I know when black holes collide, the remnant black hole has a lower mass than the sum of the original two masses. This is due to energy loss via gravitational wave emission.  Does this violate the information paradox? Does this mass come from inside the black holes? I’ve seen some explanations saying that it’s due to relativistic mass from the black holes moving, is this correct? Is this real mass loss? An explanation would be appreciated.
Since the final Black Hole (BH) had 3 solar masses less of mass than the original binary BH, it seems the 2 BHs lost mass, and with it event surface area, entropy, and information. If that came from inside the BHs it seems that it would be a contradiction of what a BH is --'nothing escapes its event horizon'. Some may say that came from the rotational energy of the pair, but the new BH now seems to have less than the two original ones summed. So, did some of that escape the horizons?
Schedule to open website I'd like to open a website at regular intervals per day, i.e., the browser should open and automatically navigate towards a pre-set URL.  I looked at options like scheduling to open browser, but I can't figure out how to open it with a default URL. (No I do not want to make this my start page)  Any help is appreciated Prove that $\lim_{n\to\infty}a_n\le \lim_{n\to\infty}b_n$ Limit Decimal Places in Android EditText After two days of installation, strangely my Ubuntu machine is restarting instead of shutdown from both desktop GUI and command line.  sudo shutdown -h now sudo halt  # (doesn't shutdown, instead freezes on boot screen Plymouth)   I had force shutdown by powering off the machine.  This is not happening all the times.  I have been using Ubuntu for 6 months and never experienced this kind of problem. I've got a DVD that I've burnt from an MSDN ISO. I'm not entirely sure if its Windows 7 64bit or 32bit.   How can I be sure? How to show that $\lim_{n \to +\infty} n^{\frac{1}{n}} = 1$? I've spent the better part of this day trying to show from first principles that this sequence tends to 1. Could anyone give me an idea of how I can approach this problem?  $$ \lim_{n \to +\infty} n^{\frac{1}{n}} $$ How can I record sound from the windows command line? Is there an application capable of recording sound that I can run from the command line on XP?  Ideally I'd start it with one command and stop it with another. Or I could specify a duration with the starting command. Just don't show UI for actions that can't be actioned Recently I just deleted one of my answer in stackoverflow where there was one comment. After deleting the answer it also show for sometime that we all know but in the comment it still allow us to up to make it useful but as I clicked it it just showed me the message:  If we are not allowed to do then what was the meaning? Why don't it just be removed or make it disable if the answer is deleted. Just don't show UI for actions that can't be actioned Getting "System program problem detected" pops up regularly after upgrade This started to happen immediately after I had rebooted the first time after doing a system upgrade. It first starts with a dialogue that says "System program problem detected". Then when I try to hit 'report problem' not much happens. I am led through a dialogue that always ends up the problem cannot be solved.  I am aware this is not a lot of information, however I'm not sure which information I need to publish and how should I obtain it to debug this problem.  Here's a screenshot! Why is time special? In Special Relativity, the spacetime interval between two events is $s^2 = -(c{\Delta}t)^2+({\Delta}x)^2+({\Delta}y)^2+({\Delta}z)^2$ giving the Minkowski metric $\eta_{\mu\nu}=\text{diag}(-1, 1, 1, 1)$. What is the justification for making time have a negative coefficient, and how closely is that related to the 2nd law of thermodynamics? Sure, by letting $\eta = \text{diag}(1, 1, 1, 1)$, we get a pretty boring spacetime, and the boosts in the Poincaré group become trig instead of hyperbolic functions, but what's the physical reasoning behind this? How to install an application that requires gksu package on ubuntu 18.04? I downloaded the Upwork desktop App on ubuntu 18.04. When I open it with Gdebi package installer I saw this error:    I tried to install gksu manually via sudo apt install gksu but I got this error  Building dependency tree        Reading state information... Done Package gksu is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source  E: Package 'gksu' has no installation candidate   How can I install this software on ubuntu 18.04 (I download it yesturday so it is the most recent version on upwork website) ? For a simple circuit with a battery supplying a voltage $V$ to a capacitor, let us assume that the charge on the capacitor is $Q$. Now, the work done by the battery or the energy supplied is given by the relation:  $$W=QV$$  But the energy stored in the capacitor is given by:  $$U = \tfrac12 QV$$  The value of $Q$ as well as that of $V$ should be the same in both the equations.  Now my question is, where is the other half of the energy that the battery supplied? better Curve/Text to Mesh generation? What MySQL query will do a text search and replace in one particular field in a table?  I.e. search for foo and replace with bar so a record with a field with the value hello foo becomes hello bar. Book series about aliens who put "caps" on people to control them Suppose we have two short exact sequences in an abelian category $$0 \to A \mathrel{\overset{f}{\to}} B \mathrel{\overset{g}{\to}} C \to 0 $$ $$0 \to A&#39; \mathrel{\overset{f&#39;}{\to}} B&#39; \mathrel{\overset{g&#39;}{\to}} C&#39; \to 0 $$ and morphisms $a : A \to A&#39;, b : B \to B&#39;, c : C \to C&#39;$ making the obvious diagram commute. The snake lemma states that there is then an exact sequence $$0 \to \ker a \to \ker b \to \ker c \to \operatorname{coker} a \to \operatorname{coker} b \to \operatorname{coker} c \to 0$$ where the morphisms between the kernels are induced by $f$ and $g$ while the maps between the cokernels are induced by $f&#39;$ and $g&#39;$.  It is not hard to show that the morphisms induced by $f, g, f&#39;, g&#39;$ exist, are unique, and that the sequence is exact at $\ker a, \ker b, \operatorname{coker} b, \operatorname{coker} c$. With the use of a somewhat large diagram shown , we can even construct the connecting morphism $d : \ker c \to \operatorname{coker} a$. However, I'm stuck showing exactness at $\ker c$ and $\operatorname{coker} a$. I thought Freyd might have had an element-free proof in his book, but it turns out he proves it by diagram chasing and invoking the Mitchell embedding theorem [pp. 98–99]. Is there a direct proof? (I am not asking how to block my posts on my timeline.)  I am asking how I can block my activity, such as posting in open groups, making comments on people's posts, adding a friend, liking a photo, liking a post, etc., from people seeing it in their news feeds?  I don't want people seeing my interactions with other people. Isomorphism of a product $C_n \times C_m$ of cyclic groups with the cyclic group $C_{mn}$ Why do only Hobbits use a combination of first- and last names? While all the Hobbits I can think of have a combination of first- and lastname (e.g., Bilbo Baggins, Peregrin Took, the Sackville-Baggins's,...), I can't think of any character* of another race that has a lastname:   Men seem to like to add a reference to their ancestors (e.g., Aragorn, Arathorn's son or Isildur's heir) Dwarves seem to like descriptive or honorary names (e.g., Thorin Oakenshield, Dain Ironfoot). They are not lastnames though, since they do not get passed on to descendants. Elves don't have a need for lastnames, since elvish names are unique. Some nevertheless seem to have an additive (e.g., Legolas Greenleaf). Likewise, I can't find any usage of lastnames among Ents, Eagles, Istari, Orcs, trolls,...   But why would a society that is quite rural and not a leader of modernization be the only one to use a modern naming system with first- and lastnames?  *Except for Tom Bombandil. But he is, well, "special". Atheros AR9485 wifi disconnects randomly