Coding and Compression of Three Dimensional Meshes by Planes

The present paper suggests a new approach for geometric representation of 3D spatial models and provides a new compression algorithm for 3D meshes, which is based on mathematical theory of convex geometry. In our approach we represent a 3D convex polyhedron by means of planes, containing only its faces. This allows not to consider topological aspects of the problem (connectivity information among vertices and edges) since by means of the planes we construct the polyhedron uniquely. Due to the fact that the topological data is ignored this representation provides high degree of compression. Also planes based representation provides a compression of geometrical data because most of the faces of the polyhedron are not triangles but polygons with more than three vertices.Comment: 10 pages, 7 figure

On disjoint matchings in cubic graphs

For $i=2,3$ and a cubic graph $G$ let $\nu_{i}(G)$ denote the maximum number of edges that can be covered by $i$ matchings. We show that $\nu_{2}(G)\geq {4/5}| V(G)|$ and $\nu_{3}(G)\geq {7/6}| V(G)|$. Moreover, it turns out that $\nu_{2}(G)\leq \frac{|V(G)|+2\nu_{3}(G)}{4}$.Comment: 41 pages, 8 figures, minor chage

Designing optimal solar water pumping stations for irrigation of agricultural lands

An investigation into the design of a stand-alone solar water pumping station for supplying rural areas is presented. It includes a study of system components and their modeling. The solar water pumping station comprises a solar panel, DC/DC buck converter, DC motor driving a centrifugal pump, and a reservoir. The fuzzy-based maximum power point tracker is developed to optimize the drive speed and the water discharge rate of the coupled centrifugal pump. These use dN/I, d(dN/dI) use parameters, and a variation of the fill factor∆α as input variables. The proposed solution is based on a judicious fuzzy adjustment of a converter fill factor, which adapts online the load impedance to the solar panel. The simulation results show the effectiveness of the drive system for both transient and steady-state operations. Hence, it is suitable to use this fuzzy logic procedure as a standard optimization algorithm for such solar water pumping stations. The modeling is carried out in MATLAB/Simulink

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements

On strongly spanning k-edge-colorable subgraphs

A subgraph $H$ of a multigraph $G$ is called strongly spanning, if any vertex of $G$ is not isolated in $H$. $H$ is called maximum $k$-edge-colorable, if $H$ is proper $k$-edge-colorable and has the largest size. We introduce a graph-parameter $sp(G)$, that coincides with the smallest $k$ for which a multigraph $G$ has a maximum $k$-edge-colorable subgraph that is strongly spanning. Our first result offers some alternative definitions of $sp(G)$. Next, we show that $\Delta(G)$ is an upper bound for $sp(G)$, and then we characterize the class of multigraphs $G$ that satisfy $sp(G)=\Delta(G)$. Finally, we prove some bounds for $sp(G)$ that involve well-known graph-theoretic parameters

Designing optimal solar water pumping stations for irrigation of agricultural lands

An investigation into the design of a stand-alone solar water pumping station for supplying rural areas is presented. It includes a study of system components and their modeling. The solar water pumping station comprises a solar panel, DC/DC buck converter, DC motor driving a centrifugal pump, and a reservoir. The fuzzy-based maximum power point tracker is developed to optimize the drive speed and the water discharge rate of the coupled centrifugal pump. These use dN/I, d(dN/dI) use parameters, and a variation of the fill factor∆α as input variables. The proposed solution is based on a judicious fuzzy adjustment of a converter fill factor, which adapts online the load impedance to the solar panel. The simulation results show the effectiveness of the drive system for both transient and steady-state operations. Hence, it is suitable to use this fuzzy logic procedure as a standard optimization algorithm for such solar water pumping stations. The modeling is carried out in MATLAB/Simulink

Elaboration of balance-optimization in economic and mathematical model of development of a large municipal unit: Real experience

The objective of the study is to develop a balance-optimizing economic and mathematical model which enables predicting steady and sustainable development of a large municipal unit. Using the method of dynamic programming introduced by Richard Bellman, the authors worked out the economic and mathematical model for optimizing the key indicators of soсial and economic development of a municipal unit. The model used and predicted indicators included in the list of the key performance indicators of municipal unit authorities. There is an analysis of the results of applying the model for a large municipal unit - Novosibirsk. The calculations made by the authors indicate that the model may work with actual economic information and may be used for predicting and making managerial decisions at a municipal level