The sequence of the power combination of expansion of the Kifilideen trinomial theorem of positive power of N is arranged in groups and patterns. Having a clearer view or picture of how the formulas of the components of the Kifilideen trinomial expansion were derived can lead to the discovery of formulating formulas for the series and sequences which follows the same pattern of progression as that of the trinomial expansion where series and sequence are not generated ...
This paper presents the four and five figures of Lekan (Power of base 5) and AntiLekan (Antipower of base 5) tables as a tool for mathematical computation.
This paper will focus on proving the four fundamental equations of the backpropagation. Then I will show how to use this algorithm combined with the stochastic gradient descent technique to implement the network for recognizing the handwritten digits. Parts of the proof are provided by the author Michael Nielsen in his online book Neural Networks and Deep Learning. Meanwhile, this paper will provide more details of his proofs and some basic definitions of gradient.
Kifilideen trinomial theorem of negative power of – n is theorem which is used to generate the series and terms of a trinomial expression of negative power of – n in an orderly and periodicity manner that is based on standardized and matrix methods. Negative power of Newton binomial theorem had been used to produce series of partial fractions of a compound fraction. The establishment of the negative power of - n of trinomial theorem would extend the number of compound fraction in whic...
Overtime the arrangement of the terms of the trinomial expansion of power of n has been an issue in the area of orderliness and periodicity which as make it difficult to assign each element of the expansion in a standardize term. The study developed Kifilideen trinomial theorem using matrix approach. The Kifilideen equations to determine the power combination of any term of kif trinomial expansion and position of any term in the series of the expansion in a group or column of a kif matrix...
The different methods used in the multiplication of numbers are long method (column method) of multiplication, grid methods and addition methods of multiplication. The utilization of the methods mentioned to solve power (index) of base number (number that multiply itself in a number of times) are horrendous, outrageous, tedious, time consuming and too long to be carried out. This study develops computation of the power of base of number using Kifilideen (matrix, combination and distributi...
Mathematics should be dynamic not static. The use of logarithm table which is based on power of base ten to solve mathematical problem has been in existence for nearly 400 years ago without any alternative which makes mathematics look static, austere and monotonous. Some real life mathematical problem encounter on daily basis in field of Engineering, Physics, Mathematics, Finance, Cosmology, Accounting, Carpentering and Medicine involve problem on other base power of number and in a...
TABLE OF CONTENTCOVER PAGE APPROVAL PAGE DEDICATION ACKNOWLEDGEMENTTABLE OF CONTENT1.1 INTRODUCTION1.2 BACKGROUND AND ITS OPERATION 1.3 SIGNIFICANCE1.4 SCOPE OF STUDY1.5 AIMS AND OBJECTIVE ...
In this work a deterministic and stochastic model is developed to investigate the dynamics of Ebola epidemic. The model includes susceptible, exposed, infected, quarantined and removed or recovered individuals. The model used in this work is based on a deterministic model. The Chowel et. al (2015) work on early detection of Ebola is modified by introducing an assumption that the quarantined class is totally successful and cannot infect the susceptible class. The resulting model is trans...
This work investigated the dynamics of coronavirus amongst the susceptible individuals. It is established herein, with a proposition that there exists a control strategy that is bounded above by 0.01 for the contact rate of susceptible individuals. It is observed that at a=d=1.5, the virus population and the human population coincides, however, at c=b=0.1, almost all the human population is infected by the virus. It is also observed that at endemic state, the corona virus population ex...
ABSTRACTIn his book (Procesi,C., 2007), Claudio Procesi suggested anew algorithm for computing covariants of binary forms underthe action of SL(2;C), based on an iterative computationsof covariants of the simpler group U+. In Procesi book thecomputation was carried out only for binary forms of degree3 and 4, but the _rst signi_cant test for the algorithm wouldbe the computation for degree 5. In 2010 summer school inAlgebra organized by ICTP in Kenya, Procesi suggested theimplementation ...
Studies have been done on the aspect ratio effect on natural convection turbulence using standard k-ε model but further studies showed that k-ω SST model performed better than both k-ε and k-ω model in the whole enclosure. Thus, there was need to do a numerical study on the natural convection fluid flow in a rectangular enclosure full of air using SST k-ω model. The left vertical wall of the enclosure was maintained at a steady high temperature Th of 323K while the ri...
AbstractAn investigation of heat and mass transfer in MHD ow about a horizontal plate past nite plate, in a porous medium was carried out. The e ect of magnetic eld on mass and heat transfer was investigated. The study was governed by Navier- stokes equations, energy equation, Ohm's law and concentration equation. These equations were formulated inform of partial di erential equations to represent the general phenomena of mass and heat. Then, the general ...
ABSTRACT In this study, the impact of a transverse magnetic field on blood flowing through an axisymmetric curved shaped stenotic artery has been investigated. This research is of importance in the field of medicine. There is an application in magnetic hyperthermia which is used to shrink tumors in the treatment of cancer. In addition to this, the externally applied magnetic field is also used to reduce/diminish blood flow in the region of stenosis and hence it is used in the treatment o...
ABSTRACT Heat transfer plays a great role in engineering processes, blowing of fluids is used in designing thrusters and prevention of corrosion. Suction is used in film cooling and coating of wires in chemical engineering. A lot of research has based on thermal reduction in processing streams and forgetting the machine efficiency. The study theoretically investigates the effect of hall current on a steady magneto convection and radiative heat transfer over a porous plate. This work is ...