How can you show that each new line drawn on a plane creates another $k+1$ regions?

The questions is      If $n$ straight lines are drawn on a plane such that each line intersects every other line and no three lines have a common point of intersection, then the plane is divided into $$\frac{n(n+1)}{2}+1$$ regions. Prove this by using mathematical induction.   I did the base case, but I do not know how to show that if $P(k)$ is true, then $P(k+1)$ is true. The worked solutions say that the addition of another line creates another $k+1$ regions. How do they get that?  Thanks


Why is the past tense used in a clause related to the present

The background is that I was doing C1 tests and got wrong the following:     It's time you ____ up your mind.   As it seems right to me, I wrote "make". However, the answer shows "made" as the correct answer.   Why is the past tense used?   I could understand the ussage of made if the word "already" was in the sentence. But it is not.  Thank you in advance!


Getting text from a file, BufferedReader, output looks ok but doesn't equal "true" or "false" (what's in the file)

I'm trying to get info from a file (it's to be used as a settings file, true or false values), using the following code:  File information = new File(aPath + "/plugins/ArenaCraft/info.acs");  ArrayList<String> info = new ArrayList<String>(); BufferedReader br = new BufferedReader(new FileReader(information)); String line; while((line = br.readLine()) != null) {      String[] sLine = line.split(":");      if(sLine[1] == "true"){          info.add("true");      }      if(sLine[1] == "false"){          info.add("false");      }      if(sLine[1] == null){          System.err.println("[ArenaCraft]  sLine[1] is NULL.");      }      if(sLine[1] != "true" && sLine[1] != "false" && sLine[1] != null){          System.err.println("[ArenaCraft]  sLine[1] is not NULL, but it's not \"true\" or \"false\".");          System.err.println("[ArenaCraft]  sLine[1] is: " + sLine[1]);      } }  br.close(); return info;   This, however, is outputting the  [ArenaCraft]  sLine[1] is not NULL, but it's not "true" or "false".   message. It then outputs, exactly,  [ArenaCraft]  sLine[1] is: true   So, I don't understand why it says it's not null or true or false. Do you guys imagine why that would happen?  The contents of the file I'm trying to read, with no encoding, follow:  notices:true   and nothing more.  Any help would be greatly appreciated, thanks in advance.


How to apply CRT to a congruence system with moduli not coprime?

$x=1 \pmod 8$  $x=5 \pmod{12}$  8 and 12 are not coprime, I could break it to:  $x=1 \pmod 2$  $x=1 \pmod 4$  and   $x=5 \pmod 3$  $x=5 \pmod 4$  But what are the next steps to solve it? By the way, $x$ should be $17$ not sure how to get that number ...  Thanks in advance.


I'm trying to serialize an object with an attribute on the root element (which is a collection).  [XmlType("Person")] public class Person {     public id Id { get; set; }     public string Name { get; set; } }  [XmlType("Persons")] public class Persons : Collection<Person> {     [XmlAttribute("Nb")]     public int Nb         get {             return this.Count;         }         set { }     } }  var persons = new Persons(); var person = new Person(); person.Id = 42; person.Name = "Toto"; persons.Add(person);  return persons;   The serialized output is the following:  <Persons>     <Person>         <Id>42</Id>         <Name>Toto</Name>     </Person> </Persons>   I'm expecting  <Persons Nb="1">     <Person>         <Id>42</Id>         <Name>Toto</Name>     </Person> </Persons>   How can I bring the Nb attribute in ?


I need to know the name of this font because I like the style of the integral and the sum


Should parsimony really still be the gold standard?

Just a thought:  Parsimonious models have always been the default go-to in model selection, but to what degree is this approach outdated? I'm curious about how much our tendency toward parsimony is a relic of a time of abaci and slide rules (or, more seriously, non-modern computers). Today's computing power enables us to build increasingly complex models with ever-greater ability for prediction. As a result of this increasing ceiling in computing power, do we really still need to gravitate toward simplicity?    Sure, simpler models are easier to understand and interpret, but in the age of ever-growing data sets with greater numbers of variables and a shift towards a greater focus on prediction capability, this might no longer even be achievable or necessary.    Thoughts?


java.lang.NullPointerException while calling a method from another class

I'm new to Java and Android development. I'm developing an app for children, in the Java section contain some classes. One of the classes is for swapping the pages named ColorCustomSwipeAdapter, and there is another class for converting text to speech named ReadName that contain a method named speakOut, the problem starts when I try to call the method speakOut through the ColorCustomSwipeAdapter class. It throws NPE and the app crashes.  Here is the code:  ColorCustomSwipeAdapter.java  package com.example.ibrahim.toddlerssmartbook;  import android.content.Context; import android.speech.tts.TextToSpeech; import android.support.v4.view.PagerAdapter; import android.util.Log; import android.view.LayoutInflater; import android.view.View; import android.view.ViewGroup; import android.widget.ImageView; import android.widget.LinearLayout; import android.widget.RelativeLayout; import android.widget.TextView; import android.widget.Toast;  import java.util.Locale;   /**     * Created by Ibrahim on 3/19/2016.  */ public class ColorCustomSwipeAdapter extends PagerAdapter {  ReadName sayName=new ReadName() ; private int[] image_resource = {R.drawable.red,R.drawable.green,R.drawable.blue,R.drawable.pink,R.drawable.gray ,R.drawable.yellow,R.drawable.brown,            R.drawable.black,R.drawable.purple,R.drawable.orange,R.drawable.white}; private String[] color_name=   {"Red","Green","Blue","Pink","Gray","Yellow","Brown","Black","Purple","Orange","White"};  private Context ctx;   private LayoutInflater layoutInflater; public ColorCustomSwipeAdapter(MainActivity ctx){this.ctx=ctx;} @Override  public int getCount() {     return image_resources.length; }  @Override public boolean isViewFromObject(View view, Object object) {     return (view==(LinearLayout)object); }  @Override public Object instantiateItem(ViewGroup container, int position) {      layoutInflater= (LayoutInflater) ctx.getSystemService(Context.LAYOUT_INFLATER_SERVICE);       View    item_view=layoutInflater.inflate(R.layout.swipe_layout,container,false);     ImageView imageView=(ImageView)item_view.findViewById(R.id.image_view);     TextView textView=(TextView)item_view.findViewById(R.id.name);     imageView.setImageResource(image_resources[position]);     textView.setText(color_name[position]);      sayName.speakOut(color_name[position]);//The ERROR IS HERE      container.addView(item_view);     return item_view;     }      @Override     public void destroyItem(ViewGroup container, int position, Object object) {         container.removeView((LinearLayout)object);     } }   Readname.java  package com.example.ibrahim.toddlerssmartbook;  import android.content.Context; import android.speech.tts.TextToSpeech; import android.support.v7.app.AppCompatActivity; import android.widget.Toast;  import java.io.IOException; import java.util.Locale;  /**    * Created by Ibrahim on 4/7/2016. */ public class ReadName extends AppCompatActivity { private int result;  public ReadName() {    result=0; }   TextToSpeech  ttsObject=new TextToSpeech(this,new              TextToSpeech.OnInitListener(){    @Override  public void onInit(int status){  if(status==TextToSpeech.SUCCESS){ result = ttsObject.setLanguage(Locale.US); }else{ Toast.makeText(getApplicationContext(),"Feature not supported in your    device.",Toast.LENGTH_SHORT).show();    }}   });   public void speakOut(String name){   if (result == TextToSpeech.LANG_NOT_SUPPORTED || result ==    TextToSpeech.LANG_MISSING_DATA) {       Toast.makeText(getApplicationContext(), "Feature not supported in your    device.", Toast.LENGTH_SHORT).show();    } else {       ttsObject.speak(name, TextToSpeech.QUEUE_FLUSH, null);    }   }    @Override    public void onDestroy() {      if (ttsObject != null) {         ttsObject.stop();         ttsObject.shutdown();     }     super.onDestroy();  } }


In an attempt to uninstall wine I ran the command sudo apt-get purge wine* which as you may have guessed removed many of the default packages. I am wondering if there is a way to use the installation disk to reinstall the default packages without overwriting the file system. Not sure if it makes a difference or not, but I am duel booting Windows 8 and Ubuntu 14.04 which was updated from Ubuntu 12.04.  Thanks in advance.


Modulo 2 binary long division in European notation

I need to represent binary modulo 2 long division in my tex document. Notation needed is same as    under Austria, Germany, etc.  I know about longdiv package, but it doesn't seem to support this.  Is there any package to achieve this? If not, how can I manually do this.  Thanks in advance


Continuity of $L^1$ functions with respect to translation

Let $f\in L^1$, consider the map $t\mapsto f_t=f(x-t)$, then how can one show that $t\mapsto f_t$ is continuous? More explicitly one wants to show that $\lim_{h\to 0}|f_{t+h}-f_t|_{L^1}=0$. I tried to use approximation by $C_0(\mathbb{R})$ functions $g^n$ to approximate $f$ in $L^1$ norm. Then one has $\lim_{h\to 0}|g^n_{t+h}-g^n_t|_{L^1}=0$, but then I came across the problem: how can one show that the two limits can exchange so that one has $$\lim_{h\to 0}|f_{t+h}-f_t|_{L^1}=\lim_{h\to 0}\lim_{n\to\infty}|g^n_{t+h}-g^n_t|_{L^1}=\lim_{n\to\infty}\lim_{h\to 0}|g^n_{t+h}-g^n_t|_{L^1}=0.$$  Can someone help me with some conditions on which two limits can be exchanged, or do you have a better way of proving the continuity? Thank you!


Can my computer components ( Monitor, Motherboard, RAM, HDD, CPU, SMPS) become damaged due to a sudden power flux. It's only needed to shut down Windows properly.  Can I solve both Hardware and Software problems without UPS?


"People with different profiles" or "people with a different background"

Speaking about technical and non-technical people (management), which word is the best in this case? Profile or Background?  The whole sentence is "To provide training for people with [different profiles] | [a different background]"


At String s1 = "str" + s.length(); the value of s1=str4 but it turns out to be false at next sysout statement during equality check

public class Foo {      public static void main(String[] args) {         foo();         bar();     }      public static void foo() {         String s = "str4";         String s1 = "str" + s.length();         System.out.println("(s==s1)" + (s1 == s));      }      public static void bar() {         String s = "str4";         String s1 = "str" + "4";         System.out.println("(s==s1)" + (s1 == s));     } }   OUTPUT  (s==s1)false  (s==s1)true   At String s1 = "str" + s.length(); the value of s1=str4 but it turns out to be false at next sysout statement during double equal (==) check  */


Let A, B, C, D and E be five points marked, in clockwise order, on the unit circle in the plane (with centre at origin). Let α and β be real numbers and set f(P) = αx + βy where P is a point whose coordinates are (x, y). Assume that f(A) = 10, f(B) = 5, f(C) = 4 and f(D) = 10. Which of the following are impossible?  (a) f(E) = 2  (b) f(E) = 4  (c) f(E) = 5  I have try this question many times , but from my point of view   the answer  is f(E) = 5 becoz it is moving in clockwise direction and after f(E) =5 then f(E)=10, so my answer is f(E)=5. I don't know   whether answer is correct or not  if anbody help  me , i would be very thankful to him...


Image of the set of natural numbers under any function is denumerable.

