Fundamental question about dimensional analysis

In dimensional analysis, it does not make sense to, for instance, add together two numbers with different units together. Nor does it make sense to exponentiate two numbers with different units (or for that matter, with units at all) together; these expressions make no sense:  $$(5 \:\mathrm{m})^{7 \:\mathrm{s}}$$  $$(14 \:\mathrm{A})^{3 \:\mathrm{A}}$$  Now my question is plainly this: why do they not make sense? Why does only multiplying together numbers with units make sense, and not, for instance, exponentiating them together? I understand that raising a number with a unit to the power of another number with a unit is quite unintuitive - however, that's not really a good reason, is it?


Why is phase space volume of a energy surface proportional to probability of a microstate of that energy?

In the book of Intro. Statistical Mechanics by Huang, at page 156, while explaining macro canonical ensemble, the author states that  We are interested in the probability of occurrence of the microstate $\left\{p_{1}, q_{1}\right\}$ of subsystem 1 , regardless of the state of system 2 : Probability that 1 is in $\mathrm{d} p_{1} \mathrm{~d} q_{1} \propto \mathrm{d} p_{1} \mathrm{~d} q_{1} \Gamma_{2}\left(E-E_{1}\right)$  where system 1 and 2 are the closed system and the heat reservoir, respectively. And $\Gamma_2 (E-E_1)=\Gamma_2(E_2)$ is the phase space volume of the reservoir having total internal energy $E_2$. However, the above statement contains an implicity assumption that the probability of system one having a state of energy $E_1$ is proportional to phase space volume over the states with that energy. Meaning that the probability of a microstate being occupied by the system is proportional to macrostate of that microstate. Hence, the occurence of microstates aren't equal overall, but rather microstates have the same probability of occurence only within the set of microstates having the same macrostates. This is different than ergodic hypothesis, which assumes all microstates have the same probaility of occurence regarless of their macrostates. Where does this assumption come from? Is there an explanation for why this must be the case?


Is there a --parents option for mv like for cp?

cp has a useful feature --parents that allows a file's directory structure to be copied to another directory:  $ cp -v --parents source/directory/from target/ ‘source/directory/from’ -> ‘target/source/directory/from’   How do I similarly move a file?


Does Sword of Sharpness's maximize damage rule apply to a Rogue’s Sneak Attack damage?

If a rogue hits someone with a scimitar of sharpness and the preconditions for sneak attack are in place, does the rogue also get to maximize the damage of sneak attacks? For reference the  states:  When you attack an object with this magic sword and hit, maximize your weapon damage dice against the target. [...]


How to crop borders/white spaces from image?

I have a lot of images which have white borders around them. I would like to crop those borders all at once, preferably from command line. I believe that it can be done with ImageMagick, but I couldn't find suitable command.  I know that it can be done with Windows program named Irfanview with "Auto crop borders" option, but I am looking for Ubuntu-based and preferably command line based solution.


Can we assume that most (if not all)  black holes are rotating, due to conservation of momentum?  I am excluding the micro world from this question, just thinking of the range of stars on the main sequence of the H-R diagram as they shrink over time.    Can anyone give me an example of non-rotating macro sized B.H., e.g a binary system where each star counter-rotates relative to the other and explain how they may, (if they can)  at least slow down each others's rotational velocity?


My lock screen looks like this.    And when I log in, my computer doesn't get lock.


Notation of a function raised to a power

$f(x)^2$ is sometimes written as $f^2(x)$.  Why is it not written as $f(x)^2$?  Is it just a matter of taste or convention?


Include leading zeros in a CSV file without importing

I have code that creates a csv mailing list for use in Excel 2013. My problem is that when the csv is clicked to open in Excel, the leading zero on zip codes is removed.   In older versions of Excel, you could add a single quote to denote that the cell should be treated as a string, but in the newer versions, the single quote is included. I've also tried double quotes and enclosing the zip code in single and double quotes with no luck.  I know that you can change the csv to a text file, and then manually import it into Excel, setting the zip column as a text column, but I would prefer make it easier on the end user.   Is there a way to import a number as a string from a csv in Excel 2013?


Show that $G=HN$ for $N$ normal and $H$ subgroup.

I have the following practice homework where I have run out of ideas: Let $G$ be a group and let $N$ be a normal subgroup in $G$ with index $p$ (prime). Let $H$ be a subgroup in $G$ which is NOT contained in $N$. Show that $G=HN$ and $[H:H \cap N]=p$ I am thinking about maybe I need to apply an isomorphism theorem but I can't get anyone to fit.


Cannot link object files because of undefined reference

I cannot link object files. Compilation works fine, but the linker gives me these error messages:      testArguments.o: In function Z6__mainiPPc':   /cygdrive/c/Users/Lukas/work/ProxyServer/src/test/testArguments.cpp:5:   undefined reference toArguments::Arguments()'   /cygdrive/c/Users/Lukas/work/ProxyServer/src/test/testArguments.cpp:6:   undefined reference to Arguments<int>::insertItem(int)'   /cygdrive/c/Users/Lukas/work/ProxyServer/src/test/testArguments.cpp:8:   undefined reference to_Unwind_Resume' testArguments.o: In function   ZNSt10_List_baseIiSaIiEED2Ev':   /usr/lib/gcc/i686-pc-cygwin/4.8.2/include/c++/bits/stl_list.h:378:   undefined reference to_Unwind_Resume' testArguments.o: In function   ZN9__gnu_cxx13new_allocatorISt10_List_nodeIiEE10deallocateEPS2_j':   /usr/lib/gcc/i686-pc-cygwin/4.8.2/include/c++/ext/new_allocator.h:110:   undefined reference tooperator delete(void*)'   testArguments.o:testArguments.cpp:(.eh_frame+0x13): undefined   reference to __gxx_personality_v0'   testArguments.o:testArguments.cpp:(.eh_frame$_ZNSt10_List_baseIiSaIiEED2Ev+0x13):   undefined reference to__gxx_personality_v0' Makefile:7: recipe for   target 'tests' failed   But these functions are defined in the cpp file (Argument::Arguments() Arguments::insertItem(int)   Here is my header file:  #ifndef ARGUMENTS_H   #define ARGUMENTS_H  #include <list>   using std::list; template<class T> class Arguments{  public:          Arguments(list<T> args);>      Arguments()>;      void insert>Item(T item);      list<T> getValues();  private:      list<T> values; }; #endif   Here the cpp file:  #include "include/Arguments.h" #include <list> using std::list;  template<class T> Arguments<T>::Arguments(list<T> args) {      values = args;  }  template<class T> Arguments<T>::Arguments() {  }  template<class T> void Arguments<T>::insertItem(T argument){     values.push_back(argument);  }  template<class T> list<T> Arguments<T>::getValues() {     return this.values;  }


Let $f\colon X\to X$ be a homeomorphism between a CW-complex $X$ and iteself.  Let $M_f=X\times [0,1]/(x,0)\sim (f(x),1)$, mapping torus of $X$ from $f$.  I want to calculate the fundamental group $\pi_1(M_f)$ of $M_f$ in terms of $\pi_1(X)$ and $f_*\colon \pi_1(X)\to \pi_1(X)$.  Are there any hint to do this?  Note: This is not a homework problem.


Dynamically allocating an array of objects

I have a class that contains a dynamically allocated array, say  class A {     int* myArray;     A()     {         myArray = 0;     }     A(int size)     {         myArray = new int[size];     }     ~A()     {         // Note that as per MikeB's helpful style critique, no need to check against 0.         delete [] myArray;     } }   But now I want to create a dynamically allocated array of these classes. Here's my current code:  A* arrayOfAs = new A[5]; for (int i = 0; i < 5; ++i) {     arrayOfAs[i] = A(3); }   But this blows up terribly. Because the new A object created (with the A(3) call) gets destructed when the for loop iteration finishes, and this means that the internal myArray of that A instance gets delete []-ed.  So I think my syntax must be terribly wrong? I guess there are a few fixes that seem like overkill, which I'm hoping to avoid:   Creating a copy constructor for A. Using vector<int> and vector<A> so I don't have to worry about all this. Instead of having arrayOfAs be an array of A objects, have it be an array of A* pointers.   I would think this is just some beginners thing where there's a syntax that actually works when attempting to dynamically allocate an array of things that have internal dynamic allocation.  (Also, style critiques appreciated, since it's been a while since I did C++.)  Update for future viewers: All of the answers below are really helpful. Martin's is accepted because of the example code and the useful "rule of 4," but I really suggest reading them all. Some are good, succinct statements of what's wrong, and some point out correctly how and why vectors are a good way to go.


If the received value is "" ,we want to delete that particular property from object

For a given object if the input "value" of a property is "" , we want to delete that property from the object .  Ex   {  "Speed": "59 MBPS",  "latitude": "90.2",  "longitude": "" }   As per the example ,since the value of longitude is "" , this should get deleted from the object. Please suggest a javascript code to achieve this .


Third person imperative recommendations/suggestions/requests

My question is on the grammatical correctness of the following sentence with regard to the form of the verb 'join':     The plan is that the group join the party.   Other sentences that I think represent the same issue (regarding the verbs sing, consider, maintain) are:     I ask that the choir sing at the banquet.      The advice is that the committee consider the alternative.      The advisor recommends that the firm maintain its involvement.   In each of these above sentences I attempt to make a command (do this: join, sing, consider, maintain) but to a third person subject (as though not speaking directly to the group/choir/committee/firm).  Microsoft Word's grammar features suggest correction to me from 'join' to 'joins'.  Is it grammatically incorrect as I have written it?  Basically I am trying to write a proposal in which I implore a recommendation.  I essentially want to say, imperatively, "do this", but more gently/politely or in a more passive tone.  I picked to say "that the group join" because to me it's as though I am saying "that the group will join" or "that the group would join", but I don't want to write that out to avoid being too pushy (saying that it 'will' do as I say) nor too nonpersuasive (telling them that they 'would' do as I say, if they feel like it.. or not.. whatever..).  Nor do I want to say "the plan is that the group joins" because my purpose is to recommend (propose) for the group to carry out the action, in the future.  What's a correct word choice or conjugation here? What's the best tense for the sentence?


What is the average & max temperature of an airplane cargo hold?

I want to take some chocolates to offer in my luggage. Chocolates are a bit sensitive to heat, though. What is the average temperature inside a cargo hold? 'Average by' itself can be misleading. What is the max temperature there?  I don't know much about airplane mechanics but I assume they have some cooling systems like any other engine. Such systems, depending on where they are placed, might influence temperature in the cargo hold. I also fear temperatures in the ground while exterior temperatures are higher, and luggage is being put inside. What are max temperatures near the airplane in such situation?


I understand that Python uses hash method to lookup the keys in the dictionary but if the dictionary grows too large and the key do no longer fit in the hashing result range (collision), how would python handle it ?  how do we handle dictionaries with billions of record(too many keys which will make collision occur at high rate), should we change the hashing function if yes, how to do it ?


How to print paragraphs in twig template?

