Journal of Mathematical Sciences & Computational Mathematics (JMSCM)
(ISSN Number (Online) - 2644-3368)
(ISSN Number (Print) - 2688-8300)

Volume2 Issue2:



THE DEVELOPMENT OF AN ENHANCED WIRELESS SENSOR NETWORK LIFESPAN USING HYBRIDIZED CLUSTER AND K-MEANS ALGORITHM

J.O. Amoo1, O. Osunade2, O.E. Makinde3, D.N. Ajobiewe4 & E.O. Adebayo5

1,4,5Department of Computer Science, School of Secondary Education (Science Programmes), Federal College of Education (Special), Oyo. Email: [email protected]
2Department of Computer Science, University of Ibadan, Nigeria. Email: [email protected]
3Department of Computer Science, Ajayi Crowther University, Oyo. Email: [email protected]
Page Number: 194-209

Wireless sensor networks (WSN) are useful in situations where a low-cost network needs to be set up quickly and no fixed network infrastructure exists. Typically, its applications are for monitoring system such as (environmental, air and water quality etc), natural disaster prevention, forest fire prevention, military exercises and emergency rescue operations. Wireless sensor network consists of large number of a group of small sensor nodes which utilizes battery and are with limited energy and life span that makes these sensors node inefficient, non-scalable, in- mobile and non-load balance. The nodes close to each other have more overlap; they sense the same data from environment and cause a waste of energy by generating repetitive data. In this study, a hybridized clustering and k-means algorithm are introduced, in each round, a certain number of nodes are specified; the nodes which have at least one neighboring node at a distance less than the threshold. Then, the wireless sensor network nodes were partitioned into different clusters and one of the nodes elected from each cluster to act as a cluster head with the use of a hybridized cluster and k mean algorithm. Among them, the nodes with less energy and greater overlap with their neighbors have been chosen to go to sleep mode. Also, the energy imbalance among sensor nodes is reduced by integrating the distance of the nodes from the base station into clustering policies. A simulator was developed with python programming language to evaluate the performance of this system. On the basis of the simulation results, the proposed scheme elongates the network life span, then, balances the load among sensor nodes further.
Keywords: Sleep mode, network infrastructure, life span, overlap, cluster head, elongate.


DOI: doi.org/10.15864/jmscm.2201

E-SUPER EDGE MAGIC LABELING ON SOME CLASSES OF GRAPHS

M.Sindhu1 & S.Chandra Kumar2

1 Research Scholar, Reg No-18213162092011, Department of Mathematics, Scott Christian College(Autonomous), Nagercoil-629003. Email:[email protected]
2Associate Professor, Department of Mathematics, Scott Christian College(Autonomous), Nagercoil-629003, Tamilnadu, India. Email: [email protected]
Page Number:210-216

A (p,q) graph G with p vertices and q edges, a bijection 𝑓: 𝑉(𝐺) ∪ 𝐸(𝐺) → {1,2, … . 𝑝 + 𝑞} is called edge magic labeling of G if 𝑓(𝑢) + 𝑓(𝑢𝑣) + 𝑓(𝑣) = 𝑘, a constant for any edge 𝑢𝑣 of G.G is known as E-super edge magic if 𝑓(𝐸(𝐺)) = {1,2, … 𝑞}.Herein, we explore some classes of E-super edge-magic graphs.
Keywords: Edge magic labeling,E-super edge magic labeling, E-super edge magic graphs.


DOI: doi.org/10.15864/jmscm.2202

OPTIMAL CONTROL OF LASSA FEVER QUARANTINE MODEL

M.O. Ibrahim1, A. A. Ahiaba2 & S.T. Akinyemi 3

1Department of Mathematics, University of Ilorin, PMB 1515, Nigeria
2Department of Mathematics, Bingham University, PMB 005, Karu, Nasarawa, Nigeria. Email: [email protected]
* Corresponding author, Department of Mathematics, University of Ilorin, PMB 1515, Nigeria.
Page Number: 217-226

In this paper, Optimal control is applied to a Quarantine Lassa fever model developed. The controls 𝑤1, 𝑤2 and 𝑤3 which represent Public education on lassa fever mode of transfer, use of Standard precautions in treatment and Environmental sanitation respectively. The existence and necessary condition for Optimal control of the disease were verified. The effects of these controls on the model are dipitched in graphical representation showing with or without controls implementation.
Keywords: Hamiltonian; Pontryagin’s maximum principle; Optimality conditions; Quarantine; adjoint.