Hi everyone I'd like to know if the following reasoning is correct, any suggestion would be great. Thanks.  Proposition: Let $Y$ be a set and let $f: \mathbb{N}\rightarrow Y$ be a function. Then $f[\mathbb{N}]$ is at most countable.   Proof: If $Y$ is finite the result follows, this is because$f[\mathbb{N}]\subset Y$ and any subset of a finite set  is finite and has at most the size of the set in which is contained.   We may assume  that the set $Y$ is infinite. We set $A:= \{\,n\in\mathbb{N}:f(i)\not=f(n) \,\,\text{ for  any }i< n\, \}$. And we define the function $g:A \rightarrow f[\mathbb{N}]$ as the restriction of $f$ in $A$. We claim that the function $g$ is a bijective map. From the definition of $A$ we already know that the map is $1:1$. We will show that also is onto.   Let $y\in f[\mathbb{N}]$. Suppose for the sake of contradiction that there is no $n\in A$ such that $g(n)=y$. Since $y$ lies in the image of $f$, then there is some $j\in \mathbb{N}$ for which $y=f(j)$. Then either $f(j)\not= f(i)$ for any $i<j$ or there exists some $i<j$ such that $f(j)= f(i)$. For the former, $j$ lies in $A$ (by its definition). For the latter, the set $\{\, n\in \mathbb{N}: f(j)=f(n)\, \text{and }\,n\not=j \}$ is non empty, and hence has a minimum element. Let $m$ be its minimum element. Then $f(m)\not=f(n)$ for any $n<m$ and thus $\,m\in A$ but $g(m)=f(m)= f(j)=y$. Thus any case leads to a contradiction. The result follows by reductio ad absurdum. Hence $f$ is surjective and injective, i.e., a bijective map.   Since there is a bijection between $A$ and the images of the natural numbers under $f$, both have the same cardinality. Also we already know that $A\subset \mathbb{N}$ and any set of the natural numbers is denumerable, thus $f[\mathbb{N}]$ is countable. $\Box$


Why does \if in a tikzpicture evaluate to true for \if 33 \empty?

I have the following code:  \documentclass[11pt]{article} \usepackage{tikz} \begin{document} \newcount\x \x=-1 \begin{tikzpicture}   \foreach \percentA in {33}   {     \if \percentA \empty \else     \global\advance\x by 1      \draw (\x,0) circle (0.2cm);      \fi   }; \end{tikzpicture} \end{document}   If I use \if instead of \ifx, this code compiles to an empty document. If I would use 66 instead of 33, it would compile to an empty document as well. But if I would use any other value (like 32 or 34 or 65), it would work just fine, and would draw a circle.  Could somebody tell me why 33 equals to \empty? I know that I should have used \ifx, but I'm wondering why 33 and 66 are so special in this case, because I would expect the same behavior for every number.


Today, the professor of Smooth Manifold's course proofed that $TS^{2n-1}$ is an embedded submanifold of $T\mathbb R^{2n}$ using the fact that $T\mathbb R^{2n}$ is diffeomorphic to $\mathbb R^{2n} \times \mathbb R^{2n}$ and describing $S^{2n-1}$ as inverse image of regular value. So, my question is:  If $M$ be a submanifold of $N$, is true that $TM$ is a submanifold of $TN$?  In above $TM$ denotes the tangent bundle of the smooth manifold $M$.


How can I clip the image to change from this:    To something like this (edited it with a drawing brush):    Like how clipping mask work on Photoshop. I tried every pathfinder option on Illustrator and there's no result i want.  Basically I want all objects that will be only visible inside the black circle and nothing goes outside.  How can I make that way with Adobe Illustrator?  Thanks.


Why is the Community User collecting hats, and who decides what she wears?

I do understand the role of the community user - it is a record keeping device that owns all activity that is no longer controlled by a specific named user. Even with that knowledge, however, I found this interesting:     Are unowned hats going to Community as well? How does Community figure out what hat she's (he?) going to wear? Is it random, or, is the Crab intentional? Was this intentional or just an interesting feature? Put another way, are the devs who implemented hats that on top of things that they considered this? If so, well, my hats off to you!


Describing a person who prefers older (not new) or vintage things

Is there a word or phrase that refers to a person who prefers older (not new)or vintage things?


I had hp laserjet m1136 MFP and i had done each and everything. Installed the driver but unable to print from it. What should I do now


What are some good introductory books for self-studying topology?

A friend of mine, who likes math and knows I do too, told me he thinks topology is really cool. So, I was wondering if someone could suggest to me some good introductory topology books. Thanks in advance!


Why do I have a large black and white artifact on the rendered image?

Cant figure out why the rendered image has a large black and white artifact (on the bottle on the right)?      Appreciate any tips!


How do I modify algorithmic \while command to type another word

How can I type another word for the statement \while in the pseudo-code? Normally, it writes, While *some termination condition* do  and I want to change it to: DONGU: *some termination condition*  And here is the MWE: \documentclass{article} \usepackage[ruled,vlined]{algorithm2e} \usepackage{algorithmic} \begin{document} \begin{algorithm}[ht] \centering \begin{algorithmic} \caption{some algorithm} \label{alg:myalgo} \While {a termination condition bla bla}{     \STATE $do\;something $\;            } \end{algorithmic} \end{algorithm} \end{document}


What order should the books in the Percy Jackson universe be read in?

There are several dozen novels, short stories and other works set in the same world as Rick Riordan's Percy Jackson and the Olympians. Many of them aren't released chronologically in relation to each other. If I was a completely new reader, what would be the best order to read these in?  Novels:   The Lightning Thief The Sea of Monsters The Titan's Curse The Battle of the Labyrinth The Last Olympian The Lost Hero The Son of Neptune The Mark of Athena The House of Hades The Blood of Olympus The Red Pyramid The Throne of Fire The Serpent's Shadow The Sword of Summer The Hammer of Thor (Unreleased) The Hidden Oracle The Dark Prophecy The Burning Maze The Tyrant's Tomb The Tower of Nero (Unreleased)   Short Stories:   The Two Headed Guidance Counselor The Library of Deadly Weapons My Demon Satyr Tea Party My Personal Zombie Apocalypse Percy Jackson and the Stolen Chariot Percy Jackson and the Bronze Dragon Percy Jackson and the Sword of Hades The Diary of Luke Castellan Percy Jackson and the Staff of Hermes Leo Valdez and the Quest for Buford The Son of Magic (Written by Haley Riordan but still canon) The Son of Sobek The Staff of Serapis The Crown of Ptolemy   Graphic Novels:   The Lightning Thief Graphic Novel The Sea of Monsters Graphic Novel  The Titan's Curse Graphic Novel The Lost Hero Graphic Novel  The Red Pyramid Graphic Novel The Throne of Fire Graphic Novel   Other:   Percy Jackson's Greek Gods Percy Jackson's Greek Heroes Demigods and Monsters (A book of real-world essays on the original series with an introduction by Riordan) Percy Jackson and the Olympians: The Ultimate Guide The Kane Chronicles Survival Guide Camp Half-Blood Classified Camp Jupiter Classified (Unreleased)   Let's just ignore the movies and video game.


Most efficient way to see if an ArrayList contains an object in Java

I have an ArrayList of objects in Java.  The objects have four fields, two of which I'd use to consider the object equal to another.  I'm looking for the most efficient way, given those two fields, to see if the array contains that object.  The wrench is that these classes are generated based on XSD objects, so I can't modify the classes themselves to overwrite the .equals.    Is there any better way than just looping through and manually comparing the two fields for each object and then breaking when found?  That just seems so messy, looking for a better way.  Edit: the ArrayList comes from a SOAP response that is unmarshalled into objects.


How to flag spam user profiles in the absence of posts to flag?

I came across , which contains links to the website of some sort of tv streaming service. A  revealed that the same text and links have been posted to dozens of websites that allow people to create user profiles or post messages that are exposed to search engines, using different names and .    However, since this user has not posted any questions, answers or comments on Stack Overflow, it is impossible to flag them. How would I go about flagging this user profile as spam?    (And also, do we have an automated process to find such spam profiles?)


Example of an increasing, integrable function $f:[0,1]\to\mathbb{R}$ which is discontinuous at all rationals?

I have really no idea about this:  Problem: Show that there exists a function $f:[0,1]\rightarrow\mathbb{R}$ such that:  $f$ is discontinuous in all $x\in \mathbb Q$. $f$ is increasing in $[0,1]$. $f$ is integrable.   EDIT: Sorry, it is not discontinuous in all $x\in \mathbb R \setminus \mathbb Q$, just in $\mathbb Q$.


How does First-Contact choices affect relationship in Stellaris?

Our empire just made first contact with another empire.  When that happened, we were some given first contact choices:    We made many contacts before and are wondering if these choices have any effect at all?


Do the Laurent polynomials over $\mathbb{Z}$ form a principal ideal domain?

I'm trying to prove whether or not the Laurent polynomials $\mathbb{Z}[x, x^{-1}]$ with coefficients in $\mathbb{Z}$ form a principal ideal domain.    I know that $\mathbb{F}[x, x^{-1}]$ is a PID when $\mathbb{F}$ is a field, but clearly $\mathbb{Z}$ is not a field so I cannot appeal to this result. And my intuitions are not serving me very well at the moment. Can anyone provide a hint or direction to take?


What is the Fastest a Character Can Move in One Turn?

At level 20 with any magic items in the DMG, and any spells, what is the fastest a DnD 5e character could move using their movement?  (i.e., not including teleportation)


How to calculate a capacitor's discharge time?

How do i calculate a capacitor with a specific capacitance loaded with a specific resistance discharge time and reach a specific voltage?  So let's say i have a 22uF capacitor charged with 12 volts and loaded with a 500 ohm load, how many seconds does it take to reach the capacitor's voltage of 6 volts?


Spoilers ahead for "Beyond the Wall" (Game of Thrones, S07E06)  Toward the end of the episode, "Beyond the Wall" (Game of Thrones, S07E06), we see a close-up shot of Longclaw        Then, once Jon Snow emerges from the water, Longclaw appears to be opening its eyes        You can get a much better picture of it .  Is this an Easter Egg from the Visual Effects department, or is there an in-universe explanation behind this?  Or was this not planned at all by the production team, and this is merely a coincidental, accidental lighting/water effect, that just happens to be timed with the dramatic tension of Jon Snow possibly being dead, and the relief of him being alive?


How to install and setup graylog-server and graylog-web on Ubuntu from repository?

