Green’s Theorem is another higher dimensional analogue of the fundamental theorem of calculus: it relates the line integral of a vector field around a plane curve to a double integral of “the derivative” of the vector field in the interior of the curve. It admits two different but completely equivalent formulations, a “flux” version for normal line integrals and a “circulation” version for tang...

NURBS curve is applied to model and machine of integral impeller get better smooth streamline in this work. In order high precision surface modeling impeller, complex method for studied through inputting curves surfaces obtained by MATLAB into CAXA Manufacturing Engineer, which solves the problem that cannot be designed directly CAD software. Grooving expanding groove tool paths are according t...

We reconsider the Euclidean version of the photon number integral introduced in [1]. This integral is well defined for any smooth non-selfintersecting curve in R . Besides studying general features of this integral (including its conformal invariance), we evaluate it explicitly for the ellipse. The result is nellipse = (ξ −1 + ξ)π, where ξ is the ratio of the minor and major axes. This is in ag...

This study investigates how students understand and apply the area under the curve concept and the integral-area relation in solving introductory physics problems. We interviewed 20 students in the first semester and 15 students from the same cohort in the second semester of a calculus-based physics course sequence on several problems involving the area under the curve concept. We found that on...

The mathematical model of many physical problems takes the form of the well-known Abel integral equation. This equation was applied by Niels Abel in 1823 to describe a sliding point mass in a vertical plane on a unknown curve under gravitational force. The point mass starts its motion without initial velocity from a point which has a vertical distance x from the lowest point of the curve [1]. U...

Abstract. The goal of this paper is to construct the p-adic analytic family of overconvergent half-integral weight modular forms using Hecke-equivariant overconvergent Shintani lifting. The classical Shintani map(see [Shn]) is the Hecke-equivariant map from the space of cusp forms of integral weight to the space of cusp forms of half-integral weight. Glenn Stevens proved in [St1] that there is ...

Here we will follow some of the presentation from Werner, Manby, and Knowles. 1 Density fitting is a way to approximate the usual two-electron integrals, (pq|rs) = dr 1 dr 2 φ p (r 1)φ q (r 1) 1 r 12 φ r (r 2)φ s (r 2), (1) where we have assumed real orbitals. We may also consider this electron repulsion integral as the repulsion between two generalized electron densities,

Let C A n be a geometrically irreducible aane curve of (geometric) genus 0 deened over Z such that C(Z) is an innnite set. We use elementary methods to describe the distribution of C(Z) in C(R) relative to the real topology. The study of integral points on aane curves has a long history. The deenitive niteness theorem, due to Siegel 5], says that a geometrically irreducible aane curve C has onl...