In my physics textbook, the following points are given:-   The Law of Conservation of linear momentum emerges from the homogenecity of space.  Isotropy of Space gives rise to the Law of Conservation of angular momentum.  Homogenity of time gives rise to the Law of Conservation of Energy.    However, no explanation for the above three points has been given in my book.Can someone provide explanation for the above 3 points? (If possible, please include mathematics in your explanation.)
is one of those surprisingly clear results of mathematical calculations, for which I am inclined to think that some kind of intuitive understanding should or must be possible. However I don't know of any, do you?  *Independence of time $\leftrightarrow$ energy conservation. *Independence of position $\leftrightarrow$ momentum conservation. *Independence of direction $\leftrightarrow$ angular momentum conservation.  I know that the mathematics leads in the direction of Lie-algebra and such but I would like to discuss whether this theorem can be understood from a non-mathematical point of view also.
If $f_k \to f$ a.e. and the $L^p$ norms converge, then $f_k \to f$ in $L^p$ jQuery ui tabs I want to know, if this bug is fixed, because all previous versions of Ubuntu didn't work for me. So I just want to know, should i leave Windows 10 and go for Ubuntu 17.10. Thanks! How to transpose a dataset in a csv file? Diamond moderators  . In the second section from the top—entitled &quot;Ask questions, get answers, no distractions&quot;—that takes us to an opportunity to select one of a page full of questions from the site as the example question used on the about page. The selections currently available on physics are a little idiosyncratic. Is there some rhyme or reason to these? I suppose that we want a good example question to:  Be accessible to the intended audience (perhaps even to the newest and most naive person in that audience) Be judged at least decent by the community (positive score) Have more than one answer which are also judged acceptable (again positive score)  What else? How does a question end up on the list? Accidentally ejected External drive while downloading file, now having problems reading I'm hoping someone can help! I recently downloaded a torrent directly onto an external hard drive, (using a 2009 MacBook Pro and 1TB Seagate Expansion portable Drive) somehow during the download the drive was accidentally ejected, since this incident when I plug the drive back in it’s having problems reading.  The drive works fine for about 10 minutes, I can read/copy/paste and access files but then starts to wreak havoc; apps hangs, it hangs the Finder, etc.  I’ve tried repairing it in Disk Utility, which reads and repairs this disk but problems inevitably continue as described above.  I’ve deleted the Torrent file also. All my files on this external drive so re-formatting is not an option until I can retrieve them. Limit point compactness implies compactness. I have a question about the following counterexample, why  $U_n = \{n\} \times Y$ has not finite collection covering $X$?   Is it because if you take a finite set $S\subset U_n$ then it's impossible to have $X\subset \bigcup S$ since X is infinite?  Counterexample:  Let $Y$ consist of two points; give $Y$ the topology consisting of $Y$ and the empty set. Then the space $X = \mathbb{Z}_{+} \times Y$ is limit point compact, for every nonempty subset of $X$ has a limit point. It is not compact, for the covering of $X$ by the open set $U_n = \{n\} \times Y$ has not finite collection covering $X.$ How to add a script to Startup Applications from the command line? I have a shell script. I want to configure my script to run automatically during startup. I know how to do this from GUI. But I wanted to do this from terminal. How can I do this?  On a primary research I found that the file needs to be moved to /etc/int.d/ directory. But this operation needs sudo permission. I wanted to do this without super user permissions.   I also found that there are files under ~/.config/autostart/ which are having some settings regarding the startup applications. But I don't know how to edit them to achieve this.   Can someone tell me the exact procedure to achieve this? Change \textwidth and \textheight in mid-document I'm looking for several ways to prove that $$\int_{0}^{\infty }\sin(x)x^mdx=\cos\left(\frac{\pi m}{2}\right)\Gamma (m+1)$$  for $-2&lt; Re(m)&lt; 0$ Difference between Space Opera and Science Fiction? A while back a guy came into the place where I was working. He had a book (I don't remember the name). The book was, according to him, scifi. I told him, "Great! My favorite scifi is the Skylark Series by EE Doc Smith!" He sort of tsked this, saying, "Oh, that's only space opera." I really didn't know what to think of what he said. The funny thing was, I remembering looking at his book thinking, what makes his book scifi any more than mine.  I started thinking about this incident the other day and am once again curious:  What is the difference between space opera and science fiction? What identifies each genre specifically?    