Wednesday, July 17. 2019
Fundamentals of Mathematical Modeling of Cognitive Digital Automata
V.V. Kozhevnikov
Technological Research Institute of Ulyanovsk State University, 1/4 Universitetskaya Naberezhnaya, Ulyanovsk, 432017, Russia
Received: 31 May 2019; accepted in revised form: 18 June 2019
Abstract An approach to the mathematical modeling of cognitive digital automata (CDA) is proposed. This approach represents a further development of the theory of digital automata and is based on the methods of mathematical modeling of conventional digital automata. At the same time, the task of formalizing the concept of cognitivity of the mathematical model of CDA comes to the fore. Cognitivity of the mathematical model, respectively, is determined by the possibility of training and generating solutions that are not provided for in the process of learning. A specific feature of the mathematical model of CDA consists in the fact that the description of the neural network (NN) structure serves as the structure diagram of digital automata, and the logical function “NOTANDOR” is used as the model of the neuron. In the case of the formation of feedbacks from the output to the inputs of the neurons, the model of the neuron is a binary trigger with a logical function “NOTANDOR” at the input. The mathematical apparatus of Petri nets (PNs) is proposed as a tool for constructing the mathematical model of CDA: marked graphs, inhibitory PNs and PNs with programmable logic. The mathematical model is constructed on the basis of the representation of CDA in the form of the state equation of PNs from the class of Murata equations (matrix equations) or a system of linear algebraic equations. The task of formalizing the concept of cognitivity is solved as a result of the synthesis of the logic of the initial CDA structure diagram or the formation of the formula of CDA. At the same time, the possibility of forming the formula of CDA depends on the critical mass of training sets and training algorithms. Hence, the task of generating the minimum training sets for a given function or experimentally determined function of CDA bears particular importance. Prediction or generation of solutions, in its turn, is performed on the basis of the mathematical model of CDA obtained in the training process. Keywords: intelligent control system, cognitive digital automata, artificial intelligence, neural networks, machine learning, cognition, Petri nets, equation of states, mathematical modeling, synthesis, generation, analysis, logic.
c 2019 European Society of Computational Methods in Sciences and Engineering
Download PDF
Friday, June 21. 2019
Effect of Fluid in the Moving Container
K. Kotrasova and E. Kormanikova Department of Structural Mechanics, Institute of Structural Engineering, Civil Engineering Faculty, Technical University of Košice, 04200 Kosice, Slovakia
Received 31 January, 2019; accepted in revised form 18 March, 2019
Abstract: When a rectangular tank contained liquid vibrates, the liquid exerts hydrodynamic pressure acting onto tank walls and tank bottom. This paper describes theoretical background of effect of fluid in moving rectangular container. The rectangular concrete container excited by the movement of the earth surface was analyzed on the example. The analysis was performed of the fluid effect on solid of container and ground motion effect on liquid filled tank.
© European Society of Computational Methods in Sciences and Engineering Keywords: Fluid, container, moving Mathematics Subject Classification: 00A69, 49Mxx
Download PDF
Friday, February 15. 2019
DEVELOPMENT OF THE THEORY FOR MODELING AND RESEARCH OF ADVANCED TECHNOLOGIES FOR ENRICHING BIOFUEL CELLS WITH GENERATOR GASES
V.N. Kovalnogov^{1,2}, T.V. Karpukhina^{2}, M.S. Boyarkin^{2}
^{1}Group of Numerical and Applied Mathematics on Urgent Problems of Energy and Power Engineering, Faculty of Power Engineering, Ulyanovsk State Technical University, Severny Venets Street 32, 432027 Ulyanovsk, Russian Federation ^{2}Department of HeatandPower Engineering, Faculty of Power Engineering, Ulyanovsk State Technical University, Severny Venets Street 32, 432027 Ulyanovsk, Russian Federation
Received: 10 December 2018; accepted in revised form: 12 February 2019
