Usage example of let expression in bash
Parenthesis in expr arithmetic: 3 * (2 + 1)
I am a physics Master's student.  I have good grades, with CGPA above 9(/10)(However, all courses in my university are graded on a curve so the actual marks are significantly lower than 90%). This has been my marks throughout my undergraduate and graduate courses and I was happy because this was above average. Also, my summer projects in UG were usually computational and any difficulty I had in theoretical aspects I attributed it to my inexperience in advanced Physics.   However, recently I have started to work on pure theoretical project and while reading for the project I realized that I consistently miss some details from each topic. I understand the general idea, can re-derive most of the equations(with some effort) however when I discuss things with my professor or when I read further topics I realize that I have missed certain key-details. This is exactly similar to the case of me missing a few key questions in my exams and getting that 9 grade point instead of 10(or at-least I think so). I was not worried about this before but now I realize that there is some flaw in the way I study (but I do not know what).   Since I want to apply for Physics PhD I realized that I will need to have solid concepts and it would be best to correct my mistakes but I do not know how or even what could be the reason for my imperfect understanding.  Any direct suggestion would help or even certain general guidelines on what I can do.    Things I've tried recently -   1) I've started to written down almost everything I read. This is slightly laborious but is certainly helping. It also helps me to gloss over the things I read previously when I come back the next day.  2) I completely avoid smartphone when I'm library/study room so that I won't get distracted. Not sure if it helps me solve the above problem but certainly helps me study better in general.  3) I've tried to read the topics from several sources. The books I am reading is somewhat like a collection of research papers and hence does not have a exercises. So I though reading from various sources might help get better ideas but it's not really helping because most other sources are too high level as an introductory text. But this will probably help me in cases where it's practical to do this.  4) Somewhat similar to point (1)- I am trying reread, whenever I can, what I've done until that point. But not sure how much this will help me in filling the gaps. In the simple linear regression model, $\hat{\beta}$ is the sum of independent normally distributed random variables.  Is it false because in linear regression there is $\beta$ and not $\hat{\beta}$? How to detect online/offline event cross-browser? Displaying layout marks in a document set with different layouts Is there any package that allows for the display of layout marks within a document where the layout changes several times throughout? I'm using the geometry facilities to issuing \newgeometry commands throughout my document, but it doesn't update the displayed layout and neither does the showframe package or the facilities of the memoir class.  EDIT: As Werner has pointed out, the showframe option of the geometry package displays correctly any updated page layout set by issuing \newgeometry commands.   My trouble came out of the fact that I'm issuing also \pagecolor commands and the page color seems to be hiding the layout lines typeset according to the geometry package. My confusion only worsened because the showframe package layout lines were not hidden by the page color (the package got the layout wrong on some pages, though). So, it all boils down to a conflict with the page color.   Even though I'm using geometry's showframe option for "debugging" ends, and I don't mind to have no page color at that stage of development, is it possible to override this problem and have at the same time both the page layout displayed by geometry as well as the page colored?   Btw, should I open a new question given that the problem is actually different from the originally posted one? Prove that $\phi(n) \geq \sqrt{n}/2$ So I'm trying to prove the following two inequalities: $$\frac{\sqrt{n}}{2} \leq \phi(n) \leq n.$$ The upper bound we get from simply noting that $\phi(n) = n \prod_{p | n}\left( 1 - \frac{1}{p}\right)$ and the fact that $(1 - \frac{1}{p}) \leq 1$. But how can we get the lower bound? I tried using the same expression for $\phi(n)$ but it seems to not really give me the inequality. Can you help? How are self-replicating mines supposed to work? Sort files alphabetically before processing I use the command  find . -type f -exec sha256sum {} \; &gt; sha256SumOutput   to hash every file in a folder hierarchy. Unfortunately, sha256sum doesn't get the file names from find in alphabetical oder. How can this be fixed?  I'd like to have them ordered before they are hashed so they are hashed in alphabetical order (this has a reason). How do I invoke a Java method when given the method name as a string? I am a beginner using QGIS (1.8.0 Lisboa) on a Mac (OS X 10.6.8 Snow Leopard). I work on a file with two layers in the following sequence (top to bottom):    a vector polygon layer with a few outlines of various buildings in France and Italy (CRS: EPSG:4326 - WGS 84 - "on the fly" re projection is activated ) a Google satellite layer uploaded via open layer plugin.   