# All Questions

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### Trigonometry from two graphs

My problem is that i have an image or rectangle which has line inside it which is rigid it will not move. I also have a graph with the same line but may be slightly bigger and may have a slightly ...
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### Find Probability that latency exceeds 10 ms given sample mean and variance

I am working on a statistics problem for my Engineering Statistics class. The problem goes like this: You are measuring the communications latency between two processors. You take 6 million data ...
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### The second differential as a differential on the double tangent bundle

I know what the second differential of $f : \Bbb R^n \to \Bbb R$ means. Nevertheless, when working with abstract manifolds and in the absence of a connection, one cannot come up with a 2-covariant ...
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Let $M$ be a smooth manifold. Let $d$ be any metric on $M$ which generates the topology of $M$. Let $f:M \to R$ be Lipschitz w.r.t the metric $d$. Is it true that $f$ is differentiable a.e? Note: ...
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### Finding an algorithm TSP with additional conditions

Can someone solve this? Basically I want to find an algorithm for Traveling Salesman Problem (TSP) with additional conditions. 1) It should be non-convex. 2)At least pass one time at every given ...
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### $I=mI$, when $I$ is not finitely generated.

Let $(R,m)$ be a commutative local ring with unit. Suppose $I$ is an ideal(not finitely generated). If $I=mI$, what can we say about $I$. If $I$ were finitely generated, then Nakayama's lemma would ...
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### Is the restriction of a Minkowski-form in $\Bbb R^n$ on a vector subspace $U$ with $\dim(U) = n - 1$ also a Minkowski-form?

Task: Is the restriction of a Minkowski-form in $\Bbb R^n$ on a vector subspace $U$ with $\dim(U) = n - 1$ also a Minkowski-form? Solution: Since a Minkowski-form has the type $(n - 1, 1)$, ...
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### Proof that $\pi=1$…

We can think of numbers as sets, so let's look at two numbers: $\pi$ and $1\over \pi$. We know that both are irrational and they both probably contain all possible numerical combinations, which means ...
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### Problem with dimension in nonlinear Gauss-Newton algorithm

I have a fundamental reasoning error, which I simply can't solve. Given the Problem to find the best solution for a nonlinear least square Problem, given m functions $f_{1...m}(\bf{x})$ with n ...
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### Is there a proof for this or we should accept that?

Why are two independent parameters necessary and enough for determining position of a point with respect to a reference point in a plane? In other words, I want to address a point from another ...
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### calculate E[X^n] with moment generating function

Say random variable X has a density function $f(x)=1$ when $0<x<1$. So this means $E[X^n]= \int_0^1 x^n.1 dx = \frac{1}{n+1}$. At the same time we can get that the moment generation function ...
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### integral solution needed for general powers of $x$

I want to find the solution to the following integral $$\int_0^{\infty} \frac{dx}{x^{\frac{\alpha}{2}}+1}$$ where $\alpha$ can be any value greater than 2 such that $\alpha /2 >1$ but can be any ...
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### Let $A=\{1,2,3,…,2^n\}$. Consider the greatest odd factor of each element of A and add them…

Let $A=\{1,2,3,...,2^n\}$. Consider the greatest odd factor (not necessarily prime) of each element of A and add them. What does this sum equal?
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### problem solving involving time

This a summary of the question (because it was really long) Everyday A leaves home before 5pm to pick B up from the train station at 5pm and drive home One day B catches an earlier train that ...
$x^3y''+(\cos2x-1)y'+2xy=0$ One have to make the anstaz that $y= x^m \sum_{j=0}^{\infty}a_j x^j$ and I have been solving problems like this before, but for this one what really confuses me is what to ...