Why didn't Obi-Wan or Owen Lars change Luke's last name?
If Obi-Wan and Yoda were trying to keep Luke safe from Vader, why would they let him keep the Skywalker name?
Evaluate the integral $\int_0^{2a}\int_0^\sqrt{2ax-x^2}\frac{\phi'(y)(x^2+y^2)x dxdy}{\sqrt{4a^2x^2-(x^2+y^2)^2}}$ Change the order of integration in:  $$\int_0^{2a}\int_0^\sqrt{2ax-x^2}\frac{\phi'(y)(x^2+y^2)x }{\sqrt{4a^2x^2-(x^2+y^2)^2}}dxdy$$ and hence evaluate it.    I changed the order of integration and got the limits $y=0$ to $a$ and $x=a-\sqrt{a^2-y^2}$ to $a+\sqrt{a^2-y^2}$. I then tried changing to polar coordinates, but it is only making the integrand more complex. Why is transferring money online to someone else's bank account so difficult in the U.S.? Did English ever have a formal version of "you"? From the top of my head, Danish "De" (practically never used), German "Sie", Chinese "您", French "vous", Spanish "usted" are a formal way of addressing someone, especially if one isn't familiar with the addressee. Did English ever have this? It sounds as though Proto-Indo-European might have had this (based on my 4 examples), but perhaps someone can enlighten me? Real Analysis question on FTC, Integral Let $g:[0,1] \rightarrow \mathbb R$ be a continuous function and assume that    $$ \int_{0}^{1} g(x) \phi'(x) dx = 0 $$   for all continuously differentiable functions $\phi: [0,1] \rightarrow \mathbb R$, where $\phi (0) = \phi(1) = 0$. Show that $g(x) = c$ for all $x \in [0,1]$ for some constant $c \in \mathbb R$.    My thoughts are applying integration by parts with $G(t) = \int_{0}^{t} g(x) dx $, since now we get  $$ 0 = \int_{0}^{1} G(t) \phi'(t) dt  + \int_{0}^{1} g(t) \phi (t) dt $$  which doesn't really go far. The second thought was applying MVT for definite integrals, which doesn't go far either as the conditions are hardly satisfied.   Any hints? If I can generally reach web pages on the Internet but can't reach a specific one, how do I troubleshoot what the cause is as an end user?       This question was a .   Read the  for more details or  yourself When I use the \tableofcontents macro in a document where the etoc package is loaded, latex pauses and reports an error. If I let the compilation continue a well formed pdf is generated.  Minimal example that can reproduce the error on my machine.  \listfiles \documentclass{article} \usepackage{etoc}  \begin{document} \tableofcontents‎‎ \end{document}   Output from pdflatex on the minimal example.  This is pdfTeX, Version 3.14159265-2.6-1.40.19 (TeX Live 2018) (preloaded format=pdflatex)  restricted \write18 enabled. entering extended mode (./mwe.tex LaTeX2e &lt;2018-04-01&gt; patch level 4 (/usr/local/texlive/2018/texmf-dist/tex/latex/base/article.cls Document Class: article 2014/09/29 v1.4h Standard LaTeX document class (/usr/local/texlive/2018/texmf-dist/tex/latex/base/size10.clo)) (/usr/local/texlive/2018/texmf-dist/tex/latex/etoc/etoc.sty (/usr/local/texlive/2018/texmf-dist/tex/latex/tools/multicol.sty)) (./mwe.aux)  ! Package inputenc Error: Unicode character ‎ (U+200E) (inputenc)                not set up for use with LaTeX.  See the inputenc package documentation for explanation. Type  H &lt;return&gt;  for immediate help.  ...                                                l.6 \tableofcontents‎                        ‎ ? R OK, entering \nonstopmode...  ! Package inputenc Error: Unicode character ‎ (U+200E) (inputenc)                not set up for use with LaTeX.  See the inputenc package documentation for explanation. Type  H &lt;return&gt;  for immediate help.  ...                                                l.6 \tableofcontents‎‎  [1{/usr/local/texlive/2018/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] (./mwe.aux)   *File List*  article.cls    2014/09/29 v1.4h Standard LaTeX document class   size10.clo    2014/09/29 v1.4h Standard LaTeX file (size option)     etoc.sty    2018/02/23 v1.08n Completely customisable TOCs (JFB) multicol.sty    2018/04/20 v1.8s multicolumn formatting (FMi)  ***********   ) (see the transcript file for additional information)&lt;/usr/local/texlive/2018/te xmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb&gt;&lt;/usr/local/texlive/2018/tex mf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb&gt; Output written on mwe.pdf (1 page, 16281 bytes). SyncTeX written on mwe.synctex.gz. Transcript written on mwe.log. What's the use of a decoupling capacitor near a reservoir capacitor? I've seen some circuits where a decoupling capacitor is used as well as a reservoir capacitor, like this (C4 and C5):    I've read about  and for me it looks as if they are meant to remove small fluctuations in the supply voltage. Then I thought - wasn't that the purpose of a  as well? Why wouldn't the reservoir capacitor be able to filter out the small fluctuations, if it is able to filter out the large fluctuations?  