We know that universe is expanding and galaxies are moving away from each other. Does this mean the galaxies are also expanding in itself and therefore I guess growing larger in volume? Depending on the answer of that, does the solar system also expands?
I have looked at other questions on this site (e.g. "why does space expansion affect matter") but can't find the answer I am looking for.  So here is my question: One often hears talk of space expanding when we talk about the speed of galaxies relative to ours. Why, if space is expanding, does matter not also expand? If a circle is drawn on balloon (2d plane), and the balloon expands, then the circle also expands. If matter is an object with 3 spatial dimensions, then when those 3 dimensions expand, so should the object.  If that was the case, we wouldn't see the universe as expanding at all, because we would be expanding (spatially) with it.  I have a few potential answers for this, which raise their own problems:   Fundamental particles are 'point sized' objects. They cannot expand because they do not have spatial dimension to begin with. The problem with this is that while the particles would not expand, the space between them would, leading to a point where the 3 non-gravity forces would no longer hold matter together due to distance Fundamental particles are curled up in additional dimensions a la string theory. These dimensions are not expanding. Same problems as 1, with the added problem of being a bit unsatisfying. The answer seems to be (from Marek in the previous question) that the gravitational force is so much weaker than the other forces that large (macro) objects move apart, but small (micro) objects stay together. However, this simple explanation seems to imply that expansion of space is a 'force' that can be overcome by a greater one. That doesn't sound right to me.
Showing that $(m)\cap (n)=(\operatorname{lcm}(m,n))$ and $(m)+(n)=(\gcd(m,n))$ for any $m,n\in\mathbb{Z}$ As I was trying to validate our pcb design, I measured the impedance matching on the digital transmission lines, and got stuck with the oscilloscope not showing what I expected. We are using the PicoScope 4227, but I suspect that the strange measurement is not directly related to the specific oscilloscope but more to general on how to measure digital signals.  My setup is as follow: I measure the output-pin of an FPGA with both oscilloscope input A and B.  Input A (blue) is measured using the oscilloscope probe set to x10.  Input B (red) is measured using a 50-ohm coxial cable terminated at the scope input with 50-ohm.  As you can see, Input B seems correct, no reflection ect.  But Input A (the probe) has some overshoot, and ringing.  The probe should be calibrated and valid to 250MHz, so I don't get was is wrong. ?  I suspect that the small probe-clip adds some inductance, and therefore we see the ringing. But I really don't know.    EDIT After reading your answers, I walked got into our lab storage and started looking, and found a probe GND clip like the one showed in the answer below.   When I use that clip, I get the output below. Which is really a huge improvement. Category Theory textbook (learning through guided discovery Dummit and Foote) Newtonian mechanics: massless particles Is there a function or method to give the last day of a month? For example if the date is 27 feb 2013, the last date should be 28 feb 2013 , it become 29 if its a leap year. if the date was 2 jan then it should return 31 Jan.  If there is no function then any ideas on how we can get this?  Thanks I'm  having some trouble editing the content of a Managed Email Template, I can quite easily modify the content of the Email Template, but when I wish to refer to an unmanaged component, like this:  &lt;messaging:attachment renderAs="PDF" filename="invoice.pdf"&gt;     &lt;c:MyComponent/&gt; &lt;/messaging:attachment&gt;   I get the error message:     Error: Unknown component c:mycomponent   Does anyone know if its possible to embed an unmanaged component in a managed Email Template? Rubbing eggplants in salt I love apples. I like to eat them with skin as it has plenty of fiber in the skin. But apples are famous for wax and pesticides on the skin which I don’t want to ingest. I have read many articles on the web and suggestions for removing the wax from the surface.   These suggestions include soaking in vinegar or hot water and other methods. They suggest that soaking apples in vinegar removes the wax that can be seen in the vinegar. I have done that, but never seen any residue of wax in the vinegar.   So I have set aside a new kitchen sink Scotch-Brite scrubber for this purpose and been scrubbing the apple skin under running water before eating. I think this method should remove most of the wax and pesticides. I would like to hear your input. Prove $\sum_{i=1}^n i! \cdot i = (n+1)! - 1$? Prove the summation:  $$\sum_{i=1}^n i! \cdot i = (n+1)! - 1$$ using induction.   