How can I highlight elements in a matrix?

I'm about to use this diagram to make computing 3x3 determinants clear and easy for my students. I tried to add this picture to my lecture but it's blurred due to the bad quality of the picture. So i want to create exactly the same figure using latex.  I've searched and read a few topics about highlighting elements and diagonals in matrix but it does not work in this case. I want to add plus signs and minus signs as in the picture, and highlight elements in the matrice with elements outside the matrice.  I appreciate all your help and your advice. Thank you in advance !


Prove ${a}^{2}+{b}^{2}={c}^{2} \Rightarrow$ 3|ab  Not sure how to approach this, I considered the contrapositive $3\nmid ab \Rightarrow {a}^{2}+{b}^{2} \neq {c}^{2}$ and then using cases, where case 1 is $ab = 3q+1$ and case 2 is $ab = 3q+2$, but was not able to continue.  Thanks in advance for any help.


Upgrade 13.04 to 13.10 - packages now unavailable

I'm trying to follow      Ubuntu Servers (Recommended) Install update-manager-core if it is not   already installed:      sudo apt-get install update-manager-core Launch the upgrade tool:      do-release-upgrade Follow the on-screen instructions.   to upgrade a 13.04 box to 13.10, but I can't even get update-manager-core installed at this point. Any ideas how to proceed? I really don't want to rebuild the box from scratch if it can be avoided.  Here's the output from the attempt to install update-manager-core  nathan@nasty-vault:~$ sudo apt-get install update-manager-core Reading package lists... Done Building dependency tree        Reading state information... Done The following extra packages will be installed:   python3-update-manager The following packages will be upgraded:   python3-update-manager update-manager-core 2 upgraded, 0 newly installed, 0 to remove and 120 not upgraded. Need to get 39.0 kB of archives. After this operation, 4,096 B disk space will be freed. Do you want to continue [Y/n]? y WARNING: The following packages cannot be authenticated!   python3-update-manager update-manager-core Install these packages without verification [y/N]? y Err http://us.archive.ubuntu.com/ubuntu/ raring-updates/main python3-update-manager all 1:0.186.2   404  Not Found [IP: 91.189.91.14 80] Err http://us.archive.ubuntu.com/ubuntu/ raring-updates/main update-manager-core all 1:0.186.2   404  Not Found [IP: 91.189.91.14 80] Failed to fetch http://us.archive.ubuntu.com/ubuntu/pool/main/u/update-manager/python3-update-manager_0.186.2_all.deb  404  Not Found [IP: 91.189.91.14 80] Failed to fetch http://us.archive.ubuntu.com/ubuntu/pool/main/u/update-manager/update-manager-core_0.186.2_all.deb  404  Not Found [IP: 91.189.91.14 80] E: Unable to fetch some archives, maybe run apt-get update or try with --fix-missing?   I've run apt-get update which also complains at this point with these types of errors  Err http://us.archive.ubuntu.com raring-backports/universe i386 Packages   404  Not Found [IP: 91.189.91.13 80] Err http://us.archive.ubuntu.com raring-backports/multiverse i386 Packages   404  Not Found [IP: 91.189.91.13 80] W: Failed to fetch http://security.ubuntu.com/ubuntu/dists/raring-security/main/source/Sources  404  Not Found [IP: 91.189.91.14 80]


How to create contact detail page using controller?  <apex:page standardController="Contact" extensions="ContactDetailController"> <apex:form > <apex:pageBlock mode="maindetail" title="Contact detail" tabStyle="Contact" id="myId">  <apex:pageBlockButtons >     <apex:commandButton action="{!Edit}" value="Edit" reRender="myId" />     <apex:commandButton action="{!Delete}" value="Delete" reRender="myId" />     <apex:commandButton action="{!cloneButton}" value="Clone"/>     </apex:pageBlockButtons> <apex:pageblockSection >          <apex:pageBlockSectionItem >          <apex:outputlabel value="First Name"/>          <apex:outputpanel >          <apex:outputfield value="{!contact.Salutation}" />          &nbsp;          <apex:outputfield value="{!contact.FirstName}" />          </apex:outputpanel>          </apex:pageBlockSectionItem>          <apex:outputField value="{!contact.homephone}"/>          <apex:outputField value="{!contact.lastname}"/>          <apex:outputField value="{!contact.mobilephone}"/>          <apex:outputField value="{!contact.Accountid}"/>          <apex:outputField value="{!contact.otherphone}"/>           <apex:outputField value="{!contact.title}"/>          <apex:outputField value="{!contact.fax}"/>          <apex:outputField value="{!contact.Department}"/>          <apex:outputField value="{!contact.Email}"/>          <apex:outputField value="{!contact.Birthdate}"/>          <apex:outputField value="{!contact.AssistantName}"/>          <apex:outputField value="{!contact.Reportstoid}"/>          <apex:outputField value="{!contact.Assistantphone}"/>          <apex:outputField value="{!contact.leadsource}"/>          <apex:outputField value="{!contact.OtherStreet}"/>          <apex:outputField value="{!contact.MailingCity}"/>          <apex:outputField value="{!contact.othercity}"/>          <apex:outputField value="{!contact.MailingState}"/>          <apex:outputField value="{!contact.otherstate}"/>           <apex:outputField value="{!contact.MailingPostalCode}"/>          <apex:outputField value="{!contact.otherpostalcode}"/>          <apex:outputField value="{!contact.MailingCountry}"/>          <apex:outputField value="{!contact.othercountry}"/>          <apex:outputField value="{!contact.Languages__c}"/>          <apex:outputField value="{!contact.Level__c}"/>          <apex:outputField value="{!contact.Description}"/>   </apex:pageblocksection>  </apex:pageblock> </apex:form>  <apex:relatedList list="Cases"/> </apex:page>


May this seem like a complete sentence or maybe complete interrogative(?), no subject intransitive verb bit, or main clause?

"But what about Sir Isaac Newton, who some contend was autistic?”   I may not get this. I may get here and there complete sentences may not contain subject verb object. I think they got to contain subject (intransitive) verb? In But what about Sir Isaac Newton, who some contend was autistic? there seems no main clause, no subject (intransitive verb) bit. May this seem like a complete sentence maybe a complete interrogative(?) not containing a main clause or complete sentence bit(?) (subject intransitive verb[?])?


The title stands for itself.  If it is not possible, how does LaTeX import an EPS file using \includegraphics?


How can a time limited signal be of infinite bandwidth and a finite bandwidth signal be of infinite duration?


What is the correct phrase to use?     I am speaking on the phone? Please keep quiet for a while.   or      I am talking on the phone? Please keep quiet for a while.   To me, the first one makes more sense.


There's plenty of discussion and even sage advice out there explaining that a caster need not have Line of Sight (LOS) on a target for their Spiritual Weapon to make an attack. I.e. a paladin can summon their SW and leave the room and still be able to make attacks with the weapon.   But is this still the case for maintaining concentration on the spell if you leave the range of the spell?   Another way to phrase the question might be is the range of the spell only a determinate in the initial casting of the spell, or is the range the max "leash" of the spell to keep it active?


How do I setup a class that represents an interface?  Is this just an abstract base class?


My highway is backing up. What can I do?

Initial note: Having read , the answers there do not help in this specific situation, as they rely on having lots space to spare - I have very little.  When I started my city, I designed a simple exit from the default highway that I thought was sustainable: I left enough space around it to upgrade the road as I needed to, which has worked up until now. However, I am now stuck with a six-lane one-way exit from the highway that isn't getting used: since cars seem to pick the most efficient lane to get where they want to go, regardless of traffic, the rightmost lane fills up, then spills over onto the highway. This blocks the highway, my bus routes, and more importantly my planned emergency routes.  My setup looks like this:    The red arrows show road direction, and the orange line is the traffic backed up. Note that in this image, I have replaced the six-lane one-way exit with a highway exit, as this is just about as efficient...  This situation is getting to be pretty bad, and is bringing half my city to a standstill. Its effects compound themselves further down the highway:    In this image, the orange line is the traffic directly caused by this exit not working. This traffic jam then blocks two exits/entrances further down, on the red crosses; the yellow line shows the traffic jam caused by these being blocked. In other words, my inefficient exit design is now blocking itself from moving.  So this is a two part problem.   Considering that I'm constructing a residential district in the space above left of the problem exit, and would like to keep the solution inside the power line, how can I redesign this exit to be more efficient? How do I solve the ring of traffic jams? Is it a simple case of just deleting and replacing a bit of road?


What resolution does Google use while crawling a site with responsive/adaptive design?

I use conditional loading and media queries, JS, and CSS techniques for building responsive/adaptive designed websites.  The HTML output for these sites depends on the number of horizontal and vertical pixels of the users's browser window.   What resolution does Google use while indexing sites, which impacts the HTML output that's returned?


check my proof, I feel like I made a mistake :)  so I'm looking to prove that when $p(n)$ is $n!<n^n$, $p(n)$ is true for all $n>1$.  Base Case $$ p(2) \iff 2!<2^2 \iff 2<4 $$  Assume p(k) is true $$k!<k^k$$  Prove p(k+1)  $$(k+1)!<(k+1)^{(k+1)}$$ $$(k+1)(k)!<(k+1)(k+1)^k$$ $$(k+1)(k)!<(k+1)(k^k+1)$$ This part above. Can I assume that $1^k$ is always $1$ given any $k$ such that $k>1$? $$(k+1)(k)!<(k+1)(k^k+1)$$ $$(k)!<k^k+1$$ Then above, can I factor out a k+1 from both sides? $$(k)!<k^k+1$$  Is this a completed proof? Would my ending statement be something like "since we assumed $p(k)$ and $p(k+1)$ is still true given $p(k)$, and since $p(k+1)$ is a higher degree than $p(k)$...." (not sure what really to say here)?  trying again  prove p(k+1)  to start, im now looking to multiply the sides by (k+1)? not replace?  so   $$k!<k^k$$ $$(k+1)k!<(k+1)k^k$$ $$(k+1)!<(k^[k+1]+k^k$$


Ubuntu 13.04 "could not find required OpenGL entry point 'glGetError'!"

Just recently upgraded to 13.04 and am having trouble running TF2 via Steam. Whenever I start Steam I get a dialog saying:     OpenGL GLX context is not using direct rendering, which may cause performance problems.   Every time I go to launch TF2 I get a dialog saying:     Could not find required OpenGL entry pint 'glGetError'! Either your video card is unsupported, or your OpenGL driver needs to be updated.   I tried updating my Nvidia drivers, hoping that would solve this issue but alas, it did not. I believe this issue is related to a fix I used to get Skype working with 13.04, specifically . Just a heads up I'm using GNOME Shell 3.8.  Let me know if you need anymore information about my system.


