I've been trying for a couple of hours to find a way to prove the next claim:  $$\gcd(n-1,a) = \gcd(\frac{(n^a-1)}{n-1},n-1)$$  I have already proven that  $$\frac{(n^a-1)}{n-1}$$ is always divisible by $(a-1)$.  which means I can set define  $$\frac{(n^a-1)}{n-1}=\frac{c(n-1)}{n-1}=c$$  then I get :    $$  \gcd(n-1,a)=\gcd(c,n-1)$$  but that's it, I'm stuck.

How to show that     $$ \gcd\bigg( {a^n-b^n \over a-b} ,a-b\bigg )=\gcd(n d^{n-1},a-b ) $$    $a,b\in \mathbb Z$   where $d=\gcd(a,b)$?    Note $\ $ Some of the answers below were merged from . The answers (and their comments) may depend on context provided in that question.


I know how to write down the local ordinary differential equation (ODE) via Newton's force law, balancing between the left and right rope tension and the gravity exerted on a infinitesimal piece of rope. The solution is  which has the form $$ y (x)= a \cosh \left(\frac{x}{a} \right) = \frac{a}{2}\left(e^\frac{x}{a} + e^{-\frac{x}{a}}\right) $$ with appropriate boundary conditions. But I only aware the way to solve from ODE. Could we solve the hanging rope shape using the variational principle? This means that we input the shape of the rope minimize the potential energy $V$ (because there is no kinetic $T$) for lagrangian $L= T-V$ (question 1: but this seems maximize the $L$ strangely?). Suppose the length of the role is fixed say $\ell$. The two hanging points out horizontal apart at $x=-l$ and $x=l$. Then we have a constraint on the length of the role is fixed say $\ell$. Then we have a constraint $$ \ell = \int_{-l}^l \sqrt{1 + y'(x)^2} dx   $$ Then we minimize potential energy $V$ (but this maximizes the lagrangian $L$ strangely?) $$ V= \rho g \int_{-l}^l y(x) \sqrt{1 + y'(x)^2} dx   $$ with $ \rho$ the constant density and gravity constant $g$. I suppose we are solving the eq of motion from Variational Principle with a Constraint like $$\boxed{ V - \lambda(\ell - \int_{-l}^l \sqrt{1 + y'(x)^2} dx )= \rho g \int_{-l}^l y(x) \sqrt{1 + y'(x)^2} dx   - \lambda(\ell - \int_{-l}^l \sqrt{1 + y'(x)^2} dx )} $$ How do we obtain $y(x)$ then by minimization or maximization ? See these two related questions show no answers (!!!):

The height of a string in a gravitational field in 2-dimensions is bounded by $h(x_0)=h(x_l)=0$ (nails in the wall)  and also $\int_0^l ds= l$. ($h(0)=h(l)=0$, if you take $h$ as a function of arc length) .  What shape does it take?  My try so far: minimise potential energy of the whole string,  $$J(x,h, \dot{h})=\int_0^l gh(x) \rho \frac{ds}{l}=\frac{g \rho }{l}\int_0^l h(x) \sqrt{1+\dot{h}^2} dx$$  With the constraint  $$\int_0^l \sqrt{1+\dot{h}^2} dx- l=0$$ If it helps, it's evident that $\dot{h}(\frac{l}{2})=0$.  Generally, this kind of equation is a case of a constrained variational problem, meaning that the integrand in  $$\int_0^l \frac{g \rho }{l}h(x) \sqrt{1+\dot{h}^2} +\lambda(\int_0^l \sqrt{1+\dot{h}^2} dx- l)dx$$  Must satisfy the Euler Lagrange equation. The constraint must also be satisfied.  But, in truth, by this point I am clueless. $\lambda$ is worked through $\nabla J  = \lambda \nabla(\int_0^l \sqrt{1+\dot{h}^2} dx- l)$. I have tried this , but get nonsensical answers.  Is this method the best? If so, in what ways am I going about it wrongly thusfar?


I was trying to use a curve modifier on some text. Everything works fine until I try to apply the modifier. I'm not sure whether I'm doing something wrong. Can someone be kind enough and give it a quick look please.

Is is possible to remove the curves and only have the mesh of a tree that was created with the saplings add-on?   I'd like to apply a decimate modifier to have a few low-poly trees, but this doesn't work because of the curves. I get this message: "Cannot apply constructive modifiers on a curve."


using System.Collections; using System.Collections.Generic; using UnityEngine; using UnityEngine.UI; using UnityEngine.SceneManagement; using System.Threading;   //Top of the script #pragma warning disable 0649  public class Player : MonoBehaviour {      // Initialize variables.     private Rigidbody rb;     private bool isMovingRight = false;     private bool hasPlayerStarted = false;     public float speed;     public float maxspeed;            [HideInInspector]     private bool canMove = true;      [SerializeField]     GameObject particle;          [SerializeField]     GameObject gems;      [SerializeField]     private Text scoreText;     private int score = 0;      public Text ScoreText { get => ScoreText1; set => ScoreText1 = value; }     public bool CanMove { get => CanMove1; set => CanMove1 = value; }     public bool CanMove1 { get => canMove; set => canMove = value; }     public Text ScoreText1 { get => scoreText; set => scoreText = value; }          // Use this for initialization     void Start () {         rb = this.GetComponent<Rigidbody> ();     }      // Update is called once per frame     void Update () {         if (Input.GetMouseButtonDown (0) && CanMove1 == true) {              // If the game hasen't started yet.             if (hasPlayerStarted == false) {                 hasPlayerStarted = true;                 StartCoroutine (ShowGems (2.5f));             }                              ChangeBoolean ();             ChangeDirection ();         }          if (Physics.Raycast (this.transform.position, Vector3.down * 2) == false) {             FallDown ();         }          // increase speed         if (speed < maxspeed)             speed += 0.1f * Time.deltaTime;      }        // Hide the gems for the first 2.5 seconds (avoiding bugs).     IEnumerator ShowGems (float count) {         yield return new WaitForSeconds (count);          // Checks if player hasn't fallen off before showing grms.         if (CanMove1 == true) {             gems.SetActive (true);         }     }               // Control player direction.     private void ChangeBoolean() {         isMovingRight = !isMovingRight;     }     private void ChangeDirection() {         if (isMovingRight == true) {             rb.velocity = new Vector3 (speed, 0f, 0f);         }          else {             rb.velocity = new Vector3 (0f,0f,speed);         }     }       // When the player falls off the platform.     private void FallDown() {         CanMove1 = false;         rb.velocity = new Vector3 (0f,-4f,0f);                         // Return to main menu.         StartCoroutine (ReturnToMainMenu (1.8f));                }      // Return to main menu.     IEnumerator ReturnToMainMenu (float count) {         yield return new WaitForSeconds (count);         SceneManager.LoadScene(0);               }       // When the player hits a gem.     void OnTriggerEnter(Collider other) {         if (other.gameObject.tag == "Gem") {              // Remove the gem.             Destroy (other.gameObject);                      // Create the particle effect.             GameObject _particle = Instantiate (particle) as GameObject;             _particle.transform.position = this.transform.position;             Destroy (_particle, 1f);              // Update the score.             score++;             ScoreText1.text = "Score: " + score.ToString();         }     } }

I wanted to add a high score to my game but I don't know how I already tried to find some videos for it but I just can't find the right one. I already have a scoreUI on my game I just wanted to add a high score.  Here is my UIManager's script which consists of different functions including the score system.  using System.Collections; using System.Collections.Generic; using UnityEngine; using UnityEngine.UI; using UnityEngine.SceneManagement;  public class uiManager : MonoBehaviour {  public Button[] buttons; public Text scoreText; int score; bool gameOver;  // Use this for initialization void Start () {     gameOver = false;     score = 0;     InvokeRepeating("scoreUpdate", 0.5f, 0.25f); }  // Update is called once per frame void Update () {     scoreText.text = "" + score; }  void scoreUpdate(){     if (gameOver == false) {         score += 1;     }   } public void gameOverActivated(){     gameOver = true;     foreach(Button button in buttons) {         button.gameObject.SetActive(true);     } }  public void Play() {     SceneManager.LoadScene("level1"); }  public void Menu(){     SceneManager.LoadScene("Menu"); }  public void Retry() {     SceneManager.LoadScene(SceneManager.GetActiveScene().name); }  public void Pause() {      if (Time.timeScale == 1) {         Time.timeScale = 0;     }     else if (Time.timeScale == 0) {         Time.timeScale = 1;     } } }   I got the score system from Charger Games. Here is the link to the   and here is what my game looks like


Here is the problem, today i started updating my ubuntu 16.04 laptop, to my surprise i got some packages that are marked as "Kept back", here are these packages   compiz compiz-core compiz-gnome compiz-plugins-default libcompizconfig0  libdecoration0   After some googling i tried to run sudo apt-get dist-upgrade i got some info on the kept back packages, like how many are there, how much memory will they use, the standard stuff and after that, the surprise i got   The following packages will be REMOVED:  ubuntu-desktop unity unity-tweak-tool   is this normal? i mean uninstall ubuntu-desktop unity ??? wont that uninstall my DE ???

This  forced removal of unity and ubuntu-desktop on my 16.04 Ubuntu system.   The offending package that is missing, but unity needs, seems to be compiz-core-abiversion-20151010. It seems to be a , and I can't find it to download.    As it happens, I mostly use LXDE on this system, but I'd be very unhappy if I used Unity...  Since I do occasionally use the Unity desktop, is there a fix for this?  Edit: related questions are rolling in. Looks like a major quality escape          Edit 2:


I want to root my android device but I have a lot of personal data stored in it. It also doesn't have a micro sd card slot. So I was wondering if there is any way to root my device without losing any data and without using a PC?

I know I'm asking for the close-to-impossible -- as a real full-backup certainly requires root permissions. But still there are many folks around not wanting to root their devices -- afraid of voiding their warranties or bricking their devices, or just not having their devices supported by any rooting method.  I also know there were a lot of questions asked already on this topic, and I checked all of them having the backup tag -- none covers the entire topic, all just have pieces, and especially people new to Android (but other non-power-users as well) would have a hard time figuring out the best way.  So I want a detailed canonical answer to the question:  Not involving root-solutions, how to achieve a backup as close as possible to a full backup?  Please do not give simple one-liner answers like "Use app xyz [full-stop]." If mentioning an app (and I doubt a single app would be the answer here), include what parts are covered by it -- as well as ideas on how to fill the gaps it leaves. (And to make it absolutely clear: I know the first thing coming to mind is Titanium Backup -- I use it myself, but this does not apply here: This question is strictly about methods for non-rooted devices!) Moreover, the answer should be as generic as possible in terms of applying to a wide range of devices (i.e. it should not be restricted to one device or manufacturer).  I already mentioned having investigated all questions here tagged backup. These will certainly be helpful providing details for answers here, so I will list up the topmost ones concerning my question:            All these provide some details for my question (so feel free to get inspired by them) -- but I feel there are still details missing. Also it would be helpful to have a summary -- say, an answer including the full description of "the maximum possible".  A last criterium: While I'd consider cloud-based solutions legit, I'd favour local solutions. If you can provide both: all the better. But some people value privacy quite high (I'm one of them), and thus would not trust their data to some cloud service.    Thanks to Ryan, we now have a solution for a really complete backup of all apps and their data -- which I didn't dare to hope for! The only disadvantage: His solution only works for less than 10% of all Android users; namely those whose devices are running at least with Android 4.x.  So again, I ask the close-to-impossible: Any solutions applicable at least on Gingerbread (2.3.x) or, better, even Froyo (2.2.x) -- so they cover the majority of current devices? These solutions may involve multiple tools (try to keep it as simple as possible though; think of your mother to follow your instructions ;)  And keep in mind: NO ROOT!    To further motivate high-quality answers (and hopefully avoid low-quality ones), I will be a harsh one here: As I rarely do, I will down-vote answers not fitting the mentioned criteria on one end -- but on the other end, I will setup a bounty for the best answer (which cannot be done immediately, but earliest after 2 days).


