Is it true that $k[\alpha,\beta]=k(\alpha,\beta)$, $\alpha$ and $\beta$ are algebraic over $k$.
Is $K[a,b]=K(a,b)$ for algebraic $a, b$?
Database Encryption scan for database  was aborted. Reissue ALTER DB to resume the scan How do I install an application from a .dmg disk image? I've downloaded Firefox and it's now sitting on my desktop as Firefox.dmg. When I double click on Firefox.dmg it opens up a window with Firefox in it so I can use it - does this mean the application has been installed?    Community Wiki'd the question because I think it's a worthwhile question to have on the site for pointing people to, it's not exactly intuitive to do and not a question I think I deserve any rep from. How do I parameterize a query containing an IN clause with a variable number of arguments, like this one?  SELECT * FROM Tags  WHERE Name IN ('ruby','rails','scruffy','rubyonrails') ORDER BY Count DESC   In this query, the number of arguments could be anywhere from 1 to 5.  I would prefer not to use a dedicated stored procedure for this (or XML), but if there is some elegant way specific to , I am open to that. Short description of the scoping rules? Plot $|z - i| + |z + i| = 16$ on the complex plane Plot $|z - i| + |z + i| = 16$ on the complex plane   Conceptually I can see what is going on. I am going to be drawing the set of points who's combine distance between $i$ and $-i = 16$, which will form an ellipse. I was having trouble getting the equation of the ellipse algebraically.  I get to the point:  $x^2 + (y - 1) ^2 + 2\sqrt{x^2 + (y - 1)^2}\sqrt{x^2 + (y + 1)^2} + x^2 + (y+ 1)^2 = 256$  $2x^2 + 2y^2 + 2\sqrt{x^2 + (y - 1)^2}\sqrt{x^2 + (y + 1)^2} = 254$  It seems like I'm and doing something the hard way. I find that often after awakening from suspend on Ubuntu GNOME 16.04 with GNOME 3.20 (I have only found this issue on the latest version, though I have not tried with GNOME 3.18 on 16.04) that I get this strange font issue which can't be fixed by restarting gnome-shell and seemingly only by restarting my entire machine:            I do not believe that this is a theme issue as I have tried all the built-in themes (including the dark and light versions) and it is the same for them all. Though it does not seem to affect gnome-shell areas, that is the top-bar, the Activities Overview, etc, are not affected for some reason. So what could this issue be caused by and how can I fix or workaround it?  Information Update:  I have had a look at  but the only options in the gnome-tweak-tool for Antialiasing are Rgba, None, and Grayscale, but none of them seem to have any affect on the issue. Is there something I'm missing? Sorting an Array of Objects in PHP In a Specific Order I have two arrays in PHP. The first array ($author_array) is comprised of user_ids in a particular order, like so: (8, 1, 6)  The second array ($user_results) is comprised of an array of objects like so:  Array (     [0] =&gt; stdClass Object         (             [ID] =&gt; 1             [user_login] =&gt; user1         )     [1] =&gt; stdClass Object         (             [ID] =&gt; 6             [user_login] =&gt; user6         )     [2] =&gt; stdClass Object         (             [ID] =&gt; 8             [user_login] =&gt; user8         ) )   I'd like to "sort" the second array so it's in this order, which matches the order of the values in the first array of (8, 1, 6). So it'd look like this:  Array (     [0] =&gt; stdClass Object         (             [ID] =&gt; 8             [user_login] =&gt; user8         )     [1] =&gt; stdClass Object         (             [ID] =&gt; 1             [user_login] =&gt; user1         )     [2] =&gt; stdClass Object         (             [ID] =&gt; 6             [user_login] =&gt; user6         ) )   I'm weak on data structures. How could I do this? :-)  Thanks in advance for your help!  -Bob Solenoid Driving Circuit I'm trying to drive a 12v (14W) solenoid and have problems figuring out the components for the driving circuit.  The solenoid draws about 1.166A and the MCU is being operated at 3.3V.  I've seen many driving circuits and they all look something like this:         &ndash; Schematic created using   My questions:   What datasheet parameters should I look for when designing this circuit? Is the IRF530PBF-ND a suitable MOSFET for driving this solenoid?    Also, how do I calculate R1's value?  I don't want to blindingly copy a circuit that may or may not work, I want to understand it.  