Journal of Mathematics Research
ISSN / EISSN : 1916-9795 / 1916-9809
Published by: Canadian Center of Science and Education (10.5539)
Total articles ≅ 960
Latest articles in this journal
Published: 9 May 2022
Journal of Mathematics Research, Volume 14; https://doi.org/10.5539/jmr.v14n3p10
In this paper, the finite difference method is used to solve the positive fractional derivative damped string vibration equations, and the vibration attenuation phenomenon of the model is described by numerical simulation. In numerical examples, the effects of the order of the positive definite fractional derivative and the damping coefficient on vibration are studied and compared respectively. The results show that, on the one hand, when the damping coefficient c is fixed, the closer the order p(0 < p < 1) is to 1, the faster the attenuation is. On the other hand, when the order p is fixed, the larger the damping coefficient c is, the faster the attenuation is.
Published: 9 May 2022
Journal of Mathematics Research, Volume 14; https://doi.org/10.5539/jmr.v14n3p20
This article establishes a geometrical and mathematical bridge between the universal constant π and the golden ratio φ by interrelating the construction of the area of a circle using two approaches: one formed using the rotation of a regular unit pentagon and the other one from the rotation of its inverse ― the pentagram of side reference φ . The mathematical end result is a linear expression of π as a function of φ . As an interesting side result, an expression for the area of a circle is derived based on the golden ratio φ and a geometrically motivated coefficient. A scripted program for the verification of the derived expressions is provided.
Published: 24 April 2022
Journal of Mathematics Research, Volume 14; https://doi.org/10.5539/jmr.v14n3p1
In most of the various stepwise confidence interval procedures formulated for identifying maximum safe dose (MSD), homogeneity of variances among different dose levels were required. But in practice, homogeneity of variance is often in doubt. This paper proposes a stepwise confidence set procedure for identifying MSD of drugs based on ratio of population means for normally distributed data under heteroscedasticity without the need for multiplicity adjustment. The procedure employed Fieller's method and obtained individual (1-α)100% confidence intervals for identification of the MSD. We illustrate the procedure with a real life example. In addition, we show that power of the procedure increases with increasing ratio of means, and sample size. Power however decreases with increase in clinical relevance margins. We also illustrate that the new procedure can properly control familywise error rate (FWER).
Published: 31 March 2022
Journal of Mathematics Research, Volume 14; https://doi.org/10.5539/jmr.v14n2p63
Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 14, No. 2
Published: 24 March 2022
Journal of Mathematics Research, Volume 14; https://doi.org/10.5539/jmr.v14n2p52
We proposed and studied a flexible distribution with wider applications called Generalized Burr X Lomax (GBX-L) distribution. Some well-known mathematical properties such as ordinary moments, incomplete moment probability weighted moments, stress-strength model, mean residual lifetime, characteristic function, quantile function, order statistics and Renyi entropy of GBX-L distribution are investigated. The expressions of order statistics are derived. Parameters of the derived distribution are obtained using the maximum likelihood method and simulation studied is carried out to examine the validity of the method of estimation. The applicability of the proposed distribution is exemplified using aircraft data.
Published: 24 March 2022
Journal of Mathematics Research, Volume 14; https://doi.org/10.5539/jmr.v14n2p39
This work introduces a new three-parameter modified extended inverted Weibull (MEIW) distribution which is a hybrid of the one-parameter inverted Weibull distribution. The density function of the MEIW can be expressed as a linear combination of the inverted Weibull densities. Some mathematical properties of the proposed MEIW model such as ordinary and incomplete moments, mean residual life, and mean waiting time, Tsallis entropy, moment generating function and order statistics are investigated. The maximum likelihood estimation method is considered to estimate the parameters of the MEIW model. The relevance of the MEIW model is studied via an application to neck cancer data.
Published: 23 March 2022
Journal of Mathematics Research, Volume 14; https://doi.org/10.5539/jmr.v14n2p19
This article presents a new way to determine the value of π, using as an approach the area formed by the interference pattern of several rotating unit squares. The same approach is then applied to other N-sided unit polygons (i.e., triangles, pentagons and hexagons) to investigate how they affect this proportionality between circularity and linearity to a degree other than orthogonal (i.e., when the system axes do not form a right-angle, expressible in the new method as an approach that uses squares). Applied examples involving the Earth’s size and an orbiting satellite constellation are given.
Published: 3 March 2022
Journal of Mathematics Research, Volume 14; https://doi.org/10.5539/jmr.v14n2p1
We give a proof of the so-called Sylvester criterion for quadratic forms (for real symmetric matrices), based on elementary optimality properties of quadratic functions.
Published: 3 March 2022
Journal of Mathematics Research, Volume 14; https://doi.org/10.5539/jmr.v14n2p6
A three-dimensional compressible problem with different components is fundamental in numerical simulation of enhanced oil recovery. The mathematical model consists of a parabolic equation for the pressure and a convection-diffusion system for the concentrations. The pressure determines Darcy velocity and plays an important role during the whole physical process. A conservative mixed volume element is used to discretize the flow equation, and improves the computational accuracy of Darcy. The concentrations are computed by the modified characteristic fractional step difference scheme, thus numerical dispersion and nonphysical oscillations are eliminated. The whole three-dimensional computation is accomplished effectively by solving three successive one-dimensional problems in parallel, where the speedup method is used and the work is decreased greatly. Based on the theory and special techniques of a priori estimates of partial differential equations, an optimal second error estimates in L^2-norm is concluded. This work concentrates on the model, numerical method and convergence analysis for modern oil recovery.
Published: 29 January 2022
Journal of Mathematics Research, Volume 14; https://doi.org/10.5539/jmr.v14n1p84
Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 14, No. 1