Siharath Phoummixay1,Guillermo III Quesada Tabios2
1Department of Environmental Engineering, Faculty of Engineering, National University of Laos
2Professor, Institute of Civil Engineering and Director of National Hydraulic Research Center, University of the Philippines, Diliman,Quezon City, Philippines 1101
Page Number: 1-17
Groundwater modeling has become a popular approach and common of conducting groundwater flow
and contaminant transport simulation. Consequently, in order to understand the behavior of groundwater
flow, this study has established and developed conceptual model of groundwater at Phukham Copper -
Gold operations mining. In addition, this study is applied Groundwater Modeling System (GMS) 6.5
software and using MOFLOW Package which employs advanced mathematics as Finite Difference
Method (FDM). Steady Flow model is set up and calibrated within target ± 2 meters; then the model is
run in MOFLOW in order to obtain acceptable observed and simulated hydraulic head by adjusting
hydraulic conductivities and recharge values. Recharge rate is adjusted between 2% to 12% from annual
rainfall 0.00475 m/d and it is found out to be 7.22 % or 0.00034 m/d. Model has come up with reasonable
finding. Hence, root mean square error of steady state: layer1, 2, 3 and 4 are 1.840 m, 1.767 m, 1.963 m
and 0.574 m, respectively. The coefficient of determination of steady state for layer1, 2, 3 and 4 are
0.965, 0.96, 0.959 and 0.985, respectively. Keywords: Groundwater, Finite Different Method, MODFLOW, Calibration.
1Federal University Wukari, Taraba State, Nigeria Department of Educational Administration and Planning
Page Number:18-33
The aim of this study is to investigate the challenges facing the planning of mathematics programme in
Federal Capital Territory, Nigeria. The study adopted descriptive research survey design. The population
of the study comprised ninety (90) respondents. Stratified and systematic sampling technique was used to
select the sample population. The study employed the used of questionnaire as instrument for data
collection. Two lecturers from Educational Administration and planning from University of Abuja was
consulted to validate the questionnaire. Three research questions and two hypotheses were developed for
the study. Test-retest reliability was employed for the study. Percentage and Chi-square test was used to
test the hypotheses and data collected from the study. The result revealed that there are challenges facing
the planning of mathematics programme of senior secondary education and the challenges includes;
inadequate data/information to plan, inadequate funding of planning of mathematics programme, poor
capacity development of few mathematics planners, inadequate professional mathematics planners
,political instability, corruption and lack of political will to support planning of mathematics education. The
study concluded that the implication of the challenges on the implementation mathematics education is poor
implementation of the mathematics programme in the senior secondary schools. The study recommends
that the government should increase the funding of educational planning in the country especially
mathematics education.
Keywords: Challenges, Planning, Mathematics Education.
1University of Port Harcourt, Choba, Rivers State, Nigeria 2University of Port Harcourt, Choba, Rivers State, Nigeria 3Department of Mathematics/Statistics, Ignatius Ajuru University of Education, Port Harcourt, Rivers State, Nigeria
Page Number: 34-55
This research work used multivariate regression analysis to analyze babies’ birth measurements which is
appropriate since there are several numbers of dependent variables and independent variables, usually the
case in a real-life situation. The dependent variables [Lean Body Mass (LBM) Y1 and Body Mass
Index(BMI) Y2] for some fixed values of the independent variables Head Circumference (CM) X1, Age
(Days) X2, Height (CM) X3 and Weight (Kg) X4]were collected. Furthermore, the work was able to fit a
multivariate regression model (MRM) to the data sets collected, estimated the model parameters and
obtained matrices of the fitted coefficients with its residual matrices. Evaluating the significance of the
multivariate regression model parameters, by using Bartlett’s approximation test statistic to determine if
any single variable Yi (Yi, i=1 and 2) is to be predicted from all the independent variables in the system.
The research work was able to fit several multivariate regression models to the data obtained. From the
models built, we notice that X2 (Age in Days) for model Y1 and also X1 [Head Circumference (CM)] and
X2 (Age in Days) for model Y2 are not significant for female and male in Bayelsa State, while X2(Age in
Days) for model Y2 is not significant for female and male in Rivers State. This result confirms that there
are some independent variables, that is
0 ij
and shows that some independent variables explain the
dependent variables.
Keywords: Multivariate Regression, Bartlett’s approximation, Lean Body Mass, Body Mass Index and Head Circumference
1Department of Mathematics, Punjab University New Campus, Lahore District-75500, Pakistan. 2Department of Mathematics, Lahore Garrison University, Lahore District-75500, Pakistan
Page Number: 56-77
A ring R satisfies the dual of the isomorphism theorem if R/Ra≅ 1(a) for all elements a of R, where 1(a)
denotes the left annihilator. We call these rings left morphic. Examples include all unit regular rings and
certain left uniserial local rings. We show that every left morphic ring is right principally injective, and use
this to characterize the left perfect, right and left morphic rings. Keywords: Primary 16E50, secondary 16U99, 16S70.
