##### A General Algorithm of the Boundary Integral Method for Solving Laplace’s Mixed Boundary Value Problem

Rajesh Kumar Pal, Pradeep Kothiyal, Deependra Nigam

Asian Research Journal of Mathematics, Page 71-85
DOI: 10.9734/arjom/2021/v17i130266

Boundary elements have emerged as a powerful alternative to finite elements particularly in cases where better accuracy is required. The most important features of boundary elements however is that it only requires descretization of the surface rather than the volume. Here, A general algorithm of the boundary integral method has been formulated for solving elliptic partial differential equations. The broad applicability of the approach is illustrated with a problem of practical interest giving the solution of the Laplace equation for potential flow with mixed boundary problems. The results and patterns are shown in tables and figures and compared well with Brebbia [1] are found in good agreement.

##### Factors Affecting Bhutanese Secondary School Students’ Ability in Solving Mathematical Word Problems: A Case Study

Phuntsho Wangmo

Asian Research Journal of Mathematics, Page 1-13
DOI: 10.9734/arjom/2021/v17i130260

Mathematical word problems are part of the school curriculum and are taught at all levels of education in Bhutan. However, it poses difficulties for many students because of the complexity of the solution process. There are various factors that affect students’ ability to solve mathematical word problems. Hence, this study was conducted to investigate the factors affecting Bhutanese secondary school students' ability to solve mathematical word problems. This study employed a qualitative case study approach. Data was collected through semi-structured interviews, classroom observations, and document analysis. Four mathematics teachers and four students were selected as participants based on purposive sampling. The data were analyzed using thematic analysis. The findings revealed that factors such as language proficiency, reading skills, and contextual understanding affect students' ability in solving mathematical word problems. Moreover, the language proficiency of students, as well as teachers, was the most important factor for solving mathematical word problems. The study recommends the Ministry of Education places more importance on reading activities across schools in Bhutan to enhance language proficiency.

##### The Existence and Uniqueness of the Solution of a Diusive Predator-Prey Model with Omnivory and General Nonlinear Functional Response

Wensheng Yang

Asian Research Journal of Mathematics, Page 14-25
DOI: 10.9734/arjom/2021/v17i130261

In this work, we consider a three species modified Lesie-Gower food web model with general  nonlinear functional response and omnivory which is defined as feeding on more than one trophic level. The carrying capacity of the model is proportional to the population size of the biotic resource plus a const. The main objective of this paper is to investigate the existence and  uniqueness of the solution of this model. It is shown that the omnivory has important influence on the existence and uniqueness of the solution of the model.

##### On Frink's Type Metrization of Weighted Graphs

Mara Florencia Acosta, Hugo Aimar, Ivana Gomez

Asian Research Journal of Mathematics, Page 26-37
DOI: 10.9734/arjom/2021/v17i130262

Using the technique of the metrization theorem of uniformities with countable bases, in this note we provide, test and compare an explicit algorithm to produce a metric d(x, y) between the vertices x and y of an anity weighted undirected graph.

##### Tracer Study of Bs in Mathematics Graduates (2001 – 2015) of the College of Science, University of Eastern Philippines

Mary Jane B. Calpa, Ida E. Esquierdo, Olga D. Unay

Asian Research Journal of Mathematics, Page 38-44
DOI: 10.9734/arjom/2021/v17i130263

A descriptive research was conducted to trace the whereabouts of the graduates of Bachelor of Science in Mathematics of the College of Science, University of Eastern Philippines. The study determined the employability of the graduates from the first batch of 2001 up to 2015. It determined the graduates who are employed whether related or not to their course; what type of jobs they have; what kind of skills they learned; and how much they earned from their jobs. Majority of the respondents are gainfully employed. Most of them are on contractual basis and are working in the Philippines. From the 110 graduates, 91 are employed while no data were gathered for the 19 graduates. Majority are professionals working as teachers in the secondary and tertiary level. Problem solving skills is most useful in their personal and professional growth. The teacher-student relationship is most rated that contributes to the degree they finished at the College of Science.

##### Constructivist Teachers Beliefs, Instructional Practices and Students’ Mathematics Performance

Mary Cris Danes Balanlay

Asian Research Journal of Mathematics, Page 45-58
DOI: 10.9734/arjom/2021/v17i130264

This study determined the role of teachers’ constructivist beliefs in the teaching and learning mathematics and the use of instructional practices in the mathematics performance of Grade 7 secondary students in the Pacific Towns of Northern Samar for the school year 2016-2017. This study utilized the descriptive-correlational research design.

The demographic profile of teachers in mathematics such as constructivist beliefs, constructivist instructional practices and performance of students was described as it exists at the present time. Multiple regression analysis was used to determine the relationship between the beliefs in mathematics and students’ mathematics performance. Similarly, statistical analysis was used to determine the relationship between instructional practices and mathematics performance of the students.

The findings showed that more than 50% of the mathematics’ teachers are aged less than 30 suggesting that most of the teachers are neophyte in the teaching career. As to educational attainment, most of the respondents are enrolled in master’s program. Only one-third have already completed master’s degree. In terms of relevant trainings, almost a half of the respondents have attended one to two trainings.