Abstract The complex of issues related to the mathematical modeling of heatandmass transfer of moisture and gas in the capillaryporous space of solid biofuel cells is discussed. This is the theoretical basis for developing of biofuel enrichment technologies which include heating with simultaneous saturation of the capillaryporous space by the synthesis gas and the combustible components of the recycle gas that in complex contributes the most complete combustion of cells and improve the fuel efficiency and environmental friendliness of the boiler plant. The mathematical model defining the kinetics of heat and humidity conditions and saturation of biofuel cells, as well as some numerical results of parameters of cell condition in the process of enrichment of recycled exhaust gases are given and discussed. Keywords: biofuels, enrichment technology, capillaryporous space, heatandhumidity state, modeling
c 2019 European Society of Computational Methods in Sciences and Engineering
Download PDF
Friday, February 15. 2019
SOFTWARE AND INFORMATION COMPLEX FOR THE COUPLED NUMERICAL SOLUTION OF THE EQUATIONS OF HEATANDMOISTURE TRANSFER AND THE STUDYING OF HEATANDHUMIDITY KINETICS OF BIOFUEL CELLS
V.N. Kovalnogov^{1,2}, T.V. Karpukhina^{2}, M.S. Boyarkin^{2}
^{1}Group of Numerical and Applied Mathematics on Urgent Problems of Energy and Power Engineering, Faculty of Power Engineering, Ulyanovsk State Technical University, Severny Venets Street 32, 432027 Ulyanovsk, Russian Federation ^{2}Department of HeatandPower Engineering, Faculty of Power Engineering, Ulyanovsk State Technical University, Severny Venets Street 32, 432027 Ulyanovsk, Russian Federation
Received: 10 December 2018; accepted in revised form: 12 February 2019
Abstract The complex of issues related to the mathematical modeling of heatandmass transfer of moisture and gas in the capillaryporous space of solid biofuel cells is discussed. The mathematical model, a difference approximation of differential equations defining the kinetics of heatandhumidity conditions and saturation of biofuel cells, as well as the calculation algorithm are given and discussed. Keywords: heatandhumidity state, coupled solution, modeling, capillaryporous space.
c 2019 European Society of Computational Methods in Sciences and Engineering
Download Full PDF
Friday, December 7. 2018
THE CONCEPT OF DESIGNING AN INTELLECTUAL ROBOT CONTROL SYSTEM BASED ON THE MATHEMATICAL MODEL OF COGNITIVE DIGITAL AUTOMATA
V.V.Kozhevnikov^{1}, B.M.Kostishko^{1}, M.Yu.Leontev^{1}, E.R.Mingachev^{1}, S.V.Pavlov^{2}, V.V.Prikhodko^{1}
^{1}S.P. Kapitsa Technological Research Institute of Ulyanovsk State University, Ulyanovsk, Russia ^{2}Sosny Research and Development Company, Dimitrovgrad, Ulyanovsk region, Russia
Received: 10 November 2018; accepted in revised form: 04 December 2018
Abstract. An intellectual control system (ICS) to control robots can be built (designed) on the basis of the mathematical model of cognitive digital automata (CDA). The intellectual control system in this case is a software and hardware complex, where the mathematical model of the CDA determines the control system as an intellectual one. The cognitive ability of the mathematical model is determined by the possibility of forming new knowledge based on the knowledge gained at the training stage. The creativity of a mathematical model is determined by the ability to construct sequences (logical chains) of generating new knowledge. A specific feature of the mathematical model of the CDA consists in the fact that the description of the neural network (NN) structure serves as the initial structural scheme of automata, and the logical function "NOTANDOR" is used as the neuron model. The mathematical apparatus of Petri nets (PN) is proposed as a tool to construct the mathematical model of the CDA. The structure, composition and algorithm of functioning of the robot’s intellectual control system based on the mathematical model of the CDA is discussed in the paper. In accordance with the algorithm, the ICS operates in three modes: training, manual and automatic control. Training a mathematical model of the CDA can be performed both in the manual mode and in the automatic control mode. The possibility of learning in the automatic control mode, in its turn, provides the possibility of regenerating knowledge and, accordingly, the possibility of cognitive control.
