I have two equations which need to be broken into multiple lines. One of the equations has a coeficiente factored out, so that it is of the form X = A(...very long...). The other does not.  The equations were written as  $\!\begin{aligned}      y &amp;= \frac{1}{A}\left(\frac{b_1\cdot{}t_{f1}^2}{2}+h_w\cdot{}t_w\left(t_{f1}+\frac{h_w}{2}\right)+\right.\\     &amp;\phantom{=}\left.+b_2\cdot{}t_{f2}\left(t_{f1}+h_w+\frac{t_{f2}}{2}\right)\right)\\     I_y &amp;= \dfrac{1}{12}\left(b_1\cdot{}t_{f1}^3+t_w\cdot{}h_w^3+b_2\cdot{}t_{f2}^3\right)+\\     &amp;\phantom{=}+b_1\cdot{}t_{f1}\left(y-\dfrac{t_{f1}}{2}\right)^2+\\ \end{aligned}$   The use of $\!\begin{aligned} instead of a standard align environment is because this is contained within a table. This results in the following output:   This is fine and is as expected. However, the global parentheses in the first equation required the use of \right. and \left. at the end of the first line and beginning of the second line, which seems to eat the space between the + and b, as becomes clear when you compare the space between them in the first and second equations.  This is a purely aesthetic issue, but I'm curious to know if it is (preferably trivially) solved.
I have a multi-line equation that I want to have matching sized parentheses. The advice I read online was to use \left( equation \right. \\ left. rest-of-equation \right) . However, this syntax leaves first half of the equation unaware of what is in the second half. For example, if you include a square root term after the break, the second parenthesis will be larger than the opening parenthesis. When you are using the aligned environment to split a long equation this can look somewhat offputting.    Compare the top equation to the bottom one. The parentheses match in size for the bottom equation, but the left hand parentheses for the top one is  noticeably smaller.  Top Code:   \begin{aligned}[t]   \gamma_{\text{u}} + \frac{1}{108}   \left(57\gamma_{\text{er}} \right. &amp;+  38\gamma_{\text{se}}\\ &amp; {}\pm  \left.\sqrt{2601 \gamma_{\text{er}}^2 + 3648  \gamma_{\text{er}}\gamma_{\text{se}} + 1444 \gamma_{\text{se}}^2}  \right)   \end{aligned}   Bottom Code:  \begin{aligned}[t] \gamma_{\text{u}} + \frac{1}{16} \left(9\gamma_{\text{er}}  +  6\gamma_{\text{se}} \pm  \sqrt{49 \gamma_{\text{er}}^2 + 76 \gamma_{\text{er}}\gamma_{\text{se}} + 36 \gamma_{\text{se}}^2} \right) \end{aligned}
Sum of (example: 0+1+2+3 = 6 , 0+1+2+3+4+5+6+7 = 28 and so on) How to toggle Scroll Lock in Excel 2010 without a Scroll Lock key in the keyboard I have a notebook with no Scroll Lock key (or any shortcut using the 'Fn' key).  Somehow Excel 2010 got the Scroll Lock on. I see it left down in the status bar and now I can't navigate through cells using the arrow keys, which is pretty annoying. It wasn't turned on some hours ago, so I think I must have hit some Scroll Lock toggle shortcut in Excel 2010 by mistake.  Anyone knows what hot to turn off Scroll Lock in Excel (shortcut or menu option)? Is the expression "yesterday afternoon" correct? Is it proper to use the following expressions  I started to London yesterday afternoon . I started to London yesterday morning  I ask because it is supposedly correct to say 'last night'. Why don't we say 'last afternoon' or 'last morning'? Proving the sum of two independent Cauchy Random Variables is Cauchy Is there any method to show that the sum of two independent Cauchy random variables is Cauchy? I know that it can be derived using Characteristic Functions, but the point is, I have not yet learnt Characteristic Functions. I do not know anything about Complex Analysis, Residue Theorem, etc.   I would want to prove the statement only using Real Calculus. Feel free to use Double Integrals if you please.   On searching, I found . However, I was wondering if I could get some help directly on the convolution formula:  $$f_Z(z)=\int_{-\infty}^\infty f_X(x)f_Y(z-x)\,dx=\int_{-\infty}^\infty\frac{1}{\pi^2}.\frac{1}{1+x^2}.\frac{1}{1+(z-x)^2}dx\tag{1}$$  Here I have supposed that $X,Y$ are Independent Standard Cauchy. But I think the general formula can be derived easily after some substitutions. I need some help on how to proceed from $(1)$.  EDIT: Just as what the hint in the hyperlink said, I got the answer using that hint. However, I am not quite sure that the hint is algebraically correct. Maybe there has been some typing mistake in the book. Money making in Runescape Install Windows 7 with Bootcamp on OS X Yosemite with USB Key I have an iMac (bought in 2011) and I recently upgraded it with Yosemite. I am trying to install Windows 7 on it via Bootcamp.  However, its optical drive does not work, so I chose the USB key solution using the trick of modifying the file info.plist of Bootcamp (type 'usb bootcamp youtube' in google to see a video of this trick).  So I follow the process religiously and end up with the classic and famous boring screen 'No bootable device -- insert boot disk and press any key'.  