NOTE: I had originally asked this on meta due to the closed question:  which is very similar to my question. It was subsequently moved to the main site. As asked in the title? Does the independence of two random variables $X$ and $Y$ imply the independence of $X$ and $X+Y$? If so, what's the easiest way to prove that? Squid IP Routing Issue I have a squid server installed with 30 additional proxy addresses. Whenever I try to use one of these proxy addresses with a browser, like chrome, my IP shows as the main server IP as opposed to the additional address. For example, say the home IP is 192.0.0.10 and the additional IP I'm trying to use is 192.0.0.13, when going to a &quot;what is my IP&quot; type of site, it shows 192.0.0.10 no matter what additional address I use. Any idea as to why this might happen? Thanks for any help. Avro Bengali keyboard switches to Malay (Jawi) after upgrade to Ubuntu 17.04 Prove that $\sqrt[n]{n!}$ is increasing and diverges I have to prove that $a_n$ is (strictly) increasing and diverges  $a_n = \sqrt[n]{n!}$ ;  n $\in$  $\ \mathbb{N}$  From sequence I see that $a_n$ increasing to infinitive.  $\sqrt[1]{1!}=1 ,\  \sqrt[2]{2!} \approx 1.41, \  \sqrt[3]{3!}  \approx 1.81 ,...,  \sqrt[n]{n!} $ Why is plain-hash-then-encrypt not a secure MAC? It seems that even in MAC-then-encrypt systems like SSL, something like HMAC is used rather than a plain hash. Why?   Suppose we use some stream cipher; then why can't we use $Encrypt(m | H(m))$ as the MAC-then-encrypted version of the message? Assuming no bad relations between $Encrypt$ and $H$, what are the possible weaknesses? It seems that in this case we are encrypting the hash with part of a secretly keyed stream cipher keystream, and the hash is secure; does this not fulfil an approximation of the ideal MAC?  This must be somehow bad, since no secure protocol seems to use it. Why? I have a Visual Studio 2008 solution with two projects (a Word-Template project and a VB.Net console application for testing).  Both projects reference a database project which opens a connection to an MS-Access 2007 database file and have references to System.Data.OleDb.  In the database project I have a function which retrieves a data table as follows   private class AdminDatabase    ' stores the connection string which is set in the New() method    dim strAdminConnection as string     public sub New()    ...    adminName = dlgopen.FileName    conAdminDB = New OleDbConnection    conAdminDB.ConnectionString = "Data Source='" + adminName + "';" + _        "Provider=Microsoft.ACE.OLEDB.12.0"     ' store the connection string in strAdminConnection    strAdminConnection = conAdminDB.ConnectionString.ToString()    My.Settings.SetUserOverride("AdminConnectionString", strAdminConnection)    ...    End Sub     ' retrieves data from the database    Public Function getDataTable(ByVal sqlStatement As String) As DataTable         Dim ds As New DataSet         Dim dt As New DataTable         Dim da As New OleDbDataAdapter         Dim localCon As New OleDbConnection           localCon.ConnectionString = strAdminConnection          Using localCon             Dim command As OleDbCommand = localCon.CreateCommand()             command.CommandText = sqlStatement             localCon.Open()             da.SelectCommand = command             da.Fill(dt)             getDataTable = dt         End Using      End Function End Class   When I call this function from my Word 2007 Template project everything works fine; no errors. But when I run it from the console application it throws the following exception     ex = {"The 'Microsoft.ACE.OLEDB.12.0'   provider is not registered on the   local machine."}   Both projects have the same reference and the console application did work when I first wrote it (a while ago) but now it has stopped work.  I must be missing something but I don't know what.  Any ideas? Is there any bidirectional 5v-3.3v level shifter? Consider a common proof of the uncountability of $(0,1]$, as presented  for example:  We assume that the reals can be arranged in a sequence $x_k$, represent every number in $x_k$ by its nonterminating decimal expansion, use the diagonal argument to create a sequence of decimal digits that differs from the nonterminating decimal expansion of each number in $x_k$ and then claim that this sequence of digits so generated must be the decimal expansion of some number not in $x_k$.  My problem is with this last step. Could it not be the case that the new sequence of digits is just the terminating decimal expansion of some number already in $x_k$?  Would it not be more correct to use the sequence $x_k$ to generate a sequence of all (both terminating and non-terminating) decimal expansion of all numbers in $[0,1)$ and then apply the diagonal argument? Cursor is set to move by increments. how to reset to normal? My cursor is moving by every selection by large increments!  Normally when I use Blender, I am able to select and move objects to any coordinate. Now, all of the sudden, when I select an object or mesh the selection moves by an inch or so in each direction.  How do I reset it to normal?