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Theoretical degrees of freedom?

So say I have some configuration space, here’s a rough example (basically one would be required to compute all of the coefficients of these polynomials, this is just an example):
$U=V=\{(x_1,x_2,\cdots,x_n,y_1,y_2,\cdots,y_n)\in\mathbb{R}^{n+n}|x_i^2+y_i^2=1; \forall i\in\{1,\cdots,n\}\}$
I have a manifold with volume one. Now I wish to find a measure of smoothness for this space. So I define the following:
$f:\mathbb{R}^n\times\mathbb{R}^n\rightarrow \mathbb{R}$ as:
$\displaystyle f(x_1,\cdots,x_n,y_1,\cdots,y_n)=\sum_{i=1}^n(x_i+y_i)$
The question is, how does one compute the theoretical degree of freedom for this thing? Since the domain is $U\subset\mathbb{R}^{n+n}$, so one cannot express the (Gaussian) measure in terms of the

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Police seek suspects in theft of coin collection at local bank

Tuesday

May 7, 2018 at 2:49 AM

By Stephen MillerJournal Staff Writer

Police are investigating a theft at a local bank after thieves stole an estimated \$500,000 in coins from a private deposit box at a bank branch in Holbrook. The burglary occurred sometime between April 30 and Sunday morning. Police are looking for three suspects who were in the bank at the time. They are described as men in their early 20s. One has black hair, blue eyes and was wearing glasses. The second has black hair and is about six feet tall. The third suspect is about five feet 11 inches tall. They were seen in the bank shortly before the theft, which occurred between 11 a.m. and 4 p.m., according to police. No suspects have been arrested.

Local duo joining overseas exhibition excursionFilippo Swartz went to Italy, where his mother was born and he spent the first year or so of his life, every summer until he had to stick around to be a part of summer football activities for the Longmont High School team. Full Story

MacIntyre says the completed project will be best in Pac-12There were bulldozers, hard hats, mud, concrete trucks, blueprints, mud, cranes, lots of noise and, uh, mud, during the last recruiting cycle when Colorado football coach Mike MacIntyre brought recruits to campus. Full Story

Most people don’t play guitar like Grayson Erhard does. That’s because most people can’t play guitar like he does. The guitarist for Fort Collins’ Aspen Hourglass often uses a difficult two-hands-on-the-fretboard technique that Eddie Van Halen first popularized but which players such as Erhard have
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