##### A New Inequality with Its Application in Solving a Problem of Inequalities

Yuanjie Guo, Kongfeng Zhu

Asian Research Journal of Mathematics, Page 1-6
DOI: 10.9734/arjom/2021/v17i1130338

This article first puts forwards and proves a new inequality, then use the inequality to solve a problem related with a series of inequalities. Detail mathematical reasoning and proofs are presented. The results are valuable to learn and research inequalities.

##### Comparing the Performance of Four Sinc Methods for Numerical Indefinite Integration

Richard Olatokunbo Akinola

Asian Research Journal of Mathematics, Page 7-41
DOI: 10.9734/arjom/2021/v17i1130339

Aims/ Objectives: To compare the performance of four Sinc methods for the numerical approximation of indefinite integrals with algebraic or logarithmic end-point singularities.

Methodology: The first two quadrature formulas were proposed by Haber based on the sinc method, the third is Stengers Single Exponential (SE) formula and Tanaka et al.s Double Exponential (DE) sinc method completes the number. Furthermore, an application of the four quadrature formulas on numerical examples, reveals convergence to the exact solution by Tanaka et al.s DE sinc method than by the other three formulae. In addition, we compared the CPU time of the four quadrature methods which was not done in an earlier work by the same author.

Conclusion: Haber formula A is the fastest as revealed by the CPU time.

##### Numerical Study of Variable Viscosity and Thermal Conductivity on Natural Convection Flow along a Vertical Flat Plate with Pressure Work and Heat Conduction

Sirazum Munira, Sree Pradip Kumer Sarker, Md. M. Alam, Minhazul Islam

Asian Research Journal of Mathematics, Page 42-58
DOI: 10.9734/arjom/2021/v17i1130340

A heated vertical flat plate in the presence of heat generation is an extremely significant technological issue, and many academics have studied this sort of problem. A vertical plate submerged in a fluid with varying viscosity will be used in this research to investigate the effects of variable viscosity and thermal conductivity on heat generation free convection flow. The boundary layer equations in this section are two-dimensional, laminar, and unstable. The fundamental governing equations are turned into non-dimensional governing equations by using the necessary variables. Using the Crank-Nicolson implicit finite-difference technique, these equations are solved numerically. Viscosity and thermal conductivity are temperature-dependent properties of a viscous, incompressible fluid. Variations in the study's numerous parameters will reveal and compare the velocities, temperatures, local skin friction, and local heat transfer co-efficient profiles. There will be a comparison between the current numerical data and previously reported data findings. Besides that, we'll compare our current work numbers to those of past released publications. Graphs and tables will be used to display the findings for a variety of key physical characteristics.

##### Stepwise Procedure for Toxicological Assessment Based on Ratio of Mean Differences for a Normally Distributed Data

Michael J. Adjabui, Jakperik Dioggban, Nathaniel K. Howard

Asian Research Journal of Mathematics, Page 59-68
DOI: 10.9734/arjom/2021/v17i1130341

We propose a new stepwise confidence set procedure for toxicity study based on ratio of mean difference. Statistical approaches for evaluating toxicity studies that properly control familywise error rate (FWER) for difference of means between treatments and a control already exist. However, in some therapeutic areas, ratio of mean differences is desirable. Therefore, we construct stepwise confidence procedure based on Fieller's confidence intervals for multiple ratio of mean difference without multiplicity adjustment for toxicological evaluation. Simulation study revealed that the FWER is well controlled at prespecified nominal level α. Also, the power of our approach increases with increasing sample size and ratio of mean differences.

##### Two – Warehouse Inventory System Model for Deteriorating Items Considering Partial Upstream Trade Credit Financing

Z. H. Aliyu, B. Sani

Asian Research Journal of Mathematics, Page 69-80
DOI: 10.9734/arjom/2021/v17i1130342

In this study, we developed an inventory system model under two – level trade credit where the supplier considers the retailer as credit risk but the retailer considers the customers as credit worthy. Therefore, the retailer is given a trade credit period on  proportion of the goods ordered whenever he/she pays for proportion of the goods immediately after delivery. In the same vein, the retailer passes the same grace to the customers but without attaching any condition as the customers are assumed credit worthy. This partial upstream trade credit is offered to reduce the risk of failure in payment on the business transaction especially that most retailers are involved in bulk orders. The relevant cost functions are determined and a numerical example is given. Sensitivity analysis was carried out to see the effect of changes in parameters on the optimal solution of the model.