It turned out the scientist didn't drink and had done all the trials using mathematical theory.
We prove (2.10) by using mathematical induction.
We proceed by using mathematical induction.
(6.2). for every by using mathematical induction.
By using mathematical concepts, we can draw interesting shapes.
I have created the following drawings by using mathematical formulas.
Make it a fun poem by using Mathematical analogies.
By using rigorous mathematical theory, the sufficient condition is drawn for the stability of error dynamics based on the Lyapunov stability theory, where the controllers are designed by using the sum of the relevant variables in hyperchaotic systems.
In this paper, the stability of the reverse dual indenter algorithms proposed by Chollacoop et al. [Acta Mater. 51 (2003) 3713] to determine the plastic properties of materials has been explored further by using the mathematical theory of inverse problems.
The dielectric constant values of 6F-PEI and 6F-CoPEI were estimated by additive group contribution calculation using mathematical equations defined by the Lorentz Lorenz's theory and the Vogel's theory, and by Vora Wang equations, respectively.
