Travel in Schengen countries on Visa Valid for Deutschland and Type D
Can I visit Schengen countries on a Type-D Schengen Visa?
Use of "save" or "save for" in sentences As I understand it, there are several models for what the universe could look like from the “outside”. I don’t know if any of these are outdated, so if they are please tell me if they are.   Expanding bubble. This model says the universe will never stop expanding, and the universe will die because the energy all turns to photons and gets spread out so much. Bubble that will eventually collapse. In this model the universe will stop expanding, and collapse. Everything merges into super-massive black holes, and the universe dies with fire. The universe is a torus. I'm not clear whether the size of the universe in this model is changing, but the central idea is that space is donut-shaped.   Those are the major ones that I have heard of. My question involves what I have heard to be the most popular of the three, #2. In this model, eventually something will "touch" the edge of the universe. Obviously, the first thing to "touch" it would be photons as they travel at, well, the speed of light. This involves all forms of energy in the universe, but I thought it might be easier to explain for something without mass.  What happens if some form of energy "touches" the edge of the universe? Logically, the energy cannot be lost without violating the law of conservation of energy. The only thing I can think of, is that it would "bounce" or be refracted off the edge.  I realize that it sounds silly, however if model #2 is correct then this situation will arise some number of billions of years from now.  I can only assume that there is either a new model that accounts for this, there is some complex explanation, or that model #2 is incorrect. What do the words 'RELATED' and 'ESTABLISHED' individually signify in RELATED,ESTABLISHED state in iptables? Solutions of bivariate cubic Diophantine equation The problem is what are the integer solutions to  $$7x^2 - 40xy + 7y^2 = (|(x - y)| + 2)^3$$  I only got $x - y = 4 (\mod 13)$. Also, how to solve it? How to Micro Manage Manipulator I need to run IE 10 in 32-bit mode on 64-bit Windows 7 Enterprise N.  When I run IE 10 from "C:\Program Files (x86)\Internet Explorer" I can see in task manager that I have only one process "iexplorer.exe" and no process "iexplorer.exe *32".  I have an application with an ActiveX that is supported only on 32-bit, and the application can't be loaded on 64-bit mode.  Is there a way I can force IE10 to run in 32-bit mode? How do you detect support for VML or SVG in a browser I'm writing a bit of javascript and need to choose between SVG or VML (or both, or something else, it's a weird world). Whilst I know that for now that only IE supports VML, I'd much rather detect functionality than platform.  SVG appears to have a few properties which you can go for: window.SVGAngle for example.  Is this the best way to check for SVG support?  Is there any equivalent for VML?  Unfortuntaly - in firefox I can quite happily do all the rendering in VML without error - just nothing happens on screen. It's quite hard to detect that situation from script. Is lemonade better when made with simple syrup? On a hot summer day and with a basketful of lemons I often want a nice cold glass of lemonade. A lot of recipes suggest making lemonade with simple syrup, which requires cooking, whereas other recipes just have stirred-in sugar.  What exactly are the benefits of making lemonade (or limeade) with simple syrup versus just stirring in sugar? Can anyone come up with an explicit example of two functions $f$ and $g$ such that: $f\circ g$ is bijective, but neither $f$ nor $g$ is bijective?  I tried the following: $$f:\mathbb{R}\rightarrow \mathbb{R^{+}} $$ $$f(x)=x^{2}$$  and  $$g:\mathbb{R^{+}}\rightarrow \mathbb{R}$$ $$g(x)=\sqrt{x}$$  $f$ is not injective, and $g$ is not surjective, but $f\circ g$ is bijective  Any other examples? 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". When and how did "momentarily" come to mean "in a moment", rather than "for a moment"? "Momentarily" used to mean "for a moment" only, and not "in a moment". Thus, newscasters could be divided into two clear groups: those who would say "we'll be back momentarily," and those who would not.  