I have a content type, basic, where i have added a Paragraph field field_pr that has two fields: field_text, field_color. I have a twig template node--basic--full.html.twig where I want to print the value of the paragraph field node.field_pr.   node.field_pr can have between one and ten paragraph values.   When I print the array for content.field_pr, I get a huge array. However, I only want the values from the field_pr.field_text and field_pr.field_color. How would I be able to do this from the node twig template?   I have tried the following but cannot seem to access the values. What am I missing?  {% for field in content.field_pr %}    {{ field[loop.index0].entity.field_text.value }}    {{ field[loop.index0].entity.field_color.value }} {% endfor %}  {% for field in content.field_pr %}    {{ field[loop.index0]['#paragraph'].field_text.value }}    {{ field[loop.index0]['#paragraph'].field_color.value }} {% endfor %}   Here is an image of the array that is printed for the node.field_pr field.


How to manage a redirect request after a jQuery Ajax call

I'm using $.post() to call a servlet using Ajax and then using the resulting HTML fragment to replace a div element in the user's current page. However, if the session times out, the server sends a redirect directive to send the user to the login page. In this case, jQuery is replacing the div element with the contents of the login page, forcing the user's eyes to witness a rare scene indeed.   How can I manage a redirect directive from an Ajax call with jQuery 1.2.6?


When referring to 1 million dollars, do you use it or them?

I am not sure because there is more than one dollar, but when referring to the one million dollars only, would you use "it"?


If $f$ continuous at $x_0$ and $f(x_0)>0$   then how to show there exist $\epsilon>0$ and $\delta>0$ such that $f(x)>0$ for $|x-x_0|<\delta$.  I don't know to start proving and then i use definition continuous function at $x_0$ is  $\forall\epsilon>0, \, \exists\delta>0 \, \text{such that if }|x-x_0|<\delta\implies |f(x)-f(x_0)|<\epsilon$


Why Vi editor can be "time-efficient" in comparison to using Nano editor?

I'm working through OSCP course where I'm getting familiar with terminal-based text editors. I'm quite comfortable with Nano and this material says that penetration testers have reported that Vi editor saved them a great deal of time. How so ? I mean, Nano editor is so straightforward and yet Vi gets the praise.


My daughter is one years old I've been putting her on the potty 1st I would put her on the big toilet, and realized she didn't like it. now she sits on the potty.some days she goes and somedays she doesn't. What am I doing wrong? And she likes to drink a lot of water and juice please help. I let her sit for about 35 minutes in the morning noon and night


I need to know EXACTLY how lighting affects combat, and if it does at all. It's listed in the DMG as just an explanation of an environmental thing, but how does it work specifically?  Does Dim Light or Darkness affect attack rolls and how? I've heard that Dim Light causes a -2 penalty, and Darkness inflicts a -5 penalty, on anyone with normal sight. WOTC refute this as incorrect.  How does Dim light or Darkness affect concealment? Do they add to the roll? Do they allow concealment to occur? Do they automatically grant concealment?  Two fighters and standing side by side taking swings at each other. One is standing in Bright Light, the other in Dim Light, or Bright Light/Darkness, or Dim Light/Darkness. Does one have an advantage over the other?  I need to know what exact mechanics occur in these circumstances, if any.


This question came up when I recently answered this question  and I found this question  which seemed to be related, but the given answers do not really satisfy me. Also this question  is about the cooling of a deodorant spray and doesn't address the cooling of the container. A web search gave conflicting, mostly not scientifically well explained answers.   In my opinion, there are three possible cooling effects:  (1) The adiabatic expansion of the gas involves work against the external pressure thus cooling the gas. This should already work for an ideal gas.  (2) The adiabatic expansion of the gas leads to a cooling due to the Joule-Thompson effect because the gas is not an ideal gas. This is due to a change of kinetic to potential energy of the molecules.  (3) The cooling of the container is due to evaporation cooling of the liquified gas inside the container.  ad (1) The problem with answer (1) is that the adiabatic expansion occurs outside the container against the air pressure. Thus the cooling should only occur for the outside gas not for the gas in the container.  ad (2) This problem should not occur  for answer (2) because the JT cooling effect already takes place inside the container upon pressure reduction. Also the cooling outside the container should occur.  ad (3) The gas is partially liquified inside the container due to the high pressure (e.g. butane) and the cooling of the container is caused by the evaporation heat of the liquid.  In the case of the aerosol spray I am now inclined to think that my answer (3) is the dominant effect in the container cooling. This does, however, not conform with the top rated answer (work due to adiabatic expansion of gas) of the mentioned identical question.   Am I right with my suspicion that a cooling by adiabatic expansion of an ideal gas cools the gas outside but not inside the container?   Is the container indeed cooled mainly by the liquid evaporation heat effect? Or is the Joule Thompson effect more important?


I have an html page which gets loaded via ajax, the newly loaded html content has the following html. It typically works great when I load the html first and then initialize the javascript.   Change password   My js:  $('.ajax-button').on('click', OnLoadContent);  function OnLoadContent(e) {     e.preventDefault();     var pageurl = $(this).data('url');     $.ajax({         type: "GET",         url: pageurl,         success: function(data) {             alert(data);             $("#content-container").html(data);             window.history.pushState({path:pageurl}, '', pageurl);         },         error: function(response) {            alert("ERROR:" + response.responseText);         }     }); }   However since it's new html content that's being loaded I think the problem is the javascript already exists when the html content is loaded via ajax, so the click functionality doesn't work unless I click again. I'm wondering how I can fix this?


Unsupervised learning for anomaly detection


Why does the first block of code get highlighted but not the second one?  Is the second code block being interpreted as part of the second list item?  If so, how do I close the second list item so I can start marking code with only 4 spaces?  Sub HereIsSomeCode()  End Sub    First list item. Next list item.  Sub HereIsSomeCode()  End Sub  (code prefixed by 8 spaces) Sub HereIsSomeCode()  End Sub


Generalization of index 2 subgroups are normal

Let $G$ be a finite group and $H$ a subgroup of index $p$, where $p$ is a prime. If $\operatorname{gcd}(|H|, p-1)=1$, then $H$ must be normal. Does somebody have a quick proof of this?


Proof by induction that fibonacci sequence are coprime

I have a bit difficulty to proofe that two consecutive numbers are coprime. I have the following  The property $P(n)$ is the equation $(F_{n+1},F_n)=1$ where F_i the sequence of fibonacci is and $n \in \mathbb {N}$.  Induction hypothesis: $gcd(F_{n+1},F_n)=1$  $P(0)$ is true because $F_1=1, F_0=1$ and $gcd(1,1)=1$  To show: $gcd(F_{n+2},F_{n+1})=1$  Proof:  Fibonacci formula says  $F_{n+2}=F_{n+1}+F_n$  This is as faar as I got. How can I now get to $gcd(F_{n+2},F_{n+1})=gcd(F_{n+1},F_n)$ which would then proofe it?


For example, given four distinct numbers $5, 6, 7, 9$ We have $2^4-1$ sums, $5, 6, 7, 9, 11, 12, 14, 13, 15, 16, 18, 22, 20, 21, 27$ which are the sums from the numbers.  But if given five distinct numbers $5, 6, 7, 8, 9$, then we see $5 + 9 = 6 + 8$, hence the possible distinct sums of them cannot be easily counted by $2^5-1$.  Is it possible to easily count all the possible distinct sums from distinct numbers? Thanks!


Lets say I have a table named users with the fields id, name, username, and password. When i write the query for getting all of the fields, is it better to write it this way  $sql = mysqli_query($con,"SELECT * FROM users LIMIT 50");   or this way:  $sql = mysqli_query($con,"SELECT id, name, username, password FROM users LIMIT 50");   for this code:  while($me = mysqli_fetch_array($sql)){  $id = $me['id']; $name = $me['name']; $user = $me['username']; $pass = $me['password']; }   Is one better then the other. Is one more finely tuned then the other. Or are they both the exact same performance wise


What is the difference between FTPS and SFTP?

Trying to set up a system for my 4 remote employees to transfer files.  It has to be secure.  Is SFTP better than FTPS?  What is the difference?


How to pass an enum that I created from view to controller using FormCollection in Asp.Net MVC

So now I can retrieve a string and integer  by doing this for string   LastName = formCollection["LastName"]   and for int  Amount = int.Parse(formCollection["Amount"])   My problem now is for enum. I tried this, still have an error    Issuer = Enum.Parse(formCollection["Issuer"]);   Issuer = Enum.Parse(typeof(Issuer), formCollection["Issuer"]);


Adding several ArrayList elements into one ArrayList

I have several "ArrayList"  Like this:   ArrayList<Integer> list1; ArrayList<Integer> list2; ArrayList<Integer> list3;       list1: [0,1,2]   list2: [22,12,23,24,53]   list3: [21,43,21,7]   I want to put all elements of all lists into one ArrayList like  sumList [0,1,2,22,12,23,24,53,21,43,21,7]   How is that to be done?  thx u


What would be a guide to review first-post?

I find a lack of coherency between the many people that review in SO specially related to new-users. The actual help says:     No Action Needed when this post needs no action from you.      I'm Done is only available if you've done one of the following:         Vote up or down to rate the answer's helpfulness   Edit to improve theanswer's appearance, clarity, or accuracy    Comment to leave constructive feedback for the author, or vote up existing comments   Flag to notify the moderators of serious problems         Be sure to leave a comment if you can help the user out, or click Skip if you are not sure and want to go to the next item.   But which is the most important which should be done first? Which would be a manual, guideline to do with this post? I adapted  to a similar question but focusing in review, not so much on interaction with the user.   Flag if it is appropiate Edit 2.1 Edit the grammar 2.2 Edit code/ quoted blocks 2.3 Edit tags Up/Down Vote Comment 4.1 Something to improve of the question 4.2 Require more details to answer the question 4.3 Refer to a manual/help page   Is this a good protocol? I tried  not to forget to .


How many closed polygons $n$ lines make on a plane?(not duplicate)

How many closed polygons will $n$ coplanar lines, all intersecting each other (no three concurrent), form on the plane?  Can we find a recursion formula for this?? Is there a way out?


How to remove space being parsed from string?

I want to read a text file containing a sequence of number as below:  1.000000  1:-0.362772 2:-0.314085 3:-0.177185 4:0.898650 5:-0.154588   Currently, I'm reading the line and I use split() method to split the number and store the numbers into an array. There are 3 variables will be used to store array elements, output,number, and value.  1.000000 will be the output as an integer, [1, 2, 3, 4, 5] will be an array of numbers, and [-0.362772,-0.314085,-0.177185,0.898650,-0.154588] will be the array of values.  Here is my code:  while (line != null) {         double output = 0;         inputs = new double[6];         String[] inputPairs = line.split(" ");         output = Double.parseDouble(inputPairs[0]);         for (int i = 1; i < inputPairs.length; i++) {             int components = Integer.parseInt(inputPairs[i].split(":")[0]);             double data = Double.parseDouble(inputPairs[i].split(":")[1]);             inputs[components] = data;         }         outputs[counter] = (int) output;         input[counter] = inputs;         counter++;         line = br.readLine();     }   However, when I execute the code I got this exception:  Exception in thread "main" java.lang.NumberFormatException: For input string: ""     at java.lang.NumberFormatException.forInputString(NumberFormatException.java:65)     at java.lang.Integer.parseInt(Integer.java:592)     at java.lang.Integer.parseInt(Integer.java:615)     at testReadFile.main(testReadFile.java:32).   I noticed that there is an extra space after the first index: 1.000000  1:-0.362772 being stored in the 2nd element of the array.  How do I remove the space? I have used trim() but it doesn't work. Or is there a way to remove the array[2] which contains the space?


