JOURNAL OF ADVANCES IN MATHEMATICS https://rajpub.com/index.php/jam en-US <p>The author warrants that the article is original, written by stated author(s), has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author(s).</p> editor@rajpub.com (Editorial Office) jam@rajpub.comJ (Bavneet Kaur) Fri, 10 Jan 2020 00:00:00 +0000 OJS 3.1.2.4 http://blogs.law.harvard.edu/tech/rss 60 The Dynamics in the Soft Numbers Coordinate System https://rajpub.com/index.php/jam/article/view/8531 <p>"Soft Logic" extends the number 0 from a single point to a continuous line, which we term "The zero axis". One of the modern science challenges is finding a bridge between the real world outside the observer and the observer's inner world. In “Soft Logic” we suggested a constructive model of bridging the two worlds by defining, on the base of the zero axis, a new kind of numbers, which we called ‘Soft Numbers’.</p> <p>Inspired by the investigation and visualization of fractals by Mandelbrot, within the investigation of the dynamics of some special function of a complex variable on the complex plane, we investigate in this paper the dynamics of soft functions on the plane strip with a special coordinate system. The recursive process that creates this soft dynamics allows us to discover new dynamics sets in a plane.</p> Moshe Klein, Oded Maimon Copyright (c) 2020 Moshe Klein, Oded Maimon http://creativecommons.org/licenses/by/4.0 https://rajpub.com/index.php/jam/article/view/8531 Sat, 04 Jan 2020 10:49:05 +0000 An Application of Computational Fluid Dynamics to Optimize Municipal Sewage Networks; A Case of Tororo Municipality, Eastern Uganda. https://rajpub.com/index.php/jam/article/view/8345 <p>Two-phase pipe flow is a common occurrence in many industrial applications such as sewage, water, oil, and gas transportation. Accurate prediction of liquid velocity, holdup and pressure drop is of vast importance to ensure effective design and operation of fluid transport systems. This paper aimed at the simulation of a two-phase flow of air and sewage (water) using an open source software OpenFOAM. Numerical Simulations have been performed using varying dimensions of pipes as well as their inclinations. Specifically, a Standard k-&nbsp;turbulence model and the Volume of Fluid (VOF) free water surface model is used to solve the turbulent mixture flow of air and sewage (water). A two dimensional, 0.5m diameter pipe of 20m length is used for the CFD approach based on the Navier-Stokes equations. Results showed that the flow pattern behaviour is influenced by the pipe diameters as well as their inclination. It is concluded that the most effective way to optimize a sewer network system for Tororo Municipality conditions and other similar situations, is by adjusting sewer diameters and slope gradients and expanding the number of sewer network connections of household and industries from 535 (i.e., 31.2% of total) to at least 1,200 (70% of total).</p> Twaibu Semwogerere, R. Awichi, J. D. Lwanyaga, Esemu Joseph Noah, Verdiana G. Masanja, H. Nampala Copyright (c) 2020 Twaibu Semwogerere, R. Awichi, J. D. Lwanyaga, Esemu Joseph Noah, Verdiana G. Masanja, H. Nampala http://creativecommons.org/licenses/by/4.0 https://rajpub.com/index.php/jam/article/view/8345 Fri, 10 Jan 2020 06:47:23 +0000 Regional Boundary Asymptotic Gradient Full-Order Observer in Distributed Parabolic Systems https://rajpub.com/index.php/jam/article/view/8543 <p>The purpose of this paper is to explore the concept of the regional boundary asymptotic gradient full order observer (RBAGFO-observer) in connection with the characterizations of sensors structures. Then, we present various results related to different types of measurements, domains and boundary conditions for distributed parameter systems (DPS<sub>S</sub>) in parabolic systems problem.&nbsp; The considered approach of this work is derived from Luenberger observer theory which is enable to estimate asymptotically the state gradient of the original system on a sub-region of the domain boundary &nbsp;in order that the RBAGFO-observability notion to be achieved. We also show that there exists a dynamical system for the considered system is not BAGFO-observer in the usual sense, but it may be regional RBAGFO-observer.</p> Raheam Al-Saphory, Zinah A. Khalid Copyright (c) 2020 Raheam Al-Saphory, Zinah A. Khalid http://creativecommons.org/licenses/by/4.0 https://rajpub.com/index.php/jam/article/view/8543 Tue, 14 Jan 2020 10:22:26 +0000