Proof that sum of integrals of same function on adjacent intervals equals the integral over both intervals

I am seeking a proof that  $$\int_a^c f(x) dx + \int_c^b f(x) dx  = \int_a^b f(x) dx$$  Please use Stewart's (Calculus: Early Transcendentals, 2016, 8e, p. 378) definition of the definite integral:    This is what I have:  Suppose   $$u=\int_a^c f(x) dx = \lim \limits_{n \to \infty} \sum_{i=0}^n f(x_i^*) (\frac{c-a}{n})$$   and   $$v=\int_c^b f(x) dx = \lim \limits_{n \to \infty} \sum_{i=0}^n f(x_i^*) (\frac{b-c}{n})$$  Then   $$u+v = \lim \limits_{n \to \infty} \sum_{i=0}^n f(x_i^*) (\frac{b-c}{n}) + \lim \limits_{n \to \infty} \sum_{i=0}^n f(x_i^*) (\frac{c-a}{n}) $$  $$=\lim \limits_{n \to \infty} \sum_{i=0}^n f(x_i^*) (\frac{b-c}{n} + \frac{c-a}{n})$$  $$=\lim \limits_{n \to \infty} \sum_{i=0}^n f(x_i^*) (\frac{b-a}{n})$$  $$=\int_a^b f(x) dx$$  Edit: As @Matthew Conroy pointed out, the $f(x_i^*)$ cannot be factored out in the sum because the values of $x_i^*$ are different for each definite integral. So, this proof is invalid.


Did The Dark Tower books ever refer to psychic powers as "The Shine?"

The recent movie isn't shy about calling the Breakers' powers "The Shine." Was there any point in the books or comic books where a character refers to a psychic power as "The Shine?"


How increases the flow rate of a fluid by increasing pipe diameter?

Can I increase flow rate of a fluid by increasing pipe diameter for a transfer line? If so, how do I calculate it?


This is an old preliminary exam problem: Let $T:C([0,1])\rightarrow C([0,1])$ be defined by $Tf(x)=\int_0^x f(t)dt$. Prove that $T$ is a compact operator, i.e. the image of the unit ball is pre compact.   So, if I understand correctly, I need to show that the image of $B:=\{f\in C([0,1]) | \sup_{x\in[0,1]}|f(x)|<1\}$ has compact closure. Here is my attempt:   Note that $TB=\{f\in C[0,1]| \sup_{x\in[0,1]} \int_0^x f(t)dt<1\}$   My first thought is to rewrite this as $TB=\{F'(x) | \sup_{x\in[0,1]} F(x)<1\}$   I think this is justified because if $F(x)=\int_0^x f(t)dt$ then $F'(x)=f(x)$ (since w.l.o.g. $F(0)=0$) for almost all $x$.   So the next step is to figure out what the closure of $TB$ looks like, but this is where I'm stuck. Any help would be appreciated. Thanks!  Update: I understand, from the answer given by user251257 that $TB$ is uniformly bounded and equicontinuous, so that, by Arzela Ascoli, any sequence in $TB$ has a uniformly convergent subsequence. But I still don't understand why this shows that the closure of $TB$ is compact. In order for $\overline{TB}$ to be compact, don't we need for any sequence in $\overline{TB}$ to have a convergent subsequence? What if we take a sequence in $\overline{TB}\backslash TB$?


C/C++ check if one bit is set in, i.e. int variable

int temp = 0x5E; // in binary 0b1011110.   Is there such a way to check if bit 3 in temp is 1 or 0 without bit shifting and masking.  Just want to know if there is some built in function for this, or am I forced to write one myself.


Box around some of the elements in an enumerate list

I need to put a box around the label of an enumerate list. This is solved in   but, my problem is that I need to do that just in some of the elements marked, for example using a command different from \item (but the numbering should be continuous).


If I earned less than $10 in interest from my bank account, do I need to report it on my taxes?

I'm preparing my taxes with Turbotax, and its asking me for all the bank accounts I earned interest from. One of these accounts has earned less than $10 total for the year. Because of that this bank is not providing me with a 1099-INT form.   Since I earned less than $10 from that bank, can I skip reporting this bank to Turbotax/my tax filing? If not, how do I report the interest without the bank giving me a 1099?


Prove that $\tan\frac{\pi}{9}+ 4\sin\frac{\pi}{9}= \sqrt{3}$ .

Prove that $$\tan\frac{\pi}{9}+ 4\sin\frac{\pi}{9}= \sqrt{3}$$   I think the best solution here is using right triangle . . . I have one too, but not pretty.


Similar to  question, a need a wireless transmitter for underwater, both fresh and salt water. Vertical range needs to be a few 100 meters, and underwater depth only 2 meters. The power supply will be a battery and the device needs to be able to run for a few hours.   Receiver will always be above water. And only one-way communication is necessary. The data that is sent is only a few bytes big, or two (decimal) floating points representing coordinates.  Any ideas in which direction I should start searching?


What does "much less both" in the following sentence mean?

Few historians have extensive training in critical theory and its   specialized languages, and the sheer volume of work in early American   history and literature challenges anyone who would master either   field, much less both.   Is it talking about the volume of work challenges people to become masters or reduces the challenges for people to become masters? Also, does "sheer" mean "many" here? I'm confused about the meaning of the whole sentence.


I was messing around in blender when I noticed that my view was snapped to an object. When I moved it so did my view.    What is this feature and how can I enable/disable it?


Null pointer exception while retrieving data from Firebase

I want to retrieve user name from my firebase data base   I have written this code and its showing error " java.lang.NullPointerException: Attempt to invoke virtual method 'java.lang.String android.os.Bundle.getString(java.lang.String)' on a null object reference"  Here's my code:  `public class MyAccount extends AppCompatActivity {  private Button mSetupButton; private EditText mSetupName; private EditText mSetupBio; private ImageButton mSetupImageButton;  private String mPostKey=null; private DatabaseReference mDatabase;  @Override protected void onCreate(Bundle savedInstanceState) {     super.onCreate(savedInstanceState);     setContentView(R.layout.activity_my_account);      mDatabase= FirebaseDatabase.getInstance().getReference().child("Profiles");     mPostKey=getIntent().getExtras().getString("profile_id");      mSetupName = (EditText) findViewById(R.id.accountName);     mSetupBio = (EditText) findViewById(R.id.accountBio);     mSetupButton = (Button) findViewById(R.id.accountButton);     mSetupImageButton = (ImageButton) findViewById(R.id.accountImageButton);      mDatabase.child(mPostKey).addValueEventListener(new ValueEventListener() {         @Override         public void onDataChange(DataSnapshot dataSnapshot) {              String post_name = (String) dataSnapshot.child("Name").getValue();             mSetupName.setText(post_name);          }          @Override         public void onCancelled(DatabaseError databaseError) {          }     }); }   }


If there would be such a thing as a complex prime number, how would it be defined?  A normal prime is defined as a number only dividable by one or itself.. would that be "1+1i" with complex numbers?    Thanks in advance :)


Let $G$ be the group of all $n\times n$ matrices with entries of the matrices from the field $\mathbb Z_p$ , $p$ prime, such that determinant of every matrix is not $[0]$ , w.r.t. matrix multiplication ; then what is the order of $G$ ?


What's the difference between 1N4004 diode and 1N4007?

I have a circuit with multiple diodes, and I was wondering if I could use a 1N4004 diode instead of 1N4007


Does anybody know why my camera is not showing anything and the Rendering is grey blank?  Rendering:  Camera View:


How do I print the cite key along with the entire .bib file?

I am trying to print an entire *.bib file. I would like to print the citation key along with all the entries in the .bib file. I can print my bibligraphic data file (.bib) but cannot get it to print my cite key. I can use BibTeX or biblatex. Any ideas how to do this?  Here is a clearer explanation:  My MCMC.bib file contains:  @ARTICLE{Ait04,   author = {Y. A\"{i}t-Sahalia},   title = {Disentangling Diffusion from Jumps},   journal = {Journal of Financial Economics },   year = {2004},   volume = {74},   pages = {487-528} }  @ARTICLE{Ait02,   author = {Y. A\"{i}t-Sahalia},   title = {Maximum-Likelihood Estimation of Discretely-Sampled Diffusions: A Closed-Form Approximation Approach},   journal = {Econometrica },   year = {2002},   volume = {70},   pages = {223-262} }   I use the following LaTeX file:  \documentclass[12pt]{article} \usepackage[style=verbose,citestyle=alphabetic,sorting=nty,natbib=true]{biblatex} \bibliography{MCMC} \begin{document} \nocite{*} \printbibliography  \end{document}   I would like the output file to contain the cite keys Ait04 and Ait02 at the start of each citation so that I know what key I have assigned to each citation. Any help would be most appreciated.


In clustering, what is the analogous of the centroid that uses the median instead of the mean?

The centroid of a cluster is defined as centroid. It is defined as the mean of each dimension across all samples of the cluster.  What is the analogous that uses the median of each dimension? As far as I know, a similar concept is the medoid, which needs to be an actual sample of the cluster.


how can i get sequential execution list of init scripts?

I write following script but it is not working during upstart,  start on startup exec echo "Current date:-" $(date) > /tmp/myscript.out   I have stored this script as /etc/init/myscript.conf  Please help me with this. Thanks in advance.


Can I install Ubuntu on a pentium dual core with 1 gb of ram. If it is not possible please suggest a version. And please tell me, which is the best version of Ubuntu with min errors.


How to use hyphens appropriately when listing multiple hyphenated terms?

If multiple hyphenated terms share the same latter half, and I wish to list them without repeating that latter half, how should the hyphens be placed?  For example:     I will be investigating control issues in ground-based, water-based, and air-based robots.   If I do not want to repeat based, could I write:     I will be investigating control issues in ground-, water-, and air-based robots.   Is it correct to just leave a hyphen dangling after ground and water?  If not, how should it be written? I know the original sentence doesn't sound too bad, but I really just want to know the punctuation rule (or the convention in American English if there is no rule).


Why do I get Exception when I'm trying to print Instance variabel as Refrence variabel?

I'm learning object and I'm trying to use a reference variable as an instance variable, but I get " java.lang.NullPointerException " even if I've given the value.   What am I doing wrong?    Here is my code:  public static void main(String[] args) {      Car car = new Car();     car.brand = "Nissan";     car.modelYear = 1998;     car.owner.name = "Marshall";     System.out.println("The car brand is "+car.brand +             "car model is "+ car.modelYear+             "cars owners name is "+ car.owner.name);     } }  class Car {     Person owner;     String  brand;     int modelYear;     int horsePower; }  class Person {     String name; }


I have mounted a Veracrypt volume just to find out that one of the two VBox machines on that volume is inaccessible. When I look into the volume I can see that this machine folder is empty - no .vdi file. However I did not delete it. What's strange is that the space used is as big as it would be with the .vdi file. The Trash folder is also empty. I've tried data recovery software but none I've tried supports network drives so they refuse to open the mounted volume. Anyone knows how to resurrect the .vdi file? After re-mounting the volume the file is missing still.


I'm trying to make one object orbit another. But I want it to repeat, rather than stop at 100 frames. It seems there is no option for this. Is there a way to make this happen?


How can I change the local system's date & time programmatically with C#?


Is there a way to find unresolved questions on a specific tag?

Is there a way to find unresolved questions, questions that have answers but none have been accepted by the OP of question on a specific tag?  I can see the option to find ones that are 'unanswered' but not the ones that are 'unresolved'.


Query to compare the structure of two tables in MySQL

To automate the backup process of one of my MySQL databases, I would like to compare the structure of two tables (current version vs old version).  Can you think of a query that can compare two tables?  Here are some example tables that you can compare.   CREATE TABLE product_today (   pname VARCHAR(150),   price int,   PRIMARY KEY (pname) );  CREATE TABLE product_yesterday (   pname VARCHAR(150),   price int,   PRIMARY KEY (pname) );  CREATE TABLE product_2days_back (   pname VARCHAR(15),   price int,   PRIMARY KEY (pname) );   The first two tables have identical structures. The last one is different. I just need to know whether two tables have different structures or not. I'm not interested in the how they differ.