Unity notifications of software updates when there are none

I keep getting numerous notifications throughout the day that there are updates. However, running the updater shows a different story. Running sudo apt update && sudo apt upgrade -y says all is up to date.   Which should I trust?


How to pluralize an acronym which ends in 'S' correctly?

When using the acronym package, how can you  an acronym which ends on 'S'?  Take the acronym: OS - operating system  It should be pluralized as OS's, but is pluralized as OSs when using \acp.


Suppose 500 individuals were asked one question having possible answers ”yes” or “no”. Denote by p the proportion of “yes” in the whole population. Estimate the probability that the proportion of “yes” in the sample (out of 500) is greater than in the whole population (p) by more than 5 %.  I was thinking of using the normal approx of the binomial where.. n = 500 p = 0.5 q = 0.5       Formula: \begin{align*}  P\left(\frac{N - np}{\sqrt{npq}}\right)\\ \end{align*} However, I'm not sure what the N value would be in this case.


How to prove $\displaystyle \lim_{x\to 0}\frac{\sin x}{x}=1$ with out Squeezing?

The same question have been asked . But almost all the answers given there use the idea of squeezing one way or another, even  geometric proof uses the idea of squeezing. So, here is my question; how to prove $$ \lim_{x\to 0}\frac{\sin x}{x}=1 $$ without the idea of squeezing involved.  Edited: No offense, but proofs of limits using integrals or derivative(or any other concepts that are defined using limits) to me is like building a house starting from the roof.  So I am not looking for those kind of proofs.


ffmpeg: how to convert mov file to gif , and gif is resized

how to use ffmpeg to convert mov file to gif , and gif is resized directly?  Here is the   I firstly convert mov to gif,  ffmpeg -i input.mov -pix_fmt rgb24 output.gif,  then use imageMagick to resize the gif.  convert   output.gif -coalesce temporary.gif convert -size 756x1504   temporary.gif -resize 189x376 smaller.gif   Here is the result:     How to use ffmpeg to do this directly, without using imagemagick


Simple and elegant way to split a string based on delimiter (ie, space) in C++

I'm trying to find a way to split a string based on space, but haven't been able to find any simple or working solutions online. In python, we had a .split() function that worked easily, but not in C++.  For example, I'm trying convert this string:  "I love 29 pies"   to this vector:  {"I", "love", "29", "pies"}   Thanks in advance!


why md5sum 2>&1 > /dev/null show error message

I have command like this:  md5sum -c {FILENAME} 2>&1 > /dev/null || ./upload {FILENAME}   and it show error if file is missing or invalid, I need to use this in order to hide the message:  md5sum -c {FILENAME} 2>/dev/null > /dev/null   why 2>&1 don't work?


Confusion about a simple proof of prime ideal implies irreducibility in UFD.

Let $R$ be a UFD if $f\neq 0$ and $\langle f\rangle$ is a prime ideal then $f$  is irreducible. Here is a short and easy proof for this claim but I do not understand the last bit. Assume for a contradiction that $f$ is not irreducible then $f=uv$ where $u$ and $v$ are not units. By $\langle f\rangle$ a prime ideal we have either $f|u$ or $f|v.$ WLOG, assume former, then $uv=f|u$, this contradicts irreducibility of $u$. My question: Where in this proof have we assumed $u$ is irreducible? {I can see that we can alter this proof a bit by using UFD property to say $f=r_1...r_k$  say where $r_i$ are irreducible then the same can follow. Alternatively $uv|u$ also contradicts $v$ is not a unit. But my question is where on this proof did we assume $u$ is irreducible?} Many thanks in advance!


Proof that a circle can be circumscribed around a quadrilateral

I'm solving a problem you can see above: $PQRS$ is a trapezoid, $HM$ and $KN$ are legs bisectors. I'm supposed to prove that $\alpha = \beta$, which as you look closely can be reduced to proving $$\measuredangle SPM = \measuredangle NQR$$ (equivalently $\measuredangle PSM = \measuredangle NRQ$).  Hypothesis  These angles somehow resemble inscribed angles on arc $NM$. A circle could be circumsribed around $PQMN$ or $NMRS$. But I'm struggling with proving that one can actually circumsribe a circle around either of these. I'd appreciate some help from you.   you can find a brilliant drawing by User Raffaele who's done a great deal of work on the problem. However, a rigorous solution has not been provided by anyone.


Find the integral solutions to $ x^2+y^2+z^2=x^2y^2$

I am unfamiliar with this type of problem. How does one solve this and under what category of math does this fall under.  Find the integral solutions for $x^2+y^2+z^2=x^2y^2$


I want to be able to default all new users created with the wp_login (register) box to have the user option: Show Toolbar when viewing site set to unchecked. I have the facility to then jump into wp-admin from within my website as and when required, but I don't want the black bar always showing. Its all works perfectly fine if the option is unchecked, but any new user is checked by default which means until I can manually uncheck it I have a problem. Thanks


I have the following query:  EXEC ('SELECT  ID,           Date,           Type,                                   FROM DB2T.BBT') AT DB2   How do I store this into a table so that I can add results from another query to do it? I'm very new to sql and have done a lot of searching but it seems everything I find is specific to that scenario. Is there a simple way to do this?


Why didn't Maester Ebrose mention Tyrion?

Why didn't he mention Tyrion?  List of things Tyrion has done:    Hand of the King  Defended Kings Landing in the battle of Blackwater Accused and convicted of killing King Joffrey.  Killed the most powerful man in the Seven Kingdoms, Tywin Lannister.  Hand of the Queen to Daenerys Targaryen.  6 Lord of Casterly Rock and Lord Paramount of the West.  Proposed the idea of elected monarchy.    Why didn't he mention him!


I'm trying to find $$\lim_{(x,y) \to (0,0)} \frac{x^2+y^2}{\sqrt{x^2+y^2+1}-1}$$  Book says answer is $2$, though nothing I tried gave me a $2$. I did $y=mx, y=0, x=0$, all ways learned in classes, but only find $0/0$ and $0$ as answers.


Let  $ f_1,\ldots,f_n$ be linearly independent linear functionals on a vector space $X$. Show that there are $n$ elements  $x_1,\ldots,x_n$ in $X$ such that the $n\times n$ matrix $[f_i(x_j) ]$ is non-singular.


Reference name of description list items in latex

I want to refer to a description list item by name instead of number. To that effect, I've added labels to each item, but when referencing them I only get the name of the section, not of the list item. How can I change it to show a custom label for each item?  \section{Definitions} \begin{description}   \item[Rule1\label{itm:1}] The Suffix to Prefix Rule.    \item[Rule2] The Substring Matching Rule \label{2}   \begin{description}     \item[Rule2-1] Character Matching Rule \label{2-1}   \end{description}   \item[Rule3] The Uniqueness Property Rule \label{3} \end{description}   i want to reference the above rules somewhere in my document but every time i call only section number is displayed


<lightning:recordViewForm will not display

I have a <lightning:recordViewForm in a custom lightning component.  When I hardcode the recordId attribute it works, but when I pass an attribute in it fails without any error messages in either the console or the debug log.  Component  <aura:handler name="init" value="{!this}" action="{!c.doInit}" /> <aura:attribute name="recordId" type="Id"></aura:attribute>  <lightning:recordViewForm recordId="{! v.recordId }" objectApiName="MyCustomObject__c">      <lightning:outputField fieldName="Name" />  </lightning:recordViewForm>   JavaScript Controller  doInit : function(cmp, event, helper) {      // var recordId = helper.getQueryStringParameter('recordId');      cmp.set("v.recordId", "a0C4E000003YMkmUAG"); }   The above does not work, even if I put the recordId directly into the attribute.  It only works when I set the Id in the recordId attribute of the <lightning:recordViewForm like below:  <lightning:recordViewForm recordId="a0C4E000003YMkmUAG" objectApiName="MyCustomObject__c">      <lightning:outputField fieldName="Name" />  </lightning:recordViewForm>


How to call a method from the main() that is in the same class?

I have the following situation.  I have a Main class in which I declared the standard public static void main(String[] args) method  Into the body of this main() method I am trying to call the following printPdf() declared into the Main class:  private void printPdf() {      /** The resulting PDF file: */     String result = "D:/SOFTLAB/massive_pdf_print.pdf";      // STEP 1 Creazione del documento in formato A4 e senza margini:     com.itextpdf.text.Document document = new com.itextpdf.text.Document(com.itextpdf.text.PageSize.A4, 0, 0, 0, 0);      try {         /* STEP 2 Constructs a PdfWriter.                   document: The PdfDocument that has to be written.                   os: The OutputStream the writer has to write to          */         PdfWriter.getInstance(document, new FileOutputStream(result));          // STEP 3:         document.open();          // STEP 4:         document.add(new Paragraph("Hello World!"));          // STEP 5:         document.close();      }catch (DocumentException ex){         ex.printStackTrace();     }     catch (IOException ex){         ex.printStackTrace();     }  }   To call it I do:  this.printPdf();   but I obtain the following error message: 'mainPkg.Main.this' cannot be referenced from a static context  So I think that it happens because the main() method is a static method but how can I correctly call my printPdf() method (that is declared in the same Main class that contains the main()) ?  Tnx


Phrase to refer to community of people who come together to exchange knowledge

I need a two word phrase to refer to a community of people (academia + non-academia) who come together to share/exchange their knowledge/ideas openly on topics of their interests/ specializations.  I would appreciate the use of small and easier/common words for the phrase. Single words are also acceptable. Feel free to throw out your creative ideas and newly invented phrases.


Replace value of global array of char* with strncpy

Say there is a common c array of type char *. I want to replace the value of a specific element, say index 0, by replacement. My code results in a segfault. What is the problem?   #include <string.h>  char * data[] = {   "aaa",   "bbb",   "ccc" };  int main(int argc, char *argv[]) {   char * replacement = "xxx";   strncpy(data[0], replacement, 3);   return 0; }


How to read int values from a JTextField?