I am trying to setup  on Ubuntu 14.04. I tried to find out installation steps on internet I found few links. but their method of installation is manual I mean installation from the source. and I don't want to follow installation from source because posts are old, some are talking about graylog2(I could not found difference between normal graylog and graylog2), their source package is old so there configuration files are not matching with latest configuration files.  so I decided to setup latest greylog from official documentation at      I have installed latest  and . after that I followed steps to install graylog-server and graylog-web from official documentation.    $ wget https://packages.graylog2.org/repo/packages/graylog-1.0-repository-ubuntu14.04_latest.deb $ sudo dpkg -i graylog-1.0-repository-ubuntu14.04_latest.deb $ sudo apt-get install apt-transport-https $ sudo apt-get update $ sudo apt-get install graylog-server graylog-web   I am able to see configuration files after installation  /etc/graylog/server/server.conf /etc/graylog/web/web.conf   I am able to see other files at   /usr/share/graylog-server /usr/share/graylog-server/bin /usr/share/graylog-server/graylog.jar /usr/share/graylog-web /usr/share/graylog-web/bin/ /usr/share/graylog-web/conf   I configured /etc/graylog/server/server.conf and /etc/elasticsearch/elasticsearch.yml with help of  and able to run graylog-server by running     java -jar /usr/share/graylog-server/graylog.jar server   this shows me   Started REST API at <http://127.0.0.1:12900/ Graylog server up and running.   After that I am not understanding how to setup graylog-server and graylog-web properly because these steps are not complete. I will appreciate if someone could give clean steps for proper setup. thanks in advance


Fantasy story where a young girl (I think) discovers magic, but must then hide from all magicians

I remember reading this story many years ago (at least ten).  A young girl (at least I think so), discovers that she has magic by throwing something. However, magic is restricted (or maybe even forbidden) and she must now hide from all magicians in her city. I think the local Thieves Guild helps her, hoping to get their own pet magician.  Other recollections:   It's low-fantasy, no elves or dragons I think there was a lot of homophobia in the setting I seem to recall that she can't control her magic and is eventually caught/taken in by the magicians.  I'm pretty sure it was a full-length novel. Possibly a novella.


I'm working on a RHEL 6.7 machine. I'd like to make a script which is owned by root BUT could be launched by other users. However I still want the actions inside the script to be launched as root. So I want to set the suid bit on this script. Right now I have the following results:  [root@devmachine BACKUP]# chmod a+s fix_properties.sh [root@devmachine BACKUP]# ls -halt fix_properties.sh -r-sr-s-r-x 1 root root 42 May 12 00:08 fix_properties.sh   This is not good enough since a lambda user would be able to execute it but wouldn't benefit from the root permissions. After some digging I learned that it could be due to the way the FS is mounted. When I check the fstab file I see the following:  /dev/mapper/systemvg-op /opt ext3 defaults,nosuid,nodev 1 2 ... /dev/systemvg/opt_backup /opt/BACKUP ext4 acl,user_xattr 1 2   Does this mean that the nosuid will be also de rigueur on the /opt/BACKUP partition?  As a work-around, I guess I could assign this file to a particular group from which my target user is part of?


Does he has store key?   Does he have store key?      Please tell me which one is correct. Also, please explain briefly difference between 'have' and 'has' and when they are used.


It is an easy exercise to show that all finite groups with at least three elements have at least one non-trivial automorphism; in other words, there are - up to isomorphism - only finitely many finite groups $G$ such that $Aut(G)=1$ (to be exact, just two: $1$ and $C_2$).  Is an analogous statement true for all finite groups? I.e., given a finite group $A$, are there - again up to isomorphism - only finitely many groups $G$ with $Aut(G)\cong A$?  If yes, is there an upper bound on the number of such groups $G$ depending on a property of $A$ (e.g. its order)?  And if not, which groups arise as counterexamples?  And finally, what does the situation look like for infinite groups $G$ with a given finite automorphism group? And what if infinite automorphism groups $A$ are considered?


Proving that $\det (M) = \det (A) \det(D-CA^{-1}B)$

So the task is the following:  Be $M\in M_{m\times n}(K)$ a block matrix  $$M = \bigg( \begin{array}{cc} A & B \\ C & D \\ \end{array} \bigg) $$  with $A\in M_m (K)$, $B,C^t\in M_{m\times n}(K)$ and $D\in M_n (K)$ and let $A$ be invertable.  Show that: (a) $\det (M)=\det (A) \det (D-C(A^{-1})B$.  (b) If $m=n$ and $AB=BA$, $\det (M)=\det (DA-CB)$.  Note for (a): Multiplicate $M$ with a proper block matrix.   I am really lost on this one... and would really appreciate any help.


dpkg warning files list file for package missing

I tried to install a package and it did, and it appears to work just fine. However when I installed it I got several warnings about packages being missing.  dpkg: warning files list file for package '...' missing, assuming package has no files currently installed.   Since it is just a warning and it appears to work anyway, I assumed that it doesn't matter, but I would like someone to confirm that.   The packages that are missing are ones that I uninstalled on purpose because they were non-essential and took up a lot of room.  EDIT: Package is tzdata. Using dpkg -i on a .deb file to install. And the above is essentially the entire warning. Just instead of ... it lists packages. python2.7-minimal, libsqlite3-0, libaprutill-dbd-sqlite3, python-minimal`  EDIT: "What exactly did you do?" I ran the command   dpkg -i tzdata_2017b-2_all.deb   to install the package tzdata.  "What did you want to achieve?" I wanted the package to install.  "What happened instead? Did you encounter any warning or error messages?" The package installed and worked fine. However, the above warning appeared for the above packages.  I cannot copy and paste since this is occurring on a separate server. But I will rewrite it here:  dpkg: warning files list file for package python2.7-minimal missing, assuming package has no files currently installed. dpkg: warning files list file for package libsqlite3-0 missing, assuming package has no files currently installed. dpkg: warning files list file for package libaprutill-dbd-sqlite3, assuming package has no files currently installed. dpkg: warning files list file for package python-minimal, assuming package has no files currently installed.   I am not looking for a fix. I am just curious if dpkg giving me a warning in this type of situation actually matters. Again the program works anyway and nothing else on my system needed those packages.


double astarisk in python string format method

I was reading  where I found this python code.    capital_country = {"United States" : "Washington",                     "US" : "Washington",                     "Canada" : "Ottawa",                    "Germany": "Berlin",                    "France" : "Paris",                    "England" : "London",                    "UK" : "London",                    "Switzerland" : "Bern",                    "Austria" : "Vienna",                    "Netherlands" : "Amsterdam"}  print("Countries and their capitals:") for c in capital_country:     format_string = c + ": {" + c + "}"      print(format_string.format(**capital_country))   I know capital_country is what is called 'dictionary' in Python. But I cannot understand the last two lines. Of course I understand the for loop iterates through the dictionary elements. Could somebody explain it to me?


He must decide who/whom to be. Which is correct?

Which of the following two sentences is correct?  He must decide who to be. He must decide whom to be.  I can think of arguments for both sides, but I'm not sure. To elaborate, is who(m) the object of decide, the subject of be, or the object of be? Does the infinitive form of be have any bearing on the answer? And is there anything else to consider about the position or role of who(m) in this particular sentence that would inform the answer? The answers to the linked question  say to "substitute he and him for who and whom." However, that doesn't give a clear answer in this context, because neither of those pronouns sounds right: "He must decide to be he"? "He must decide to be him"? Normally we'd use a reflexive pronoun here ("He must decide to be himself") and it's not clear what case that corresponds to.


Compute the last three digits of   $$\sum_{k=1}^{2017} k^3*\binom{2017}{k}$$   I'm looking for combinatoric way to "translate" this into something much easier to compute. The Sum is the number of ways of choosing a $k$-member committee with three jobs within them (can all be the same person).      I think we could do this by choosing the jobs first and then the committee. We proceed by casework on jobs.  One person has all three jobs: $2017\cdot 2^{2016}$  One person has two jobs: $2017\cdot 2016\cdot 2^{2015}$  Every job is occupied by a different person $2017\cdot 2016\cdot 2015\cdot 2^{2014}$  However if we add these cases up it is not equal to our original summation. How can I fix this? Thanks!


C++ multiple-definition error for globally declared variables

Dear StackOverflowers,  I am learning to code object-oriented C++. For a project, I'm programming an esp32 using the Arduino core. I'm getting some linking errors that I really don't understand. There are many similar questions out there already, but they didn't help me to solve my question.  I have ISR functions that have to be declared globally. I've put those functions in a global.h and global.cpp file. The variables needed for those functions are declared in the .h file and defined in the .cpp file. To prevent things from being compiled twice I put this around it:  #ifndef GLOBAL_H #define GLOBAL_H  #endif   The code compiles fine, but when the linking process starts I get an error message that says:  .pioenvs\nodemcu-32s\src\ULAM.cpp.o:(.bss.buttonState+0x0): first defined here .pioenvs\nodemcu-32s\src\global.cpp.o:(.bss.oldButtonState+0x0): multiple definition of `oldButtonState' .pioenvs\nodemcu-32s\src\ULAM.cpp.o:(.bss.oldButtonState+0x0): first defined here .pioenvs\nodemcu-32s\src\global.cpp.o:(.bss.oldEncPos+0x0): multiple definition of `oldEncPos' .pioenvs\nodemcu-32s\src\ULAM.cpp.o:(.bss.oldEncPos+0x0): first defined here .pioenvs\nodemcu-32s\src\main.cpp.o:(.bss.oldButtonState+0x0): multiple definition of `oldButtonState' .pioenvs\nodemcu-32s\src\ULAM.cpp.o:(.bss.oldButtonState+0x0): first defined here .pioenvs\nodemcu-32s\src\main.cpp.o:(.bss.oldEncPos+0x0): multiple definition of `oldEncPos' .pioenvs\nodemcu-32s\src\ULAM.cpp.o:(.bss.oldEncPos+0x0): first defined here .pioenvs\nodemcu-32s\src\main.cpp.o:(.bss.buttonState+0x0): multiple definition of `buttonState' .pioenvs\nodemcu-32s\src\ULAM.cpp.o:(.bss.buttonState+0x0): first defined here .pioenvs\nodemcu-32s\src\main.cpp.o:(.bss.encoderPos+0x0): multiple definition of `encoderPos' .pioenvs\nodemcu-32s\src\ULAM.cpp.o:(.bss.encoderPos+0x0): first defined here .pioenvs\nodemcu-32s\src\main.cpp.o:(.bss.bFlag+0x0): multiple definition of `bFlag' .pioenvs\nodemcu-32s\src\ULAM.cpp.o:(.bss.bFlag+0x0): first defined here .pioenvs\nodemcu-32s\src\main.cpp.o:(.bss.aFlag+0x0): multiple definition of `aFlag' .pioenvs\nodemcu-32s\src\ULAM.cpp.o:(.bss.aFlag+0x0): first defined here .pioenvs\nodemcu-32s\src\main.cpp.o:(.data.mux+0x0): multiple definition of `mux' .pioenvs\nodemcu-32s\src\ULAM.cpp.o:(.data.mux+0x0): first defined here   Some errors say that there are multiple definitions between ULAM.cppp and global.cpp, other say it's between ULAM.cpp and main.cpp. With the knowledge that I have about the compilation and linking processes it has to do something with the way I structured my #includes.  in main.cpp I have: #include <Arduino.h> #include "ULAM.h"  in ULAM.h I have: #include <Arduino.h> #include <Adafruit_MAX31856.h> #include <SPI.h> #include <PID_v1.h> #include "../include/defines.h" #include "global.h" #include "ulamProgram.h"  in ULAM.cpp: #include "ULAM.h"  in global.h: #include <Arduino.h> #include "../include/defines.h"  and in global.cpp: #include "global.h"   Anybody knows what goes wrong here?


My laptop's cpu runs at more than 150% maximum frequency

I recently noticed that my CPU is running at higher than it's base clock speed. Processor : Intel i5-8300H (2.30 GHz) I used to get many Blue Screen (BSoD) errors when I play games like FIFA or even when I use any video converter software and any other heavy application. I have tried many fixes: chkdsk, sfc, DISM restore health but they didn't work for me. I have been using my laptop for 2 years and it has been able to handle heavy application quite well. I don't understand if my CPU running at higher speeds is related to this or not. Here is a screenshot of my Resource Manager:  It reaches 170-180% when I use something heavy. Is it normal? EDIT: My Laptop has also started heating up a lot recently.


