Is the classification of particles into matter and anti-matter arbitrary?
Identification of particles and anti-particles
How does the Hogwarts Headmaster know whom to invite to school? So all wizards get an invitation to Hogwarts at 11... How do they know whom to invite?  If a wizard is Muggle-born, then nobody would know about their existence.  Or do they register some weird magical stuff being done by them before 11? I followed Mike's solution from my first question:    My next question is how to add entries (for the abstract and acknowledgements pages) into the table of contents. What is the correct way to create a single-instance WPF application? How could I find $x$ in this equation $x^2-x+6 \equiv 0 \pmod {9}$ This equation is like this: $$x^2-x+6 \equiv 0 \pmod{9}$$  I want to find x by using modular arithmetic. How I could do that?   My solution was:     $$\begin{align*}  x(x-1) &amp;\equiv -6 \pmod{9}\\ x(x-1) &amp;\equiv 3 \pmod{9} \end{align*}$$      So $x$ is either:   $$ x \equiv 3\pmod{9}$$      or       $$x - 1 \equiv 3 \pmod{9}$$      Which is $x \equiv 4 \pmod{9}$   I know what I have done is very dumb. So what is the correct solution? Give me the instructions also please. Variation of Pythagorean triplets: $x^2+y^2 = z^3$ I need to prove that the equation $x^2 + y^2  = z^3$ has infinitely many solutions for positive $x, y$ and $z$. I got to as far as $4^3 = 8^2$ but that seems to be of no help.  Can some one help me with it? Calculating with Mathematica, one can have $$\int_0^{\pi/2}\frac{\sin^3 t}{\sin^3 t+\cos^3 t}\,\mathrm dt=\frac{\pi}{4}.$$   How can I get this formula by hand? Is there any simpler idea than using $u = \sin t$?     Is there a simple way to calculate $$ \int_0^{\pi/2}\frac{\sin^n t}{\sin^n t+\cos^n t}\,\mathrm dt $$ for $n&gt;3$? Could anyone come up with a reference for this exercise? Project Euler Question 14 (Collatz Problem) Finding the radius of a third tangent circle Sorry if this is a foolish question, but I'm having difficulty understanding how to solve for $r_3$ in the following diagram...    According to WolframAlpha's page on tangent circles, the radius of $c_3$ can be calculated using the following formula $r_3=\frac{r_1 \times r_2}{(\sqrt{r_1}+\sqrt{r_2})^2}$, which can be simplified to $\frac{1}{\sqrt{r_3}}=\frac{1}{\sqrt{r_1}} + \frac{1}{\sqrt{r_2}}$.  To be completely honest, I'm having a hard time understanding understanding how this formula works (as I'm a very visual person). What exactly is happening here? I have this run.sh file, and I've create a symbolic link into my desktop.   When I double-click on it the file the following dialog appearsr    And I have to click on "run" each time. How can I create a link that runs by default? Shrink the database only up to its initial size which is set after creating database In SQL server every database has a property Initial Size (MB) which can be seen in properties of database in SSMS. By default it will be 3 MB for mdf and 1 MB for ldf file.  So now if create a new database then it will be set to default size(i.e 3 MB for mdf and 1 mb for ldf file). But after creating the database  I change the initial size to some other value say For mdf 10 MB and ldf 5 MB.(In real-time some database administrator may want to change initial after creating database)  But now if shrink the database it will shrink beyond the initial size I have set after creation(consider that no data is there in database otherwise it will shrink to its actual content size). It will shrink till the initial size it had during creation of database(i.e 3mb for mdf and 1 mb for ldf). I was expecting to shrink till the initial size which I have set(i.e 10 mb for mdf and 5mb for ldf). Can it be possible to do? If possible then how?  In some article i saw like dbcc SHRINKFILE can be used to shrink beyond initial size and dbcc SHRINKDATABASE cannot shrink beyond initial size. But I want to shrink only till the initial size to which I have set.  Note: I know that shrink is bad and should not be done.But I want to know how it can be done? If sql server considers only the initial size set during creation of database then what is the use of setting the initial size after creating database?  EDIT:  From microsoft shrink related article: Using DBCC SHRINKDATABASE you can not shrink database below its initial size.  My question is Can I change the initial size of existing database itself?  EDIT:  I have about 5 sql server instance. All the database where created with default size of 3 mb for data and 1 mb for log(about 3 years back). Now all the databases are in the range of 100-1000 mb. I wont shrink the database normally as it is not good practice. But some database grow more than 10 GB(mdf file itself as i insert so much data in it). So when database is large I will shift unimportant and old contents from this database to another server as it is not required in that server for me. So that database size reduces from 10 GB to 1 GB. Now the remaining 9 Gb left unused. Now I  want to specify database size to be reduced to 2 GB so that i will get 1 GB free space(Also 2 Gb is the ideal size for this database), Which can be used to avoid autogrowth till next 1 Gb of data is filled. Also i have set 100 MB auto-growth for this kind of large database which has more writes. So instead of specifying size as 2 GB in shrinkfile command,if it was possible to change initial size to 2 GB (which shrink considers) then it would have been better. During this database creation there was no plan about size ,autogroth etc. As it was created about 3 years back. Now i am planning to set autogrowth etc. I cant again create new database with new initial size and shift data. So I was asking whether I can change the Initial size for existing database? Why can't variables be declared in a switch statement? What factors determine enemy levels or: How do enemy levels scale to the player character's? When I finished Normal Mode at around Level 30 and went back to the  (still at Normal mode), I found that all enemies there are now very easy to kill, meaning they didn't level up (or hit a level cap).  