Memristive Structure-Based Chaotic System for PRNG

This paper suggests an approach to generate pseudo-random sequences based on the discrete-time model of the simple memristive chaotic system. We show that implementing Euler’s and Runge–Kutta’s methods for the simulation solutions gives the possibility of obtaining chaotic sequences that maintain general properties of the original chaotic system. A preliminary criterion based on the binary sequence balance estimation is proposed and applied to separate any binary representation of the chaotic time sequences into random and non-random parts. This gives us the possibility to delete obviously non-random sequences prior to the post-processing. The investigations were performed for arithmetic with both fixed and floating points. In both cases, the obtained sequences successfully passed the NIST SP 800-22 statistical tests. The utilization of the unidirectional asymmetric coupling of chaotic systems without full synchronization between them was suggested to increase the performance of the chaotic pseudo-random number generator (CPRNG) and avoid identical sequences on different outputs of the coupled systems. The proposed CPRNG was also implemented and tested on FPGA using Euler’s method and fixed-point arithmetic for possible usage in different applications. The FPGA implementation of CPRNG supports a generation speed up to 1.2 Gbits/s for a clock frequency of 50 MHz. In addition, we presented an example of the application of CPRNG to symmetric image encryption, but nevertheless, one is suitable for the encryption of any binary source.

Mathematical Modelling of Gene Regulatory Networks

This research includes the use of an artificial intelligence algorithm, which is one of the algorithms of biological systems which is the algorithm of genetic regulatory networks (GRNs), which is a dynamic system for a group of variables representing space within time. To construct this biological system, we use (ODEs) and to analyze the stationarity of the model we use Euler's method. And through the factors that affect the process of gene expression in terms of inhibition and activation of the transcription process on DNA, we will use TF transcription factors. The current research aims to use the latest methods of the artificial intelligence algorithm. To apply Gene Regulation Networks (GRNs), we used a program (MATLAB2020), which provides facilitation to the most important biological concepts for building this biological interaction

Mathematical Modelling of Vertical Looped Water Slide Using Matlab

A conceptual mathematical model of a water slide with vertical loops is developed. The principle used is the conservation of energy. The thrill experienced by a rider on a water slide is mainly due to the variation of G-force acting on the rider through the course of the ride. The geometry of the slide is developed by plotting G-force variation with the arc length of the loop. The G-force exposure limits should meet with the standards set by the F24 committee on amusement parks and rides. The coordinates of the slide geometry are determined by using Euler’s method of discretized equations. Keywords: G-Force, Centripetal acceleration, Clothoid curve, Weightlessness, Potential Energy, Kinetic Energy

Existence and Uniqueness of Caputo Fractional Predator-Prey Model of Holling-Type II with Numerical Simulations

We suggested a new mathematical model for three prey-predator species, predator is considered to be divided into two compartments, infected and susceptible predators, as well as the prey and susceptible population based on Holling-type II with harvesting. We considered the model in Caputo fractional order derivative to have significant consequences in real life since the population of prey create memory and learn from their experience of escaping and resisting any threat. The existence, uniqueness, and boundedness of the solution and the equilibrium points for the considered model are studied. Numerical simulations using Euler’s method are discussed to interpret the applicability of the considered model.

ԷՅԼԵՐԻ ՄԵԹՈԴՈՎ ՈՐՈՇ ՏԵՔՍՏԱՅԻՆ ԽՆԴԻՐՆԵՐԻ ԼՈՒԾՈՒՄԸ ՈՐՊԵՍ ՍՈՎՈՐՈՂՆԵՐԻ ՏԵՍՈՂԱԿԱՆ ՄՏԱԾՈՂՈՒԹՅԱՆ ԶԱՐԳԱՑՄԱՆ ԱՌԱՆՁՆԱՀԱՏՈՒԿ ՄԱԹԵՄԱՏԻԿԱԿԱՆ ՄԻՋՈՑ / SOLUTION OF SOME TEXT PROBLEMS BY EULER'S METHOD AS A UNIQUE MATHEMATICAL TOOL FOR DEVELOPING VISUAL THINKING OF STUDENTS

Հոդվածում դիտարկված է Էյլերի տրամագրերի (դիագրամների) միջոցով մաթեմատիկայի դասընթացից բազմություններին առնչվող որոշ խնդիրների լուծման նոր մեթոդական հնար, որը հնարավորություն է տալիս առավել դյուրացնել և ակնառու դարձնել տեքստային խնդիրների լուծումը՝ զարգացնելով սովորողների տեսողական մտածողությունըֈ:/ The article touches upon a new methodological approach to solving some textual mathematical tasks associated with sets using Euler diagrams, which facilitates the solution of mathematical tasks, developing the visual thinking of students.

