External instantiation of nested template in another class
Why can templates only be implemented in the header file?
Prove $(a^2+b^2)(c^2+d^2)\ge (ac+bd)^2$ for all $a,b,c,d\in\mathbb{R}$.  So $(a^2+b^2)(c^2+d^2) = a^2c^2+a^2d^2+b^2c^2+b^2d^2$  and $(ac+bd)^2 = a^2c^2+2acbd+b^2d^2$  So the problem is reduced to proving that $a^2d^2+b^2c^2\ge2acbd$ but I am not sure how to show that Is there a way to turn option strict off for just a single line of code?    I'm doing some maintenance work and I need to "cheat" in just one place and I don't want to lower the standard for the entire file. I  that there are two folders for unit files (not in user mode). /usr/lib/systemd/system/: units provided by installed packages /etc/systemd/system/: units installed by the system administrator  Conflicting with this understanding is the answer to this question: . Can someone fill in the missing information so that I understand what is going on? (UPDATE: The answer has been updated, and my understanding no longer conflicts with it.) Also, it seems that the scripts are organized in subfolders within the /etc/systemd/system/ folder: getty.target.wants multi-user.target.wants  In another location I read that there are other locations. It seems these are for user-specific services. /usr/lib/systemd/user/ where services provided by installed packages go. /etc/systemd/user/ where system-wide user services are placed by the system administrator. ~/.config/systemd/user/ where the user puts its own services.   Update 2015-08-31: For the sake of others, here is a link to a related question I recently asked: What constitutes an observation/measurement in QM? Fundamental notions of QM have to do with observation, a major example being The Uncertainty Principle.    What is the technical definition of an observation/?  If I look at a QM system, it will collapse. But how is that any different from a bunch of matter "looking" at the same system?  Can the system tell the difference between a person's eyes and the bunch of matter?  If not, how can the system remain QM?  Am I on the right track? Why can't a CNAME record be used at the apex (aka root) of a domain? This is a  about CNAMEs at the apices (or roots) of zones   It's relatively common knowledge that CNAME records at the apex of a domain are a taboo practice.  Example: example.com. IN CNAME ithurts.example.net.  In a best case scenario nameserver software might refuse to load the configuration, and in the worst case it might accept this configuration and invalidate the configuration for example.com.  Recently I had a webhosting company pass instructions to a business unit that we needed to CNAME the apex of our domain to a new record. Knowing that this would be a suicide config when fed to BIND, I advised them that we would not be able to comply and that this was bunk advice in general. The webhosting company took the stance that it is not outright forbidden by standard defining RFCs and that their software supports it. If we could not CNAME the apex, their advice was to have no apex record at all and they would not provide a redirecting webserver. ...What?  Most of us know that  insists that A CNAME record is not allowed to coexist with any other data., but let's be honest with ourselves here, that RFC is only Informational. The closest I know to verbiage that forbids the practice is from :     If a CNAME RR is present at a node, no other data should be   present; this ensures that the data for a canonical name and its aliases   cannot be different.   Unfortunately I've been in the industry long enough to know that "should not" is not the same as "must not", and that's enough rope for most software designers to hang themselves with. Knowing that anything short of a concise link to a slam dunk would be a waste of my time, I ended up letting the company get away with a scolding for recommending configurations that could break commonly used software without proper disclosure.  This brings us to the Q&amp;A. For once I'd like us to get really technical about the insanity of apex CNAMEs, and not skirt around the issue like we usually do when someone posts on the subject.  is off limits, as are any other Informational RFC applicable here that I didn't think of. Let's shut this baby down. Google map only loading half of itself MySQL remove duplicates from big database quick Why is the probability that a continuous random variable takes a specific value zero? My understanding is that a random variable is actually a function $X: \Omega \to T$, where $\Omega$ is the sample space of some random experiment and $T$ is the set from which the possible values of the random variable are taken.  Regarding the set of values that the random variable can actually take, it is the image of the function $X$. If the image is finite, then $X$ must be a discrete random variable. However, if it is an infinite set, then $X$ may or may not be a continuous random variable. Whether it is depends on whether the image is countable or not. If it is countable, then $X$ is a discrete random variable; whereas if it is not, then $X$ is  continuous.  Assuming that my understanding is correct, why does the fact that the image is uncountable imply that $Pr(X = x) = 0$.  I would have thought that the fact that the image is infinite, regardless of whether it is countable or not, would already imply that $Pr(X = x) = 0$ since if it is infinite, then the domain $\Omega$ must also be infinite, and therefore  $$Pr(X = x) = \frac{\text{# favorable outcomes}}{\text{# possible outcomes}} = \frac{\text{# outcomes of the experiment where X = x}}{|\Omega|} = \frac{\text{# outcomes of the experiment where X = x}}{\infty} = 0$$  What is wrong with my argument?  Why does the probability that a continuous random variable takes on a specific value actually equal zero? pygame.event.get() not returning any events when inside a thread How to convert string to boolean php I need a formula for conditional formatting to make an Excel 2010 spreadsheet alternate highlighting when a single column changes.  This question, "", is exactly what I want to do, but the suggested solution didn't work for me--it just highlights the first row of each matching value.  