This restriction made sense to me, because having both definitions would promote ambiguity if a unique interpretation could not always be derived from the context. But in recent years it seems "momentarily" is regularly, maybe even more often, used to mean "in a moment" by newscasters of every caliber, and in fact this is even shown to be the definition when looked up in most dictionaries.  When did this word's meaning change? How did it come about? undefined control sequence when using \addchap When I compile my thesis.tex file which is compiled fine including the \addchap, I noticed that I have used \usepackage{unnumberedtotoc}. When I want to use my thesis.tex file on another computer it says tex capacity exceeded, sorry [input stack size=5000]. When I uncomment \usepackage{unnumberedtotoc}, it says ! undefined control sequence  \addchap.  Here I have pasted all the beginning of the packages that I have used in my thesis but I still get some problems in compilation, I don't know why, but I think if I can compile this code, then I can solve the problem  :   \immediate\write18{makeindex \jobname.nlo -s nomencl.ist -o \jobname.nls} \documentclass[12pt]{report} \DeclareMathSizes{12}{30}{16}{12} \usepackage[utf8]{inputenc} \usepackage{graphicx} \usepackage{lineno} \usepackage{amsmath}  \usepackage{array, nccmath}  \usepackage[nottoc]{tocbibind} \newcolumntype{L}{&gt;{$}l&lt;{$}} \newcolumntype{m}{&gt;{\displaystyle}l} \usepackage{framed} \usepackage{cclicenses} \usepackage{makecell} \usepackage[french]{babel} \usepackage{setspace} \usepackage{mathptmx}  \usepackage{multirow}  \usepackage{gensymb}  \usepackage{empheq}   \usepackage{mathtools}   \usepackage{array}   \renewcommand{\arraystretch}{1.9}   \newcolumntype{P}{&gt;{\centering\arraybackslash$}p{1.6em}&lt;{$}}   \newcolumntype{C}{&gt;{\centering\arraybackslash$}c&lt;{$}}   \usepackage{makecell}   \usepackage{booktabs}   \usepackage{subcaption}   \usepackage[intoc]{nomencl}   \makenomenclature   \setcounter{secnumdepth}{4}   \setcounter{tocdepth}{4}   \usepackage[justification=centering]{caption}    \usepackage{etoolbox}     \usepackage{unnumberedtotoc} %https://github.com/johannesbottcher/unnumberedtotoc/     \usepackage[automark,     plainheadsepline,     headsepline,     plainfootsepline,      footsepline,     markcase=ignoreupper]{scrlayer-scrpage}    \clearpairofpagestyles    \ihead*{\leftmark}    \cfoot*{\pagemark}    \setkomafont{pageheadfoot}{\scshape}    \usepackage{titlesec}    \graphicspath{{imagesthesis/}}    \def\frenchlistfigurename{Liste des figures}    \usepackage[a4paper,right=20mm,left=25mm,top=26mm, bottom=26mm]{geometry}    \makeatletter    \titleformat{\chapter}[display]    {\normalfont\huge\bfseries}{\chaptertitlename\ \thechapter}{20pt}{\Huge}    % this alters "before" spacing (the second length argument) to 0    \titlespacing*{\chapter}{0pt}{0pt}{20pt}    %\patchcmd{\@makechapterhead}{\vspace*{20\p@}}{}{}{}% Removes space above \chapter head    %\patchcmd{\@makeschapterhead}{\vspace*{20\p@}}{}{}{}% Removes space above \chapter* head    \makeatother    \title {itle of the thesis}    \titleformat{\paragraph}    {\normalfont\normalsize\bfseries}{\theparagraph}{1em}{}    \titlespacing*{\paragraph}     {0pt}{3.25ex plus 1ex minus .2ex}{1.5ex plus .2ex}     \usepackage[thin, , thinc]{esdiff}  \usepackage{subcaption}  \usepackage{caption}  \usepackage{framed}    \usepackage{nomencl}   \setlength{\nomitemsep}{-\parskip}\usepackage{booktabs,multirow}  \renewcommand{\cellset}{\renewcommand{\arraystretch}{0.5}}   \begin{document}  \renewcommand\arraystretch{0.8} %\noindent  \doublespacing  \maketitle  \tableofcontents %\listoffigures  \addchap{Publications et communications}   \section*{$\:$  a. Publications:}  \section*{$\:$  b. Communications:}  \addchap{Remerciements}  \end{document} How are NFL matchups determined for each season? During the 2012 NFL Season, the Pittsburgh Steelers and Baltimore Ravens play each other in weeks 11 and 13, two weeks (in both NFL schedule and time) apart. To me, that seems too close for comfort.   