How do I reach enclosed chests?
Can you get to blocked-in areas?
When the trace of the Frobenius homomorphism is zero? Let's consider an elliptic curve over a finite field $\mathbb F_p$.  The trace of the Frobenius homomorphism is defined as:  $$a_p=p+1-\#E(\mathbb F_p)$$  See for example .  I read that this value is zero if and only if the elliptic curve is supersingular. Unfortunately there is no proof give. So I am looking for a proof of this. (For example a good reference). Unable to play MP3 or MP4 files in Rhythmbox or Movie Player I am unable to play any MP3 or MP4 files. When I try to open any MP3 or MP4 file, both show an error, a Python 2.7 plug-in is required. Calculate distance between two latitude-longitude points? (Haversine formula) How do I calculate the distance between two points specified by latitude and longitude?  For clarification, I'd like the distance in kilometers; the points use the WGS84 system and I'd like to understand the relative accuracies of the approaches available. A library to convert ANSI escapes (terminal formatting/color codes) to HTML I'm looking for a code library that converts ANSI escape sequences into HTML color, via plain  tags or CSS. For example, something that would convert this:  ESC[00mESC[01;34mbinESC[00m ESC[01;34mcodeESC[00m ESC[01;31mdropbox-lnx.x86-0.6.404.tar.gzESC[00m ESC[00mfooESC[00m  Into this:  &lt;span style="color:blue"&gt;bin&lt;/span&gt; &lt;span style="color:blue"&gt;code&lt;/span&gt; &lt;span style="color:red"&gt;dropbox-lnx.x86-0.6.404.tar.gz&lt;/span&gt; foo   Converting breaks into &lt;br/&gt; isn't necessary, it's just the escape codes that I don't know. I could hack it together myself, but I'd probably miss something important like underlines or mess up how background colors work. I'd rather just sit on top of someone else's code.  Does such a tool (command line linux) or library (perl, python, or ruby preferably) exist? error: requested operation requires superuser privilege How to close view windows? I would like to close some view windows that I opened accidentally.  See the image below:    Edit: another note: I tried searching for the solution, but only found things like "Join Area", which don't seem to work in this situation. Why does range(start, end) not include end? Proof that the coefficients in an OLS model follow a t-distribution with (n-k) degrees of freedom Background  Suppose we have an Ordinary Least Squares model where we have $k$ coefficients in our regression model, $$\mathbf{y}=\mathbf{X}\mathbf{\beta} + \mathbf{\epsilon}$$  where $\mathbf{\beta}$ is an $(k\times1)$ vector of coefficients, $\mathbf{X}$ is the design matrix defined by  $$\mathbf{X} = \begin{pmatrix} 1 &amp; x_{11} &amp; x_{12} &amp; \dots &amp; x_{1\;(k-1)} \\ 1 &amp; x_{21} &amp; \dots  &amp;       &amp;   \vdots \\ \vdots &amp;   &amp; \ddots &amp;       &amp;   \vdots \\ 1 &amp; x_{n1} &amp; \dots  &amp; \dots &amp;   x_{n\;(k-1)}     \end{pmatrix}$$ and the errors are IID normal,  $$\mathbf{\epsilon} \sim \mathcal{N}\left(\mathbf{0},\sigma^2 \mathbf{I}\right) \;.$$  We minimize the sum-of-squared-errors by setting our estimates for $\mathbf{\beta}$ to be $$\mathbf{\hat{\beta}}= (\mathbf{X^T X})^{-1}\mathbf{X}^T \mathbf{y}\;. $$   An unbiased estimator of $\sigma^2$ is  $$s^2 = \frac{\left\Vert \mathbf{y}-\mathbf{\hat{y}}\right\Vert ^2}{n-p}$$ where $\mathbf{\hat{y}} \equiv \mathbf{X} \mathbf{\hat{\beta}}$ ().   The covariance of $\mathbf{\hat{\beta}}$ is given by $$\operatorname{Cov}\left(\mathbf{\hat{\beta}}\right) = \sigma^2 \mathbf{C}$$ where $\mathbf{C}\equiv(\mathbf{X}^T\mathbf{X})^{-1}$ () .  Question  How can I prove that for $\hat\beta_i$, $$\frac{\hat{\beta}_i - \beta_i} {s_{\hat{\beta}_i}} \sim t_{n-k}$$ where $t_{n-k}$ is a t-distribution with $(n-k)$ degrees of freedom, and the standard error of $\hat{\beta}_i$ is estimated by $s_{\hat{\beta}_i} = s\sqrt{c_{ii}}$.    My attempts  I know that for $n$ random variables sampled from $x\sim\mathcal{N}\left(\mu, \sigma^2\right)$, you can show that  $$\frac{\bar{x}-\mu}{s/\sqrt{n}} \sim t_{n-1} $$ by rewriting the LHS as $$\frac{ \left(\frac{\bar x - \mu}{\sigma/\sqrt{n}}\right)  }   {\sqrt{s^2/\sigma^2}}$$ and realizing that the numertor is a standard normal distribution, and the denominator is square root of a Chi-square distribution with df=(n-1) and divided by (n-1) ().  And therefore it follows a t-distribution with df=(n-1) ().  I was unable to extend this proof to my question...  Any ideas?  I'm aware of , but they don't explicitly prove it, they just give a rule of thumb, saying "each predictor costs you a degree of freedom". What happened to the ia32-libs package? The ia32-libs package is no longer present in Ubuntu 12.04 repositories for a 64bit system. Are there any available replacement packages available for download? Fly and Two Trains Riddle What is the use of percent signs (%) at the end of lines? (Why is my macro creating extra space?) I see that the code in many packages and examples contains percent signs % at the end of (many) lines. What are they used for? Do they affect the parsing of those lines? Surjective, Injective, Bijective Functions from $\mathbb Z$ to itself Understanding Tag badges I very recently earned the below badge. But I am sorry, I do not understand it.    