I was thinking about some physics (relativity in particular), when it suddenly occurred to me that all my life I had been balancing chemical equations assuming conservation of mass, but I was disregarding energy!  For example, consider combustion: $$\rm CH_4 + 2O_2 \to 2H_2O + CO_2 + {Energy}$$  However, since energy was released, some mass should have been converted to energy right? Why is the equation reflecting a balance in mass?
Is mass converted into energy in exothermic chemical/nuclear reactions?  My (A Level) knowledge of chemistry suggests that this isn't the case. In a simple burning reaction, e.g.   $$\mathrm{C + O_2 \to CO_2}$$  energy is released by the $\mathrm{C-O}$ bonds forming; the atoms lose potential energy when they pull themselves towards each other, in the same way that a falling object converts GPE to KE. There are the same number of protons, electrons etc. in both the reactants and products. I would have assumed that this reasoning extends to nuclear fission/fusion as well, but one physics textbook repeatedly references very small amounts of mass being converted into energy in nuclear reactions.  So I just wanted to know if I was wrong about either of these types of reactions, and if so, what mass is lost exactly?
Windows 8.1 fresh install with Windows 8 licence For the Pell's equation where $d=2$: $$x^2-2y^2=1$$ What are all the integer solutions to the equation. Apparantly there are infinitely many solutions, but how would I represent them in an expression? For $X$ and $Y$ random variables; $X$ follows the uniform distribution.  (1): if $Y=-\log X$  (2): then it can be shown that $-\log X$ is distributed as $\exp(1)$ {i.e. exponential with mean 1}.  Why is this so? Intuitively statement (2) make sense to me. But i'd like a mathematical proof.  -Probably wrong working:  (1) seems to imply $\exp(-Y) = X$ (which is like saying $X$ is exponentially distributed, which is a contradiction, since its actually uniform!); or is it incorrect for me to do this since $X$ and $Y$ are random variables?  Ultimately how do I prove (2)?  Thanks "Everything is a file" in the UNIX World.  Above sentence is famous. When I run echo "hello programmer" &gt;&gt; /dev/tty1 , I can watch the given string on TeleType 1  , ....  What and where is file per each socket? Suppose my friend connects to my PC, and its IP is h.h.h.h , how can I access the respective file? Is it possible? How to select polygons facing camera instead of polygons located in the opposite side I want to select marked face:    however back face gets selected:    Is there an option in blender to only select facing polygons camera ? Storage order vs Result order This is a spin-off question from .   says this on the subject of storage order (clustered index) and the output order     A lot of people believe that a clustered index guarantees a sort order on output. But that's not what it does; it guarantees a storage order on disk.   See, for example, .   I've read the blog post by Hugo Kornelis and understands that an index doesn't guarantee that the sql server reads the records in a specific order. Yet I have a hard time accepting that I can't assume this for my scenario?  CREATE TABLE [dbo].[SensorValues](   [DeviceId] [int] NOT NULL,   [SensorId] [int] NOT NULL,   [SensorValue] [int] NOT NULL,   [Date] [int] NOT NULL, CONSTRAINT [PK_SensorValues] PRIMARY KEY CLUSTERED  (   [DeviceId] ASC,   [SensorId] ASC,   [Date] DESC ) WITH (     FILLFACTOR=75,     DATA_COMPRESSION = PAGE,     PAD_INDEX = OFF,     STATISTICS_NORECOMPUTE = OFF,     SORT_IN_TEMPDB = OFF,     IGNORE_DUP_KEY = OFF,     ONLINE = OFF,     ALLOW_ROW_LOCKS = ON,     ALLOW_PAGE_LOCKS = ON)   ON [MyPartitioningScheme]([Date])   My original query was this:  SELECT TOP 1 SensorValue   FROM SensorValues   WHERE SensorId = 53     AND DeviceId = 3819     AND Date &lt; 1339225010   ORDER BY Date DESC   But I suggest that I could as well use this one (read below for my explanation):  SELECT TOP 1 SensorValue   FROM SensorValues   WHERE SensorId = 53     AND DeviceId = 3819     AND Date &lt; 1339225010   As you can see, my table rows are small (16bytes) and I've got only one index, a clustered. In my scenario, the table consists of 100.000.000 records at this moment (and this will most likely increase tenfold).  When the database server queries this table it has two ways of finding my rows, either it seeks the primary key and thereby reading and returning my values in desc. order of Date, or it has to do a full table scan. My conclusion is that a full table scan on all those records will be way too slow and the database server will therefore always seek the table via its primary key and thereby returning the values sorted by Date DESC When do "well" and "good" mean the same? Given a hotkey, how can I find which program owns it? Why am I getting different results from two servers that located in the same destination network? There's two servers with the same network IP, and the only difference between them is the last two numbers like: 37.211.15.247 and 37.211.166.178. The Hosting Provider claims that the subnet mask for both networks is 255.254.0.0  When I try the command Tracert (Traceroute) to test the ping and to see what hops does it take to reach the destination server, I get different ping times and different forward path results which is strange because they are all located in the same company host.  Is there something wrong? Shouldn’t it take the same path too?  I have added the the full IP addresses to both servers as requested by some commenters. Well the two servers aren’t “International” anyways, so as far as I know, the only thing that comes to mind is the possibility that the two are configured on different subnetworks just like what . Though it’s suspicious.  UPDATE: After doing so much research, I found out the Subnet of these two hosts. They are on a /15 (255.254.0.0) subnet mask. Unfortunately, this is what that hosting provider claimed to me which is not true, and the true Subnet they apparently use is a /17 (255.255.128.0) Subnet mask. It turns out that they were definitely on different Subnets. That's why I got different traceroutes when I tested these two IPs 37.211.15.247 and 37.211.166.178  because they are clearly on different Subnets. Thank you everyone for these good answers, especially  his answer helped me a lot. Does assumption of normality of each mixture components implies that each margins is normal I just would like to understand some information about the joint normality and the margins. I read that the normal joint distribution almost always implies that the univariate margins are all normal.   