I know very little about quantum physics, but I just can't wrap my head around the fact that non-spherical orbitals appear to be "oriented", constituting a set of fixed "frame of reference axes".  Does it really work like that? Are there for a single atom given directions in which the orbitals "protrude"? And if so, what are they based on? If I understand it right, the nucleus is seemingly spherical - symmetrical with no unique axis of symmetry. What would then decide the orientation of the orbitals in space (with respect to the surroundings)?  Edit: I understand any orientation works to satisfy the wave equation. I was more curious why the atom would choose one direction, instead of any of the others. Is that fundamentally random? And is this setup retained further, or can it change at any time?
It is well established that:   'In quantum mechanics, the behavior of an electron in an atom is described by an orbital, which is a probability distribution rather than an orbit.   There are also many graphs describing this fact: : (hydrogen atomic orbital - one electron) In the figure, the shading indicates the relative probability to "find" the electron, having the energy corresponding to the given quantum numbers, at that point.  My question is: How do these symmetries shown in the above article occur?                 What about the 'preferable' axis of symmetries? Why these?
Why does sstatic.net serve cookies? According to :  This is a fast, cookieless domain intended for static content delivered to the   However, all responses from the server set a cookie anyway: $ http https://sstatic.net/ HTTP/1.1 200 OK CF-RAY: 162b88245bc406be-LHR Cache-Control: max-age=604800 Connection: keep-alive Content-Encoding: gzip Content-Type: text/html Date: Sun, 31 Aug 2014 19:11:04 GMT ETag: W/&quot;d5474fdfb5c3cf1:0&quot; Last-Modified: Fri, 29 Aug 2014 18:20:12 GMT Server: cloudflare-nginx Set-Cookie: __cfduid=db60cc6f3e7f6482e37f1f2b85c9dc5881409512264375; expires=Mon, 23-Dec-2019 23:50:00 GMT; path=/; domain=.sstatic.net; HttpOnly Transfer-Encoding: chunked Vary: Accept-Encoding [...]  Is this intentional, or just funny? Edited to add: I understand that the cookie is used to track visiting browsers so that cloudflare can distinguish them from misbehaving hosts using the same or a nearby IP address. However, if the policy is intentionally to serve cookies, then the self-documentation of sstatic.net as a &quot;cookieless domain&quot; is incorrect. I have a script that does a number of different things, most of which do not require any special privileges. However, one specific section, which I have contained within a function, needs root privileges.  I don't wish to require the entire script to run as root, and I want to be able to call this function, with root privileges, from within the script. Prompting for a password if necessary isn't an issue since it is mostly interactive anyway. However, when I try to use sudo functionx, I get:  sudo: functionx: command not found   As I expected, export didn't make a difference. I'd like to be able to execute the function directly in the script rather than breaking it out and executing it as a separate script for a number of reasons.  Is there some way I can make my function "visible" to sudo without extracting it, finding the appropriate directory, and then executing it as a stand-alone script?  The function is about a page long itself and contains multiple strings, some double-quoted and some single-quoted. It is also dependent upon a menu function defined elsewhere in the main script.  I would only expect someone with sudo ANY to be able to run the function, as one of the things it does is change passwords. When I tried to connect my Ubuntu 13.10 to my VM Centos 6.5 using ssh appear the message "Connection refused" or "No route to host" even than I change the port, noting change.    I need to use SSH, VPN and Samba, but this IP in my VM Centos do not work.  How Can I resolve this problem? Why do we need to dummy code categorical variables How to identify cells in Column A that contain any of the values in Column B First off, I'm not that advanced of an Excel user. I'm certain Excel can do what I'm about to ask, but I've yet to find a way in any of my attempts or searches.  My question is very similar to  except that A) the answers there didn't work for me, and B) even if it did, it's not quite the correct output I need.   Basically, I have 2 columns. Column A contains URLs (16388 rows). Column B contains URL slugs (202 rows).   