Keywords: intellectual control system, robots, cognitive automata, artificial intelligence, neural networks, machine learning, cognition, thinking, Petri nets, equation of states, mathematical modeling, synthesis, generation, analysis, logic.
c 2018 European Society of Computational
Methods in Sciences and Engineering
Download Full PDF
Monday, November 12. 2018
NICOLETA E. TARFULEA DEPARTMENT OF MATHEMATICS, PURDUE UNIVERSITY NORTHWEST, USA
Abstract. HIV can infect cells via celltocell and virustocell transmissions. These two types of transmission may occur in a combined way and enable viral spread. In this paper, we investigate analytically and numerically the influence of these two transmission modes, as well as the viral loss due to infection of Tcells. We introduce, analyze, and compare three mathematical models and show that viral loss due to infection of cells has little effect on the dynamics of HIV. Moreover, we show that additional conditions for the steady state stability are needed when virustocelltransmission is included and a critical value for this parameter is provided. Numerical simulations illustrate the theoretical results and further investigate the differences between these systems.
c 2018 European Society of Computational
Methods in Sciences and Engineering
Download Full PDF
Monday, October 15. 2018
N. Chaabane^{1,a}, B. Riviere^{a}, Mikhail Sekachev^{b} and Henri Calandra^{b} ^{a}CAAM department, Rice University ^{b}Total E&P Research & Technology USA, LLC ^{1}Email: nc33@rice.edu
Abstract: In [7], a sequential approach was
introduced to solve the Biot system where the pressure and displacement
variables are decoupled. A stabilization term was added and the discontinuous
Galerkin method was used to discretize the equations in space and the backward
Euler method was used to discretize the equations in time. The convergence of
the method was established both theoretically and numerically. In this work, we
run several numerical experiments to further validate this approach. Cases with
more complex boundary conditions and realistic input parameters are solved. We
also carry out a strong scalability analysis to show the efficiency of this
method on supercomputers.
c 2018 European Society of Computational
Methods in Sciences and Engineering
Keywords: Poroelasticity; Biot system;
Discontinuous Galerkin; BarryMercer; sequential method; parallel
implementation
Mathematics Subject Classiffication: 65M60
Download Full PDF
Monday, September 3. 2018
R. Boonklurb^{1}, A. Duangpan^{2} and T. Treeyaprasert^{3} ^{1,2}Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand ^{3}Department of Mathematics and Statistics, Thammasat University, Rangsit Center, Pathumthani 12120, Thailand
Received 10 January 2018; accepted in revised form 27 August 2018
Abstract: We propose a modified finite integration method (FIM) by using the Chebyshev polynomial, to construct the first order integral matrix for solving linear differential equations in one and two dimensions. The grid points for the computation are generated by the zeros of the Chebyshev polynomial of a certain degree. We implement our method with several examples arose from realworld applications. In comparison with the finite difference method and the traditional FIMs (trapezoidal and Simpson's rules), numerical computations show that our modified FIM using Chebyshev nodes require the less computational cost to achieve significant improvement in accuracy.
c 2018 European Society of Computational Methods in Sciences and Engineering Keywords: Finite integration method, Linear differential equations, Chebyshev polynomial. Mathematics Subject Classication: 65L05, 65L10, 65N30
Download Full PDF
Monday, July 16. 2018
V.V. Kozhevnikov^{1}, V.V. Prikhodko^{1}, V.V. Svetukhin^{1}, A.V. Zhukov^{1}, A.N. Fomin^{1}, M.Yu. Leontyev^{1}, D.Ya. Vostretsov^{1}, A.A. Sobolev^{1}, V.I. Skrebtsov^{1}, V.E. Kiryukhin^{1}, V.V. Levschanov^{1}, D.S. Lavygin^{1}, E.M. Chavkin^{1}, E.R. Mingachev^{1}, R.G. Bildanov^{1}, S.V. Pavlov^{2}, V.N. Kovalnogov^{1}
^{1} S.P. Kapitsa Research Institute of Technology (Technological Research Institute) of Ulyanovsk State University, Ulyanovsk, Russia ^{2} Sosny Research and Development Company, Dimitrovgrad, Ulyanovsk region, Russia
Received 29 June, 2018; accepted in revised form 17 July, 2018
Abstract Principal directions of developing the methods for designing intelligent systems of robot control assume technologies based on the use of artificial neural networks. The neural networks, where the model of a neuron was developed as the simplest processor element, performing the computation of the transfer function of a scalar product of an input data vector and a weight vector, can give interesting results regarding generation of dependencies and forecasting. However, their obvious drawback is the lack of an explicit algorithm of action. Memorization of information in the learning process occurs implicitly as a result of selection of the weight coefficients of the neural network, therefore the problem of cognition (the formation of new knowledge) on the basis of those obtained earlier in the learning process seems difficult to resolve. A positive solution to this problem will open the way to the creation of the fullfledged artificial mind. From this point of view the promising area is where the mathematical model of the neural networks is built on the basis of mathematical logic. The intelligent control system in this case is a software and hardware complex, where the mathematical model of the neural network identifies the control system as an intellectual one.
