Market share is a major indication of business success. Understanding the impact of numerous economic factors on market share is critical to a company’s success. In this study, we examine the market shares of two manufacturers in a duopoly economy and present an optimal pricing approach for increasing a company’s market share. We create two numerical models based on ordinary differential equations to investigate market success. The first model takes into account quantity demand and investment in R&D, whereas the second model investigates a more realistic relationship between quantity demand and pricing.

In this study, a brand-new double transform known as the double INEM transform is introduced. Combined with the definition and essential features of the proposed double transform, new findings on partial derivatives, Heaviside function, are also presented. Additionally, we solve several symmetric applications to show how effective the provided transform is at resolving partial differential equation.

Breast cancer has got much attention in the recent years as it is a one of the complex diseases that can threaten people lives. It can be determined from the levels of secreted proteins in the blood. In this project, we developed a method of finding a threshold to classify the probability of being affected by it in a population based on the levels of the related proteins in relatively small case-control samples. We applied our method to simulated and real data. The results showed that the method we used was accurate in estimating the probability of being diseased in both simulation and real data. Moreover, we were able to calculate the sensitivity and specificity under the null hypothesis of our research question of being diseased o

Background: The pandemic crisis prompted the world to adopt unexpected approaches to continue life as normally as possible. The education sector, including professors, students, and the overall teaching system, has been particularly affected. Objective: This study seeks to evaluate the benefits, challenges, and strategies related to COVID-19 from the perspectives of college students, particularly those in higher education in Iraq. Method: The online survey questionnaire was distributed via Google Forms and specifically aimed at undergraduate dental students. Results: A total of 348 students participated in the survey. There was a significant correlation (P > 0.01) between student satisfaction with hybrid learning and their experi

This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n ＋ 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended appro