Edit for clarity- The bulbs are not flickering or flashing. They periodically (> 10 minute intervals) turn off and then on in unison.  I have a chandelier with 5 bulbs. I recently replaced all 5 60w incandescent bulbs with 40w equivalent Philips LEDs. The chandelier is on a dimmer.  The bulbs work fine but after about 10 or 15 minutes, all 5 bulbs blink once at the same time. Then there will be another long pause and it will happen again. Rinse. Repeat.  I thought it might be the dimmer which is about 25 years old so I replaced it with a new Leviton slider dimmer(LED compatible). The same thing just happened again. The only common element to the five bulbs is the dimmer switch, right? There are no electronics in the chandelier.  What else could cause them all to act in unison?

Something is causing some of my LED lights to flicker in three locations. Here are two examples:       There are a few peculiar aspects.   The lights flicker sometimes and not at other times. Each time the flicker period is prolonged. I would say the lights flicker about 30-40% of the time. The lights flicker at different "flicker frequencies" as you can see in the videos. The flicker frequency also varies from time to time. There are three different rooms/circuits where the LED lights flicker. (They don't flicker in other rooms/circuits.) In each of the rooms, the light bulbs are of a different brand. There are 4 brands in total: Torchstar, Feit Electric, Hyperikon, Philips. Each of the three rooms uses a different kind of switch: Lutron dimmer (DV-600P), Lutron dimmer (DVW-600PH), and a dumb switch. The flicker sometimes stops if I replace one of the lights on the switch with an incandescent bulb. In one of the rooms, I have two sets of lights on two different switches, on a single circuit. Occasionally one set flickers more than the other.   A bad connection anywhere along the path is out of the question.  Any insight would be greatly appreciated!


I have two displays running in my current setup: A 27" monitor (it's not 4k, but it's got a somewhat higher resolution than 1920x1080), and a 15" MacBook with the Retina display.   The minor inconvenience I'm running into is that the mouse sometimes gets stuck on the large monitor and won't cross the gap to the laptop display.  As far as I can tell, this is because the edges of the displays are not scaled/mapped to each other's edges. So if the mouse is in the top-right or bottom-right corners of the larger display it's can't cross to the laptop because no shared edge exists there:     I remember running into this issue on a Linux machine and being able to change the mapping/scaling of the display edges so that the mouse can always cross that gap.   So I'm wondering, on El Capitan or Sierra, is there a way to make both displays share a common edge? Either through a setting, config, or even a third-party app?

I use a Full HD 24" external display besides my 15" MacBook Pro Retina, on which I use the option for most screen estate regarding the Retina display. In the display arrangement screen, the MacBook Pro is therefore a bigger rectangle than the external display. Is there a way to size these rectangles regarding their "real world size" instead of resolution? I'm annoyed by my cursor teleporting vertically whenever I move from one display to another.


In quantum mechanical tunneling particle doesn't scale the potential but instead find a short route to cross barrier. Then why is tunneling only possible in case of finite square well potential and not in infinite well.

I am studying basic quantum theory. My question is:  Why can't a particle penetrate an infinite potential barrier?  The reasoning that I have applied is that particles under consideration have finite energy. So, to cross an infinite potential barrier the particle requires infinite energy. But I cannot think of the mathematical relation between potential and energy so that indeed I am convinced that to cross an infinite potential barrier the particle needs infinite energy.  What is the relation between the potential and energy of quantum mechanical particles?


Let $A$ be a commutative ring with $1$ and $S$ be a multiplicatively closed subset of $A$. Can $S$ contain zero-divisors of $A$ and still we get $S^{-1}A \ne \{0\}$? My confusion is in the following point: For all $s \in S \ ; \ \frac s1$ is a unit in $S^{-1}A$. Also if $a \in A$ is a zero divisor then $\frac a1$ is a zero divisor in $S^{-1}A$. So if $S$ contains a zero divisor $a$ then $\frac a1$ is both a unit and a zero divisor which is a contradiction. Where am I going wrong?

Let $R$ be a commutative ring with identity, and $S$ a multiplicative subset of $R$ not containing $0$. Which step in my reasoning is wrong?   Every element of $S$ is a unit in $S^{-1}R$. Every element of $S$ that's a zero divisor in $R$ is a zero divisor in $S^{-1}R$. But zero divisors can't be units. Therefore it's not possible to localize $R$ at $S$.


How to integrate this :   $\int \frac{\cos 5x+\cos 4x}{1-2\cos 3x}\,dx$  My approach :   We know that $\cos A+cosB = 2\cos(\frac{A+B}{2})\cos(\frac{A-B}{2})$ But it is not working here, please suggest, thanks.

What I've done is this:$$\int\dfrac{\cos5x+\cos4x}{1-2\cos3x}{dx}$$ $$\int \dfrac{\sin 3x}{\sin 3x}\left[\dfrac{\cos5x+\cos4x}{1-2\cos3x}\right]{dx}$$ $$\dfrac {1}{2}\int\dfrac{\sin 8x -\sin 2x +\sin 7x -\sin x}{\sin 3x - \sin 6x}$$ $$-\dfrac {1}{2}\int\dfrac{ \sin \frac{7x}{2} +\sin \frac{5x}{2} } {\sin \frac{3x}{2} }$$ $$-\int\dfrac{ \sin {3x}\cos \frac{x}{2} } {\sin \frac{3x}{2} }$$ $$-\int\dfrac{2\sin \frac{3x}{2} \cos \frac{3x}{2}\cos \frac{x}{2} } {\sin \frac{3x}{2} }$$ $$-\int {2\cos \frac{3x}{2}\cos \frac{x}{2} }$$ $$ -\left(\frac{\sin 2x}{2} +\sin x \right) +c $$ Is there any other way to do so ? Is it possible to do it by substitution ?


I'm trying to complete my local installation and add SSL by following the example at:  but when I try to create certificate request file I keep getting this error: $ sudo openssl req -new -key server.key -out request.csr Password: unable to load Private Key 4578909804:error:09FFF06C:PEM routines:CRYPTO_internal:no start line:/AppleInternal/BuildRoot/Library/Caches/com.apple.xbs/Sources/libressl/libressl-47.140.1/libressl-2.8/crypto/pem/pem_lib.c:684:Expecting: ANY PRIVATE KEY  I searched but cannot find any clues, can someone please offer some help? Thank you!

I am developing MDM solution for that I need to create several certificates. For that I have following this .  When I'm firing this command, I am getting this error.  openssl rsa -in key.pem -out private.key   Error:     unable to load Private Key   4713004652:error:09FFF06C:PEM routines:CRYPTO_internal:no start line:/BuildRoot/Library/Caches/com.apple.xbs/Sources/libressl/libressl-47.11.1/libressl-2.8/crypto/pem/pem_lib.c:684:Expecting: ANY PRIVATE KEY   could any one guide me, how to resolve this issue?


I have been thinking about this problem  Yes, let's simplify the problem by assuming the set of only positive integers $Z$ I know if I take a range of numbers say $1$  to  $10$ , there are only three perfect square existing here; which are $1$ , $4$ and $9$  So the probability is $3/10$  If I increase my range the probability becomes lesser, so I can conclude there are more imperfect-square numbers than perfect squares.  My question Is there any fixed value assign to this, can I know the minimum and maximum value of this probability

While reading about the prime number distribution I came across this fact that the percentage of natural numbers that are perfect square is zero. How do I prove this ?


the problem at hand is:  Prove that there is an irrational number $a$ such that $a{^\sqrt{3}}$ is rational.  Hint: Consider $\sqrt[3]{2}^\sqrt{3}$ and argue by cases.  Any help on this problem would be greatly appreciated!

Can an irrational number raised to an irrational power be rational?  If it can be rational, how can one prove it?


I am trying to understand and prove theorems about polynomial factorization mod $q$. Theorem Let $P(X) \in \mathbb Z[X]$ be an irreducible polynomial of degree $p$ a prime. There exists a prime $q$ such that $P(X)$ is irreducible mod $q$. They came from the following source:  the proof of the 2nd theorem is on page 24. I don't understand the proof. Can anybody explain roughly how this is proved?

Problem: Is there an irreducible $f\in \mathbb{Z}[x]$, whose image in every $(\mathbb{Z}/p\mathbb{Z})[x]$ has a root for $p$ prime? If there is, what is the minimal degree possible?   I can only prove that $x^2-c$ is impossible, by quadratic reciprocity and Chinese remainder theorem. Even the case of $a x^2 - c$ is unknown to me.  Meanwhile, if $f$ is not required  to be irreducible, but only have no root in $\mathbb{Z}$, then $(x^2-a)(x^2-b)(x^2-ab)$ is a solution for non-sqaure $a,b,ab$, since if both $a,b$ are not squares in $\mathbb{Z}/p\mathbb{Z}$, then $ab$ is a square. Yet I still don't know if this is of minimal degree.  Also, it is natural to pose generalizations   When $p$ is not necessarily prime (equivalently for all prime powers). When $p$ is odd prime. When $p$ represents sufficiently large primes (equivalently all but a finite number left).


