Education Commons^™

(R2054) Convergence Of Lagrange-Hermite Interpolation Using Non-Uniform Nodes On The Unit Circle, Swarnima Bahadur, Sameera Iqram, Varun .

Applications and Applied Mathematics: An International Journal (AAM)

In this research article, we brought into consideration the set of non-uniformly distributed nodes on the unit circle to investigate a Lagrange-Hermite interpolation problem. These nodes are obtained by projecting vertically the zeros of Jacobi polynomial onto the unit circle along with the boundary points of the unit circle on the real line. Explicitly representing the interpolatory polynomial as well as establishment of convergence theorem are the key highlights of this manuscript. The result proved are of interest to approximation theory.

Early Exposure/Long-Term Gains: Encouraging Underrepresented Middle School Students To Pursue Stem Careers, Trinetia Respress, Owen Johnson, Londee Boyd, Twianie Roberts

The Journal of the Research Association of Minority Professors

Preparing middle school students in STEM for their transition to high school and ultimately for post-secondary endeavors requires early exposure to STEM subjects. This early exposure not only builds a foundation for the ever-changing skills that are needed for the workforce, but also boosts student achievement and test scores (STEM Education Works, 2021). The MUREP project focuses on increasing the number of underrepresented minority students interested in STEM fields. The purpose of this study is to examine underrepresented minority middle school students’ attitudes toward STEM and their expressed interest in STEM post-secondary subjects and careers after participation in the MUREP …

(R2052) Flow Patterns For Newtonian And Non-Newtonian Fluids In A Cylindrical Pipe, Erick Sanchez, Dambaru Bhatta

Applications and Applied Mathematics: An International Journal (AAM)

A fully developed laminar steady flow of an incompressible, viscous fluid in a horizontal cylindrical pipe is considered here. Flow patterns for an incompressible, viscous fluid for both Newtonian and non-Newtonian fluids such as shear-thinning, shear-thickening and Bingham plastic fluids are analyzed in this study. Assuming that the flow is only due to the wall shear stress and the pressure drop, the velocity component in the axial direction for these cases is derived. Computational results of the velocity profiles for various cases are obtained using MATLAB and presented in graphical forms. It is observed that the velocity profile is parabolic …

The Impact Of Personal And Service-Related Factors On The Perceived Academic Success Among College Students, Ronnie Davis, Geraldine Doucet, Terayana Lamb, Sonya Sneed, David Fletcher

The Journal of the Research Association of Minority Professors

In recent years, student completion of the first year and second-year college curriculum has become a significant barrier to student success and retention especially at Historically Black Colleges and Universities. Despite low pass and retention rates, many degree programs in the U.S. require at least one college-level mathematics course, and the failure in this math course has contributed disproportionately to the failure to complete the first- and second-year curriculum.

The purpose of this study was to examine the predictability of the relationship between selected personal, academic, and service-related factors and the perceived academic success in mathematics among college students. Specifically, …

An Optimal Control Problem Solution For Chemical Reactor, Dias Nurmagambetov

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we describe one of the solutions of a nonlinear optimal control problem for a chemical reactor. A solution on finding a chemical reactor’s optimal temperature regime for having a maximum concentration of final product is presented. The optimal control has been found by immersion method for boundary value problem with a phase and control restrictions. This method is reducing the original boundary value problem to a special optimal control problem, using the general solution of the Fredholm integral equation of the first kind. With this method's solution had been created a software for the problem calculations. Analysis …

Theoretical Study Of Mach Number And Compressibility Effect On The Slender Airfoils, Abrar Hoque, Masudar Rahman, Ashabul Hoque

Applications and Applied Mathematics: An International Journal (AAM)

Theoretical development of the velocity potential equation for compressible flow and its various consequences has been presented. The geometrical interpretation of potential equation and conformal mapping technique are discussed where the mappings link the flow around a circular cylinder of a slender airfoil. The lift and drag coefficients are determined for the slender airfoils based on the Mach number and compressibility effects. The calculated lift coefficients show that with the increasing of attack angle it increases linearly and a higher lift coefficient is found for a smaller Mach number for any certain attack angle. Similarly, the drag profiles are determined …

Modeling And Analysis Of The Impact Of Vocational Education On The Unemployment Rate In Nigeria, Abayomi Ayoade, Opeyemi Odetunde, Bidemi Falodun

Applications and Applied Mathematics: An International Journal (AAM)

Unemployment is a major determinant of a weak economy and a good measure of living standard in a country. Nigeria is faced with the problem of unemployment at present. By that, a mathematical model is formulated to investigate the effect of vocational education on the unemployment challenges in Nigeria. The model is tested for the basic requirements of a good mathematical model. The equilibrium analysis of the model is conducted and both the unemployment-free and the unemployment endemic equilibria are obtained. The threshold for the implementation success of the vocational education program is also derived following the approach of epidemic …

An Interpolation Process On The Roots Of Ultraspherical Polynomials, R. Srivastava, Yamini Singh