Remove row after inserting them with clone() with jQuery

I've a table that allow me to add or remove row. <button data-action="add-item">Add line</button>

             Line	             Element

                              1             	                              <input type="text" name="element[]">             	                              <button data-action="remove-item">                     Remove                 </button>

             	             Total:	                              <input type="number" name="EST_ItemsSum">

  My issues is are:  How can I insert the line number in front of each line ? How can I remove the line when I click on the Remove button (dynamic way with event propagation) ?  Here my JS code: // Add item $('[data-action="add-item"]').click(function(){     $('table > tbody > tr:first').clone().find('input').val('').end().insertBefore('table > tbody > tr:last'); })  // Remove item $('[data-action="remove-item"]').click(function(){     $(this).closest('tr').remove(); })


These two loops do not produce the same result:  \documentclass{article}  \usepackage{tikz}  \begin{document}  \foreach \i in {a,b,c} {%     \i+ }  \def\Index{a,b,c} \foreach \i in {\Index} {%     \i+ }  \end{document}     Why is this? How do I get \foreach to iterate over the comma-separated content of \Index even though it looks like a single token?


Characteristic map of a n-cell in a CW complex

I have a problem in understanding the purpose of the definition of a CW complex. What really would help me is to understand the following:  Let $\sigma$ be a n-cell and $\Phi_\sigma:\mathbb D^n \to X$ be the characteristic map. Is there any relation between $\Phi_\sigma(\mathbb S^{n-1})$ and $\partial \sigma$ following directly from the Definition? I know, for example, that $\Phi_\sigma(\mathbb S^{n-1})\subset X^{n-1}$, $X^{n-1}$ being the $(n-1)$-Skeleton, but what does this tell me about the boundary of $\sigma$?


Is accepting an answer discouraging more answers?

Sometimes I read a question that has an accepted answer, and I feel I won't add any value if I answer.  Should one wait to accept an answer in order not to discourage a potentially better answer?


Can I install Ubuntu on a Samsung Wave 2 S8530 phone that is running Bada OS?

I'm using Bada OS Version 1.2 on my Samsung Wave 2 S8530.  My phone's hardware is: ⠀• 1GHz processor ⠀• 512MB RAM ⠀• 2GB Internal memory ⠀• Hummingbird chipset ⠀• 73MB GPU memory    I have a 32GB UHS 1 Class 10 microSD card. Please tell me can I install Ubuntu on my phone?


Calculate the gradient of a linear scalar field

I am trying to calculate the following gradient $$\nabla_{\mathbf{X}} \left( \mathbf{a}^{T} \mathbf{X} \mathbf{a} \right)$$ where I am using the convention that $\mathbf{a}$ is a column vector. I am wondering what the steps are to extract the solution from the matrix cookbook, which is: $$\nabla_{\mathbf{X}} \left( \mathbf{a}^{T} \mathbf{X} \mathbf{a} \right) = \mathbf{a}\cdot\mathbf{a}^{T}$$


How do I use context with SharedPreferences?

Currently I use this way to get context:  SharedPreferences sharedPref;      @Override     protected void onCreate(Bundle savedInstanceState) {         super.onCreate(savedInstanceState);         setContentView(R.layout.activity_main);         Context context = MyApplication.getAppContext();         sharedPref = context.getSharedPreferences("MyPref", Context.MODE_PRIVATE);     }   MyApplication class:  public class MyApplication extends Application {      private static Context context;      public void onCreate() {         super.onCreate();         MyApplication.context = getApplicationContext();     }      public static Context getAppContext() {         return MyApplication.context;     } }   I'm trying to call a method in MainActivity from MovieUpdatesService class   MainActivity method:  public void checkNow() {         new Thread(() -> {             String site = null;             if (sharedPref.contains("site")) //line 153                 site = sharedPref.getString("site", "Not available");              //codes...          }).run(); }   MovieUpdatesService class:  public class MovieUpdatesService extends JobService {      //codes...      public void doBackgroundWork(final JobParameters params) {         if (jobCancelled)             return;          new MainActivity().checkNow();          Log.d(TAG, "Job finished");         jobFinished(params, false);     }      //codes... }   I get NullPointerException when running and I think it has something to do with context  Error:  java.lang.NullPointerException: Attempt to invoke interface method 'boolean android.content.SharedPreferences.contains(java.lang.String)' on a null object reference         at com.tashila.movieupdates.MainActivity.lambda$checkNow$0(MainActivity.java:153)   How do I fix this? I'm new to Android so I'm hoping for a simplified answer (:


Suppose the mean noon-time temperature for September days in San Diego is $24^{∘}$ and the standard deviation is $3.2$. (Temperature in this problem is measured in degrees celsius).  Using Chebyshev’s theorem, what is the minimal probability (in percents) that the noon-time temperature of a september days is between $17.6^{∘}$ and $30.4^{∘}$? A.  On September 26, 1963, the all-time record of noon-time temperature in San Diego of $44^{∘}$ was hit. Assume the temperature distribution is symmetric around the mean, what is the Chebyshev bound for the probability of breaking (or tieing) this record? B.


mentions that sugar "at a certain level acts as a preservative". I've always been taught that microorganisms eat sugar and expel acids, that is why sugary food are damaging to teeth. How is it that sugar acts as a preservative, then?  Googling the question I've found   though I don't credit the sources as being especially reputable. What is the real reason that sugar can act as a preservative?


Run piece of code atomic or after application kill (Ctrl+C)

In my program I approaching text files in every iteration of loop to not lost any data from running. It is brutal uneffective and still I lost that data yesterday.  I have 2 Queues - "what have I done" and "what to do". After some time I need to end this application and remember these queues for next app run. I usually kill the applicatiaon with Ctrl+C.  Is there any way to run saving these Queues to files after app kill? Or how to End console application as a User correctly.  Is it possible to run piece of code atomically? I mean when I update some "Queue file" by removing first line of it I need to copy whole file to tmp than delete original file and than copy tmp file to original. But sometimes I hit Ctrl+C right after orig. file delete and I lost one queue.


new added references not working from bib file

I am writing an article using latest version of TeXmaker and MiKTeX. I have previously saved incomplete report. Everything was working fine on old laptop and old versions of texmaker. I am using a bib file to add references of biblatex type. Old references are properly working even if I am citing them again in article, they are working fine but when I try to add a new reference, it does not work, I copy bibtex reference from Google Scholar and paste in bib file and cite in my article. Problem is only with new references. The references show as [liu2019mid], [11], [nugrahaningsih2019soft], the middle one [11] is an old reference which was previously added in bib file and the other two are not showing properly and they are also not showing in bibliography. This screenshot includes recently added two references.


I was going through the java Method.class (Decompiled) and I found something that caught my eye.  @Override public boolean isSynthetic() {     return super.isSynthetic(); }   "Synthetic". What does that mean?  Is it usable in code?  .  And since I found this in the Method class, I was wondering, is it that an entire method could be "synthetic", or is it that it contains something synthetic?  Thanks in advance.  .  not a copy of


What happens when a photon reaches the "edge" of the universe?

As I understand it, there are several models for what the universe could look like from the “outside”. I don’t know if any of these are outdated, so if they are please tell me if they are.   Expanding bubble. This model says the universe will never stop expanding, and the universe will die because the energy all turns to photons and gets spread out so much. Bubble that will eventually collapse. In this model the universe will stop expanding, and collapse. Everything merges into super-massive black holes, and the universe dies with fire. The universe is a torus. I'm not clear whether the size of the universe in this model is changing, but the central idea is that space is donut-shaped.   Those are the major ones that I have heard of. My question involves what I have heard to be the most popular of the three, #2. In this model, eventually something will "touch" the edge of the universe. Obviously, the first thing to "touch" it would be photons as they travel at, well, the speed of light. This involves all forms of energy in the universe, but I thought it might be easier to explain for something without mass.  What happens if some form of energy "touches" the edge of the universe? Logically, the energy cannot be lost without violating the law of conservation of energy. The only thing I can think of, is that it would "bounce" or be refracted off the edge.  I realize that it sounds silly, however if model #2 is correct then this situation will arise some number of billions of years from now.  I can only assume that there is either a new model that accounts for this, there is some complex explanation, or that model #2 is incorrect.


Trying to ssh root, why get permssion denied in 16.04?

I'm trying to set up passwordless ssh between root accounts in 16.04 (needed for Hadoop installs). I set up a password for root by sudo su - root and passwd.  When I try e.g.   ssh -l root slave3 or ssh-copy-id -i $HOME/.ssh/id_rsa_root.pub  root@master  I get   Permission denied, please try again.  I have tried all the advice I can find i.e. making the following edits (one at a time) to /etc/ssh/sshd_config:  PermitRootLogin without-password  PermitRootLogin yes  RSAAuthentication yes PubkeyAuthentication yes #StrictModes yes UsePAM no AllowUsers root hduser   Followed by sudo service ssh reload after each, but still I get permission denied. Any help is much appreciated.


Prove that for the $\mathbb R^{n\times n}$ vector space doesn't exist a basis from $n^2$ matrices, such that AB=BA for every two matrices in base.

Prove that for the $\mathbb R^{n\times n}$ vector space doesn't exist a basis containing  $n^2$ matrices, such that AB=BA for every two matrices $A$, $B$ in the base. $(n>1)$  I think it is true because I did not get any example which makes it false. Thanks in advance.


Can ESTA holder do some remote work from US for a UK company?

I'm an ESTA holder regularly travelling to the US to see my girlfriend. I am a UK resident, in full time employment for a UK company.  This summer, I want to go over to US for 2-3 months (up to 90 days as ESTA permits), but I'd like to carry on working for my UK company over the internet. I would get paid to my UK current account - same way as it currently is. My employer is fine with that. I would go back to the UK within 90 days - as per ESTA's terms.  Is this legal or can I get in trouble? I'm finding very contradicting answers all over the internet.  In case you wonder, I'm the software developer.  Thanks.


Show that a next polynomial function sequence converges uniformly to $\sqrt{x}$

Show that polynomial function sequence $(P_n)$ define recursively as $P_0(x)=0$ and $P_{n+1}(x)=P_n(x)+\frac{1}{2}(x-P_n^2(x))$ converges uniformly in $[0,1]$ to the function $f(x)=\sqrt x$.  I've tried to show that is a Cauchy's sequence but I've not got something. Because I don't know how to explain that $|P_n^2(x)-x|$ is a small quantity.


comparing means for two groups with some overlap

How can I compare the means of two data sets where there is some overlap in the samples so that the groups are neither paired nor independent? That is there has been some change in the samples with some subjects providing data in BOTH sets, some respondents only providing data in the first set and others only providing data in the second set?


My question is simple:  Should I use fseek with SEEK_END to get to the end of a file and then get the length of it ? Because in the man it is said:        Library implementations are allowed to not meaningfully support SEEK_END (therefore, code using it has no real standard portability).      Right now I am using stat (from C) which is better ?


How to place labels under a vector layer?

I want to place the labeling under a layer. In QGIS 2.2 apparently the label appears automatically at the top. Can someone help me. (see attachment)      example:


I want to get the cpu usage. I tried this command  top -bn1 | grep "Cpu(s)" | sed "s/.*, *\([0-9.]*\)%* id.*/\1/" | awk '{print 100 - $1}'   Could you confirm if this command is correct?


