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In this paper we are addressing a counting problem of discrete mathematics, more precisely of digital geometry. In the Euclidean plane the shortest path between any two points is given by the straight line segment connecting the points. In discrete mathematics, the shortest path is usually not unique, e.g., in graphs there could be several shortest paths between two vertices. In this paper, a special infinite graph, the square grid, (i.e., the usual digital plane) is used. In digital geometry there are various digital, i.e., path based distance functions. A neighborhood sequence B gives the condition for each step of a B-path separately what type of neighborhood is used in that step. Therefore, the length and also the number of the shortest paths between two points depend not only on the respective positions (coordinate differences) of the points but also on the neighborhood sequence B. We give an algorithm and also closed formulae to compute the number of shortest B-paths. [ABSTRACT FROM AUTHOR]

In this paper a novel explicit and unconditionally stable numerical algorithm is introduced to solve the inhomogeneous non-stationary heat or diffusion equation. Spatial discretization of these problems usually yields huge and stiff ordinary differential equation systems, the solution of which is still time-consuming. The performance of the new method is compared with analytical and numerical solutions. It is proven exactly as well as demon-strated numerically that the new method is first order in time and can give approximate results for extremely large systems faster than the commonly used explicit or implicit methods. The new method can be easily parallelized and it is handy to apply regardless of space dimensions and grid irregularity. [ABSTRACT FROM AUTHOR]

In this paper we propose a parallel iterative hybrid methods for finding a common element of the solution sets of a finite family of pseudomonotone equilibrium problems and the fixed points set of a semigroup-nonexpensive mappings in Hilbert spaces. Under mild conditions, we obtain the strong convergence of the proposed iterative process. Some numerical experiments are given to verify the efficiency the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper we discuss the approach for optimal switching control problem with unknown switching points. The case with unknown switching point is more general and generalizes the results existing in the literature. By using suitable transformation, the main problem is reduced into a problem with known interval and further the unknown boundary of the integral in the minimization functional is reduced to the known one. This fact is illustrated by an example. The reduced problem is solved numerically by using the Gradient Projection Method Algorithm. [ABSTRACT FROM AUTHOR]

The number of formal concepts generated from the input context is an important parameter in the cost functions of concept formation algorithms. The calculation of concept count for any arbitrary context is a hard, NP-complete problem and only rough approximation methods can be found in the literature to solve this problem. This paper introduces an efficient numerical approximation algorithm for contexts where attribute probabilities are independent from the objects instances. The preconditions required by the approximation method are usually met in the FCA applications, thus the proposed method provides an efficient tool for practical complexity analysis, too. [ABSTRACT FROM AUTHOR]

Our goal is to create a propositional logic formula to model a directed graph and use a SAT solver to analyse it. This model is similar to the well-know one of Aspvall et al., but they create a directed graph from a 2-SAT problem, we generate a 2-SAT problem from a directed graph. In their paper if the 2-SAT problem is unsatisfiable, then the generated directed graph is strongly connected, in our case, if the directed graph is strongly connected, then the generated 2-SAT problem is a black-and-white 2-SAT problem, which has two solutions: where each variable is true (the white assignment), and where each variable is false (the black one). If we see a directed graph as a communication model of a network, then we can ask in our model whether a node can send a message to another one through the network. More specifically we can ask whether all nodes can send messages to all other ones, i.e., the graph is strongly connected or not. [ABSTRACT FROM AUTHOR]

This work focuses on the class of multivalued regularized equilibrium problems in the context of uniformly prox-regular sets introduced and studied in [Noor, M.A.: Multivalued regularized equilibrium problems. J. Global Optim. 35, 483-492 (2006)]. The algorithms and results presented in the paper cited above are investigated and analyzed and some fatal errors in them are detected. Meanwhile, the correct version of the corresponding algorithm and results is given. [ABSTRACT FROM AUTHOR]