So I feel like I have a basic misunderstanding here. What is the purpose of a decoupling capacitor next to a reservoir capacitor, when we assume we place both equally near to the power consuming part? Or is the only advantage of the decoupling capacitor that it is smaller and can therefore be easily placed more near to the power consuming part? What are the downsides of removing ubuntu-desktop metapackage? What is the difference between "citizen" and "denizen" Citizen: 1. A legally recognized subject ornational of a state or commonwealth, either native or naturalized. 2. An inhabitant of a particular town or city.  Denizen: 1. An inhabitant or occupant of a particular place.  Same thing? I'm using ubuntu 14.04 LTS. When I start my pc and click on any bookmark from the file manager it shows this error:   Unable to find the requested file. Please check the spelling and try again. Unhandled error message: Error when getting information for file '/media/angel/DOC/edu': No such file or directory   But when I open DOC drive and again clink on the same bookmark it works properly. Can anybody tell me why is this happening and how to solve this issue?   Edit: Output of lsblk is following: (ubuntu is installed in sda5)  NAME   MAJ:MIN RM   SIZE RO TYPE MOUNTPOINT sda      8:0    0 119.2G  0 disk  ├─sda1   8:1    0  91.3G  0 part  ├─sda2   8:2    0     1K  0 part  ├─sda5   8:5    0  24.1G  0 part / └─sda6   8:6    0   3.8G  0 part [SWAP] sdb      8:16   0 465.8G  0 disk  ├─sdb1   8:17   0  93.2G  0 part  ├─sdb2   8:18   0     1K  0 part  ├─sdb5   8:21   0  93.2G  0 part  ├─sdb6   8:22   0  89.3G  0 part  ├─sdb7   8:23   0  93.2G  0 part  ├─sdb8   8:24   0  93.2G  0 part  └─sdb9   8:25   0   3.8G  0 part  sr0     11:0    1  1024M  0 rom     After opening the disk drive the output of lsblk is bellow:   NAME   MAJ:MIN RM   SIZE RO TYPE MOUNTPOINT sda      8:0    0 119.2G  0 disk  ├─sda1   8:1    0  91.3G  0 part  ├─sda2   8:2    0     1K  0 part  ├─sda5   8:5    0  24.1G  0 part / └─sda6   8:6    0   3.8G  0 part [SWAP] sdb      8:16   0 465.8G  0 disk  ├─sdb1   8:17   0  93.2G  0 part  ├─sdb2   8:18   0     1K  0 part  ├─sdb5   8:21   0  93.2G  0 part  ├─sdb6   8:22   0  89.3G  0 part /media/angel/DOC ├─sdb7   8:23   0  93.2G  0 part  ├─sdb8   8:24   0  93.2G  0 part  └─sdb9   8:25   0   3.8G  0 part  sr0     11:0    1  1024M  0 rom   The output of sudo blkid gives the following information about sdb6:  /dev/sdb6: LABEL="DOC" UUID="04280A22280A12FA" TYPE="ntfs" Why is sample standard deviation a biased estimator of $\sigma$? According to the Wikipedia article on  the sample SD   $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \overline{x})^2}$$  is a biased estimator of the SD of the population. It states that $E(\sqrt{s^2}) \neq \sqrt{E(s^2)}$.   NB. Random variables are independent and each $x_{i} \sim N(\mu,\sigma^{2})$   My question is two-fold:   What is the proof of the biasedness? How does one compute the expectation of the sample standard deviation    My knowledge of maths/stats is only intermediate. Selecting a database in mysql with spaces in its name I want to select my particular database in mysql console, but the problem is that my database name has a space in between and mysql ignores the part after the space. For instance, when i give the command:  use 'student registration'   I get the message:  cannot find database 'student' Pluralizing Noun Phrase? On webmail every user gets error "ERROR: Message not sent. Server replied: 354" while sending mails.   But mails are sent properly and reaches properly.  Can you tell me where is problem, and why it is occurred?  