How to avoid becoming stressed while playing endurance games?

Although I am asking for Super Hexagon, I've noticed there is a multitude of games (rhythm games in particular) where the more stressed I am, the worse I play and/or are more likely to make a mistake. Often then the games are designed in such a way to induce stress, such as various ways of telling me how far I am, which also is telling me just how much it would suck if I were to fail right now.  This leads to a stress cycle, where I am noticing I am stressed, and I am aware of this being a bad thing, which makes me more stressed, over and around until I eventually fail.  This often means that I probably could've done <some new level I just unlocked> just fine, except I saw that it was new, got stressed about it and started the stress cycle.  So how can I:   Avoid getting stressed while playing Defuse the stress cycle once it has inevitably started   One thought I had for this is simply taking deep breaths, but particularly in Super Hexagon, there is no way to pause and taking deep breaths is distracting enough to make me fail.


I've installed dash-to-cock for customization my desktop. when I change the dock position to bottom or right ,the left dock still showing. what can I do?


90s teen "counter-Earth" TV show; kid goes to a parallel Earth on the other side of the sun

I remember a TV show from the 90s in which a boy from our Earth somehow ends up on a parallel Earth in a pre-industrial society. IIRC, it's a counter-Earth on the other side of the sun.  The part I remember most distinctly is that he meets a girl of a similar age, and he tried to explain a heliocentric solar system to her by rotating around her. The villagers mistake this as some kind of courtship dance and get upset.  I have a vague recollection of it being maybe a BBC or CBC production, but I'm not certain.


For example:  If there are 5 houses in the village and I passed 4 houses and now at 5th house I finally arrived to the destination. It took me how many houses to get there or after how many houses I finally found the right place I had to get to?   After 5 or after 4 houses?  Or another example to understand me:  If I am trying to find the right video or song and I watched already watched 4 videos and now I am on 5th video and that is the video I was looking for.  And someone asks me after how many videos did you find the video you were looking for? Should I say: AFTER 5 videos or AFTER 4 videos?  Or another example:  You have had 3 girlfriends in total. 2 before and now you have 3rd and she is the one you love the most. Would you say: I finally found the right one after 2 girls or 3 girls?  The question is should I count in the one which was considered the right one?


"What this thing was" vs "what was this thing"

Example:     What this new plan was I had no idea.      What was this new plan I had no idea.   What's the difference between the two? Is one more common than the others?


How to find the sum      $$\frac {1}{6} + \frac {5}{6.12} + \frac {5. 8}{6.12.18} + \frac {5.8.11}{6.12.18.24}  + \cdots.$$   I have tried to make this series in  the form $1 + n x  + \frac {n (n + 1) x^2}{2!} + \frac {n (n+1) (n+2)x^3}{3!} +  \cdots$. But I failed to do so. Can anyone please help me


Definite Integral: $\int_0^1\frac{x^{2} -1}{\log x}\,dx$

How to figure out the following integral? I have not been able to solve it from some time. $$\int_0^1\frac{x^{2} -1}{\log x}\,dx$$


If $z,s\in \mathbb{C}$ ( with norm less than $1$)  then show that $\left|\frac{1-s/z}{1/z-\overline{s}}\right|<1$. I'm hoping for an algebraic proof but possibly also a proof by geometric means if possible ( even with a picture if possible).


How can I specify the coordinates in a boxplot as black dots?

How can I specify the coordinates (here outliers) as black dots? The color in the square brackets is already defined as black, if I insert "mark=*" in the square brackets the boxplots disappear.  \documentclass{article} \usepackage[utf8]{inputenc} \usepackage{pgfplots} \usepackage{tikz} \usepgfplotslibrary{groupplots} \usepgfplotslibrary{statistics} \pgfplotsset{compat=1.3}  \begin{document} \begin{tikzpicture}    \begin{axis}     [     boxplot/draw direction=y,     xtick={1,2},     ymin={0},     ymax={890000},     ]     \addplot+[color=black,      boxplot prepared={             median=231040,             upper quartile=307800,             lower quartile=189576,             upper whisker=568892,             lower whisker=92821     },     ] coordinates {(1,790724)(1,603189)(1,574542)};      \addplot+[color=black,       boxplot prepared={       median=290626,     lower whisker=97525,     lower quartile=218151,     upper quartile=379487,     upper whisker=674757     },     ] coordinates {(3,835414)(3,752967)(3,737438)(3,737438)};   \end{axis} \end{tikzpicture} \end{document}


Is it good grammar to say or write "different to"?

To me it seems natural to say something like:   "I am different from you." or "You can't marry him, he belongs to a different species than you do."  But recently it seems to be more and more common to read or hear on TV phrases like:  "...looked very different to..."  And that really annoys me and makes me want to zap the user with a lightening bolt or something.  So is it correct grammar or bad and annoying grammar to use the phrase "different to" instead of "different from or "different than"?


Is there a way not to process "#include" directives and process only #if, #ifdef etc.?

I have a C file with some #include directives as well as #if, #ifdef, etc.  I do NOT want #include directives to be expanded with the contents of the included files.  I want #if directives and friends to be processed normally.  How to do that with GCC?  I first tried -fdirectives-only option, but it processes both #include and #if directives.  Say I have a C file like this  #include <stdio.h> #if FOO int foo() {} #else int bar() {} #endif   I want to get a preprocessed file  #include <stdio.h> int foo() {}   or   #include <stdio.h> int bar() {}   depending on you give -DFOO=1 or -DFOO=0.  However, with   gcc -E -DFOO=1 -fdirectives-only a.c    (or with any command line I tried, for that matter), I always get #include <stdio.h> part expanded into > 1000 lines.  Note that my goal here is to generate multiple source files from a single file for humans to read, for which completely expanding #include and macros is NOT what I want.


Adobe Flash plugin update needed on Linux Fedora 20?

I am little confused about whether I may or not update Adobe Flash plugin for Firefox, on a Fedora 20 machine.  Every time I try to see, let's say a YouTube video, I get a warning message about my Flash plugin being outdated and a potential danger.   My current config is  [root@localhost ~]# yum info  flash-plugin Plugin abilitati:refresh-packagekit Pacchetti installati Nome         : flash-plugin Arch         : i386 Versione     : 11.2.202.400 Rilascio     : release Dimensione   : 18 M Repo         : installed Sommario     : Adobe Flash Player 11.2 URL          : http://www.adobe.com/downloads/ Licenza      : Commercial Descrizione  : Adobe Flash Plugin 11.2.202.400 Fully Supported: Mozilla SeaMonkey 1.0+, Firefox 1.5+, Mozilla 1.7.13+   And Firefox seems to be up to date:  [root@localhost ~]# yum info firefox Plugin abilitati:refresh-packagekit Pacchetti installati Nome         : firefox Arch         : i686 Versione     : 38.0 Rilascio     : 4.fc20 Dimensione   : 115 M Repo         : installed Dal repo     : updates Sommario     : Mozilla Firefox Web browser URL          : http://www.mozilla.org/projects/firefox/ Licenza      : MPLv1.1 or GPLv2+ or LGPLv2+ Descrizione  : Mozilla Firefox è un browser web open-source, creato nel rispetto degl : standard, massimizzando performance e portabilità.   I am not sure what I am doing wrong.


Exponential generating function to find recurrence formula $a_n$

Given $a_0 = 1$ and $a_n = (n + 1)a_{n - 1} + 3^n$ for $n \geq 1$, find formula for $a_n$.   First remind the definition of power series $F(x) = \sum_{n \geq 0}f_n \frac{x^n}{n!}$ and exponential generating function $G(x) = \sum_{n \geq 0}\frac{x^n}{n!} = e^x$   Note we have to use exponential generating function to solve this question. So let $f(x) = \sum_{n \geq 0}a_n\frac{x^n}{n!}$, multiplying both sides of  $a_n = (n + 1)a_{n - 1} + 3^n$ by $\frac{x^n}{n!}$ and sum over all $n \geq 1$. We get, $$\sum_{n \geq 1}a_n\frac{x^n}{n!} = \sum_{n \geq 1}(n + 1)a_{n - 1}\frac{x^n}{n!} + \sum_{n \geq 1}3^n\frac{x^n}{n!}$$ $$\sum_{n \geq 1}a_n\frac{x^n}{n!} = \sum_{n \geq 1}na_{n - 1}\frac{x^n}{n!} + \sum_{n \geq 1}a_{n - 1}\frac{x^n}{n!} + \sum_{n \geq 0}\frac{(3x)^{n}}{n!} - 1$$ $$\underbrace{\sum_{n \geq 0}a_n\frac{x^n}{n!}}_{f(x)} - 1 = x\underbrace{\sum_{n \geq 1}a_{n - 1}\frac{x^{n-1}}{(n-1)!}}_{f(x)} + \underbrace{\sum_{n \geq 1}a_{n - 1}\frac{x^{n}}{(n)!}}_{\int{f(x)} = F(x) + C} + e^{3x} - 1$$ $$F'(x) - 1 = xF'(x) + F(x) + e^{3x} - 1   + C$$ $$F'(x)(1 - x) - F(x) = e^{3x} + C$$ I think I'm essentially stuck here, I'm trying my best to manipulate each term so that we can express each term in terms of $f(x)$. But I can't go further from here because it doesn't like look this form can lead us to the solution.   Any feedback or suggestion?


Show that the polynomial $x^2+y^2-1$ is irreducible over $\mathbb{Q}[x,y]$.    Theorem : Let $A$ an integral domain and $I$ a proper ideal of $A$. If $f(x) \not \equiv a(x)b(x) \pmod I$ for any polynomials $a(x)$, $b(x)$ $\in A[x]$ of degree $\in [1, \deg(f))$, then $f(x)$ is irreducible in $A[x]$  I think I have to use this theorem, maybe in using the ideal $(y^2)$  The fact that $\mathbb{Q}[x,y]=\mathbb{Q}[x][y]$ and $\mathbb{\mathbb{Q}[y]}$ is a unique factorization domain could it help me here? Is anyone could help me at this point?


Can I export Shotwell pictures database saving all the tags?

I've imported lots of pictures into Shotwell and spent some time setting tags. Are those tags locked-in in Shotwell or I can export them (and import again or use with other software)?


