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Journal of Mathematics Research
Number of Followers: 0  Open Access journalISSN (Print) 1916-9795 - ISSN (Online) 1916-9809 Published by CCSE  [43 journals]
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- Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 13,
No. 6
PubDate: Mon, 29 Nov 2021 12:18:43 +000
- Analysis of Social-Economic Factors on Population Change in Heilongjiang
Province
Abstract: 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.
PubDate: Mon, 29 Nov 2021 01:38:48 +000
- Extended Pythagoras Theorem Using Hexagons
Abstract: 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.
PubDate: Mon, 22 Nov 2021 01:43:25 +000
- Determinants of Capital Adequacy Ratio of Banks in Botswana
Abstract: 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.
PubDate: Sat, 13 Nov 2021 04:03:25 +000
- N(2,2,0) Algebras and Related Topic
Abstract: 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.
PubDate: Fri, 29 Oct 2021 02:54:42 +000
- A New Framework for the Determination of the Eigenvalues and
Eigenfunctions of the Quantum Harmonic Oscillator
Abstract: 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.
PubDate: Wed, 27 Oct 2021 10:19:50 +000
- Linearized Homotopy Perturbation Method for Two Nonlinear Problems of
Duffing Equations
Abstract: 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.
PubDate: Wed, 27 Oct 2021 09:32:42 +000
- Novel Modeling of Parameters Related to Intra-Firm Diffusion Innovation
Abstract: 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.
PubDate: Wed, 20 Oct 2021 00:55:16 +000
