Let $p$ and $q$ be positive numbers having a sum of $1.$ What is the minimum value of $(p+(1/p))^2 + (q+(1/q))^2?$
Proving inequality $(a+\frac{1}{a})^2 + (b+\frac{1}{b})^2 \geq \frac{25}{2}$ for $a+b=1$
Similar Matrices and Linear Transformations Two logos in beamer after certain frame How can I store and retrieve a custom list in a blend file? I am trying to create a script that will allow me to generate a list and store it in the blend file. The list starts out blank and then strings get added to the list, resulting in: [&quot;test1&quot;,&quot;test2&quot;,&quot;test3&quot;] I create a PropertyGroup Class for the enum, define a new scene property as a CollectionProperty type with access to that enum Class, before appending a new item into the enum: import bpy  class item_set(bpy.types.PropertyGroup):     myItems = []     enums = bpy.props.EnumProperty(name=&quot;My Items&quot;, items=myItems) bpy.utils.register_class(item_set)  bpy.types.Scene.myItemSet = bpy.props.CollectionProperty(type=item_set)      newItem = bpy.context.scene.myItemSet.add() newItem.myItems.append(&quot;test&quot;)    I need to be able to add items to the list, save the blend file, re-open the file, run the script again and retrieve the list from the scene. However, the  states:  One thing to keep in mind is that after saving and reloading your blend-file, your new property will have disappeared...    ...To make the values you assigned in a previous session available again, you need to redefine the property. So after reopening the blend-file you need to rerun: bpy.types.Object.myProperty = bpy.props.StringProperty()   I can do the appending into and retrieval of the property values absolutely fine upon an initial run, but as the documentation states, the property is unavailable when trying to view it's contents on a reload of the file (after having run the script, saved and re-opened the file), but I am unsure how to redefine it without clearing all it's values. If I redefined the scene property, it would presumably also need the enum Class to be available, which would currently set myItems back to [] (empty). Do I need to change the way I am initially setting the items in the class or am I on entirely the wrong track with all of this? All I need to do is store a list in the blend file, so if there is a better way please let me know. Thanks. (I would hope, eventually, to be able to store sub lists [[&quot;a&quot;,&quot;b&quot;],[&quot;c&quot;,&quot;d&quot;],[&quot;e&quot;,&quot;f&quot;]], I'm just trying to get normal lists to work first.) I need to solve $3x^2 + 6x +1 \equiv 0 \pmod {19}$  I saw the same problem here -     but didn't understand how he got to the conclusion   $x(x+2) \equiv 6 \pmod {19}$  and anyway im trying to solve it how we learned in class -   multiply both sides and the modulo by $4a$ then solve the two equations  $y^2 \equiv b^2 -4ac \pmod {4an}$  $2ax + b \equiv y \pmod {4an}$  so I tried multiplying the hole thing by $4a$ , that is $4 \times 3$  and got to $(2 \times 3x + 6)^2 \equiv 36 -4 \times 3 \pmod {19 \times 4 \times 3}$  now I am stuck . any help will be appreciated Resubmitted rejected suggested edits It seems that when a user’s suggested edit gets rejected they can simply re-suggest it, and given the  of affairs of the suggested review queue the suggested edit is quite likely to be approved (or if not this time, then it will almost certainly be approved if they are persistent).    As an example I saw the following  which was rejected, very shortly after I saw almost the  suggested again, this time it got two approvals.  Should there perhaps be some sort of delay until a user can suggest an edit after their suggestion was rejected for the same post? Perhaps a check can be made how large of a difference there is between the two suggestions (though I’m not sure it’s worth doing just for this, and a delay is probably sufficient)?   I do understand that a user should be able to re-suggest an edit after it was rejected, since after all perhaps they made a better suggestion after seeing that it was rejected, however in cases like these I don’t think that is what is happening.  I did see  saying that after some rejected edits a user cannot suggest any further edits until a week has passed, but as this is clearly not happening here I guess that may have changed since that post. How does the coin limit work? The new gym update , including a limit of 50 coins earned per day. How does this limit work? Is each pokemon limited to accruing 50 coins per day? Are all my pokemon limited to a collective 50 per day? My teammates keep feeding my Dragonite and she has been at the gym for almost a week; will she return with 50 coins for each day she was there? Fewer than 50 for the days I had other pokemon in the gym? Or will she accumulate vast sums of coins over the week, but only deliver me 50 (or fewer) when she comes back based on what I have collected from returning pokemon that day? Compute approximately the probability that more than 50 of the observations of the random sample are less than 3. Let $X_1,X_2,...,X_n$ be a random sample of size $n = 72$ from a distribution with probability density function $f(x) =\begin{cases} 1/x^2,&amp; 1 &lt; x &lt; infinity\\0,&amp;\text{otherwise}\end{cases}$ Compute approximately the probability that more than $50$ of the ob- servations of the random sample are less than $3$. I've seen multiple servers where you can connect from any (recent) major version. (Example, 1.9, 1.8 OR 1.7) And they all seem to be able to do it. Alas, a simple google search did not fix the problem. Any ideas? Thanks guys.  (PS: The Minecraft server is running on the latest Spigot for 1.10 as of 6/27/16) I've only found a recursive algorithm of the extended Euclidean algorithm. I'd like to know how to use it by hand. Any idea? Quotient group $G/H$ is abelian iff $[G,G] \subseteq H$ What IDEs are available for Ubuntu? This question exists because it has historical significance, but it is not considered a good, on-topic question for this site, so please do not use it as evidence that you can ask similar questions here. See  for more information.   This is a community wiki for IDEs available on Ubuntu. Please post one IDE per answer (including more than just a screenshot or a link, please at least put a short description).  In your answer, tell us what the IDE is for (which language(s) or if it is RAD capable). Beamer Tikz-cd Problem Infinite algebraic extensions of $\mathbb{Q}$ I need help to solve the following exercise:   If $K$ is an algebraic extension of $\mathbb{Q}$ (finite or infinite), then we let $O_{K}$ denote the ring of algebraic integers in $K.$ If $\frak{P}$ is a prime ideal of $O_{K}$ then $\frak{P}∩\mathbb{Z}$ is a prime ideal of $\mathbb{Z}.$ Moreover, if $\frak{P}$ is non-zero, then so is $\frak{P}∩\mathbb{Z}$ . Thus $\frak{P}∩\mathbb{Z}=$$ p\mathbb{Z}$ for some prime $p.$ Show that $O_{K}/\frak{P}$  is a field, and is an algebraic extension of $\mathbb{F}_{p}$; then show that it is Galois over $\mathbb{F}_{p}$ with abelian Galois group.  Now suppose that $K/F$ is a (finite or infinite) Galois extension. Let $\frak{P},$  $O_{K}$ be as before and put $\frak{p}=\frak{P} \cap $$O_{F}$, a prime ideal of $O_{F}.$  Show that $\mathrm{Gal}(K/F)$ acts transitively on the set of prime ideals of $O_{K}$ above $\frak{p}.$   Thanks in advance I want to quantify the relationship between two variables, A and B, using mutual information. The way to compute it is by binning the observations (see example Python code below). However, what factors determines what number of bins is reasonable? I need the computation to be fast so I cannot simply use a lot of bins to be on the safe side.  from sklearn.metrics import mutual_info_score  def calc_MI(x, y, bins):     c_xy = np.histogram2d(x, y, bins)[0]     mi = mutual_info_score(None, None, contingency=c_xy)     return mi How do I create silhouettes in a studio environment? The trick to creating silhouettes in the field, as far as I know, is to use spot-metering and to expose for the background. However, this is a bit more difficult in a studio environment. What is the key to creating "artificial" silhouettes?  One solution that I'm considering is placing a bright flash directly behind the subject - would that work? It started happening today... all of a sudden, no apparent reason!  Here's the output from df:   assp:~# df -k Filesystem           1K-blocks      Used Available Use% Mounted on /dev/simfs             6291456   1378384   4913072  22% / tmpfs                  8202680         0   8202680   0% /lib/init/rw tmpfs                  8202680         0   8202680   0% /dev/shm  assp:~# df -i Filesystem            Inodes   IUsed   IFree IUse% Mounted on /dev/simfs           55781934   83005 55698929    1% / tmpfs                2050670       2 2050668    1% /lib/init/rw tmpfs                2050670       1 2050669    1% /dev/shm  assp:~# df -h Filesystem            Size  Used Avail Use% Mounted on /dev/simfs            6.0G  1.4G  4.7G  22% / tmpfs                 7.9G     0  7.9G   0% /lib/init/rw tmpfs                 7.9G     0  7.9G   0% /dev/shm   Here's an actual entry from /var/log/mail.warn:   Dec 11 17:55:37 assp postfix/smtpd[30614]: warning: not enough free space in mail queue: 0 bytes &lt; 1.5*message size limit Dec 11 17:55:37 assp postfix/cleanup[30617]: warning: 4361D850D54: write queue file: No space left on device   . I'm trying to solve the well known Coupon Collector's Problem by explicitly finding the probability distribution (so far all the methods I read involve using some sort of trick). However, I'm not having much luck getting anywhere as combinatorics is not something I'm particularly good at.   The Coupon Collector's Problem is stated as:  There are $m$ different kinds of coupons to be collected from boxes. Assuming each type of coupon is equally likely to be found per box, what's the expected amount of boxes one has to buy to collect all types of coupons?  What I'm attempting:  Let $N$ be the random variable associated with the number of boxes one has to buy to find all coupons. Then $P(N=n)=\frac{|A_n|}{|\Omega _n|}$, where $A_n$ is the set of all outcomes such that all types of coupons are observed in $n$ buys, and $\Omega _n$ is the set of all the possible outcomes in $n$ buys. I think $|\Omega _n| = m^n$, but I'm not even sure about that anymore, as all my attempts so far led to garbage probabilities that either diverged or didn't sum up to 1. Entering Unicode characters in LaTeX How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$? We are asked the following:      let $f(x)$ be a continuous function on $[0, 1]$ such that   $$\int _ {0} ^ {1} \ f(y) dy = 1$$   prove that $f(x) = 1$ for some $x ∈ [0, 1]$   The question asks to take into account Rolle's Theorem and Mean Value Theorem.  I'm aware of the definitions, but I am really unsure how to answer this question and my tutors are not really responding till after easter.    Could someone please help? Why is there a "y" involved?  Thanks you Combining randomForests in R, why are the err.rate, mse and rsq components NULL From ?combine in :     The confusion, err.rate, mse and rsq components (as well as the   corresponding components in the test compnent, if exist) of the   combined object will be NULL.   Why are the err.rate, mse and rsq components for the combined NULL? Is there an efficient way to re-calculate these metrics?  I ask because I would like to figure out a way to use the oob re-sampling method with the parRF model in .