My question is:  1- Is this apply for Gaussian mixture models? For example, in the Gaussian mixture model, each mixture component follows a Gaussian distribution. Hence, does it imply that each margin will be a Gaussian distribution as well? "I understand that mixture components are used to describe the dependency structures, and they are the joint distribution. is that correct?  2- I read this from one answer to a question in this site . "So yes, the assumption of joint normality is a sufficient condition for all marginal distributions to be normal, irrespective of the dependence structure. Hence, the theory of Copulas does not affect this result in any way."  However, I really do not understand this: irrespective of the dependence structure. As I understand if the joint distribution in normal then the dependence structure is normal.   Could someone help me with my questions, please? What does the exclamation mark do before the function? Is is possible to restore the MFT of a NTFS partition after a format? I'm using soul to letterspace headings in a Hungarian document and compiling it with lualatex.  For some reason soul drops some of the accented letters at the end of a word, but not all. In the example below, only ő and ű are affected:  \documentclass{minimal} \usepackage{fontspec} \setmainfont[Ligatures = TeX]{TeX Gyre Pagella} \usepackage{soul} \begin{document} \noindent \so{áll llá ÁLL LLÁ}\\ \so{íll llí ÍLL LLÍ}\\ \so{űll llű ŰLL LLŰ}\\ \so{őll llő ŐLL LLŐ}\\ \so{üll llü ÜLL LLÜ}\\ \so{öll llö ÖLL LLÖ}\\ \so{úll llú ÚLL LLÚ}\\ \so{óll lló ÓLL LLÓ}\\ \so{éll llé ÉLL LLÉ} \end{document} Python: Uniqueness for list of lists Does casting a spell from an item allow you to apply class abilities that are used when casting a spell? This question is updated to request additional answers and details in light of information now available in the Dungeon Master's Guide. In the released DM basic rules, Lost Mine of Phandelver, Hoard of the Dragon Queen, and the DMG teaser there are wands, staves, and rings that you can use to cast spells.  Do abilities that trigger from casting a spell activate when casting a spell from an item?  Can the character modify the spell using class abilities when casting a spell from an item?   Examples include:  An abjurer Wizard's arcane ward recovering hit points from a Dispel Magic cast from a Ring of Spell Storing  A sorcerer using Twinned Spell on a ray of enfeeblement from a Staff of Power  An evocation wizard using Sculpt Spell on a fireball from a Wand of Fireballs.   Now that the DMG is out we have some clearer rules on casting spells from items (DMG p. 141):  Some magic items allow you to cast a spell from the item.  The spell is cast at the lowest possible spell level, doesn't expend any spell slots, and requires no components, unless the item's description says otherwise  The spell uses its normal casting time, range and duration, and the user of the item must concentrate if the spell requires concentration. A magic item, such as certain staffs, may require you to use your own spellcasting ability when you cast a spell from the item.  Does whether or not you can apply class abilities to the casting of the spell depend whether the item uses the user's own spellcasting ability (such as the Staff of Fire) versus an item that comes with a fixed spellcasting ability built-in (such as the Wand of Fireballs)? Does it matter if it's something that triggers more or less automatically like Arcane Ward, versus something you have to control, like Careful Spell? Making 3 points stick on a plane / flag with wind I have a flag I want to waft in the wind. I imported the shape as an SVG from Adobe Illustrator.  I converted the mesh to a curve.  It wouldn't let me make some subdivisons but it still seems to work with the cloth property.    When I press play, you can see the structure of the flag stops.  How can I make those last 3 points intact? Also the fill colour seems to have disappeared, do you know why and how I can bring it back?    Thanks  Steve  File here: What is the order of the Crisis on Earth X episodes in the Arrowverse? Why is the subject omitted in sentences like "Thought you'd never ask"? "Thought you'd never ask" is "I thought you'd never ask" with "I" omitted. "Hope this helps" is "I hope this helps" with "I" omitted.   In English grammar, normally every sentence should have a subject, right?   My first thought is that these two examples are so often used that they are like set phrases. But these are not really set phrases. You can alter the words after "thought" and "hope".  Another possible explanation is the tendency to drop the subject if it is the first person pronoun. It seems that in many languages, such as Spanish, Italian and Japanese, the first person subject is usually omitted. Maybe English is going the same way? (Not exactly the same, since in Italian, verb forms change according to the person, so the subject is not necessary to understand who one's referring to.)  And, apparently, such omission is more common in spoken English than in written English.  Are there more examples of such first person subject omission? How frequent is it? How to parse a month name (string) to an integer for comparison in C#? I need to be able to compare some month names I have in an array.  It would be nice if there were some direct way like:  Month.toInt("January") &gt; Month.toInt("May")   My Google searching seems to suggest the only way is to write your own method, but this seems like a common enough problem that I would think it would have been already implemented in .Net, anyone done this before? Is there a way to do concurrent editing? Is there a MediaWiki-like method for supporting concurrent editing of text bodies in Drupal 7?  If no feature currently exists, what are some decent PHP diff libraries that could be wrapped up by a Drupal module that could do the job?