I want to search to see if any of the values in column B are contained within any of the values of Column A. If they are, I want to return the value TRUE in column C.   From what I've read, VLOOKUP ought to work for this, but for the life of me I can't get it to work. I also tried in the answers in the link above that use COUNTIF and MATCH, but in both of those cases, all I got were FALSE returns, when I know that there are values in Column B that are contained in a URL in Column A.   Does that make sense?  EDIT: Both answers are providing results (thank you!), but I suspect I may not have asked the question correctly. In both of the answers, I'm getting TRUE results, but it looks like the TRUE is correlating to the slug in Column B rather than the URL in Column A. Let me put it this way:  I'll move the slugs from Column B to C so that B can be used for the TRUE responses. What I want the fomula to do is:   Look at URL in A1 Are any of the values in Column C contained within the URL in A1? If yes, then return TRUE in B1. If FALSE, leave it blank.    So I will be able to see which of the URLs contain the slugs I am searching for. I apologize for not being clearer in my original ask (though I feel like it's only a slight tweak from the answers I've already been given.) I have recently been reading about Quantum Electrodynamics which I found very interesting, but even more confusing.  I understand photons mediate the electromagnetic force and interactions between charges can be described by virtual photon exchange. And that in Quantum Mechanics particles paths can be evaluated by sum over all paths...  An electron travelling from one point to another will take all paths, emitting and reabsorbing virtual photons. Does the electrons take all paths including those that involve faster than light velocities?  Is this question null, Does it mean anything to ask about properties of virtual particles?  Do I have the wrong idea about what virtual particles are? Every partial order can be extended to a linear ordering Why is `[` a shell builtin and `[[` a shell keyword? How to add a node in the middle of the line with tikz? actually it's an easy question, but I could find an answer with Google or the included search on StackExchange ;)  How do I add in the middle of the line a node with Tikz? I want somethink like this:  --------------&gt;      text   Normally I did it with an additional node at command. If I will resize the the arrow then I need to change the position of the node also.  ----------&gt;    text   Which is not the best way for big things. I try to find something in the manual and didn't find an answer yet.   Thanks.  Best regards. How are Wolverine's claws still in his body? Everyone knows that Wolverine's adamantium claws are super-sharp — sharper than even a razor — and virtually indestructible. What puzzled me the first time I saw Wolverine is: how do the claws stay in his body?  As it is shown, Wolverine's flesh and skin are human in strength, but the healing factor makes it superhumanly durable and strong. Still, when Wolverine slashes something, or someone, extremely hard, dense, or thick (as he has to use great amount of force), the claws don't tear through his hand and leave his hand through the opposite side of the palm (because of the action having equal and opposite reaction). How can I get admin access to a Mac without knowing the current password? My Father died last year and I inherited his Mac Mini. My wife has retired and we are trying to set up the mini for her use but the changes we want to make require admin access and we do not have the information my father used to set up the machine.  Is it possible to reset the admin information without having the old information? If so, how would I go about it?   I am not a Mac user usually so any guidance will have to be pretty simple! How do I set up a global locale for the computer?  I have recently installed Kubuntu 14.04LTS in english but since I am in Spain, I chose Spain as a country and then changed locale options so that I get all country specific configuration such as digit grouping, decimal separator, date format, etc. I also added the spanish language.  Now all applications complain that locale is wrong. check-language-support tells me I'm using en_ES.UTF-8 as system's locale, and that locale is indeed wrong, there is no locale for english language in Spain.  