It says      Earned at least 100 total score for at least 20 answers in the java tag.   But I have answered 140 questions under Java tag and pretty sure would have earned more than 100 points. Then why did I receive it so late. Currently I have 3.3K points on SO.  Secondly if so, I have answered about 41 questions under Scala tag, then why didn't I receive this badge for Scala? Replacing non-English characters in attribute tables using ArcPy and Python? I have a few shapefiles where some of the attributes contain the non-English characters ÅÄÖ. Since some queries doesn't work with these characters (specifically ), I tried to change them in advance with a simple script and add the new strings to another field.  However, change in characters works fine but not updating the field with arcpy.UpdateCursor.   What is an appropriate way of solving this?  I have also tried to do this via the Field Calculator while posting "code" to the codeblock, with the same error.  Error message: Runtime error  Traceback (most recent call last):   File "", line 1, in    File "c:/gis/python/teststring.py", line 28, in      val = code(str(prow.Typkod)) UnicodeEncodeError: 'ascii' codec can't encode character u'\xc4' in position 3: ordinal not in range(128)  Code:  # -*- coding: cp1252 -*- def code(infield):     data = ''     for i in infield: ##        print i         if i == 'Ä':             data = data + 'AE'         elif i == 'ä':             data = data + 'ae'         elif i == 'Å':             data = data + 'AA'         elif i == 'å':             data = data + 'aa'         elif i == 'Ö':             data = data + 'OE'         elif i == 'ö':             data = data + 'oe'         else:             data = data + i     return data   shp = r'O:\XXX\250000\DB\ArcView\shape.shp'  prows = arcpy.UpdateCursor(shp)  for prow in prows:     val = code(unicode(str(prow.Typkod), "utf-8"))     prow.Typkod_U = val     print val     prows.updateRow(prow)   The values of Typkod are of the type: [D, D, S, DDRÄ, TRÄ] etc.  I use ArcMap Basic (10.1) on Windows 7.    New Error message:  Runtime error  Traceback (most recent call last):   File "", line 1, in    File "c:/gis/python/teststring.py", line 29, in      val = code(unicode(str(row.Typkod), "utf-8")) UnicodeEncodeError: 'ascii' codec can't encode character u'\xc4' in position 3: ordinal not in range(128)  &gt;&gt;&gt; val 'DDRÄ' &gt;&gt;&gt; type(val) type 'str'      It appears as if the output from the function is wrong somehow. When there's ÅÄÖ involved it returns data = u'DDR\xc4' and not (as was my intention) data = 'DDRAE'. Any suggestions on what might cause this? CSV text files loading error / crash in QGIS 2.18.8 I got a problem when I try to load tab-separated text files in the "Create a layer from the delimited text file" tab (that one with de comma symbol). After normally selecting the X and Y fields and clicking OK, the reference coordinate system (SRC) selector screen appears, then the program closes by itself. I had uploaded more than a hundred of this type of file by the same procedure in the previous version of QGIS (2.14 Essen) and have no problem, but since I updated to version 2.18.8 (Las Palmas) I can not load any files or .CSV type.   Do anyone knows what's happening? Am I doing anything wrong? g++ undefined reference with a shared library Should we restrict signup for a service to Facebook accounts only? Browse for Servers does not display local instance I just installed SQL Server and SQL Server Management Studio but it doesn't show anything in servers list and I don't know how to connect to it.  This shows that I have installed SQL Server:        But in this image you can see that my Browse for Servers dialog is empty:        Network servers is empty too. Exporting 2D vector graphic from ArcScene to Illustrator How can I export 2d vector graphic from ArcScene so I can edit it with Adobe Illustrator? I've tried changing the options when I export 2D scene as AI file or PDF file, but they always remain as a unique image that does not allow me to edit the lines and polygons. I get the following error when I try to typeset a beamer document.  kpathsea: Running mktexpk --mfmode / --bdpi 600 --mag 0+525/600 --dpi 525 mathkerncmssi8 gsftopk: fatal: map file `cid-base.map' not found. mktexpk: don't know how to create bitmap font for mathkerncmssi8. mktexpk: perhaps mathkerncmssi8 is missing from the map file. kpathsea: Appending font creation commands to missfont.log.  ) !pdfTeX error: pdflatex (file mathkerncmssi8): Font mathkerncmssi8 at 525 not found  ==&gt; Fatal error occurred, no output PDF file produced!   But if I remove sansmathaccent.sty from the TeX Live tree, the document typesets fine. Here is a minimal working example.  \documentclass[10pt]{beamer}  \begin{document}  \begin{frame}{A very short beamer document}  $e^{i\pi}+1=0$  \end{frame}  \end{document}