I'm doing android app where I need to communicate with special tablo via Bluetooth.  I have an error with java.lang.NullPointerException  I’ve announced everything that I need. What I need to do?  Java class  public class SearchTabloActivity extends AppCompatActivity {      ListView listView;      BluetoothAdapter mBluetoothAdapter;      @Override     protected void onCreate(Bundle savedInstanceState) {         super.onCreate(savedInstanceState);         setContentView(R.layout.activity_search_tablo);          listView = (ListView)findViewById(R.id.listView);          mBluetoothAdapter = BluetoothAdapter.getDefaultAdapter();          if (mBluetoothAdapter == null) {             Toast.makeText(getApplicationContext(), "Bluetooth not support!", Toast.LENGTH_SHORT).show();             startActivity(new Intent(SearchTabloActivity.this, MainActivity.class));         }          Set<BluetoothDevice> pairedDevices = mBluetoothAdapter.getBondedDevices();          List<String> s = new ArrayList<String>();         for(BluetoothDevice bt : pairedDevices)             s.add(bt.getName() + "\n" + bt.getAddress());          listView.setAdapter(new ArrayAdapter<String>(this, R.layout.activity_search_tablo, s));      } }   Error  2020-04-24 09:47:56.208 12121-12121/com.kvaksmanyt.exoy E/AndroidRuntime: FATAL EXCEPTION: main     Process: com.kvaksmanyt.exoy, PID: 12121     java.lang.RuntimeException: Unable to start activity ComponentInfo{com.kvaksmanyt.exoy/com.kvaksmanyt.exoy.tablo.SearchTabloActivity}: java.lang.NullPointerException: Attempt to invoke virtual method 'java.util.Set android.bluetooth.BluetoothAdapter.getBondedDevices()' on a null object reference

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I have a Lenovo x120e that is not booting properly.  When I turn it on, it just opens to a blank screen.  The machine is running Ubuntu 10.04.  Main Details: I shut the lid of the computer while it was running, and then opened it later and noticed that I couldn't get out of suspend / hibernate mode.  I subsequently powered it down by holding the power button.  Now when I turn it back on, it just opens to a blank black screen, as if it is still in suspend / hibernate.  Other Details: The 10.04 operating system (A) was installed while this HD was in another laptop.  Since I moved the HD into this machine, I have been booting another OS (B), and never updated drivers in A to work with this machine.  (Does this matter for this particular situation / problem?)    What I have tried so far: I found the REISUB method  but I don't have a SysReq button.  What are my next steps to troubleshoot / solve?

I am trying to boot Ubuntu on my computer.  When I boot Ubuntu, it boots to a black screen.  How can I fix this? Table of Contents:


I am trying to get the image type in the database but the below isn't working. How do I detect if the image is png, jpeg or gif?  if(isset($_POST['submit'])) {     $fileType = $_FILES['image']['type'];     $tmpname = $_FILES['image']['tmp_name'];     $fp = fopen($tmpname,'r');     $data = fread($fp,filesize($tmpname));     $data = addslashes($data);     fclose($fp);      $update = mysql_query("UPDATE avatar SET image1='$data',type='$fileType' WHERE username='$user'",$this->connect); } else {     echo "<form enctype='multipart/form-data' action='http://www.example.com/cp/avatar' method='post'>
Upload

<input type='hidden' name='MAX_FILE_SIZE' value='102400' /><input type='file' size='25' name='image' />

<input type='submit' name='submit' class='button' value='Save Changes' />
         </form>"; }

I am looking for a way to take a user uploaded image that is currently put in a temporary location ex: /tmp/jkhjkh78 and create a php image from it, autodetecting the format.  Is there a more clever way to do this than a bunch of try/catching with imagefromjpeg, imagefrompng, etc?


Were the people of the galaxy not concerned that Palplatine had named a Sith Lord as his number 2 in the Empire?

When Darth Vader first becomes Palpatine's apprentice, very few know of his existence and connection to the Emperor: the members of the Trade Federation (whom he dispatches) and Yoda, Kenobi, Organa, and their associates are all that seem to know at the end of Episode III.  Ultimately, the Resistance would know about him as they would be fighting him, and Organa could have been able to inform them about his identity and the fact that he is a Force user. The military of the Empire would know of his existence, but even high-ranking members likely wouldn't know his past or identity. However, they would know about the fact that he is a Force user due to his tendency to use his "sorcerer's ways" to choke people.  So, how much would the general public have known about Vader? Would they have known him as just another military leader, or would they have known he was Palpatine's right-hand man? Would they have known about his ability to use the Force, and therefore the possibility that he was a Sith?


My friend wants to travel but she has a passport with names abcd and a date of birth which males 23yrs.. she wants to make another passport this time with named bc and change to a much younger date of birth but with the same photo. Is it legal, okay or possible?

I want to issue another passport but i have one already. I need to change my names with the same photo and different age. So is it possible.


started displaying weird text. Is it the case with me only? I'm not sure whether this is the right place to put this question; but I was completely baffled by seeing that. I guess this chat room is hacked. I went on to take the screen shot and the messages disappeared. I'm sure some of the chatrooms have been compromised. If this is not the place please let me know where I could put my query. My mind is not working right now. I'm sorry for this weird post.

According to , the SE chat sites may have individual Easter eggs, depending on the site. If you find them, please post. Because it's so easy to make this stuff up, a screenshot as proof would be nice. (Although Photoshop isn't that hard either...)


The puzzle I'm facing comes from when I was participating in , so although I can think of ways to manage this by using baked image sequences or sync'ing up a mask to roughly match the movement of the light source, I'd rather achieve this purely using nodes.  In my scene, I have only a single light source that moves around and this means that the camera can sometimes see the dark side of the object.  I want the dark side of the object to become an emission shader and the side with light hitting it to be a diffuse shader.  I've tried having both shaders cover the whole object and turning the brightness of the light up very high so the emission is barely visible over the reflections from the diffuse shader on the side where the light hits but they are still visible.  Is there any way to add a node that outputs a value based on how much light hits it?  In the image below, both shaders cover the whole object, the light source is off to the right, the emission shader is emitting blue for the land, yellow for the cities and nothing for the oceans in the left half of the earth which is in darkness but you can see the yellow cities on the right, daytime half and the whole thing is tinged a bit blue.

I was watching the  tutorial by Andrew Price and I was able to follow along in Cycles until I hit the part where he mixes the day and night materials together so that the lights show up on the "dark side" of the earth.  How can I recreate this effect in cycles? I thought I could use the ray information to tell me if there was incoming light but I've found no such node to give me this information.


The superhuman strength of Colossus is given to him only when he transforms or does he have superhuman strength all the time?  If possible I would like answer both from comic universe and x-men movie universe

How strong is Colossus? Before he became the new Juggernaut, everybody said he could lift over 100 tons. Now they're saying can lift 70 tons.    When he was a teenager he could only lift 40 tons. However, when Colossus was a teenager, he was strong enough to knock down the original Juggernaut () and if he was lifting 40 tons at that time, he wouldn't be able to do that.   I personally believe he's a  or else he wouldn't be able to go toe to toe with the heavy hitters of the Marvel Universe. Can anyone explain this discrepancy?


I found this:   as well as this:  Neither however seem to make sense to me as I have been using the following:  \newtheorem{theorem}{Theorem}[section] \begin{theorem} \emph{(Fundamental Lemma)} Let $A$ and $A'$ with collections $\partial$ and  Stuff goes here: But it becomes "italicized" \end{theorem}   However it seems that with the above two links one is either just defining whole new constructs (which I somewhat understand), or just using \textbf, which I don't want the \textbf to override the italics as I don't want bold faced text.  What I am after is being able to construct a "Theorem" which keeps track of the numbering and updates itself i.e. 1.1 to 1.2 if another theorem tag is added before.

What package should I use, or what setting can I make to the font in theorems so that the text wouldn't be italic. I use amsmath, and from default, everything I write in theorem environments becomes italic and I don't want that. Thank you


Just noticed this, cron is constantly maxing out my cpu on Ubuntu under the user sabnzbd. Sabnzbd isn't doing anything active. Stopping Sabnzbd doesn't kill that process.  How do I get to the bottom of what's causing this?  PID USER      PR  NI    VIRT    RES    SHR S  %CPU  %MEM     TIME+ COMMAND                                                                                1736 sabnzbd   20   0   76344   8408    752 S 399.7   0.1  20:46.45 cron

I was hacked this morning!  Does anyone have an idea of what the entry of the crontab below might mean?  1st They created a dir structure  .rsync/ ├── a │   ├── a │   ├── anacron │   ├── cron │   ├── init0 │   ├── run │   └── stop   2nd: The executed this cronjob from: crontab -l  0 */3 * * /home/ftpuser/.nullcache/a/upd>/dev/null 2>&1 @reboot /home/ftpuser/.nullcache/a/upd>/dev/null 2>&1 5 8 * * 0 /home/ftpuser/.nullcache/b/sync>/dev/null 2>&1 @reboot /home/ftpuser/.nullcache/b/sync>/dev/null 2>&1 0 0 */3 * * /tmp/.X17-unix/.rsync/c/aptitude>/dev/null 2>&1   Last: ran all my CPU's at 100% and sucked all the bandwith from the network.  I killed all associated PID'S to ftpuser and everything went back to normal


I want to develop a web application which will allow any person to view map as per their interest combining different parameters. For example- I have literacy wise district map of some state and I wish to give an user interface(web based) which allow them to select district of their choice and represent map based on required query which is literacy in this case.   I am trying geo server but i am not sure this will help or not.

I want to start working on a web map at work to map some of our statistics by city.    I have an idea, but I'm not exactly sure where to start.   Are there any definitive resources that provide step by step guidance on how to do this?


It is well known that $2^{\aleph_0}>\aleph_0$. This seems to imply that there is an $n \in \mathbb{N}$ such that $2^{|n|} = \aleph_0$. If so, what is known about the least permitted value of $n$ such that this statement is true?

Let $A$ be a set.  If $A$ is finite then so is $\mathcal{P}(A)$.  If $A$ is not finite then it has a countably infinite subset $B$, in which case $\mathcal{P}(B)$ is uncountable and thus so is $\mathcal{P}(A)$.  Can I say that given an arbitrary set its power set may be finite or uncountably infinite but never countably infinite?


I came across a post, which was basically gibberish like "hsuheuduehuhfuheufhufe".  Originally I marked it as spam, but it was not accepted.  Why?  It should have been marked at rude and abusive.  Perhaps a new feature could be to separate the 2, so that such a post, which is definitely abusive, but not rude?  Thanks.

When flagging, there are two special case options: spam and rude or abusive.   What is spam, and when should I flag content as such? What is considered offensive, rude or abusive content? How does the spam flag differ from the rude or abusive flag? What is the effect of these special flags? When are these flags removed?


Graphic Design SE just came out of Beta, we are all chuffed over there.   However; I cannot seem to suggest migration from StackOverflow to GraphicDesign via the flag options. Here is what happens when I flag a question for migration. GD simply is not an option:    I can do it manually, by using the "other" option and write it, but surely that means more work for the mods here than necessary.

I think there should be more Stack Exchange networks available when flagging a question to be migrated. For example I'd think that the following question:    ...would be a better fit on unix.stackexchange.com instead of Stack Overflow. But without the option to mark it so, I feel hesitant to mark it.


So I wanna compute a covexhull but in the I want the right and left sets seperately. I cannot understand what Java is doint right here exactly.  So I first call the hullset function for the right part and then put it in rightCov (at that point right set has 3 points). After that I can hullset for the left set . The problem is that even though I have "saved" the 3 points of the right set after the second call of the hullset,for the left set only,the variable rightCov takes all the 5 points of the covexhull without me using it again. The calls are below.  hullset(A, B, rightSet, covexHull); ArrayList<Point> rightCov=covexHull;  hullset(A,B,leftSet, covexHull);

I have an ArrayList<String> that I'd like to return a copy of.  ArrayList has a clone method which has the following signature:  public Object clone()   After I call this method, how do I cast the returned Object back to ArrayList<String>?