UPDATE: I found in some resources that this is not an error but standard information message. On the other side, it's annoying. Can you tell me if it is a true, and if it is how can I avoid it? I have a dedicated server with 2 TB storage.   My problem is that the whole storage is allotted to the root partition.   Whenever I try to resize it using lvresize, the root partition gets corrupted and then I have to reprovision the server.   Is there any option to resize the root partition without unmounting in lvm?  I am trying to reduce the root partition to 100GB.  Vgs  root@s93079:/home/customer# vgs   VG        #PV #LV #SN Attr   VSize VFree   s93079-vg   1   2   0 wz--n- 1.82t    0   Lvs  LV     VG        Attr       LSize  Pool Origin Data%  Meta %  Move Log Cpy%Sync Convert   root   s93079-vg -wi-ao----  1.79t    swap_1 s93079-vg -wi-ao---- 32.00g   Fdisk - l  Device     Boot  Start        End    Sectors  Size Id Type /dev/sda1  *      2048     499711     497664  243M 83 Linux /dev/sda2       501758 3907028991 3906527234  1.8T  5 Extend /dev/sda5       501760 3907028991 3906527232  1.8T 8e Linux  Disk /dev/mapper/s93079--vg-root: 1.8 TiB, 1965782204416 byt es, 3839418368 sectors Units: sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk /dev/mapper/s93079--vg-swap_1: 32 GiB, 34355544064 byte s, 67100672 sectors Units: sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes   Vgdisplay   --- Volume group ---   VG Name               s93079-vg   System ID   Format                lvm2   Metadata Areas        1   Metadata Sequence No  3   VG Access             read/write   VG Status             resizable   MAX LV                0   Cur LV                2   Open LV               2   Max PV                0   Cur PV                1   Act PV                1   VG Size               1.82 TiB   PE Size               4.00 MiB   Total PE              476870   Alloc PE / Size       476870 / 1.82 TiB   Free  PE / Size       0 / 0   VG UUID               dPrEwA-77pM-pGai-9jZB-ldMZ-iL20-HAe9 Dj   lvdisplay /dev/s93079-vg/root   --- Logical volume ---   LV Path                /dev/s93079-vg/root   LV Name                root   VG Name                s93079-vg   LV UUID                bpGNau-XirV-P7PA-8d6k-OCOy-TAwN-HXl FVI   LV Write Access        read/write   LV Creation host, time s93079, 2016-08-27 09:22:05 -0500   LV Status              available   # open                 1   LV Size                1.79 TiB   Current LE             468679   Segments               1   Allocation             inherit   Read ahead sectors     auto   - currently set to     256   Block device           254:0   Lvdisplay /dev/s93079-vg/swap_1  --- Logical volume ---  LV Path                /dev/s93079-vg/swap_1  LV Name                swap_1  VG Name                s93079-vg  LV UUID                j74PLZ-E9gK-9Bbb-EkKq-xRJv-TuU4-FgH gm  LV Write Access        read/write  LV Creation host, time s93079, 2016-08-27 09:22:05 -0500  LV Status              available  # open                 2  LV Size                32.00 GiB  Current LE             8191  Segments               1  Allocation             inherit  Read ahead sectors     auto  - currently set to     256  Block device           254:1   Df - h  /dev/dm-0       1.8T  923M  1.7T   1% / udev             10M     0   10M   0% /dev tmpfs           3.2G  8.5M  3.2G   1% /run tmpfs           7.9G     0  7.9G   0% /dev/shm tmpfs           5.0M     0  5.0M   0% /run/lock tmpfs           7.9G     0  7.9G   0% /sys/fs/cgroup /dev/sda1       236M   33M  191M  15% /boot This seems to be a basic issue, but I just realized that I actually don't know how to test equality of coefficients from two different regressions. Can anyone shed some light on this?   More formally, suppose I ran the following two regressions:  $$ y_1 = X_1\beta_1 + \epsilon_1 $$ and  $$ y_2 = X_2\beta_2 + \epsilon_2 $$ where $X_i$ refers to the design matrix of regression $i$, and $\beta_i$ to the vector of coefficients in regression $i$. Note that $X_1$ and $X_2$ are potentially very different, with different dimensions etc. I am interested in for instance whether or not $\hat\beta_{11} \neq \hat\beta_{21}$.   If these came from the same regression, this would be trivial. But since they come from different ones, I am not quite sure how to do it. Does anyone have an idea or can give me some pointers?   