# All Questions

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### $n$-vertex $3$-edge-colored graphs with exactly $6$ automorphisms which preserve edge color classes, but permute the edge colors distinctly?

In each of these $3$-edge-colored graphs, there are exactly $6$ automorphisms which preserve the set of edge color classes: (These automorphisms don't necessarily map e.g. green edges to green ...
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### looking for some exercise to test understanding of convector

I am trying to understand the concept of "convector" so that I can work with it for problems I come across in PDE. My knowledge on differential geometry is very little. And my topological background ...
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### Sets of Egyptian fractions which sum to 1

Let an 'Egyptian unity sum set' be a set of positive integers {a, b, c ...} such that their Egyptian fractions sum to 1; and none of the elements are equal. That is: 1/a + 1/b + 1/c ... = 1 Let the ...
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### The relationship between subfields and subgroups of a finite field.

I am trying to get my head around the structure $GF(p^n)$ when viewed as a vector space of dimension $n$ over $GF(p)$ (mainly the relationship between the additive and multiplicative structures). I'm ...
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### Dual group of $\mathbb Z$

We know $\hat{\mathbb Z}=\mathbb T$ and the map $\alpha\longmapsto\chi_{\alpha}$ is an isomorphism of $\mathbb T$ on to the character group of $\mathbb Z$, but i cant prove this map is continuous? I ...
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### Model-theoretic characterization of local modal correspondence

I've been reading van Benthem's dissertation (available on ILLC's website) on modal correspondence theory. In Section I.3, he develops a model-theoretic characterization of modal formulas having ...
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### Vector in function format

Not sure how to interpret the follow: Find the intersection point(s) of the line $r(t)=(0, -2, -1)+t(1, 1, 1)$ and the plane $x+2y-4z=-3$ Does $r(t)=(0, -2, -1)+t(1, 1, 1)$ mean $r=(0, -2t, -t)$?
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### Factoring bivariate quadratics with real coefficients (for high school students).

I was tutoring a Year 10 student last night (he's learning about quadratics). Unfortunately, we ran into a class of problems that I couldn't explain how to solve (beyond simply guessing and checking), ...
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### Julia and Mandelbrot Sets [on hold]

I need to know how escape, prisoner, Julia and Mandelbrot sets work. Are they all in one sequence or are they separate.
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### Bayesian statistics proof for a continuous uniform distribution

I know that if the prior distribution is chosen to be a continuous uniform distribution, then the exact posterior distribution will simply the normalized version of the likelihood function. I was ...
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### Need help with Logic Question

ATTEMPT Given F $\subseteq$ G Writing out logical form of Goal we have $\exists$A$\in$F(x$\in$A) $\rightarrow$ $\exists$A$\in$G(x$\in$A) Now assuming(putting to list of givens) ...
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### Modulus Problem [on hold]

I do not understand how to solve such a question: $$|x+1| - |x| + 3|x-1| -2|x-2| = x+2.$$ How would you go about all the possibilities with which sign the modulus could take? Appreciate any help!
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### Finding the Control Point in a bezier curve

This is a basic (and probably a stupid) question, math is not my forte and I don't know much about math, in this site: http://www.ams.org/samplings/feature-column/fcarc-bezier in the bezier curves ...
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### Continued Fraction Counting Problem

The house of my friend is in a long street, numbered on this side one, two, three, and so on. All the numbers on one side of him added up exactly the same as all the numbers on the other side of him. ...
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### at lest one of 100 consecutive integers is relatively prime to all natural numbers less or equal 100

for an arbitrary integer $n$ define $A_n=\{i|n \leq i \leq n+99 \text{ where i is an integer}\}$ (i.e. $A_n$ is 100 consecutive integers) is it true that for any integer n there is an element in ...
I have complex-valued data. At each one of about 100 linearly spaced $x$ values, I have a corresponding measurement of a complex quantity with well-defined Gaussian uncertainties on both the real and ...
Question: Let $Q_{c}(z) = z^{2} +c$ which $c \in \mathbb{C}$ and suppose that $z_{0} \in K _{c}$ for the filled Julia Set, $K_{c}$ of $Q_{c}$. Suppose further that $z_{1} = Q_{c}(z_{0})$ and it ...