Declaring the same variable name in a loop
What is the scope of variables in JavaScript?
Example of a group where $o(a)$ and $o(b)$ are finite but $o(ab)$ is infinite Let G be a group and $a,b \in G$. It is given that $o(a)$ and $o(b)$ are finite. Can you give an example of a group where $o(ab)$ is infinite? How do I set my wireless network to be private instead of public? Trying to maintain good security settings on my laptop, I want my home network to be interpreted as private and the university network at school to be interpreted as public. However, my home network is currently showing as public.  Here is what my Network and Sharing Center looks like:    How do I change my home network from public to private on Windows 8 Consumer Preview? I always use lm() in R to perform linear regression of $y$ on $x$. That function returns a coefficient $\beta$ such that $$y = \beta x.$$  Today I learned about total least squares and that princomp() function (principal component analysis, PCA) can be used to perform it. It should be good for me (more accurate). I have done some tests using princomp(), like:  r &lt;- princomp( ~ x + y)   My problem is: how to interpret its results? How can I get the regression coefficient? By "coefficient" I mean the number $\beta$ that I have to use to multiply the $x$ value to give a number close to $y$. How to add features to a PostGIS layer using Quantum GIS? I am using Quantum GIS and the PostGIS dbms. I am able to call the PostGIS layer into QGIS but i am unable to add feature to it. I am using the method of adding features to a Shapefile but still it is not getting reflected in the layer, and I don't know how to save it to the PostGIS database if I am able to add the feature to the PostGIS layer.  I may not have used some technical term for this problem because i don't know what to call it, I am expressing the problem in my own terms. 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? How to reset the Xorg / xserver? Xserver keeps crashing on my general user account both in Unity 3D and 2D. It doesn't do it on the guest account.  That's why I want to reset / rollback everything xserver related, hoping this is going to fix it.  Most answers on this involve sudo dpkg-reconfigure xserver-xorg. However, this does nothing for me (generates no output) and I read in other forums, that it's deprecated.  So, what's the current way to reset all xserver / xorg options; what's the alternative to sudo dpkg-reconfigure xserver-xorg? X crashes during work, not before login or so. And the effect of a crash is, that I get thrown out of the session, not a freeze or machine crash. The book says:     Concentration. Some spells require you to maintain concentration in order to keep   their magic active. If you lose concentration, such a spell ends.   So what happens if, for example, you are already concentrating on a spell, and cast Witch Bolt without concentrating. Would you get the initial arc of blue energy, or would it not even go off?  I am asking if you can cast a spell that says concentration without concentrating for an immediate effect. This would be useful to avoid interrupting your existing concentration. In essence, if you are concentrating on thing A (doesn't have to be a spell since other things need concentration), can you cast a concentration spell getting an immediate effect without losing concentration on thing A?  Since the definition of concentration is to keep the spell active (meaning it is already active) I would think that you would get the initial effect (if it had one) without the need to concentrate on it. How can I use colours to separate texture node treatment? I'm a bit confused about the concept of ground, and perhaps voltage as well, particularly when trying to analyze a circuit. When I learned about Ohm's law in grade school, I learned how to apply the law to calculate current, voltage, and resistance of simple circuits.   For instance, if we were given the following circuit:    We would be could be asked to calculate the current passing through the circuit. At the time, I'd simply compute (based on the rules given) 1.5V/1Ohms=1.5A.  Later on, however, I learned that the reason the voltage of the resistor would be 1.5V is because voltage is really the difference in potential between two points, and that the difference of the voltage across the battery would be the same as that of the resistor (correct me if I'm mistaken), or 1.5V. I got confused, however, after the introduction of the concept of ground.   The first time I tried to do the current calculation for a circuit similar to the previous circuit on a simulator, the program complained about not having a ground and "floating voltage sources". After a bit of searching, I learned that circuits need ground as a reference point or for safety reasons. It was mentioned in one explanation that one can pick any node for ground, although it's customary to design circuits so there is a "easy place" to pick ground.   Thus for this circuit    I picked ground at the bottom, but would it be okay to pick ground between the 7 ohm and 2 ohm resistor - or any other place? And what would be the difference when analyzing the circuit?  I've read that there are 3 typical ground symbols with different meanings - chassis ground, earth ground, and signal ground. A lot of circuits I've seen used in exercises either use earth ground or signal ground. What purpose is there in using earth ground? What is the signal ground connected to?  