If a subgroup has smallest prime index, then it is normal
Normal subgroup of prime index
How does AdamW weight_decay works for L2 regularization? hello I have a question about weight regularization in Adam apparently the weight_decay in the AdamW function  has the same impact as an L2 regularization my questions are: is that parameter the same as lambda that we have in the regularization term?  how does it exactly work? and what is its impact on the model complexity? Assume that $0 &lt; a_n \leq 1$ and that $\sum a_n=\infty$. Is it true that  $$ \sum_{n \geq 1} \frac{a_n}{(a_1+\ldots+a_n)^2} &lt; \infty $$ ?  I think it is but I can't prove it. Of course if $a_n \geq \varepsilon$ for some $\varepsilon &gt; 0$ this is obvious.  Any idea? Thanks. What happens when a photon hits a mirror? When a photon of light hits a mirror does the exact same photon of light bounce back or is it absorbed then one with the same properties emitted? If the same one is bounced back does it's velocity take all values on $[-c,c]$ or does it just jump from $c$ to $-c$ when it hits the mirror?  Or, is the phenomenon of a mirror better explained using a wave analogy? If so, what is this explanation? I read this book once when I was in middle school. A girl solves a murder or a mystery on a spaceship. It was a thin paperback books.   All I can remember is that there was an alien, and there was a movie star or actress or famous makeup artist on the ship traveling with another woman. By the end of the book the murderer was the woman the actress was traveling with who forced her to use her makeup skills to disguise her, and she was really some kind of alien. Properties of $y$ if $\frac{d^2y}{dx^2}+xy=0$, $x \in [a,b],$ and $y(a)=y(b)=0.$ Let $y$ be a nontrivial solution of the boundary value problem  $$\frac{d^2y}{dx^2}+xy=0,\ x \in [a,b]$$  $$y(a)=y(b)=0$$ Then:   $b&gt;0$ $y$ is monotone in $(a,0)$ if $a&lt;0&lt;b$. $y'(a)=0$. $y$ has infinitely many zeros in $[a,b]$   I have no idea how to solve it and which options is/ are correct. please help me. db_update Query Issue I am using ubercart guest checkout module. I am able to submit  the order as guest etc works fine.   After Reviewing the order and submitting it throws me this error   Recoverable fatal error: Argument 2 passed to db_query() must be an array, string given, called in /var/www/html/dev.demo.net/sites/all/modules/ubercart_guest_checkout/uc_guest_checkout.module on line 263 and defined in db_query() (line 2342 of /var/www/html/dev.demo.net/includes/database/database.inc).   This is the query which is causing that issue    db_query('UPDATE {users} SET name = "%s", mail = "%s" WHERE uid = %d', $name, $mail, $account-&gt;uid);   I tried to change this query like this  db_update('users') -&gt;fields(array(     'name' =&gt; $name,     'mail' =&gt; $mail )) -&gt;condition('uid',$account-&gt;uid,'=')        -&gt;execute();   still no luck, it throws me same above specified error.    How can i resolve the query of above one in order to avoid the error. Any suggestions w.r.t query will be nice.Thanks in advance. Why do files sometimes change but not the inode or vice versa? When a file is updated then the corresponding inode gets updated. But sometimes the following condition occurs    file is same and inode is new  file gets changed but corresponding inode is older   Why ? What do we mean by hyperparameters? Can anyone give me full details about what we mean by hyperparameters, and what in the Dirichlet distribution are called hyperparameters? A practice example for the estimation of those parameters would also be useful. Prefix or adjective meaning "one and a half" Is there a prefix or adjective that means "one and a half", as "tri-" or "triple" is for "three"?  The exact usage I have is to describe "18" in terms of a dozen. Where I live they've started making 18-egg cartons, and the local grocer was wondering what name to give them in his computerised cash register, hoping for a single word.  Even slang, informal or invented term would do if there isn't such a term already. Why are the dineutron and diproton unbound? Where can I find the status of the released versions of Ubuntu? I want to know where I can find updated information about all the stable and in-development versions of Ubuntu, where I can find this information?     This question is meant to be a canonical question. It expects to answer the following questions:         Is X version stable yet?   Is X version in beta?   Is X version still supported?   What versions are still supported?   What are the versions in Beta/Alpha?   