The Principle of Mathematical Induction: Applications in Physical Optics by Joseph Ivin Thomas

“…The bare rudiments of the principle of mathematical induction as a method of proof date back to ancient times. …”
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Global Exponential Stability of a Discrete-Time Rayleigh System with Delays by Bangyu Shen

“…By using the mathematical induction method, some sufficient conditions are proposed for the global exponential stability of the discrete-time Rayleigh system. …”
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Global exponential synchronization of discrete-time high-order BAM neural networks with multiple time-varying delays by Er-yong Cong, Li Zhu, Xian Zhang

“…We investigate novel delay-dependent global exponential stability criteria for the error system by proposing a mathematical induction method. The global exponential stability criteria that have been obtained are described through linear scalar inequalities. …”
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Periodic Solution for a Max-Type Fuzzy Difference Equation by Changyou Wang, Jiahui Li

“…Then, the expression for the periodic solution of the max-type ordinary difference equations is obtained by the iteration, the inequality technique, and the mathematical induction. Moreover, we can obtain the expression for the periodic solution of the max-type fuzzy difference equation. …”
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Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional Subdiffusion/Superdiffusion Equations by Meilan Qiu, Liquan Mei, Dewang Li

“…Discretizing the time Caputo fractional derivative by using the backward Euler difference for the derivative parameter (0<α<1) or second-order central difference method for (1<α<2), combined with local discontinuous Galerkin method to approximate the spatial derivative which is defined by a fractional Laplacian operator, two high-accuracy fully discrete local discontinuous Galerkin (LDG) schemes of the time-space fractional subdiffusion/superdiffusion equations are proposed, respectively. Through the mathematical induction method, we show the concrete analysis for the stability and the convergence under the L2 norm of the LDG schemes. …”
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