# All Questions

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### Number of polyhedron diagonals

Suppose that I have a polyhedron with given number of faces, edges and vertices are given. Is there a formula that gives me the number of polyhedron diagonals, ...
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### $G$ be a finite group of order $n$ , $H$ be a proper subgroup of order $m$ such that $(n/m)!<2n$ ; $G$ is not simple

Let $G$ be a finite group of order $n$ , $H$ be a proper subgroup of order $m$ such that $(n/m)!<2n$ ; then how to show that $G$ is not simple ? I have proceeded by Cayley's theorem , $\ker f$ is ...
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### Can Two Different Polynomials Agree on an open interval? [duplicate]

Question: For a high degree polynomial $P_1$ , can we have another polynomial $P_2$ that is a part of $P_1$ (or they agree on open interval)? TBN: This question is partially answered in ...
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### 3-sigma approximation

I am making a system involving a sensor who has to be really precise. I found on their datasheet a diagram that shows the typical performance of the sensor. There's the mean value, the +3 sigma, ...
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### color conversion from RGB to YIQ

I want to convert RGB color to YIQ. AS my knowledge the formula is below: To practice this math i went a to this link Color Conversion. I enter here RGB values 32,65,32. I found the result is YIQ = ...
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### Is it right to say that if two vectors, $A$ and $B$, have same $L^p$ norms, for all $p$, then $A = B$?

Is it right to say that if two vectors, $A$ and $B$ (all elements of $A$ and $B$ are positive), have same $L^p$ norms, for all p, then $A = B$ ?. Thanks.
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### Computing limits example: Swaping limit to $0$ into infinity.

I have found the following example: $$\lim_{x\to 0^{+}} \frac{e^{\frac{-1}{h}}}{h} = \lim_{z\to\infty} ze^{-z} = 0$$ Could you explain to a kid nice and slowly why does the limit of $x$ to ...
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### Why is the Lagrange Multipliers Theorem not working?

Consider the function $h: K \to \mathbb{R}$ where $K := \{x \in \mathbb{R}^3:x,y,z \geq 0, x+2y+3z\leq 6\}$. $h$ is defined as: $$h(x) = xe^{(x+2y+3z)}$$ Find the supremum and the ...
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### Expected % of heads flipping coins of different odds

So this is an analogy for a real world example but for simplicity. So if I were to flip a normal coin ten times I would expect heads 50% of the time or 5 head results. I could then compare this to the ...
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### Integral values satisfying a inequality

Consider the following inequality : $$\frac{x^2+a^2}{a(4+x)} \ge 1$$ I am trying to find the range of integral values of $a$ for which this inequality holds for all $x$ belongs to $(-1,1)$ I ...
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### Recovering a basis from an isomorphism with the dual space.

Let $V$ be a finite dimensional vector space, then given a basis for $V$ constructing an isomorphism $V \rightarrow V^*$ is easy, but how about the reverse direction? Given an explicit isomorphism ...
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### SVD decomposition of matrix

Is it correct to say that a matrix $A$ and the matrix $A^HA$ have the same eigenvectors? Proof: $$A= U \Sigma V^* \\ A^HA= U \Sigma^2 U^H$$ Am I correct?
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### Topics to master (be literate at) before differential equations?

Good evening, I'm really enthusiastic about learning differential equations because it was said that D.E. is the most important tool of mathematics "can be used for modelling real-world physical ...
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### Minesweeper probability

I ran into the situation pictured in the minesweeper game below. Note that the picture is only a small section of the entire board. Note: The bottom right 1 is the bottom right corner tile of the ...
### Can the determinant of an integer matrix with $k$ given rows be the gcd of the determinants of the $k\times k$ minors of those rows?
I'm interested if the following is true: Let $n\geq k\geq1$ be integers and let A=\begin{pmatrix}a_{11}&\cdots&a_{1n}\\ \vdots&\ddots&\vdots\\ ...
Question A particle moves along the curve of the intersection of the cylinders $y=-x^2$ and $z=x^2$ in the direction in which $x$ increases. (All distances are in cm.) At the instant when the ...