So I tried to use Unetbootin (  ) to make my USB Key bootable, and tried to boot on it through the screen that appears when you maintain the Option key (Alt button) while starting the mac. Result: I never managed to have my Unetbootin-formatted USB key appear on this screen :(  I read some stuff about reFit (  ) and GParted, but I just don't know how to use them...  If someone managed to install Windows 7 on his/her iMac with Yosemite using a USB Key, please help me understand why I can't see the USB as a boot option. OpenLayers and OSGB 1936 (CRS 27700) I've been working with loads of shapefiles projected according to OSGB 1936 (CRS 27700). The project CRS is set to EPSG:27700 and "On the fly reprojection" to EPSG:27700 is set (I keep this as a default as I work with OSGB 1936 95% of my time).  I decided to download OSM layers from the OpenLayers plugin. When I load this, the EPSG in the bottom right of the screen goes from EPSG:27700 to EPSG:3857   Question 1: should this be happening anyway as it would suggest that the whole project has been re-projected to EPSG:3857?   As soon as the OSM layer is loaded it's way out of alignment but a quick pan seems to bring it altogether quiet nicely.   What I have noted is that (Question 2), if I try to re-specify the CRS to 27700, then the shapefiles "move" by a few tens of meters with respect to the OSM. Does this suggest that QGIS is doing a second re-projection (from what to what?)?   Also (Question 3), does it mean that if I import another shapefile that would be originally a dataset digitised with EPSG:27700 it would be re-projected to EPSG:3857 because the CRS in the bottom right of the screen was set to EPSG:3857 after the OSM import. This is all a bit confusing and logic would suggest that the import of a non-ESPG:27700 (project default CRS) should not go and change the EPSG setting in the bottom right of the screen. Anita Graser's book says on page 34 "Your project CRS will automatically be changed to Pseudo Mercator when you load a background map using the OpenLayers plugin option".   Does that mean there is no way of keeping ESPG:27700 active in the project when importing basemaps from OpenLayers? If so, what alternatives are there?  What I am trying to bottom out is to understand the correct way of importing basemaps (usually Google, Bing or OSM through the OpenLayers plugin) into my projects (always EPSG:27700) without losing alignment and getting layers to correctly re-project. I'm trying to support greater use of QGIS in my company but don't want to lose credibility by promoting the use of a tool that is misaligning datasets. Don't get me wrong. QGIS is a great tool and I am very fond of it but importing layers with different CRS's is quite common these days and getting this right from the start is half the job done.  I did quite an extensive Google search before posting and didn't come up with a recent, clear cut answer to my questions above. There is a bit of content out there on problems with older versions of QGIS, PROJ4, etc. but nothing recent for QGIS 2.0 so worth an update. SF Story about human adapting to alien environment This is a story that was read on BBC radio about thirty years ago, and this is about as right as I can remember it: The human pilot of a spacecraft is doing some reconnaissance on an alien planet. He crashes but survives. For some reason, no one will know where to look for him. He sees something in the distance that looks like a building of some sort. When he gets there, it seems to be a home. Very much like a human home. There's furniture, but it's strange and uncomfortable . There's food, but it's inedible. There's a faucet but what comes out of it seems more like acid. Everything looks as though it should be right, but it's not. He leaves the house, wanders and after a few days is desperate for water. But there isn't any water anywhere. He's close to death, crawling on the ground and then something happens. There are cracks in the soil and there appears to be water bubbling up from perhaps some underground stream. The water revives him. He goes back to the house and tries the food again. It's delicious and he eats enough to gain back his strength. Then he decides to try the water again. It's pure and wonderful. He takes a shower and the last line of the story is how refreshing the water is on his skin and something about him lifting his tail. Advantages of ROC curves What is the advantages of the ROC curves?  For example I am classifying some images which is a binary classification problem. I extracted about 500 features and applied a features selection algorithm to select a set of features then I applied SVM for classification. In this case how can I get a ROC curve? Should I change the threshold values of my feature selection algorithm and get sensitivty and specificity of the output to draw a ROC curve?  