Benford’s law is widely applied in testing anomalies in various dataset, including accounting fraud detection and population numbers. It is a statistical regularity, which is said that it works better with larger datasets that span large orders of magnitude distributed in a non-uniform way. In this study, we examine the potential metrics in small-sized Quran dataset that are applicable for the Benford’s law. Against our expectations, we find that the Quran dataset conforms to the Benford’s law. We provide evidence that metrics such as total paragraph per chapter and total verse per chapter conform to Benford’s distribution. However, total verse is closer to Benford’s law prediction compared to total paragraph.

The study was quantitative and explanatory in nature. The population comprised all the teaching and non-teaching staff of the institution. A Simple Random Sampling techniques was used for selecting the sample from the population. Primary data was collected by administering questionnaires to the teaching and non-teaching faculty members of the school. Data was analyzed using frequencies, mean, standard deviation, one sample t-test and a multiple linear regression. After the analysis, it was found that the interpersonal justice aspect of performance appraisal fairness had a significant effect on employee performance. Staff were indifferent with performance appraisal systems, but according to management, frequently undertaken performance appraisal helps to recognize individual training and developmental needs. For this reason, performance appraisal is undertaken to examine and evaluate the performance of staff of Kumasi Technical University. One key challenge performance appraisal as identified from the management perspective indicated that the assessment of employees does not translate into an enhanced performance management. As part of employee performance, the staff agreed to possess increase knowledge on job, work with little supervision, improved skills due to new learning methods, and committed to work due to new skills acquired.

Several different approaches are implemented and used to solve higher order non-linear boundary value problems (BVPs). Galerkin weighted residual technique (GWRT) are commonly used to solve linear and non-linear BVPs. In this paper, we have proposed GWRT for the numerical computations of general third order three-point non-linear BVPs. Modified Legendre and Bezier Polynomials, over the interval [0, 1], are chosen separately as a basis functions. The main advantage of this method is its efficiency and simple applicability. Numerical result is presented to illustrate the performance of the proposed method. The results clearly show that the proposed method is suitable for solving third order nonlinear BVPs

In this paper, we prove commutativity of prime near rings by using the notion of β-derivations. Let M be a prime near ring. If there exist p,q ϵ M and two sided nonzero β-derivation f on M, where β:M→M is a homomorphism, satisfying the following conditions:

f([s,t])=s^p [β(s),β(t)]s^q ∀ s,t ϵ M
f([s,t])=-s^p [β(s),β(t)]s^q ∀ s,t ϵ M

In this paper, we prove commutativity of prime near rings by using the notion of β-derivations. Let M be a prime near ring. If there exist  and two sided generalized β-derivation G associated with the non-zero two sided β-derivation  on M, where  is a homomorphism, satisfying the following conditions:

1. G([p_1,q_1 ])=〖p_1〗^(u_1 ) [β(p_1 ),β(q_1)]〖p_1〗^(v_1 ) ∀ p_1,q_1 ϵ M
2. G([p_1,q_1 ])=〖p_1〗^(u_1 ) [β(p_1 ),β(q_1)]〖p_1〗^(v_1 ) ∀ p_1,q_1 ϵ M

Then M is a commutative ring.

In this paper, we prove commutativity of prime near rings by using the notion of β-derivations. Let M be a zero symmetric prime near ring. If there exist p ≥ 0, q ≥ 0 and a nonzero two sided β-derivation d on M, where β : M → M is a homomorphism, such that d satisfy one of the following conditions:

• [β(s),d(t)] = s^p(β(s)oβ(t))s^q ∀ s, t ∈ M
• [β(s),d(t)] = −s^p(β(s)oβ(t))s^q ∀ s, t ∈ M
• [d(s),β(t)] = t^p(β(s)oβ(t))t^q ∀ s, t ∈ M
• [d(s),β(t)] = −t^p(β(s)oβ(t)t^q ∀ s, t ∈ M

In this study, we proposed a malaria-hygiene mathematical model using non-linear differential equation. The model equations are divided into seven compartments consisting of five human compartments (Hygienic Susceptible, Unhygienic Susceptible, Hygienic Infected, Unhygienic Infected, and Recovered) and two vector compartments (Non-Disease Carrier vector and Disease carrier vector). Differential Transformation Method (DTM) is applied to solve the mathematical model. The solutions obtained by DTM are compared with Runge-Kutta order 4th method (RK4). The graphical solutions illustrate similarity between DTM and RK4. It therefore imply that DTM can be consider a reliable alternative solution method.

In this paper we study an SIR epidemic model with vertical transmission and vaccination. By carrying out a global analysis of the model and studying the stability of the disease-free equilibrium and the endemic equilibrium, we show that the vertical transmission and vaccination did not.

We establish the existence of continuous solutions to initial value problem for first order functional integro-differential inclusion. The study holds in the case when the set-valued function has Lipschitz selection, also we discuss the existence of maximal and minimal solutions. The continuous dependence and uniqueness of the solution will be proved. As an application, the initial value problem for the arbitrary-order differential inclusion will be studied.

The present study is related to the numerical solution of the human immunodeficiency virus (HIV) infection model with full logistic proliferation and variable source term (depending on the viral load) used for the supply of new CD4+ T-cells from thymus instead of using simple logistic proliferation and constant source term. In simple logistic proliferation term only the healthy or infected CD4+ T-cells proliferation are considered while in full logistic proliferation term both the proliferation of healthy and infected are considered. Consequently, the variable source term is used for the supply of new healthy CD4+ T-cells from thymus, which is a decreasing function depending on the concentration of viral load. Continuous Galerkin-Petrov method, in particular cGP(2)-method has been invoked for finding the approximate solution of the model. For cGP(2)-method, we have two unknowns on each time interval which have to be calculated by solving 2 × 2 block system. This method is an accurate of order three in the whole time interval and shows the convergence of order four in the discrete time points. We examined the impact of various clinical parameters and study the existence of the infected state. Additionally, the Runge Kutta method of order four briefly RK4-method has also been used to verify and strengthen the results obtained by cGP(2)-method. Obtained results are displayed both graphically and in tabular form. The results obtained in this study confirm the idea that the cGP(2)-method is a powerful technique which can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering.