Our main result-Theorem 3-gives a condition on the integrand that is necessary and sufficient for such represen- tation of the integral, with the largest natural class of Riemann sums. Some of the motivation for
运用D(x)函数说明在证明可测函数与简单函数的关系定理时把[0,n]划分的必要性以及鲁津定理的意义 In proving the theorem of relations between the measurable and the simple functions and significanc...
Linear Approximation of a Function at a Point Differentials and Amount of Error Summary of Linear Approximations and Differentials Introduction to Maxima and Minima Extrema and Critical Points Summary of Maxima and Minima Introduction to the Mean Value Theorem The Mean Value Theorem Summary...
Average Value of a Function Summary of the Definite Integral Introduction to the Fundamental Theorem of Calculus The Mean Value Theorem for Integrals Fundamental Theorem of Calculus Summary of the Fundamental Theorem of Calculus Introduction to Integration Formulas and the Net Change Theorem ...
Theorem 9.14 Finding a minimum star-shaped (resp. convex) partitioning of a simple polygon P with n vertices can be done in O(n5N2log n) time (resp. O(N2 n ln n)) where N is the number of reflex vertices of P. In the same paper, Keil also studies partitioning problems in which...
(s) < ε, A SIMPLE PROOF OF THE GENERALIZED STRONG RECURRENCE 3 hold when τ satisfies | exp(iτ log pn) − 1| < δ by (2.3) and Kronecker's approximation theorem (see for example [10, Lemma 1.8]). Because of the triangle inequality, there exists a D′ > 0 such that νT ...
Note, the gamma function is also well-defined for complex numbers, though this implementation currently does not handle complex numbers as input values. Nemes' approximation is defined here as Theorem 2.2. Negative values use Euler's reflection formula for computation. gamma(n: number): number ...
In the following, based on the fractional-order extension of the Lyapunov direct method and the new property of fractional derivatives, we will find a suitable Lyapunov function and propose the stability condition of the fractional chaotic system. Theorem 2 Take the fractional-order system $$ {...
Theorem 2.1. There exist a deterministic algorithm which provides an FPTAS for computing Z(λ, G) for an arbitrary graph/activity pair (G, λ) when Δ and λ are constants. Thus, while the running time of the algorithm depends polynomially on 1/δ (hence Fully Polynomial ...
One consequence of this theorem is that: If a curved surface is developed upon any other surface whatsoever, the measure of curvature in each point remains unchanged. In other words, surfaces with the same Gaussian curvature can be mapped into each other without any distortion. For example, sur...