I have 2 JTextField on my form and I declared these 2 variables globally      int order = Integer.parseInt(textOrder.getText());    int history = Integer.parseInt(textHistory.getText());   but I got these errors.      java.lang.NullPointerException at FrameController.<init>(FrameController.java:39)//this is line 39: int history=Integer.parseInt(textHistory.getText());  at FrameController$1.run(FrameController.java:56)//this is line 56:     FrameController window = new FrameController(); at java.awt.event.InvocationEvent.dispatch(Unknown Source) at java.awt.EventQueue.dispatchEventImpl(Unknown Source) at java.awt.EventQueue.access$500(Unknown Source) at java.awt.EventQueue$3.run(Unknown Source) at java.awt.EventQueue$3.run(Unknown Source) at java.security.AccessController.doPrivileged(Native Method) at java.security.ProtectionDomain$JavaSecurityAccessImpl.doIntersectionPrivilege(Unknown Source) at java.awt.EventQueue.dispatchEvent(Unknown Source) at java.awt.EventDispatchThread.pumpOneEventForFilters(Unknown Source) at java.awt.EventDispatchThread.pumpEventsForFilter(Unknown Source) at java.awt.EventDispatchThread.pumpEventsForHierarchy(Unknown Source) at java.awt.EventDispatchThread.pumpEvents(Unknown Source) at java.awt.EventDispatchThread.pumpEvents(Unknown Source) at java.awt.EventDispatchThread.run(Unknown Source)


Chrome updates fail with error when updating repository information

When running sudo apt-get update I get the error:     Failed to fetch  Unable to find expected entry ‘main/binary-i386/Packages’ in Release file (Wrong sources.list entry or malformed file)   But this used to work until a few days ago. The mentioned web address dl.google.com/.../stable/Release actually exists but it contains only Architectures: amd64. The error message mentions binary-i386, which is not amd64.  I tried all the usual fixes for general "Failed to fetch" problems but it did not make any difference in this case. Any suggestions? How can I fix the error message?


javascript, how to create a string using C similar function "printf"

In C there is a printf function that I can put %d in the statement and pass the value into it later.  I ma just wondering is there a similar function in Javascript so that I can do something like printf("The number is: %d", 18) and it return a string "The number is:18"?  I searched online and I found an open source call sprint, but it seems to be over-kill since I don't use this frequently in my project.  Many thanks!


Number of digits in binary representation of n

For n $\in$ N let $\beta(n)$ denote the number of digits used in the binary representation of n. For example         $\beta(1)$ = 1         $\beta(2)$ = 2         $\beta(3)$ = 2         $\beta(4)$ = 3 Find a closed formula for an arbitrary n $\in$ N  where N is the set of natural numbers.  So what I have is the representation of n = 1...12 in binary so,         n = 1: $2^0$          n = 2: $2^1$         n = 3: $2^0$ + $2^1$          etc. But the closed form solution isn't apparent


The expression "sleep together" has a sexual context, but I'm looking for the expression when two or more people are literally sleeping together. Is there such an expression? The usage would be for cute fictional character stories.     They both climbed into the bed, snuggled up like cats and slept together.


I need to expand the root partition of the server (not LVM) because of the need of testing. How can I expand the root partition without shutting the server down?  $ df -h Filesystem      Size  Used Avail Use% Mounted on udev            3.8G     0  3.8G   0% /dev tmpfs           779M  3.5M  776M   1% /run /dev/sdb2       126G   24G   96G  20% / tmpfs           3.9G     0  3.9G   0% /dev/shm   $ sudo fdisk -l Disk /dev/sda: 128 GiB, 137438953472 bytes, 268435456 sectors Units: sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disklabel type: dos Disk identifier: 0x4b512b27  Device     Boot Start        End    Sectors  Size Id Type /dev/sda1  *     2048  268433407  268431360  128G 83 Linux


What are the requirements for a member to be elligible to participate in a Clan War?

What are the requirements to war in clash of clans?   We have 12 members but every time we war, one of our members can't participate.  We are the only clan this member has been in so why is he ineligible for wars?


What are the back stories behind the two halves of the Brady Bunch family?

Is there a back story to:     Here's the story of a lovely lady   Who was bringing up three very lovely girls   All of them had hair of gold, like their mother   The youngest one in curls        Here's the story of a man named Brady   Who was busy with three boys of his own   They were four men living all together   Yet they were all alone   Why were they all alone? Death in a war? Irreconcilable differences in former marriage(s)?   Is there a back story?


Should I be able to 'manually' rotate the headset?

When I wrap my fingers around my roadie's headset, I'm able to 'rotate' some parts of it freely around.   Should this be happening? If it should not be happening, what is causing this and is it dangerous? The bolt that attaches the stem to the headset near the topcap (not sure if that's the proper way to describe it) is tightened, so it won't be due to a loose bolt.


Assign a value to element in list of list that assigning to a row of values

I created a list of lists like this  In [1]: list_of_list = [ [0] * 4]* 4 In [2]: list_of_list  Out[2]: [[0, 0, 0, 0],           [0, 0, 0, 0],           [0, 0, 0, 0],          [0, 0, 0, 0],]   And when I assign a value to the element in this list_of_list it assigns it to a column of elements.  In [3]: list_of_list[2][3] Out[3]: 0  In [4]: list_of_list[2][3] = 1  In [5]: list_of_list Out[5]: [[0, 0, 0, 1],           [0, 0, 0, 1],           [0, 0, 0, 1],           [0, 0, 0, 1],]   Why python behave like this ?   Thank you.


How to sort text file by column starting at certain character position?

Considering the following input file (example)...  afaefkl    aaa al kmm     ddd aajwoe     bbb bnm aefp   ccc   ... what would be the most straight-forward way to sort it by column 2 (starting at character position 12 in each line) using standard Unix/Linux tools only?  Note that the whitespace consists of spaces only, there are no tabs, so sort -k2 fails for obvious reasons.  The expected output would be as follows:  afaefkl    aaa aajwoe     bbb bnm aefp   ccc al kmm     ddd


I’m having an interesting conversation with my friend who’s a developer. I’m a database admin. I say file is a basic form of database. I believe whatever that stores data can be called a database. He says only engine like sql server is a database. I think he’s confused between a database and database management system? Please share your thoughts. Am I right or wrong ? Btw he agrees an excel is a database since it has rows and columns. I say a simple word document is also a simple form of database without coming into the argument of whether it’s efficient or what are it’s capabilities!


I'm wondering why WordPress does not support sessions and many people out there claim that putting the following code in functions.php might not be a good idea (it in fact works for me but returns PHP warnings, too):  function cp_admin_init() { if (!session_id()) session_start(); }  add_action(‘init’, ‘cp_admin_init’);   Is it good idea to enable sessions in WordPress? What would be the correct way to do this?


How to install a QGIS plugin when offline?

Due to various IT policies at my workplace, QGIS is installed on a machine that is not connected to the internet. I wish to install a couple of QGIS plugins on this system.  I have downloaded the required plugins from . How do I install them in QGIS?


How to get a file's Media Type (MIME type)?

How do you get a Media Type (MIME type) from a file using Java?  So far I've tried JMimeMagic & Mime-Util. The first gave me memory exceptions, the second doesn't close its streams properly. How would you probe the file to determine its actual type (not merely based on the extension)?


Which one should I choose:     Don't you think it's time you tell vs told Adrea the truth?


Meta Titles appearing incorrectly on Google

I was hoping you could help me with a question about a Meta Title query as they seem to be appearing inaccurately - and its driving me mad. Few considerations:  Google seems to be displaying our old business name in SERPs (on some pages). Homepage displays old business name on Mobile, but new business name on Desktop (Chrome browser). We havent made any recent changes to Metas and the biz name was changes 2 years ago. It's not in the < title > tag or anywhere else in the page source (when you CTRL+F and search: "business name").  Is there a way of checking where it is pulling this string of text from? Could there be two conflicting references in the code that sets parameters globally? Any help would be much appreciated. Thanks!


Multiplicative Inverse in $S=\{a+b\sqrt{2} \mid a,b \in \mathbb Q\}$

I have to prove that $S=\{a+b\sqrt{2} \mid a,b \in \mathbb Q\}$ is a field and so far everything worked out for me except for finding the multiplicative inverse over $(S\backslash\{0\}, \cdot)$ which is: $$\forall a \in S: \exists (a^{-1}) \in S: a\cdot(a^{-1})=1$$  As a proof I thought of: $(a+b\sqrt{2}) \cdot (a+b\sqrt{2})^{-1} \Rightarrow (a+b\sqrt{2}) \cdot \frac{1}{(a+b\sqrt{2})}$ but I am stuck with the fraction. It is non-trivial for me to compute the inverse of an element $a \in S$.  Any help is highly appreciated! Thank you!


How to disable Ctrl+Q system wide?  I read the other answers but they did not help. Reassigning the shortcut is not possible, since pressing the key combination quits the settings window, so it does not have any effect.  Thanks in advance.


User cannot delete their own comment on migrated question

When a question is migrated, the user can no longer edit or delete their comment(s). Would be worth fixing unless that's by design?


Security when plugging a USB device into machine running GNU/Linux (Debian)

I’m wondering what kind of security measures may be in place or which I could enable in GNU/Linux (Debian specifically) to mitigate the risk of USB-based attacks. I understand that USB sticks which are ostensibly storage mediums may actually behave as input devices when plugged in.  They could pretend to be keyboard/mice and carry out malicious acts.  I don’t recall my OS ever asking permission for my keyboard to type keys nor for my mouse to behave as a pointing device when I’ve plugged either in, so I suppose I must be vulnerable to such attacks. Is there a way for me to make the OS more cautious about the devices I plug in?  I’d like to not be “tricked” by a bad USB, or even by a once-good-USB-turned-bad (I’ve heard USBs could be “infected” if plugged into a computer with a virus). In my search I’ve only seen solutions that involve disabling auto-opening a file browser when storage mediums are inserted.  I’m not concerned about that.


Why does C# forbid generic attribute types?

This causes a compile-time exception:  public sealed class ValidatesAttribute<T> : Attribute {  }  [Validates<string>] public static class StringValidation {  }   I realize C# does not support generic attributes. However, after much Googling, I can't seem to find the reason.  Does anyone know why generic types cannot derive from Attribute? Any theories?


What did the Doctor mean when he said that he'd "walked in universes where the laws of physics were devised by the mind of a mad man"?

From The Rings of Akhaten.     Doctor: I walked away from the last Great Time War. I marked the passing of the Time Lords. I saw the birth of the universe and I watched as time ran out, moment by moment, until nothing remained. No time. No space. Just me. I walked in universes where the laws of physics were devised by the mind of a mad man. I've watched universes freeze and creations burn. I've seen things you wouldn't believe. I have lost things you will never understand. And I know things. Secrets that must never be told. Knowledge that must never be spoken. Knowledge that will make parasite gods blaze. So come on, then. Take it! Take it all, baby! Have it! You have it all!   (Series 7, Episode 7, The Rings of Akhaten).   Was he referring to anything specific that we've seen in an episode, or was he describing something that happened off-screen?