C++ weird rounding when decimal passed into function

I'm new to C++ and messing around with functions. I have two cpp files and one header. One of my cpp files is main.cpp where the following code is: a->change(42.57);  I then have another cpp where the following code for change is: bool Student::change(float mark)  and then the header where the following code is: bool change(float mark);  When I pass the float in, it is 42.57. However, after it is passed in it suddendly chnages to 42.5699997. Could someone please explain why this happens?


Why is Cantor's diagonal argument valid?

This question is about the validity of the  itself, not about uncountability of sets or otherwise which can probably be proved in ways I'm unfamiliar with. It seems, to me, that the diagonal argument assumes its conclusion. For a diagonal proof to be valid, the diagonal must be a diagonal of a square matrix.  "counterexample" if the matrix is not square: 0 1 0 0 0 0 1 0 0 1 1 1   Cantor's diagonal argument seems to assume the matrix is square, but this assumption seems not to be valid. The diagonal argument claims construction (of non-existent sequence by flipping diagonal bits). But, at the same time, it non-constructively assumes its starting point of an (implicitly square matrix) enumeration of all infinite sequences of binary digits. What happens when we actually attempt to construct an enumeration of all infinite sequences of binary digits? Here is one such construction: Count from $0$ to $\infty$ in binary with least significant bit first (for example: 0, 1, 01, 11, 001, 101, 011, 111, 0001, etc). As you count, put those numbers in a list, filling in extra 0s on most significant side (on the right) as needed First few iterations of the resulting matrix: 0  0 1  00 10 01  00 10 01 11  000 100 010 110 001  ...  We immediately see the consequence of any information encoding, the width of the matrix increases $O(\log_2 n)$, while the height of the matrix increases $O(n)$. Where $n$ is the number of sequences in the matrix. While $\lim_{n \to \infty} \log_2(n) = \infty$ and $\lim_{n \to \infty} n = \infty$, which make it seem like a square matrix. Another way to frame being a square matrix is to ensure that the ratio of ${width \over height} = 1$. We notice that $\lim_{n \to \infty} {\log_2(n) \over n} = 0$ and $\lim_{n \to \infty} {n \over \log_2(n)} = \infty$. Does this not mean that the ratio diverges, demonstrating the enumeration of all infinite sequences of binary digits cannot be a square matrix? Doesn't this, in turn, make the diagonal argument not valid? sidenote: The above construction, in the limit, when we flip bits along the diagonal, would result in an infinite sequence of 1s, 1111111.... There is nothing about the construction that prevents it from generating an infinite sequence of 1s in the limit, which I think is noteworthy and takes away from what seems like diagonal argument's almost mystical generation of non-included bit sequence along the diagonal when we think only of a random arrangement of sequences instead of ordered one.


Can I change the contents of the Keyboard Shortcut List that shows up when I hold down super?

It occurred to me that this could be a very convenient way to keep a little bit of information sitting just in the background, ready whenever I need it.  I am referring to this list


Learning about Grothendieck's Galois Theory.

I have background in category theory and I am familiar with the very basics of algebraic geometry - Chapters I and II of Hartshorne. What would be a recommended (self-contained, maybe?) text for learning about Grothendieck's Galois theory ?


Use \newcommand with variable math environment

I'm writing a text where the variable I_{a,b,c}^{d,e,f} occurs a lot. It occurs as well in plain text as in mathematical environments. I would like ONE command, that can be used in both cases, something like  \newcommand{\Ioften}{$I_{a,b,c}^{d,e,f}$}   However this will only work, when I use it in plain text, not in the mathematical environment. That is I could use it now \Ioften, but not in the equation $3\cdot \Ioften$


What is the word for being too greedy for money?

I need a word that implies   a person's insatiable hunger for more than required wealth   Something like "hoard" or "more than required" but not quite


Any integer in 99, 999, 9999... sequence is not a perfect square

I am learning number theory and trying to understand how does below statement is true .  Show that no integer in the following sequence can be a perfect square: 99, 999, 9999, 99999, ...


Symbols instead of numbers as footnote markers

How can I make LaTeX use symbols (*, †, ‡, and so on) instead of numbers to mark footnotes?  (The numbers are confusing because I use superscripted numbers for citations.)


Prove that $$|\frac{a-b}{1-\bar{a}b}|<1$$ if $|a|<1$ and $|b|<1$.  After doing some calculation I ended up in a dead end  $$|\frac{a-b}{1-\bar{a}b}|=\sqrt{\frac{|a|^2+|b|^2-(a\bar{b}+b\bar{a})}{1+|a|^2|b|^2-(a\bar{b}+b\bar{a})}}$$  How do I proceed further ?  Is there any alternating ways like using cauchy's inequality ?


I want to read an entire file into a string. The file however is in the program arguments. I have been trying to use Scanner in order to:  Scanner scan = new Scanner(args[0]);           scan.useDelimiter("\\Z");           String content = scan.next();          System.out.println(content);   My result is just the name of the file that is in "args[0]" instead of the actual contents of the file.   I figured a loop would not work since I am not hardcoding the file into the program.


Why does friction point radially inwards when a car is turning in a circular path?

When a car is turning along a circular path with a constant speed, it requires a centripetal force to keep it moving along that path. This force is a frictional force which points toward the center of the circle which the car traces. But why exactly does friction have to point radially towards the center? From my understanding, friction opposes the car's tangential motion, which means that friction should also be tangential but opposite to the velocity. I already understand that static friction will prevent the car from sliding along the path which its tangential velocity indicates, but I don't understand why the friction has to be perpendicular to the car. Please, if anyone knows, explain this using a vector diagram showing where exactly this perpendicular friction vector comes from. I would highly appreciate it! Thanks.


Please suggest a Linear Algebra book with an introduction and rigorous theory (description) on Eigenvectors , eigen-values , Cayley-Hamilton theorem , Diagonalisation of matrices ; Quadratic forms ( Sylvester's Law , rank , signature , reduction to canonical forms ) .   Thanks in advance


In C++ I could use pointer arithmetic to grab everything from a start position to the end of an array. What do you do in C# to accomplish the same thing?  using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Threading.Tasks;  namespace ConsoleApp1 {     class Program     {         static string GetText(byte[] value, uint startPos)         {             // TODO - What goes here?             return "";         }          static void Main(string[] args)         {             byte[] value = new byte[] { 0x41, 0x42, 0x42, 0x42 };             string result = GetText(value, 1);             Console.WriteLine(result);         }     } }   Expecting output: BBB


A separable Banach space is isometrically isomorphic to a subspace of $\ell_{\infty}$

I'm aware that this question has been answered here    But I want to prove this result a different way.   Suppose that $\mathcal{B}$ is separable and define $i : \mathcal{B} \to L^{\infty}(\mathbb{N})$ in the following way: For a dense subset of the unit ball in $\mathcal{B}$, denoted by $\{ f_n \}$, define $x_n = (\cdot, f_n)$ and thus define $i(y) = ((y,f_n))_{n=1}^{\infty}$. It is clear that this map is linear, injective and that $\| i(y) \|_{L^{\infty}(\mathbb{N})} = \| y \|_{\mathcal{B}}$. It remains to show that $i$ is bounded. This is where I'm stuck.


a1, a2, ..., an sequence numbers are given. Now, give an algorithm with O(nlg n) running time to calculate the number of pairs (i, j) for i < j and ai > aj.  Input: The number of test cases has came in first. For each test case number has came n number for first and then a1, a2, ..., an in the next line. N <= 100000  ai <= 100000000   Now, I want the output as follows:  Output: For each test is printed only one number (that is the asked value in the beginning of the question).  Sample Input:  2 4 3 2 1 5 5  8 9 3 2 1   Sample Output:  3  9


Ubuntu shows that i'm in offline mode while trying to connect to internet

I have lenovo Z580 laptop and dual-booted my system with windows 8 and ubuntu 13.04. I can connect to internet using windows 8(both wired & wireless) but cannot connect using ubuntu(both). It always shows me that "I am in offline mode"


Missing /etc/hosts file – How can I create a new hosts file?

I have googled and searched Ask Ubuntu on this, but got no relevant answers. I have no hosts file in /etc, I cannot find a hosts file in search, I am talking about the system hosts file not lampp/etc. I mention that because there is no hosts file there either - maybe that is a clue.  I want to know how to create a hosts file in Ubuntu or obtain a sample file I could copy and paste or I am happy to use the terminal if someone can help with best way to create the file and edit it.  I am not even sure what extension it should have - basically I just want the default hosts file that I understand Ubuntu should come with in my /etc folder.


Which is the best software of making a calendar. Coreldraw or Illustrator? What is the standard size of calendar? And is there any inbuilt format or template fro making calendar in both Corel or Illustrator? Also, even though Photoshop is a rasterised software but still wanted to ask can it be designed in Photoshop also?


I am currently using this command to get some information about some specific processes:  ps -C beam.smp -o pid,user:20,%cpu,%mem,args   As I use it for two process names, I would like to do it in one command in order to get a snapshot. Like that:  ps -C beam.smp,docker -o pid,user:20,%cpu,%mem,args   The problem is that the output does not display a specific column with beam.smp or docker, which would be really useful for me. How could I get a new line in my output showing that?


Why does amount of protons define how matter is?

My question might sound convoluted but my mind is twisting right now so my apologies in advanced.   Why is it that when I have one proton and one electron it is Hydrogen a clear flammable gas, and when I have say, twelve, it is carbon the driving force of life as we know it and then we end up with 239 and we have uranium a radioactive element.   How does the amount of protons affect what matter will be? Why does the amount of these particle things magically make one thing air and another cyanide?  If I have one pebble it is a pebble, if I have 13 its just more of the same pebbles. What makes protons different?  Sorry this is so convoluted,  any reply is appreciated


Use Type.GetType() to get the type and how to new an object in this typical type?

Type typesample = packet.GetType();   Then I want to new an object in the type of typesample


San Francisco seems an odd choice for Starfleet Headquarters to me, especially within sight of the Golden Gate Bridge.  It's such a densely populated area, I would figure that it's one of the last places one would want to place a new military facility - especially one which surely must be kept at the forefront of technological innovation.  If anywhere in the U.S., I'd more likely have expected Starfleet's home to be closer to an existing NASA facility that is more intimately involved in spaceflight operations.  The obvious choices would have been Kennedy Space Center in Florida, or Johnson Space Center in Texas.  The closest facility to San Francisco would be Ames Research Center in Mountain View, which doesn't quite compare to the other centers from the layman's perspective.  The next spot I could think of is Bozeman, Montana - site of Zephram Cochrane's flight of the Phoenix.  But that's half-way across the continent.  Has there ever been an explanation in canon, production notes, or interviews, that explains why they chose San Francisco to be the home of Starfleet?


Float a Div to bottom-right corner of a div

I'm having a lot of trouble finding a solution for floating an element to the bottom-right of a div.   It's dynamically aligned (both the div and the button). I need text to be able to wrap around the button, and the button to stick to the bottom right corner of a div.   I'm looking for anything, be it pure CSS or with some Javascript mixed in to get this functionality.   Basically:

Dynamic text area
         Click Here!
   I need the .btn (also dynamic, may be one to three lines of text in it, width is set to 110px) to be floated to the right and sit on the bottom, and the text to wrap around the button (which throws absolute/fixed positioning out the window).   This has been marked as a duplicate, but there is no answer in that question that specifically solves this problem, as they all assume a fixed height.


