# All Questions

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### Real Analysis. Bounds, Infrimum and Supremum

Given that S={x|4x^(2) > x^(3) +x} (1)Determine whether S is bounded (2)Determine their Supremum and Infrimum.
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### L1 norm differentiablility

I am trying to understand the Least Absolute Deviation algorithm, which basically is min l1-norm(z) subject to z=Ax-b I want to understand how is the l1-norm ...
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### Comparison of Cramer Rao bound - deduction and conceptual question

The CRB gives the variance of the estimation error of the estimates and a lower value is preferred. I have computed the cramer rao bound (CRB) of the estimates of the coefficients $\mathbf{h^T}$ for ...
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### Modified arithmetical functions from a modified Möbius function

In this post when $n>1$ we assume that $n=\prod_{k=1}^{\omega(n)}p_{n}^{e_{k}}$ its factorization in prime powers, where $\omega (n)$ is the number of distinct primes. It is well known the ...
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### Finding the Zero's of a Second Derivative to Determine Points of Inflection

I have been told to graph the function $y=\cos \left(x^2\right)$ for -2π ≤ x ≤ 2π. I have determined key features of the graph but need help when it comes to determining the points of inflection for ...
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### Get parameters for given point on quadratic bezier triangle

I have a 2 dimensional quadratic bezier triangle described by the position of its corners $v_0$, $v_1$ and $v_2$ and a handle for each side $h_0$, $h_1$ and $h_2$. The parametric equation with the ...
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### Prove that $F_1$ and $F_2$ are continuous and that $\int_{\gamma_1}F_1(z) dz = \int_{\gamma_2}F_2(z) dw$

Let $\Omega_1, \Omega_2 \subseteq \mathbb{C}$ and let $\gamma_1: [a,b] \to \Omega_1$, $\gamma_2: [c,d] \to \Omega_2$ be paths. Let $f$ be a continuous function defined on $\gamma_1 \times \gamma_2$ ...
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### What is $\int_0^{\pi} \frac{e^{\sin x}\cos(x)}{1+e^{\tan x}} \, dx$?

I read this question. The integral has a special property, so it might possibly be evaluable? No one tried evaluating it, so I created this. Not very often I ask question like this, but here it is. ...
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### Symplectic group and Quaternion Inner product

I have a problem understanding a passage from "Naive Lie theory"(by Stillwell), here is the passage from section $3.9$ ,page $71$: The idea of treating orthogonal, unitary, and symplectic groups ...
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### what is the difference between statiscal averagre and average?

I'm reading a book on synthetic aperture radar and it is said that: The term $\sigma^{\circ}$ is the averaged radar cross section per unit area, also called the scattering coefficient or ...
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### What is the source of the error in the Sherman-Morrison formula application?

The Sherman-Morrison formula results in small errors in relation to the standard matrix inverse operation after each application, as shown here. From what I understand, the Sherman-Morrison identity ...
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### Proofs by analysing games

I recently read the following article giving a novel proof of the uncountability of $\mathbb{R}$ by analysing a particular game, amongst other results. ...
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### $m(E)=0$ or $m(E^c)=0$

The question comes from former qualifying exam of the graduate school I'm going to attend. Q: Suppose $E$ is measurable and $E=E+\frac{1}{n}$ for every natural number $n\geq 1$. Show that either ...
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### Field norm of $F(\sqrt[n]{a})$

Let $F$ be a field of characteristic zero that contains a primitive $n^{th}$ root of unity. Pick $a$ such that $K=F(\sqrt[n]{a})$ is a cyclic extension of $F$ of degree $n$. Let $\sigma$ be a ...
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### Spaces whose all their metrizations are complete [duplicate]

Which metrizable topological spaces $(X,\tau)$ posses the following property: Every compatible metric (i.e one which induces the same topology $\tau$) is complete. Compact metrizable spaces satisfy ...
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### Formula that's only satisfiable in infinite structures

What formula in first order logic can I write that's only satisfiable over infinite structures, over a dictionary without the = sign?
### Finding the definite integral $\int_{0}^{2\pi} \frac{e^{|\sin x|}\cos(x)}{1+e^{\tan x}} \, dx$
$$\int_0^{2\pi} \frac{e^{|\sin x|}\cos(x)}{1+e^{\tan x}} \, dx$$ My try: $$I=\int_0^\pi \frac{e^{\sin x}\cos(x)}{1+e^{\tan x}} dx+\int_\pi^{2\pi} \frac{e^{-\sin x}\cos(x)}{1+e^{\tan x}} dx$$ also ...