I have working development project of Drupal 7 using PHP 5.x. I changed the PHP version to PHP 7 using nginx webserver. It does not work and I have got the following error message:   Fatal error: Uncaught Error: Undefined class constant  'MYSQL_ATTR_USE_BUFFERED_QUERY' in  C:\xampp-2\htdocs\d738\includes\database\mysql\database.inc:46 Stack  trace: #0 C:\xampp-2\htdocs\d738\includes\database\database.inc(1689):  DatabaseConnection_mysql->__construct(Array) #1  C:\xampp-2\htdocs\d738\includes\database\database.inc(1479):  Database::openConnection('default', 'default') #2  C:\xampp-2\htdocs\d738\includes\database\database.inc(2570):  Database::getConnection() #3  C:\xampp-2\htdocs\d738\includes\cache.inc(348):  db_escape_table('cache_bootstrap') #4  C:\xampp-2\htdocs\d738\includes\cache.inc(329):  DrupalDatabaseCache->getMultiple(Array) #5  C:\xampp-2\htdocs\d738\includes\cache.inc(56):  DrupalDatabaseCache->get('module_implemen...') #6  C:\xampp-2\htdocs\d738\includes\module.inc(723):  cache_get('module_implemen...', 'cache_bootstrap') #7  C:\xampp-2\htdocs\d738\includes\module.inc(892):  module_implements('system_theme_in...') #8  C:\xampp-2\htdocs\d738\modules\system\system.module(2502):  module_invoke_all('system_theme in  C:\xampp-2\htdocs\d738\includes\database\mysql\database.inc on line 46   This error means that Drupal 7 is using obsoleted MySQL functions and it is not support with PHP any more!  However, I don't think Drupal still uses this obsoleted PHP extension. So I have a strange error as I think!


Sending SMS in iPhone without redirecting to Messages app

I am wondering whether it is possible to send an SMS in iPhone, without redirecting to the Messages app.  In the app, the user should be able to input text and hit a button inside the app without redirecting to the Messages app. If this is possible, I would very much appreciate assistance on how to do it.  Thank you,  Dean


Automatically generating label lines in QGIS?

I've been experimenting with orthographic projections and I've run into a problem with the labels.    I would like to label the countries but I want the labels to run west-east along the country which isn't (currently) an option in the QGis labeling options.  So, I know I can place them along a line but I lack the patience to draw a line in each country. So I'm looking for an automatic way to draw a line through the centroid of a polygon and to the edges so that I can use it as a label placement line.   By 'label placement line' I mean I need a line that crosses the country that I can use as the basis of my labels so that I can use follow line (parallel I think) in the labeling panel. (see for example this ). So they will be a straight horizontal line in EPSG:4326 but nicely curved in my orthographic projection (+proj=ortho +lat_0=51.470129 +lon_0=-0.452751 +x_0=0 +y_0=0 +a=6371000 +b=6371000 +units=m +no_defs).  Ideally it would be a dense line so it curves when reprojected but I can always run a densify process on the output.


Using real football player photo in a trivia quiz game, is it legal?

I don't know whether this question was already been asked before, but my team is currently developing a trivia quiz game about football (soccer not NFL). And we want to put player's images or club emblems as part of the questions and answers. My question is, is it legal? Or should we just put text without the images? Please your help is much needed. Thank you.


Checking for divisibility between $n^{300}+100$ and $n+10$

I've been doing a bit of study in number theory and modulo operations to prove certain things. This one in particular is a question I came across recently:  $$\text{Find the largest and smallest positive values of n for which} (n^{300}+100)\text{is divisible by} (n+10)$$  This is what I was able to come up with:  Take $d=n+10 \rightarrow n=d-10$  $\begin{align} n^{300}+100 &= (d-10)^{300} \\  &\equiv 10^{300}+100 \quad \bmod d \end{align}$  $\begin{align} 10^{300}+100 &= 10^2(10^{298}+1) \\ &= 100(100^{149}+1) \\ &= 100((101-1)^{149}+1) \end{align}$  So from 100 the smallest factor one can produce from d is 1, but that would lead to a negative value for n($-9$) which should probably also work but still.  The next one thus is 10 which gives $n=0$, something that could've been guessed from the beginning when you think about it. But I'm not entirely sure if 0 would be counted as a positive integer so I'd go for $20 \implies n=10$ and from the expression in brackets the $\bmod 101$ from both are -1 and 1 respectively so they cancel out. Thus the expression is divisible by 101.  The greatest factor you can produce then should be the greatest from $100$ and $100^{149}+1$ which is $101 \cdot 100 = 10100$  $n=10100-10=10090$  Am I right or can you still get a bigger factor? Or is my logic flawed at any step?


Translation invariant measures on $\mathbb R$.

What are all the translation invariant measures on $\mathbb{R}$?  Except Lebesgue measure on $\mathbb R$ I didn't find any translation invariant measure. So I put this question?  I know that if $\mu$ is a measure then $c \times \mu$ is again a measure where $c>0$.


Faster-than-light communication using Alcubierre warp drive metric around a single qubit?

The  has been criticized on the points of requiring a large amount of exotic matter with negative energy, and conditions deadly for human travellers inside the bubble. What if the Alcubierre metric is used to just span a tiny bubble around a single spin-1/2 particle to transport either classical or quantum information faster than light? Wouldn't known small-scale effects, such as the Casimir force, suffice to provide the exotic conditions required for an Alcubierre bubble large enough to fit at least one particle? My question explicitly addresses the feasibility of a microscopic bubble using known microscopic effects.


Is the punctuation of generational suffixes dropped when they occur at the end of a sentence?

Is the punctuation of generational suffixes (e.g. "Jr.", "Sr.") dropped when they occur at the end of a sentence?  For instance,     I liked Gerald Rudolph Ford Jr.   The obvious answer seems to be yes, since having two periods back-to-back seems incorrect. If that is the case, however, it seems strange because there appears to be "information loss" in that the shortening of the generation suffix and the end of the sentence both share the same punctuation.


How do I add text to the beginning of a file with a new line

How do I add a new empty line to the beginning of a file under MacOS and Linux?   I have tried the below command and it produces a new line character under MacOS  sed -i.bak '1s/^/TESTe\n/' test.py


Relationship between positive rational numbers and their ``prime factorization vectors"

While thinking about primes I just noticed a nice structural relationship between prime-factorization and infinite-dimensional integer vectors and I'm wondering what's known about this. Here is the setup: Let $\mathbb Z_{>0}$ be the set of positive integers and $\mathcal P = \{2, 3, 5, \dots\}$ the set of primes. Any positive integer $n$ can uniquely be written as $$n = 2^{k_{n,2}}3^{k_{n,3}}\dots = \prod_{p \in \mathcal P}p^{k_{n,p}},$$ where only finitely many of the coefficients $k_{n,p}\in\mathbb Z_{\ge 0}$ are nonzero. Actually, if we allow the coefficients to take on negative values then we can write each positive rational number $q \in \mathbb Q_{>0}$ in a similar way: $$q = 2^{k_{q,2}}3^{k_{q,3}}\dots = \prod_{p \in \mathcal P}p^{k_{q,p}},$$ for some $k_{q,p} \in \mathbb Z$ (if we assume that the fraction $q$ is fully simplified, the coefficients are uniquely determined). So we can associate each positive rational number $q$ uniquely with some infinite dimensional vector $$(k_{q,2}, k_{q,3}, \dots).$$ Let's call such a vector a ``prime factorization vector". Note that adding two such vectors corresponds to multiplying their associated positive rational numbers and subtracting them corresponds to dividing their associated positive rational numbers. Of course, vectors can not only be added and subtracted but one can perform all kinds of geometric operations with them. Question: What is known about the relationship between the geometry of the ``prime factorization vectors" introduced above and their associated positive rational numbers? (or about the relationship of prime factorization vectors and their associated positive integers?)


I have already generated a report successfully but now I need to know which font is used;  font type = ?


Need help with proof for Dedekind cuts on $\mathbb{Q}^+$

I am working on a proof about Dedekind cuts on the positive rational numbers. I have been stuck for a while on the following point and would appreciate any help.  Given $x\in \mathbb{Q}^+$ such that $x^2<2$, how to find $y\in \mathbb{Q}^+$ such $y>x$ and $y^2<2$?


Using Field Calculator to auto-increment in ArcMap?

I am trying to edit the basic sequential numbers in a field script using Python in the Field Calculator.  I set the Parser to Python, and for my Pre-logic Script:  rec=0 name="manhole" def autoIncrement():   global rec   pStart = 1    pInterval = 1   if (rec == 0):     rec = pStart    else:     rec += pInterval    return name, rec   And for the box below:  autoIncrement()   Would this not be how to go about this?   Essentially I just want "manhole1" then "manhole2" then "manhole3", etc.


What do you call a question where you don't expect a response?

When I ask a person a question such as, "When did you last go to church?" I am not asking them to give me an answer ("Last August"); but I am expecting them to answer the question within themselves, to stimulate their thinking about whether they are doing something we both agree they should be doing. Is this a rhetorical question, or is there a better definition for this type of question?  A better example would be posting this type of question on social media, such as Facebook.  UPDATE: It has been suggested that the answer is a rhetorical question. But my understanding of a rhetorical question is that it has no answer. There is an emotional context to the question: "What, are you stupid?" The person you are addressing is made to understand they are DOING something stupid, an actual answer is not necessary or even wanted. I THINK that my type of question is different, but I am not sure. My question is intended to make the person ask themselves. If the answer is "last week", it isn't necessary to tell me "next week". My purpose of reminding them that they should be attending church regularly is achieved, and an actual answer is not required. If that is still a rhetorical question, so be it, but the definitions I found didn't suggest that it was. I would prefer to be precise, so if there is a better term for that type of question, that is what I want to know.


How to edit detailed image metadata (exif)?

How can I edit detailed image metadata (exif) fields?  In Windows 7 this is just a right click on the file in the folder.  I've searched and not found a way to edit detailed metadata (exif) fields in Ubuntu 14.04.  I'm not interested in running something from the command line.   With Shotwell Photo Manager I can only edit Title, Comment, Date and Time. With Shotwell Photo Viewer it is only possible to adjust Date and Time. With Gimp it is possible to edit Title, Author, Description, Keywords. I tried Phatch but it wasn't intuitive and didn't appear to have an option to edit metadata, only add or remove metadata.   What I can't figure out how to do is edit Location.  What I really want to be able to do is right click on the image file in the folder browser and directly edit the metadata like in Windows.  How can I do this?


Elves were awoken during the Years of the Trees (Telperion & Laurelin) in Culvienen.  Men were awoken the first Year of the First Age in Hildorien  Dwarves were created and awoken somewhere east of the Blue mountains  At what time period did Hobbits appear and where did they come from?