Another approach to the curvature of a unit-speed plane curve $\gamma$ at a point $\gamma (s_0)$ is to look for the ‘best approximating circle’ at this point. We can then define the curvature of $\gamma$ to be the reciprocal of the radius of this circle. Carry out this programme by showing that the centre of the circle which passes through three nearby points $\gamma (s_0)$ and $\gamma (s_0 \pm \delta_s)$ on $\gamma$ approaches the point $$\epsilon (s_0) = \gamma (s_0) + \frac{1}{\kappa_s (s_0)}n_s(s_0)$$ as $\delta_s$ tends to zero. The circle $C$ with centre $\epsilon (s_0)$ passing through $\gamma (s_0)$ is called the osculating circle to $\gamma$ at the point $\gamma (s_0)$, and $\epsilon (s_0)$ is called the centre of curvature of $\gamma$ at $\gamma (s_0)$. The radius of $C$ is $\frac{1}{|\kappa_s (s_0)|} = \frac{1}{\kappa (s_0)}$, where $\kappa$ is the curvature of $\gamma$– this is called the radius of curvature of $\gamma$ at $\gamma (s_0)$.     I have done the following:  The three points $\gamma (s_0), \gamma (s_0 + \delta_s), \gamma (s_0 - \delta_s)$ are on the circle with radius $r$ and centre $\epsilon$.  So $$r^2=\|\gamma (s_0)-\epsilon\|^2=\|\gamma (s_0 + \delta_s)-\epsilon\|^2=\|\gamma (s_0 - \delta_s)-\epsilon\|^2$$   Since we want show that the centre of the circle tends to $\epsilon (s_0)$ we do the following:   \begin{align} |\epsilon (s_0)-\epsilon| &=|\gamma (s_0) + \frac{1}{\kappa_s (s_0)}n_s(s_0)-\epsilon| \\ &\leq | \gamma (s_0) -\epsilon|+\frac{1}{|\kappa_s (s_0)|}|n_s(s_0)| \\ &=r+\frac{1}{|\kappa_s (s_0)|}|n_s(s_0)|. \end{align}   Is this correct so far? How could we continue?  EDIT:   We have that the radius of $C$ is $\frac{1}{|\kappa_s (s_0)|}$ so we get  \begin{align} |\epsilon (s_0)-\epsilon| &=|\gamma (s_0) + \frac{1}{\kappa_s (s_0)}n_s(s_0)-\epsilon| \\ &\leq | \gamma (s_0) -\epsilon|+\frac{1}{|\kappa_s (s_0)|}|n_s(s_0)| \\ &=r+\frac{1}{|\kappa_s (s_0)|}|n_s(s_0)| \\ &=\frac{1}{|\kappa_s (s_0)|}+\frac{1}{|\kappa_s (s_0)|}|n_s(s_0)| \\ &=\frac{1}{|\kappa_s (s_0)|}(1+|n_s(s_0)|) \\ &=\frac{1}{|\kappa (s_0)|}(1+|n_s(s_0)|). \end{align}   What do we get from that?


get the apache document root using shell script

I am creating an RPM and in the pre stage, I want to determine apache's document root so I can copy the web application files there.  First, I check if apache is installed. If apache is installed, the script will look for the location of httpd.conf file since it contains the document root param. But I do not know how to handle the return of the command find / -name httpd.conf. I'm just new to shell scripts and RPM. Would like also to know if this is possible. The goal to have the RPM so it can be deployed at any system, without much manual intervention. Bellow is the code I was planning. It is not yet working.  if [ "$(expr substr $(httpd -v) 17 6)" == "Apache"]; then     echo "Apache is installed";     find / -name httpd.conf     //need to handle the return of find and store to a location var to be used on the next line     grep -i 'DocumentRoot' $location/httpd.conf     //need to store the return document root to a var el     echo "Apache is not installed"; fi


Forgot username while in recovery mode (have password), what to do?

Ruined the update from 14 to 16 when I caused a freeze during the update, and now while in recovery mode, I forgot my username (I do know the password) which it keeps asking for while in safe mode. What to do besides a reformat? I can't do terminal options in recovery without first logging in, at least from what I've been able to do preboot (cannot boot UI). It's all recovery-esc fashions I'm able to do anything at all, but without my username I can't do anything (despite knowing my password 100% sure). The profile I always logged intgo was just called "D", so I'm assuming the actual name is just something I did in the beginning which I don't remember.


I looked in the online manual, but all I am trying to do for example is set (Cube 1) on layer 1 and take (Cube 2) and put that on layer two but I cannot figure out please help thank you!


Why do I keep randomly losing bits of reputation?

This is the second time this has happened.  Granted, it isn't the end of the world, but a little shocking when I find I had 1,266 rep, then a day later, 1,206.  I've checked my activity thoroughly, and not 1 action there which deducted my reputation.  anyone have an idea?


I have been trying for a while to install vlc 3.0 on ubuntu 17.10, with no luck. I even installed the snap version but it doesn't seem to play videos outside of the home folder, so I can't view videos on my other partitions.  Thing is, when I try to install vlc 3.0 from the stable PPA, I get vlc 2.2.6 instead. After adding the PPA and run sudo apt-get update, I get the following error   E: The repository 'http://ppa.launchpad.net/videolan/stable-daily/ubuntu artful Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default.   I have tried removing the PPA and adding it back but it still says the same thing. Am I missing something  EDIT: I have tried the solution from this  but I still get the release file not found error


Cannot access methods with instantiated object in chess game

#pragma once #include "SFML\Graphics.hpp"  class Tile {  public:     Tile();     sf::RectangleShape getRect() const;     sf::Vector2f getPos() const;       void highlightTile();     bool isTileHighlighted() const;     void turnOffHighlight();      void setPos(const sf::Vector2f&);     void setColor(const sf::Color&);  private:     sf::RectangleShape m_tile;     bool m_isHighlighted; };   #include "Tile.h"  Tile::Tile() : m_tile(sf::Vector2f(0, 0)), m_isHighlighted(false) { }   #pragma once #include "SFML\Graphics.hpp" #include "Windows.h" #include "Tile.h"    #include <iostream>  class Grid { public:     Grid();     Grid(float);     sf::Vector2f getCoords(int, int) const;     sf::Vector2i windowCoordsToRowCol(const sf::Vector2i&, float) const;     bool isGamePieceOnTile(const sf::RectangleShape&) const;      void drawBoard(Windows&);     void update(Windows&, const sf::Event&, float);      ~Grid(); private:     sf::Vector2f m_gridMap[8][8];     Tile m_tileSet[8][8]; };   Grid::Grid(float squareDim)  {     Tile tilePiece();     sf::Vector2f position(0, 0);     int counter = 0; //counter for whether the column is even or odd     int counter1 = 0; //counter for whether we are on an even or odd row     for (int row = 0; row < 8; row++) {         for (int column = 0; column < 8; column++) {              if (counter1 % 2 == 0 && counter % 2 == 0 || counter1 % 2 != 0 && counter % 2 != 0) {                 tilePiece.setColor(sf::Color::Red);             }             else {                 tilePiece.setColor(sf::Color::White);             }              tilePiece.setPosition(position);             m_tileSet[row][column] = new tilePiece;             m_gridMap[row][column] = sf::Vector2f(tilePiece.getPos().x + squareDim / 2, tilePiece.getPos().y + squareDim / 2);             position.x += squareDim;             counter++;         }         position.y += squareDim;         position.x = 0;         counter = 0;         counter1++;     } }   I instantiate Tile in the Grid constructor and cannot do any tilePiece.___. it says it must have class type and that error does not make sense to me...  hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh


I have a problem with installing stuff. (HP LAPTOP G62)

So this computer is a few years old and a year ago installed Ubuntu Studio. I am not currently using this computer but me and my little brother want to play a game together. The problem is I can't install anything. This problem started a few years ago. The error message looks like this.  Please help me fix this problem I don't know what to do. The output of sudo apt update is:   [sudo] password for zachary:  *there was a bunch of errors here.* Reading package lists... Done E: The repository 'cdrom://Ubuntu-Studio 19.04 _Disco Dingo_ - Release amd64 (20190416) disco Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. E: The repository 'cant add more than ten linksRelease' no longer has a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. E: The repository 'cant add more than ten links Release' no longer has a Release file N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. E: The repository 'cant add more than ten links disco-updates Release' no longer has a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. E: The repository 'cant add more than ten links Release' no longer has a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. E: The repository cant add more than ten links does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details.   And the output for cat /etc/lsb-release is   DISTRIB_ID=Ubuntu DISTRIB_RELEASE=19.04 DISTRIB_CODENAME=disco DISTRIB_DESCRIPTION="Ubuntu 19.04"


I'm attempting to recreate tiny brick imperfections similar to the Lego Movie, but I'm having a hard time finding realistic textures to accomplish this effect.    Generating a mix of noise textures and scratches comes close, but still looks a bit too artificial. Any idea what kind of texture I'd need to create/find to reproduce something like this?


Understanding /dev and its subdirs and files

$ ls -l /dev/stdin /dev/fd/0 lrwx------ 1 tim tim 64 2011-08-07 09:53 /dev/fd/0 -> /dev/pts/2 lrwxrwxrwx 1 root root 15 2011-08-06 08:14 /dev/stdin -> /proc/self/fd/0 $ ls -l /dev/pts/2 /proc/self/fd/0 crw--w---- 1 tim tty  136, 2 2011-08-07 09:54 /dev/pts/2 lrwx------ 1 tim tim     64 2011-08-07 09:54 /proc/self/fd/0 -> /dev/pts/2    I was wondering if all the files under /dev and its subdirectories are all file descriptors of devices? Why are there so many links from each other? For example, /dev/fd/0, /dev/stdin, /proc/self/fd/0 are all links to /dev/pts/2. If l in lrwx------ mean link, what does c in crw--w---- mean?


I have a machine without dconf-tools installed.  It also does not have internet access, and can not be made to have it.  I have to disable auto opening of nautilus windows on device mount. There are instructions at . This requires editing some dconf keys.  How can I edit these keys without dconf-tools, and without installing anything else? Are they in the file system somewhere?


Is there a known problem with ESTA form online?passport validity?

I have a passport which was issued on Oct 26, 2011 and expires on Jul 26, 2022. Therefore it is valid for 10 years and 9 months.  I am applying for an ESTA, but the website won't let me progress as it states:   "Passport Issuance Date more than 11 years from the Passport Expire Date."  Is this a known problem?


Is there an all-day metro pass in London?  For example in Tokyo, Japan there's an  and there's  in Cologne, Germany.  Does London also have something similar? I have heard of Oyster, but it's pay as you go, and usually those all-day or all-month passes have greater value. I will be traveling extensively by metro and tram and perhaps also buses.


HA configuration for KVM Guest on iSCSI shared storage

My requirement is to provide HA to a Zimbra Server. We want Zimbra files to be installed in a Netapp SAN which is providing around 5.7 TB as a SAN iSCI Drive. Since Netapp comes in with Dual Controller and stable performance, we are unlikely to have any down time.  I have 2 servers each having Xeon processor 6 Core, 32 GB RAM and 2 x 250 GB SSD. These are the two servers where I have installed CentOS 7.6. We would like to have one as primary and the second one as secondary.  Idea is to use the same principle of KVM HA ( What Redhat and even VMware) provides, so that if the primary goes down the IP gets switched to secondary, to create a simple Hot Redudant system.  We have a very few users on Zimbra, but there are a lot of automated emails coming in and we require a very large storage, and hence we are using the Netapp box.  I am able to switch between the KVMs. However I am struggling to figure out how I need to mount the iSCI target, so that the mail application stays alive.  Zimbra typically installs on /opt/. Do I mount the target on /opt/, and if so will it work? Or am I missing something else?  Or should I run the VM of the shared storage itself, and if so how can I configure it.  Zimbra itself is a combination of a database and files, and uses a number of services to keep itself active. Idea of using a shared storage is for Redundancy and high availability.  I have tried to configure HA but i was stuck over STONITH fence_agents.  By the way i followed this Documentation-    Appreciate your response and support.


Which one is correct or are both correct?     The boy's name is nice.   The name of the boy is nice.     I'm really confused these two sentences?  Which one is more suitable?


