I noticed that it is quite difficult to earn the [synonymizer] badge, and very few indeed earned it on SO.  Would it be appropriate to upgrade this badge from bronze to silver?
I noticed that Synonymizer is only a bronze badge. Yet in order to obtain this badge you need to have 2500 reputation or more to even create tag synonyms. Then, on top of that you also need to be able to find a tag synonym.  Only 514 of these have been awarded... This makes the BRONZE badge Synonymizer rarer to have than most the gold medal badges. So my question is, why is this a bronze badge?
On-shell and off-shell transformations in Noether's theorem For any transformation of the fields,  $$\varphi\to\varphi'=\varphi+\delta\varphi$$ the change in the Lagrangian can be written as  $$\delta\mathcal L = \text{EoM} + \partial_\mu j^\mu\tag{1}$$where "EoM" represents the equations of motion (Euler-Lagrange equations) and all other terms can be written as a total derivative of some function $j^\mu$, which is a known function in terms of the Lagrangian.   I would like to distinguish the different realizations of transformations. Let's assume that the transformation (1) leaves the action invariant, $\delta S=0$.    $\delta\mathcal L=0$   EoM $=0$, "on-shell": Noether current is conserved, $\partial_\mu j^\mu=0$. EoM $=\partial_\mu b^\mu\neq0$, "off-shell": modified Noether current $J^\mu = j^\mu+b^\mu$ is conserved, $\partial_\mu J^\mu=0$.   $\delta\mathcal L =\partial_\mu a^\mu \neq 0$, "quasi-symmetry"   EoM $=0$, "on-shell": modified Noether current $J^\mu = j^\mu-a^\mu$ is conserved, $\partial_\mu J^\mu=0$.  EoM $=\partial_\mu b^\mu\neq0$, "off-shell": modified Noether current $J^\mu = j^\mu-a^\mu+b^\mu$ is conserved, $\partial_\mu J^\mu=0$.     Is this listing correct?      What roles do the terms "on/off-shell" and "(quasi) symmetry" play in Noether's theorem?   Related: , , , , . Lets say I have a domain already, for example www.automobile4u.com (not mine), with a website fully running and all.  The title of my "Website" says:    &lt;title&gt;Used cars - buy and sell your used cars here&lt;/title&gt;   Also, lets say I have fully SEO the website so when people searching for the term buy used cars, I end up on the second or first page.  Now, I want to end up higher, so I go to the google adwords page where you can check how many searches are made on specific terms.  Lets say the term "used cars" has 20 million searches each month.  Here comes the question, could I just go and buy that domain with the search terms adress, in this case www.usedcars.com and make a redirect to my original page, and this way when people search for "used cars", my newly bought domain name comes up redirecting people to my original website (www.automobile4u.com)?  The reason I believe this benefits me is because it seems search engines first of all check website adresses matching the search, so the query "used cars" would automatically bring www.usedcars.com to the first result right?  What are the downsides for this?  I already know about google spiders not liking redirects, but there are many methods of redirecting...  Is this a good idea generally? Why does the sum of the reciprocals of factorials converge to $e$? I've been asked by some schoolmates why we have $$ \sum_{n=0}^\infty \frac{1}{n!}=e.$$ I couldn't say much besides that the $\Gamma$ function, analytic continuation of the factorial, is defined with an integral involving $e$. Then I also know that actually $$ \sum_{n=0}^\infty \frac{x^n}{n!}=e^x.$$ Is there a reason for these facts?  P.S. I added the tag "intuition", please remove it if you think it is not pertinent. Why must $a$ and $b$ both be coprime when proving that the square root of two is irrational? Suppose we wish to prove that the square root of two is irrational. We begin by assuming that it is rational.  Namely, where both $a$ and $b$ are integers $$\frac{a}{b} = \sqrt 2  % MathType!MTEF!2!1!+- % faaagCart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedmvETj % 2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0x % bbL8FesqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaq % pepae9pg0FirpepeKkFr0xfr-xfr-xb9Gqpi0dc9adbaqaaeGaciGa % aiaabeqaamaabaabaaGcbaWaaSaaaeaacaWGHbaabaGaamOyaaaacq % GH9aqpdaGcaaqaaiaaikdaaSqabaaaaa!31D3! $$  Why is it so important that both $a$ and $b$ be coprime and the fraction be irreducible?  That is, if $a$ and $b$ are not coprime and the fraction is indeed reducible, then$$\frac{a}{b} \ne \sqrt 2  % MathType!MTEF!2!1!+- % faaagCart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedmvETj % 2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0x % bbL8FesqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaq % pepae9pg0FirpepeKkFr0xfr-xfr-xb9Gqpi0dc9adbaqaaeGaciGa % aiaabeqaamaabaabaaGcbaWaaSaaaeaacaWGHbaabaGaamOyaaaacq % GHGjsUdaGcaaqaaiaaikdaaSqabaaaaa!3294! $$ How to calculate the following sum: How may one calculate  $$\lim_{n\to\infty} \ \left(\left(\sum_{k=1}^{n} \frac{1}{3k-1}\right) - \frac{\ln n}{3}\right) \ ?$$ Studying for CISSP these choices seemed limited:     What is the advantage of digital signatures over message authentication codes?         