There is a command   if [ -f ~/.bashrc ]; then     . ~/.bashrc    I need to know why there is "." right before ~/.bashrc?
I came across this example when trying to mount a usb device inside a openvz container and I have never seen the construct in the second line before. Can you explain what it signifies?  #!/bin/bash . /etc/vz/vz.conf
Spectral radii and norms of similar elements in a C*-algebra: $\|bab^{-1}\|<1$ if $b=(\sum_{n=0}^\infty (a^*)^n a^n)^{1/2}$ Let $A$ be a unital $C^*$-algebra and $a\in A$ such that $r(a) &lt; 1$. Define b  = $(\sum_{n=0}^\infty (a^*)^n a^n)^{1/2}$. We can prove that $b\geq e$ and that $b$ is invertible. I want to show $\| b a b^{-1} \| &lt; 1$.   From the definition of $b$ we see that $a^* b^2 a = b^2-e$ and we know $r(bab^{-1}) = r(a) &lt;1$.   So it suffices to prove $r(b a b^{-1}) = \| b a b^{-1} \|$. It can follow from the fact $c = ba b^{-1}$ is a normal element... I don't know how to prove it (I have tried to compare $c^* c$ and $c c^*$...).    Context: The question appears in Murphy's book, page 74.   I have managed to prove the first part. The second part of the question is to prove $$r(a)= \inf_{c\in Inv(A)}\{\|cac^{-1} \| \}$$ It's easy to see $$r(a) \leq \inf_{c\in Inv(A)}\{\|cac^{-1} \| \}$$ But I can't prove $$r(a) \geq \inf_{c\in Inv(A)}\{\|cac^{-1} \| \}$$ If we have had $r(a) = \|b a b^{-1} \|$ then it was obvious... But this is not true, so how we can prove this inequality? Classic ASP SQL Injection Protection What is a strong way to protect against sql injection for a classic asp app?  FYI I am using it with an access DB.  (I didnt write the app) I am trying to use mathematical induction to prove  $$(2n)!\ge2^n(n!)^2\quad\text{for }n\in\mathbb{N}$$  I am stuck at the $n=k+1$ point. Determine whether or not a point lies within a rotated rectangle If an astronaut had stationed in International Space Station for the duration of mission, 17 years, would he be older? Today the NASA International Space Station started the 100000 orbit after 17 years in the space. I just wonder if there were a team of astronauts which were in the Lab for all the duration of last 17 years, how much older they would be due to the combination of Einstein's especial theory of relativity and general theory of relativity?   Here is the link to NASA's youtube video. No internet after upgrade to 17.10 Why are the characters on the keyboard all capitalized? Why are all the letters (A, B etc) and all the writings (Home, Page Up etc) on the keyboard, capitalized?    Especially, the letters, because a new user could rightly expect uppercase letters to be entered upon pressing those keys to find the contrary. Why did sampling boost the performance of my model? I have an imbalanced dataset with 88 positive samples and 128575 negative samples. I was reluctant to over/undersample the data since it's a biological dataset and I didn't want to introduce synthetic data. I built a Random Forest Classifier with this original dataset. I got an F1 score of 0 for the positive class. Zero precision. Zero recall. I cross-checked the predictions and test data. The model predicts some positives none of which are actually positive. Worst performance.  So, I tried to oversample the positive class. I upsampled the positives to 1000 samples. To my surprise, the F1 score for this dataset was 0.97, for the positive class. Then I tried lesser samples. I was able to achieve an F1 score of 0.83 with 200 positive samples, which is just 2.25 times of the original positive samples.  I would like to know why this occurs. For 88 samples, F1 score is 0.00 (rounded off to two digits). For 200 samples it's 0.83. There is no data leakage. All the features are engineered. I used imbalanced-learn module for oversampling. Can someone explain why is this difference in performance? How to check if a value already exists to avoid duplicates? I've got a table of URLs and I don't want any duplicate URLs. How do I check to see if a given URL is already in the table using PHP/MySQL? Is Bezout's lemma enough to confirm the GCD of a number. Is Bezout's lemma enough to confirm the GCD of a number?  So suppose we have $$ax+by=z$$ does this mean $$\gcd(a,b)=z$$ How do you get JavaScript/jQuery Intellisense Working in Visual Studio 2008? I thought jQuery Intellisense was supposed to be improved with SP1. I even downloaded an annotated version of jQuery 1.2.6, but intellisense will not work in a separate jscript file. I have the jQuery library referenced first on my web page in the &lt;head> tag. Am I doing anything wrong? How do I stop Outlook Out-Of-Office from replying to certain addresses? When I am out of the office, if I turn Out-of-Office on, it auto-replies to the automated emails I get from our Bug Tracking system, which leads to our Bug Tracking system getting full of message about my holiday.  