Department of Physics, Dharsa Mihirlal Khan Institution, Howrah-711112, India. Kalpana Chawla Centre for Space and Nano Sciences (KCCSNS), Kolkata-700010, India.
Page Number: 78-83
The main aim of this paper is to study late time accelerated expansion of the universe with the help of kessence scalar field. We have chosen non-canonical k-essence lagrangian of the form 𝑉(𝜙)𝐹(𝑋), and
converted to canonical lagrangian with the help of scaling ralation √𝑋𝐹𝑋=Ca−3. The obtained lagrangian
has two generalised co-ordinate, logarithm of the scale factor (q=ln𝑎) and scalar field (𝜙). From the
obtained lagrangian we studied two most important cosmological parameter, Equation of state parameter
(𝜔 ≈ −1) and deceleration parameter (𝑞0 ≈ −1) which are to some extent consistent with the current
observations. Both the parameters indicates an accelerated expansion of the universe driven by negative
pressure known as dark energy.
Keywords: k-essence, Dark energy, Hubble parameter, Acceleration of Universe.
1, 2, 3, 4, 5, 6Institute of Engineering & Management, Salt Lake Electronics Complex Kolkata-700091. India
Page Number: 84-89
Here we have briefly discussed the various applications of number theory in the fields of Computation with
special emphasis on Encryption algorithms.We have laid special emphasis on prime numbers and briefly
touched upon their importance in modern day Cryptography , especially in RSA Encryption which is the
most widely used encryption technique nowadays.
Keywords: Number theory, encryption, algorithm, prime numbers, cryptography, RSA encryption.
Department of Education, Schools Division of Calbayog City, Calbayog 5 District. Northwest Samar State University Brgy. Aguit-itan, Calbayog City, Samar, Philippines
Page Number: 90-128
This study is an experimental pre-test and post-test design which essentially needed to compare the
effectiveness of Computer Aided Modular Instruction with the Traditional Method of teaching word
problem involving fractions to the grade six (6) pupils of Gadgaran Integrated School, Calbayog City,
Samar during the school year 2019-2020.Computer aided modular instruction is a teaching technique that
enable pupils interact with the lesson programmed to the computer given to the experimental group. The
Traditional Method on the other hand, is a usual way of teaching composing with lecture-discussion given
to the control group. A single class consisting of regular grade six (6) pupils was chosen as the subject of
the study. Their average grade is approaching proficiency level in Mathematics subject during the first
grading period both of experimental and control group. They were randomly assigned and chosen using
odd or even technique. The instrument used in this study was researcher made test in Mathematics and was
carefully validated. The content topics in the Computer Aided Modules were based on the DepEd Learning
competencies set for the grade six level. These are further checked and validated by the Mathematics
teachers of Calbayog IV District, Division of Calbayog City. The evaluation survey questionnaire on
pupils’ difficulties, reactions and attitudes towards Computer Aided Modular Instruction was adapted from
the study of Saladaña on SIM-Based Instruction. The questionnaires were revised by the present researcher
of this study. The control and experimental group have significant mean difference in the pre-test and posttest scores but have no significant mean difference in the mean percentage gain of scores. The Computer
Aided Modular Instructions and the Conventional Method of Instruction resulted for the same level of
achievement for the pupils with slight challenges on the part of pupils and facility in teaching of the
teachers. Based on the result it was recommended on the implementation and adaptation of this strategy
into the classroom utilizing Computer Aided Instruction in enhancing the better-learning output. Keywords: Computer-Aided, Module, Problem Solving, CAMI, Instruction, and Difficulties Encountered
Department of Applied Sciences & Humanities, Rajkiya Engineering College Azamgarh, U.P. India
Page Number: 129-144
In the present article, we use modified Bernstein polynomial (B–polynomial) as a basis for the numerical
approximation of heat transfer in hyperthermia treatment. A set of continuous polynomials over the spatial
domain is use to expand the desired solution using discretization in time variable only. The Galerkin method
is use to determine the expansion coefficients to construct initial trial functions. The system of equations
has been solved using fourth–order Runge-Kutta method. The accuracy of the solutions is dependent on the
size of the B–polynomial basis set. Also, Homotopy Perturbation Method has been applied to solve Matrix
form of initial value differential equations which is transformed from boundary value differential equation
of desired problem by using central difference scheme. The results thus obtained are in very good agreement
with the previous results and it is presented graphically. Keywords: Bio-heat equation; Bernstein polynomial; Galerkin method; Finite difference equations; Homotopic perturbation method
State Aided College Teacher & Former HoD, Department of Computer Science, M.U.C. Women’s College, Burdwan, West Bengal, India
Page Number: 145-157
The novel corona virus had shattered the entire living world. Its fast spreading transmission is still not
under control. In this new normal post- Corona Virus Disease (COVID), Telemedicine is the safest mode
of getting health services being confined within homes. Patients can easily consult their doctors through
telemedicine software. Thus, the risks of getting COVID attacks at hospitals are completely eradicated. It
ensures treatments along with social-distancing parameters. Testing is an integral component of such
telemedicine software. White box testing plays a pivotal in developing such online healthcare software. It
is done with intent to locate all hidden errors inside the Telemedicine system. This paper presents a
testing strategy on online healthcare software in this post COVID context. It is useful for the software
engineers who are engaged in developing such COVID online healthcare software for preserving the
patients’ data security.