Splitting the digits of an integer into groups of 1, 2, 3 etc. digits

I want to write a program to split an integer's digits into groups of n digits, assuming that the number of digits is divisible by n.  For example, say I had the integer 123456789, and n=3, this would produce the list:  [123, 456, 789]   Or if the number was 12345678, and n=2, I would want the list:  [12, 34, 56, 78]   So the order of the digits remains the same. It is okay if the numbers in the list are strings, as this is easy to change.   EDIT: I apologise it seems that this question has already been asked. I shall look there for answers. Thank you to those who answered.


Presentation $\langle x,y,z\mid xyx^{-1}y^{-2},yzy^{-1}z^{-2},zxz^{-1}x^{-2}\rangle$ of group equal to trivial group

Problem: Show that the group given by the presentation $$\langle x,y,z  \mid xyx^{-1}y^{-2}\, , \, yzy^{-1}z^{-2}\, , \, zxz^{-1}x^{-2} \rangle $$ is equivalent to the trivial group.   I have tried all sorts of manners to try to show that the relations given by the presentation above imply that $x=y=z=e$. However, I am stuck and would appreciate any hints as to how I should move forward.


I would like to get the probability distribution (either pdf or cdf) for a variable, by knowing the first n-moments of the distribution. I ask:   Is there a standard way to deal with this, and maybe a python package? It is a matter of inverting the moment generating function or the characteristic function, that are expressed as series of moments. Is it legit to truncate these series to the first n-moments? When yes and when not? What if I don't know the exact moments, but I rather estimate them from data? Does the inversion process above work well with noisy data?


Finding the Transform matrix from 4 projected points (with Javascript)

I'm working on a project using Chrome - JS and Webkit 3D CSS3 transform matrix. The final goal is to create a tool for artistic projects using projectors and animation - somewhat far away from using maths... I'm using a projector to project several squares over several shapes - as seen in the picture. What I would like to do is for the user to draw 4 points on the screen (2D x and y) and from there extract a matrix object that I could apply to a regular DIV element of a dimension of 100px by 100px. By finding scaleX, scaleY, rotation, rotationX, rotationZ and probably some perspective that I could apply to the div to relatively match the surface. I'm not really familiar with geometry beyond sin and cos, and 3D in general and don't even know if that is something doable. If anyone could help me get started or point me in the right direction, I would greatly appreciate. Here is an animated gif (click to enlarge), hoping it makes it more clear to understand.


Fitting a model to a variable with many zeros and few but large values in right tail

I would like to fit a model to a dependent variable distributed like the one below (see picture).    The distribution is a count of people (with specific characteristics) in various districts. This means that, there are no negative numbers; in the great majority of districts the variable is 0, but there also exists very large numbers (up to 80,000) with very low frequency.  Following Moti Nisenson's advice, I edit some graphs into this post that make the distribution clearer. If I drop all 0, the graph looks the same because there are a lot of 1's, 2's, etc.  If I drop all < 100, it looks like this:    If I drop all < 1000, it looks like this:     If I drop all < 5000 it looks like this:     My goal is to find a regression that does well in predicting the zeros and, more importantly, the extreme values in the right tail of the distribution.  I understand that Ordinary Least Squared is not ideal here. I have looked into Poisson regressions which seem to be a great deal more adequate for my purposes.   Is there any regression model that is even more appropriate? Which else options might be helpful?  Additional edit: These are the summary stats. The Variance is much (much) higher than the mean which according to  is a sign that Poisson is not appropriate.   Additional edit 2: Here is the distribution of the variable in log as requested.


black border around screen ati radeon hd 4550 graphic card on hdmi on windows 7 32bit

I have bought a LG monitor 22 inch when I connect my PC buy HDMI cable to it there is a black border around the screen like this :    my graphic card model is ATI hd 4550 .I have with her searched  for this problem and I found there were same problem for other peoples and in the solution I installed AMD Catalyst Control Center (in some of theme there was this name : ATI Catalyst Control Center) But In their solution this software is like this :   But when I run  AMD Catalyst Control Center in my pc scaling options is missing like this :     how can I fix it ?


How can I move an object towards another along a straight line

How can I move an object (like a cube) towards another object?  Let's say that we have a red cube in the center of a floor, and a blue cube in another location, there aren't objects between this two, so the movement is along a line.  How can I move the blue cube towards the red one?


I cannot reset my Security Token in Sandbox Org. The "Reset My Security Token" button in the My Settings, Personal tab doesn't appear. Any idea?


I currently have a cron job running every minute on my server, and I can do that without problem:  * * * * *   But how would I run two different files on alternate minutes?  So file '1.php' on even minutes, and '2.php' on odd minutes?  so...   00:00 - run 1.php 00:01 - run 2.php 00:02 - run 1.php 00:03 - run 2.php 00:04 - run 1.php   etc!


Probability of two uniform random numbers being more than $\frac{1}{2}$ apart

Two numbers are chosen randomly and independently from the unit interval $(0,1)$.  What is the probability that they differ by more than $\frac{1}{2}$? Hint: Think of the $2$ numbers chosen as coordinates in the Cartesian plane. Draw a square with vertices at $(0,0)$,$(1,0)$,$(1,1)$, and $(0,1)$. Allowable choices for the $2$ points lie below the line $y=x-\frac{1}{2}$ or the above $y=x+\frac{1}{2}$. Find the combined area of these regions.  I need help on this. I know what $y=x-\frac{1}{2}$ and $y=x+\frac{1}{2}$ looks like but I am not understanding the problem as a whole


This might be a stupid question but is there a way to update records (yes many records and duplicate ones) in a DE without a primary key? I am not the owner of the DE which is already structured for several years so I cannot change its fields.  Thanks.


Who gets the broccoli stick? Random walk in a circle.

Suppose we have $n+1$ people in a circle ${0,1,2,3....n}$, we pass around a broccoli stick. The person $k$ has probability $p$ to pass the stick to $k+1$ and probability $q = 1-p$ to pass it to the $k-1$ person. And $p>0.5>q$.   NOTE: THIS IS NOT A SYMMETRIC WALK!   One wins if he is the last person remaining that has not touched the stick.  Where should a person situate to get the best possibility of winning?  I Want to calculate P(person i-1) gets the stick, passes it to i+1 without going through i. And P(person i+1) gets stick, passes it to i-1 without going through i, then condition.


What is the correct way to install Adwaita theme on Ubuntu 12.04?

I want to have Adwaita theme on Ubuntu 12.04. On my previous installation I had it in unity right after installing gnome3 shell. Gtk2 apps didn't have tabs like what it would be expected on Gtk3 and they were ugly. For example Gedit had Adwaita tabs, but Firefox settings page didn't.  Now, I have a new installation of Ubuntu 12.04, and I want to have Adwaita theme. What is the correct way to install Adwaita theme so that those problems won't occur?  Thanks in advance


GR was formulated before atomic clocks and radio signals between earth and space probes allowed actual measurements to be made.   Atomic clocks count a beat frequency, but the frequency of emitted photons is actually a measure of the energy levels within an atom. As an atomic clock is lowered doing work, its slowed rate is proof that the energy to do that work came from the energy $E = mc^2$ of its matter. This leads to a simple differential equation $c^2 dm = m d\Phi$ with solution $m = m_0 e^{\Phi/c^2}$  Thus gravitational potential has a physical effect on matter and by consideration of the effect on the time delay on radio signals deduce that the lengths of rulers and the rate of clocks are affected by factors of $e^{\Phi/c^2}.$  GR coincides with this in the weak field approximation which equates to the first two terms of the exponential series. Correcting our understanding of gravity by replacing the weak field approximation with exponential function, we avoid the concepts of event horizons and singularities.  So bearing the above in mind, are black holes hiding behind even horizons, or is their light simply red shifted too far to detect?


When Sauron saw Frodo at Mount Doom, why doesn't he do anything?

In the film (3.15), the Eye of Sauron sees Frodo on the corner of Mount Doom.  Maybe he didn't think that they are the ones trying to destroy the ring, but at least he sees someone who is a stranger in his land.  Shouldn't he react this situation in some way?  Edit: I am talking about this scene:


I want to create a block in every frame like this     Because I don't like to use classical blocks like this  Could you please give me the necessary code ? Thank you


I'm trying to remember a novel I read in the late 1980s or early 1990s. Earth has been taken over by a robotic culture that has destroyed almost everything animal, vegetable, or human. A small number of humans survive like vermin in the corners, sneaking food, tools, and other supplies out of the factories. The different parts of the robotic culture are not completely unified into a single planetary mind. One faction has been experimenting with humans and has joined together some number (5? 8?) of humans at the temples. This "human starfish" can think as a single entity to some degree, and floats in a sort of amniotic tank in the robot's laboratory.


A limit about the greatest integer function

Let $[x]$ be the greatest integer function. How to find  $\displaystyle\lim_{n\to\infty}\frac{1}{n}\sum_{k=1}^{n}\left(\left[\frac{2n}{k}\right]-2\left[\frac{n}{k}\right]\right)$?


Difference between $dM/dt $ and $\partial M/\partial t$

$\frac{dM}{dt} = 0$ represents a constant of motion $M.$ Why not $\frac{\partial M}{\partial t}$ represent a constant of motion $M$?


Getting PCA eigenvectors with the values of opposite sign

I am performing a PCA analysis in Matlab on a $110\times 7$ dataset using some custom code. I am checking my code against Matlab's princomp and my eigenvectors are the same except that the 3rd and the 7th column are of the opposite sign.   What does that mean? And why does this happen?  My code is:   mu = mean(data); data = bsxfun(@minus,data,mu); sigma = transpose(data) * data / size(data, 1); [eigenvectors, eigenvalues]=eig(sigma); eigenvalues=diag(eigenvalues) [ev index]=sort(eigenvalues,'descend'); eigenvectors=eigenvectors(:,index); pc = data*eigenvectors';


Can $p ∧ q$, where $p$ and $q$ are propositional variables, be a proposition?

Edit: I have removed the original text in favor of showing the specific passages in the book that I am stuck on. Sorry about the inconvenience. I am wondering whether $p ∧ q$ can be a proposition when $p$ and $q$ are both propositional variables. It seems to me that my book in one case says that a proposition can't have a variable truth value and then states that $p ∧ q$ is a proposition, even though it surely also has a variable truth value. Page 2:  Consider the following sentences.  What time is it? Read this carefully. $x + 1 = 2$ $x + y = z$  Sentences 1 and 2 are not propositions because they are not declarative sentences. Sentences 3 and 4 are not propositions because they are neither true nor false. Note that each of sentences 3 and 4 can be turned into a proposition if we assign values to the variables.  Page 26:  Note that we will use the term "compound proposition" to refer to an expression formed from propositional variables using logical operators, such as $p ∧ q$.  Rosen, K. H. (2019). Discrete Mathematics and Its Applications Eighth Edition. New York, NY: McGraw-Hill Education. Couldn't we have stated the following? "$p ∧ q$ is not a proposition because it is neither true nor false. Note that it could be turned into a proposition if we assign values to the variables $p$ and $q$."