I want to divide my chapters into sub chapters in same fashion as described in this question:   However I am not getting correct results. while Chapter name/counts are fine, subsections are incorrectly numbered.  Consider the modified file as provided in the accepted answer to above question:  \documentclass{report} \usepackage{etoolbox}% http://ctan.org/pkg/etoolbox %\usepackage{hyperref}% http://ctan.org/pkg/hyperref \newcounter{subchapter}\renewcommand{\thesubchapter}{\alph{subchapter}} \makeatletter % \patchcmd{<cmd>}{<search>}{<replace>}{<success>}{<failure>} \newcommand{\updatechaptercounter}{} \patchcmd{\@chapter}{\@afterheading}{\updatechaptercounter\@afterheading}{}{}% Regular patch of \@chapter %\patchcmd{\Hy@org@chapter}{\@afterheading}{\updatechaptercounter\@afterheading}{}{}% Hyperref patch of \@chapter \makeatother \providecommand{\theHchapter}{}% \newcommand{\startsubchapters}{%   \setcounter{subchapter}{0}% Reset sub-chapter numbering   \renewcommand{\thechapter}{\arabic{chapter}\thesubchapter}% Update chapter number display   \renewcommand{\theHchapter}{\arabic{chapter}\thesubchapter}% Update chapter number display (for hyperref)   \renewcommand{\updatechaptercounter}{\addtocounter{chapter}{-1}}% Update chapter number   \let\oldchapter\chapter%   \renewcommand{\chapter}{\stepcounter{subchapter}\oldchapter}% Increment subchapter } \newcommand{\stopsubchapters}{%   \renewcommand{\thechapter}{\arabic{chapter}}% Reset chapter numbering   \renewcommand{\theHchapter}{\arabic{chapter}}% Reset chapter numbering (for hyperref)   \let\chapter\oldchapter% Restore regular \chapter command   \renewcommand{\updatechaptercounter}{}% Clear chapter counter update   \stepcounter{chapter}% Update chapter counter } \begin{document} \tableofcontents \chapter{First chapter} \section{one one} \section{one two} \startsubchapters \chapter{Second sub-chapter} \section{2 A one} \section{2 A two} \chapter{Second sub-chapter} \section{2 B one} \section{2 B two}  \stopsubchapters \chapter{Third chapter} \chapter{Fourth chapter} \end{document}   (I just added sections nothing more)  Provides me with following output:  It should be section 2A.1, 2B.1 etc. instead of 1A.1 1B.1 etc. What am I doing wrong?  (compiled using pdfTeX 3.14159265-2.6-1.40.17 (TeX Live 2016/W32TeX), on windows)

I would like to append a character to the chapter number in some cases but not everywhere. The change should also be reflected in the table of contents. The chapter numbering should look like this:  1 2a 2b 3  How can I accomplish this?


I have a query that gets about 80k rows from said table with about 3m.  I only need to paginate ten rows at a time, but with ORDER BY (a+b) DESC (a and b are integer type columns.)  Right now my query's taking about 4 seconds to do this.  If I ORDER BY the primary key instead, it avoids seq scans and takes 200ms, which I would be happy with.  So I created an index on (a+b) DESC.    My thinking there is that the ORDER BY and primary key both have indexes (as do all the things in the WHERE clause--and those indexes are being used just fine), so the subquery should be able to accomplish everything it needs to without a seq scan, give up 10 indexed primary keys to the outer query, which, if it needs a seq scan because of the *, only needs to find ten rows.  It didn't make a difference, anyway.  Unfortunately, I can't share full table details, but I can say that my table has 21 columns, with some text, two integer, several timestamps and even one ts_vector. Aside from the expression one there are 4 indexes: the PK (text) is btree, I have another btree text, a btree timestamp, and a gin index on the tsvector.  Further: I can also order by the indexed timestamp and the non-primary-key indexed text, and just like the primary key, this reduces query time to 200ms thanks to index usage.  It's just my expression index that doesn't seem to work this way in the subquery context.  Other options, none of which seem great:   Add a computed column for (a+b) so the index is just on one column.  If it works for ORDER BY on the pk it should work for that column, right? Cheat by somehow guesstimating a happy limiter on (a+b) due to its distribution.  I'm not sure how I would always know because the query inputs are dynamic, but in this case, if I add a simple AND (a+b) > 1000000, I still get ten rows back but it only takes 200ms--and uses my expression index for the WHERE clause where the seq scan would normally be.  (About the not knowing, I could start doing some kind of binary-search-esque thing, trying high numbers and reducing by half until I get at least 10 rows back and then calling it a day.  If I get it within less than 20 tries, I'm still ahead.  But this is beyond kludgy...)   Any ideas?  How can I get it to use my expression index and avoid a seq scan?  The reason I don't understand the above is that the docs (going back to 9.4 at least) explicitly put it this way:     Index expressions are relatively expensive to maintain, because the derived expression(s) must be computed for each row upon insertion and whenever it is updated. However, the index expressions are not recomputed during an indexed search, since they are already stored in the index.   So how on earth is other_column any less expensive to ORDER BY than a+b when both are indexed?    Regarding query plans, let's try to get to the heart of it.  I've posted .

(Follow up from this post: )    PostgreSQL 9.5.  I can't divulge full details, but table has 22 columns and 5 indexes:   primary key ('pk'), text (btree) another text (btree) a timestamp with time zone (btree) a tsvector (gin) my latest one, a bigint (btree)   (From the previous post you know that I was trying to avoid creating this additional column, and just use an expression index--adding two integer columns together--without success.  The bigint column here probably could have been just 'integer' but I made a mistake creating it; it took about an hour to add the column, populate it, and reindex, so I'm hoping this isn't relevant but mentioning it just in case it is.)  All are btree except the tsvector.  The following queries all take only 12ms and use just an Index Scan:   SELECT pk FROM table ORDER BY pk DESC LIMIT 10 SELECT pk FROM table ORDER BY text_column DESC LIMIT 10 SELECT pk FROM table ORDER BY timestamp_column DESC LIMIT 10   But if I try to use my new bigint index for ORDER BY:  SELECT pk FROM table ORDER BY bigint_column DESC LIMIT 10  ...it takes 2.7s and uses Limit -> Sort -> Seq Scan.  My "cheating" method is the closest I seem to be able to get to making use of the index:  SELECT pk FROM table WHERE bigint_column > 1000000 ORDER BY bigint_column DESC LIMIT 10   This takes 12ms and uses Limit -> Sort -> Bitmap Heap Scan (bigint_column > 1000000) -> Bitmap Index Scan (bigint_column > 1000000).  This is after a VACUUM ANALYZE after adding the index.  I thought it strange that my expression index was not being used in the other question.  Now it's just a plain old column (I haven't even added what would be the necessary triggers to actually go this route.)  Why isn't my newest index being used, when the other three work "just fine"?  (As pointed out in the comments at  , an Index-Only Scan would be even better.  I fail to see why all of these queries wouldn't use at least an Index Scan, let alone an Index-Only Scan, instead of a full Seq Scan.)  The index definition has DESC NULLS LAST (although it's a non-nullable column.)


I'm trying to build a MultiArch Application for Ubuntu. I have to compile it separately on different Architectures. However I have to do a lot of manual changes Each time the Architecture changes. For Instance-  #linux-g++:LIBS += $$DESTDIR/lib32/libusb-1.0.so      #arch-specific changes linux-g++:LIBS += $$DESTDIR/lib64/libusb-1.0.so  Here I have to comment and uncomment a line every time I'm compiling for a different Architecture. I have to do this on a number of places. However if there is a way to specify the Linux Architecture in the .pro file itself then my task will become much easier. I know that we can use win32 and macx scope variables and linux-g++ for Ubuntu. But I want to distinguish between ubuntu 32 bit and 64 bit Architectures. Is there any way this might be achieved a little more elegently? I have already seen  and I just want to specify that I'm looking to distinguish between linux32bit and linux64bit .

Is there a "win64" identifier in Qmake project files?  documentation does not mention other than unix / macx / win32.  So far I've tried using:  win32:message("using win32") win64:message("using win64") amd64:message("using amd64")   The result is always "using win32".  Must I use a separate project-file for x32 and x64 projects, so they would compile against correct libraries? Is there any other way to identify between 32-bit and 64-bit environments?


The battery backup of my Lenovo G50-45 laptop is very low of around 3hrs on full charge.   This was approximately double when I was working with Windows 8.1. Can you please suggest the possible fixes to overcome this issue?

Last year I purchased a Dell Inspiron 5315 laptop shipping with Windows 7 preinstalled. I installed Ubuntu 10.10 alongside it with dual-booting. On upgrading to Ubuntu 11.10, I was upset to find I now get less than one hour of battery life! Windows 7 gives me 2.5 hours of running time.  Is there any possible explanation why  my battery is running out faster with Ubuntu? Can anybody tell me better power options?


Knowing that a meromorphic function f requires f to be either analytic or has a pole at every point in its domain, what does bijective meromorphic mean?

Just based on some reading, I know that every Möbius transformation is a bijection from the Riemann sphere to itself.   I'm curious about the converse. For any holomorphic bijection on the sphere, why is it necessarily a Möbius transformation? Is there a proof or reference of why this converse is true? Thanks.  (I would appreciate an explanation at the level of someone whose just self-studying complex analysis for the first time.)


I have looked at the answers to the question , however I have found that even though they indicate how to switch input-sources through Terminal, they do not show how to switch between the modes of the input-sources. For instance I have "Japanese (Anthy)" installed which has several different mode settings section: Input mode, Typing mode, Segment mode, and Dictionary mode. In each of these there are different modes you can set for these settings. Like the Input mode one provides input modes such as Hiragana and Katakana, the Typing mode one allows you to change between Romaji, Kana, and Thumb shift, and the others have other various options you can change between to change the input-source mode.  These are very easy to change through the GUI as there is just a pull-down menu in the AppIndicator bar however as I will be needing to use TTYs for a while and not have access to the normal GUI, I need to know how to switch between these different modes in Terminal. So how can this be done?  At very least I need to know how to switch between the Input mode modes.  I am running Ubuntu GNOME 15.10 with GNOME 3.18.

How I change keyboard layouts from the command-line?  For example, I want to switch from English to Hebrew.  I'm able to do it from lightdm with the little icon in the corner of my screen.


I'm using Calibre and it seems that it uses xdg-open to open files. This, even when tried in terminal, only opens nautilus and the file is selected, but not opened. It doesn't matter if I try to open .cbz or .pdf.  This seems fine: /usr/share/applications/defaults.list  application/x-cbr=evince.desktop application/x-cbz=evince.desktop   Sure when I open the file in Nautilus it opens, but this approach is quite annoying.

since some days my Files lens opens only nautilus but not the correct application which is associated with the file extension.  For example, if I choose a PDF file, Nautilus is openend, pointing to the directory there the file is (and the file is selected) but Adobe Reader is not opened.  Then I do the same in the terminal with   xdg-open sample.pdf   only Nautilus is opened too.  xdg-mime shows me this info:  $ xdg-mime query default application/pdf acroread.desktop   The /usr/share/applications/acroread.desktop file:  [Desktop Entry] Name=Adobe Reader 9 MimeType=application/pdf;application/vnd.fdf;application/vnd.adobe.pdx;application/vnd.adobe.xdp+xml;application/vnd.adobe.xfdf; Exec=acroread  Type=Application GenericName=PDF Viewer Terminal=false Icon=AdobeReader9 Caption=PDF Viewer X-KDE-StartupNotify=false Categories=Application;Office;Viewer;X-Red-Hat-Base; InitialPreference=9   The same with other file types like images, music files and office documents.  Then I doubleclick the file in Nautilus everything is ok and the correct applications are opened.  I assume this behaviour has something to do with Thunar which I've installed some days ago but deinstalled after these problems.  Any suggestions?


