13.Generating Funtion and a New Calculating Formula of the Sum Power of Natural Numbers幂和序列的生成函数与幂和新的计算公式 14.Two Sided Power Series and Singular Point of the K-analytic FunctionK-解析函数的双边幂级数与孤立奇点 15.A new method of derivative of power-exponential function;幂指...
integral formulatransformationcalculusIn the evaluation of the power flow in some millimeter RF structures, a new kind of integral of the type int[Azeta v(kr)+Bzeta -v(kr)][Azeta v (kr)+Bzeta -v(kr)]dr/r, in which zeta plusmnv (kr) denotes arbitrary Bessel functions of real order...
Comparing this formula with (2.6) we obtain (2.7).□ Lemma 2.1 shows that under the power transformation (2.4) the vector exponents Q and the vector coefficients FQ undergo linear transformations as vectors of the dual spaces ℝn and ℝ*n respectively, since their scalar products are preser...
elements then the formula to find the number of subsets of a set in a power set is given by: |p(a)| = 2 n for example, set a = {1, 2, 3} n = number of elements of a = 3 so, the number of subsets in a power set of a will be: subsets of a = {}, {1}, {2},...
The SC technique signal we deduce the duty cycle formula by: $$\alpha = \frac{1}{{{V_{dc}}}\left( {{V_{dc}} - {V_{PV}} + L\dot M - \frac{L}{{T_2}}{\sigma_{I_L}}} \right)$$ (41) Figure9illustrates the working principle of the proposed MPPT-SC technique. Figure...
(differential calculus and Lagrange multipliers) are applied to determine limits on power yield in thermal generators (engines). For the upper fluid, the so-called Carnot temperature T’ is introduced as an effective quantity that replaces the bulk temperature T1 in the Carnot formula applied for...
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This results in the contradiction that \theta _u(a)>\pi as mentioned above. Let us give some indication as how to obtain the last-mentioned differential inequality. Again by the coarea formula \begin{aligned} -\mu _w^\prime (t)+\mu _{w_0}^\prime (t)=\int _{\{w=t\}}\frac{...
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such as fast convergence and avoiding trapping in a local minimum [44]. Thus, CGO has been used in solving many engineering problems [45,46,47]. From the above discussion, the controller enhancements come from the appropriate fractional calculus, using a cascade controller (CC), and fine-tuni...