Applied Mathematics Research Papers/Topics

Convergence theorems for a fixed point of η-demimetric mappings in banach spaces

Abstract: The purpose of this paper is to propose and investigate an algorithm for solving a fixed point of η-demimetric mappings. We establish the strong convergence of the proposed algorithm under some mild conditions in Banach spaces. We apply these results to obtain new strong convergence theorems which are connected with the η-demimetric fixed point problems in Hilber/Banach spaces.

On dynamics of heart rate variability

Abstract: Heart rate variability refers to the variations in time interval between successive heart beats. An understanding of its dynamics can have clinical importance since it can help distinguish persons with healthy heart beats from those without. Our aim in this thesis was to characterise the dynamics of the human heart rate variabilty from three different groups: normal, heart failure and atrial fibrillation subjects. In particular, we wanted to establish if the dynamics of heart rat...

Modelling substance abuse in Botswana in presence of multiple amelioration stages and outpatient rehabilitation, optimal control and fractional-order dynamics

Abstract: Substance abuse in Botswana is a growing problem with a variety of drugs being abused including cocaine, heroin, methamphetamine, marijuana and alcohol among others. At the front line of attempting to address the drug abuse problem is the Botswana Substance Abuse and Support Network (BoSASNet) which operates outpatient rehabilitation and support ser vices that constitute its clinical programme. Due to the criminalisation and stigma associated with drug use and dealing in drugs, the...

Generation of Kifilideen’s Generalized Matrix Progression Sequence of Infinite Term

Considering a cluster of different hierarchical order with various barrier or cadre levels and steps within levels, there is no availability of a structural framework to help exclusively analyze, formulate, identify, differentiate, and design standardized provisional values to cluster members at various barrier levels and steps within levels. This study designs stepwise analysis, generation, and applications of Kifilideen’s Matrix Structural Framework for an infinite term of increasing...

Stepwise Analysis and Generation of Kifilideen Matrix Structural Framework for Infinite terms of Kifilideen Generalized Matrix Progression Sequence

Considering a cluster of different hierarchical order with various barrier/cadre levels and steps within levels, there is non availability of structural framework to help to exclusively analysis, formulate, identify, differentiate and design standardized provisional values to cluster members at various barriers levels and steps with levels. This study invents stepwise analysis and generation of Kifilideen matrix structural framework for infinite terms of increasing elements of successive co...

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 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.

Proofs for the Four Fundamental Equations of the Backpropagation and Algorithms in Feedforward Neural Networks

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.

About Crawling Scheduling Problems

Abstract This paper investigates the task of scheduling jobs across several servers in a software system similar to the Enterprise Desktop Grid. One of the features of this system is that it has a specific area of action – collects outbound hyperlinks for a given set of websites. The target set is scanned continuously (and regularly) at certain time intervals. Data obtained from previous scans are used to construct the next scanning task for the purpose of enhancing efficiency (shortening ...