Digital Signature provides integrity verification while message authentication code does not   Digital Signature provides confidentiality while message authentication code does not   Digital Signatures provide authenticity while message authentication code does not   Digital Signatures works faster than message authentication codes      Using the following chart as a reference, I'm leaning towards #2, but none of the choices really fit properly…  Cryptographic primitive | Hash |    MAC    | Digital Security Goal           |      |           | signature ------------------------+------+-----------+------------- Integrity               |  Yes |    Yes    |   Yes Authentication          |  No  |    Yes    |   Yes Non-repudiation         |  No  |    No     |   Yes ------------------------+------+-----------+------------- Kind of keys            | none | symmetric | asymmetric                         |      |    keys   |    keys   Hopefully an expert here can clarify. Why does inductor current lag the applied voltage at its terminal by 90 degrees? I studied electromagnetism and I am currently working with Inductors.  I could not figure out the physical reason based on electromagnetics on why inductor current lags the applied voltage by 90 degrees?  Everywhere I find the Formula as the starting point of explanation which is partially satisfying.    Induced EMF =L di(t)/dt    From the above equation, I understood that when there is a change in current there will EMF induced in the coil terminals. But How this induced EMF makes the current to lag the supply voltage V(t) = Vm*sin(wt)? (Please don't just differentiate and say there is a lag, I am looking for a physical sense on why this happens)  Lets us consider the AC voltage is applied across the terminal at time t=0; At this time there is almost no current. From this transient state how the steady-state is reached where the current is delayed with respect to the voltage?  Can someone help me to figure out why the current lags the Supplied voltage by using electromagnetism, the motion of Charges or any other basic concepts? Finding and removing duplicate files in osx with a script From:  How do I modify this to only delete the first version of the file it sees.  Open Terminal from Spotlight or the Utilities folder Change to the directory (folder) you want to search from (including sub-folders) using the cd command. At the command prompt type cd  for example cd ~/Documents to change directory to your home Documents folder At the command prompt, type the following command:   find . -size 20 \! -type d -exec cksum {} \; | sort | tee /tmp/f.tmp | cut -f 1,2 -d ' ' | uniq -d | grep -hif – /tmp/f.tmp &gt; duplicates.txt   This method uses a simple checksum to determine whether files are identical. The names of duplicate items will be listed in a file named duplicates.txt in the current directory. Open this to view the names of identical files There are now various ways to delete the duplicates. To delete all the files in the text file, at the command prompt type:   while read file; do rm "$file"; done &lt; duplicates.txt Punctuation of direct speech, edge cases I recently learned that I have developed a consistent, but entirely wrong approach to punctuating direct speech in fiction. I am in the unenviable position of trying to relearn.  Previously I wrote such things as:     "I'm done." She said.   when the quoted speech was definitely, absolutely the end of a sentence. So now I know I need.     "I'm done," she said.   This follows the rule that a period is only allowed when the end of the spoken sentence is also the end of the sentence in the narrative. For example:     "I'm done." She slammed the door on the way out.   So, it now looks odd to me when there are multiple sentences in the speech:     "I can't take her. I'm done," she said.   Can you reassure me that is correct, or give the correct form? Please don't suggest rewriting the sentence to put 'she said' in the middle - I'm aware of that: I'm specifically asking about the punctuation rules.  The other odd case is speech ending with an ellipsis. Do sentence terminating ellipses (four periods normally) become:     "I can't take her. You know, ...," she said, nodding towards Jane.   If so, are non-terminating ellipses dealt with the same way?     "I can't take ...," she nodded towards Jane, "any more!"   or can non-terminating ellipses be used unadorned?     "I can't take ..." she nodded towards Jane, "any more!"   I'd be very grateful if you could point me at references as well as answers. For the record I am a British writer writing for both British and US publication, so any variation is also interesting to me! Open Safari / Google Chrome developer tools programmatically from JavaScript I am buing assamble self PC for playing games.  I am wondering, all the drivers, which are most likely for Windows, can i just use them on Ubuntu?  So if i understand you right, it will automaticaly detect the drivers, no need for installs ? or it find custom drivers for ubuntu.  This is the setup, will there be any problem with it? Did Darth Sidious and Vader ever discover how to cheat death? In Episode 3 Revenge of the Sith Palpatine/Sidious strings Anakin along to the dark side with the promise that together the two of them will be able to re-discover Darth Plagueis' secret to cheating death.      "To cheat death is a power only one has achieved, but if we work together, I know we can discover the secret."   From the end of Revenge of the Sith to their deaths in Return of the Jedi did Darth Sidious and Darth Vader ever manage to re-discover this secret? Agreement With Compound Subjects Joined by And I was surfing the internet the other day when I found this phrase: Instead your precious time and attention is wasted. To my ears, it sounds wrong. But I'm not a native English speaker, so I consulted with a number of them, and some of them said that it was "is" because the adjective modifies only the noun "time" and not "attention". Others said it "is" because that's just how it is. But I still believe it should be "are". Any help is appreciated. Why can't enum's constructor access static fields? Why can't enum's constructor access static fields and methods? This is perfectly valid with a class, but is not allowed with an enum.  What I'm trying to do is store my enum instances in a static Map. Consider this example code which allows lookup by abbreivation:  public enum Day {     Sunday("Sun"), Monday("Mon"), Tuesday("Tue"), Wednesday("Wed"), Thursday("Thu"), Friday("Fri"), Saturday("Sat");      private final String abbreviation;      private static final Map&lt;String, Day&gt; ABBREV_MAP = new HashMap&lt;String, Day&gt;();      private Day(String abbreviation) {         this.abbreviation = abbreviation;         ABBREV_MAP.put(abbreviation, this);  // Not valid     }      public String getAbbreviation() {         return abbreviation;     }      public static Day getByAbbreviation(String abbreviation) {         return ABBREV_MAP.get(abbreviation);     } }   This will not work as enum doesn't allow static references in its constructor. It however works just find if implemented as a class:  public static final Day SUNDAY = new Day("Sunday", "Sun"); private Day(String name, String abbreviation) {     this.name = name;     this.abbreviation = abbreviation;     ABBREV_MAP.put(abbreviation, this);  // Valid } How to determine a matching color code from a physical sample? I need to make a restaurant menu design that matches restaurant wallpapers. For some reason my client cannot get color codes used in wallpaper, but he provided me with a sample. (see below)    How can I get the correct color codes from the wallpaper? (someone mentioned that there are scanners for this purpose, but I could not find any information regarding that)  Let me know if this question should be in another site. How do I search for questions with specific tags?       For more information about searching, see &quot;&quot; in the . Which part of speech is "Be assured"? Which of the spans in 1.1 is the stronger? Be assured, you are in numerous company if you pick the left one at first glance, where the struts and wires are doing nothing useful at all.   Could you please tell me what is "Be assured" here?  I mean whether it is an adverb, adjective, so on?  And, would you please show me some examples exactly like such the following, considering my original sentence?     Be assured, ... As mentioned in many of my previous questions, I'm working through K&amp;R, and am currently into the preprocessor. One of the more interesting things &mdash; something I never knew before from any of my prior attempts to learn C &mdash; is the ## preprocessor operator. According to K&amp;R:     The preprocessor operator ##   provides a way to concatenate actual   arguments during macro expansion. If a   parameter in the replacement text is   adjacent to a ##, the parameter is   replaced by the actual argument, the   ## and surrounding white space are   removed, and the result is re-scanned.   For example, the macro paste   concatenates its two arguments:      #define  paste(front, back)  front ## back      so paste(name, 1) creates the token   name1.   How and why would someone use this in the real world? What are practical examples of its use, and are there gotchas to consider? What is the difference between Shrink Database and File? DBCC ShrinkDatabase() DBCC ShrinkFile()    Do I need to run both DBCC commands in order to shrink the database? What is the difference between these two above? Does the 90 days VWP rule expire if you travel from the US to Canada? I'm on a New Zealand passport.  From most US Embassy webpages:     The Visa Waiver Program (VWP) enables nationals of certain countries,   including Australia, New Zealand, and the U.K., to travel to the   United States for tourism or business for stays of 90 days or less   without obtaining a visa, if certain requirements are met. Under the   VWP, time spent in Canada, Mexico, and adjacent islands counts towards   the maximum of 90 days stay allowed under the program.   I'll be there on a 1-year working holiday visa starting when I arrive in Vancouver. I'm spending 3 days in Hawaii en route to Vancouver. This seems to imply that 90 days after landing in Hawaii, my time will be up and I won't be able to get back into the US, as my living in Canada will not reset the clock. What if after this time I want to say, pop across the border to Seattle? How can I restart the 90 days, without having to resort to say, flying to Japan and back just to reset it?