My problem in detail: My first intuition was to look at the confidence intervals, and if they overlap, then I would say they are essentially the same. This procedure does not come with the correct size of the test, though (i.e. each individual confidence interval has $\alpha=0.05$, say, but looking at them jointly will not have the same probability). My "second" intuition was to conduct a normal t-test. That is, take   $$ \frac{\beta_{11}-\beta_{21}}{sd(\beta_{11})} $$  where $\beta_{21}$ is taken as the value of my null hypothesis. This does not take into account the estimation uncertainty of $\beta_{21}$, though, and the answer may depend on the order of the regressions (which one I call 1 and 2).   My third idea was to do it as in a standard test for equality of two coefficients from the same regression, that is take  $$ \frac{\beta_{11}-\beta_{21}}{sd(\beta_{11}-\beta_{21})} $$   The complication arises due to the fact that both come from different regressions. Note that   $$ Var(\beta_{11}-\beta_{21}) = Var(\beta_{11}) + Var(\beta_{21}) -2 Cov(\beta_{11},\beta_{21}) $$ but since they are from different regressions, how would I get $Cov(\beta_{11},\beta_{21})$?  This led me to ask this question here. This must be a standard procedure / standard test, but I cound not find anything that was sufficiently similar to this problem. So, if anyone can point me to the correct procedure, I would be very grateful! I have a script myscript.sh  #!/bin/sh  echo $1 $2   which is used something like ...  ./myscript.sh foo bar   which gives me an output of ...  foo bar     but how can i make this script include custom command options? for example ...  ./myscript.sh -a foo and corespond to $1   and  ./myscript.sh -b bar and corespond to $2 When I entered the -al attribute with the  command, I got the following:  anupam@JAZZ:~/blog$ ls -al total 76 drwxrwxr-x 13 anupam anupam 4096 Aug 28 21:45 . drwxr-xr-x 34 anupam anupam 4096 Aug 28 20:52 .. drwxrwxr-x  8 anupam anupam 4096 Aug 28 12:19 app drwxr-xr-x  2 anupam anupam 4096 Aug 28 12:19 bin drwxrwxr-x  5 anupam anupam 4096 Aug 28 12:19 config -rw-rw-r--  1 anupam anupam  154 Aug 28 12:19 config.ru drwxrwxr-x  3 anupam anupam 4096 Aug 28 12:37 db -rw-rw-r--  1 anupam anupam 1339 Aug 28 12:19 Gemfile -rw-rw-r--  1 anupam anupam 2871 Aug 28 12:19 Gemfile.lock drwxrwxr-x  7 anupam anupam 4096 Aug 28 21:45 .git -rw-rw-r--  1 anupam anupam  466 Aug 28 12:19 .gitignore drwxrwxr-x  4 anupam anupam 4096 Aug 28 12:19 lib drwxrwxr-x  2 anupam anupam 4096 Aug 28 12:29 log drwxrwxr-x  2 anupam anupam 4096 Aug 28 12:19 public -rw-rw-r--  1 anupam anupam  249 Aug 28 12:19 Rakefile -rw-rw-r--  1 anupam anupam  478 Aug 28 12:19 README.rdoc drwxrwxr-x  8 anupam anupam 4096 Aug 28 12:19 test drwxrwxr-x  6 anupam anupam 4096 Aug 28 12:33 tmp drwxrwxr-x  3 anupam anupam 4096 Aug 28 12:19 vendor   What does each column mean, and what does the total 76 signify here? Inequality involving $\limsup$ and $\liminf$: $ \liminf(a_{n+1}/a_n) \le \liminf((a_n)^{(1/n)}) \le \limsup((a_n)^{(1/n)}) \le \limsup(a_{n+1}/a_n)$ Some websites and textbooks refer to $$\Delta x \Delta p \geq \frac{\hbar}{2}$$ as the correct formula for the uncertainty principle whereas other sources use the formula $$\Delta x \Delta p \geq \hbar.$$ Question: Which one is correct and why?  The latter is used in the textbook "Physics II for Dummies" (German edition) for several examples and the author also derives that formula so I assume that this is not a typing error.  This is the mentioned derivation:     $\sin \theta = \frac{\lambda}{\Delta y}$      assuming $\theta$ is small:      $\tan \theta = \frac{\lambda}{\Delta y}$      de Broglie equation:      $\lambda = \frac{h}{p_x}$      $\Rightarrow \tan \theta \approx \frac{h}{p_x \cdot \Delta y}$      but also:      $\tan \theta = \frac{\Delta p_y}{p_x}$      equalize $\tan \theta$:      $\frac{h}{p_x \cdot \Delta y} \approx \frac{\Delta p_y}{p_x}$      $\Rightarrow \frac{h}{\Delta y} \approx \Delta p_y \Rightarrow \Delta p_y \Delta y \approx h$      $\Rightarrow \Delta p_y \Delta y \geq \frac{h}{2 \pi}$      $\Rightarrow \Delta p \Delta x \geq \frac{h}{2 \pi}$   So: Which one is correct and why?