Most of the teachers believe that teaching should involve real world connections. Teachers believe that they should create real-world environments that employ the context in which learning is relevant. Beliefs about emphasizing prior knowledge were also manifested by the teacher-respondents. Highly demonstrated beliefs include encouraging the use of multiple modes of representation to facilitate easy understanding and recall and the learner's previous knowledge constructions, beliefs and attitudes are considered in the knowledge construction process. In terms of social interaction beliefs, teachers manifested support for collaborative construction of knowledge through social negotiation.

Result of the test conducted in mathematics by the researcher showed that more than half of the students got fair performance. Only one performed satisfactorily. Beliefs about emphasizing prior knowledge and beliefs in social interaction significantly predicted mathematics performance of students. Real world connection did not significantly predict mathematics performance.

Respondents’ constructivist instructional practices did not offer a significant role in developing the mathematics ability of the students. Teachers did not play an active role in assimilating knowledge into students’ existing mental framework and reconstructing new knowledge.

##### Evaluating Measure of Reformed Rotatability for Second Degree Polynomial Using a Pair of Incomplete Block Designs with Two Unequal Block Sizes

P. Jyostna, B. Re Victorbabu

Asian Research Journal of Mathematics, Page 59-70
DOI: 10.9734/arjom/2021/v17i130265

In this paper, a study on evaluating measure of reformed rotatability for second degree polynomial using a pair of incomplete block designs with two unequal block sizes (like symmetrical unequal block arrangements with two unequal block sizes) is suggested which enables us to assess the degree of reformed (modified) rotatability for a given response surface design.

##### Test for Aggregational Gaussianity (AG) in Petroleum Prices Returns

M. E. Archibong, I. D. Essi

Asian Research Journal of Mathematics, Page 86-98
DOI: 10.9734/arjom/2021/v17i130267

The work aims at investigating and establishing if Aggregational Gaussianity, (AG) is in the dynamics of petroleum prices. This AG aspect is the phenomenon in which the empirical distribution of log-returns tends to normality (or as the time scale over which the returns are calculated increases). In order to achieve this, the petroleum price series was tested for arch effects. In addition, tests for Aggregational Gaussianity, (AG) were carried out using qualitative (graphical) approach and inferential approach, (involving statistical inference). The study shows that the presence of arch effects does not guarantee existence of AG. It is also observed that qualitative (graphical) approach may suggest normality and hence, presence of  AG, on the other hand, inferential approach (involving statistical tests) gives a better picture of the actual conclusion, of the presence (or otherwise) of AG in the data set, with a 99.97% rejection from normality by the three tests-Kolmogorov-simonorv,Shapiro-Wilks, and Anderson-darling. In the circumstance, there is no evidence to confirm a discernible presence of AG in the dynamics of petroleum prices. The non-existence of AG in the study shows the instability in the dynamics of petroleum prices, since one cannot invoke normality as an invariant property this, among other factors, make the economy unstable as it is oil- driven. However, since the highest percentage of the budget for the country is based on the petroleum sales, which as this study reveals is unstable, hence, diversification of the economy is proposed. The softwares used in the work are Eviews 10, Minitab 18, Spss 17, Easy-fit 5.6 professional, and R 3.2.2.

##### On the Existence of Time Delay for Rotating Beam with Proportional–Derivative Controller

Y. A. Amer, Taher A. Bahnasy, Ashraf M. Elmhlawy

Asian Research Journal of Mathematics, Page 99-122
DOI: 10.9734/arjom/2021/v17i130268

A rotating beam at varying speed mathematical model is studied. Multiple time scales method is applied to the nonlinear system of differential equations and investigated the system behavior approximate solution in the instance of resonance case. We studied the system in case of applying the delayed control on the displacement and the velocity with Proportional–derivative (PD) controller. The consistency of the steady state solution in the near-resonance case is reviewed and analyzed using the Routh-Huriwitz approach. The factors on the steady state solution of the various parameters are recognized and discussed. Simulation effects are obtained using MATLAB software package. Different response curves are involved to show and compare controller effects at various system parameters.

##### Mathematical Modelling of the Dynamics of COVID-19 Disease Transmission

A. B. Okrinya, E. Esekhaigbe

Asian Research Journal of Mathematics, Page 123-137
DOI: 10.9734/arjom/2021/v17i130269

We construct a simple mathematical model that describes the dynamics of the transmission of COVID-19 disease in a human population. It accounts for the various phases of the disease and its mode of contact through infectious humans and surfaces. The contribution of asymptomatic humans in the dynamics of the disease is well represented. The model is a system of ordinary dierential equations that describes the evolution of humans in a range of COVID-19 states due to emergence of an index case. The analysis includes establishment of the basic reproduction number, R0, where, R0 < 1 signifies a disease free state that is locally asymptotically stable. A key result in this study shows some long term damped oscillatory behaviour that do not seem to end soon.