It is well known that the classical Simpson quadrature formula is not applicable when the function ϕ is not four times differentiable or when its fourth derivative \phi ^{(4)} is unbounded over the interval (\sigma ,\rho ). Recently, various authors have drawn attention to Simpson-type ...
This is not true in unbounded domains. Consider for example a smooth bounded non-constant function φ(x), –∞ < x < +∞ with a bounded derivative which has limits φ(±∞) at plus and minus infinity. Translations of this function (133)φ(x−ct), −∞<x<+∞,...
Question: If a function {eq}f :[a,b] \rightarrow \Re {/eq} is bounded and has at most finitely many discontinuities on {eq}[a,b] {/eq}, prove that {eq}f \in R[a,b] {/eq} }] Reimann Integration for Discontinuous Funct...
The pH closed-loop (21) in z coordinates results differentiating (10) with respect to time and the control law (20). (ii) We propose (12) as candidate ISS Lyapunov function and we compute its time derivative along the solutions of (21) as follows (22)H̄̇z=−k1‖∇z1Hz‖...
We extend the Matomäki–Radziwiłł theorem to a large collection of unbounded multiplicative functions that are uniformly bounded, but not necessarily bounded by 1, on the primes. Our result allows us to estimate averages of such a functionfin typical intervals of length, withand whereis ...
whereTTis transmissivity [L²/T],SSis storativity [-],ttis time since pumping began [T] andw(u)w(u)is the Theis well function [-]. Similarly, head buildup due to the recharging image well located at a distancer2r2from the observation well is given by: ...
structure function exponentsWe investigate a class of one-dimensional bounded random cascade models which are multiplicative and stationary by construction but additive and non-stationary with respect to some, but not all, of their statistical properties. In essence, a new parameter H>0 is introduced...
adjective.having bounds or limits. Mathematics. (of a function) having a range with an upper bound and a lower bound. Can unbounded sequence converge? Sounbounded sequence cannot be convergent. Can a divergent sequence be bounded? Abounded sequence cannot be divergent....
Almeida, R.: A Caputo fractional derivative of a function with respect to another function. Commun. Nonlinear Sci. Numer. Simul., 44, 460-481 (2017) https://doi.org/10.1016/j.cnsns.2016.09.006 Article MathSciNet MATH Google Scholar Almeida, R., Malinowska, A. B., Monteiro, M. T....
Fig. 2. (a) State responses (b) Variation in control input (c) Lyapunov function (d) Individual Lyapunov function for both discrete events (e) Derivative of Lyapunov function (f) Individual derivative of Lyapunov function for both discrete event with matched uncertainties. Download: Download high...