##### Alenezi Transform–A New Transform to Solve Mathematical Problems

Asian Research Journal of Mathematics, Page 1-8
DOI: 10.9734/arjom/2020/v16i1230249

In this paper, we present a new integral transform called Alenezi-transform in the category of Laplace transform. We investigate the characteristic of Alenezi-transform. We discuss this transform with the other transforms like J, Laplace, Elzaki and Sumudu transforms. We can demonstrate that Alenezi transforms are near to the condition of the Laplace transform. We can explain the new Properties of transforms using Alenezi transform. Alenezi transform can be applied to solve differential, Partial and integral equations.

##### Generalized Weighted Rama Distribution: Properties and Application to Model Lifetime Data

Samuel U. Enogwe, Chisimkwuo John, Happiness O. Obiora-Ilouno, Chrisogonus K. Onyekwere

Asian Research Journal of Mathematics, Page 9-37
DOI: 10.9734/arjom/2020/v16i1230250

In this paper, we propose a new lifetime distribution called the generalized weighted Rama (GWR) distribution, which extends the two-parameter Rama distribution and has the Rama distribution as a special case. The GWR distribution has the ability to model data sets that have positive skewness and upside-down bathtub shape hazard rate. Expressions for mathematical and reliability properties of the GWR distribution have been derived. Estimation of parameters was achieved using the method of maximum likelihood estimation and a simulation was performed to verify the stability of the maximum likelihood estimates of the model parameters. The asymptotic confidence intervals of the parameters of the proposed distribution are obtained. The applicability of the GWR distribution was illustrated with a real data set and the results obtained show that the GWR distribution is a better candidate for the data than the other competing distributions being investigated.

##### The Capability of Students towards Mathematics Using Student’s Feedback

Muteeullah Memon, Muhammad Waleed, Shahzaib Ahmed, Suresh Kumar Beejal, Owais Ali, Faiz Muhammad

Asian Research Journal of Mathematics, Page 38-43
DOI: 10.9734/arjom/2020/v16i1230251

The attitude of students towards mathematics is most important factor especially for the engineers in their practical observation relating to the understanding of particular problems in their field. To analyze this reservation, the study is conducted using students’ feedback towards the performance of students in Calculus and Differential Equation subjects. During the analysis, a case study of 17A and 17B batches of 1st and 2nd semesters are selected. The marks of the Mathematics subjects namely Applied Mathematics-I (Calculus) and Applied Mathematics-II (Differential Equation) is collected from the students individually using university students portal and the results is calculated by using Statistical Package for Social Sciences (SPSS v.16) which shows  the overall students’ perception towards the mathematics subjects. The results imply that there is no significant relationship between the marks of calculus and differential equation. Furthermore, the null hypothesis is rejected for the disciplines such as Civil, Mechanical, Electrical, Mechatronics and Textile of 17A and Civil, Mechanical and Electrical of 17B Batch. Although the null hypothesis is accepted only for the Electronics department of 17A and Mechatronics, Electronics and Textile of 17B Batch. It is recommended that the teachers must put efforts on the students for the understanding of Mathematics concepts and improve their attitude towards it, so that they can perform better in their future practical life.

##### Accurate Time Calculations of Falling Bodies in the Earth's Gravitational Field and Comparisons with Newton's Laws of Vertical Motion

A. Ebaid, Shorouq M. S. Al-Qahtani, Afaf A. A. Al-Jaber, Wejdan S. S. Alatwai, Wafaa T. M. Alharbi

Asian Research Journal of Mathematics, Page 44-53
DOI: 10.9734/arjom/2020/v16i1230252

The Earth is exposed annually to the fall of some meteorites and probably other celestial bodies which cause a potential danger to vital areas in several countries. Consequently, the accurate calculation of the falling time of such bodies is useful in order to take the necessary procedures for protecting these areas. In this paper, Newton’s law of general gravitation is applied to analyze the vertical motion in the Earth’s gravitational field. The falling time is obtained in exact form. The results are applied on several objects in real life.

##### Mathematical Dispositions of Graduating Students of the College of Engineering, University of Eastern Philippines (UEP)

Lonel I. Morado, Benjamin D. Varela

Asian Research Journal of Mathematics, Page 54-64
DOI: 10.9734/arjom/2020/v16i1230253

This study was conducted to determine the mathematical disposition of graduating engineering students of the UEP College of Engineering in the School Year 2016-2017. Specifically, the study assessed the profile of the graduating students in terms of their age, sex, average grade in calculus and academic performance in professional subjects; the mathematical disposition in terms of self-efficacy component; math as sensible component; and perseverance component; the relationship between the profile and mathematical disposition of students, and between the mathematical disposition and academic performance in professional subjects of the respondents.

The 132 graduating students taking up Bachelor of Science in Agricultural Engineering (BSAE), Bachelor of Science in Civil Engineering (BSCE), Bachelor of Science in Electrical Engineering (BSEE), and Bachelor of Science in Mechanical Engineering (BSME) who are officially enrolled in the second semester of the school year 2016-2017 were the respondents of this study.

The study found out that there were more graduating engineering students whose age is beyond 22 to 24 years old; more males; and have passing performance in calculus subjects.

Generally, the graduating engineering students for the school year 2016-2017 have good mathematical disposition, specifically described as more efficacious, sensible, and more persevering.

The students’ performance in calculus subjects was significantly related to mathematical disposition, while the age and sex of respondents have nothing to do with mathematical disposition.

Specifically, respondents’ age and sex did not affect the three components of mathematical disposition, while average grade in calculus subjects was found to have something to do with their sensibility and perseverance level in mathematics.

