Journal of Mathematics Research
ISSN / EISSN : 1916-9795 / 1916-9809
Published by: Canadian Center of Science and Education (10.5539)
Total articles ≅ 946
Latest articles in this journal
Published: 21 November 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n6p52
The population is a constituent element of human society and is one of the indicators of a country's comprehensive strength. The quantity and quality of population directly determine the level of development of a country or region. Too small a population makes a country or region lack the motivation to develop, and too large a population strains local resources. Therefore, the state introduces relevant policies to regulate the population quantity in China. The analysis of the factors influencing the change in population size helps assess the current state of development and is essential for planning its future prosperity. This paper analyzes the impact of social-economics factors on population size change in Heilongjiang province since China's reform and opening up using double-logarithmic model (DLM) estimated by Elastic Net estimation (ENE). Meanwhile, this paper provides some policy recommendations to promote the growth of population size in Heilongjiang Province.
Published: 21 November 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n6p46
This article provides the geometric and algebraic proof of the variant equation of the Pythagorean theorem x^2-xy+y2=z^2 . The hypothesis that will be proven is that just as squares govern the original version x^2+y^2=z^2 , hexagons are found to govern x^2-xy+y^2=z^2 . Both the special case x=y and general case of x≠y are examined.
Published: 9 November 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n6p38
Capital Adequacy Ratio (CAR) plays a very important role in the financial success of banks and acts as a buffer to prevent and absorb any unexpected losses. This study examines explanatory variables that influence CAR for nine banks in Botswana. Multiple linear regression was used for analysis, with CAR as the dependent variable and thirteen financial ratios as the independent variables. The study period is 2015-2019. Based on the data for this period, it was established that out of the thirteen financial ratios utilised, only four were found to have significant impact on the CAR of the nine banks under study, which are: Asset to Equity Ratio (A E), Return on Equity (ROE), Non-Performing Loans Ratio (NPL RATIO) and the Cost-to-Income Ratio (C I). The A E Ratio was found to be the most influential driver of the CAR and the NPL Ratio was found to be the least influential driver of the CAR for the banks under study.
Published: 28 October 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n6p27
In this paper, we investigate the elementary properties of the N(2,2,0)-algebra. Especially, some properties of nilpotent N(2,2,0)-algebras are presented. Also some relationships between nilpotent N(2,2,0)-algebra and other algebras with the type of (2,0) are obtained.
Published: 27 October 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n6p10
In the paper, we solve two nonlinear problems related to the Duffing equations in space and in time. The first problem is the bifurcation of Duffing equation in space, wherein a critical value of the parameter initiates the bifurcation from a trivial solution to a non-trivial solution. The second problem is an unconventional periodic problem of Duffing equation in time to determine period and periodic solution. To save computational cost and even enhance the accuracy in seeking higher order analytic solutions of these two problems, a modified homotopy perturbation method is invoked after a linearization technique being exerted on the Duffing equation, whose nonlinear cubic term is decomposed at two sides via a weight factor, such that the Duffing equation is linearized as the Mathieu type differential equation. The constant preceding the displacement is expanded in powers of homotopy parameter and the coefficients are determined to avoid secular solutions appeared in the derived sequence of linear differential equations. Consequently, after setting the homotopy parameter equal to unity and solving the amplitude equation, the higher order bifurcated solutions can be derived explicitly. For the second problem, we can determine the period and periodic solution in closed-form, which are very accurate. For the sake of comparison the results obtained from the fourth-order Runge-Kutta numerical method are used to evaluate the presented analytic solutions.
Published: 27 October 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n6p20
This study was designed to obtain the energy eigenvalues and the corresponding Eigenfunctions of the Quantum Harmonic oscillator through an alternative approach. Starting with an appropriate family of solutions to a relevant linear di erential equation, we recover the Schr¨odinger Equation together with its eigenvalues and eigenfunctions of the Quantum Harmonic Oscillator via the use of Gram Schmidt orthogonalization process in the usual Hilbert space. Significantly, it was found that there exists two separate sequences arising from the Gram Schmidt Orthogonalization process; one in respect of the even eigenfunctions and the other in respect of the odd eigenfunctions.
Published: 20 October 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n6p1
In this paper, we present a novel intra-firm diffusion model to predict the variation of Penetration Level (PL) with the Intensity of Use (IU) and Speed of Adoption (SA) with respect to information and communication technologies (I.C.T) within Tunisian Small Medium Enterprises (SMEs). The study was motivated by the work of Youssef et al., (2014), and its inspired data scope/range. The method of modeling focuses on optimization and non-linear regression. The first model has the capacity to compute the variation of PL with IU. However, this first model was modified to a second model through transformation in order to derive physical meaning to the parameters. The modified second model shows a quasi-vertical curvature which approximates the reciprocal of hyperbolic tangent. The Variation of PL with the SA was computed using the second model which estimated the parameters with the variables explaining about 62% variation in PL with SA χ2=0.0655, R2=0.61651 . We further formulated a third model to predict correlation of SA with PL, while imposing boundary assumptions to avoid problems of divergence; with the final model having a PL as the only adjustable parameter. The model exhibited a plateau effect at points (0.9933,0.4373) and (0,0) between two steeply vertical asymptotes at -0.06105 and 1.0013, respectively. The developed model can be useful for eliciting information when data from different countries (or surveys) are compared for same or different span time through examining the behavior of the parameters, especially after Covid-19 era.
Published: 29 September 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n5p32
In this paper, we introduce Tribonacci and Tribonacci-Lucas hybrinomials and derive these hybrinomials by the matrices. We present Binet formulas, generating functions, exponential generating functions and summation formulas, some properties of these hybrinomials. Moreover, we obtain relationship between the Tribonacci and Tribonacci-Lucas hybrinomials.
Published: 22 September 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n5p24
The Extended Routh Array (ERA) settles the asymptotic stability of complex polynomials. The ERA is a natural extension of the Routh Array which applies only to real polynomials. Although the ERA is a nice theoretical algorithm for stability testing, it has its limitations. Unfortunately, as the order of the polynomial increases, the size of calculations increases dramatically as will be shown below. In the current work, we offer an alternative algorithm which is basically equivalent to the ERA, but has the extra advantage of being simpler, more efficient, and easy to apply even to large order polynomials. In all the steps required in the construction of the new algorithm, only one single and simple algebraic operation is needed, which makes it a polynomial order-independent algorithm.
Published: 21 September 2021
Journal of Mathematics Research, Volume 13; https://doi.org/10.5539/jmr.v13n5p14
In this paper, Label Setting Algorithm and Dynamic Programming Algorithm had been critically examined in determining the shortest path from one source to a destination. Shortest path problems are for finding a path with minimum cost from one or more origin (s) to one or more destination(s) through a connected network. A network of ten (10) cities (nodes) was employed as a numerical example to compare the performance of the two algorithms. Both algorithms arrived at the optimal distance of 11 km, which corresponds to the paths 1→4→5→8→10 ,1→3→5→8→10 , 1→2→6→9→10 and 1→4→6→9→10 . Thus, the problem has multiple shortest paths. The computational results evince the outperformance of Dynamic Programming Algorithm, in terms of time efficiency, over the Label Setting Algorithm. Therefore, to save time, it is recommended to apply Dynamic Programming Algorithm to shortest paths and other applicable problems over the Label-Setting Algorithm.