I get the following error when I run my Perl script:     "Can't locate autovivification.pm in @INC"   How can I install this module on my system?


A question about the last security update for Ubuntu ("ATTENTION: Due to an unavoidable ABI change...")

I'm subscribed to the Ubuntu Security Notes, so everytime that I receive an e-mail, a new update is avalable.  But in the last update, they wrote something in the end that I coudn't undertand much, so can anyone please tell me what does that means?  ATTENTION: Due to an unavoidable ABI change the kernel updates have been given a new version number, which requires you to recompile and reinstall all third party kernel modules you might have installed. If you use linux-restricted-modules, you have to update that package as well to get modules which work with the new kernel version. Unless you manually uninstalled the standard kernel metapackages (e.g. linux-generic, linux-server, linux-powerpc), a standard system upgrade will automatically perform this as well.   I tried to ask to my friend (who also uses Linux), but he don't know much about kernel.


How To Remove Lines Not Containing A Word

I have a large text file with lines and I just want to keep the lines that have the word "cat" in it. Is there anyway to achieve this with regex? I'm using VS code for the editing. Any help you can provide would be greatly appreciated.  To clarify it further, I'm trying to remove the lines that doesn't contain the word "cat" like below.  my text document looks like this (example)  cat 1 dog 2 cat 3 dog 4 fish 1


$\int\tan x\ dx$ by integration by parts

Can anyone help me figure out what is wrong in the following step:  $$\begin{align}\int \tan x\ dx &= \int (\sec x \sin x)\ dx\\ &= -\sec x \cos x + \int \sec x\tan x\cos x\ dx\\ &= -1 + \int \tan x dx\end{align}$$  So I got $\displaystyle\int \tan x\ dx = -1 + \int \tan x\ dx$ that is $0 = -1$ ?  Any help will be really appreciated!    Now I understand. So an indefinite integral can be defined only upto a constant. Thanks a lot!


Is there a way to move the dock to the top of the screen in GNOME? I wanted to test the new GNOME but not being able to set the dock to the top of the screen in previous GNOME versions was a deal-breaker so I have been running Mint for years.


Grisly Spectacle has two parts if the first part fails does the second still happen

states:     Destroy target nonartifact creature. Its controller puts a number of cards equal to that creature's power from the top of his or her library into his or her graveyard.   If a creature is indestructible the first part will have no effect, but will the second part still happen?


When I type (Eq.\ref{eq.15}) The output is     Obviously the spacing between "Eq." and "1.15" is too closed. But when I type (adding a space) (Eq. \ref{eq.15})  The output is:    Obviously the spacing between "Eq." and "1.15" is too wide!  My question is how I can get appropriate spacing.


Optimizing a screenshot for adding in a document and printing

This question is not directly related to graphic design, but I think you guys can help.  I am writing a thesis and I need to add several screenshots of the tools I have used and screenshots of web sites too. When I hit print screen my Fedora OS saves it on the my desktop folder. When I view them in the default image browser, they look fine. But when I add them in my document they are hardly legible.  I am going to print my thesis on A4 size paper at 600 DPI, color laser printer. How can I preprocess the images in Photoshop or GIMP so that they look correct? Should I make an A4 size 600 DPI image in Photoshop and gimp and then add screenshots to them and then optimize them?


Dark zone appearing on pictures when using an external flash

(Moved here from chat) I faced a trouble with my Canon 6D and a Canon SpeedLite 430ex II...   I took some shots and here is the result I've had :   I've used the very same shutter speed as I was using on my previous camera, a Canon 450D. I was using 1/250.  It looks like I have some shutter/curtain problem, such as them closing too quickly and I can see them on the picture (something related to this)... I therefore tried to decrease my exposure speed to 1/160 and then it worked perfectly...  I'm a bit confused by this tho...    How can my 450D be better than my 6D ?  There should be a compromise that Canon did regarding that parameter but I have difficulties to understand properly the whole concept...    I mean, since my flash is powerful, I could simply get slower, it probably won't change the exposure of my scene.  But,... If I'm using a long lens, let's say my lens has a focal of 400, I'm using a flash and for some reason I want to handhold it (probably stupid example but let's pretend)... I need a shutter speed that is faster than 1/400 or I'll get blur because of my hands shaking...  If I cannot go faster than 1/180 (I've found this value as maximum shutter speed synchronisation for my Canon 6D), how will I manage to do that ?


I have used this export PATH = $ PATH:/usr/local/java/bin And when I use which java the path where java is found, but if I turn off my computer or close session when I put which java /usr/local/java/bin is no longer part of the PATH variable.


The definite article implying the generic idea of something

I know that the definite article "the" can be used to mean a generic idea of something as in "the lion is the king of the animals." In this sentence, the in "the lion" is used to imply the general image of lions, so not specifying a particular lion.   However, I am confused in identifying where a "the" in a sentence is used for a general idea or a specific reference. For example, in the sentence "the price of gas is soaring", I heard that "the" in the sentence is an example of the generic use of the. Although I can easily understand the generic use of "the" in the lion example, but I do not understand how there is an general idea about gas price. Soaring gas price is something real,and gas prices in different regions( in a hypothetical situation) can be different. So, if I say "the price of gas is soaring", do I mean the price of gas that is determined by the world's oil system or can I say "the gas price" even when I am indicating the state of gas price in "a particular region"?    I know it is even difficult to understand my question, but I hope someone could find what I am confused about and give an answer.


Surjective endomorphisms of finitely generated modules are isomorphisms

My Problem: Let $M$ be a finitely generated $A$-module and $T$ an endomorphism. I want to show that if $T$ is surjective then it is invertible.    My attempt: Let $m_1,...,m_n$ be the generators of $M$ over $A$. For every $b = b_1 m_1 + ... + b_n m_n$ with $b_i \in A$ there is $a = a_1 m_1 + ... + a_n m_n$ with $a_i \in A$ such that  $$ T(a)=b $$ or in matrix-vector notation $$ T \vec{a} = \vec{b} $$ where $\vec{x}$ is the column vector of $x_1,...,x_n$ where $x = x_1 m_1 + ... + x_n m_n$. I multiply by the adjugate matrix to get $$ \mathrm{adj}(T) \vec{b} = \mathrm{adj}(T) T \vec{a} = \det(T) I_n \vec{a} = \det(T) \vec{a} \ . $$ Now take $\vec{b}=0$. Then $\vec{0} = \det(T) \vec{a}$ and thus $T$ is injective if and only if $\det(T)$ is not a zero divisor.   If I prove that $T$ is injective, then I'll get it is invertible. For that, I think the way is to prove that $\det(T)$ is not a zero divisor.  The importance of finitely generated condition:  Let $M = A^{\aleph_0} =\{ ( a_1 , a_2 , ... ) \mid a_i \in A \}$ be a not finitely generated $A$-module. Let $T : M \to M$ defined by $$ T(a_1, a_2, a_3, ... ) = (a_2, a_3, ... ) \ . $$ Then clearly $T$ is surjective but not injective ($\ker T = \{ ( a , 0 , 0 , ... ) \mid a \in A \}$), and thus not invertible.  The importance of surjective and not injective condition:  Need to find a counter-example.


Prove ${\lim\limits_{m \to +\infty}} \ln{\left(1+\frac{r}{m}\right)} = \frac{r}{m}$

How do you prove ${\lim\limits_{m \to +\infty}} \ln{\left(1+\frac{r}{m}\right)} = \frac{r}{m}$, where $0 < r < 1$?  I encountered this problem while trying to reproduce the third to last step in this .


Give disadvantage always, when attacking a non-visible target

RAW, advantages and disadvantages cancel each others out, always. Here I am interested in the case, where these two (found at PHB - Combat - Unseen Attackers and Targets) cancel each others out:  When you Attack a target that you can’t see, you have disadvantage on the Attack roll.   When a creature can’t see you, you have advantage on Attack rolls against it.  I just don't like how combining these work out. I mean, take an ax and go chopping some incapacitated or prone wood while blindfolded, and see how it goes. And then there are the "abuses" of this, like turning IMHO big disadvantages (fluff-wise, like 600' long bow shot) into a straight roll by creating an area of Darkness, which you can then move behind/into between looking at the enemy and actually taking the attack action. But this isn't the question, but just for the context, explaining why I am asking the following question: On an upcoming campaign, I am planning to have the house-rule: If you don't see the target you are attacking, you will have disadvantage. What are the balance and game play implications of this house rule? Will it break something, or have some nasty unintended consequences?


How to revert software sources back to default?

Possible Duplicate:          I had a little problem with the sources of my update, I'm running Ubuntu Natty Narwhal and I was tinkering with binaries for installing a Firefox add-on called fire sheep and I think that some how my update sources were altered and evertime I try to upate I get this error message  An unresolvable problem occurred while initializing the package information.  Please report this bug against the 'update-manager' package and include the following error message:  'E:Type 'See' is not known on line 2 in source list /etc/apt/sources.list'


I have a severe permissions' issue. I hope there are some really clever people out there, who might know how to solve this using the Terminal, expert-level hacking or in some really simple way so I at least can backup my data despite the faulty permissions.  This is the cause of the issue  Being a curious person, in Finder I right-clicked my User and hard-drive unit and removed "staff" as well as changed permissions for "everyone" under permissions. After this my Mac (Macbook Pro, 13 ", early 2013, latest version of Yosemite) hung and every time I try to start it up, it gets stuck loading before the login screen.  This is what I have tried and all have failed   Booting the faulty computer and letting it be to see if it would finish loading. Rebooting it with cmd+r, entering disk utility, repairing permissions. This outputs  User differs on private/var/db/displaypolicyd; should be 0; user is 244. Group differs on private/var/db/displaypolicyd; should be 0; user is 244. Repaired "private/var/db/displaypolicyd"   However, when I reboot the permissions' issue remain and when entering Disk Utility again, I get the same permissions' repair messages. Rebooting it and creating a new ACL. Using another Macbook Pro, mounting the faulty one with the help of rebooting it in Target Mode. However, the permissions' issue doesn't permit me to access the drive this way. In Disk Utility, I can select the drive with the faulty permissions, but I can't select the option repair permissions. Using another Macbook Pro, mounting the faulty one with the help of rebooting it in Target Mode and creating a new image (dmg) of its hard-drive to the functional computer. Looked at the answers in , but they don't help in solving my problem   This I need help with   How can I repair the permissions considering this specific case and what has been tried already? Or (if there is no easy way out of this) is it possible to make a backup of the drive so I can reinstall everything without loosing data?


Why is Princess Reiners called a monster?

We got introduced to Princess Reiners in season 2, episode 1, and we were given flashes in the ending theme that she had a dark personality. This was later confirmed in episodes 9 and 10 when her brother, Prince Zanac, calls her a monster to her face. When she turned around, she had the anime crazy face, but didn't actually change form into a literal monster of any kind.  Over on the MAL forum for , they simply refer to her as a yandere. On , they say she's a psychopath.  I always considered the anime crazy face to be a metaphor for viewers, not a literal change for other characters in-story. Aside from her dark personality / face twisting, and the fact that she plans out big, complicated, moves, I don't understand what the big deal is. Why would she be called a monster? How would anyone else in Yggdrasil would know that she is a "monster"? Or is she a monster in a literal sense?


