Utilizing ACP Alpha Beta (αβ) Nonlinear Mathematics for Analyzing Astrophysics and Electrostatic Separation Data (Applications 3 and 4)  

作　　者：Ralph W. Lai Melisa W. Lai-Becker Grace Cheng-Dodge Michael L. Rehmet Ralph W. Lai;Melisa W. Lai-Becker;Grace Cheng-Dodge;Michael L. Rehmet(28 Cornerstone Ct., Doylestown, PA, USA;Harvard Medical School, Harvard University, Cambridge, MA, USA;Independent Educational Consultants, West Hartford, CT, USA;Department of Applied Mathematics and Computer Science, Brown University, Providence, RI, USA)

机构地区：[1]28 Cornerstone Ct., Doylestown, PA, USA [2]Harvard Medical School, Harvard University, Cambridge, MA, USA [3]Independent Educational Consultants, West Hartford, CT, USA [4]Department of Applied Mathematics and Computer Science, Brown University, Providence, RI, USA

出　　处：《Journal of Applied Mathematics and Physics》2024年第11期3706-3727,共22页应用数学与应用物理（英文）

摘　　要：Analyses of astrophysics and electrostatic separation data were illustrated with the Asymptotic Curve Based and Proportionality Oriented (ACP) nonlinear math for relating two physical variables. The fundamental physical law asserts that the nonlinear change of continuous variable Y is proportional to the nonlinear change in continuous variable X. Mathematically, this is expressed as dα{Y, Yu, Yb} = −Kdβ{X, Xu, Xb}, with Yu, Yb, Xu, and Xb representing the upper and baseline asymptotes of Y and X. Y is the continuous cumulative numbers of the elementary y and X is the continuous cumulative numbers of elementary x. K is the proportionality constant or equally is the rate constant.Analyses of astrophysics and electrostatic separation data were illustrated with the Asymptotic Curve Based and Proportionality Oriented (ACP) nonlinear math for relating two physical variables. The fundamental physical law asserts that the nonlinear change of continuous variable Y is proportional to the nonlinear change in continuous variable X. Mathematically, this is expressed as dα{Y, Yu, Yb} = −Kdβ{X, Xu, Xb}, with Yu, Yb, Xu, and Xb representing the upper and baseline asymptotes of Y and X. Y is the continuous cumulative numbers of the elementary y and X is the continuous cumulative numbers of elementary x. K is the proportionality constant or equally is the rate constant.

关 键 词：Alpha Beta (αβ) Nonlinear Math Asymptotic Concave and Convex Curve Upper and Baseline Asymptote Demulative Numbers (Opposite to Cumulative Numbers) Coefficient of Determination (COD) Proportionality and Position Constant Skewed Bell and Sigmoid Curve 

分 类 号：O17[理学—数学]