I am practicing for USACO Bronze and came across the Fence Painting Problem from USACO 2015 December. My code is working on Eclipse and everything is fine but when the USACO website tests it, I get this error: Error: Could not find or load main class Paint Caused by: java.lang.NoClassDefFoundError: introduction/Paint (wrong name: Paint) I have no idea what is causing this. This is my code: package introduction;  import java.io.*; import java.util.*; public class Paint {     public static void main(String args[]) throws IOException {         PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("paint.out")));                  Scanner keyboard = new Scanner(new FileReader("paint.in"));                  int a = keyboard.nextInt();         int b = keyboard.nextInt();         int c = keyboard.nextInt();         int d = keyboard.nextInt();                  if (a<c && b==d) {             out.println(b-a);         }         if (a<c && b<d) {             out.println(d-a);         }         if (a<c && b>d) {             out.println(b-a);         }         if (a>c && b==d) {             out.println(d-c);         }         if (a>c && b<d) {             out.println(d-c);         }         if (a>c && b>d) {             out.println(b-c);         }         if (a==c && b==d) {             out.println(b-a);         }         if (a==c && b<d) {             out.println(d-c);         }         if (a==c && b>d) {             out.println(b-a);         }         out.close();     } }  Please help me. Thank you!

I am getting a NoClassDefFoundError when I run my Java application.  What is typically the cause of this?


I am debugging an application someone else wrote which runs as a Windows Service unless it is started from the Console and passed parameters.  I would like to start this program from the Console, including some parameters, and then step into the debugger.  I'm not sure how to do this since before I execute the command to start it, there is no process to attach to, and once I execute the command, it's too late to catch it (errors begin almost instantly).  I'm trying to figure out if there's a way in Visual Studio to set up the debugger to attach to a process before it's actually running (or perhaps something effectively similar, given the description of my problem).  I have a breakpoint on the very first line of Program.Main and I'm essentially trying to figure out how I can launch the application from the Command Prompt and then immediately hit my breakpoint.  Is this even possible?  I'm running VS 2013 on Windows Server 2012 Datacenter, by the way.

I'm developing a C++ command-line application in Visual Studio and need to debug it with command-line arguments. At the moment I just run the generated EXE file with the arguments I need (like this program.exe -file.txt) , but this way I can't debug. Is there somewhere I can specify the arguments for debugging?


This is beyond maddening. I have been using Windows since the early 90s. I've never seen something so horribly designed.  I recently abandoned my beloved Win7, because security. I can mostly live with Win10's shortcomings. Except for this one. Today at 5pm I walked away from my machine for 30 minutes. Come back at 5:30pm to this popup telling me I have 4 minutes to prevent a reboot that I never asked for. And yes, I took this photo with a camera, since the popup commandeered all other input on my machine.  What if I was running a super important task that took 72 hours to complete and it was 99% finished? Is MS really ok with just forcefully rebooting client machines on a moment's notice? This is almost enough to make me stop using Windows entirely (I already have Linux and OSX machines, I only use Windows for gaming mostly).

We've upgraded some machines to Windows 10 and realized there were some updates which updated as required. However, I realized there was no option available to stop the download similar to that on Windows 7 and 8.1. The only way I could stop the download was to stop the Windows Update service.  My question is does anyone know of a way to stop auto updates or is stopping the service is the only solution?


I'm trying to understand the main differences (if there are) between analytic and holomorphic functions.  I know that a function is holomorphic in a connected open set if it is differentiable in each point.  Also I know that a function is analytic if it can be written in terms of Taylor expansion in each neighborhood of $x_0$.  So which are the differences between these two classes of functions? Or which topic should I use to show they are the same thing?  Thank you!

A function $f : \mathbb{C} \rightarrow \mathbb{C}$ is said to be holomorphic in an open set $A \subset \mathbb{C}$ if it is differentiable at each point of the set $A$.  The function $f : \mathbb{C} \rightarrow \mathbb{C}$ is said to be analytic if it has power series representation.  We can prove that the two concepts are same for a single variable complex functions. So why these two different terms? Is there any difference between these two concepts in general, please give example.  Thank you for your help.


So like, if I have a profile on puzzling.StackExchange.com and StackOverflow.com, can I remove myself from the puzzling.SE community, rather than deleting my entire account?

How I can remove myself from some Stack Exchange sites, but keep my profile? (For example, I subscribed to some sites just for curiosity; I just browsed without posting or replying.)  I found a delete option but I am afraid to click!   Would it be possible also to unsubscribe from sites where I have been active?


I don't know how to test if a player is holding an item with a specific name, but I know it's something like  /testfor @e[type=Player,SelectedItem=example_id,Slot=0], but I probably got it totally wrong... Can you guys help?

I'm trying to make a command block that spawns an item in front of you if you are holding an item with a specific name. I've got these two working scripts;  /testfor @p[r=10] {Inventory:[{tag:{display:{Name:"Item Name"}}}]}  /testfor @p[r=10] {SelectedItemSlot:0,Inventory:[{Slot:0b,id:"minecraft:diamond_sword"}]}   but I can't get them together. The block should only look for an item in the active slot.


Quaternion group, $(Q_8, .)$ is defined by  $Q_8= \{1, -1, i, -i, j, -j, k, -k\}$  And the binary operation $\cdot$ is defined as follows:  $\forall a\in Q,  1\cdot a=a\cdot 1=a, (-1)\cdot a=a\cdot (-1)=-a$ and $(-1)\cdot (-1)=1$  $i\cdot i=j\cdot j=k\cdot k=-1$    $i\cdot j=k, j\cdot k=i, k\cdot i=j$  $j\cdot i=-k, k\cdot j=-i, i\cdot k=-j$    I need to show that the binary operation $.$ follows the law of associativity. I cannot thought of checking $8^3=512$ cases. Can anyone help me?

Consider the eight objects $\pm 1, \pm i, \pm j, \pm k$ with multiplication rules:   $ij=k,jk=i,ki=j,ji=-k,kj=-i,ik=-j,i^2=j^2=k^2=-1$,   where the minus signs behave as expected and $1$ and $-1$ multiply as expected. Show that these objects form a group containing exactly one involution.  Well, it is easy to determine closure from the definition. $1$ is clearly the identity, and the inverses can also be determined $(i,-i),(j,-j),(k,-k)$, $-1$ with itself, and $1$ with itself. The only involution is $-1$. Is there an easy way to check associativity of this group? There are too many possible combinations $(ab)c=a(bc)$ to check directly. ($8^3$ possible combinations)


Consider the following lines   $x-y-1=0$ $x+y-5=0$ $y=4$   The line 1 is the axis of the parabola, the line 2 is the tangent at the vertex to the same parabola, and the line 3 is another tangent to the same parabola at some point $P$.  Now let a circle $C$ circumscribe the triangle formed by tangent and normal at the point $P$ and the axis of the parabola.  Then how can I find the equation of the circle?  I found that the vertex of this parabola is $(3,2)$. Don't know how to proceed further.

Consider the following lines   $x-y-1=0$ $x+y-5=0$ $y=4$   The line 1 is the axis of the parabola, the line 2 is the tangent at the vertex to the same parabola, and the line 3 is another tangent to the same parabola at some point $P$.  Now let a circle $C$ circumscribing the triangle formed by tangent and normal at the point $P$ and the axis of the parabola.  Then how can I find the equation of the circle?  I have tried and found that the vertex of this parabola is (3,2). Need help....don't know how to proceed further.... Thanks in advance...


I wanted to draw a convex lens in tikzpicture. I'm fairly new to writing these commands, so I drafted the following. % Convex lens  % \convex[R0,R1,w,h] at (x,y); \def\convex[#1,#2,#3,#4] at (#5,#6){     % circle-circle intersection maths     % with adjustment for clipping at specified height     \def\R{#1};\def\r{#2};\def\d{(\R+\r-#3)};     \def\x{(((\d*\d)-(\r*\r)+(\R*\R))/(2*\d))};\def\c{(\d-\x)};     \def\y{sqrt((\R*\R)-(\x*\x))};\def\yh{min(\y,#4)};     \def\g{asin(\yh/\R)};\def\p{asin(\yh/\r)};          % sphere0 curves     \draw ({#5-\x+\R},#6) arc (0:\g:\R);     \draw ({#5-\x+\R},#6) arc (0:-\g:\R);          % sphere1 curves     \draw ({#5+\c-\r},#6) arc (180:180+\p:\r);     \draw ({#5+\c-\r},#6) arc (180:180-\p:\r);          % connecting lines (if clipped)     \def\xg{\R*cos(\g)};\def\xp{\r*cos(\p)};     \draw ({#5+\xg-\x},{\yh}) -- ({#5-\xp+\c},{\yh});     \draw ({#5+\xg-\x},{-\yh}) -- ({#5-\xp+\c},{-\yh});     }  This works, but I'd like to improve it a bit. Specific questions follow.  Does it make sense to pass R0, R1, w, and h in this way? Is there a more standard way to pass arguments that is more in line with tikz/pgf philosophy? How can I pass optional arguments such as thick to my \draw commands? It seems like \def does not allow optional arguments. Is there another command I can use to define my lens? Is there a better way to do this math in tikz/pgf (i.e. can it be done in fewer commands/with less braces and parentheses)?

How can I make a convex lens with TikZ?  I tried using arcs but this doesn't look right.  \documentclass[tikz]{standalone} \begin{document} \begin{tikzpicture}   \pgfmathsetmacro{\xr}{0.35}   \pgfmathsetmacro{\yr}{2}    \draw (0, 0) coordinate (O) arc[x radius = \xr cm, y radius = \yr cm,   start angle = 90, end angle = 270];   \draw (O) arc[x radius = \xr cm, y radius = \yr cm,   start angle = 90, end angle = -90]; \end{tikzpicture} \end{document}   I would like the arcs to meet at a sharp corner not rounded.


I have a low end steel MTB, which is heavy by itself, and I also a heavy man weighting in at 100kg, and on my MTB I have knobby dirt tires.  As you can imagine, riding on the road any faster than 20km/h is a pain. I would be satisfied if I could cruise at 30km/h easily, which I can't now. I'm finding comfort in 20km/h.  What do I need? Road tires? Loose weight? Get more fit?  I was thinking on purchasing a set of Schwalbe Marathon tires, in 26x1.75 size for my MTB to potentially lower the rolling resistance and go faster.  Currently I have Kenda tires, made for the dirt in the 26x2.10 size. These tires also sound horrible, making a lot of noise on the pavement.   How could I increase the speed of my bike?   Also, at what pressure should I inflate my current Kenda tires to potentially go faster? I currently have them at around 60PSI.

