Existence of specific unitary transformation
Unitary map between sets of vectors
Problem understanding the logistic regression link function Deleting Objects in JavaScript On every bootup it's the same:  /dev/sda1: clean, 908443/38690816 files, 44176803/154733312 blocks   Is it some kind of option Ubuntu uses to ensure filesystem consistency or is there something wrong with my HDD? fsck takes up to 30s while booting and so about triples the time needed otherwise.  Full output (partly in German):  Begin: Loading essential drivers ... done. Begin: Running /scripts/init-premount ... done. Begin: Mounting root file system ... Begin: Running /scripts/local-top ... done. Begin: Running /scripts/local-premount ... done. Begin: Running /scripts/local-bottom ... done. done. Begin: Running /scripts/init-bottom ... done. fsck von util-linux 2.20.1 /dev/sda1: sauber, 908443/38690816 Dateien, 44176803/154733312 Blöcke udevd[623]: unknown key 'SYSFS{idVendor}' in /lib/udev/rules.d/45-libticables.rules:6  udevd[623]: invalid rule '/lib/udev/rules.d/45-libticables.rules:6'   * Starting mDNS/DNS-SD daemon                                                 [ OK ]  * Starting Reload cups, upon starting avahi-daemon to make sure remote queues are populated                                                                   [ OK ]  * Starting configure network device security                                  [ OK ]  * Starting bluetooth daemon                                                   [ OK ]  ####* Starting all other stuff How we differentiate between flash memory and SD card memory? Does a card that affects 'each' creature affect creatures that enter the battlefield after it resolves? What is vertex and edge shading? Reflection to Identify Extension Methods In C# is there a technique using reflection to determine if a method has been added to a class as an extension method?  Given an extension method such as the one shown below is it possible to determine that Reverse() has been added to the string class?  public static class StringExtensions {     public static string Reverse(this string value)     {         char[] cArray = value.ToCharArray();         Array.Reverse(cArray);         return new string(cArray);     } }   We're looking for a mechanism to determine in unit testing that the extension method was appropriately added by the developer.  One reason to attempt this is that it is possible that a similar method would be added to the actual class by the developer and, if it was, the compiler will pick that method up. Just for curiosity, sometimes while installing software throught apt-get install software_name the terminal prompt me for a confirmation "type Yes or No", but not allways.  I dont mean the sudo password prompt, but the message "Will be downloaded and configrated XXX Kb, continue?" (or something similar)  Why? Installing from source. How to resolve dependencies without destroying the package manager ACPI error when trying to make dual boot with Ubuntu 18.04 and Windows 10 Programmatically create a user and assign a role I'm programmatically creating a user with the following code.  $newUser = array(   'name' =&gt; $mail,    'pass' =&gt; 'password',  // note: do not md5 the password   'mail' =&gt; $mail,    'status' =&gt; 1,    'init' =&gt; $mail,   'roles' =&gt; array(5) ); $user = user_save(null, $newUser);   I have got a role with the role ID equal to 5; when I create the user, in the table "users_roles" there is only a row with the value 0 for the role ID, but if I print the user object with var_dump(), it looks like the roles are created.  What am I doing wrong? Why are some muggles allowed to know of the magical world? Don't heavier objects actually fall faster because they exert their own gravity? The common understanding is that, setting air resistance aside, all objects dropped to Earth fall at the same rate. This is often demonstrated through the thought experiment of cutting a large object in half. The halves clearly can't then fall more slowly just by being sliced in two.  However, I believe the answer is that when two objects fall together, attached or not, they do "fall" faster than an object of less mass alone does. This is because not only does the Earth accelerate the objects toward itself but the objects also accelerate the Earth toward themselves. Considering the formula: $$ F_{\text{g}} = \frac{G m_1 m_2}{d^2} $$  Given $F = ma$ thus $a = F/m$, we note that the mass of the small object doesn't seem to matter as when calculating acceleration the force is divided by the $m$ term, its mass. However, this overlooks that the force is actually applied to both objects, not just to the smaller one. The acceleration on the second, larger object is found by dividing $F$, in turn, by the larger object's mass. The two objects' acceleration vectors are exactly opposite, so closing acceleration is the sum of the two:  $$ a_{\text{closing}} = \frac{F}{m_1} + \frac{F}{m_2} $$  Since the Earth is extremely massive compared to everyday objects, the acceleration imparted on the object by the Earth will radically dominate the equation. As the Earth is $\sim 5.972 \times {10}^{24} \, \mathrm{kg} ,$ a falling object of $5.972 \, \mathrm{kg}$ (just over 13 pounds) would accelerate the Earth about $\frac{1}{{10}^{24}}$ as much, which is one part in a trillion trillion.  