A Banach space $X$ is reflexive iff $X^*$ is reflexive

I have already shown that if $X$ is reflexive then $X^*$ is reflexive, but I need some help on the other direction. The canonical mapping is defined by $$ J : X \to X^{**}, \ J(x) (f) = f(x)$$  For the other direction suppose that $X^*$ is but $X$ is not reflexive. It follows that the canonical mapping $J : X \to X^{**}$ is not a surjection, so there must exist some element $\lambda \in X^{**}$ such that $\lambda \not \in J(X)$. Since $J$ is an injective linear isometry it follows that the set $J(X)$ is closed, and hence $$ \operatorname{dist} (J(X), \lambda) > 0$$ It is also clear that the image of $X$ is a subspace of $X^{**}$. From a corollary of the Hahn-Banach theorem it follows that there is a non-zero $\Lambda \in X^{***}$ such that $$ \forall y \in J(X), \ \Lambda (y) = 0$$ Now since $\Lambda \in X^{***}$ and $X^*$ is reflexive it follows that the canonical map $J^* : X^{*} \to X^{***}$ is a surjection and hence a bijection. This implies that there exists $\alpha \in X^*$ such that $$ J^* (\alpha) = \Lambda$$ and in particular $$ \forall y \in J(X), \ J^* (\alpha) (y) = 0 \implies \forall y \in J(X), \  y(\alpha) = 0$$ Now if I am able to show that $\alpha = 0_{X^*}$ I am done since this implies that $$ \Lambda = J^*(0_{X^*}) = 0_{X^{***}}$$ which is a contradiction since $\Lambda$ is non-zero.   I am unsure how I would show this though. I suppose I could construct some $y \in J(X)$ which would do it. Any ideas?  Edit : I think I have it. We have $$ \forall y \in J(X), \ y (\alpha) = 0 \iff \forall x \in X, \ J(x) (\alpha) = 0 \iff \forall x \in X, \ \alpha(x) = 0$$ So $\alpha = 0_{X^*}$ and the theorem follows.


How to show $\ln{(\frac{x+1}{x})}\geq \frac{1}{x+1}$?

I used mathematica to check the values of $\ln{(\frac{x+1}{x})}- \frac{1}{x+1}$ are positive for any $x\geq 0$.  How do I analytically show the statement is true for all $x\geq 0$?   Any idea?


Is this tutorial using "to [verb]-ing" the right way? When should I just use "to [verb]"?

That  says     Exploratory Data Analysis (EDA) is an approach to analyzing datasets to summarize their main characteristics. It is used to understand data, get some context regarding it, understand the variables and the relationships between them, and formulate hypotheses that could be useful when building predictive models.     Both "to doing" and "to do" are used in this sentence, "an approach to analyzing datasets to summarize their main characteristics".  By "to doing" and "to do", I mean "to analyzing" and "to summarize" respectively.  I know "doing (in this case, analyzing data sets)" is a gerund that could be the subject or object of sentences, but when should I use "to doing"? This kind of usage confuses me, so I searched these keywords.  This  discussed "to doing" but didn't give a doable guide when to use which. I guess that's why the asker didn't mark any of the answer as accepted.  Leave a general talking alone, consider this particular case, is that tutorial use "to doing" the right way? When should I use "to doing"?  Note: I am asking what situation should I use "to doing" rather than what is gerund.


How do programs access ~/Library/Mail under OSX 10.14 (Mojave)

After upgrading to 10.14, I am unable to access the ~/Library/Mail directory, either as the user or as root.  [~/Library/Mail 14:01:42]$ ls -l ls: .: Operation not permitted [~/Library/Mail 14:04:11]$   So that's pretty weird. It happens even if I am root.  No system flags are set on the directory.  So presumably, this is another system integrity or sandboxing thing. Unfortunately, I have code that wants to access the sqlite3 database inside the ~/Library/Mail directory.  So how do I grant my software access to my mail?  This seems to be related to the 10.14 privacy protections.


I recently had this integral in my homework and don't really know how to proceed.   $\int^1_0\frac{\ln (1+x^{2+ \sqrt3})}{x+1}dx$  So far I figured that $ \int^1_0\frac{\ln (1+x^{a})}{x+1}dx= \int^1_0\frac{\ln (1+x^{-a})}{x+1}dx+a\frac{\pi^2}{12}$,   but this doesn't seem too useful.


"The new guys are dressed a lot nicer than we/us"

Does anyone know the correct word choice between "we" and "us", and explain the reason why? Thanks!


I've been wondering about this ever since I signed up on SO. With answers, it's easy to determine what to upvote. Is it helpful, is it informative, is it correct?  None of that really applies to a question though. So which criteria are we supposed to use for upvoting questions? (And for that matter, which purpose does it serve? Upvoted answers are listed first, so here the effect is obvious. What difference does it make whether a question gets upvoted?)


how do we access the image files from static resource in css?

I am trying to display images from a static resource in a css property.  .PDF {     width:50px;     height:50px;     background-image: url("{!URLFOR($Resource.FileTypes, 'png/pdf.png')}";  }   What i am trying to do is to display an image instead of displaying the filetypes in contentversion object. So what i thought of was to have a div with a class of the filetype

   The html generated is all coming correct but the image does not appear. Further checking on firebug, the background-image tag in the css is not displayed at all. Not sure if its an issue with how i am using the static resource. The zip file has a folder called png and it has the images of all the file types.  Any ideas why the image is not getting displayed. The div gets displayed with the height and width as 50px


What is the Integration factor found by inspection of the Equation Below

This equation $(x^3+xy^2−y)dx+(y^3+x^2y+x)dy=0 $ is Integration factor found by inspection. The answer on the book is $2\arctan(\frac{y}{x})=c-x^2-y^2$


Apt update failed because public key not available

Please help, how do I fix this? I can't update because it just says for one of the entries: The following signatures couldn't be verified because the public key is not available. How do I install the public key needed?


Can two new and one old mobile phones be taken to India?

I am an Indian residing in Italy. Am I allowed to take two new mobile phones purchased in Italy along with the one I use to India? Can someone get me the rules/law about the gadgets? Thank you.


I have a small icon called "favorite" and when I click on it I call a jquery event handler to change the icon and change the class name.  But when I click on it again it doesnt go to the event handler of the class that I have added to it, it goes back to its original event handler  This is the icon  <input style="float:right" type="image" name="unfavorite" id="unfavorite" class="unfavorite" src="images/unfavorite.png" />   and my jquery is:      $('.unfavorite').click(function()     {         $(this).removeClass('unfavorite');         $(this).addClass("favorite");         $(this).attr("src","images/favorite.png");     });      $('.favorite').click(function()     {         $(this).removeClass('favorite');         $(this).addClass("unfavorite");         $(this).attr("src","images/unfavorite.png");     });   so basically I want to change the icon each time is clicked. But when I addClass(favorite) the event handler for favorite class is never called, it always goes to unfavorite  What should I do?  thank you


I'm theming a view which name is testimonials, I would like to make the view block a slider, so I'm creating the twig file as views-view-unformatted--testimonials.html.twig.   When I inspect I'm getting {{ row.content }} from the default template. I would like to give div to each and every field I'm getting inside the twig.  How do I access the field contents in the twig.   I've a number of views for each view, I would like to theme it different ways, so can I created views-view-fields for each view?


How can I delete photos from camera roll and leave in an album?

I created a named album on my iPhone and placed photos from my camera roll in there. I would then like to delete these photos from the camera roll. However, when I try to do so an error messages warns that the photos (which currently reside in the the camera roll and named album) will also be deleted from the album.   Is there a way to delete the photos from the camera roll and leave them in the specific album?


How do I install a driver for a Broadcom BCM43142?

I need help installing a driver for a Broadcom BCM43142 on 14.04.2.  If I run lspci I indeed find the device as:  network controller: Broadcom Corporation BCM43142 802.11b/g/n (rev 1)   But Ubuntu apparently does not come with this driver pre-loaded. I don’t have a clue what command to run to get this, where to get it, and how to install the driver once I do get it. I am completely new to Linux.


Extract data from Geopackage .gpkg using lat long bounds

I have a .gpkg.tar.gz data file whose size is 3.8 GiB. Uncompressed to .gpkg, its size is 8.5 GiB.   It is spanning a large geographical area. I want to extract data from this for a small area, given by lat-long bounds.  It is fine if there are features in/crossing this area but extending beyond it - I don't want to bother with chopping/clipping features. But I want to exclude features that are entirely outside of the given bounds.  With .pbf (Openstreetmap) data I have a way of doing this, example:  osmconvert india-latest.osm.pbf -b=78.55834,12.54397,80.3558,13.71654 --complete-ways -o=small.pbf   Is there a similar command / process we can do with .gpkg?  I understand it is originally SQLite; and I've read that one doesn't need to load the entire file into memory to work with that. So some specific queries - table names, column names might be there? This file is too big for me to load up in QGIS etc at the moment to be able to investigate its contents.  Ref:


I just got a Chrome phishing warning on main for   Is it just me, Chrome screwing things up or do you people have work to do?  The message in English:     Known phishing site detected.   Google Chrome has denied the access to stackoverflow.com. This site is reported as phishing site.      Phishing sites are designed to mislead you, so that you disclose your login credentials, password or other personal data. These sites occur as sites which you probably trust.


Suppose we want to show that $$ n! \sim \sqrt{2 \pi} n^{n+(1/2)}e^{-n}$$  Instead we could show that $$\lim_{n \to \infty} \frac{n!}{n^{n+(1/2)}e^{-n}} = C$$ where $C$ is a constant. Maybe $C = \sqrt{2 \pi}$.   What is a good way of doing this? Could we use ? Or maybe take the log of both sides (e.g., compute the limit of the log of the quantity)? So for example do the following $$\lim_{n \to \infty} \log \left[\frac{n!}{n^{n+(1/2)}e^{-n}} \right] =  \log C$$


How can I dynamically load the functions of java.lang.Math

I need to dynamically load the functions of java.lang.Math and when chosenbe able to use that function.   I've tried this but it didn't work.It gives me a null pointer exception.  private static Class<Math> Math;   for (PropertyDescriptor propertyDescriptor                 : Introspector.getBeanInfo(Math).getPropertyDescriptors()) {              System.out.println(propertyDescriptor.getReadMethod());         }


Actually yesterday I've upgraded from Ubuntu 16.04 to 17.04 and I got a problem that, if connect LAN cable it does not showing anything and  remains disconnected. But i can connect with WiFi. I don't know what's the problem. Actually its showing "device not managed" under the "Ethernet Network" and both were disabled. I've searched for the solution, but did not found yet.


A capacitor stores half the energy when charged from a battery each and every time?

I understand that when a battery is connected to a capacitor that half the energy is stored in the capacitor while the other half is lost to heat or whatever other losses are involved once the capacitor is charged to the exact same voltage level of the battery.  Only a one time direct connection with a simple switch from open to closed that charges the capacitor up to the voltage level of the battery is what is being referred to. My question is does this occur each and every time?   Once the capacitor is charged to the voltage level of the battery then there should be 7.2 milliJoules of energy in the capacitor.  If the answer is yes that half the energy is transferred into the capacitor each and every time then what would the capacitor voltage have to be in order to equal 100% of the energy if it were to come from the battery?  I understand that in practice this will never happen, which is why the statement equal to 100% of the energy is indicated. (Meaning by some other method of charging means)         – Schematic created using


Where is the stdin if `input()` not assigned to a variable

In shell script, If no variables are listed after the read command, a default variable: REPLY will be assigned all the input       $ read     test     $ echo $REPLY     test   Nevertheless, in python       In [1]: input(": ")     : test     Out[1]: 'test'     In [2]: #it's gone   Where could I find the 'test'?


There are at least three mutually non-isomorphic rings with $4$ elements?

Is the following statement is true?     There are at least three mutually non-isomorphic rings with $4$ elements.   I have no idea or counterexample at the moment. Please help. So far I know about that a group of order $4$ is abelian and there are two non isomorphic groups of order $4$ like $K_4(non cyclic)$ and $\mathbb Z_4(cyclic)$.