I'm an occasional biker. I bought a mountain bike (nothing fancy) with the idea that I might use it off-road or on mountain trails (of which there are many here in Calgary). However, since I've bought it I've done nothing but bike in the city on streets and paved bike trails.  Is there anything worth doing to my bike to convert it to something more suited to urban biking? In particular, the tires have me wondering; they have large rubber off-roading lugs that surely aren't doing me any favors on pavement. I'm not looking to spend a tons of money on a retrofit, but will do so if its worthwhile.


I have written a letter. I wrote a letter.  Do they mean the same thing or there is a difference?  If there is a difference then where should I use "have written" and "wrote"? (I'm also talking about every other verbs)

To me, using Present Perfect form means the event can occur again. So, saying      someone has died   may not be grammatically correct.  Also, I noticed (it might be just coincidence):     passed away   is used more often than     has passed away   Is using Present Perfect correct here?


A classmate told me this, but he didn't tell me how to evaluate the integral.  $$\int_0^1 \int_0^1 \frac{1}{1-xy}dxdy=\int_0^1 \int_0^1\sum_{n=0}^\infty (xy)^n dxdy=\sum_{n=1}^\infty \frac{1}{n^2}=\zeta(2)$$  So if you can evaluate that integral this might be an easy way to solve the Basel problem.  I tried substituting $\frac{1}{x}=v$ and $\frac{1}{y}=t$ to get $$\zeta(2)=\int_1^\infty\int_1^\infty\frac{1}{vt-1}-\frac{1}{vt}dvdt=\lim_{N\to\infty}\left(\int_1^N\int_1^N\frac{1}{vt-1}dvdt-\ln(N)^2\right)$$  The areas of the cross sections of $\frac{1}{vt-1}$ are going to be infinite near $(1,1)$ so this seems like a dead end.

I've read somewhere on this site that if you consider:  $$\int_0^1 \int_0^1 \frac{1}{1-xy} \,dy\,dx$$  Then using the power series, we have this is equal to $\sum_{n=1}^{\infty} \frac{1}{n^2}$ which I decided to try and was able to show.  Apparently we can show this is equal to $\frac{\pi^2}{6}$, and using what little I know about double integrals from a few khan academy videos (I haven't taken multivariable  calculus yet), I tried to evaluate this double integral by techniques of single variable calculus $u=xy$..and I got this:  $$-\int_{0}^{1} \frac{\ln (1-x)}{x}dx$$  The usual way I would evaluate this is with a Taylor series, but that just that just leads us in circles.  So I want to know how can I evaluate this, so we can prove $\sum_{n=1}^{\infty} \frac{1}{n^2}=\frac{\pi^2}{6}$.


This system is linux mint 18.3, basically ubuntu.  sudo du --apparent-size -sb /tmp yields 476mb on my system currently.  if I run sudo du --apparent-size -sb /tmp/* /tmp/.??* and add it all up, I get about 4mb.  (I know -b includes --apparent-size, just want to be explicit for this question)  Actually, to find the sum since I'm lazy, so I ran:  sudo du --apparent-size -sb /tmp/* /tmp/.??* | cut -f 1 | paste -sd+ - | bc  Why the difference?  Are there some hidden files in /tmp that du isn't finding, or is there a mistake in my commands?  edit:  despite my poor .??* to catch .dirs and .files, there were no .a, .b, .c etc files in this case.

I am a graduate student of computational chemistry with access to a Linux cluster.  The cluster consists of a very large (25 TB) fileserver, to which several dozen compute nodes are connected.  Each compute node consists of 8 to 24 Intel Xeon cores.  Each compute node also contains a local disk of about 365 TB.  Since the fileserver is routinely accessed by a dozen or so users in the research group, the fileserver is mainly used for long term file storage (it is backed up nightly, whereas the compute nodes' local disks are never backed up).  Thus, the system administrator has instructed us to run simulations on the local disks -- which have faster I/O than the fileserver -- so as to not slow down the fileserver for the other users.  So, I run simulations on the local disks and then, after they are finished, I copy the trajectory files -- I am running molecular dynamics (MD) simulations -- to the fileserver for storage.  Suppose I have a trajectory file called traj.trr in a directory on the local disk of a node, /home/myusername/mysimulation1/traj.trr.  For long term storage, I always copy traj.trr to a directory in the fileserver, ~/mysimulation1/traj.trr, where ~ represents my directory in the fileserver, /export/home/myusername.  After copying it, then I habitually use du -h to verify that /home/myusername/mysimulation1/traj.trr has the same file size as ~/mysimulation1/traj.trr.  This way, I can be at least reasonably sure that the transfer to the fileserver was successful.  For example:  cd /home/myusername/mysimulation1/ cp -v traj.trr ~/mysimulation1/ du /home/myusername/mysimulation1/traj.trr -h du ~/mysimulation1/traj.trr -h   If the two calls to du -h give the same human-readable file size, then I can be reasonably sure that the transfer/copy was successful.  (My typical traj.trr files range in size from about 15 to 20 GB, depending on the exact simulation I have run.)  If I run du (i.e., without the -h switch) on the two traj.trr files, their sizes in bytes are usually very, very similar -- usually within just a few bytes.  I have been using this overall method for the past year and a half, with no problems.   However, recently I have run into the following problem: sometimes du -h reports that the two traj.trr files are different in size by several GB.  Here is an example:  cd /home/myusername/mysimulation1/            # this is the local disk cp -v traj.trr ~/mysimulation1/ du traj.trr -h cd ~/mysimulation1/                           # this is the fileserver du traj.trr -h   The output from the two calls to du -h is as follows, respectively:  20G     traj.trr 28G     traj.trr   I believe that the former (i.e., the traj.trr in the local disk, /home/myusername/mysimulation1/) is the correct file size, since my simulation trajectories are expected to be about 15 to 20 GB each.  But then how could the file on the fileserver actually be larger?  I could see how it could be smaller, if somehow the cp transfer failed.  But I don't see how it could actually be larger.    I get similar output when I execute the same commands as above, but without the -h switch given to du:  20717480        traj.trr 28666688        traj.trr   Can you think of any reason for the difference?    If, by some unlikely chance, du is somehow malfunctioning, I can be okay with that.  But I just really need to make sure that the copy of traj.trr on the fileserver is complete and identical to its source version on the local disk.  I need to delete the local file so that I have enough local disk space to run new simulations, but I can't afford to have the version of traj.trr on the fileserver be corrupted.    The  is a binary format, not text.  Thus, I am not sure if the files can be reliably compared by a program such as diff.


I want the PC to shut down without any dialogue, but let time for the applications to close properly.  One solution is, to change powerbtn.sh to: shutdown -h now but that does not wait for all applications to close.

When I press the power button a dialog opens, but I want to shutdown the system without receiving "Do you really really want to shutdown?". How can I choose a direct shutdown action on a pressed power button?   I had the same problem with the 11.04 version, but I don't remember the solution and yesterday I upgraded to Ubuntu 11.10.


I'm trying to download Heroku for the first time onto my Ubuntu 16.04 and I'm following the Heroku website's instructions exactly by the following:   sudo add-apt-repository "deb https://cli-assets.heroku.com/branches/stable/apt ./" curl -L https://cli-assets.heroku.com/apt/release.key | sudo apt-key add - sudo apt-get update sudo apt-get install heroku   But every time I get to sudo apt-get update I receive the following errors:  W: the repository 'http:''cli-assets.heroku.com/branches/stable/apt ./ Release' does not have a Release file. N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use.  N: See apt-secure(8) manpage for repository creation and user configuration details. E: Failed to fetch http://cli-assets.heroku.com/branches/stable/apt/./Packages 403 Forbidden [IP: 52.84.3.182 80] E: Some index files failed to download. They have been ignore, or old ones used instead. W: Duplicate sources.list entry https://cli-assets.heroku.com/branches/stable/apt ./Release   Suggestions?

I downloaded Heroku from Heroku toolbelt using  wget -qO- https://toolbelt.heroku.com/install-ubuntu.sh | sh   in the terminal, which they recommended on their site.   My Ubuntu (14.04.1) didn't recognize the -q0-, so I took it out.  It then seemed to download fine - I see the  in the directory I was in when i downloaded it.   Now, however, it still doesn't recognize heroku as a command.  It also won't show me where it is with the 'whereis' command.  But when I look in the current directory with ls -a, it shows up.  It seems to be there.   How do I install it?


I've found this phrase across the internet and  they use "A user interface" instead of "An user interface".  Is it an error that has been propagated or is it correct? If it's correct, why?

I was writing a text when I came to say 'a union', then it struck me that I need to change the 'a' to 'an'. But for some reason, 'an union' didn't sound right.   Why doesn't it work? Is it because its a mass noun, instead of a regular noun?


Hi I am look to run 100 amp sub panel to my shop from my 200 amp panel in my basement. It about 175 ft in middle of both panel box . I was looking for someone help me out on wire size and what I would need to do it ?

What wire size for 100 Amp sub panel 100ft in length form 200 Amp main panel?   Do I have to buy all 3 wires (2 hot and 1 neutral) the same size? Or can neutral wire be smaller size?


I'm having trouble designing a database for a project I was working on recently. It's to do with a garage management system.  So I've realised I need to store multiple types of parts (Tyres, engines, wheel bases, this list needs to grow), with multiple types of details, some that each part shares (name, part number, condition, quantity) and some that are unique to each part (engines have weight and power, tyres have size and alloy type) and that also needs to grow too. This can't be limited to just 2 kinds of unique information, it needs to be infinite, so that more can be added at a later date if required  How can I design a database that is capable of storing all of this information without having tables for each specific part, so a table for tyres, a table for engines etc? I want to keep it so the least amount of tables as possible is used, so once designed, no new tables are added as new data is added.  Any help is appreciated.

We process a routine data feed from a client who just refactored their database from a form that seems familiar (one row per entity, one column per attribute) to one that seems unfamiliar to me (one row per entity per attribute):  Before: one column per attribute  ID   Ht_cm   wt_kg   Age_yr  ...  1      190      82     43    ... 2      170      60     22    ... 3      205      90     51    ...   After: one column for all attributes  ID    Metric   Value  1     Ht_cm     190  1     Wt_kg     82  1     Age_yr    43  1      ...  2     Ht_cm     170  2     Wt_kg     60  2     Age_yr    22  2     ...  3     Ht_cm     205  3     Wt_kg     90  3     Age_yr    51  3     ...   Is there a name for this database structure?  What are the relative advantages?  The old way seems easier to place validity constraints on specific attributes (non-null, non-negative, etc.) and easier to calculate averages.  But I can see how it might be easier to add new attributes without refactoring the database.  Is this a standard/preferred way of structuring data?


Flights from Lima to Houston don't allow passengers to bring water on board (even if purchased after the security checkpoint):    They do screen passengers' carry-on baggage right before boarding.  Which flights to the US don't permit passengers to bring water or other liquid on board (even if purchased after the security checkpoint)? Does that apply to any international flight to the US nowadays? Or only from some airports or countries?