Of course in everyday situations, we can for all practical purposes treat objects as falling at the same rate because of this negligible difference—which our instruments probably couldn't even detect. But I'm hoping not for a discussion of practicality or what's measurable or observable, but what we think is actually happening.  Am I right or wrong?  What really clinched this for me was considering dropping a small Moon-massed object close to the Earth and a small Earth-massed object close to the Moon. This made me realize that falling isn't one object moving toward some fixed frame of reference, but that the Earth is just another object, and thus "falling" consists of multiple objects mutually attracting in space. MySQL: LEFT JOIN not working as expected I have a 2015 MBP for work, which I connect my iPhone (6 plus, iOS 10) to charge, and I don't want to trust the computer, ever. However, I must click "Don't Trust" every single time I connect for charging. This is asymmetric to the "Trust" selection, which remembers my decision.  Does anyone know if it's possible to stop the 'Trust/Don't Trust' modal from appearing every time, and have the machine not be trusted?  If possible, can you please tell me how? If not possible, can you please provide proof or evidence that lead you to this conclusion?  Finally, I am not concerned with arguments or opinions about this feature. Only what is outline above. Are there other explanations for slow tyre pressure loss? I rode my road bike on Friday and the tyres were at the correct pressure then, around 100psi.  On Tuesday, I jumped on without checking them and quickly realised something was wrong with the rear tyre.  It wasn't completely flat but was fairly soft.  I hadn't gone far so went home and took the car to work instead.  When I got home later, I was surprised to find the tyre, while still soft, hadn't lost all pressure by any means.  It was around 40psi and felt the same as when I left it in the morning.  I decided there must be a slow leak somewhere, but I couldn't find one anywhere, putting the inner under water and going around it methodically looking for bubbles.  I've never failed to find a leak before that way.  I've switched it out anyway because I don't want to mess around with my commute, but I'm curious ... is there another explanation for that amount of pressure loss?  Or must there have been a puncture somewhere that I missed somehow?  The tyres (whole bike) are pretty new and in excellent condition. My computer no longer boots Windows or the installed operating system. Instead, I may get this error:  PXE-E61: Media test failure, check cable -or- Check cable connection!  PXE-M0F: Exiting PXE ROM.   and/or one of the following messages or similar:  Operating System not found  No boot device available- No bootable devices--strike F1 to retry boot, F2 for setup utility  No bootable device -- insert boot disk and press any key  No Boot Device Found. Press any key to reboot the machine  Default Boot Device Missing or Boot Failed  Reboot and Select proper Boot device or Insert Boot Media in selected Boot device   What does this mean and what can I do?     This question comes up often and the answers are usually the same. This post is meant to provide a definitive, canonical answer for this problem. Feel free to edit the answer to add additional details. What does "formal" mean? I know the definition of formal power series, power series and polynomials. But what does the adjective "formal" mean? In , does it mean "9. Of or relating to linguistic or logical form as opposed to function or meaning" or maybe another one in the link?   Or does "formal" have some mathematical meaning which is other than usual dictionary meaning? When does a gerund become a verb? My question is a follow-up to one in which I identified stealing and killing in a particular sentence as gerunds. Bill J commented to the effect that if objects followed these gerunds, the latter became verbs.   My questions are why and what form of the verb? For me the grammatical distinction between “I dislike killing” and “I dislike killing sheep” is simply that the gerund complement in the first becomes a gerund phrase complement in the second. How to prove that a limit does not exist? Let $x \in \mathbb{R}$ and let $\lfloor y\rfloor$ be the largest integer less than or equal to $x$. $$ f(x) = \frac{1}{x} - \left\lfloor\frac{1}{x}\right\rfloor$$ How does one prove that the $ \lim_{x\to 0} f(x)$ does not exist by using a Epsilon Delta proof? There is a hint given that you can use a proof by contradiction.