I do know that teams play other teams in their division twice. How does the NFL schedule procedure work? How to eliminate Cycles artifacts with many overlapping volumes? I have encountered an issue with Cycles Volumetrics in a recent scene. I am using Blender 2.72, and both CPU and GPU render options. In both I get a solid black artifact when I have two volumes overlapping, as in this campfire smoke test:    I have a solid cube, with a volume scatter and volume absorption material, duplicated by a particle system. As you can see, when the particles get higher up and farther apart, and are no longer overlapping, the artifacts disappear. induction proof: $\sum_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$ I encountered the following induction proof on a practice exam for calculus:  $$\sum_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$$  I have to prove this statement with induction.  Can anyone please help me with this proof? Batch processing LiDAR files (.las to raster) with PyQGIS? for layers in glob.glob("*.las"):         processing.runalg("grass7:r.in.lidar", "input_las",5,1,"",1,100,"","",5,"","",False,True,True,"331289.57265,337990.42735,4558790.0,4560890.0",0,layers+"E:/las_new/.tif")      {'output': 'PNOA_2016_CAT_huso31_346-4560.lasE:/las_new/.tif'}   {'output': 'PNOA_2016_CAT_huso31_346-4562.lasE:/las_new/.tif'}   {'output': 'PNOA_2016_CAT_huso31_346-4564.lasE:/las_new/.tif'}   {'output': 'PNOA_2016_CAT_huso31_346-4566.lasE:/las_new/.tif'}   {'output': 'PNOA_2016_CAT_huso31_346-4568.lasE:/las_new/.tif'}   {'output': 'PNOA_2016_CAT_huso31_346-4570.lasE:/las_new/.tif'}   output_ras=("E:/las_Ras")   for layers in glob.glob("*.las"):     processing.runalg("grass7:r.in.lidar", "input_las",5,1,"",1,100,"","",5,"","",False,True,True,"331289.57265,337990.42735,4558790.0,4560890.0",0,layers+"output_ras.tif")      {'output': 'PNOA_2016_CAT_huso31_346-4560.lasoutput_ras.tif'}   {'output': 'PNOA_2016_CAT_huso31_346-4562.lasoutput_ras.tif'}   {'output': 'PNOA_2016_CAT_huso31_346-4564.lasoutput_ras.tif'}   {'output': 'PNOA_2016_CAT_huso31_346-4566.lasoutput_ras.tif'}   {'output': 'PNOA_2016_CAT_huso31_346-4568.lasoutput_ras.tif'}   {'output': 'PNOA_2016_CAT_huso31_346-4570.lasoutput_ras.tif'}     for layers in glob.glob("*.las"):     processing.runalg("grass7:r.in.lidar", "input_las",5,1,"",1,100,"","",5,"","",False,True,True,"331289.57265,337990.42735,4558790.0,4560890.0",0,"output_ras.tif")      {'output': 'output_ras.tif'}   {'output': 'output_ras.tif'}   {'output': 'output_ras.tif'}   {'output': 'output_ras.tif'}   {'output': 'output_ras.tif'}   {'output': 'output_ras.tif'}   I would like to batch process many LAS files to rasters using the PyQGIS algorithm. As you can see in the code, I think the final problem is with the output. It does not write the files out to my defined output pathway as tif files. Also how can I make sure the naming of output rasters are according to the original LAS they are generated from? What am I doing wrong here? Not a pro at Python. Started 3 days ago. I have a char in c#:  char foo = '2';   Now I want to get the 2 into an int.  I find that Convert.ToInt32 returns the actual decimal value of the char and not the number 2.  The following will work:  int bar = Convert.ToInt32(new string(foo, 1));   int.parse only works on strings as well.    Is there no native function in C# to go from a char to int without making it a string?  I know this is trivial but it just seems odd that there's nothing native to directly make the conversion. Kill process spawned by ssh when ssh dies How do threads work in Python, and what are common Python-threading specific pitfalls? I've been trying to wrap my head around how threads work in Python, and it's hard to find good information on how they operate. I may just be missing a link or something, but it seems like the official documentation isn't very thorough on the subject, and I haven't been able to find a good write-up.  From what I can tell, only one thread can be running at once, and the active thread switches every 10 instructions or so?  Where is there a good explanation, or can you provide one? It would also be very nice to be aware of common problems that you run into while using threads with Python. SQL Server - how to determine if indexes aren't being used?