I tried using Kubuntu's country/region &amp; language settings but it doesn't fix it. I tried using export LANG=en_GB.UTF-8 and export LC_ALL=en_GB.UTF-8 and then sudo dpkg-reconfigure locales and that caused check-language-support to say that I now have a correct configuration but if it is, it's only in that konsole session. This problem also prevents konsole from showing unicode characters and I cannot use dead keys or enter any 'international character' such as ñ or ç (those work on other applications such as Firefox, that I'm using to post this question).  So the question is: How do I set up a global locale for the computer?  This is not a bug report, I will probably reinstall my computer eventually if I can't fix it. But I really want to know how I can perform this REALLY basic task.  Thank you.  $ check-language-support perl: warning: Setting locale failed. perl: warning: Please check that your locale settings:         LANGUAGE = "en:es:en",         LC_ALL = (unset),         LC_PAPER = "en_ES.UTF-8",         LC_ADDRESS = "en_ES.UTF-8",         LC_MONETARY = "en_ES.UTF-8",         LC_NUMERIC = "en_ES.UTF-8",         LC_TELEPHONE = "en_ES.UTF-8",         LC_IDENTIFICATION = "en_ES.UTF-8",         LC_MEASUREMENT = "en_ES.UTF-8",         LC_TIME = "en_ES.UTF-8",         LC_NAME = "en_ES.UTF-8",         LANG = "en_ES.UTF-8"     are supported and installed on your system. perl: warning: Falling back to the standard locale ("C"). locale: Cannot set LC_CTYPE to default locale: No such file or directory locale: Cannot set LC_MESSAGES to default locale: No such file or directory locale: Cannot set LC_COLLATE to default locale: No such file or directory hunspell-en-ca libreoffice-help-en-gb libreoffice-l10n-en-gb libreoffice-l10n-en-za mythes-en-au wspanish  $ cat /etc/default/locale LANG="en_US.UTF-8" LC_NUMERIC="es_ES.UTF-8" LC_TIME="es_ES.UTF-8" LC_MONETARY="es_ES.UTF-8" LC_PAPER="es_ES.UTF-8" LC_NAME="es_ES.UTF-8" LC_ADDRESS="es_ES.UTF-8" LC_TELEPHONE="es_ES.UTF-8" LC_MEASUREMENT="es_ES.UTF-8" LC_IDENTIFICATION="es_ES.UTF-8"   $ locale locale: Cannot set LC_CTYPE to default locale: No such file or directory locale: Cannot set LC_MESSAGES to default locale: No such file or directory locale: Cannot set LC_ALL to default locale: No such file or directory LANG=en_ES.UTF-8 LANGUAGE=en:es:en LC_CTYPE="en_ES.UTF-8" LC_NUMERIC=en_ES.UTF-8 LC_TIME=en_ES.UTF-8 LC_COLLATE="en_ES.UTF-8" LC_MONETARY=en_ES.UTF-8 LC_MESSAGES="en_ES.UTF-8" LC_PAPER=en_ES.UTF-8 LC_NAME=en_ES.UTF-8 LC_ADDRESS=en_ES.UTF-8 LC_TELEPHONE=en_ES.UTF-8 LC_MEASUREMENT=en_ES.UTF-8 LC_IDENTIFICATION=en_ES.UTF-8 LC_ALL= $ update-locale perl: warning: Setting locale failed. perl: warning: Please check that your locale settings:         LANGUAGE = "en:es:en",         LC_ALL = (unset),         LC_PAPER = "en_ES.UTF-8",         LC_ADDRESS = "en_ES.UTF-8",         LC_MONETARY = "en_ES.UTF-8",         LC_NUMERIC = "en_ES.UTF-8",         LC_TELEPHONE = "en_ES.UTF-8",         LC_IDENTIFICATION = "en_ES.UTF-8",         LC_MEASUREMENT = "en_ES.UTF-8",         LC_TIME = "en_ES.UTF-8",         LC_NAME = "en_ES.UTF-8",         LANG = "en_ES.UTF-8"     are supported and installed on your system. perl: warning: Falling back to the standard locale ("C"). How to change maximum number of cores? It says in  that there is a maximum number of 8 cores supported by default in Ubuntu 12.04 Desktop/Server 32-Bit. What is the way to increase the maximum number of cores from the default of 8 to a higher value, like 12?  The reason I ask is because I have just built a machine with 6 hyper threading cores.  There were issues installing the 64-bit version of the software from a CD (it "panicked" and crashed several times).  The 32-bit installed with no problem, but I only see 8 of the 12 cores.  The BIOS is fine.  If I turn hyper-threading off and reboot, I see 6 cores as expected.  I am nervous to try and compile a kernal, I am still new to all of this.  Is there a config setting somewhere that I should change? Incompatibility between TikZ and babel Do I really need to encode '&' as '&amp;'? Why am I seeing two JPG files instead of RAW + JPG with a Canon 1100D? Why was the previous Code of Conduct FAQ (and all answers) removed? I noticed that the  was deleted.   When the  came out, I tried to look for my old answer as well as others for comparison.  Why not just mark the old one superseded by [insert link]?  Note: I don't care about lost rep. There were a lot of useful links in answers and comments there (and some less-than-useful ones too).     Old CoC FAQ may be available  and . Source: (, ). Book recommendation on the history of PDE/ODE? Product norm on infinite product space Suppose that $n \ge 2$. How to prove that the set $\mathcal D \subset M_n(\mathbb R)$ of the diagonalizable real matrices is not dense in $M_n(\mathbb R)$?