Sometimes when changing the scale (scrolling in and out) the Google layer updates a little wrong in size or position compared to the polygon layer. But as soon as I "pan" the map everything reconstructs right. Now the problem I have concerns the print composer.  The result of any kind of export - pdf, or image or svg - of my map (vector layer + Google layer in the background) differs from what is shown in the preview of the print composer: the vector layer and the Google layer positions are mismatching and in a different scale. I can send some pictures showing screenshots of the print composer preview and the final results if required.  I tried almost everything:    new files with different CRS settings "cache" update preview "render" update preview different paper sizes,  different scales,   The problem appears only using an open layer map (Google, OpenStreetMap...). If I try the same using two vector layer (shapefile) - one with the buildings, another one with the city in background - everything works out great.  ...exasperating! Since it is a real important research project I would be very grateful for some help and tips. "any other verbs then being located in VP" -- is this acceptable? if the sentence you are analysing contains a modal verb, then it is positioned in ‘I’,any other verbs then being located in VP.      (English Syntax and Argumentation - Bas Aarts)   At first, I think the The bold clause should be "...is located..." but then I realize it might be in the form of a non-finite clause (ing clause with a subject) but I'm not sure. If it isn't, how you describe this usage? Is this common in English? Effect of switching response and explanatory variable in simple linear regression Let's say that there exists some "true" relationship between $y$ and $x$ such that $y = ax + b + \epsilon$, where $a$ and $b$ are constants and $\epsilon$ is i.i.d normal noise. When I randomly generate data from that R code: x &lt;- 1:100; y &lt;- ax + b + rnorm(length(x)) and then fit a model like y ~ x, I obviously get reasonably good estimates for $a$ and $b$.  If I switch the role of the variables as in (x ~ y), however, and then rewrite the result for $y$ to be a function of $x$, the resulting slope is always steeper (either more negative or more positive) than that estimated by the y ~ x regression. I'm trying to understand exactly why that is and would appreciate it if anyone could give me an intuition as to what's going on there. "Overclocking" an AVR In AVR datasheets under the Electrical Characteristics section you will typically find a graph like this (this one is from the ATMega328):    I've seen designs that seem to "work" but operate outside the shaded envelope. Specifically, I've seen 3.3V (Arduino) designs that run the clock from an external 16MHz crystal. Clearly, this is out of spec. What are the practical negative consequences of running outside this envelope? How many combinations are possible in the game tic-tac-toe (Noughts and crosses)?  So for example a game which looked like: (with positions 1-9)  A1   --   B1  A2   --   B2  A3   --   --   [1][3][4][6][7] would be one combination During the Time War why didn't the Daleks blow up at least one TARDIS while in the Time Vortex? From the Cracks in time and space story arc it's known that if a TARDIS is blown up (possibly while in the Time Vortex) it rips creation itself apart. Also, from the Stolen Earth / Journey's End we learn the Daleks' masterplan which is subjugating creation itself via destroying it with the Reality Bomb (unfading Z-neutrino energy radiation).  In the Last Great Time War all sorts of temporal weapons were used and it's known that Daleks have the ability of time travel as well. Why didn't they use the Time Vortex back then to win the war once and for all via detonating a TARDIS while inside? What is the safest way to clean up /boot partition? I have 200 MB assigned for the /boot partition.  Whenever I try to update the kernel, I receive an error message that basically states /boot is full.  What can I do to cleanup /boot and remove/backup the older kernels? How do I rename all folders and files to lowercase on Linux? How to input integer value to an array, based preceeding row + column values? GPS PPS signal corresponds to data time? I currently have an Adafruit Ultimate GPS connected to an Arduino that outputing GPS data (nmea sentences) once per second.  There is also a pin on the GPS outputting 1 PPS signal.    My question is whether the pulse of the PPS suppose to match the time that the GPS data is coming in i.e are they are coming in at the same time?    Also does PPS pulse come in at the beginning of a UTC second or is it random and simply once a second? What are bitwise operators? I want my Ubuntu to look like Mac OS X. Just icon and theme if possible! Is it possible? Is there any way to install slingshot launcher?