c 2018 European Society of Computational Methods in Sciences and Engineering
Download Full PDF
Friday, April 6. 2018
R. Arcucci^{ab1}, L.Carracciuolo^{c} and R.Toumi^{d} a: University of Naples Federico II, Naples, Italy b: Euro Mediterranean Center on Climate Change, Italy c: National Research Council, Naples, Italy d: Imperial College London, London, United Kingdom
Received 1 February, 2017; accepted in revised form 03 April, 2018
Abstract: Data Assimilation (DA) is an uncertainty quantication technique used to incorporate observed data into a prediction model in order to improve numerical forecasted results. As a crucial point into DA models is the ill conditioning of the covariance matrices involved, it is mandatory to introduce, in a DA software, preconditioning methods. Here we present rst results obtained introducing two dierent preconditioning methods in a DA software we are developing (we named S3DVAR) which implements a Scalable Three Dimensional Variational Data Assimilation model for assimilating sea surface temperature (SST) values collected into the Caspian Sea by using the Regional Ocean Modeling System (ROMS) with observations provided by the Group of High resolution sea surface temperature (GHRSST). We present the algorithmic strategies we employ and the numerical issues on data collected in two of the months which present the most signicant variability in water temperature: August and March.
c 2018 European Society of Computational Methods in Sciences and Engineering
Keywords: Data Assimilation, oceanographic data, Sea Surface Temperature, Caspian sea, ROMS Mathematics Subject Classication: 65Y05, 65J22, 68W10, 68U20 PACS: 02.70.c
Download Full PDF
Monday, March 26. 2018
O. Ozturk Department of Mathematics, Faculty of Arts and Sciences, Bitlis Eren University, 13000 Bitlis, Turkey
Received 10 October, 2016; accepted in revised form 22 March, 2018
Abstract: Fractional calculus and its generalizations are used for the solutions of some classes of differential equations and fractional differential equations. In this paper, our aim is to solve the radial Schrödinger equation given by the Makarov potential by the help of fractional calculus theorems. The related equation was solved by applying a fractional calculus theorem that gives fractional solutions of the second order differential equations with singular points. In the last section, we also introduced hypergeometric form of this solution.
© European Society of Computational Methods in Sciences and Engineering Keywords: Fractional calculus, Generalized Leibniz rule, Radial Schrödinger equation, Makarov potential Mathematics Subject Classification: 26A33, 34A08
Download Full PDF
Tuesday, February 7. 2017
William F. Mitchell
^{}Applied and Computational Mathematics Division National Institute of Standards and Technology Gaithersburg, MD, USA 208998910
Abstract: One aspect of adaptive mesh refinement in the finite element method for solving partial differential equations is the method by which elements are refined. In the early 1980’s the dominant method for refining triangles was the redgreen algorithm of Bankand Sherman. The red refinements are the desired refinements, but will result in an incompatible mesh when used alone. The green refinements are used to recover compatibility for stability of the finite element discretization, and are removed before the next adaptive step. Prof. Bob Skeel raised the question as to whether it is possible to perform adaptive refinement of triangles without this complicated patching/unpatching process. As a result, a new triangle refinement method, called newest vertex bisection, was devised as an alternative to redgreen refinement in the mid 1980’s. The new approach is simpler and maintains compatibility of the mesh at all times, avoiding the patching/unpatching of the green refinement. In this historical paper we review the development of the newest vertex bisection method for adaptive refinement, and subsequent extensions of the method.