Automorphisms of a structure of non-zero rational numbers with multiplication

I'm given the structure $\mathcal{M} = (\mathbb{Q} \setminus \{0\}; =; \cdot)$ and I need to prove that Aut $\mathcal{M}$ is continual. In other words, first of all, I want to find all (or at least most of) bijections $\alpha : \mathbb{Q} \setminus \{0\} \to \mathbb{Q} \setminus \{0\}$ so that $\alpha(a \cdot b) = \alpha(a) \cdot \alpha(b) \;\; \forall a, b \in \mathbb{Q} \setminus \{0\}$. The problem is, I can't think of any automorphisms except for the identity and $\alpha(x) = \dfrac1x$, of course. I mean, let's take polynomials $\alpha \in \mathbb{Q}[x]$, then only $\alpha(x) = x^n, n \in \mathbb{N}_+$ "saves" multiplication as mentioned above, but it's not a bijection since $\sqrt[n]{y}$ could be irrational. Same for $\alpha(x) = \dfrac1{x^n}$. For obvious reasons, there's no way logarithms, exponential or trigonometrical functions can be used. So I'm basically stuck in the beginning of this problem and would be glad if someone helped/gave a clue!


Force line break on `\citep{}` inside `longtable` (XeLaTeX)

I am trying to create a quite long table that will also contain citations inside, but the \breakcites macro apparently does not work inside tabular environment. Placing \citep inside \makecell does not work, either.  Here is MWE: (I am using XeLaTeX)  \documentclass[fontsize=12pt]{scrbook} \usepackage[paperwidth=8.5in, paperheight=11in, top=1.88in, bottom=1.25in, left=1.25in, right=1.13in]{geometry} \usepackage{newlfont} \usepackage{epstopdf} \usepackage[utf8]{inputenc} \allowdisplaybreaks  \usepackage{breakcites} \usepackage{longtable} \usepackage{setspace} \usepackage{fontspec} \setmainfont{Times New Roman} \pagestyle{plain} %\usepackage[style=authoryear,backend=biber]{biblatex}   \usepackage[natbibapa]{apacite} \bibliographystyle{apacite}  \doublespacing \usepackage{times}  \begin{document}  \begin{longtable}{ll} \caption{Summary of relevant computational parameters from various computational studies. This table is modified from \cite{Rojas}.} \hline Computational parameter            & Utilized parameter \\  \hline Program                            & \begin{tabular}[c]{@{}l@{}}\makecell{Spanish Initiative for Electronic Simulation with \\ Thousands of Atoms (SIESTA) \citep{lopezcorral,Sigal}} \\  \\ Vienna Ab-Inito Simulation Package (VASP) \\ \citep{Gurel,Rojas,ZhouMiao,Li2015,ChiChen} \\ Gaussian 09 \\ \citep{Gholami2016,Rad} \\ Quantum Espresso \\ \citep{Khodadadi,Wong} \\ DMol3 \citep{Jungsuttiwong} \end{tabular}                     \\ \hline \end{longtable}  \bibliography{biblio}  \end{document}   I used a separate bib file for the references. Here is screenshot of what happens when I compile the code above:    Is there a way to force line breaks at the \citep?   Note: I know the tabular inside tabular is not the optimal way to do stuff but I did not change it to another form since the output looks nice, and I don't think it has something to do with the problem. I have tried a cleaner code but the same problem arises.


Look at the diffreent output of ls versus ls -1  $ ls  filea1.txt   fileb.txt    listB1.xml   listC.xml  filea.txt    listA1.xml   listB.xml   'name with spaces 2.txt'  fileb1.txt   listA.xml    listC1.xml  'name with spaces.txt'  $ ls -1 filea1.txt filea.txt fileb1.txt fileb.txt listA1.xml listA.xml listB1.xml listB.xml listC1.xml listC.xml 'name with spaces 2.txt' 'name with spaces.txt'   Which is quite OK for me. Thing go different if you redirect the output to file. I'd expect that file diffes, but they are identical.  $ ls -1>/tmp/ls-1.out $ ls >/tmp/ls.out  $ cat /tmp/ls-1.out filea1.txt filea.txt fileb1.txt fileb.txt listA1.xml listA.xml listB1.xml listB.xml listC1.xml listC.xml name with spaces 2.txt name with spaces.txt  $ cat /tmp/ls.out filea1.txt filea.txt fileb1.txt fileb.txt listA1.xml listA.xml listB1.xml listB.xml listC1.xml listC.xml name with spaces 2.txt name with spaces.txt   Why is the latter just one-column output but not the multi-column as when there's no redirection to file?


I'm looking for a rigorous introduction to probability to help prepare me for a future course I plan on taking, "Advanced Introduction to Probability". Something possibly like Spivak's, where proofs are key.  Any help is appreciated.


How to show that $\int_{0}^{\pi}{\sin^5 x\over 1+\cos^3 x}\mathrm dx=\ln 3?$

Given the integral $(1)$     $$\int_{0}^{\pi}{\sin^5 x\over 1+\cos^3 x}\mathrm dx=\ln 3\tag1$$   This integral seems to be quite tough, I can't even know where to start. I have try substitution $u=1+\cos^3 x$ and $u=\cos^3 x$, can seem to remove the x variables.  We have the following identities   $$\sin^5a={5\over 8}\sin a-{5\over 16}\sin 3a+{1\over 16}\sin 5a\tag2$$  $$\cos^3 a={3\over 4}\cos a+{1\over 4}\cos 3a\tag3$$  We may write $(1)$ as  $$\int_{0}^{\pi}{\sin x(1-\cos^2 x)^2\over 1+\cos x(1-\sin ^2 x)}\mathrm dx\tag4$$  $u=1-\sin^2 x\implies \mathrm du=-2\sin x\cos x\mathrm dx$ then $(4)$ becomes  $${1\over 2}\int_{0}^{1}{(1-u)^2\over \sqrt{u}+u^2}\mathrm du\tag5$$  $u=v^2\implies du=2vdv$ then $(5)$ becomes  $$\int_{0}^{1}{(1-v^2)^2\over v+v^4}\cdot{v\mathrm dv}\tag6$$ Simplify to  $$\int_{0}^{1}{(1-v)(1-v^2)\over 1-v+v^2}\mathrm dv\tag7$$  I guess using partial decomposition of fraction and integrate term by term, seem lengthy process  How else can we prove $(1)$?


How can I change my sign-in account through Yahoo to Stack Exchange?

I have installed the new Stack Exchange app on my android. Since I log into my SE accounts with my Yahoo OpenID on the desktop site, I tried logging into the SE app through Yahoo but it gives a security warning & doesn't allow me to log into SE.  Can I transfer my existing account from using Yahoo to the Stack Exchange OpenID? I obviously don't want to start fresh with a totally new account.


How prove this inequality $\sum\limits_{cyc}\frac{x+y}{\sqrt{x^2+xy+y^2+yz}}\ge 2+\sqrt{\frac{xy+yz+xz}{x^2+y^2+z^2}}$

let $x,y,z$ are postive numbers,show that $$\dfrac{x+y}{\sqrt{x^2+xy+y^2+yz}}+\dfrac{y+z}{\sqrt{y^2+yz+z^2+zx}}+\dfrac{z+x}{\sqrt{z^2+zx+x^2+xy}}\ge 2+\sqrt{\dfrac{xy+yz+xz}{x^2+y^2+z^2}}$$  My try: Without loss of generality，we assume that $$x+y+z=1$$ and use Holder inequality,we have $$\left(\sum_{cyc}\dfrac{x+y}{\sqrt{x^2+xy+y^2+yz}}\right)^2\left(\sum_{cyc}((x+y)(x^2+xy+y^2+yz)\right)\ge\left(\sum_{cyc}(x+y)\right)^3$$ then we only prove this $$\dfrac{8}{\sum_{cyc}(x+y)(x^2+xy+y^2+yz)}\ge  2+\sqrt{\dfrac{xy+yz+xz}{x^2+y^2+z^2}}$$ then I can't  Thank you


How To: Execute command line in C#, get STD OUT results

How do I execute a command-line program from C# and get back the STD OUT results? Specifically, I want to execute DIFF on two files that are programmatically selected and write the results to a text box.


What Legends material did The Force Awakens explicitly contradict?

Star Wars Legends (formally the Star Wars Expanded Universe) already had lots of events set after Star Wars VI: Return of the Jedi.  Did Star Wars VII: The Force Awakens explicitly contradict any of those events? If yes (most likely), what are they?    NOTE: some of the suggested events were NOT explicitly contradicted by canon.   Imperial Remnant could still have happened. Mara Jade could still have happened (that might change by Episode VIII of course). Even Han and Leia having twins is NOT directly contradicted by new canon — nowhere does it say Ben didn't have a twin (we know Rey isn't that twin as she is 10 years younger)


Figure out if a fourth point resides within an angle created by three other points

If I have a point that is considered the origin and two lines that extend outwards infinitely to two other points, what is the best way to determine whether or not a fourth point resides on or within the angle created by those points?  The process I'm currently using is to get the angle of all three lines that extend out from the origin and then check to see whether the third angle is within the range of the first two.  Grid space is defined as Screen Space, that is, 2D Cartesian with the Y-Axis flipped so "up" is negative y and the origin is the upper left corner.


I've a EC2 instance acting as a proxy for a webserver that are in other region.  This setup works great at the beginning but then, some users start receiving   Proxy error The proxy server received and invalid response frmo an upstream server. The proxy server could not handle the request  Reason: Error reading from remote server.   I guess the connection was resetted, so I added a changed in the configuration file of apache:    ProxyPass / http://.. retry=1 acquire=3000 timeout=600 Keepalive=On   Now, I would like to try to reproduce the problem again, is there any tool that can help me with this purpose? maybe ab?


emerging caption in the fourth edge of a larger square containing figures on other three edges

How can I insert 3 figures in a one column format article as below:     but the result of this answer will be


Getting Cash from Credit Card without Fees

I currently: Pay with a credit card, get my 3% cashback, and then pay off the credit card with my debit card.  What I would like to do is: Use a credit card (to get my 3% Cash back) to withdraw cash, then spend the cash, then pay off the credit card with my debit card.   Is there any way to do this without paying a cash advance fee (or any fees in general)?


there are strange things:  on my virtualbox： centos7  Interfaces：  enp0s3: 192.168.10.110/24 lo:0 10.0.3.110/24 (ip alias)   route：  default via 10.0.3.2 dev lo 192.168.10.0/24 dev enp0s3  enp0s3 is plugged in 10.0.3.0/24   I have enabled the ip_forward (net.ipv4.ip_forward = 1)    My Question：  ping 10.0.3.2 works，but why?  tcpdump can't get packets on enp0s3，but does get packets on lo.  The default route is lo; why does ping 10.0.3.2 work? Why can't I get packets on enp0s3?


