Unified Functional Method for Solving General Polynomial Equations of Degree Less Than Five

A unified method for solving that incorporate a computational formula that relate the coefficients of the depressed equation and the coefficients of the standard polynomial equation is proposed in this study. This is to ensure that this method is valid for all It shall apply the undetermined parameter method of auxiliary function to obtain solutions to these polynomial equations of degree less than five in one variable. In particular, the result of our work is a unification and improvement on the work of several authors in the sense that only applicable for the case of polynomial equation of degree one. Finally, our results improve and generalize the result by applying standard formula methods for solving higher degree polynomials. It is recommended that the effort should be made toward providing other variant methods that are simpler and friendly.

THE STABILITY OF THE CRITICAL POINTS OF THE GENERALIZED GAUSE TYPE PREDATOR-PREY FISHERY MODELS WITH PROPORTIONAL HARVESTING AND TIME DELAY

In the marine ecosystem, the time delay or lag may occur in the predator response function, which measures the rate of capture of prey by a predator. This is because, when the growth of the prey population is null at the time delay period, the predator’s growth is affected by its population and prey population densities only after the time delay period. Therefore, the generalized Gause type predator-prey fishery models with a selective proportional harvesting rate of fish and time lag in the Holling type II predator response function are proposed to simulate and solve the population dynamical problem. From the mathematical analysis of the models, a certain dimension of time delays in the predator response or reaction function can change originally stable non-trivial critical points to unstable ones. This is due to the existence of the Hopf bifurcation that measures the critical values of the time lag, which will affect the stabilities of the non-trivial critical points of the models. Therefore, the effects of increasing and decreasing the values of selective proportional harvesting rate terms of prey and predator on the stabilities of the non-trivial critical points of the fishery models were analysed. Results have shown that, by increasing the values of the total proportion of prey and predator harvesting denoted by qx Ex and qy Ey respectively, within the range 0.3102 ≤ qx Ex ≤ 0.9984 and 0.5049 ≤ qy Ey ≤ 0.5363, the originally unstable non-trivial critical points of the fishery models can be stable.

PROJECT-BASED INCIDENT RATE BASED ON WEIGHTED AVERAGE METHOD

The incident rate has been widely used to indicate safety performance. The incident rate of a company can be compared with the national or international incident rate within similar industry or among different type of industries. The comparison is particularly very useful as a safety benchmark to gauge performance with other companies in the same business area. However, many existing methods produce the annual incident rate, which has been formulated on an annual basis. This will lead to incompatibility of the method used in calculating the incident rate for a project that runs for a specific period. This is because the annual incident rate does not consider the duration of the project; it becomes less meaningful in indicating the safety performance of project-based activities such as those in construction industries. The proposed method which is Project-Based Incident Rate (PIR) is found to be able to reflect the actual situation of project-based companies better than the existing annual incident rate method, and it is also can be expressed both on a monthly and yearly basis.

STABILITY ANALYSIS OF A PROPOSED SCHEME OF ORDER FIVE FOR FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS

This paper presents the stability analysis of a proposed scheme of order five (FCM) for first order Ordinary Differential Equations (ODEs). The proposed FCM is derived by means of an interpolating function of polynomial and exponential forms. The properties of FCM were discussed extensively. The linear stability of FCM in the context of the Third Order One-Step Method (TCM) and Second Order One-Step Method (SCM) for the solution of initial value problems of first order differential equations is presented. The stability region of FCM, TCM and SCM is investigated using the Dahlquist’s test equation. The numerical results obtained via FCM are compared with TCM and SCM. Moreover, by varying the step length, the accuracy and convergence of the methods in terms of the final absolute relative error are measured. The results show that FCM converges faster and more stable than its counterparts.

ON A NEW GENERALIZED BETA FUNCTION DEFINED BY THE GENERALIZED WRIGHT FUNCTION AND ITS APPLICATIONS

Various extensions of classical gamma, beta, Gauss hypergeometric and confluent hypergeometric functions have been proposed recently by many researchers. In this paper, we further generalized extended beta function with some of its properties such as symmetric properties, summation formulas, integral representations, connection with some other special functions such as classical beta, error, Mittag – Leffler, incomplete gamma, hypergeometric, classical Wright, Fox – Wright, Fox H and Meijer G – functions. Furthermore, the generalized beta function is used to generalize classical and other extended Gauss hypergeometric, confluent hypergeometric, Appell’s and Lauricella’s functions.

Machine Learning Techniques for Heart Failure Prediction

This paper discusses the performance of four popular machine learning techniques for predicting heart failure using a publicly available dataset from kaggle.com, which are Random Forest (RF), Support Vector Machine (SVM), Naive Bayes (NB), and Logistic Regression (LR). They were selected due to their good performance in medical-related applications. Heart failure is a common public health problem, and there is a need to improve the management of heart failure cases to increase the survival rate. The vast amount of medical data related to heart failure and the availability of powerful computing devices allow researchers to conduct more experiments. The performance of the machine learning techniques was measured by accuracy, precision, recall, f1-score, sensitivity, and specificity in predicting heart failure with 13 symptoms or features. Experimental analysis showed that RF produces the highest performance score, which is 0.88 compared to SVM, NB, and LR. Further experiments with RF were also conducted to determine the important features in predicting heart failure, and the results indicated that all 13 symptoms or features are important.

