Is there a black 'dot' symbol that I can use?
How to look up a symbol or identify a letter from a math alphabet or other character?
How to squeeze error message out of PDO? How can I stream the same music to multiple computers? Is there a way to stream the same playlist on multiple computers at the same time? I want to be able to sync what's playing on multiple computers (for parties etc). How can the contact point of rolling body have zero velocity? They say that for a rolling body, the velocity of the contact point is zero. I'm not getting this. How can it be zero when it's in continuous motion? I was hoping someone could give an overview as to how the Lie groups $SO(3)$ and $SU(2)$ and their representations can be applied to describe particle physics?  The application of Lie groups and their representations is an enormous field, with vast implications for physics with respect to such things as unification, but I what specifically made these groups of physical importance and why there study is useful.  I have just started studying these two groups in particular, but from a mathematical perspective, I'd very much appreciate understanding some sort of physical motivation. Is the orbit in Schwarzshild metric a path with maximal proper time? In curved spacetime particles follow timelike geodesics, which should have maximal proper time (at least locally). I thought this path usually corresponds to a global maximum, and there are only strange exceptions. Propably I was wrong, or I really don't understand something, because it doesn't seem to be true for the case of orbitals in Schwarzschild geometry.  The Schwarzschild metric is (with +--- signature)  $$ g_{\mu\nu} = \textrm{diag}\left(1-\frac{2GM}{r},-\left(1-\frac{2GM}{r}\right)^{-1},-r^2,-r^2\sin^2\theta\right) $$  An observer with fixed $r,\theta,\phi$ coordinates will age according to $d\tau_1 = \sqrt{g_{tt}}dt$. An observer, which orbits the center at the same constant radius with $\theta=\pi/2$ will age according to $d\tau_2 = \sqrt{g_{tt}-\omega^2r^2\sin^2\theta}dt$, so he ages slower during the same amount of coordinate time $dt$. If the two observers start from the same point, they will meet again after a full rotation of the orbiting observer, and the orbiting observer will age less. What I don't understand is that the orbit is the geodesic (if the angular velocity is set properly), so why didn't he age more? He should have been on the path with maximal proper time. I get      every few minutes on Kubuntu (KDE), and the panels disappear.  It restarts itself automatically, so it's not a real problem, just an annoyance, but it is a big annoyance.  I've tried sudo apt install --reinstall plasmashell plasma-desktop, but that made no difference.  When I try a backtrace from the error message, it says it's unable to produce a useful backtrace. How to get Scilab 6.0.1 working on Ubuntu 18.04 LTS? I have installed clean Ubuntu MATE 18.04 LTS and installed Scilab from repository here with    sudo apt-get update sudo apt-get install scilab   After installation I tried to launch it from GUI (Applications → Other → Scilab) - it does not start. Then I tried to launch it from terminal with scilab command. Terminal output is as follows:  $ scilab /usr/bin/scilab-bin: error while loading shared libraries: libjava.so: cannot open shared object file: No such file or directory   so it can't find Java. I reported  about this problem.  I checked existence of libjava.so:  $ dpkg -S libjava.so   openjdk-11-jre-headless:amd64: /usr/lib/jvm/java-11-openjdk-amd64/lib/libjava.so   so it is in place.  What should I do to get Scilab 6.0.1 working on Ubuntu 18.04 LTS? Which of the following is also an ideal? If $U,V$ are ideals of a ring $R$, then which of the following is also an ideal of $R$?   $U+V=\{u+v\mid u\in U,v\in V\}$ $U\cdot V=\{u\cdot v\mid u\in U,v\in V\}$ $U\cap V$   My attempt: I have proved $U+V$ and $U\cap V$ are ideals of $R$.  My problem: I have problem about the second option. I think it is not ideal of $R$. If I am wrong then please prove this otherwise give one counter example to show that $U\cdot V$ is not ideal of $R$. What are the differences between git pull and git fetch? LED light needs replacing every few weeks I have two GU5.3 bulbs in my bathroom - one of them went off a month or so ago so I bought the following 3 pack:   I've gone through 2 of the new bulbs in the space of weeks. I have never seen the bulbs fade out while being on, it's only when we turn the light switch on that they don't come back on (like this morning, I was first in the bathroom and the bulb was off again). No fuses blown or any indication of tripping.  