Keywords: COVID, Telemedicine, White Box Test, Control Flow Graph, Adjacency Matrix
1, 2, 3, 4Federal College of Education (Special), Oyo Oyo State, Nigeria
Page Number: 158-168
This study investigated the impact of integrating ICT on pupils’ academic achievement in mathematics in
primary schools in Afijio Local Government Area, Oyo State, Nigeria. The quasi-Experimental research
design was employed in this study. The targeted population consists of the Primary Schools Pupils in
Afijio Local Government Area, Oyo State. One hundred Pupils (50 males and 50 females) from one
school for the treatment group in a school and one hundred Pupils (50 males and 50 females) were
selected for the Control Group in another school. Stratified Random Sampling was used to ensure the
generalization and the accuracy of the data. The instrument used was the Mathematics Achievement Test
(MAT) consists of 20 multiple-choice questions. The instrument was given face and content validity by
two experts. The reliability of the instrument was established using the Test-Retest Method. The result of
the test was analyzed using Pearson Product Moment Correlation (PPMC), the reliability coefficient of
the instrument was found to be 0.91. The mean, standard deviation and mean difference was used to
analyze the research questions. The study revealed that there is a difference in the mean scores of the
pupils taught with ICT and those taught without ICT, and there is a difference in the mean scores of the
female and male pupils taught with ICT and those taught without. The study concluded that there is a
significant role that ICT plays in improving Pupils’ academic achievement in mathematics. Based on the
result, it was recommended among others that efforts should be made by the government to make ICT
facilities available and to provide teachers with the skills and knowledge of how to implement ICT in
teaching of mathematics to primary school pupils. Keywords: Academic Achievement, Mathematics, Integrating, ICT and Pupils
Institute of Engineering & Management, Salt Lake Electronics Complex, Kolkata-700091. India.
Page Number: 169-180
Efficiently determining Shortest Paths on Road Maps has been a heavily engineered function for
many routing apps like Google Maps & Yandex Maps for years now. Dutch computer scientist,
Edsger W. Dijkstra set the stepping stone by formulating the now famous, Dijkstra’s algorithm for
shortest paths. Later it was improved upon by newer algorithms like A*. We introduce a way to
implement modern algorithms such as Contraction Hierarchy, Highway Hierarchy and PHAST
Algorithm to find optimal shortest paths in real life scenario road maps. It bases heavily on
constructing a virtual “highway” which the shortest path should pass through theoretically as they are
heavily traversed in real life generally. It considers parameters such as Road Distance between
nodes(Edge Weight), Importance Factor during Contraction Hierarchy Phase, Cartesian Distance
From Target, External Real Time Factors like Weather and Traffic. We determine a Heuristic
Function using the above parameters and then use that to run a Bi-Directional PHAST based A* from
both the source and the target node and then determine the shortest path once a common highway
exists in both directional search’s settled vector or a fallback stage is reached. Keywords: graphs, shortest-paths, goal-directed-search, road-networks, dijkstra,a*-algorithm, contraction-hierarchy, highway-hierarchy, phast-algorithm
Surajo Isa Gaya1, Tanimu Bala2 ,Ibrahim A. Lawan3 ,Umar Ishaq 4
1, 2Computing and Mathematics Education Department, Kano University of Science and Technology, Wudil Nigeria
3Department of Information Technology Bayero University Kano, Nigeria
4Department Science Education Kano University of Science and Technology, Wudil Nigeria.
Page Number: 181-193
This research adopted a descriptive survey design to determine the effect of social media on academic
performance among university mathematics education students in three universities. The universities are
Kano University of Science and Technology Wudil, Yusuf Maitama Sule University Kano, and Bayero
University Kano, all in Kano State, Nigeria. To achieve the purpose of the study, three (3) null hypotheses
were formulated to guide the study. The population of the study was 1,750 undergraduate students of the
Department of Computing and Mathematics Education in the 2019/2020 academic session. A stratified
simple random sampling technique was used to select a sample size of 350 students, using the Taro
Yemane (1984) formula. A modified four-point Likert-scale type questionnaire was used to gather data.
Before use, the questionnaire was validated and also subjected to a reliability test which yielded an index
of 0.83 using Pearson's product moment correlation statistics. Results showed that a large number of
students in the Universities are addicted to social media. Findings show that the use of Facebook,
WhatsApp and Instagram platforms would likely affects the academic performance of the University
students in Kano State. It was recommended that social media should be used for promoting educational
purposes, social networking sites should be broadened and new platforms created to enhance academic
activities and improve students' academic performance. It is also suggested that a one-credit course on the
use of social media should be included during the orientation/induction programmes, awareness campaign
and handbooks of the fresh students in the universities. Keywords: Social media effect, academic performance, Facebook, WhatsApp, Instagram, Mathematics education