Another question: since the ground is at unknown potential, wouldn't there be current flowing to or from ground to the circuit? From what I've read we treat the ground as 0V, but wouldn't there be some sort of effect because of a difference in potential of the circuit and ground? Would the effect be different depending on what ground was used?  Finally: In nodal analysis, one customarily picks a ground at the negative terminal of the battery. However, when there are multiple voltage sources, some of them are "floating". What meaning does the voltage of a floating voltage source have? Is there a proof that the ratio of a circle's diameter and the circumference is the same for all circles, that doesn't involve some kind of limiting process, e.g. a direct geometrical proof? In my preamble, you'll find:  \renewcommand{\baselinestretch}{1} \renewcommand{\familydefault}{\sfdefault} \usepackage[sfmath]{kpfonts} \usepackage[mathrmOrig]{sfmath} \usepackage{amsmath} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{animate} \usepackage{anysize} \usepackage{arcs} \usepackage{array} \usepackage[scale=0]{background} \usepackage{blindtext} \usepackage{calc} \usepackage{cancel} \usepackage{chngcntr} \usepackage{CJK} \usepackage{CJKspace} \usepackage{CJKpunct} \usepackage{colortbl} \usepackage{enumitem} \usepackage{epstopdf} \usepackage{etoolbox} \usepackage{fancybox} \usepackage{fancyhdr} \usepackage{float} \usepackage{framed} \usepackage{graphicx} \usepackage{hyphenat} \usepackage{ifthen} \usepackage{latexsym} \usepackage{lmodern} \usepackage{multicol} \usepackage{multirow} \usepackage{mwe} \usepackage{pgffor} \usepackage{rotating} \usepackage{tabularx} \usepackage{textcomp} \usepackage{tgheros,tgtermes,tgcursor} \usepackage{tikz} \usepackage{times} \usepackage{tipa} \usepackage{varwidth} \usepackage{wasysym} \usepackage{wboiboites} \usepackage[abs]{overpic} \usepackage[breaklinks,colorlinks=true,linkcolor=red,citecolor=red, urlcolor=blue]{hyperref} \usepackage[framemethod=TikZ]{mdframed} \usepackage[breakable, theorems, skins]{tcolorbox,empheq} \usepackage[default]{gillius} \usepackage[document]{ragged2e} \usepackage[latin1]{inputenc} \usepackage[spanish]{babel} \usepackage[T1]{fontenc} \usepackage[total={18.59cm,26.5cm},left=1.5cm,top=2.5cm]{geometry} \usetikzlibrary{matrix,arrows, positioning,shadows,shadings,backgrounds,calc, shapes, tikzmark} \usetikzlibrary{shadows.blur} \usetikzlibrary{shapes.symbols} \usetikzlibrary{patterns,fadings} \tcbuselibrary{skins,breakable,listings,theorems}    I'm trying to draw an arrow for X axis and Y axis.   \begin{tikzpicture} \draw[yellow!10, fill=blue!5](-1, -1) rectangle (7, 5); \draw[dotted] (-0.75,-0.75) grid (6.75,4.75); \node[below] at (-0.25,0){$O$}; \draw[-&gt;,black, thick] (-0.75,0)--(6.75,0); \end{tikzpicture}   But I get this error:    Additionally, if I remove -> from the options of \draw the tikz picture compiles normally. Does anyone know how to make the character picker appear more quickly?   I use it enough now in my German language studies that it has become second nature for the critical marks and much faster than using the alt+keypress shortcuts.   Only problem is that it's so second nature that sometimes it doesn't pop up quickly enough so I end up typing the character and the number shortcut sometimes (IE u2 instead of ü). Anyone know how to make it appear with less delay? Ideally, I'd love if I could just hold the character and press the number but it appears that OSX insists on waiting for the menu to pop up. Using The Terminal Command to Shutdown, Restart and Sleep My Mac? I'm getting more interested in using Terminal as an alternative way to address solutions on my Mac. I have seen this question entitled .  I would therefore like to know:  How to shut down, restart and sleep my Mac using the Terminal command exclusively ? Let $\mu(\Omega)$ be a probability measure (i.e. $\mu(\Omega) = 1$), and let $f,g$ be non-negative measurable functions on $\Omega$ such that $fg \geq 1$. Show that $1 \leq (\int f^p )(\int g^p)$ for all $0 &lt; p &lt; \infty$   I'm a bit at a loss of what to do. I know that since $fg \geq 1$, we may obtain:  $$\int_{\Omega} d\mu = \mu(\Omega) = 1 \leq \int_{\Omega} fg = \int_{\Omega} |fg|$$ The right-most integral is true since $fg$ is positive and it is equal to $||fg||_1$.  By Hölder's inequality, we obtain:  $$1 \leq \int |fg| \leq ||f||_p ||g||_q = (\int f^p)^\frac{1}{p}(\int g^q)^\frac{1}{q}$$  where $p$ and $q$ satisfy $\frac{1}{p} + \frac{1}{q} = 1$. Raising the left-most and right-most sides of this inequality to the power $p$, I may obtain:  $$1 \leq (\int f^p)(\int g^q)^\frac{p}{q}$$  I now wish to show that $(\int g^q)^\frac{p}{q} \leq \int g^p$, but I've been at a loss of how to do it. Any tips or hints would be greatly appreciated. Why does light in a room not form constructive and destructive interference patterns? Compute Taylor error of $10^{-5}$ for $\cos(\pi/20)$ I use Ubuntu 18 and have little experience with Linux commands. I have two files:  file 1:  a,txt1,v1 b,txt2,v2 c,txt3,v1 d,txt4,v2   file2:  a,txt5,v2 b,txt6,v1 c,txt7,v1 d,txt8,v2   I want to print the 1st and 3rd column values where the the 1st column value is identical and the 3rd column value has changed from v1 to v2. So my expected output should be:  a   The second query is for the 3rd column values that has changed from v2 to v1. So my expected outcome:  b Why don't metals bond when touched together? What does Morgoth look like? Is Morgoth, the original enemy in J. R. R. Tolkien's Middle-earth ever visually described? I envisage him as a bigger, meaner version of the physical Sauron, but I cannot find any reference in The Simarillion. Flag pop-up hidden beneath answer box (and it's still transparent!)