base case:  $n=1$: \begin{align*} \sum_{i=1}^1 i! \cdot i &amp;= (1+1)! - 1 \\ 1 &amp;= 2 - 1 \\ 1 &amp;= 1 \end{align*}   This is a question from my test review packet, currently have the base case completed and I am a bit lost on where to go from there. Any help/hints are appreciated. How can I deduce/identify an app from a notification icon? Could Muggles enter Diagon Alley from Leaky Cauldron? Courtesy of , I found the a bit of  (currently un-cited):  The Leaky Cauldron The pub serves as a way of entering into Diagon Alley from the Muggle world for Muggle-borns and their parents (both of whom, until the first letter from Hogwarts, have no magical knowledge or means of entering). The rear of The Leaky Cauldron opens onto a chilly little courtyard, in which a particular brick must be tapped three times to open a path to Diagon Alley.  But from what I can see, Muggleborns and their parents wouldn't be able to enter from Leaky Cauldron, because - based on what I can tell - that requires one to use a wand:  He {{Hagrid}} tapped the wall three times with the point of his umbrella. The brick he had touched quivered – it wriggled – in the middle, a small hole appeared – it grew wider and wider – a second later they were facing an archway large enough even for Hagrid, an archway on to a cobbled street which twisted and turned out of sight.  Is there some canon information confirming the Wikipedia assertion that Muggle parents and not-yet-wand-owning Muggleborns could enter Diagon Alley from the courtyard behind Leaky Cauldron? Preferred languages: C/C++, Java, and Ruby.  I am looking for some helpful books/tutorials on how to write your own compiler simply for educational purposes. I am most familiar with C/C++, Java, and Ruby, so I prefer resources that involve one of those three, but any good resource is acceptable. Chapter on the right side - How to turn it off? What do you call snow that has collected between a car body and the tire? How to create a color of the same brightness and saturation? Let's consider three colors: Red, Green and Blue. For blue I created a specific shade, something like #F2F5F7. If you see this color, it has a certain level of shade, brightness and saturation value of blue.  I want to create the same equivalent color but for Green and Red, how to get that? Adding a reference between Eclipse Java projects Proving an infinite number of primes of the form 6n+1 The proofs given on other sites weren't that clear and used different methods that I have yet to learn.    Prove that there are an infinite number of primes of the form 6n+1.  The hint that was given was: Let p = p1, p2, ..., pk + 1, where p1 = 2, p2 = 3,...pk are the first k primes.  Show that p is prime.  (p1 means p sub 1, p2 means p sub 2, and pk is p sub k.  Wasn't sure how to write it on this.)    Can someone explain this hint on how they came about of p1 = 2, p2=3, etc, and prove this please?    Also, how would the proof change if the form changed?  ("Prove that there are infinite number of primes of the form....") Rename All Files with a Certain Name I'm trying to find certain files with the name "stringx" and replace the name (but not the extension) with "stringy". So basically for stringx.txt and stingx.cs, I'd want stringy.txt and stringy.cs. I've attempted to test my rename command regex using following, but it returns no results:  rename -n 'stringx./s/\*$stringy./\/' stringx.*   I'm running csh under Centos. I can see that my regex is probably not correct, but I can't see any results to verify this. I can see that there are files that are named stringx. with the following:  find ./ -name 'stringx.*' "No worthy mechs found" when trying to relay email to Gmail using Postfix I've been trying to configure email to forward to Gmail, using Postfix to relay email to smtp.gmail.com. However, I'm failing to get it to authenticate with smtp.gmail.com, which is a rather vital prerequisite to getting anything working…  The mail logs show only:  Oct 29 15:50:14 gsnedders-1 postfix/master[6596]: daemon started -- version 2.7.1, configuration /etc/postfix Oct 29 15:50:19 gsnedders-1 postfix/pickup[6598]: EBA1F78750: uid=1000 from=&lt;gsnedders&gt; Oct 29 15:50:19 gsnedders-1 postfix/cleanup[6603]: EBA1F78750: message-id=&lt;20111029145019.EBA1F78750@mail.gsnedders.com&gt; Oct 29 15:50:19 gsnedders-1 postfix/qmgr[6599]: EBA1F78750: from=&lt;gsnedders@gsnedders.com&gt;, size=324, nrcpt=1 (queue active) Oct 29 15:50:19 gsnedders-1 postfix/cleanup[6603]: F2D557874F: message-id=&lt;20111029145019.EBA1F78750@mail.gsnedders.com&gt; Oct 29 15:50:19 gsnedders-1 postfix/local[6605]: EBA1F78750: to=&lt;me@gsnedders.com&gt;, orig_to=&lt;me&gt;, relay=local, delay=0.04, delays=0.03/0.02/0/0, dsn=2.0.0, status=sent (forwarded as F2D557874F) Oct 29 15:50:19 gsnedders-1 postfix/qmgr[6599]: F2D557874F: from=&lt;gsnedders@gsnedders.com&gt;, size=454, nrcpt=1 (queue active) Oct 29 15:50:19 gsnedders-1 postfix/qmgr[6599]: EBA1F78750: removed Oct 29 15:50:20 gsnedders-1 postfix/smtp[6606]: warning: SASL authentication failure: No worthy mechs found Oct 29 15:50:20 gsnedders-1 postfix/smtp[6606]: F2D557874F: SASL authentication failed; cannot authenticate to server smtp.gmail.com[74.125.157.108]: no mechanism available   And the postfix config is:  relayhost = [smtp.gmail.com]:587  smtp_use_tls = yes smtp_sasl_auth_enable = yes smtp_sasl_password_maps = hash:/etc/postfix/sasl/passwd smtp_sasl_security_options = noanonymous  smtp_tls_eccert_file = smtp_tls_eckey_file = smtp_tls_security_level = may smtp_tls_CAfile = /etc/postfix/cacert.pem smtpd_tls_received_header = yes tls_random_source = dev:/dev/urandom smtpd_tls_security_level = may How to re-enable tray icons for applications in Ubuntu?