I know how to use conditional formatting, but for the life of me I can't figure out or find any pointers on the net so far to make this work.  Ideas?  Here is a link to a picture of how I want my spreadsheet to look when I'm done.  Basically I want every other Disp Number value row to be highlighted.  Seems like it would be a common thing to want to do, and I've seen this asked for in various places, but people struggle with making it work. Event binding on dynamically created elements? I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option. Is a URL allowed to contain a space? Is a URI (specifically an HTTP URL) allowed to contain one or more space characters? If a URL must be encoded, is + just a commonly followed convention, or a legitimate alternative?    In particular, can someone point to an RFC that indicates that a URL with a space must be encoded?  Motivation for question: While beta-testing a web site, I noted that some URLs were constructed with spaces in them. Firefox seemed to do the right thing, which surprised me! But I wanted to be able to point the developers to an RFC so that they would feel the need to fix those URLs. Check tag classes with watir? Is there a page listing all fields? When new users edit a post, the review is posted to a review queue and other reputable users can review the edit and choose to approve or reject it. However, I feel that a lot of people do it pretty quickly.    to . He was fixing broken links in the answer, and as soon as I saw it I knew it would have been a good edit. However, only one reviewer found so, and three others rejected it. I ended up manually doing the edit, and poor Onato didn't get any credit for it (in fact, he got an undeserved 'rejected' for it).  The point I want to bring is that, first and foremost, the person who wrote the answer probably knows best if an edit is acceptable or not. Could there be a time frame where the author of the answer (or question) can overturn a review decision?    EDIT: one more  was rejected by overeager reviewers as well. I absolutely disagree with the notion that the community knows better. The community repeatedly proves that it only wants Internet points.    EDIT: I told a commenter to fix something himself in one of my posts, but . I went back and applied the changes myself. It's not credited to him and his stats got a rejected edit now (which really should be an approved edit). The reason ("This edit is incorrect or an attempt to reply to or comment on the existing post") is blatantly wrong and shows once more that the community has much less insight into edit quality than the people who wrote the answers in the first place. It's true that the UI didn't make it easy for them, but those guys clearly didn't read the comment thread; I did, because as the author, I was notified.    EDIT: This time around, a user fixed a blatant (though small) mistake in one of my accepted answers. One hour later, another, unrelated 10k user , even though it had been approved by the community. I went back to undo his undo.  This goes on again to show that an active user is the best judge for the quality of an edit, and that since I can have the last word on edits on my own posts, I should be allowed to retroactively overturn a community edit vote and accordingly credit the person who proposed the change.    EDIT I wrote a  years ago. Some guy found it and tried to fix it but the community thought that it wasn't worth it. I think that the changes are great and once more I'll integrate them by myself into my post. Unfortunately for this user, he won't be credited for it. I still don't understand why I can't have a binding vote on edits on my posts. I know how to solve "simple" recurrence relations. For instance, say you have:  $$c_0 = 20$$ $$c_1 = 30$$ $$c_n = 3 c_{n-1} - 2 c_{n-2}$$  We can write the characteristic equation as:  $$3x^{n-1} - 2x^{n-2} = x^n$$  Solving this with $n=2$, we get $x = 1$ or $x = 2$. This lets us write the relation $c_n = \alpha_1 1^n + \alpha_2 2^n$, and we can solve for $\alpha_1$ and $\alpha_2$ with the initial states $c_0$ and $c_1$.  However, this depends on the fact that $3x^{n-1} - 2x^{n-2} = x^n$ has two roots.  Now, I'm stuck on another problem where the characteristic equation has fewer roots than terms.  Say I have this recurrence relation instead:  $$a_0 = 0$$ $$a_1 = 2$$ $$a_2 = −1$$ $$a_n = 9a_{n-1} - 15a_{n-2} - 25a_{n-3}$$  The characteristic equation would be:  $$9x^{n-1} - 15x^{n-2} - 25x^{n-3} = x^n$$  However, solving with $n=3$, we only get two roots: $x=-1$ or $x=5$. There are not enough roots to write a relation in the form of $a_n = \alpha_1 r_1^n + \alpha_2r_2^n + \alpha_3r_3^n$. How do I proceed? Converting string of 1s and 0s into binary value I'm trying to convert an incoming sting of 1s and 0s from stdin into their respective binary values (where a string such as "11110111" would be converted to 0xF7). This seems pretty trivial but I don't want to reinvent the wheel so I'm wondering if there's anything in the C/C++ standard libs that can already perform such an operation? Can more than one antibody bind the same antigen I'd like to clear something up about antibodies that I'm not sure I've understood in the articles I've read. Looking at concepts such as "affinity maturation", "monovalent antigens" and "polyvalent antigens" it seems as if there are multiple antibodies which can bind to the same antigen. (Although I think I'm right in saying that individual antibodies can only bind to one antigen?) However, when I read sentences like "It has been estimated that humans generate about 10 billion different antibodies, each capable of binding a distinct epitope of an antigen" on the Wikipedia page (for antibody) it does make it sound like it's one antibody per antigen? Is this the case? Or is it one antibody per epitope. Either way, to put this question in a nutshell:  Is it true to say that the same substance could bind with (and, therefore, be recognised by) more than one antibody, or not?  Also, if the answer is no, does that mean that antibodies with different binding affinities are classed as the same antibody or not? What are good advanced LaTeX books?