Until where X version will be supported?   Have X version ceased support?   When will be X version released?   Where I can download any release?   When will the next LTS version of Ubuntu be released?         The list is not exhaustive. Infinite algebraic extension of a finite field I have recently started studying algebraic field extensions and I got to know that algebraic closures $\overline{F}$ of finite fields $F$ are infinite. Therefore, I've asked myself the following question and couldn't come up with an answer.  Suppose $F$ was a finite field, i.e. $|F| &lt; \infty$. Is it possible to construct an algebraic extension $F'$ of $F$ sucht that $|F'| = \infty$ and $F' \subsetneq \overline{F}$? Meaning, that $F'$ is not algebraically closed. Problem with IMPORTRANGE function in Google Sheets I’m trying to get IMPORTRANGE to work for me with no success. I made two simple spreadsheets:  and . In the destination sheet I’m using the import range function:  =importrange(“1-5F1_zz0ZpGj7SfeQhewsCe0CsrA0eyPbjfmUrLBsyk”,”Sheet1!a1:a1”)   I tried already:   Replacing the , with ; Referencing just the key as well as the full URL in the first argument Switching from “ to ‘ With the sheet name and without it   Not sure what else to do.  Any ideas? This question is a duplicate of  (but this question can't be marked as a duplicate because that question is on meta.stackoverflow.com, and this question is on meta.stackexchange.com).  I'm seeing a bug on stackoverflow.com. I'm not sure if the culprit is Stack Overflow, Google Chrome, or macOS.  (Below I refer to a "code box". By that I mean some text that begins with 4 spaces when editing a question or answer.)  When I hover over a code box that contains one long line of code, a horizontal scrollbar appears. When I stop hovering over the code box, very frequently (maybe 3 out of 4 times) the scrollbar does not disappear. Clicking elsewhere on the page also does not dismiss the scrollbar. The only way to dismiss it is to refresh the page.  ...After experimenting more, it appears to always happen if I enter the box from below, but not always when I enter from above. It seems to be triggered by hovering over the lower half of the box.  Also if I enter from the top and scroll to the right, then until I refresh the page again that scrollbox will behave normally (only show a scrollbar when scrolling, and disappear after). In that case the scrollbar also has a different appearance, being much less tall (maybe a quarter of the height of the code box rather than half as tall).  Further, if I get a box and scrollbar into that functional state and then hover over the lower part of the box for a bit, then sometimes eventually it will break and stay broken until refresh again.  And in any case hovering over the lower part of the box causes the scrollbar to get taller.  Here is a screenshot of the issue:        Google Chrome 71.0.3578.98 (Official Build) (64-bit)  macOS High Sierra 10.13.6  Here is a code box that repros the issue for me:  fooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo   Here is another:  foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo foo Skip certain tables with mysqldump Finding specific records of US WW2 veterans? Logit or arcsine transformation for proportion in meta-analysis Pure virtual destructor in C++ I thought people would be working on little code projects together, but I don't see them, so here's an easy one:  Code that validates a valid US Zip Code. I know there are ZIP code databases out there, but there are still uses, like web pages, quick validation, and also the fact that zip codes keep getting issued, so you might want to use weak validation.  I wrote a little bit about zip codes in a side project on my wiki/blog:    There is also a new, weird type of zip code.     I can do the javascript code, but it would be interesting to see how many languages we can get here. Is there any way to force SQL Server NOT to mark subscriptions as inactive, ever?  It happens sporadically when there are connection issues and I don't want to have to reinitialize the subscription every time.  Note, I'm not talking about the subscriptions being marked as expired...just as inactive.  We have retention set to 0 (infinite). I'd rather have a big distribution database than have to reinitialize a 15GB database to a subscriber over the WAN. Anyway, the real issue here is that they are getting marked as inactive within just a few hours sometimes...or sometimes a few days...it seems sporadic. Is there any way to tell WHY SQL decided in its wisdom to mark them inactive?