On the relationship between mathematical disposition components and the academic performance in professional subjects of graduating engineering students, it was found out that only the math as sensible component affected their performance in professional subjects.

The result of this study also revealed that these students who were more efficacious, more sensible and more persevering performed good in their professional subjects.

##### Differentiated Instruction in Plane Trigonometry Class

Julita Notarte-Alburan

Asian Research Journal of Mathematics, Page 65-73
DOI: 10.9734/arjom/2020/v16i1230254

This study aimed to determine the effectiveness of differentiated instruction on students’ achievement in Plane Trigonometry. It tried to determine the pretest and posttest performance of experimental and control groups, the difference on scores of students in the pretest and in the posttest, and the difference from pretest to posttest scores in the two groups of students. The quasi-experimental design was used in the study. Two intact class of first year college students enrolled in Plane Trigonometry in School Year 2017-2018 were purposively sampled and used for the study. One class was randomly assigned to experimental group while the other served as the control group. Instructions were made using flexible groupings and varied formats (cooperative learning, individual or group projects, and whole-class discussion) with various strategies such as agenda, compacting, cubing, vocabulary choice boards, tier assignment, think-tac-toe, and RAFT activity. The students explored, collaborated, worked in pairs or groups in different activities. Data were tabulated and analyzed using frequency counts, percentages, and t-test for independent samples with the aid of the statistical package for Social Sciences (SPSS) software. The findings revealed that the experimental group and control groups showed significant improvement in students’ performance in plane trigonometry.  However, the score suggested that the improvement of the scores under the experimental group was defined and noticeable. Generally, the results revealed that students who were taught differentiated instruction performed better than those taught using the conventional instructional approach.

##### Strategic Way of Factoring Modulus $$N = p^r q$$

Sadiq Shehu, Abdullahi Hussaini, Zahriya Lawal

Asian Research Journal of Mathematics, Page 74-86
DOI: 10.9734/arjom/2020/v16i1230255

Cryptography is fundamental to the provision of a wider notion of information security. Electronic information can easily be transmitted and stored in relatively insecure environments. This research was present to factor the prime power modulus $$N = p^r q$$ for $$r \geq 2$$ using the RSA key equation, if $$\frac{y}{x}$$ is a convergents of the continued fractions expansions of $$\frac{e}{N - \left(2^{\frac{2r+1}{r+1}} N^{\frac{r}{r+1}} - 2^{\frac{r-1}{r+1}} N^{\frac{r-1}{r+1}}\right)}$$. We furthered our analysis on $$n$$ prime power moduli $$N_i = p_i^r q_i$$ by transforming the generalized key equations into Simultaneous Diophantine approximations and using the LLL algorithm on $$n$$ prime power public keys $$(N_i,e_i)$$ we were able to factorize the $$n$$ prime power moduli $$N_i = p_i^r q_i$$, for $$i = 1,....,n$$ simultaneously in polynomial time.

##### Analysis of Inventory Model with Time Dependent Quadratic Demand Function Including Time Variable Deterioration Rate without Shortage

Md. Atiqur Rahman, Mohammed Forhad Uddin

Asian Research Journal of Mathematics, Page 97-109
DOI: 10.9734/arjom/2020/v16i1230258

This paper deals with an inventory model for deteriorating items along with time dependent demand which is quadratic function of time. In this model, the deterioration rate follows deterministic deterioration which is quadratic function of time. Here shortages are not allowed. The main purpose of this paper is to investigate minimum total cost per unit time of the inventory model. The result are validated with the help of numerical example. The sensitivity analysis of the optimal solution with respect to various parameters is carried out. Finally the behavior of the relation between parameters and total inventory cost have been shown using figure.

##### Spectral Adomian Decomposition Method for the MHD Three-Dimensional Flow due to a Stretching Sheet in a Porous Medium

Yassir Daoud, Mohammed Abdalbagi, Ahmed A. Khidir

Asian Research Journal of Mathematics, Page 87-96
DOI: 10.9734/arjom/2020/v16i1230256

An approximate solution is obtained of the steady, laminar three-dimensional ow for an incompressible, viscous uid past a stretching sheet using the Spectral Adomian Decomposition Method (SADM). The governing partial dierential equations are transformed into ordinary dierential equations using suitable transformations. A comparison between the obtained results with solutions obtained early in the literature and the numerical solution has been made to test
the validity, accuracy and convergence of the SADM. The eects of physical parameters on the velocity are determined and discussed.

##### Thermal Diffusion and Diffusion Thermo Effects on Casson Nanofluid Flow in the Presence of Chemical Reaction with Inclined Magnetic Field

T. W. Akaje, B. I. Olajuwon

Asian Research Journal of Mathematics, Page 110-124
DOI: 10.9734/arjom/2020/v16i1230259

Present paper studies the thermal-diffusion and diffusion-thermo effects on Casson nanofluid flow in the presence of chemical reaction with inclined magnetic field. A similarity analysis was used to transform the system of partial differential equations, together with boundary conditions into a system of dimensionless couple ordinary differential equations. A robust spectral collocation method has been adopted to obtain the solution of the transformed flow equations with corresponding boundary conditions. The impact of various controlling parameters on dimensionless velocity, temperature and nanoparticle concentration are presented graphically and discussed. The effect of the flow pertinent parameters on skin friction, Nusselt number and Sherwood number are presented in tabular form. Finally, an increase in Prandtl number and thermophoresis parameter reduce the temperature field of the flow, while increase in Eckert number enhanced the temperature profile.