DOI: doi.org/10.15864/jmscm.2203

BAYESIAN ESTIMATION OF SHAPE PARAMETER OF POWER LOMAX DISTRIBUTION UNDER DIFFERENT LOSS FUNCTION

Arun Kumar Rao & Himanshu Pandey

Department of Mathematics & Statistics, DDU Gorakhpur University, Gorakhpur, INDIA. E-mail: [email protected]
Page Number: 227-235

In this paper, the power Lomax distribution is considered for Bayesian analysis. The expressions for Bayes estimators of the parameter have been derived under squared error, precautionary, entropy, K-loss, and Al-Bayyati’s loss functions by using quasi and gamma priors.
Keywords: Bayesian method, power Lomax distribution, quasi and gamma priors, squared error, precautionary, entropy, K-loss, and Al-Bayyati’s loss functions.


DOI: doi.org/10.15864/jmscm.2204

A MATHEMATICAL MODEL TO RESOLVING MIXED DNA SAMPLES BY USING LINEAR MIXTURE ANALYSIS

Pranjal Chowdhury1, Sourav Paul2, Partho Protim Sarkar3, Miso Dhar Chando4, Prinkle Chowdhury5

1,2,3Department of CSE, Institute of Engineering & Management, Salt Lake Electronics Complex, Kolkata700091. Email: [email protected]
4Department of CSE,University Of Science & Technology Chattogram, Zakir Hossain Road, Foy’s Lake, Khulshi, Chattogram 4202, Bangladesh. Email: [email protected]
5Department of ETCE, Shree Ramkrishna Institute of Science and Technology, Dakshin Gobindapur, Rajpur Sonarpur, Kolkata, West Bengal 700145. Email: [email protected]
Page Number: 236-251

The advent of PCR-based STR writing systems, mixed samples is separated into their individual polymer profiles. Quantitative peak data will facilitate during this analysis. Despite such advances, rhetorical mixture analysis still remains a arduous art, with the high value and energy usually precluding timely reportage. We introduce here a replacement machine-driven approach to partitioning rhetorical polymer mixtures. Our linear mixture analysis (LMA) may be a easy mathematical approach that may integrate all the quantitative PCR knowledge into one fast computation. LMA has application to numerous mixture issues. As incontestable here on laboratory STR knowledge, LMA will assess the standard and utility of its solutions. Such fast and sturdy ways for computer-based analysis of polymer mixtures could facilitate in reducing crime.
Keywords: forensic science, DNA typing, STR, DNA mixture, DNA database, criminal casework, mathematics, linear algebra, least squares, heuristic algorithm.


DOI: doi.org/10.15864/jmscm.2205

EFFECTS OF SENSITISATION AND EARLY TREATMENT ON FUTURE OUTBREAK OF LASSA FEVER IN NIGERIA

A.A. Ahiaba1, M.O. Ibrahim2, M. Ahiaba3

1Department of Mathematics, Bingham University, PMB 005, Karu, Nasarawa, Nigeria.
2Department of Mathematics, University of Ilorin, PMB 1515, Nigeria.
3School of Applied Science, Department of Mathematics and Statistics, Kogi State Polytechnic Lokoja, PMB 1101 Nigeria. Corresponding author Email: [email protected]
Page Number: 252-265

We exploit the dynamics of Lassa fever model with sex structure of the human population with the rat population. The objectives of the research were to: (i) solve for the equilibrium point of the disease free of the model; (ii) obtain basic reproduction number R0 , for the model; (iii) investigate local and global stability of the model; and (iv) analyze the sensitivity of parameters of the model. It was found that the disease free equilibrium point was locally asymptotically stable whenever the basic reproduction number ( Ro ) is less than one and unstable otherwise. The global stability of the model at disease free equilibrium was found. The analysis of the contribution of each parameter was performed using sensitivity analysis. All positive value parameters are in direct proportionality with the basic reproduction number Ro and all negative value parameters are inversely proportional to the basic reproduction number. Thus, increase in the values of all parameters with positive sensitivity value would increase Ro . Conversely, increase in the value of all parameters with negative sensitivity value would decrease Ro .
Keywords: Epidemiology, stability analysis, differential equation, theorem.