How to create predicate with at least two parameters in C

I want to create filtered ls function in C which takes path to file or dir and outputs only files and directories allowed by passed filter function. This filter function have to take at lest two arguments. The question is, how do I pass arguments that are "stored" in ... of the parent function? Something like this: #libs here  //let assume I have this filter. //So, file should be regular and its' size should be less than maxSize int  regfile_size_filter(const char *name, struct stat info, off_t maxSize) {     return S_ISREG(info.st_mode) && info.st_size < maxSize; }  //here is filtered ls function //second argument is a pointer to the filter function //which take at least two parameters - name of a file and its' stat void  filtered_ls(const char *path, int (*filter)(const char *, struct stat, ...), ...) {     //let's open passed dir, then copy path somewhere else for later use.     DIR *dir = opendir(path);     char fullpath[PATH_MAX];     snprintf(fullpath, PATH_MAX, "%s/", path);     size_t fplen = strlen(fullpath);      //now let's read the directory     struct dirent *dinf;     while (dinf = readdir(dir))     {         //cat strings so we could get info with stat function         snprintf(fullpath + fplen, PATH_MAX - fplen, "%s", dinf->d_name);                  //skip file if stat failed         struct stat info;         if (lstat(fullpath, &info) == -1)             continue;          //------> here is the problem: //        how do I pass extra argument into filter function? //        I know about va_arg, but how do use it here?         if (filter(dinf->d_name, info, ...))             printf("%s\n", fullpath);          //same goes for recursive call         if (S_ISDIR(info.st_mode))             filtered_ls(fullpath, filter, ...);     }     closedir(dir); }  int main(int argc, char **argv) {     if (argc < 3) return 1;     char *dirPath = argv[1];     int maxSize = strtol(argv[2], NULL, 10);      filtered_ls(dirPath, &regfile_size_filter, maxSize);     return 0; }


Is it possible to change the directory of a layer's source file without deleting and re-importing the layer?


Xcode update 11.1 stuck on MacOS Catalina

I’ve been trying to update Xcode and it seems to be stuck after the download. After sitting and waiting for a while, it seems to have restarted the entire process of downloading and updating again. I’ve currently been staring at it stuck the second time around for about 8 minutes. I’ve included a screenshot of what it looks like alongside the console.  Any tips?


Not booting from USB or CD (SYSLINUX Message)

I am trying to install linux on my laptop, a Toshiba Satellite C6550-S5200. I did it once but something happened so I removed it then I had to destroy all data on hard drive so now I have nothing on it. Well I got a iso file burned to a CD and to a flash drive. With the flash drive I get.   SYSLINUX 4.06 EDD 4.06-pre7 Copyright (C) 1994-2012 H. Peter Anvin et al  With the CD it will start booting it but somewhere loading it up, the dots turn all orange and stay that way and my CD drive turns quiet.  Oh and some more info the images work because I tried loading them up on another pc and it worked just fine.  I manage to get the CD to boot I just had to let me pc boot up first then insert the CD and have it boot the CD then. Once I get done installing ubuntu it works fine but I have to leave the PC on 24/7 for if I turn it off the PC will freeze 5-10 seconds after booting back up no matter how I install it.


How to find the point where two normal distributions intersect?

I have two normal distributions. Say for example, one with a mean of .76 and one with a mean of .62. Both standard deviations = .05. How do I find which point on the x-axis is where the two distributions cross? In other words, x-coordinate at the deepest part of the valley in between the two distributions?  P.S. I am using R, but non-R related answers would be welcome and appreciated too.


Should I partition a RAID or just create a file system on it?

Given a RAID 6 created from 6 drives /dev/md0 which should be used fully for data (no booting from it, root and swap are on a different drive), should I create one partition on that device and then create a file system in that partition, or should I just create a file system on the device?  parted /dev/md0   <create a partion> mkfs -t ext3 /dev/md0p1   or just  mkfs -t ext3 /dev/md0   And why?  (This is Ubuntu Server, just in case it matters.)


Difference between function() and new Function()

while searching around the internet i found two ways of writing javascript function.  One is Function() constructor  var myFunction = new Function("a", "b", "return a * b");  var x = myFunction(4, 3);   Second is simple defining function  var myFunction = function (a, b) {return a * b};  var x = myFunction(4, 3);   When i used above both method i found no difference between these 2.  Is there any difference between these 2 or is there any use of using function constructor??


Can I draw something like this programmatically with LaTeX?    I drew these with Adobe Illustrator, but it gets pretty time-consuming. Even with relatively few nodes. What it attempts to demonstrate is the number of "symmetric" cryptographic keys required for secure communication between n parties - for which the formula is n(n-1)/2 (I tried to render that with LaTeX/MathJax, but it won't let me for some reason).    And it's hard to get it perfect. It's always off by a small amount, as you can see here. It might not seem like much but with a lot of nodes, it can add up and skew the output, and cause problems when trying to get everything to fit properly.    I wanted to draw a big one with up up to 100 nodes, so it would be best if I could do it programmatically, rather than having to type up several hundred lines of code manually. Is that kind of thing possible with LaTeX? I heard someone say TeX is a full Turing complete programming language. If that's true, I'm not sure, but it would probably make it pretty useful for generating diagrams with this kind of data, kinda like .  As you can see, by the time you get to 10 or 11 vertices, it can be pretty unruly:


My macbook pro 13' 2015 keyboard and track pad not working

Suddenly the keyboard and trackpad of my macbook pro 13' 2015 model stopped working, this issue happened when I upgrade from sierra to high sierra. Also I already tried re-installing the OS from the internet recovery way, still the issue is present. Then I tried booting my macbook pro on Remix OS (android) both the keyboard and trackpad is working fine.


What happens if I use two cards with the same sort of effect?

When I am choosing my cards for a dig, I know I get three cards. Usually, I end up with three different ones, but I started to wonder - if I have a mission to collect, say, a lot of coal, can I stack card effects to make it easier?  For example, can I use both a Coal Galore card that says "100% more Coal blocks. 12% of Coal blocks are explosive" and a More Coal card that says "100% more Coal blocks", and have the effects combine? Or does it just select the "better" card?


Does the use of bit.ly URL shortener prevent social traffic attribution in Google Analytics

I have a client which noticed that the traffic from Twitter did not match up to expectations.they are using bit.ly URLs for all their tweets. Does this affect how traffic is viewed in GA? It looks like it is coming through as Direct.


Rescuing a possibly corrupt PDF in Acrobat

I have a large Acrobat file (currently 92 pages, 25MB) which is constructed from lots of different sources (1 InDesign and 80 Illustrator files). Since I first brought these sources together, each page of it has been replaced a good dozen times, and the file is starting to creak under the weight. Acroat is giving me warnings about possible corruption, and crashes occasionally when saving.  No data has been lost yet, but it's enough to give me pause. I could reconstruct the file from sources if I had to, but it would take forever to get all the bookmarks and links set up just the way they used to be.  Is there any way of getting Acrobat to rebuild the file from the ingredients and make it easier to work with?


Trigonometric integral of $f(x)=(x^2)(\sin(x^2))$.

I've tried with the chain rule and $u$-subtitution ($u=\sqrt{x}$) but I get nothing. Can you help me please? $$\int (sqrt{x})(\sin(x)) \ dx$$


New measures to reduce bad answer flood on high traffic questions

I think it is a fairly well recognized phenomenon that questions in some tags attract more terrible answers at faster speed than others. And the site already does a fairly decent job at taking care of them. I am not sure how many of them get flagged, but they usually end up deleted after a few downvotes.  I don't have any statistics here, so maybe someone how has access to the mod tools would be a bit more informed here than I am.  It seems to me that given a lot of these terrible posts are coming from new users or low rep users well on their way to a question ban, that we should be able to deal with the problem with even less user intervention.  I also think the current situation of being bombarded at the beginning with tons of answers which later disappear might be confusing to the questioner. I think we can do better.  I propose a (short) automatic protect interval of 5-10 minutes on new questions to the site. This should be accompanied by a helpful message different from the normal protected question message indicating that after they have thought about it and still want to post, that they will be able to do so shortly; inviting them to proofread and improve their post in the meantime.  I expect to probably get downvoted for this because the consensus seems to be that this is a solved problem. While I feel that the current system works, I feel it could work better. This proposal might also be counterproductive.  I am probably missing something important, so feel free to criticize brutally.


I would like to use Ipython in the console to perform tasks more easily.   How can I do that?   I want to use Ipython because I prefer to program with it. I would like to have TAB-completion because the attribute of QGIS module made me crazy.


I am wondering if it is possible to have a bit of code run whenever an object is deleted. Looking around I haven't seen anything that really suggests that it is possible except for maybe a modal operator. Is it possible, and if so how would one go about doing it.


How can I adjust the preferred WiFi order?

I am using 13.04 Ubuntu. I want to make order on multiple wireless access.  Is there any way to do this?


$F=ma$ calculation taking relativity into account?

Newton's second law of motion states that $f = ma$. However, in this equation, theoretically there could be a value of $f$ and $m$ that results in an acceleration that is enough to push an object past the speed of light. In my case I have a value of newtons that is large enough (I think) to accelerate an object past the speed of light if $f=ma$ held. Is there any way, knowing that value of newtons, and the mass of the object it is acting on to find the acceleration in an Einsteinian universe?


Multi-line group capturing between braces

I have something like this in a file testtt:   {It captures this! } // question: 2572410  name: Question 2  ::Question 2::[html] Is it going to be -40 tomorrow?  { It can't capture this!!! why? }   when I do:  grep -o '{\([^}]*\)}' testttt   It can't capture the multi-line braces. Any help to modify it in way that it could capture both would be apppreciated!  PS. I have also tested the given solution from:  and it gives the following error:   grep: unescaped ^ or $ not supported with -Pz   You can find the text file of the output and file contents


How do I get the time a file was last modified in Python?

Assuming the file exists (using os.path.exists(filename) to first make sure that it does), how do I display the time a file was last modified?  This is on Linux if that makes any difference.


I have ubuntu 12.04 LTS with a dual boot of Windows 7, Can I reinstall Windows 7, without changing partitions?

I initially had Windows 7 as my primary operating system. I decided to install Ubuntu 12.04 LTS as a dual boot. However, I realized that my Windows 7 OS wasn't installed properly (not because of Ubuntu). I already created partition sizes for both OS's. Is it possible to reinstall Windows 7 without having to chnage around my Ubuntu setup?   Thanks


Apparent violation of the law of conservation of angular momentum in the torques experienced by two interacting electric dipoles

Question Consider two dipoles $({p_1}\hat{i}$ and ${-p_2}\hat{j})$ kept in the $x-y$ plane at $(0,0)$ and $(d,0)$ respectively. Calculate the torque about the COM. Approach 1 Suppose we select the COM as the origin. Then, we label the 4 particles $1,2,3,4$. Let their position vectors be  $r_{1},r_{2}..etc$. Then, when we consider the Force on the $i$th particle due to the $j$th particle= $F_{ij}$. The Torque about the COM.= $r_{i}\times F_{ij}$. When we sum these torques over all particles, and use the following facts:  $F_{ji}=-F_{ij}$ $r_{i}-r{j}=r_{ij}$ $r_{ij}\times F_{ij}=0$  $$r_{1}\times({F_{21}+F_{31}+F_{41})}+r_{2}\times({F_{12}+F_{32}+F_{42})}$$ $$+r_{3}\times({F_{13}+F_{23}+F_{43})}+r_{4}\times({F_{14}+F_{24}+F_{34})}$$ $$= (r_{1}-r_{2})\times F_{12}+(r_{1}-r_{3})\times F_{13} ....$$ $$=0 + 0 ...0$$ We conclude that the net Torque about the COM is is zero. This is somewhat expected, there are no "external" elements in our system. (In fact, this argument suggests that the Torque about any point in the x-y plane is zero. We will still end up with the same expression, as the difference of two position vectors is independent of the choice of the origin.) Approach 2 However, qualitatively, when we use our knowledge of electric fields, we can see that both dipoles seem to experience an anticlockwise torque. They will add up, and thus The net torque is non zero. This appears to be a contradiction. The latter finding is bizarre in the sense that it seems to suggest that the angular momentum of an isolated system is not constant. And the only way that argument 1 can be wrong , is if: $$F_{ij}=-F_{ji}$$ does not hold. I have seen this happen, but the explanation was that the "3rd law of motion" is actually a statement of the conservation of momentum, and in that particular case, some portion of the momentum (of the particles) was carried away by the associated electromagnetic field. I don't think that something of this sort is responsible for my particular case, since there is no $B$ field, and therefore no $S$, which appears in the momentum density of the fields. Apart from this, the two arguments seem to be quite valid individually. So what's going on here? My initial thought was that the fields might be storing angular momentum, but like I said, there is no $B$. Edit 1: I think I have a hypothesis: In approach 2, as the dipoles rotate for some time say $dt$ , they start producing a $B$ field (since we now have moving charges). We now have both $E$ and $B$ fields, so we actually have an angular momentum associated with the field, which perhaps cancels out with the angular momentum produced by the dipoles(=$(T1 +T2)dt$).


