How to merge a 4 band tfwx file into one tif for use in Qgis I have a tfwx file and when I open it in arcmap it is displayed as 4 bands.  I would like to use the georeferenced file in qgis since I know nothing about arcmap.
Using Georeference information stored in tfwx (from ArcGIS) in QGIS? I have georeferenced some images (ArcGIS -> Update Georeferencing) which creates a *.tfwx file with the new parameters for georeferencing.   I renamed it to *.tfw but QGIS is not able to read the georeferencing information.   Does anybody has any useful tips how to fix this?
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $ Inspired by , I was wondering if there is a simple logical argument to   Show that $ a,b, \sqrt{a}+ \sqrt{b} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b} \in\mathbb Q $  Note that the original link is using a computational method, where as I am looking for a simple logical argument.  I tried (unjutifiably) to argue that if some of two square roots is rational then each one is rational, this is a different than the (incorrect) argument that if sum of two algebraic numbers is rational then each one is rational ( counter example $a=1-\sqrt{2},b= 1+\sqrt{2} $) First, I'll state some background that lead me to the question.  I was thinking about quantization of space-time on and off for a long time but I never really looked into it any deeper (mainly because I am not yet quite fluent in string theory). But the recent discussion about  got me thinking about the topic again. Combined with the fact that it has been more or less decided that , I decided I should give it a go.    So, first some of my (certainly very naive) thoughts.  It's no problem to quantize gravitational waves on a curved background. They don't differ much from any other particles we know. But what if we want the background itself to change in response to movement of the matter and quantize these processes? Then I would imagine that space-time itself is built from tiny particles (call them space-timeons) that interact by means of exchanging gravitons. I drawed this conclusion from an analogy with how solid matter is built from atoms in a lattice and interact by means of exchanging phonons.  Now, I am aware that the above picture is completely naive but I think it must in some sense also be correct. That is, if there exists any reasonable notion of quantum gravity, it has to look something like that (at least on the level of QFT).  So, having come this far I decided I should not stop. So let's move one step further and assume string theory is correct description of the nature. Then all the particles above are actually strings. So I decided that space-time must probably arise as condensation of huge number of strings. Now does this make any sense at all? To make it more precise (and also to ask something in case it doesn't make a sense), I have two questions:        In what way does the classical space-time arise as a limit in the string theory? Try to give a clear, conceptual description of this process. I don't mind some equations, but I want mainly ideas.   Is there a good introduction into this subject? If so, what is it? If not, where else can I learn about this stuff?      Regarding 2., I would prefer something not too advanced. But to give you an idea of what kind of literature might be appropriate for my level: I already now something about classical strings, how to quantize them (in different quantization schemes) and some bits about the role of CFT on the worldsheets. Also I have a qualitative overview of different types of string theories and also a little quantitative knowledge about moduli spaces of Calabi-Yau manifolds and their properties. LINQ's Distinct() on a particular property Array index out of bound behavior Can anyone please tell me whether the following function $d:\mathbb{R}^2 \times \mathbb{R}^2 \to  \mathbb{R}$ is really a metric or not on $\mathbb{R}^2$.  $$ d((x_1,x_2),(y_1,y_2))= \begin{cases} |x_1-y_1|, &amp;\text{ if } x_2=y_2\\ |x_1|+|y_1|+|x_2-y_2|, &amp;\text{ if } x_2 \neq y_2. \end{cases} $$  If it really is indeed a metric, please give the proof of triangle inequality.(I'm OK with the other two conditions). I don't need a recommendation or a list but my knowledge of GPS and "navi"s and the differences between them is an utter mystery to me.  But often I'm lost in backstreets in random countries where access to something like a live Google Maps would be awesome. I absolutely cannot afford a smartphone with worldwide roaming though.  