Evaporator System of Water Desalination Based on Ranque-Hilsch Vortex Effect

AbstractThe vortex tube of the water desalination evaporator system is studied based on the Ranque-Hilsch vortex effect. Vortex effects mathematical model is based on Reynolds Equations which is completed by k-w SST turbulence differential model. One of the goals of the research is to define the geometry of the vortex tube scaled model. Another goal of the research is to define the input parameters for Reynolds Stress Turbulence Model. The results of the research are the defined optimal geometry parameters of the vortex tube prototype and input parameters required for Reynolds Stress Turbulence Model analysis

Linear and Fisher Separability of Random Points in the d-dimensional Spherical Layer

Stochastic separation theorems play important role in high-dimensional data analysis and machine learning. It turns out that in high dimension any point of a random set of points can be separated from other points by a hyperplane with high probability even if the number of points is exponential in terms of dimension. This and similar facts can be used for constructing correctors for artificial intelligent systems, for determining an intrinsic dimension of data and for explaining various natural intelligence phenomena. In this paper, we refine the estimations for the number of points and for the probability in stochastic separation theorems, thereby strengthening some results obtained earlier. We propose the boundaries for linear and Fisher separability, when the points are drawn randomly, independently and uniformly from a $d$-dimensional spherical layer. These results allow us to better outline the applicability limits of the stochastic separation theorems in applications.Comment: 6 pages, 3 figures IJCNN 2020 Accepte

Faster Algorithms for Sparse ILP and Hypergraph Multi-Packing/Multi-Cover Problems

In our paper, we consider the following general problems: check feasibility, count the number of feasible solutions, find an optimal solution, and count the number of optimal solutions in $P \cap Z^n$, assuming that $P$ is a polyhedron, defined by systems $A x \leq b$ or $Ax = b,\, x \geq 0$ with a sparse matrix $A$. We develop algorithms for these problems that outperform state of the art ILP and counting algorithms on sparse instances with bounded elements. We use known and new methods to develop new exponential algorithms for Edge/Vertex Multi-Packing/Multi-Cover Problems on graphs and hypergraphs. This framework consists of many different problems, such as the Stable Multi-set, Vertex Multi-cover, Dominating Multi-set, Set Multi-cover, Multi-set Multi-cover, and Hypergraph Multi-matching problems, which are natural generalizations of the standard Stable Set, Vertex Cover, Dominating Set, Set Cover, and Maximal Matching problems