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Clash Royale CLAN TAG #URR8PPP up vote 1 down vote favorite Would anyone be able to provide Klingenberg's claimed proof in his " Lectures on closed geodesics " of the existence of infinitely many prime closed geodesics on any closed simply connected Riemannian manifold (contingent on the divisibility lemma). I believe it is around $§4.3.4$ in his book. Thanks in advance! reference-request geodesic loop-spaces share | cite | improve this question edited Jul 23 at 18:49 asked Jul 23 at 18:39 Multivariablecalculus 495 3 13 add a comment  |  up vote 1 down vote favorite Would anyone be able to provide Klingenberg's claimed proof in his " Lectures on closed geodesics " of the existence of infinitely many prime closed geodesics on any closed simply connected Riemannian manifold (contingent on the divisibility lemma). I believe it is around $§4.3.4$ in h...

Clash Royale CLAN TAG #URR8PPP up vote 0 down vote favorite With three men and four women, the maximum number of rounds the algorithm can go with men proposing. please can someone help me with this question algorithms share | cite | improve this question asked Jul 23 at 18:39 lala 1 Could you give some details, or a reference for, for the form of the G-S algorithm you are using? – Lord Shark the Unknown Jul 23 at 18:50 1 Welcome to MSE. "Please help me" alone will not attract a favorable response. You should add more information to the body of your question : what have you tried, how far have you gotten, where are you having trouble? It's hard to help you if you don't sy what your difficulty is. – saulspatz Jul 23 at 18:50 add a comment  |  up vote 0 down vote favorite With three men and four women, the maximum number of rou...

Clash Royale CLAN TAG #URR8PPP up vote 1 down vote favorite I'm a computer science student and for a project I'm taking sensor data and normalizing it into a 0 - 255 range. Problem is when I get the data I don't know the minimum and maximum (it varies very widely based on where the sensor is located) and that really affects how normalizing the data goes. I would just find the min and max in the data set but it's noisy enough outliers screw this up. This image isn't my data, but the graph looks similar. My question is how to find a reasonable minimum and maximum to normalize against. I was thinking about finding the average minimum (average of all the lows) and average maximum (average of all the highs) and using those, but I'm not sure how I would go about doing that in an efficient way. Currently I'm graphing the data in excel and deciding a reasonable minimum and maximum but that isn't feasible in the long term. For the graph I linked, I w...

Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite 1 Let $P$ be a cyclic group of order $p^n$. Let $M$ be a $mathbbZ_p[P]$-module and $M_p :=mathbbQ_potimes M$ be the associated $mathbbQ_p[P]$-module. When will $M_p$ have a direct summand isomorphic to $mathbbQ_p[P]$? We know $mathbbQ[P]simeq bigoplus_dmid p^nmathbbQ(zeta_d)$. If $M_psimeq bigoplus_dmid p^nM_p,d$ where $M_p,d$ is a vector space over $mathbbQ(zeta_d)otimes mathbbQ_p$ and $m_d$ is its dimension, then $M_psimeq bigoplus_d (mathbbQ(zeta_d)otimes mathbbQ_p)^m_d$ as $mathbbQ_p[P]$-modules. When does $M_p$ have a free rank one direct summand? abstract-algebra group-theory number-theory modules representation-theory share | cite | improve this question edited Jul 23 at 20:35 Fabio Lucchini 5,579 1 10 25 asked Jul 23 at 18:45 debanjana 375 1 11 1 Perhaps I do not understand the question. Is the answer not just: when $m_dgeq 1$ for all $dmid p^n$? The ring ...