Thank you so much in advance! How do I change permissions on a FAT32 formatted drive? Xorg: High CPU Usage (94%) on Moving Mouse (Ubuntu 18.04) whenever I move my mouse enough it causes high cpu usage. Screenshot provided is on a fresh X session.    This also causes some frequent freeze ups if I'm running some other programs e.g gaming.  [1075299.085] (II) event4  - Corsair Corsair Vengeance M90 Mouse: SYN_DROPPED event - some input events have been lost. [1077813.434] (II) event4  - Corsair Corsair Vengeance M90 Mouse: SYN_DROPPED event - some input events have been lost. [1077814.079] (II) event4  - Corsair Corsair Vengeance M90 Mouse: SYN_DROPPED event - some input events have been lost. [1077814.246] (II) event4  - Corsair Corsair Vengeance M90 Mouse: SYN_DROPPED event - some input events have been lost. [1077814.682] (II) event4  - Corsair Corsair Vengeance M90 Mouse: SYN_DROPPED event - some input events have been lost. [1077831.975] (EE) client bug: timer event4 debounce: offset negative (-18ms) [1077831.975] (II) event4  - Corsair Corsair Vengeance M90 Mouse: SYN_DROPPED event - some input events have been lost. [1077831.975] (II) event4  - Corsair Corsair Vengeance M90 Mouse: WARNING: log rate limit exceeded (5 msgs per 30000ms). Discarding future messages. [1120008.128] (II) event4  - Corsair Corsair Vengeance M90 Mouse: SYN_DROPPED event - some input events have been lost.   Is there any way for the CPU usage not to be this high?  EDIT:  I tried with other mice. The CPU usage appears to increase with the Mouse DPI or to be exact, a generic mouse will cause a CPU usage spike, but not as much as a gaming mouse.  I also checked if I have hardware acceleration enabled.  $ glxinfo | grep "direct rendering" direct rendering: Yes   EDIT 2:  CPU is an AMD FX-6350  GPU is AMD RX Vega 56 Is the phrase "for free" correct? Re-use aliased field in SQL SELECT statement Allow bounty to be set with reputation from another site? Fill cylinder cap with quads Is there any way of converting the triangle fan found on a cylinder cap into quads. I installed Ubuntu alongside Windows but I did not disable secure boot as someone told me it could cause problems with boot loader. So when installation finished and I rebooted, the system went straight into Windows. I went to Ubuntu IRC Support and they told me to turn off the secure boot and reinstall Ubuntu. I did that but my system still boot into windows.  This is a picture of partitions on my system:    This is my first Ubuntu install on my new laptop. I followed everdaylinux guide to install it and I used something else option. How much of 32-bit support is dropped in macOS Catalina? macOS Catalina is said to have dropped support for 32-bit apps. It’s not clear how much support is dropped.   Is there any supported way for a 64-bit app to request the kernel to create a 32-bit code segment? How to change the snapping increment in different units? I would like to know how to change the increments used for snapping transforms.  This would be useful in a number of situations but my problem now is that when I change the units it does not scale the snapping increments to match.  So when holding down ctrl the cube snaps from here:    To here:    I would like it to snap to the 1 foot grid, or possibly any other amount I find useful.  It would also be nice to be able to change the rotation snap as well. Can my friend and I play minecraft together with different mods? : So how many named special cases of each modal verb are there, in toto? There's   1. subjunctive should, and   2. mandative should, and   3. , at least;   and I s[up]pose 4. Should we? is suggestive should, and   5. Shouldn't we? is tag **should**, and I can think of a lot more.    I ask about only operative uses of this modal verb including literary and formal usage,  but please omit anything obsolete. I'm trying to classify them and learn the formal terms describing each. Are there any apt others in addition to the ones above? (I added the enumeration below)  1. What's 'subjunctive should'?  Whenever should is conjugated in the subjunctive mood? 5. What's a tag **should** ? 6. Where does  should/would  feature? What's it called? This should is detailed in   or  or . Is the external micro SD card path the same for all devices? I am using a Samsung Tab 2.  There is a path: /mnt/external_sdcard/myfile. Here, I can save, read, or write my file to the external micro SD card.  I'm just wondering if this path is the same for all devices, or if it may be different.