In this problem, we want to find the derivative of an integral, but since these are inverse processes, they essentially undo one another, and give us the function right back. We often write this as ddx∫axf(t) dt=f(x) This is often called the first part of the fundamental t...
(1.1) SHARP L2 BOUNDS FOR OSCILLATORY INTEGRAL OPERATORS WITH C ∞ PHASES Let T be an oscillatory integral operator on L^2(R) with a smooth real phase function S(x,y). We prove that, in all cases but the one described below, afte... VS Rychkov - 《Mathematische Zeitschrift》 被引量...
A problem of boundary control of string vibrations with the fixed end with a bounded control resource is studied. The integral of the second derivative module of the boundary control is minimized. Estimates of upper and lower bounds are found for the extremum. In the vibration suppression problem...
Bounds of the Derivative of Some Classes of Rational Functions Let $r(z)$ be a rational function with at most $n$ poles, $a_1, a_2, \\ldots, a_n,$ where $|a_j| > 1,$ $1\\leq j\\leq n.$ This paper investigates the estimate of the modulus of the derivative of a ration...
Proportional(P)-Integral(I)-Derivative(D) control is the most common control method since 1950 s [75]. A generic PID controller tracks a reference input by generating a control signal as a weighted linear combination of three terms that are proportional to the instantaneous error, the cumulative...
This paper discretizes the states, a method introduced in [18] for constant delayed systems, not only in constructing the Lyapunov–Krasovskii (L–K) functional but also in designing the integral inequality technique [17,19] for time-varying delayed systems, which increase the order of uncorrelat...
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of the Fractional Differential Equations. North-Holland Mathematics Studies. Elsevier, Amsterdam (2006) Google Scholar Koornwinder, T.H.: Fractional integral and generalized Stieltjes transforms for hypergeometric functions as...
B=bp.integral(0,rq) A=ap.integral(0,rq)/(mass*mq/100.) C=(B/(A))**(1/5) cost=opt_dict[kernel] N=len(self.p.Id)**(1/5)returnC*cost/N 开发者ID:lowks,项目名称:OpOpGadget,代码行数:32,代码来源:analysis.py 示例6: get_derivatives ...
This let us apply delay-dependent stability conditions as a function of the upper bounds on the time-varying delay magnitude and variation, that are treated in the integral quadratic constraint (IQC) framework. Final discussions are provided regarding expected tracking capabilities and agreement of ...
On the conformable fractional calculus.Journal of computational and Applied Mathematics, 279, pp. 57-66, 2015. 10.1016/j.cam.2014.10.016Search in Google Scholar [18] U. N. Katugampola, New approach to a generalized fractional integral, Appl. Math. Comput., vol.218, no.3 pp. 860-865, ...