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An easy corollary of the Szemerédi Regularity Lemma is that dense graphs contain linear sized $varepsilon$-regular bipartite subgraphs whose density is similar to that of the parent graph. As...
Asked on 12/27/2021 by alpmu
1 answerIn the 2-dimensional case, Brouwer's fixed point theorem (BFPT) says that every continuous function $D^2to D^2$ has a fixed point, where $D^2$ is the disk. Now fix a...
Asked on 12/27/2021 by R. Srivastava
1 answerI found a statement that the second derivative can be defined as: $$lim_{x to a} frac{f '(x)-f '(a)}{x-a}$$. Does this definion follow from the definition of the first derivative as:...
Asked on 12/27/2021 by kiwifruit
5 answerIf you study undergraduate medicine, mnemonics are almost indispensable - there is so much factual material to learn. I was never given any mnemonics in my time as a maths...
Asked on 12/27/2021 by almagest
5 answerRegarding the proof of Lemma 2: Matrix $A$ is totally unimodular if and only if the matrix $[A |I]$ is TU, I do not understand the first step...
Asked on 12/27/2021
2 answerFind the distance between the two lines defined by :$$mathbb L_{1}= begin{cases} ...
Asked on 12/27/2021
3 answerUsing L'hopital rule: $lim_{x to x_i, y to y_i} frac{x-x_i}{sqrt{(x-x_i)^2 + (y-y_i)^2}} = lim_{x to x_i, y to y_i} frac{frac{d(x-x_i)}{dx}}{frac{dsqrt{(x-x_i)^2 + (y-y_i)^2}}{dx}} = lim_{x to x_i, y to y_i}...
Asked on 12/27/2021 by Possible
3 answerIf 1-9 is filled in the $3 times 3$ determinant, and each number appears once,then the maximum value of the determinant is $412$. For example, the following...
Asked on 12/27/2021
1 answerI don't know if it's been asked before (if it has please give me the link), and I don't understand latex or anything so I'll write it in plain words:...
Asked on 12/27/2021
0 answerWe can show that in an Integral Domain I if $x^2=1$ then $x=pm 1$. Is the converse true? i.e if for any x in I with $x^2=1...
Asked on 12/27/2021
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