When I went to  as a Level 36 character in True Vault Hunter Mode, I noticed that the enemies are the same level as me.  What factors determine enemy levels?   Specifically, I would like to know:       Are enemies affected by what level a character accepted a mission?      Or is it what level a character is when they first entered an area?      How does Normal Mode, True Vault Hunter mode, and the Ultimate True Vault Hunter Mode affect enemy levels?     Are there enemies that will scale to the player level, as the player levels up? Any enemy leveling differences specific to the DLC areas?         EDIT:   There is now  that explains how this works generally: "In playthrough 1, outside of the DLC, there's no such thing as scaling. Enemy levels are determined solely by the area they're in and your mission." Can anyone expound on that, and comment or provide an answer on what are the specific enemy levels on specific areas and/or missions?    states that "enemies do not actually "scale", or at least from what we know of..." and lists specifics for enemy levels on certain areas in the game (sans DLC areas). Can anyone expound on that and/or add specifics for enemy levels in the DLC missions or areas in TVHM (PT 2.0) and/or UTVHM? The  update has just been released, can anyone provide info about enemy levels on that mode, including the DLC areas or missions? I'm looking for a way to search files where two word instances exist in the same file.  I've been using the following to perform my searches up to this point:  find . -exec grep -l "FIND ME" {} \;   The problem I'm running into is that if there isn't exactly one space that between "FIND" and "ME", the search result does not yield the file.  How do I adapt the former search string where both words "FIND" and "ME exist in a file as opposed to "FIND ME"?  I'm using AIX. Showing that if the center of a group is trivial, then the center of its automorphism group is trivial How do I completely remove Ubuntu 12.04 on my Mac? I have dual booted Ubuntu 12.04 on my Mac using disk utility and the rEFIt tool.The battery life is very bad and therefore I want to switch back to Ubuntu 10.04 . How can I completely remove the 12.04 partition? Groups with Same Number Of Elements and Subgroups What is the optimal path between $2$ fixed points around an invisible obstructing wall? Every day you walk from point A to point B, which are $3$ miles apart. There is a $50$% chance each walk that there is an invisible wall somewhere strictly between the two points (never at A or B). The wall extends $1$ mile in each direction perpendicular to the line segment (direct path) between A and B, and its position can be at any random location between the two points. That is, it can be any distance between A and B such as $0.1$ miles away from A, $1.5$ miles away, $2.9$ miles away.... You don't know if the wall is present or where it is until you walk into it.  You must walk around the wall if present as there is no other way to circumvent it.  Assume the wall is negligible thickness (like a force field), all ground is perfectly flat, and the y coordinates at both A and B are $0$ (although I don't think the optimal path will change much if they weren't).  What strategy minimizes the average expected walk distance between A and B?  How do we know for certain this strategy yields the shortest average walking distance?  To get the $100$ bounty points, I would like a convincing argument from you as to why you feel your solution is optimal and cannot be beaten.  For those of you using computer simulation, anything reasonably close to optimal is a candidate for the bounty.   Can anyone beat the optimal solutions submitted so far?  There are still a few days to try.  Even a slight beat (if not due to roundoff error or some other error) would help prove previous solutions are non-optimal.  You can just use the table of $31$ points (x-y coordinates) and compute that path length and then if you can find better then I will accept that answer.  I think by Sunday night I may have to award the bounty otherwise it may get auto-awarded. Why is the derivative of a circle's area its perimeter (and similarly for spheres)? When differentiated with respect to $r$, the derivative of $\pi r^2$ is $2 \pi r$, which is the circumference of a circle.  Similarly, when the formula for a sphere's volume $\frac{4}{3} \pi r^3$ is differentiated with respect to $r$, we get $4 \pi r^2$.  Is this just a coincidence, or is there some deep explanation for why we should expect this? Canonical map $R/(I\cap J)\rightarrow R/I\times _{R/(I+J)} R/J$ is an isomorphism What is the best way to copy a folder and all subfolders and files using c#