Is there any (even the most subtle) difference between the meaning (or connotation) of that is and i.e.?  I used to be convinced that they were synonyms, until an editor of a scientific journal changed all occurrences of i.e. into that is.


How test if a value is (or is not) a valid pointer?

For a unit test of C dode, I want to ascertain that a value passed as a void * is, indeed, a valid pointer.  I don't think that I can prove that it definitely is a valid pointer, but how can I say that it probably is? Or definitely is not?  I am developing and unit testing on a 64 bit Intel processor, and the target is an ARM 9. I am not averse to assembler inserts.   is there a minimum value for a valid pointer? 0x08 doesn't look very pointer-ish, wheras values above 0x1000000 do. must it be divisible by something (say 8)? can I say with 100% certainty that an odd number is not a valid pointer?   I don't need a flawless answer, just something to catch most errors.    [Update] I am considering looking at the link map, although that seems like overkill. The problem is occuring when casting to remove compiler wanrings.  Some system calls require a char * or void *, and csting to those is masking some coding errors.


How to stretch the size of a plot to the whole area of a shape

I can not get the plot stretched to the whole area of the figure. When I call the tight_layout, the required height of the plot is obtained, but I can not achieve the required length:     Code:  self.figure = plt.figure()     self.canvas = FigureCanvas(self.figure)     # self.figure.set_figheight(15)     # self.figure.set_figwidth(5)     #self.figure.tight_layout()     self.figure.set_size_inches(1, 7)     self.graphBox.addWidget(self.canvas)      # ------------------------------------------------------------------     # ------------------------------------------------------------------     t = np.arange(0.0, 2.0, 0.01)     s = np.sin(2 * np.pi * t)     ax = plt.subplot2grid((1, 1), (0, 0))     ax.set_facecolor(color='#b3ff66')     ax.plot(t, s)     self.canvas.draw()     #plt.tight_layout(h_pad=1.0, w_pad=1.0)     # ------------------------------------------------------------------     # ------------------------------------------------------------------


How can I invite people to my chat room?

I have created the chat room for magento. I would like to invite top users of magento tag. How can I do this?


How do soldiers advance their psionic skill?

What is needed for a soldier to advance his/her psionic abilities?


Hyperref, bibentry & natbib conflict - incorrect hyperlink

Problem  I want to cite references in text as well as quote the entire entry plus have a reference list at the end. For this I use hyperref, bibentry and natbib. I've taken as inspiration . The only difference is that I want to include a reference list as well.  The problem is that the hyperlink points to the \bibentry rather than the entry in the reference.  MWE  \documentclass{article} \usepackage{natbib} \bibliographystyle{abbrvnat}  \usepackage{bibentry} \makeatletter\let\saved@bibitem\@bibitem\makeatother \usepackage{hyperref} \makeatletter\let\@bibitem\saved@bibitem\makeatother  \begin{document} \nobibliography* Here is a citation \citet{elvis} %\newpage %uncomment this line and the line below eliminates error but hyperlink still points to \bibentry  Here is the full entry \bibentry{elvis} %\newpage %uncomment this line   \bibliography{bibliography} \end{document}   The bib file, bibliography.bib  @Book{elvis,     author = "Elvis Presley",     title = "Turn Me One More Time",     publisher = "Jail House Books",     year = 1963, }   Warning  The above code gives a warning:  destination with the same identifier (name{cite.elvis}) has been already used, duplicate ignored   Solution?   Interestingly, adding \newpages to split up the \citet and \bibentry onto separate pages eliminates the warning but the hyperlinking is still wrong. Removing natbib but again hyperlinking does not work.   Does anybody have any ideas how I can solve this problem?


You sometimes see on tank trucks or petrol tankers carrying gas or oil or other liquids that catch fire quickly the word inflammable painted in bold red on them.Should not the correct word be ?


In trying to understand the y values of a normal distribution plot I use this code: %reset -f  import numpy as np from scipy.stats import norm import matplotlib.pyplot as plt  data = [10,10,20,40,50,60,70,80,90,100]  # Fit a normal distribution to the data: mu, std = norm.fit(data)  # Plot the histogram. plt.hist(data, bins=10, density=True, alpha=0.6, color='g')  # Plot the PDF. xmin, xmax = plt.xlim() x = np.linspace(xmin, xmax, 100) p = norm.pdf(x, mu, std) plt.plot(x, p, 'k', linewidth=2) title = "Fit results: mu = %.2f,  std = %.2f" % (mu, std) plt.title(title)  plt.show()  to generate this plot:  The data is the age in years of people in a group: [10,10,20,40,50,60,70,80,90,100] How to interpret the y values of the generated pdf plot? For instance, how should the bar with play approx equal to 0.027 be interpreted? I've read various posts such as :  But can't find information that details an interpretation of the y axis values of the plot. Is 0.027 the probability the age is in the range from 0 to approx 20 ?


Seeking open source alternative of Las Tools

I am finding any open source alternative of Las tools , i Google but i found las Utitly which is also not the Open source alternative But i want open source alternative of Las Tools,


How can we conclude that the transcendental entire functions need not have any fixed points?For example consider $$f(z)=e^z+z,$$ why is it so?


I am asked to fill the genotypes in the spaces provided but looks like I am aving a little bit of trouble. can anyone help? thanks in advance!


Why does camera this tracking fail completely even when the solution value is very low?

The attached animated gif shows some frames of a video with a mesh box placed at each tracking marker used to successfully track (solution error <.4) an 800 frame chunk of video.   The point is to illustrate just how poorly the camera tracker calculated: when the box is at a marker placed at the top of a faraway building on the left, it is actually visually much larger than when it is at the tracking marker closest to where the real camera was. I went to great lengths to be sure that the camera's sensor size and focal length are correct, and manually placed and followed all markers to be sure they were accurately tracking.   There is not a lot of parallax motion over the 800 frames, but there should have been enough to at least know that the point closest to the camera moved more than the point furthest away. Sometimes it seems to work, sometimes it doesn't. Does anybody know how to improve this?


I can't install Skype on my Ubuntu Computer (15.04)

I was trying to install Skype, but everytime I can't connect to an IP-address. My wifi is fine, my computer as well. I don't know what it could be. Presently I am using Ubuntu [15.04] version and am new to this environment. Kindly fix this problem.  It says:  missing cdrom://Ubuntu 15.04 Vivid Vervet - Release amd64 (20150422) vivid/main amd64 Packages  missing cdrom://Ubuntu 15.04 Vivid Vervet - Release amd64 (20150422) vivid/restricted amd64 Packages missing cdrom://Ubuntu 15.04 Vivid Vervet - Release amd64 (20150422) vivid/main i386 Packages  missing cdrom://Ubuntu 15.04 Vivid Vervet - Release amd64 (20150422) vivid/restricted i386 Packages


Is "for all I know" without may/might/etc. "correct"?

I have seen "for all I know" used in both of the following forms:   For all I know, he may as well be Santa in disguise. For all I know, he's Santa in disguise.   From what I've understood so far, both forms mean the same thing, more or less (they're both wild speculation).  Are both forms considered equally acceptable in scholarly spheres etc., or is one considered "to avoid"?


I had wubi installed on my pc with Windows 7 and recently I removed wubi and the partition I had my wubi installed (I removed wubi because I had installed Ubuntu on a separate partition as a dual boot). This lead me to grub rescue problem. But I was able to resolve this my issuing the commands mentioned in the first answer .  This got me my windows and ubuntu on the grub back but had to re-issue the commands every time I restarted my machine. To get rid of this I used the  tool to fix it as was suggested on the web.   Now this had lead me to a situation where I have ubuntu but can't see the windows 7 on the grub list. Can someone please let me know how do I get it back?


Is multiplication comutitive  in numbers I.e   Is  N×M equal    M×N?? Where N and M any numbers   And why??


Can you add a math related site to the "Trilogy"?

A SO style site for math questions seems like it would do well.  It would be a helpful place for questions like  one about the probability of rolling a certain dice combination.  Is there any chance that a math related site will be opened?


Which input of NAND is preferred and why?

Let A and B be two inputs of the NAND gate. Say input A arrives at the NAND gate later than input B. To optimize delay of the two series NMOS inputs A and B which one would you place near to the output?   Edit: Input A arrives Later than Input B. To optimize delay in the NMOS section. how do you place inputs A and B.


How does choosing a team (colour) that is strong in my area affects endgame gameplay?

Is it beneficial to join a strong team? Do I get any valuable bonuses (lure modules installed in your area worth it?) from high-level friendly gyms?   Or is it better to choose weaker team in order to have more opportunities to fight?  Does the choice matter for endgame (level 20+ let's say)?


Another phrase for "a chicken and egg situation"

Is there any other phrase that conveys the same meaning as  the phrase "a chicken and egg situation" especially if one has to use this phrase in an official/corporate set up?


Can "emigrate" and "immigrate" be used interchangeably?

To emigrate means to leave a country, so I'm confused that people use the word where I would expect the word "immigrate", eg. "He emigrated to Italy." How do you "leave to" a place? I checked Google to see the numbers for "emigrate to" and "emigrate from". To my surprise, the "emigrate to" usage was 3.5x more common (3.5 million results)! I found a related construct, "He emigrated from Spain to Italy." This one makes sense to me, but I don't see how you can leave out the "from Spain" part and still have a logical sentence. Are those 3.5 million people doing it wrong?


How does one view what the contents of symbolic link are, instead of the destination?

Is there some way in which I can view/edit what the contents of a symbolic link are? I don't want to view the destination the link points to, but the symbolic link itself.  Suppose I have a file, file.txt and I create a link to file.txt as      ln -s $HOME/path/to/file.txt .   Now, if I copy this link to a different system, this link will point to nothing if $HOME expands to something different on the other system, even if the path after $HOME is still the same. Is there some way to edit the link file so that $HOME is not expanded before creating the file, but is a part of the file itself?


modular exponentiation $14^{20} \pmod{33}$

How do I find 14^20 mod 33 ?  I tried writing 14^20 as 14^(2+4+8+6) but still no simplification.  Should I just check all the power of 14 mod 33 and hope that some of them give nice numbers (1 or 2)  What is a good method ?