With Outlook Out-of-Office, how do I set it to not respond to certain 'From' addresses? I see its something to do with the optional Rules in the O-o-O dialog, but its not that clear how to stop it from replying using the rules.  I'm on Outlook 2003 and Exchange 2003 but advice for any version will probably be useful to people. If I start a Google+ Hangout, is there anyway to send my friends a link directly to that Hangout post? I couldn't find any options.   So I have to send people a link to my profile, and let them click on the join hangout button. I prefer not to do that since the hangout post may be buried by my other updates. Find out which process is locking a file or folder in Windows How can I find out which process is locking a file or folder in Windows?  For instance, when trying to delete a folder, Windows reports this:     The action can't be completed because the folder is open in another program   Happens the same with a file, but how do I find out what program or application is currently using it and preventing me from deleting the file or folder? How to find required information in man The man command brings up a nice manual for many programs, but how can I use it more effectively? For example man gcc brings:  NAME        gcc - GNU project C and C++ compiler  SYNOPSIS        gcc [-c|-S|-E] [-std=standard]            [-g] [-pg] [-Olevel]            [-Wwarn...] [-Wpedantic]            [-Idir...] [-Ldir...]            [-Dmacro[=defn]...] [-Umacro]            [-foption...] [-mmachine-option...]            [-o outfile] [@file] infile...         Only the most useful options are listed here; see below for the        remainder.  g++ accepts mostly the same options as gcc. .... many text   But what if I need only some part of it? What is the best way to jump to the section where -Idir is described, for example? Is system cleanup/optimization needed Does Ubuntu need regular cleanups like Windows. For example:   Cleaning the logs Temporary files Package cache Dependencies left over   I am not referring to web browsers only.  In case I never do a cleanup, will I have a system like new without my hard drive being full of temporary files, packages, etc.?  Will the performance degrade overtime if a cleanup is not done. Limiting range of value types in C++ A little bird told me that if $2^n+1$ is prime, then $n$ is a power of $2$. I tend not to trust talking birds, so I'm trying to verify that statement independently.  Suppose $n$ is not a power of $2$. Then $n = a \cdot 2^m$ for some $a$ not a power of $2$ and some integer $m$. This gives $2^n+1 = 2^{a \cdot 2^m}+1$. Now I suspect there's a way to factor that, but I don't see how. Can someone give me a hint? Donating winning lottery ticket to 501(c)3 Private Foundation: cost-basis deduction + full tax free redemption for foundation? US 501(c)3 Private Foundations are typically controlled by the primary donator, so that is a nice perk, but in exchange for that perk I realize the tax deductions for donating are significantly lowered than for charities. Aside from being lower, the tax code doesn't recognize appreciated property and only allows for a deduction based on the donating taxpayer's cost-basis: ie. the price they paid for the property no matter its current market value.  When there is a significant delta of price paid vs current redeemable value, it seems this can still be a perk for the donating taxpayer in some circumstances, such as with lottery tickets that are known winners already.  If the donating taxpayer pays $1 for the ticket. Their cost basis is $1. If the ticket is now worth $100,000,000 but has not been redeemed, is it accurate that the donating taxpayer can donate this to their private foundation for a deduction at cost basis, and the private foundation can redeem the $100,000,000 ticket completely exempt from all lottery withholding income taxes?   (Other taxes unique to private foundations are known and outside the scope of this question.)  Most literature I can find is about appreciated marketable securities, and occasionally real estate. It doesn't seem that the tax code specifies any distinction between property, but it also doesn't seem the answer to this question is part of the general collective conscious even if it really is that obvious if my understanding is already correct. Remove "Set as desktop background" from Windows context menu When I right click an image file in Windows, one of the context menu options is "Set as desktop background". I know some entries can be , so I'd like to know if it's possible to remove the "Set as background" option.  Note that while  can be found under HKEY_CLASSES_ROOT\, the "set as background" option seems to be located somewhere else.