Probably a very stupid question, but how can I put an array into an ArrayList?  Example:  String[] strings = {"ex","okay",}; ArrayList<String> stringslist = new ArrayList<String>();   Now how do I put everything in strings, into stringlist?


Proof of $\sum_{i=0}^{n} \binom{i+k-1}{k-1} = \binom{n+k}{k}$

I put the above expression into mathematica/wolfram alpha, and it gives this expression, but it doesn't show why this is true, and I can't find any information about this anywhere. How would you go about proving this? $$\sum_{i=0}^n \binom{i+k-1}{k-1} = \binom{n+k}{k}$$


Error updating custom metadata types through Talend

I am trying to update a custom metadata type record through the standard Salesforce connectors in Talend. But I receive an error that says "unable to update entity type".  Are we able to update these records through API? If yes, how do I achieve it?  Thanks in advance.


I have a sort of a pop-up windows form. It pops up to show gathered data. Problem is it gains focus when it loads and interrupts work. I need it not to get focus when loaded. How to do that?


Change 3d viewport to othrogonal in python

I would like to change the 3d viewport to orthogonal from a python script. From the key mapping I found this command "view3d.view_persportho". I always find it tricky when I have to mess with the context (Which I think is nescesary). Anyway, I tried this: for area in bpy.context.window.screen.areas:         if area.type == 'VIEW_3D':             for region in area.regions:                 if region.type == 'WINDOW':                     override = bpy.context.copy()                     override['area'] = area                     override['region'] = region                     override['scene'] = bpy.context.scene                                           bpy.ops.wm.setup_ui(override)                      # Maybe I can set perspective here somehow?  class MYOP_setup_ui(bpy.types.Operator):     bl_idname = "wm.setup_ui"     bl_label = "Setup UI"     def execute(self, context):         context.space_data.show_region_ui = True # This opens the sidebar panels correctly         # I know that I can't pass arguments to operators like in the next line.         # bpy.ops.view3d.view_persportho('ORTHO') # 'PERSP', 'CAMERA'                     return {'FINISHED'}  I found these, which is pretty much what I want, but I can't get it to work. Maybe pre 2.8?


What are the differences between "May" & "Might" / "May have" & "Might have" in strict English?

The more I learn about Modals, the more confused I get. English Modals are very unstructured or adhere to a rigorous structure & that makes foreigners hard to understand them.  According to      Some people insist that you should use may (present tense) when   talking about a current situation and might (past tense) when talking   about an event that happened in the past. For example:      I may go home early if I’m tired. (present tense)      He might have visited Italy before settling in Nuremberg. (past tense, might here refers to posibility)   However, the site also states     In practice, this distinction is rarely made today and the two words   are generally interchangeable:      I might go home early if I’m tired.      He may have visited Italy before settling in Nuremberg.      But there is a distinction between may have and might have in certain   contexts. If the truth of a situation is still not known at the time   of speaking or writing, either of the two is acceptable:      By the time you read this, he may have made his decision.      I think that comment might have offended some people.      If the event or situation referred to did not in fact occur, it's   better to use might have:      The draw against Italy might have been a turning point, but it didn't   turn out like that. (might here prefers to Ability, not Posibility)   My questions are those:   Should we always use "may" for the present & "might" for the past as suggested by ?  That means we should never say "I may have done something", but we should say "I might have done something" As mentioned above, people do not distinguish "may have" & "might have", both refer to the past (The past can be "present perfect", "past perfect" or "simple past". My question is:  Is there any slight difference between "may have" & "might have" in today English? For example, "I may have done this" corresponds to "Present perfect" & "I might have done this" corresponds to "Past perfect" or "simple past"?  Ex 1: The baby may have been sleeping for 2 hours (similar to Present perfect, the action lasts from the past to the present time)  Ex 2: The baby might have been sleeping for 2 hours (similar to Past perfect, the action had lasted from the past to a point in the past)  But I am not sure my thinking is right or not because noone has ever brought this up.


Regex to get specific numbers from string

I have specific string like this   372591089, jni, oduction, to, A, hnr, android, -"The, mAt,352, 268, 638, 257, 65, JI, 0, 00, 0, 0, al, 31/07/2015, oHa, Jile, 786118029,   I want to extract specific sequence of numbers in this string 352, 268, 638, 257, 65, I only know this sequence of digits can be 14 digit like example or 16 digit, this numbers changes every time not static numbers.  What is best way to extract it? any regex or specific way ? I can solve it by split - match than join but my string can be more than 1000 letter. So can anyone suggest better way? Thanks


Why does my camera lens only work with a Polaroid .43x lens?

I got a brand new Canon Rebel T6i and along with it came an ef-s 18-55mm lens, and a Polaroid studio series .43x wide angle lens (which I believe is a telephoto lens). The camera worked fine, but after I put the Polaroid lens on the 18-55mm lens, the 18-55mm lens is completely out of focus, and only acts normally with the Polaroid lens on. Is this normal? Would a factory reset on the camera do anything?


Meaning of Simplify's tolerance parameter

The standard parameters of Douglas-Peucker's simplify algorithm are geometry and tolerance (e.g  in PostGIS). What's the meaning of the tolerance parameter? I know that the bigger the value, the coarser the geometry will be. But does the number has any unit or it is just arbitrary?


Prove or disprove the convergence of improper integral

Prove or disprove that $$\int_0^\infty \left|\frac{\sin{x}}{x}\right|dx < \infty.$$  I tried by Wolframalpha and this integral seems to satisfy the Cauchy property, but I do not know how to prove it.  Thank you very much.


How to prove that $\lVert x + y\rVert = \lVert x\rVert + \lVert y \rVert \implies \lVert tx + (1-t)y\rVert = t\lVert x\rVert + (1-t)\lVert y \rVert$?

If a norm on a vector space is given by an inner product then we have $\lVert x + y\rVert = \lVert x \rVert + \lVert y \rVert$ only when $x=\lambda y$ for some constant $\lambda$ (this follows from the Cauchy-Schwarz inequality). This does not hold for general (unitary invariant) norms. E.g. when considering generalised Ky Fan norms: $$ \lVert x\rVert_s = \sum_i s_i \lvert x\rvert_i^\downarrow$$ where $s_i\geq 0$ and $\lvert x\rvert^\downarrow$ is $\lvert x\rvert$ rearranged with the components from biggest to smallest. So for example the operator (sup) norm has $s_1 = 1$ and $s_i=0$ for $i>1$, while the trace norm has $s_i=1$ for all $i$. For these norms it is in general possible to find $x$ and $y$ so that the norm is additive for these vectors, while $x$ and $y$ are not multiples of each other.  Now my question is the following. Given a unitarily invariant norm and vectors $x$ and $y$ such that $\lVert x + y\rVert = \lVert x\rVert + \lVert y \rVert$, can we then conclude that $\lVert tx + (1-t)y\rVert = t\lVert x\rVert + (1-t)\lVert y \rVert$ for $0\leq t \leq 1$?   This is true for these generalised Ky Fan norms and for all norms that come from inner products. It is also true for all $p$-norms as this additivity still only holds for $x$ and $y$ that are multiples of each other (even though $p$-norms don't come from an inner product).  My intuition behind this is that this additivity property (when $x$ and $y$ aren't multiples of each other) forces the norm to be "linear" in a certain way, such that the norm has to be very similar to a generalised Ky Fan norm. So as a bonus question: If there are $x$ and $y$ that aren't multiples of each other, such that the norm is additive for these $x$ and $y$, show that the norm is a generalised Ky Fan norm. Note that this can only be true when we assume the norm to be unitary invariant since otherwise we can construct a counter-example of this (take $(X_1,\lVert\cdot\rVert_1)\oplus (X_2,\lVert\cdot\rvert_2)$ with the norm $\sup\{\lVert\cdot\rVert_1,\lVert\cdot\rVert_2\}$ where $\lVert\cdot\rVert_1$ is a Ky Fan norm and $\lVert\cdot\rVert_2$ is some other norm).


When I ssh into my Ubuntu 18.04 box I get the motd  1 update could not be installed automatically   Which goes on to tell me to check the unattended-upgrades log.  The log shows no problems. How can I clear this bogus message?


If $A^2$ and $B^2$ are similar matrices, do $A$ and $B$ have to be similar?

I know that the converse is true; that is, if A and B are similar matrices, then $A^2$ and $B^2$ are similar . However, I'm not sure about the reverse.


prime ideals of $\mathbb{R}[X,Y]/(X-Y^2,X+Y)$

I'm trying to understand an example in my lecture notes, it states that $Spec(\mathbb{R}[X,Y]/(X-Y^2,X+Y))$ has only two points. Can anyone develop more please ? and how would these points be like ?  Thanks for the help.


What is a "Session 0"?   When is it done? What does it contain? Is it recommended, if not mandatory? What is each person's role (DM/GM, players, etc.)? What topics are best discussed there?   Usually with my groups, we go directly to the meat of the game right after the character creation, but I see a lot of answers that basically say "you should have a session 0", but it's never explained what it is made of, so it's kind of an enigma for me.


Proof verification: For isomorphism $\phi: G\to H$, show that $|\phi (a)|=|a|$ for all $a\in G$.

Could someone please verify my following proof?     For isomorphism $\phi: G\to H$ of the groups $G$ and $H$, show that $|\phi (a)|=|a|$ for all $a\in G$.   Proof: Let $a\in G$ with $|a|=n$. Then $a^{n}=e_{G}$, the identity of $G$. Let $|\phi(a)|=m$. Then $(\phi (a))^{m}=e_{H}$, the identity of $H$, or $\phi (a^{m})=e_{H}$. Since $\phi(e_{G})=e_{H}$, it must be that $a^{m}=e_{G}$. Then it must be that $m=n$. Therefore, $|\phi (a)|=|a|$ for all $a\in G$.


How to re-apply after refusals for both settlement and visitor visas?

