We present an improvement to the direct flux reconstruction technique for equilibrated flux a posteriori error estimates for one-dimensional problems. The verification of the suggested reconstruction is provided by numerical experiments.
We present a mathematical description of wetting and drying stone pores, where the resulting mathematical model contains hysteresis operators. We describe these hysteresis operators and present a numerical solution for a simplified problem.
We present an algorithm of finding the Hamiltonian cycle in a general undirected graph by minimization of an appropriately chosen functional. This functional depends on the characteristic polynomial of the graph Laplacian matrix and attains its minimum at the characteristic polynomial of the Laplacian matrix of the Hamiltonian cycle.
We investigate the properties of the least-squares solution of the system of equations with a matrix being the incidence matrix of a given undirected connected graph and we propose an algorithm that uses this solution for finding a vertex-disjoint cycle cover (2-factor) of the graph .
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