Why I have both HWE and non-HWE kernels in Ubuntu 18.04

In Ubuntu 18.04 I have both HWE and non-HWE kernels installed. I only use the HWE kernel (5.0) and in the past I had removed the non-HWE kernel (4.15, both images and headers). However, after some updates I noticed that 4.15 got installed again. Note that after each kernel update I also use apt autoremove to remove the older kernel.  Why is the non-HWE kernel installed again? Can I completely uninstall it? How?  Below are the linux images installed on my pc:  $ dpkg --list | grep linux-image rc  linux-image-4.15.0-48-generic              4.15.0-48.51                                 amd64        Signed kernel image generic rc  linux-image-4.15.0-50-generic              4.15.0-50.54                                 amd64        Signed kernel image generic rc  linux-image-4.15.0-51-generic              4.15.0-51.55                                 amd64        Signed kernel image generic rc  linux-image-4.15.0-52-generic              4.15.0-52.56                                 amd64        Signed kernel image generic rc  linux-image-4.15.0-55-generic              4.15.0-55.60                                 amd64        Signed kernel image generic ii  linux-image-4.15.0-58-generic              4.15.0-58.64                                 amd64        Signed kernel image generic rc  linux-image-4.18.0-15-generic              4.18.0-15.16~18.04.1                         amd64        Signed kernel image generic rc  linux-image-4.18.0-18-generic              4.18.0-18.19~18.04.1                         amd64        Signed kernel image generic rc  linux-image-4.18.0-20-generic              4.18.0-20.21~18.04.1                         amd64        Signed kernel image generic rc  linux-image-4.18.0-21-generic              4.18.0-21.22~18.04.1                         amd64        Signed kernel image generic rc  linux-image-4.18.0-22-generic              4.18.0-22.23~18.04.1                         amd64        Signed kernel image generic rc  linux-image-4.18.0-24-generic              4.18.0-24.25~18.04.1                         amd64        Signed kernel image generic rc  linux-image-4.18.0-25-generic              4.18.0-25.26~18.04.1                         amd64        Signed kernel image generic ii  linux-image-5.0.0-23-generic               5.0.0-23.24~18.04.1                          amd64        Signed kernel image generic ii  linux-image-5.0.0-25-generic               5.0.0-25.26~18.04.1                          amd64        Signed kernel image generic ii  linux-image-generic                        4.15.0.58.60                                 amd64        Generic Linux kernel image ii  linux-image-generic-hwe-18.04              5.0.0.25.82                                  amd64        Generic Linux kernel image   And the headers:  $ dpkg --list | grep linux-headers ii  linux-headers-4.15.0-58                    4.15.0-58.64                                 all          Header files related to Linux kernel version 4.15.0 ii  linux-headers-4.15.0-58-generic            4.15.0-58.64                                 amd64        Linux kernel headers for version 4.15.0 on 64 bit x86 SMP ii  linux-headers-5.0.0-23                     5.0.0-23.24~18.04.1                          all          Header files related to Linux kernel version 5.0.0 ii  linux-headers-5.0.0-23-generic             5.0.0-23.24~18.04.1                          amd64        Linux kernel headers for version 5.0.0 on 64 bit x86 SMP ii  linux-headers-5.0.0-25                     5.0.0-25.26~18.04.1                          all          Header files related to Linux kernel version 5.0.0 ii  linux-headers-5.0.0-25-generic             5.0.0-25.26~18.04.1                          amd64        Linux kernel headers for version 5.0.0 on 64 bit x86 SMP ii  linux-headers-generic                      4.15.0.58.60                                 amd64        Generic Linux kernel headers ii  linux-headers-generic-hwe-18.04            5.0.0.25.82                                  amd64        Generic Linux kernel headers


I'm asking this because the  site has been in public beta for 838 days and is still using the default beta-site theme which seems quite inappropriate for a site full of graphical designers.


How to prevent/report potential mod power abuse?

On Stackoverflow with it's higher visibility and factual natural, this might not come across often, but on stack exchange for say "interpersonal skills", a lot of non-factual opinions are expressed, so that can cause moderator bias.  For example if you don't like someone's wording on something or believe in certain things, you can remove all opposing comments when they are completely legit. For example, . Mutiple people pointed out that the correct top two answer aren't useful. It might sound nice to "simply to truthful and respectful and ask", but that's not what the OP is asking and he clearly mentions it (that he doesn't want to risk offending the other person). Even the question is posted as "how to check" not "how to politely ask". All such comments were deleted for some random reason... Why?


Split a scanned photo across multiple pages (with a predifined splitting point)

I am a relative (La)TeX newbie! I want to split an A4 scanned image across two pages! Is there a  package to achieve this or is it possible to do this manually so that to be able to define the exact  splitting point?


Whenever I'd run sudo apt-get update it always never ends well  ...  W: Failed to fetch https://deb.nodesource.com/node/dists/qiana/main/source/Sources  HttpError404  W: Failed to fetch https://deb.nodesource.com/node/dists/qiana/main/binary-amd64/Packages  HttpError404  W: Failed to fetch https://deb.nodesource.com/node/dists/qiana/main/binary-i386/Packages  HttpError404  E: Some index files failed to download. They have been ignored, or old ones used instead.   Is there some way to fix this and remove the missing index? I'm pretty sure I'm not even using it. This started happening the moment I ran curl -sL https://deb.nodesource.com/setup | sudo bash -.


i have huawei g5000-5000 mobile whith 512 mb ram which has 479 mb free and a quad-core processor.offlate i have seen it has 0mb free ram and i am not able to do any work.whenever i open any app it automatically closes. i dont have many app heavy game and no heavy app loaded on my phone.i jjst have whatsapp,ucbrowser,truecaller,etc which i think should not be a problem. i have an unrooted phone.so please tell me what to do?


How to access static int from nested class?

How can I access a1, and a2 from c1::c2::func?  class c1 {     public:     class c2     {         protected:         static void func();     };      public:     static int a1;     private:     static int a2; };    void c1::c2::func() {     int f1= c1::a1; //works     int f2= c1::a2;      c1::a1= 1;  //fails     c1::a2= 2;      printf("func");  }   error:     prog.cpp:(.text+0xc): undefined reference to c1::a1'   prog.cpp:(.text+0x16): undefined reference toc1::a2'


NullPointerException in file Java Misanderstanding

i must write a programm that it translate grade in letter form like as A, B, C, D or F into number form (4, 3, 2, 1, 0 respective). The grade can have + or - too (+ increase grade of 0.3, - decrease of same number). I wrote this programm:  public class Grade{    private String letterGrade;    private String letter;    private String symbol = "n";    private double numericGrade;    private double grade;    private final double PLUS = 0.3;    private final double MENO = -0.3;     public Grade(String letterGrade) {       this.letterGrade = letterGrade;    }     public double getNumericGrade() {       if (letterGrade.length() > 1) {          letter = letterGrade.substring(0, 1);          symbol = letterGrade.substring(1, 2);       }        if (letter.equals("A")) {          numericGrade = 4.0;           if (symbol.equals("+")) {             symbol = "n";          }       }       else if (letter.equals("B")) {          numericGrade = 3.0;       }       else if (letter.equals("C")) {          numericGrade = 2.0;       }       else if (letter.equals("D")) {          numericGrade = 1.0;       }       else if (letter.equals("F")) {          numericGrade = 0.0;       }        if (symbol.equals("+")) {          grade = numericGrade + PLUS;       }       else if (symbol.equals("-")) {          grade = numericGrade + MENO;       }       else {          grade = numericGrade;       }        return grade;    } }   And the programm tester:  import java.util.Scanner; public class GradeTester{     public static void main(String[] args) {         Scanner in = new Scanner(System.in);          System.out.print("Please enter the grade in letter form: ");         String letterGrade = in.next();          if (letterGrade.equals("A") || letterGrade.equals("A+") || letterGrade.equals("A-")) {             Grade graduation = new Grade(letterGrade);              System.out.println("The grade in number form is: " + graduation.getNumericGrade());         }         else if (letterGrade.equals("B") || letterGrade.equals("B+") || letterGrade.equals("B-")) {             Grade graduation = new Grade(letterGrade);              System.out.println("The grade in number form is: " + graduation.getNumericGrade());         }         else if (letterGrade.equals("C") || letterGrade.equals("C+") || letterGrade.equals("C-")) {             Grade graduation = new Grade(letterGrade);              System.out.println("The grade in number form is: " + graduation.getNumericGrade());         }         else if (letterGrade.equals("D") || letterGrade.equals("D+") || letterGrade.equals("D-")) {             Grade graduation = new Grade(letterGrade);              System.out.println("The grade in number form is: " + graduation.getNumericGrade());          }         else if (letterGrade.equals("F")) {             Grade graduation = new Grade(letterGrade);              System.out.println("The grade in number form is: " + graduation.getNumericGrade());         }         else {             System.out.println("Not permissed!");         }     } }   But when i'm try it, only for letter without + or - this error appear:  Exception in thread "main" java.lang.NullPointerException         at Grade.getNumericGrade(Grade.java:20)         at GradeTester.main(GradeTester.java:13)   I don't understand what's the problem.


$f:S^1 \rightarrow R$ continuous means there exists a point $x$ such that $f(x) = f(-x)$.

Let $S^1$ be the unit circle in $\mathbb{R}^2$, then for a continuous map from $S^1$ into $\mathbb{R}$, there exists $x \in S^1$ such that $f(x) = f(-x)$.    I know that $S^1$ is path connected and so connected.  And the intermediate value theorem.  For any choice of $-x, x$, and any $r$ between $f(-x)$ and $f(x)$ there is $c \in S^1$ such that $f(c) = r$.  Let $\psi : [0,2\pi] \rightarrow S^1, \ x \mapsto e^{i(a + x)}$ for any $a\in \mathbb{R}$ be a circular path in $S^1$ identified with the circle group as a subset of $\mathbb{C}$.  Let $g(x) = f(x) - f(-x)$.  Let $a\in S^1$ be any point such that there exist points in the image of $g$ to the right of $g(a)$ for at least a run of $\epsilon$.  Now translate everything to near the origin with $h(x) = g(x) - g(a) - \epsilon/2$  Can't figure this one out.


How can I draw this graph in the picture attached below by using tikz

I would like to draw this graph in the pic via tikz, could you please help me


I'm getting a file from an OpenFileDialog which returns a string with the absolute path to the selected file. Now I want that path as a relative path to a given path (in this case the path to my application).  So let's say I get a path to the file: c:\myDock\programming\myProject\Properties\AssemblyInfo.cs  and my application is located in  c:\myDock\programming\otherProject\bin\Debug\program.exe  then I want the result:   ..\..\..\myProject\Properties\AssemblyInfo.cs


Please revisit the CAPTCHA & China issue

Back in 2012 when China first blocked all Google services, thereby preventing non-VPN users from proving their non-roboticness, someone quickly opened this thread on Meta:    The consensus at the time was "we can't think of a better way of doing things".  Well, 3 years have passed and China is showing no signs of unbanning Google. Meanwhile, CAPTCHA technology has evolved. Can the SE admins please revisit this situation? People in China without a VPN are completely unable to prove they are not bots. I couldn't even search for the phrase "pgp" on Security.SE without hitting the human verification barrier. Blocking questions is one thing, but searches also? I think that's too strict.  (yes, I wrote this with my VPN)


What is the largest number $n$ with $\lambda(n)=k$ for a given $k$?

Let $k\ge 2$ be a natural number.      What is the largest number $n$ with $\lambda(n)=k$, where $\lambda(n)$ is the Carmichael-function. (See :  ) ?   For $k=2$, the maximum seems to be $24$.  For $k=4$, the maximum seems to be $240$.  For $k=6$, the maximum seems to be $504$.  For $k=60$, I found many $n's$, currently I arrived at $227,146,920$. (The program just found a higher number, so the number is not maximal)  I am not sure, but a maximum should exists for every $k$, thus defining the number $n(k)$.     Which growth rate will $n(k)$ probably have ? Exponential ?