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.
On: Travelling salesman problem under categorization: Operations Research Letters 12 (1992) 89-95
We introduce two new classes of traveling salesman problems (TSP1 and TSP2) which subsume the classical traveling salesman problem and the bottleneck traveling salesman problem. It is shown that these problems are strongly NP-complete on Halin graphs eventhough their extreme cases (i.e. traveling salesman problem and bottleneck traveling salesman problem) are solvable in polynomial time on such graphs. It is also shown that TSP2 is solvable in polynomial time on Halin graphs if an associated parameter p is fixed, but TSP1 still remains NP-complete. For TSP2, a polynomial time (for fixed p) heuristic is suggested which produces a solution whose objective function value is no worse than twice that of the optimal solution whenever the underlying graph is complete, undirected and edge weights satisfy the triangle inequality.