Regression Using Tangents Of Curve

Many identical cars coasting down a perfectly consistent and level road.
Each starting at an arbitrary speed.
I can see how fast the cars are going.
I have snapshots of random periods while they rolled down the road, with how far they travelled during those periods.
How can I calculate an equation that would allow me to figure out how far a car is going to roll over some period of time, knowing only its speed.

ag.algebraic geometry – Fitting point on a Quadric curve

Dear Researchers/Friends/People,

I come in peace…..
I am working on research project.I am currently using cloud compare for my project.And calculates the gaussain curvature and Mean curvature to extract the geometric features of the points.I have a set of point(around 10) ,I want them to be fitted on a quadric surface so that i can calculate gaussain curvature and geometric features of those points.Yes,I know cloud compare does it automatically.But I want to know the math behind it.I want to know how to fit them.I have read the paper http://mesh.brown.edu/taubin/pdfs/taubin-pami91.pdf by taubin.But i dont understand it properly.
Can you guys suggest me any books,Videos or examples that i can refer ?

RegionFunction with a parametric curve

I would like to produce contour and density plots for a known function of x and y for x>=0 and y>=0. The function has a singularity curve in the x-y plane and I only want to evaluate the function inside that curve. However, the curve is known only parametrically so it is not clear to me how to use RegionFunction. Suggestions?

reference request – Embedding theorems for fractional Sobolev spaces $W^{s,p}(Gamma)$ where $Gamma$ is closed piecewise $C^1$ curve in $Bbb R^2$

I am interested in embedding theorems for the fractional Sobolev space $W^{s,p}(Gamma)$ where $Gamma$ is closed piecewise $C^1$ curve in $Bbb R^2$ such as the boundary of a triangle or rectangle. What are basic results for this? Also, is there some $p$ for which $W_{s,p}(Gamma)subset C(Gamma)?$

Let’s use $Gamma=partial Omega$ where $Omega$ is a square as our basic example.
This is supposedly a smooth manifold as it is homemorphic to a circle, is that right? So we can define $W^{s,p}(Gamma)$ as Brezis mentions in the comments of Chapter 9 in his functional analysis books.

parametrization – Parametrize a curve $vec{y(t)= rcos(wt)i+rsin(wt)j+hwtk$ $-infty

I have a curve $vec{y(t)} = rcos(wt)i+rsin(wt)j+hwtk$, $-infty < t < infty$ and $w = (r^2+h^2)^{frac{-1}{2}}$ and $r,h,w$ are all positive…

I am trying to work out the Frenet Frame field, I have tried rigorously using the given curve and have just drawn myself into more and more confusion at each attempt. I now realised that perhaps maybe this curve needs to be parametrized? I don’t know how to do that and any hints would be welcome and much appreciated.

tag removed – Generate Equation of Parabola, Given X Intercepts of 0 & 1 and Area under curve equaling 1

How do I generate an Parabolic equation whose;

  1. A could be -1 or 1
  2. X intercepts are between 1 and 31
  3. Area Under the curve Equals 1
  4. And IF posable, be able to set the maximum above a x value

I want to be able to translate such a calculator into excel, but I need to understand the math for it before I can begin to do that. As for Why I need it, I want to be able to spread a sales goal across the days of a month, and thought this might be a fun thing to try. Of course I want the intercepts around the beginning and end of the month and the bump somewhere in the middle. I’d like to be able to choose when the bump happens.

Any Help or Direction is Appreciated.

at.algebraic topology – Spaces homotopy equivalent over the topologist’s sine curve

Consider $$T=left{ left( x, sin tfrac{1}{x} right ) : x in (0,1) right} cup {(0,0)}subset mathbb{R}^2$$
with its subspace topology.

Denote $p_0=(0, 0)in T, p_1=(1, sin 1)in T$.

A TSC-homotopy between continuous maps $f, g:Xto Y$ is a continuous map $H:Xtimes Tto Y$ such that $H(x, p_0)=f, H(x, p_1)=g$.

What can be said about pairs of spaces $X, Y$ such that there exist continuous maps $f:Xto Y, g:Yto X$ and TSC-homotopies $fcirc gsim mathrm{id}_Y, gcirc fsimmathrm{id}_X$?

inverse – How to get x value where area under curve is some number?

My goal is to get x value where area under the curve (from the x ~ infinity) is about 0.05. But the code which I have tried shows errors. How to correct it?

Solve(!(
*SubsuperscriptBox(((Integral)), (x), ((Infinity)))(
*FractionBox((
*SuperscriptBox((E), ((-x)/2)) 
*SuperscriptBox((x), (3/2))), (3 
*SqrtBox((2 (Pi))))) (DifferentialD)x)) == 0.05, x)

analytic number theory – What’s the average order of the reduction of a section of an elliptic curve

Suppose $E$ is an elliptic curve over $mathbb Q$ and $x in E(mathbb Q)$ is not torsion. We can reduce $x pmod p$ for a prime $p$ of good reduction and it will have some order $n_p$ in the group $E(mathbb F_p)$. Has there been any work on the asympotitcs of $n_p$ as $p to infty$?

More generally, suppose $x,y in E(mathbb Q)$ are two linearly independent sections and let them generate subgroups $G_x(p),G_y(p) subset E(mathbb F_p)$ for a prime of good reduction. Have the asymptotics of $G_x(p)cap G_y(p)$ been studied?

This question seems tangentially related.

Elliptic curve over $mathbb{Q}(T)$ receiving only constant maps from modular curves

Is there an elliptic curve $E/mathbb{Q}(T)$ such that any map $X_1(N)to E$ for any $N>0$ is constant?