DOI: doi.org/10.15864/jmscm.2206

MATHEMATICAL MODELLING OF THE STABILITY OF HIGHLY PATHOGENIC AVIAN INFLUENZA WITH SATURATED CONTACT RATE

Akpan Collins Emmanuel & Ibrahim Mohammed Olanrewaju1,1

1Department of Mathematics, University of Ilorin, Ilorin, Nigeria. Email: [email protected], [email protected]
Page Number: 266-286

In this paper, we present a Highly Pathogenic Avian Influenza model with Saturated Contact rate. We assume that human can only contact HPAI by direct contact with infected birds. A mathematical model consisting of ordinary differential equations has been proposed in order to analyze / determine time evolution of susceptible birds and infected birds. Analysis based on the model shows that the population of domestic birds can be made secured against infection by proper vaccination and proper removal of infected birds. During the study the basic reproduction number of the model was calculated and the following conclusion was made. If R0< 1, disease - free equilibrium is stable, the disease will die out; if however, R0> 1, there exists an endemic equilibrium which is stable, Avian Influenza will spread.
Keywords: mathematical modelling, avian influenza, ordinary differential equation, reproductive number.


DOI: doi.org/10.15864/jmscm.2207

STABILITY ANALYSIS OF A STAGED PROGRESSION HIV/AIDS MODEL WITH SCREENING AND CONDOM USAGE

Aminu, M.1, Ibrahim, M.O.2, Mustafa, A3, Abdullahi, I .4

1Department of Mathematics, Waziri Umaru Federal Polytechnic Birnin Kebbi, Kebbi State, Nigeria.
2Department of Mathematics, University of Ilorin, Kwara State, Nigeria
3Department of Mathematics, Usmanu Danfodiyo University Sokoto, Sokoto State, Nigeria
4Department of Mathematics, Sokoto State University, Sokoto State, Nigeria
*Corresponding author.E-mail:[email protected]
Page Number: 287-304

In this Paper, a staged-progression model for HIV/AIDS transmission dynamics is formulated and analyzed to study the impact of Screening, Condom usage and Condom compliance. The local stability for the disease free equilibrium (DFE) was proved for Rc < 1 and Kransnoselki sublinearity trick was used to show that the endemic equilibrium (EE) is locally asymptotically stable for a special case whenever Rc > 1. Numerical simulation was also carried out to investigate the effects of screening unaware (unscreened) asymptomatic individuals and Condom compliance. The result shows the influence of condom compliance and screening on the transmission dynamics of HIV/AIDS. The result clearly shows that increase in the compliance of Condom usage and increase of screening rate of HIV individuals reduces the total number of HIV/AIDS individuals. This point that increase in Condom usage and screening reduces HIV/AIDS burden.
Keywords: HIV/AIDS, Staged progression, Screening, Condom


DOI: doi.org/10.15864/jmscm.2208

CONSUMER BUYING BEHAVIOUR IN BIG-BAZAAR DURGAPUR

Sk Shahin Ferdows1, Dr.Sk Samim Ferdows2, Sk Wasim Firdaus3, Joydeep Dey4, Prof. Dr. Sunil Karforma5

1Student of HSMS Durgapur, Paschim Bardhaman, West Bengal, India. Email: [email protected]
2Faculty Member (SACT) Department of Mathematics, M.U.C. Women’s College, Burdwan, West Bengal, India. Email: [email protected]
3Student of Aliah University Kolkata. Email: [email protected]
4Faculty Member (SACT) Department of Computer Science, M.U.C. Women’s College, Burdwan, West Bengal, India. Email: [email protected]
5Professor & Head, Department of Computer Science, The University of Burdwan, Burdwan, West Bengal, India. Email: [email protected]
*Corresponding Author-Sk Shahin Ferdows. Email: [email protected]
Page Number: 305-316