Keywords: finite elements; adaptive mesh refinement; newest vertex bisection Mathematics Subject Classification: 6503, 65N30, 65N50 PACS: 02.60.Lj, 02.70.Dh
Download Full PDF
Tuesday, February 7. 2017
Gaussian Scale Mixtures Miguel Martins Felgueiras ^{1 *}, João Paulo Martins^{**}, Rui Filipe Santos^{**}
^{*} CEAUL Lisbon and ESTG, CIGS, Polytechnic Institute of Leiria, Portugal ^{**} CEAUL Lisbon and ESTG, Polytechnic Institute of Leiria, Portugal
Abstract: In this paper we present a parsimonious approximation of a Gaussian mixture when its components share a common mean value, i.e. a scale mixture. We show that a shifted and scaled Student’s tdistribution can be approximated to this type of mixture, and use the result to develop a hypothesis test for the equality of the components mean value. A simulation study to check the quality of the approximation is also provided, together with an application to logarithmic daily returns.
Keywords: Gaussian scale mixture, Student’s tdistribution, logreturns, simulation. Mathematics Subject Classification: 60E05; 62P20.
Download Full PDF
Friday, June 17. 2016
Eva Volna and Martin Kotyrba^{1}
Faculty of Science Department of Informatics and Computers, University of Ostrava, 30 dubna 22, 70103 Ostrava, Czech Republic
^{1}Corresponding author. Email: martin.kotyrba@osu.cz
Abstract: The Vehicle Routing Problem (VRP) is one of the most challenging combinatorial optimization tasks. This problem consists in designing an optimal set of routes for a fleet of vehicles in order to serve a given set of customers. Vehicle routing problem forms an integral part of the supply chain management, which plays a significant role in productivity improvement in organizations through an efficient and effective delivery of goods/services to customers. This problem is known to be NPhard; hence many heuristic procedures for its solution have been suggested. For such problems, it is often desirable to obtain approximate solutions, so they can be found fast enough and are sufficiently accurate for the purpose. In this paper, we have performed an experimental study that indicates a suitable use of genetic algorithms for the vehicle routing problem. We tested instances from Capacitated Vehicle Routing Problem Library (CVRPLIB) series A, B, E, M and X. The obtained experimental outputs were compared with the following heuristics: the Clarke and Wright heuristic, sweep algorithm, and Taillard's algorithm.
Keywords VRP  Vehicle Routing Problem, combinatorics, Clarke and Wright heuristic, Sweep algorithm,Taillard's algorithm, Genetic algorithm. Mathematics Subject Classification: 97K20, 90C59
Download Full PDF
Monday, February 1. 2016
A. Alaimo, V. Artale, G. Barbaraci, C.L.R. Milazzo, C. Orlando and A. Ricciardello
Kore University of Enna,Faculty of Engineering and Architecture, Cittadella Universitaria  94100  Enna
andrea.alaimo@unikore.it, valeria.artale@unikore.it, calogero.orlando@unikore.it, cristina.milazzo@unikore.it, angela.ricciardello@unikore.it
Abstract: In this paper the mathematical model representing the dynamic of a Unmanned Aerial Vehicle (UAV) is studied in order to analyse its behaviour. In order to stabilize the entire system, linear Quadratic Regulator (LQR) control is used in such a way to set both PD and PID controls in position variables. A set simulation is performed to carry out the results for linear and non linear models. The LQRPD and LQRPID allow to move the plant's poles of UAV in the left half plane since without controller the systems is unstable. Simulations, LQRPD and LQRPID controllers are designed by using Matlab/Simulink. The simulations are performed to show how LQR tuned PD and PID controllers lead to zero the error of the position along Z earth direction, stop the rotation of Unmanned Aerial Vehicle (UAV) around body axes and stabilize the hexarotor.
Keywords: Hexarotor; LQR, PID and PD controller.
Download Full PDF