Comparison of Statistical and Quantum Numerical Methodology for Solving Energy and Momentum Equation

Statistical and Quantum numerical method are implemented in this study to solve various cases in partial differential equations (PDEs). One -dimensional with two lattices arrangements as well as two-dimensional with nine lattices arrangements are employed. The stability and the accuracy have been investigated either using statistical technique or using Euler’s method. The numerical limitations of using LBM method have been obtained and compared with those obtained by Euler’s method finite difference method. The main goal of this study is to investigate the ability of a statistical method in solving various ODEs or PDEs in energy and momentum equations and comparing them with those obtained by a classical numerical technique... The results show the ability of the statistical method for solving ODEs and PDE’s with more stable and accurate results. Consequently, statistical technique is a powerful and promising numerical technique for scientists who are struggling for solving ODEs or PDEs. The next study will be extended to cover upwind scheme technique.

An Analysis on Infected Cases of Corona Virus Using Scientific Computing Methods

The Corona Virus disease is a worldwide health care issue, and international efforts to manage it have been suggested and discussed. Despite the fact that numerous studies have been done using clinical data and documented infected cases, there is always need for more study since a lot of complex factors are involved in future prediction. As a result, mathematical modeling is an essential tool for estimating critical transmission parameters and forecasting disease model dynamics. We analyze and offer various models for the Corona Virusin this study, which can answer significant concerns regarding global health care and provide crucial suggestions. Euler's method, Runge–Kutta method of order two (RK2) are two well-known numerical approaches for solving such problems. The results, which are based on the numerical approaches provide approximate solutions, provide critical answers to this worldwide challenge. The number of infected, recovered, and quarantined persons in the future can be estimated using numerical findings. The findings might also support worldwide efforts to develop more preventions and enhance intermediation programs. The proposed model can be refereed to be a realistic description of this pandemic.

Approximation of Torricelli's law with Euler's method and an instrumented water tank with ultrasonic sensor

In this work, the development of a computer system that has as processing core, an Arduino Nano based board, that collects and processes the signals of a low-cost ultrasonic sensor is presented. The computer system allows monitoring the evolution over time of the height of the water into a container once it begins to empty through a hole in the bottom of it, thus revisiting Torricelli's law with a technological approach using a instrumented container by a computerized electronic data capture and processing data system. The work presents the electrical connection diagrams to interconnect the microcontroller based board and the ultrasonic sensor, as well as the source code used during data acquisition and processing. A comparison of the experimental results is made with results obtained when using the particular analytical solution for the problem, also with the results obtained from implementing the Euler method in obtaining an approximate numerical solution. The presented computer system can be modified and adapted for various academic, educational and research purposes in the various fields of computer engineering, computer systems and mechatronics.

Modeling School Reopening Options in Response to COVID-19

School administrators have the daunting challenge of rolling out school reopening policies and safety standards. While it is important to have children in school to maximize learning, it is critical to ensure that it is done in a manner which prioritizes the safety of staff and students on campus. This research explores models that can be used to examine the spread of COVID-19, and then applies them to evaluate school reopening policies within the United States. A variety of factors are accounted for, including the student population, the rate at which students are infected, the rate at which students are quarantined, and the proportion of students that are susceptible to COVID-19. We primarily utilize Euler’s method and nondimensionalization of the differential equations for each model. Our graphical results are displayed using Excel. We show that multiple variables such as rate of infection and recovery can be written solely as a function of one parameter: R0. We first analyze the SIR model and then introduce the new scenario of quarantining students to derive the SIQR model. Our findings show that reducing and maintaining R0 below 1 is the key to reopening schools and we outline practices to help achieve this outcome.