Can GPS's do what I want or am I barking up the wrong tree? If they can is it only high end ones than can? How does a pharmacy discount card work? Show that the operator norm is submultiplicative We had in our lecture on numerical analysis the following: Let $\mathrm{Lin}(X,Y)$ be the set of all linear maps $X\rightarrow Y$. Let $A\in\mathrm{Lin}(\mathbb R^l,\mathbb R^n)$ and $B\in\mathrm{Lin}(\mathbb R^n,\mathbb R^m)$ and $\|C\|_{op}:=\max_{\|x\|\leq1}\|C(x)\|$. Then our lecturer followed $\|A\circ B\|_{op}\leq\|A\|_{op}\cdot\|B\|_{op}$. So he didn't prove it and so I've tried it by my own. My attempt: $$\begin{aligned} \|A\circ B\|_{\mathrm{op}} &amp;= \max_{\|x\| &lt; 1}\|(A \circ B)(x)\| \\ &amp; \leq \max_{\|x\| &lt; 1} \|A\|_{\mathrm{op}} \|B(x)\| \\ &amp;= \|A\|_{\mathrm{op}} \max_{\|x\|\leq1}\|B(x)\|\\ &amp;= \|A\|_{\mathrm{op}}\|B\|_{\mathrm{op}} \end{aligned}$$ But this seems too easy. I am really interested in a nice proof so anybody could help? Thanks a lot! How Do I insert a image in LaTex from my computer How do I create a file in windows from where LaTex can extract the pdf or Jpg file I want to insert in my document? In other words I need an example of inserting either images or pdf files in my document Here's the image I want to insert    The Image will be placed center to the page just beneath this codes  \[ \overline \rho = \overline P + 0.645 \Big (\frac { \overline P}{K}\Big) ^{\frac {3}{4}} \tag { Tazkera} \] How to run updmap-sys after installing cm-super? My original question was:   The answer that seems suitable to my cause is to install cm-super. I did that (using package manager [winxp 32 bit, MikTex installation 2.9 recently updated]). But still the command  \usepackage{cm-super}    yields an error.  User H Cavendish suggested to run updmap-sys, but I am not sure about how to do that on WinXP.   2011 November 04 edit: I made it sure that I have installed 'cm-super' - but still get the same error:   I have also tried updating the file name databases - but no avail. What does a two overlapping circles symbol mean in an electrical schematic/diagram? In the datasheet for a A3503 Hall Effect Sensor, I saw a circuit diagram labeled 'Functional Block Diagram', and it shows a symbol I have not seen before. It's shown here between 3 - Output and 2 - Ground.  What is this supposed to represent?    The full datasheet is available Useless math that became useful I'm writing an article on  and some people pointed out that this is completely useless.  My idea is to amend my article with some theories that seemed useless when they are created but found use after some time.  I came with some ideas like the Turing machine but I think I'm not grasping the right examples.  Can someone point me some theories that seemed like the Lychrel numbers and then become 'useful'? Why is a method not identical to itself? Change the default size of square brackets in latex math mode Personally I think the default size of square brackets in latex math mode is too small. For example, for an interval [a,b], I would prefer \big[\big] as opposed to plain []. My question is, what can I do to change the default size of [], so that when I input [] in math mode, they will show up automatically the same size as \big[\big]?  Right now I'm defining a new command called \b{} which takes one argument and inserts it between \big[ and \big], but the code looks ugly. Apparently \newcommand (or \def or \let) does not allow [ to be refined.  Any help is much appreciated. Thanks. Learning ArcPy? Where can I start to learn ArcPy? Making pen and ink corrections on a UK visa form? Suppose $ \alpha, \beta&gt;0 $. Compute:   $$ \int_{0}^{\infty}\frac{\cos (\alpha x)-\cos (\beta x)}{x}dx $$   Here is what I do: $$\begin{align} \int_{0}^{\infty}\frac{\cos (\alpha x)-\cos (\beta x)}{x}dx &amp;= \int_{0}^{\infty}dx\int_{\alpha}^{\beta}\sin (yx)dy\\ &amp;=\int_{\alpha}^{\beta}dy\int_{0}^{\infty}\sin(yx)dx\\ &amp; \\ &amp;   \qquad\text{let $ yx=u $}\\ &amp; \\ &amp;=\int_{\alpha}^{\beta}\frac{1}{y}dy\int_0^{\infty}\sin u du\\ &amp;=\int_{\alpha}^{\beta}\frac{1}{y}dy\left( -\cos u|_{\infty}+\cos u|_0 \right)\\ &amp;=\log\frac{\beta}{\alpha}(-\cos(\infty)+1)\\ &amp;=\log\frac{\beta}{\alpha}-\cos(\infty)\log\frac{\beta}{\alpha} \end{align}$$  But $ \cos(\infty) $ does not exist right? Does it mean the integral actually diverse?  Edit: The question comes from   Who can point out my mistake in the above deduction? Is there a "previous sibling" selector? says:  Bash attempts to determine when it is being run with its standard input connected to a network connection, as when executed by the remote shell daemon, usually rshd, or the secure shell daemon sshd. If Bash determines it is being run in this fashion, it reads and executes commands from ~/.bashrc, if that file exists and is readable.  This Bash sources ~/.bashrc: ssh user@host :  But this Bash sources ~/.bash_profile: ssh user@host  I don't see a difference in these two commands according to the spec. Isn't stdin connected to a network connection in both cases? How to interpret Vgs(th) min/max in a MOSFET datasheet? This is a screenshot of IRF9640 MOSFET datasheet. Will you please tell me, what is meant by max and min value of Vgs threshold voltage. Also what they mean by test condition.  Whether the max and min values are only applicable for specified test condition? What will be the threshold voltage for a switching circuit and how the range varies?  My doubt is, for p channel mosfet to turn on Vgs &lt; Vgs(th). For IRF9640 in what volt it will turn on -3 or -5? When i used in my application Vs is 6v and Vg is 3v hence Vgs=-3v but it won't turned on, Why? It turned on when Vgs=-3.3v.  If we consider -2v as threshold, it should turn on when Vgs=-3v. Why they given a range for threshold voltage. Whether we have to test each mosfet to know their threshold. What i am pointing is that, if we have two IRF9640, will Vgs(th) is differ from each other?