In my case what is the purpose of creating a ROC curve? How long does it usually take for published articles to show up on Google Scholar? The title pretty much says it all - what's the typical delay with which Google Scholar indexes newly published articles? (Note I'm not talking about citations, but about the article showing up at all.)  Edit: the article in question went for over six months after being published (in a well-regarded Springer journal with its own Wikipedia page) without appearing on Google Scholar, until it received a citation, at which point it was added to Google Scholar almost immediately. One more motivation to write papers that get cited. :)  Edit 2: Another article in an even more mainstream journal took a little over seven weeks. I have some simple python code that searches files for a string e.g. path=c:\path, where the c:\path part may vary. The current code is:  def find_path(i_file):     lines = open(i_file).readlines()     for line in lines:         if line.startswith("Path="):             return # what to do here in order to get line content after "Path=" ?   What is a simple way to get the text after Path=? Send urgent mail in Gmail Is it possible to set the "urgent" flag in Gmail for outgoing mail? I'd like to be able to flag time-sensitive emails as such. This is a summary of the excerpt:  Given that we have:  *$10^9$ people  *each person has a chance of 0.01 of going to a hotel  *we have $10^5$ hotels, each hotel holds 100 people  *Thus, $P(2 \text{ persons meet on the same hotel in any given day}) = 0.01 \cdot 0.01 \cdot 10^{-5}$  *and $P(2\text{ persons on the same hotel in $2$ day}) = P(2 \text{ persons on the same hotel in any given days})^2 = 10^{-18}$  the book "Mining of Massive Dataset" said that the expected number of pairs who stay in the same hotel for 2 days is:  $P(2 \text{ persons on the same hotel in $2$ days}) \cdot ( \text{number of pairs of people} ) \cdot (\text{number of pairs of days})$  this is the part where I got stuck. Can't understand how it come to this derivation. Can anybody explain it in more elaborate detail.  You can find the content on page 6 of this link:  (it is freely available) On June 13th 2017 all SharePoint calculated columns with HTML markup stopped working.   Basically the fields now render text (regardless of setting the data type to number). The gist of the notice from Microsoft () is:     In Microsoft SharePoint lists and libraries, calculated fields that   are running in the classic UI mode can be used to display results   based on Excel-like formulas. This is a long standing capability, and   is documented in Calculate data in lists or libraries.      Some users have added HTML markup or script elements to calculated   fields. This is an undocumented use of the feature, and we will begin   blocking execution of custom markup in calculated fields in SharePoint   Online from June 13, 2017 onwards. We are also providing this as a   configurable option for on-premises in SharePoint Server 2016 and   SharePoint Server 2013 via the June 2017 and subsequent Public   Updates.   As we don't have on premise SharePoint (online), we have to find an immediate work around, given that this impacts our processes and thus, business.   Is anyone aware of third party applications that will allow for HTML, script markup (that works with SP online)? Manipulate runs fine normally, but gives errors as a CDF On finding polynomials that approximate a function and its derivative (extensions of Stone-Weierstrass?) Why is the subject omitted in sentences like "Thought you'd never ask"? What is the average number of times it would it take to roll a fair 6-sided die and get all numbers on the die?  The order in which the numbers appear does not matter.  I had this questions explained to me by a professor (not math professor), but it was not clear in the explanation.  We were given the answer $(1-(\frac56)^n)^6 = .5$ or $n = 12.152$  Can someone please explain this to me, possibly with a link to a general topic? Context: I was looking at . I didn't know the result referred to in Brian M. Scott's answer is hard enough to require a separate proof   ― .  ― .  (1)  ― What's the intuition? Is Bezout Identity supposed to be intuitive?  (2) — Why doesn't this try work? Let $c$ be any common divisor of $a, b$. Therefore $c\mid a, c\mid b \iff cj_1 = a, cj_2 = b$ for some integers $j_1, j_2$.     Call $g = \gcd$. By definition $\gcd(a,b)\mid a$ and $\gcd(a,b)\mid b$ and $c \le \gcd(a,b)$. Therefore $g\mid a, g\mid b \iff gk_1 = a, gk_2 = b$ for some integers $k_1, k_2$.   The two paragraphs together precipitate $cj_1 = a = gk_1,  cj_2 = b = gk_2$ but this only proves $c\mid gk_1, c\mid gk_2$?    Origin - Elementary Number Theory, Jones,  p9, Exercise 1.8 is it safe to keep database connections open for long time I have a .net client application which is connected to a remote database. Is it safe to keep a single connection open for the lifetime of the client (hours)? Does the answer hold if I have multiple (10 or 100) clients running?