How should I approach this? Resolving ambiguous overload on function pointer and std::function for a lambda using + What happens if my ESTA expires on the day of arrival? I'm French and will travel the 14th of June to the US. My ESTA expires the 14th of  June 2013 and I'm wondering if my ESTA will be valid when I'll land in the US on the 14th of June 2013.  Does someone know anything about that? Include the "People Reached" and "Helpful Flags (count)" data in SEDE I know mathematically the answer to this question is yes, and it's very obvious to see that the dimensions of a ratio cancel out, leaving behind a mathematically dimensionless quantity. However, I've been writing a  (the specifics of which are out of scope), which has me thinking about the problem because I decided to handle angle units as dimensioned quantities, which seemed natural to enable the unit conversion with degrees. The overall purpose of the library is to disallow operations that don't make sense because they violate the rules of dimensional analysis, e.g. adding a length quantity to an area quantity, and thus provide some built-in sanity checking to the computation. Treating radians as units made sense because of some of the properties that dimensioned quantities seemed to me to have:  The sum and difference of two quantities with the same dimension have the same physical meaning as both quantities separately. Quantities with the same dimension are meaningfully comparable to each other, and not meaningfully comparable (directly) to quantities with different dimensions. Dimensions may have different units that are scalar multiple (sometimes with a datum shift).  If the angle is treated as a dimension, my 3 made up properties are satisfied, and everything &quot;makes sense&quot; to me. I can't help thinking that the fact that radians are a ratio of lengths (SI defines them as m/m) is actually critically important, even though the length is cancelled out. For example, though radians and steradians are both dimensionless, it would be a logical error to take their sum. I also can't see how a ratio of something like (kg/kg) could be described as an &quot;angle&quot;. This seems to imply to me that not all dimensionless units are compatible, which seems analogous to how units with different dimensions are not compatible. And if not all dimensionless units are compatible, then the dimensionless &quot;dimension&quot; would violate made-up property #1 and cause me a lot of confusion. However, treating radians as having dimension also has a lot of issues, because now your trig functions have to be written in terms of $\cos(\text{angleUnit}) = \text{dimensionless unit}$ even though they are analytic functions (although I'm not convinced that's bad). Small-angle assumptions in this scheme would be defined as performing implicit unit conversions, which is logical given our trig function definitions but incompatible with how many functions are defined, especially since many authors neglect to mention they are making those assumptions. So I guess my question is: are all dimensionless quantities, but specifically angle quantities, really compatible with all other dimensionless quantities? And if not, don't they actually have dimension or at least the properties of dimension? What bizarrities lurk within the decimal expansion of an irrational number? i.e. can we write  $\pi = 3.14159\dots X\dots$  where $X$ consists of (say) $10^{100}$ consecutive zeroes?  [Originally asked on reddit without response :-( ] How does the Higgs mechanism work? CreateService get error: ERROR_INVALID_ADDRESS (0x000001e7) $\mathbb R$ has the same cardinality of any interval How can I determine if someone's SSH key contains an empty passphrase? Some of my Linux &amp; FreeBSD systems have dozens of users. Staff will use these "ssh gateway" nodes to SSH into other internal servers.  We're concerned that some of these people use an unencrypted private SSH key (A key without a . , because if a cracker ever gained access to their account on this machine, they could steal the private key and now have access to any machine which uses this same key. For security reasons, we require all users to encrypt their private SSH keys with a passphrase.  How can I tell if a private key is not-encrypted (e.g. Does not contain a passphrase)? Is there a different method to do this on an ASCII-armored key vs. a non-ASCII-armored key?  Update:  To clarify, assume I have superuser access on the machine and I can read everybody's private keys. Set shortcuts to change keyboard layout in Windows 10? Is there any way to set keyboard shortcuts to quickly change to a different language/keyboard layout? The old shortcuts still seem to work (when set back in Windows 7), but I can't seem to find anything to change it in Windows 10.