In a , I found that the U.S. requires flights from Hong Kong that are bound for the U.S. to confiscate liquids in containers above 100 mL from carry-on luggage in a secondary screening at the gate. However, this did not occur on a recent (June 2014) flight I took to the U.S. from Incheon, South Korea. I've also read forum posts where this has not applied to others going to the U.S. from Seoul or parts of Europe, but also where it has applied to those flying to the U.S. from some other places, including Latin America.  So, under what conditions are U.S.-bound flights required to confiscate liquids from carry-on items at the gate (as opposed to only confiscating them at security checkpoints and allowing items purchased airside to be taken on the plane, as happens on U.S. domestic flights?)  Is this only from certain countries whose primary screening isn't approved by the U.S. DoT (or DHS, as the case may be) for some reason? If so, is there a definitive list of which countries require (or, conversely, don't require) this check at the gate?  Is there an element of randomness to whether liquids acquired airside may be allowed on any given U.S.-bound international flight or is the procedure generally the same from a given departure point? It appears that, , the gate check is always applied, but I'm wondering about the general case of U.S.-bound international flights.  In order to limit the scope of the question, I'm not referring to items purchased in duty-free shops and the special rules and circumstances that may be involved with those. I'm just concerned with filling up or buying a water bottle or buying a soda or some such thing airside and taking it on the plane.


I have defined a sequence $x_n$ as follows: $$x_{n+1}=x_n+\frac{1}{x_n}, \space\space\space x_0=1$$ After convincing myself that there is no nice closed-form formula for $x_n$, I decided to try and find an asymptotic formula for $x_n$ (unfortunately, I have very little experience with asymptotic formulae). I noticed that the recurrence is equivalent to $$\Delta x_{n}=\frac{1}{x_n}$$ and so a solution can be approximated by solving the corresponding differential equation for $y(t)$: $$y'=\frac{1}{y}$$ This differential equation (with initial value $y(0)=1$) yielded $$y=\sqrt{2t+1}$$ which led me to believe that $$x_n\approx \sqrt{2t+1}$$ When I plotted $x_n$ and $y(n)$ side by side, it did indeed appear that they were very close to each other. However, this isn't enough for me... I would like to prove that $y(n)$ is a good approximation for $x_n$, either by proving that $$\lim_{n\to\infty}(x_n-\sqrt{2n+1})=0$$ ...or, even better, by finding a zero-approaching function $f$ satisfying $$x_n=\sqrt{2n+1}+O(f(x))$$ This is where I got stuck. How do can I prove (or disprove?) the statement in the first equality, and find $f$ satisfying the second?  NOTE: There may be a closed-form that I wasn't able to find. In fact, the similar sequence $$y_{n+1}=\frac{y_n}{2}-\frac{1}{2y_n}$$ has closed form formula $$y_n=\frac{1}{\tan(2^n\arctan(y_0^{-1}))}$$ ...but even if you do find a closed form, I would still like to know how to prove the above statements, since the techniques would be useful to know for future problems.

Today, we had a math class, where we had to show, that $a_{100} > 14$ for  $$a_0 = 1;\qquad a_{n+1} = a_n + a_n^{-1}$$  Apart from this task, I asked myself: Is there a closed form for this sequence? Since I didn't find an answer by myself, can somebody tell me, whether such a closed form exists, and if yes what it is?


NOTE:  does not answer this question. The suggested fixes in this question is to set up FB, IG, and other social media pages. We have had these for months. We have 576 Instagram followers, 293 followers on Facebook, 17,425 views on Vimeo, Youtube, Pinterest and LinkedIn presence. Here is the response in a YouTube search:  Let's be clear. If you search for my company name and product name YT changes the spelling to something that doesn't exist and suggests a video with no matching result terms (using either spelling) disparaging OTHER luxury handbags, while leaving the viewer with the impression it is referring to our handbags. Google When a user searches for our business, , Google changes the spelling to Aslan Vaughn and displays these results:  If you misspell part of the name (aslan vaugn or aslaen vaughn), it shows my company at the top of the results. For the first few months it just seemed like it was taking some time to percolate, but over 7 months we have had 17,500 unique visitors and 90 backlinks.  The only results for Aslan Vaugn is the birth announcement of the second child of a musician in New Jersey. It is a Facebook post and has 14 likes. Google is favoring a spelling that has only two results with 14+ views over my company with dozens of results and tens of thousands of views. How is this possible? An FB post with 14 likes is that much more popular than a business with 17,500 unique visitors and 40,000 page views (despite the Google obfuscation)? Do I have an enemy at Google? On other search engines my company covers the first few pages in results. Through Google, you cannot find our company no matter how many pages in you go. Unless you search for the term in quotes, . In which case we cover the first few pages here like in the other search engines:

I have reviewed this:   but it does not answer my question. The suggested fixes in this question is to set up FB, IG, and other social media pages. We have had these for months. We have 576 Instagram followers, 293 followers on Facebook, 17,425 views on Vimeo, Youtube, Pinterest and LinkedIn presence. Here is the response in a YouTube search:  Let's be clear. If you search for my company name and product name YT changes the spelling to something that doesn't exist and suggests a video with no matching result terms (using either spelling) disparaging OTHER luxury handbags, while insinuating it is referring to my handbags. When a user searches for our business, , Google and Youtube changes the spelling to Aslan Vaughn and displays these results:  For the first few months it just seemed like it was taking some time to percolate, but over 7 months we have had 17,500 unique visitors and nearly 90 backlinks.  The only results for Aslan Vaugn is the birth announcement of the second child of a musician in New Jersey. It is a Facebook post and has 14 likes. Google is favoring a spelling that has only two results with 14+ views over dozens of links and tens of thousands of views. How is this possible? An FB post with 14 likes is that much more popular than a business with 17,500 unique visitors (despite the Google obfuscation)? Is my company on some list? On other search engines my company covers the first few pages in results. Through Google, you cannot find our company no matter how many pages in you go. Unless you search for the term in quotes, . In which case we cover the first few pages here as well:


I am looking to open my own business, and am trying to find an Ubuntu alternative to QuickBooks Professional.  I would love to find a SOLID business management system that allows estimating, invoicing, customer retention, full banking functions, and finally full accounting ability that makes tax time easy work for my CPA.  If anyone has any ideas, or are currently using an open-source program to run their business, I would be extremely interested in hearing from you, and your personal input on the software functionality.

I've just installed Ubuntu to replace Windows. I can't seem to find a good alternative to  to run on Ubuntu. Any help would be appreciated.


I live in scandinavia and the Market for paid applications is not available here yet. Is there any way I can enable it? Or a workaround?

I'm travelling to country X. I want to install an application which isn't available in my country, but is available in country X; but I prefer to download and install it in advance, while the data connection is still cheap.  Unfortunately, the Play Stores does not allow me to install this app. Is there any way to circumvent this limitation?


If $A$ and $B$ are $n×n$ matrices, then $|A+B^T|=|A^T+B|$ can I prove that it's t/f without giving a value to the matrices?

How can you show that $$ \det(A + B^T) = \det(A^T + B)$$ for any $n\times n$ matrices $A$ and $B.$


Suppose I have a "Type mytype", and if I do "mytype.ToString()", I get "System.Collections.Generic.List`1[Example1.Employee]", how do I get the list item type, which is "Example1.Employee"? Do I have to parse this string to get this list item type? Is there a more elegant way, such as "mytype.ItemType"? Also, why is there a "`1" appendix at the end of "System.Collections.Generic.List`1"? And, why is there a "`2" at the end of "System.Collections.Generic.Dictionary`2"?

Let's say I have a generic member in a class or method, like so: public class Foo<T> {     public List<T> Bar { get; set; }          public void Baz()     {         // get type of T     }    }  When I instantiate the class, the T becomes MyTypeObject1, so the class has a generic list property: List<MyTypeObject1>. The same applies to a generic method in a non-generic class: public class Foo {     public void Bar<T>()     {         var baz = new List<T>();                  // get type of T     } }  I would like to know what type of objects the list of my class contains. So what type of T does the list property called Bar or the local variable baz contain? I cannot do Bar[0].GetType(), because the list might contain zero elements. How can I do it?


$a,b,c,~$and $d$ are rational numbers. $b>0$ and $d>0$ the $\sqrt{b}$ and the $\sqrt{d}$ are both irrational.   if $a+\sqrt{b}=c+\sqrt{d}$  show that $a = c$ and $b = d$.  I know that a=c and b=d intuitively, but I'm not sure how to prove it.

Let $a, b, c, d$ be rational numbers, where $\sqrt{b}$ and $\sqrt{d}$ exist and are irrational. If $a + \sqrt{b} = c + \sqrt{d}$, prove that $a=c$ and $b=d$.


I want to check whether a string entered is NAN in typescript. Currently I am doing like  if (isNaN(parseInt(input))) return "It's not a number."   This works fine if I enter @@@@ or #### but if I enter "444@@@@", this is not working.

I'm hoping there's something in the same conceptual space as the old VB6 IsNumeric() function?


It often occurs that there are many answers on a single post and thus makes it time-consuming to scroll down and click "Add Answer" on the iOS app, a perfect example is the , with a whopping 1360 answers. Can we get a sticky "Add Answer" button so I don't have to scroll down?

Tried to add an answer to  via ios-app, but tired to reach "add an answer" button by scrolling down.   Is it possible to add an answer without scrolling over all existing answers via ios-app?   On the web I need to scroll only answers on the first page to reach desired button.


There seems to be a lot of problems with installing Spotify in 16.04. I tried this guide  to make sure I wasn't just screwing up, but it never worked. Turns out, this question is a little out-dated. To help out new users, I'll ask the question, give some information, then answer this.  I'm trying to install spotify in Ubuntu 16.04. I tried a few different guides. Here's the steps I've done in the previously mentioned guide. First, I pasted in  echo 'deb http://repository.spotify.com stable non-free' | sudo tee --append /etc/apt/sources.list   Then I added the key using:  sudo apt-key adv --keyserver hkp://keyserver.ubuntu.com:80 --recv-keys 94558F59   Finally I updated and tried installing Spotify using  sudo apt-get update && sudo apt-get install spotify-client

A while ago Spotify (the streaming music service) came out with a preview for Linux of their client.  So what should I do?


I'm on Lubuntu 17.04 and unfortunately I don't see my local 5ghz wifi network.  However I have no problem with connecting to 2.4ghz network after installing firmware-b43-installer. Also when I had Ubuntu 17.04 installed it didn't have any problems with seeing and connecting to any network (and I didn't have to install anything). I've checked similar answers but all lead to installing same b43 driver. So what is Lubuntu missing that is present on Ubuntu (17.04)?   My card is: Broadcom Limited BCM4331 802.11a/b/g/n

I'm having serious problems installing the Broadcom drivers for Ubuntu. It worked perfectly on my previous version, but now, it is impossible.   What are the steps to install Broadcom wireless drivers for a BCM43xx card?  I'm a user with no advance knowledge in Linux, so I would need clear explanations on how to make, compile, etc.    lspci -vnn | grep Network showed:   Broadcom Corporation BCM4322 802.11a/b/g/n Wireless LAN Controller [14e4:432b]      iwconfig showed:  lo        no wireless extensions. eth0      no wireless extensions.   NOTE: Answer below is updated every time new information is added and confirmed working.


