JOURNAL OF ADVANCES IN MATHEMATICS

The Dynamics in the Soft Numbers Coordinate System

Moshe Klein, Oded Maimon — Sat, 04 Jan 2020 10:49:05 +0000

"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’.

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.

An Application of Computational Fluid Dynamics to Optimize Municipal Sewage Networks; A Case of Tororo Municipality, Eastern Uganda.

Fri, 10 Jan 2020 06:47:23 +0000

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- 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).

Regional Boundary Asymptotic Gradient Full-Order Observer in Distributed Parabolic Systems

Raheam Al-Saphory, Zinah A. Khalid — Tue, 14 Jan 2020 10:22:26 +0000

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_S) in parabolic systems problem. 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 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.