JOURNAL OF ADVANCES IN MATHEMATICS

Recent Modification of Decomposition Method for Solving Nonlinear Partial Differential Equations

Zainab Hadi Kareem — 2020-05-22

In this paper, efficient modification of Adomain decomposition method is proposed to solve nonlinear partial differential equations. Yields solution in rapid convergent series from easily computable terms to get exact solution, and yields in few iterations we get exact solution. Moreover, this modification does not require any linearization, discretization, or perturbations and therefore reduces the computations. Two illustration examples are introduced and illustrate the procedure of modification is simple yet highly accurate and rapidly converge to exact solution compares with the ADM or other modifications. The methodology presented here is useful for strongly nonlinear problems.

The Dynamics in the Soft Numbers Coordinate System

Moshe Klein — 2020-01-04

"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.

Twaibu Semwogerere — 2020-01-10

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 — 2020-01-14

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.

Implementation of the Logistic Regression Model and its Applications

Elmira Elmira Kushta — 2020-01-18

The purpose of an analysis using this method is the same as that of any technique in constructing models in statistics, namely to find the best and most reasonable model to describe the relationship between a result variable and a set of variables independent. We are interested in how the costs affect them and if a customer has a travel card.

Credit card customers are shown to be 6 times more likely to use it regardless of the cost they make.
It is also shown that a customer is more likely to use a travel card when costs increase Through logistic regression, which gives the probability that a result is an exponential function of the independent variables, we will see how through our data we will come to very important conclusions.

Approximating Fixed Points of The General Asymptotic Set Valued Mappings

Salwa Salman Abed — 2020-02-03

The purpose of this paper is to introduce a new generalization of asymptotically non-expansive set-valued mapping and to discuss its demi-closeness principle. Then, under certain conditions, we prove that the sequence defined by y_n+1 = t_n z+ (1-t_n )u_n , u_n in Gⁿ( y_n ) converges strongly to some fixed point in reflexive Banach spaces. As an application, existence theorem for an iterative differential equation as well as convergence theorems for a fixed point iterative method designed to approximate this solution is proved

New Conditions of The Existence of Fixed Point in Δ- Ordered Δ Banach Algebra

Boushra Hussein — 2020-02-07

The main idea is to construct a new algebra and find new necessary and sufficient conditions equivalent to the existence of a fixed point. In this work, an algebra is constructed, called Δ - ordered Banach algebra, we define convergent in this new space, Topological structure on Δ ordered Banach Algebra and prove this as Hausdorff space. Also, we define new conditions as Δ- lipshtiz,, Δ- contraction contraction , in this algebra construct, we prove this condition is the existence and uniqueness results of the fixed point. In this paper, we prove a common fixed point if the self-functions satisfy the new condition which is called Ф-contraction.

New Schrödinger Wave Mathematics Changes Experiments From Saying There Is, To Denying There Is Quantum Weirdness

Jeffrey Boyd — 2020-02-21

With a clever new interpretation of the Schrödinger equation, those quantum experiments that allegedly prove that the quantum world is weird, no longer do so. When we approach the math from an unexpected angle, experiments that appeared to prove that time can go backwards in the quantum world, no longer say that. Experiments that appeared to demonstrate that a particle can be in two places at the same time, no longer say that. This requires that we take a counter-intuitive approach to the math, rather than a counter-intuitive approach to the quantum world. QM makes sensible assumptions and discovers that the quantum world is weird. Our math from the Theory of Elementary Waves (TEW) makes weird assumptions and discovers that the quantum world is sensible. We pay the weirdness tax up front. QM does not pay the weirdness tax and is penalized with a permanent misperception of the quantum world. This article is paired with a lively YouTube video that explains the same thing in 18 minutes: “New Schrödinger wave mathematics changes experiments from saying there is, to denying there is quantum weirdness.” That video can be found at the website ElementaryWave.com.

New Approach for Solving Partial Differential Equations Based on Collocation Method

Alaa Almosawi — 2020-05-01

In this paper, a new approach for solving partial differential equations was introduced. The collocation method based on LA-transform and proposed the solution as a power series that conforming Taylor series. The method attacks the problem in a direct way and in a straightforward fashion without using linearization, or any other restrictive assumption that may change the behavior of the equation under discussion.

Five illustrated examples are introduced to clarifying the accuracy, ease implementation and efficiency of suggested method. The LA-transform was used to eliminate the linear differential operator in the differential equation.

If the propagator of QED were reversed, the mathematics of Nature would be much simpler

Jeffrey Boyd — 2020-05-22

In Quantum ElectroDynamics (QED) the propagator is a function that describes the probability amplitude of a particle going from point A to B. It summarizes the many paths of Feynman’s path integral approach. We propose a reverse propagator (R-propagator) that, prior to the particle’s emission, summarizes every possible path from B to A. Wave function collapse occurs at point A when the particle randomly chooses one and only one of many incident paths to follow backwards with a probability of one, so it inevitably strikes detector B. The propagator and R-propagator both calculate the same probability amplitude. The R-propagator has an advantage over the propagator because it solves a contradiction inside QED, namely QED says a particle must take EVERY path from A to B. With our model the particle only takes one path. The R-propagator had already taken every path into account. We propose that this tiny, infinitesimal change from propagator to R-propagator would vastly simplify the mathematics of Nature. Many experiments that currently describe the quantum world as weird, change their meaning and no longer say that. The quantum world looks and acts like the classical world of everyday experience.