I plug in the printer, the system recognizes it, but when I try to print something nothing happens.   OS: Ubuntu 18.04 LTS

Let's assume that one has some modern HP printer and/or scanner which is not supported by HPLIP package from official repository. Currently Ubuntu versions have :  trusty (14.04LTS): 3.14.3-0ubuntu3.4 xenial (16.04LTS): 3.16.3+repack0-1 bionic (18.04LTS): 3.17.10+repack0-5 focal (20.04LTS): 3.20.3+dfsg0-2 groovy (20.10): 3.20.5+dfsg0-3build1 hirsute (21.04): 3.21.2+dfsg1-2   What can one do if printer is supported in newer version of HPLIP (checked this in )?


the following useful find command , print the value from Name tag   find /tmp -type f -name '*.xml' -exec grep -o -P '(?<=<Name>).*(?=</Name>)' {} \;   the problem is in case we have couple xml files under /tmp then we never know which xml file have the Name tag  or in other words this find syntax will print the value of Name   but without the xml file name  please advice how to print the file name when grep matched the:  (?<=<Name>).*(?=</Name>)

When using find, how do I return the file name and the line number when searching for a string? I manage to return the file name in one command and the line numbers with another one, but I can't seem to combine them.  File names: find . -type f -exec grep -l 'string to search' {} \;  Line numbers: find . -type f -exec grep -n 'string to search' {} \;


I have a title with a flask jinja2 input. I want to update the title along with some div tags. I update the div tags with setInterval and jquery like this: <script type="text/javascript"> $(document).ready(function() { /// Wait till page is loaded setInterval(timingLoad, 15000); function timingLoad() { $.get().done(doc => {   $("#main").html($(" #main", doc))   $("#count").html($(" #count", doc)) }); } }); //// End of Wait till page is loaded </script>  My title looks like this: <title id="online_count">{% block title %} ({{online_num}}) Online{% endblock %} </title>  How can I in the setInterval function have the title refresh as well? Adding $("#online_count").html($(" #online_count", doc)) doesn't work.

I have a webpage that implements a set of tabs each showing different content. The tab clicks do not refresh the page but hide/unhide contents at the client side.  Now there is a requirement to change the page title according to the tab selected on the page ( for SEO reasons ). Is this possible? Can someone suggest a solution to dynamically alter the page title via javascript without reloading the page?


Can there be a search option when trying to go through my "Favorite" questions? If I have a lot of questions marked as favorite, it is quite a task to go through them and check if I have already an answer to a question that I currently have.  We can have a search box, where we can type tags that might describe the problem we have at hand and it returns the list of favorite questions which "might" fit our description thereby reducing the time required to zero in on the correct "answer" question.  It will help find/manage content better, IMHO.  A related question:

I don't know about anyone else, but I have a reasonable list of favourites now, and it can be rather difficult to find the relevant ones at any given time. Sometimes, I have a specific one in mind, others I just want to see all favourites relating to a specific topic. It would be nice if there were a way to organise my favourites by tag, or OP, or possibly just search them.  How can we improve the favourites feature?  Please post your ideas on how we might improve the favourites feature of the Stack Exchange sites. Try to keep each answer to one idea so that the votes reflect the popularity of a single idea.


I apologize for my noobidity, but how can I disable this gradient thing? I need accurate, solid colors. Thank you in advance.

I unwrapped a simple plane and applied the following 80x80 pixel picture:    Yes, it's quite small. The problem is, the result is all blurry, like so:    How do I make it accurate to the pixel?


how do i can change my username Ubuntu? because i tried one more time to change my own username, so please help me to this question about user change. thank you.

Some time ago, when I installed Ubuntu, I chose a rather stupid username for my account that I do not want to use anymore. How do I change this (including the name of my home directory, and the name in the terminal) without losing settings for applications? How do I keep permissions and my keys for various authentification (e.g. email, SSH, GPG and more)? What settings could possibly get lost if I changed my username?


I have a load of tools that are kept in the /opt directory. The tools are organised like this: /opt/toolname/tool.sh. My question is, how can I add the tools in my /opt folder to my path, so i can run them from any directory in a terminal.  I have managed to do this with some tools by creating a symlinks in /usr/bin; but with over 200 tools it is a very tedious way of doing things. is there a better way to do this?

What should I do if I want to be able to run a given program regardless of my current directory? Should I create a symbolic link to the program in the /bin folder?


Problem: prove that after putting in 11 1 by 2 tiles in the 6 by 6 chessboard, there is definitely room to put in another tile. Tiles cannot overlap with each other. So I found this similar problem:  Apparently if you cover the whole chessboard with 18 tiles, you can find a line without crossing each tile. But is this a related problem to the original problem?

OEIS sequence  (based on ) describes the     minimum number of dominoes on an $n \times n$ chessboard to prevent placement of another domino.   The sequence begins:  0, 2, 3, 6, 9, 12, 17, 22, 27, 34, 41, 48, 57, 66, 75   Fifteen terms are known, and a few folks have conjectured that $$    A280984(n) = \left\lceil \frac {n^2}3 \right\rceil \text{ for } n > 1. $$  Andrey Zabolotskiy has a proof that (1) this is a lower bound, and (2) this conjecture holds when $n$ is a multiple of $3$.  In order to prove the conjecture it is sufficient to give a tiling strategy for the $(3n+1)\times(3n + 1)$ and $(3n+2)\times(3n+2)$ boards.  Example of $3n \times 3n$ boards.  To achieve this bound for the $3n \times 3n$ boards you can just do the naive placement, but for the other boards, it's not clear which placement strategy to use.  (Notice that the second and third examples are not optimal: the last two boards have $35$ tiles and $42$ tiles respectively, but there exist $34$ and $41$ tile placements.)      Question  Is there simple strategy for the $(3n+1) \times (3n+1)$ and/or the $(3n+2) \times (3n+2)$ boards that attains the lower bound? Or is the conjecture false?


How do I center a div at the middle of my page in html using CSS?  Something like www.google.com, when you go to the site, you will see the search bar and the logo are centered in the middle of the page.  Any way to go around this?

Best way to center a <div> element on a page both vertically and horizontally?  I know that margin-left: auto; margin-right: auto; will center on the horizontal, but what is the best way to do it vertically, too?


Recently we have migrated our application (both web app and database) to Azure (IASS). There we have a VM with SQL Server 2014 installed. Also I have restored all the necessary databases and SQL Server jobs on the server (from the existing On-Premise DB server). All the settings are verified and the application was working fine for a week.   Then we noticed a problem with the log file size (size is increasing  and reached around 42 GB and not able to execute any of the basic query and everything breaks :( ). The same DB and Job ran in on-premise server for a year and  this issue didn't happen.   Some information about the application and DB   The application contains a couple of SQL scheduling jobs which run each 2 hours of a day and the job take maximum of 5-8 minutes to complete. Application contains less than 200 users and concurrent users are around 20-30.   So please let me know any one of your comments/input on this (Transaction log file size increment) issue. Also please let me know if you need any other information

This one seems to be a common question in most forums and all over the web, it is asked here in many formats that typically sound like this:  In SQL Server -  What are some reasons the transaction log grows so large? Why is my log file so big? What are some ways to prevent this problem from occurring? What do I do when I get myself on track with the underlying cause and want to put my transaction log file to a healthy size?


From a physicist's perspective there are several situations in which somehow arbitrary choices of mathematical structures can be made. One can describe a system from different perspectives, etc. without changing anything in the physical properties. (see gauge invariance, picture changing etc.) In the situation when these choices impose a mathematical structure one has limitations in the subsequent choices (are these limitations physical???). However, there are situations when this prescription does not hold. The best example is in this case the Black-Hole complementarity principle (if it is well defined in the first place).  So, the question about how mathematical structures "interact" in a logical way is not a bad one. Again: what is the interaction between, say, locality and Hausdorff-ity in the case of a black hole? Or what is the true relation between metrizability and hausdorff-ity of a space in the context of a black hole? The question about how mathematical structures assigned (innocently) at some point interact in different situations is in my opinion a quite relevant one...


I wanted to know where can I began learning VFX in blender. I know that blender has a great compositing, camera tracking and masking etc. capabilities and I want to know how can I use them effectively to create effects like the ones in Infinity War and Harry Potter series. I know some YouTube channels have tutorials for this like  and  but their tutorials teach how to achieve specific effects (like fire, smoke etc.) whereas I am looking for systematic tutorials from basics like the ones Blender Guru has for modelling. So it would be really helpful if someone guides me regarding this. Thanks.

Since asking for tutorials, videos, resources, links to other content or downloads is considered off topic here, this is a specifically created Community Wiki which gathers resources for Blender and it has been approved by the .  Just write in the appropriate answer/section. If you have concerns, questions, post a  question, so we don't clutter the comments, but you can link your meta question from the comments.  Questions regarding such resources are not allowed anymore, except for very specific and on topic requests (ask on  if you're unsure about your question). Follow the instructions made in the question about how to post, what can be posted, etc.  Learning             Assets    (also see: )   Reference Images/Blueprints (also see: )    Tools    (also see: )      Other   Special Interest ()     Also see the .


I accidentally formatted an external hard drive on mac with Disk Utility from NTFS to FAT32. I'm looking at TestDisk to see if I'm able to recover the data that was on there, but I can't seem to figure out how to get it back..   Is this even possible? And if so, how would I do this?

I have a harddisk with two partitions: one for windows and one for data. I've reinstalled windows on the first partition and formatted the data partition with full format (without /Q option) making sure that all my data is backed up. After that I've created the same folder structure (without files inside) on data partition as it was before formatting.   I then realized that all my photos were NOT backed up :((((  I've tried several tools to recover my data without any success:   Wordershare Photo Recovery Active File Recovery R-Studio PhotoRec from CGSecurity Recuva   There are max 50Mb of new data on that partition, so data overwriting is minimal.  What is the reason why I'm not able to recover my data with data recovery tools: full format or same folder structure?  And... can I get my photos back or they are lost forever?


I am Egyptian and I just have Bulgarian visa. My flight will have transit in Athens for 20 h, will it be a problem to stay in the airport without Schengen visa?

I found many related questions on this site but I am still not sure about the rules. How can I decide if I need a visa to transit? Schengen members as of May 2021 are as follows:  Austria Belgium Czech Republic Denmark (excluding Greenland and the Faroe Islands - but an open border with the Schengen Area is maintained) Estonia Finland France (excluding overseas departments and collectivities) Germany Greece Hungary Iceland Italy Latvia Liechtenstein Lithuania Luxembourg Malta Netherlands (excluding Aruba, Curaçao, Sint Maarten and the Caribbean Netherlands) Norway (excluding Svalbard) Poland Portugal Slovakia Slovenia Spain (except Ceuta and Melilla) Sweden Switzerland