Consumer’s behaviour is often studied because certain decisions are significantly affected by their behaviour or expected actions. For this reason consumer behaviour is said to be applied discipline.In a general sense, the most important reason for studying consumer behaviour is the significant role it plays in our lives. Much of our time is spent directly in the market place, eating or engaging in other activities. A large amount of additional time is spent thinking about products and services, talking to friends about them, and seeing or hearing advertisements about them. These general concerns alone are enough to justify our study of consumer behaviour. However, many seek to understand the behaviour of consumers for what are thought to be more immediate and tangible reasons. The main reason behind this project was to find out the buying behaviour of the consumer while shopping at big bazaar because most of the population surveyed preferred to shop at malls and how day by day the consumers demands are increasing and through this project I came to know that what are the various behaviour of a typical customer who shops at big bazaar.
Keywords: Consumer, significant, buying behaviour, products and services.


DOI: doi.org/10.15864/jmscm.2209

SOME IMPORTANT APPLICATIONS OF SEMIGROUPS

Iqra Liaqat1 & Wajeeha Younas2

1,2Department of Mathematics, Punjab University, New Campus, Lahore District-75500, Pakistan. Email:[email protected]
Page Number: 317-321

This Paper deals with the some important applications of semigroups in general and regular semigroups in particular.The theory of finite semigroups has been of particular importance in theoretical computer science since the 1950s because of the natural link between finite semigroups and finite automata via the syntactic monoid. In probability theory, semigroups are associated with Markov process. In section 2 we have seen different areas of applications of semigroups. We identified some Applications in biology, Partial Differential equation, Formal Languages etc whose semigroup structures are nothing but regular.
Keywords: Semigroups of Operators, Abstract Cauchy problem, Coagulation.


DOI: doi.org/10.15864/jmscm.2210

ON SOME SOLUTIONS OF THE MULTIVARIATE BEHRENS FISHER PROBLEM

Gulumbe SU1, Shehu B2, Dahiru S3

1Professor of Statistics, Department of Mathematics, Usmanu Danfodiyo University Sokoto. Email: [email protected]
2Department of Mathematics, Kebbi State University of Science and Technology, Aliero. Email: [email protected]
3Department of Mathematics, Kebbi State University of Science and Technology, Aliero. Email: [email protected]
Page Number: 322-335

Multivariate Behrens-Fisher Problem is a problem that deals with testing the equality of two means from multivariate normal distribution when the covariance matrices are unequal and unknown. However, there is no single procedure served as a better performing solution to this problem, Adebayo (2018). In this study effort is made in selecting five different existing procedures and examined their power and rate to which they control type I error using a different setting and conditions observed from previous studies. To overcome this problem a code was designed via R Statistical Software, to simulate random normal data and independently run 1000 times using MASS package in other to estimate the power and rate at which each procedure control type I error. The simulation result depicts that, in a setting when variance covariance matrices S1 > S2 associated with a sample sizes (n1 > n2) in Table 4.1, 4.2, 4.5, and 4.6, shows that, Adebayos’ procedure performed better but at a sample sizes (n1 = n2 and n1 < n2) Hotelling T2 is recommended in terms of power. For type I error rate where robustness and nominal level matters we found that under some settings none of the procedure maintained nominal level as revealed in Table 4.11 and 4.15. The results presented in Table 4.9 to 4.16 shows that when nominal level matters Krishnamoorthy came first, followed by Adebayos’, Yaos’, Johansons’ then Hotelling T2 were recommended in the sequentially under the settings used in this study.
Keywords:Behrens-Fisher, Power, Type I error, Hotelling’s T2 , Yoa, Johansen, Krishnamoorthy, Adebayo.


DOI: doi.org/10.15864/jmscm.2211