A smooth curve in A is defined as a mapping c : I→ A of class C∞, where I is a non-empty open interval of ℝ, for example ]−1, 1[. Any such curve is said to be analytic if it is of class Cω. If E is a complex locally convex space, suppose again that A is a ...
Our techniques also enjoy good numerical performance, even in complex settings, and so offer a viable practical alternative to existing techniques, as well as providing theoretical optimality. 展开 关键词:Bandwidth curve estimation change point diagnostic discontinuity kernel least squares nonparametric ...
A regular oriented curve in a Finsler manifold (M, F) is a stationary point of the functional LF if and only ifγ is a geodesic from p to q. A curve γ from p = γ(0) to q = γ(1) is said to be minimizing if dF(p, q) = LF(γ). Since minimizing curve is a stational...
How do you fit the smoothest curve through a set of points? Suppose you have a set of increasing x valuesx1,x2,x3, … ,xnand a corresponding set ofyvaluesy1,y2,y3, … ,yn. You want to find the smoothest functionf(x) such thatf(xi) =yifor i = 1, 2, 3, …,n. The smoo...
We introduce a new smooth estimator of the ROC curve based on log-concave density estimates of the constituent distributions. We show that our estimate is asymptotically equivalent to the empirical ROC curve if the underlying densities are in fact log-co
A new mathematical method of fitting a smooth curve to a set of given points in a plane is developed, and a computer subroutine is programmed to implement the method. This method is devised in such a way that the resultant curve will pass through all the given points and will look smooth...
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We prove that the bracket width of the simple Lie algebra of vector fields Vec(C) of a smooth irreducible affine curve C with a trivial tangent sheaf is at most three. In addition, if C is a plane curve, the bracket width of Vec(C) is at most two and if moreover C has a unique...
To obtain the curve from [29], the equations from [52] were first used to calculate 𝑑𝑐𝑒𝑛𝑡𝑒𝑟/𝑑𝑐dcenter/dc (depending on 𝜃θ, ℎ/𝑑𝑐h/dc, and their relationship for the inception position), applicable to constant width chutes. Then, the equation developed ...
Namely, if f(ϕ, z) = a + bϕ + cz, where b∞ 0, then f(ϕ, z) = 0 along the curve {(sin((a+cz)/b),cos((a+cz)/b),z),z∈R}, which is a helix, hence a geodesic. Otherwise, if b = 0, z is a constant, which also corresponds to a geodesic on S. The ...