
Balanced problems on graphs with categorization of edges
Suppose a graph G = (V, E) with edge weights w(e) and edges partitioned into disjoint categories S1, . . . , Sp is given. We consider optimization problems P on G defined by a family of feasible sets D(G) and the following objective function: L5(D) = max 1≤i≤p ( max e∈Si∩D w(e)− min e∈Si∩D w(e) ) For an arbitrary number of categories we show that the L5-perfect matching, L5-a-b path, L5-spanning tree problems and L5-Hamilton cycle (on a Halin graph) problem are NP-complete. We also summarize polynomiality results concerning above objective functions for arbitrary and for fixed number of categories.
Categorized bottleneck-minisum path problems on networks
We introduce two path problems on a network, where edges of the network are grouped into categories. The value of a path is calculated by first taking maximum (or sum) of lengths of edges of the path within each category and second taking sum (or maximum) of the obtained values among categories. It is shown that both problems are NP-complete even if all edges of the network have lengths equal to 1. Several special cases of the problems are also investigated, some of which are shown to be solvable in polynomial time and some of which are proved to be NP-complete.