A Lagrangian-type numerical scheme called the "comoving mesh method" or CMM is developed for numerically solving certain classes of moving boundary problems which include, example, classical Hele-Shaw flow problem and well-known mean curvature problem. This finite element exploits idea that normal velocity field can be extended throughout entire domain definition using, instance, Laplace operat...

Let G be a graph and KG be the set of all cliques of G, then the clique graph of G denoted by K(G) is the graph with vertex set KG and two elements Qi, Qj ∈ KG form an edge if and only if Qi ∩ Qj 6= ∅. Iterated clique graphs are defined by K0(G) = G, and K(G) = K(Kn−1(G)) for n > 0. In this paper we determine the number of cliques in K(G) when G = G1+G2, prove a necessary and sufficient conditi...

The paper studies a model of repairable systems which is exible enough to incorporate the standard imperfect repair and many other models from the literature. Palm stationarity of virtual ages, inter-failure times and degrees of repair is studied. A Loynes type scheme and Harris recurrent Markov chains combined with coupling methods are used. Results on the weak, total variation and moment conv...

Conditions on compact convergences to be topological are (and have been) investigated. New variants are obtained for both filter and cover compact-like properties such as countable compactness and Lindelöfness. The recently developed coreflectively modified continuous duality plays a crucial role in this quest. In particular, the results on compactness evoked above can be obtained either as byp...

Topological sequential spaces are the fixed points of a Galois correspondence between collections of open sets and sequential convergence structures. The same procedure can be followed replacing open sets by other topological concepts, such as closure operators or (ultra)filter convergences. The fixed points of these other Galois correspondences are not topological spaces in general, but they c...

We consider vector lattices endowed with locally solid convergence structures, which are not necessarily topological. show that such a is defined by the to 0 on positive cone. Some results unbounded modification were only available in partial cases generalized. Order characterized as strongest monotone nets converge their extremums (if they exist). partially characterize sublattices order restr...

In this papers we analyze the minimization of seminorms ‖L · ‖ on R under the constraint of a bounded I-divergence D(b,H ·) for rather general linear operators H and L. The I-divergence is also known as Kullback-Leibler divergence and appears in many models in imaging science, in particular when dealing with Poisson data. Often H represents, e.g., a linear blur operator and L is some discrete d...