Applications and Applied Mathematics: An International Journal (AAM)

The paper is devoted to studying a Pál-type interpolation problem on the roots of Ultraspherical polynomials of degree n-1 with parameter k+1 on the closed interval -1 to 1. The aim of this paper is to find a unique interpolatory polynomial of degree at most m equal to 2n+2k+1 satisfying the interpolatory conditions that is, function values of the polynomial of degree m at the zeros of the function values of the ultraspherical polynomials and the first derivative values of the polynomial of degree m at the zeros of the first derivative values of the ultraspherical polynomials.We will use the …

A Numerical Method For Functional Hammerstein Integro-Differential Equations, L. Saeedi, A. Tari

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a numerical method is presented to solve functional Hammerstein integro-differential equations. The presented method combines the successive approximations method with trapezoidal quadrature rule and natural cubic spline interpolation to solve the mentioned equations. The existence and uniqueness of the problem is also investigated. The convergence and numerical stability of the problem are proved, and finally, the accuracy of the method is verified by presenting some numerical computations.

Farlie-Gumbel-Morgenstern Family: Equivalence Of Uncorrelation And Independence, G. Barmalzan, F. Vali

Applications and Applied Mathematics: An International Journal (AAM)

Considering the characteristics of the bivariate normal distribution, in which uncorrelation of two random variables is equivalent to their independence, it is interesting to verify this problem in other distributions. In other words, whether the multivariate normal distribution is the only distribution in which uncorrelation is equivalent to independence. In this paper, we answer to this question and establish generalized Farlie-Gumbel-Morgenstern (FGM) family is another family of distributions under which uncorrelation is equivalent to independence.

On The Stability Of A Pexiderized Functional Equation In Intuitionistic Fuzzy Banach Spaces, Nabin C. Kayal, Pratap Mondal, T. K. Samanta

Applications and Applied Mathematics: An International Journal (AAM)

During the last few decades several researchers have been devoted to establishing stability of different kinds of functional equations, differential equations, functional differential equations, fractional differential equations, etc. under different sufficient conditions in different spaces like Banach spaces, Banach modules, fuzzy Banach spaces etc. In this paper, we remain confined in the discussion of stability of functional equations in intuitionistic fuzzy Banach spaces. Ulam was the first person who introduced an open question concerning the stability of a group homomorphism in an international conference. Thereafter several researchers have replied and are still replying to this open question in different contexts. …

An Optimal Reinsurance Contract From Insurer's And Reinsurer's Viewpoints, Ali P. Bazaz, Amir T. Payandeh Najafabadi

Applications and Applied Mathematics: An International Journal (AAM)

This article constructs two classes of appropriate reinsurance contracts from both an insurer’s and a reinsurer’s viewpoints. The first class, say C; has been constructed by minimizing the conditional tail expectation, say CTE, of an insurer’s random risk. Then an optimal reinsurance contract has been obtained by estimating the reinsurance’s random risk, using the Bayesian estimation method while the second class of reinsurance contracts, say C*; is obtained by minimizing a convex combination of the CTE of both the insurer’s and reinsurer’s random risks. These two approaches consider both the insurer’s and reinsurer’s viewpoints to establish an optimal reinsurance contract. …

On Calculation Of Failure Probability For Structures Designed Based On Magnitudes Of Historical Event, Farzad Noubary, Reza Noubary

Applications and Applied Mathematics: An International Journal (AAM)

During their operational life, structures may be subject to various types of live load caused by events such as earthquakes, high speed winds, etc. Given the design life of a structure, the probability for a specific live load to cause a failure depends on the magnitude of the load structure it is designed to withstand (designed load). In this article, methods are developed for calculation of the failure probability for structures designed to withstand loads comparable to historical loads at the site of interest.

Seir Model Of Seasonal Epidemic Diseases Using Ham, Nirmala P. Ratchagar, S. P. Subramanian

Applications and Applied Mathematics: An International Journal (AAM)

SEIR mathematical model of childhood diseases measles, chickenpox, mumps, rubella incorporate seasonal variation in contact rates due to the increased mixing during school terms compared to school holidays. Driven by seasonality these diseases are characterized by annual oscillations with variable contact rate which is a periodic function of time in years. Homotopy Analysis Method (HAM) is considered in this paper to obtain a semi analytic approximate solution of non-linear simultaneous differential equations. Mathematica is used to carry out the computations. Results established through graphs show the validity and potential of HAM for amplitude of variation greater than zero. Also, when …

Reverse-Traditional/Hands-On: An Alternative Method Of Teaching Statistics, Aliakbar M. Haghighi, Roozbeh Vakil, Johnson K. Wetiba

Applications and Applied Mathematics: An International Journal (AAM)

This paper presents a method for teaching statistics called the Reverse-Traditional/Hands-On (RT/HO) method. The method includes student-generated data, use of a statistical computing package such as MINITAB to introduce statistical terms and methods, and a statistical research component. An analytic comparison of students’ successes in courses using the Traditional and RT/HO methods is presented.