scholarly journals Exponential Functions with Base e in Growth Analysis and Deriving Them from Rotations of Axes of Time Described using Euler's Formula

10.5109/4527 ◽  
2003 ◽  
Vol 48 (1/2) ◽  
pp. 65-69
Author(s):  
Masataka Shimojo ◽  
Kentaro Ikeda ◽  
Yoki Asano ◽  
Reiko Ishiwaka ◽  
Tao Shao ◽  
...  
Keyword(s):  
Growth Analysis ◽  
Exponential Functions ◽  
Euler’S Formula

From universalism to individualism: New approaches to economic growth analysis

2019 ◽  
pp. 108-126
Author(s):  
Ivan L. Lyubimov
Keyword(s):  
Economic Growth ◽  
Structural Transformation ◽  
Emerging Economies ◽  
Growth Analysis ◽  
Extended Period ◽  
Economic Policies ◽  
Adequate Account ◽  
New Approaches ◽  
Catching Up

This paper examines the evolution of academic and applied approaches to analyze the problem of economic growth since the mid-XX century. For quite an extended period of time, these views were corresponding to universalist economic policies taking no adequate account of particularities and limitations that a certain catching-up economy embodied. New approaches analyzing the problems of economic growth, on the contrary, individualize growth diagnostics, structural transformation and the organization of reforms processes for the emerging economies. We argue that individualist approaches might be potentially more effective than the universalist ones for solving the problem of slow economic growth.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

scholarly journals Cauchy matrix and Liouville formula of quaternion impulsive dynamic equations on time scales

2020 ◽  
Vol 18 (1) ◽  
pp. 353-377 ◽  
Author(s):  
Zhien Li ◽  
Chao Wang
Keyword(s):  
Time Scales ◽  
Quaternion Algebra ◽  
Matrix Exponential ◽  
Dynamic Equations ◽  
Necessary Condition ◽  
Quaternion Matrix ◽  
Exponential Functions ◽  
Cauchy Matrix ◽  
Adjoint Matrix ◽  
Sufficient And Necessary Condition

Abstract In this study, we obtain the scalar and matrix exponential functions through a series of quaternion-valued functions on time scales. A sufficient and necessary condition is established to guarantee that the induced matrix is real-valued for the complex adjoint matrix of a quaternion matrix. Moreover, the Cauchy matrices and Liouville formulas for the quaternion homogeneous and nonhomogeneous impulsive dynamic equations are given and proved. Based on it, the existence, uniqueness, and expressions of their solutions are also obtained, including their scalar and matrix forms. Since the quaternion algebra is noncommutative, many concepts and properties of the non-quaternion impulsive dynamic equations are ineffective, we provide several examples and counterexamples on various time scales to illustrate the effectiveness of our results.

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