Selectively disable iCloud keychain syncing for WiFi passwords

I have iCloud Keychain sync enabled, but I want to stop it syncing WiFi passwords.  I have a portable WiFi hotspot which I use for my laptop and iPad, but I don't want my iPhone to connect to it since it has it's own 3G  Because iCloud is syncing the settings, within about 30 seconds of connecting my laptop to the 3G hotspot, my iPhone will connect itself. If I go into wifi settings on the iPhone and manually disconnect, about 30 seconds later my laptop will disconnect too. It seems with iCloud wifi sync on, I can’t connect my laptop to WiFi without my phone also connecting.  The only way to get around it seems to be disabling Keychain sync in iCloud. I’ve tried Googling, but got no real help on how to disable it without turning off Keychain, which is what I’ve done at the moment.  I also don't want to enable 'Ask before joining networks' on my iPhone, since I'll be manually re-connecting it constantly.


Getting wrong date '01:00:00' when using SimpleDateFormat.parse()

I got wrong result when using SimpleDateFormat.parse(). Code here:  public static void main(String[] args) throws ParseException {         String format = "yyyyMMdd";         String date = "19890416";         SimpleDateFormat simpleDateFormat = new SimpleDateFormat(format);         java.util.Date date2 = simpleDateFormat.parse(date);         System.out.println("date2 = " + date2);         System.out.println("Locale.getDefault() = " + Locale.getDefault()); }   result:  date2 = Sun Apr 16 01:00:00 CDT 1989 Locale.getDefault() = zh_CN   there is my question: why in the result it shows up 01:00:00, instead of 00:00:00?  What should I do if I want 00:00:00?  Anyone can help? Thanks!  Update: I want to know, when define format as "yyyyMMdd", why the default hour shows up "01", thanks.


Ideal class group of $\mathbb{Q} ( \sqrt{-23} ) $ is $\cong \mathbb{Z}/3$ by Minkowski bound.

I am trying to show the above result. First, I compute that the Minkowski bound must be strictly lower than 4. Therefore, for every ideal class, there is a representative, so that its norm is at most 3. Now every ideal $a$ can be decomposed into prime ideals $p_1, \ldots, p_k$. Noting that every rational prime $p$ is contained in some $p_i$, so $N(p_i)$ is a power of $p$. Now $N(a) = N(p_1) \ldots N(p_k) \leq 3$. Therefore $p \leq 3$. Next I would try to decompose (2) and (3) and look at their factors to get the result. My problem actually is to decompose them into prime ideals. How do I do that?


Find lost device without Gmail account configured and without SIM card

I recently misplaced a phone that did not have gmail account configured and did not have a SIM card in it either. Is there any way I can track it ?   All of the tracking apps either require sending an SMS (needs SIM card) or OTA install(needs Gmail account).   I do have the IMEI number of the phone.


In Java critical sections, what should I synchronize on?

In Java, the idiomatic way to declare critical sections in the code is the following:  private void doSomething() {   // thread-safe code   synchronized(this) {     // thread-unsafe code   }   // thread-safe code }   Almost all blocks synchronize on  this, but is there a particular reason for this? Are there other possibilities? Are there any best practices on what object to synchronize on? (such as private instances of Object?)


Are there fields that are not algebraically closed fields but such that any quadratic polynomial has a root?  Suppose now $n$ is a fixed natural number, $n\geq 2$. Is there a field $K_n$ such that every polinomial of degree $\leq n$ with coefficients in $K_n$ has a root in $K_n$, but $K_n$ is not algebraically closed?     I was thinking that perhaps a tower of algebraic extensions of $\mathbb{Q}$ might work, but then I realized that in order to be "quadratically closed" I might have to close under all extensions of degree $2^k$ for some $k$.   Is $K_2=\bigcup \left\{\mathbb{Q}[\alpha]: [\mathbb{Q}(\alpha):\mathbb{Q}]=2^k\text{  for some $k$}\right\}$ going to work as a field that is quadratically closed but not algebraically closed?


Bioinformatician here. I'm wondering what the main differences between both of these approaches is. I just want to clarify that a formal mathematical treatment would likely be too much for me.   From what I can tell, a GLM does not assume a normal distribution of response variables. Am I to infer that an LM does? What other important differences are there? If the distribution is normal, would an LM and GLM give the same results? I don't know enough to ask any more questions but would welcome any other details you think are important.


Possible Duplicate:          I want a shell script method to test/report if a package is installed. I don't need details, only a yes/no.  I've come up with this method. Is there a more direct way?  is_installed=0 test_installed=( `apt-cache policy domy-ce | grep Installed: ` ) [ ! "${test_installed[1]}" == "(none)" ] && is_installed=1


I have the following Json structure on my project:  "disputas": [     {       id: "",       tipo_negociacao: "",       historico:[{          fl_usuario: "",          created_at: "",          updated_at: "",          created_by: null,          updated_by: null,          texto: "",       }]     } ]   I want to add a new index of historico when I click on a button but don't know how to do it, I want it to look like this:   "disputas": [         {           id: "",           tipo_negociacao: "",           historico:[{              fl_usuario: "",              created_at: "",              updated_at: "",              created_by: null,              updated_by: null,              texto: "",           },            {              fl_usuario: "",              created_at: "",              updated_at: "",              created_by: null,              updated_by: null,              texto: "",           }         ]     } ]   So far, I've done something like this (function that the button calls):       recusaProposta() {         this.disputa.historico[this.i].texto = "something";            this.i++; }   now, since i starts on 0 this works on the first time I click on the button, but if I click on it again I'll get this error:     Cannot set property 'texto' of undefined   Can someone help me? thanks


Every positive integer can be expressed uniquely as $N = a_0 + a_1 2 + a_n 2^n $ and all $ a_i $ belongs to $\{0, 1\}$

I am trying assignment problems of an Institute in which I don't study. I am unable to think about this problem.      Problem ->Prove that every positive integer can be expressed uniquely as $N = a_0 + a_1 2 + a_n 2^n $ and all $ a_i $ belongs to $\{0, 1\}$.    Can someone please help.


The wiki article on the Hubble volume says that the Hubble volume is often confused with the limit of the observable universe. This thread:  seems somewhat inclusive and is related, but not identical. Is it possible for us to see beyond the Hubble sphere? I would think it isn't because it makes no sense if you think about seeing something which is receding faster than light. I think that light from us will never reach the body, and hence will never reflect off the body to come back to us. But apparently it works somehow.  My focus is upon the counter-intuitive nature of the Hubble Volume's definition, rather than the actual equations which describe the furthest point identifiable.


Let A be $3\times3$ matrix such that $Au$ and $u$ are orthogonal for each column vector $u\in\Bbb R^3$. Prove that $A^T=-A$. I thought  $(A+A^T)u\cdot u=0$ but it doesn't imply $A^T=-A$, so I'm stuck... Edit : Does this property also hold when we replace 3 by an arbitrary $n$?


I have a select option which is working perfectly but only one time, the request does not executes again.  I think it's because of the 'onchange' event.  This is my ajax code :  jQuery(document).ready(function($) { $('#referenceProduit').change(function(){     //on recupere la valeur de l'attribut value pour afficher tel ou tel resultat     var req=$('#referenceProduit').val();     //requête ajax, appel du fichier function.php     $.ajax({         type: "POST",         url: "include/php.php",         data: "referenceProduit="+req,         dataType : "json",         //affichage de l'erreur en cas de problème         error: function(XMLHttpRequest, textStatus, errorThrown) {             alert(XMLHttpRequest + '--' + textStatus + '--' + errorThrown);         },         //function s'il n'y a pas de probleme         success:function(data){             //On affiche la réponse du serveur             $('.produit').empty();             $('.produit').prepend(data.produit);             $('input[name="designation"]').val(data.resDisplayForm.designation);             $('input[name="prix"]').val(data.resDisplayForm.prix);         }     }); }); });    HTML code :
   Reference
     <select class="form-control" name="referenceProduit" id="referenceProduit">       <option selected="selected" disabled="disabled">Choisir</option>       <?php foreach($lesProduits as $unProduit){?>       <option name="<?php echo $unProduit['id'];?>" value="<?php echo $unProduit['id'];?>"><?php echo $unProduit['reference']?></option>       <?php } ?>     </select>


This question might have been answered somewhere but have not been able to find it. So, I have a Mid-2009 MacBook Pro where I am still running OS X Yosemite since I forgot to update to OS X El Capitan when it was on the App Store before they changed it to macOS Sierra.  If I try to install macOS Sierra through the App Store it doesn't let me because it says that:  "This version of macOS 10.12 cannot be installed on this computer."    I started looking to see if I can find OS X El Capitan but there is no result through the Mac App Store nor Apple Developers site. So my last resort was through Google, where I found several options on where to download OS X El Capitan version 10.11.  So, my main question is if I download from these third party websites, can I install on top of my current OS like it is done through the App Store or do I have to do a clean install?  Would appreciate any help.


I'm trying to do a comparison in Java with 2 strings containing a extended ASCII character.  boolean result = "éasdfasdf".substring(0,1).equals("é");   Can somebody explain why this results false? I think it has something to do with character encoding, but I can't figure out what exactly the problem is here...  Update: ideone.com does successfully run these 2 lines, so the problem is locally in my box. I think I found some more proof of that:  System.out.println("éb".charAt(1) == 'b');   Does also fails... Can it be the problem of 2 different character encodings?


Windows 10 Start Button Repeatedly Becomes Non-Responsive

I found a fix for reinstalling the Start Button and all its features when it becomes non-responsive i.e. nothing happens when pushed on the keyboard or clicked on.    However, this non-response has recurred many times so I have had to apply the above fix multiple times as well i.e. the fix seems to be only temporary. Does anyone know what in my system might be causing this to happen?


Proving linear bijection of vector space mapping.

As the title states above, I am trying to show that if $T : U \rightarrow V $ is a linear bijection, then $T^{-1} : V \rightarrow U$ is also a linear bijection where U and V are vector spaces.   Representing $U = \lbrace u_1, u_2, u_3...,u_n \rbrace $ and $V = \lbrace v_1, v_2, v_3,....,v_n\rbrace$ for some $n \in \mathbb N$, I understand that the bijectivity of T means that each vector in $U$ will map onto only one vector of $V$ (as the assumption suggests). However I do not how I can translate this knowledge to $T^{-1}$.   Thank you in advance (I am new to proofs).


Rounding a variable to two decimal places C#

I am interested in how to round variables to two decimal places. In the example below, the bonus is usually a number with four decimal places. Is there any way to ensure the pay variable is always rounded to two decimal places?    pay = 200 + bonus;   Console.WriteLine(pay);


Illustrator CS6: Change artboard size / final saved file dimensions to match bounds of content

Consider the following two images:    The second image is my desired result: the artboard dimensions perfectly match the layer/selection/content. However, I had to resize the artboard manually. Is there a way to do this automatically? Ultimately I'm saving the file as an SVG. Rather than resizing the artboard, is there some setting that tells illustrator to export a file with the final dimensions being the size of the content or selection? Some googling suggests that this was possible in CS3 using Save for Web, but I didn't see any option like this in CS6.


How can I own an IP address like I do with domains?  I have done some research and it seems that you can't buy a single IP, but rather you have to purchase a range of IP addresses.  Update : Important Note I want this IP to use it with my servers. for example I had a VPS, it went bad, I want to be able to use the same IP on another VPS from another company.


How are simultaneously-triggered Readied actions resolved?

Concerning the following scenario:   On her turn of the combat round, Alice readies an action to attack Bob as soon as he's within her weapon's reach. On his subsequent turn in the same round, Bob readies an action to attack Alice as soon as she's within his weapons's reach, and moves adjacent to Alice.   In what order are Alice and Bob's attacks resolved?