In February 2018, I applied for a UK settlement visa to get married to my partner of 4 years. It was refused because, when we applied, our savings account did not have sufficient funds. I did not understand that we needed £62,500 to be in his bank account for 6 months and we only had £18,000 at the moment of application, It was refused, obviously, after 3 long months of waiting for a response.   Since it had been so many months wsince I had seen my partner, I decided to apply for a visitor visa right after my refusal. I planned to spend 6 weeks with him, while we waited to get the money needed and have it there for 6 months.  This visa was also refused, stating that my intentions might have not changed. They also pointed out that I said that the previous application was for a fiance visa but it was actually for a settlement visa .   How can I apply for a visitor without it being refused again? I want to see my partner and me going there is the only way, since he's very busy with work.


An employee of US Company posted at Bangalore.  The salary is credited by US company after Deduction of tax as per US laws then credited to the Bank  account in India.  Employee is resident because of residing in India more than 180 days.  How to claim credit of tax paid in foreign country when accounting periods are different? Where I have to disclose in the return(i.e.ITR 1) the taxes already deducted by US entity when I am going to file return in India?


I am looking for a way to create a permanent keyboard short cut to paste a text. Example: Whenever I press strg+shift+F1 I would like to paste "Quod erat demonstrandum." Maybe there is way to do this with the default Ubuntu settings or CompizConfig?


Too many "and"s and commas in a sentence

Sometimes when I write some scientific papers, I feel there are too many "and"s and commas in a sentence which might lead to some confusion because usually the logic in scientific papers is quite complex. E.g.,  Today, I wet met my friends, Aaron, Bob, and Carlo, and we had a lot of fun talking about science, philosophy, and politics.  First are the comma before "and"s mandetory. I heard different versions. I am confused. How to avoid them? Or this is clear for most people?


Like in subject. I got null pointer, how it is possible ?       java.lang.NullPointerException: Attempt to invoke virtual method 'void android.widget.Button.setOnClickListener(android.view.View$OnClickListener)' on a null object reference    public class MainActivity extends AppCompatActivity {     Button button, button2;     TextView textView, textView2;     String abc;     public List list = new ArrayList<>();     int size;      @Override     protected void onCreate(Bundle savedInstanceState) {         super.onCreate(savedInstanceState);         setContentView(R.layout.activity_main);          list.add("abc");         abc = (String) list.get(0);          button.setOnClickListener(new View.OnClickListener() {             @Override             public void onClick(View view) {                 textView.setText(abc);             }         });          button2.setOnClickListener(new View.OnClickListener() {             @Override             public void onClick(View view) {                   size = list.size();                 textView2.setText(size);             }         });     } }


Prove that $G$ is cyclic group of prime order

I'm at the beggining of a Group Theory course, and I'm trying to solve this problem:  Let $G = 1$ (being $1=\{e\}$, $e$ the neutral element in $G$) be a group containing no subgroup different from $1$ and $G$. Prove that $G$ is cyclic of prime order.  I've consider using that, given $g\in G$, $n\in\mathbb{N}$, $r=|g|$, I can conclude that $$g^n=e \Leftrightarrow r|n \text{ ($r$ divides $n$)},$$ but I'm not sure if it's useful without proving first that $G$ is cyclic, and I'm not sure how to do it. Any help will be appreciated.


System always start with "System program problem detected" dialog

Hello,  I'm getting this error every time when I boot my computer. My Ubuntu installation is fresh and I was got a few error on last step while install Ubuntu (because i have problem with my CDROM driver). Anyway, installation is continued .   For example when i tried to open ADDITIONAL DRIVER and LANGUAGE SUPPORT (on System Settings) nothing happened, it's not opening.  When i try this in terminal gnome-language-selector i'm getting this error  Traceback (most recent call last):   File "/usr/bin/gnome-language-selector", line 8, in <module>     from LanguageSelector.gtk.GtkLanguageSelector import GtkLanguageSelector   File "/usr/lib/python2.7/dist-packages/LanguageSelector/gtk/GtkLanguageSelector.py", line 34, in <module>     from aptdaemon.gtk3widgets import AptProgressDialog   File "/usr/lib/python2.7/dist-packages/aptdaemon/gtk3widgets.py", line 61, in <module>     class AptStatusIcon(Gtk.Image):   File "/usr/lib/python2.7/dist-packages/aptdaemon/gtk3widgets.py", line 66, in AptStatusIcon     def __init__(self, transaction=None, size=Gtk.IconSize.DIALOG): AttributeError: type object 'GtkIconSize' has no attribute 'DIALOG'   Also getting this error for jockey-gtk  Traceback (most recent call last):   File "/usr/bin/jockey-gtk", line 418, in <module>     sys.exit(u.run())   File "/usr/lib/python2.7/dist-packages/jockey/ui.py", line 461, in run     self.ui_show_main()   File "/usr/bin/jockey-gtk", line 81, in ui_show_main     col_icon.set_sizing(Gtk.TreeViewColumnSizing.AUTOSIZE) AttributeError: type object 'GtkTreeViewColumnSizing' has no attribute 'AUTOSIZE'   I'm worrying about are there any lack . I don't know what's wrong with my installation.  Are there any way, check my installation (packages, files etc..) .


Allow applications downloaded from anywhere in macOS Sierra

In previous versions of the OS in the security pane, you are provided an option of:    But in this version there is no option anywhere:    Is there a way that I can turn on anywhere? (via Terminal maybe?)


NoData Value = 0, problem when creating NDVI, Erdas

I try to create an NDVI from Landsat and ASTER satellite images using Erdas Imagine. In Erdas, the satellite images have a nodata value of 0.   After creating an NDVI, the nodata value is still 0, but obviously there are also file pixels with the value 0 now (NDVI ranges from -1 to +1). So if I reset the NoData value to 0 (it is not done automatically), some pixels in my raster are missing since they are now classified as "nodata"   Any suggestions?


Doing a math function of the type def.  def integral_error(integral,f):     ------stufff-------     print integral   gives something like: '<function simpsons at 0xb7370a74>'  is there a way to get just simpsons without string manipulations? ie just the function name?


Does one capitalize "communism" and "communist"?

Suppose I have the following sentence:     I lived in a communist country during the fall of communism in 1989.   Should "communist" and "communism" be capitalized?


DebugPlugin.getDefault() returning null in plug-in project

When I try to finish a activity listener plugin project in Eclipse, I get null returned by DebugPlugin.getDefault() in my project, the code like below:  public class SampleHandler extends AbstractHandler {  @Override public Object execute(ExecutionEvent event) throws ExecutionException { //      System.out.println("hello1");     BreakpointListener bl = new BreakpointListener();     DebugEventSetListener desl = new DebugEventSetListener(); //      System.out.println("hello2");     System.out.println(bl.toString());      System.out.println(DebugPlugin.getDefault());//print null       System.out.println(DebugPlugin.getDefault().getBreakpointManager());    DebugPlugin.getDefault().getBreakpointManager().addBreakpointListener(bl);     DebugPlugin.getDefault().addDebugEventListener(desl);      return null;     } }   I'm sure I have imported org.eclipse.debug.core, but DebugPlugin.getDefault() give me a null.  How can I solve this problem? Why this problem occured?


Is it a bug or intended that Unarmored defense from barbarian and monk do not stack with each other?

As an experiment, I made a level 1 monk and level 1 barbarian character.  I set all the stats to 18.    Monk's unarmored defense defines your AC = 10 + Dex + Wis.  The Barbarian's feature adds Con.    Yet the AC was still only 18.   Is this intended or is it a bug with dndbeyond?


Why does ```doub(int x)``` not change the actual value of the int x?

I am learning about programming in C++ specifically dealing with pointers. In the code below, I don't understand why doub(int x) does not change the value of y while both trip(int* x) and quint(int& x) do. I understand that the last two functions both take in the address of the object while first takes in the object. Any explanation or links to resources is greatly appreciated thanks!  #include <iostream> using namespace std;  void doub(int x) {   x = x * 2; } void trip(int* x) {   *x = *x * 3; } void quint(int& x) {   x = x * 5; }  int main() {   int y = 7;   doub(y);   cout << y << endl; // prints 7 why does this not print 14?   trip(&y);   cout << y << endl; // prints 21   quint(y);   cout << y << endl; // prints 105 }


I installed ubuntu 14.4 (x86) on my dell laptop  and after installation no  wifi  showing my on my connection ?   while i run   sudo modprobe -r iwlwfi       result :Modprobe:fatal:module iwlwfi not found   lspci -vq | grep -i wireless       Result:  Subsystem: Dell Wireless 1390 WLAN miniCard   lspci -vq | grep -i wireless       ob:00:0 Network Controller : Broadcom coperation BCM4311 802.11b/g   WLAN (rev 01)   How to solve this Error, ubunutu can detect my hardware but it seems not working ?  regards


How to increase the width and height of the Rich Text area field in Visualforce Page?

i have to increase the width and height of the Rich Text area field in Visualforce page. I have tried the following:  Method 01:  <apex:pageBlockSection title="Notes" columns="4"> <apex:pageBlockSectionItem>                     <apex:outputLabel value="Special notes" for="tts_notes"/>                     <apex:inputTextarea id="tts_notes" value="{!Territory__c.Special_notes__c}" cols="50" rows="30" richText="true"/><p/>                 </apex:pageBlockSectionItem> </apex:pageBlockSection>    Method 02:   <apex:pageBlockSection title="Notes" columns="4">         <apex:inputField value="{!Territory__c.Special_notes__c}" style="width: 1000px; height: 700px;"/>  </apex:pageBlockSection>   I have tried with Cols & rows attribute also but there is no change.  Can you guys help me?


MacBook Air number pad keyboard alternative?

Is there any way to set the keyboard on a MacBook Air laptop so that I can toggle between normal keys and a number pad?  Seems a little ridiculous to use the mouse for calculator entry and while the number row is adequate for normal typing, it seems like there should be a way to add this functionality.  (FWIW: late 2012 i7 Intel MBAir, OSX Sierra)    per Tom's Comment, as of 12/29/2016 according to their website, "" & just last week there was an . Here is an old website with some .


RTL8723be: poor and unstable wireless in Ubuntu (from 14.04 to 15.04)

I have a Lenovo G40-70 laptop, which comes with RTL8723be driver.  I'm using Ubuntu 14.04 LTS (with Kernel 3.16.0-38-generic), but this bug also occurs in 14.10 and 15.04.  Even with options rtl8723be fwlps=0 ips=0, the problem is not fixed yet. Wireless is unstable, lots of websites keeps loading forever and Ping command frequently shows data loss. It's very annoying. :(  BIOS version is the latest.  Blacklisting ideapad_laptop also doesn't work.  Sorry my english and thank you!


On a site there are some pages from a Content-type. Some of those pages (for the Belgium language only) need to be only accessible for Dokters.  So when you try to reach the URL of one of those pages you are redirected to a login-page.  But the role 'dokters' needs to have an extra login-field. Or only this field to login is even better if thats possible! It should be a field with 11 digits. Or if this is to complicated (Username, Password, 11-digit field).  How (which modules) are best practices to built this functionality?  UPDATE:  Now i managed to do a workaround with . I made a role 'doctor'. And now only users with role 'doctor' can access those pages.  But is there something to do like when the Doctors visit those restricted pages they are redirected to a custom login-page. On this page you have a small form: Fill in your 11-digit code to access this page.  Because all doctors have their own 11-digit code. We don't have to send all doctors the username name and password for role 'doctor', instead they can access the content directly, with their 11-digit code! The only validation should be that the field contains 11 digits.  How do i manage this in the simplest/best way?