ELECTRONIC PARTICIPATION INITIATIVES IN AFRICA: EXTRACTION FROM LITERATURE REVIEW PERSPECTIVES

The main objective of this research is to examine the use of Information & Communication Technologies (ICT) and derive the success factors of eParticipation initiatives according to the electronic government (eGovernment) content evaluation. For this purpose, an African study took place using a two-step methodological technique: ‘review of the United Nations’ eGovernment survey report; and a wide review from the existing literature. The results suggest that the tools and technologies presently applied are mainly general purpose and not exactly designed for eParticipation. In addition, the results indicated that success factors can be categorized into seven groups of factors: government commitment; usability; combination of both online and offline networks; comprehensive communication and encouraging plan; security and privacy, organizational issues; and topics complexity. A comparison with reviewed factors of eParticipation initiatives success suggests there are similarities and significant differences on ICT usage among countries. This study anticipates that its results could be of interest to practitioners as it highlights some knowledge in a practical way. Furthermore, this research could be of interest to researchers as it contributes in validating eParticipation evaluation models.

A MIXED INTEGER GOAL PROGRAMMING (MIGP) MODEL FOR DONATED BLOOD TRANSPORTATION PROBLEM – A PRELIMINARY STUDY

Blood Supply Chain (BSC) concerns with flow of blood products from blood collection by donors to transfusion of blood components to patients. BSC comprises of collection, testing, processing, storage, distribution and transfusion activities, which are normally responsibility of Blood Centre and hospitals. In Malaysia, National Blood Centre (PDN) is responsible to organize blood donation, collection and processing. Current procedure practised by PDN is to have vehicles sending staffs and equipment while one vehicle is assigned to collect donated blood from donation sites and transport the blood to PDN within six hours. As consequence, vehicles shortages are encountered and resources optimization unachieved especially when many blood donation sites involved per day. This paper presents the results of a preliminary study which aims at proposing blood collection optimal routes for blood collecting vehicles that adhere to all pre-determined time windows for blood collection at blood donation sites. A Mixed Integer Goal Programming (MIGP) model based on Vehicle Routing Problem with Time Windows (VRPTW) has been formulated. The MIGP model pursues four goals, namely, to minimize total distance travelled, to minimize total travel time, to minimize total waiting time of vehicles and to minimize number of vehicles (routes). The model was solved using preemptive goal programming approach and existing heuristics for the VRPTW. Based on the results, it can be concluded that the donated blood can be collected and transported using reduced number of vehicles as proposed by the MIGP model’s optimal compared to the total number of vehicles used by current practice, Thus, the proposed VRPTW based MIGP model has promising significant impact for donated blood transportation in terms of resources optimization and costs savings. The model and approach could be easily extended to solve larger problem involving large number of donation sites with variants of time windows for the sites.

IMPLEMENTATION OF BLOM’S KEY PREDISTRIBUTION SCHEME BY USING ELLIPTIC CURVE CRYPTOGRAPHY

Cryptography, along with its various methods is used to serve the security communication purpose. Cryptography is said to be secure if the encryption key is hard to break by the attacker. Initially, Blom’s Key pre-distribution uses an integer finite field which makes this scheme easy to be intervened by attackers and criminal activists. Hence, this study suggests implementing the Elliptic Curve Cryptography to better enhance the security of the original Blom’s. In this proposed scheme, points generated from the elliptic curve will be appointed as public identifiers to be used in the original scheme. The private key and session key of each user are generated using the addition law mathematical operation with public identifiers assigned. Two users who intend to communicate with each other will obtain a common session key. Overall, the modification of Blom’s Key pre-distribution scheme will be presented in this study.

EFFECTIVE ROUTING PROTOCOL FOR WIRELESS SENSOR NETWORKS USING CRT-LEACH ALGORITHM

Wireless Sensor Networks (WSNs) consist of huge number of sensor nodes dispersed in a domain of enthusiasm with at least one sink for watching the environment and physical situation. These sensor hubs are circulated in threatening conditions and are unprotected to deficiencies, for example, power dissemination, equipment glitches, communication link errors and malicious attacks, among others. It has been established that essentialness, speed and unwavering quality are the chief test in the usefulness of WSNs as they are controlled with compelled imperativeness and restricted equipment assets. Accordingly, it is necessary to structure vitality proficient steering conventions for WSNs applications. Chinese Remainder Theorem (CRT)- based packet splitting integrated with Low-Energy Adaptive Clustering Hierarchy (LEACH) algorithm routing protocol was proposed so as to decrease vitality utilization during correspondence and improve message dependability in WSNs. The consequences of exploratory reproductions show that the proposed structure delivered powerful directing convention for WSNs when contrasted with existing routing protocols to the extent essentialness usage, speed, equipment necessities and transformation delay continuously WSNs.