Can silicon droplets bouncing on a vibrating surface be a model for Quantum Mechanics?
What are the similarities/differences between the behaviors of Quantum particles and bouncing droplets?
How to receive sms from our android app? I read Griffiths EM today and it says something very interesting but a little bothering to me. It states for an atom, the position of center of mass of an electron cloud lies in the center of the proton.  But my question is why? What will happen if this is not true? How to increase label size of OpenLayers plugin basemap layers? To prove that $(\mathbb{P(N)},d)$ is a metric space To prove that $(\mathbb{P(N)},d)$ is a metric space where $\mathbb{P(N)}$ is the power set of $\mathbb{N}$.  And $d:\mathbb{P(N)}\times \mathbb{P(N)} \mapsto\mathbb{R}$ is defined by $d(A,B)=\begin{cases} 0, &amp; \text{if A} \Delta \text{B=}\emptyset  \\ m^{-1}, &amp; \text{where m is the smallest member of} A\Delta B \end{cases} $.   Attempt: $x \in P\Delta Q=(P-Q)\cup(Q-P) \implies x\in (P-Q) \text{ or } x\in (Q-P) $. But $(P-Q)\cap(Q-P)= \emptyset \implies x \in P \text{ and} \notin Q \text{ or }x \in Q \text{ and} \notin P. \ \ \ $    (*)  To prove the triangle inequality:  Take any three sets $A,B,C \subset \mathbb{P(N)}$ such that none of them are equal to another. Now,  $\min A \Delta B  =m_1, \min B \Delta C  =m_2,  \min A \Delta C  =m_3   $. To prove $d(A,B) \leq d(A,C)+ d(B,C)$. By (*), $m_1 \in A$ or $m_1 \in B$ but not both.   Again,  $m_2 \leq m_1$  or $m_3 \leq m_1$. Either way, we are done. When $A \neq B$ and either $B =C $ or $A=C$ (not both), we have respectively $A=C$ , $B=C$ . Which satisfies the triangle inequality. When $A=B$ it is evident.   Symmetry: We know $A \Delta B =B \Delta A$. $d(A,B)= d(B,A)$  Non-negativity and $0 \iff A=B$:   $d(A,B)=0 \iff A \Delta B= \emptyset \iff A \subset B \text{ and } B \subset A \iff A=B$. By definition $d(A,B) \geq 0$  Is this okay? Please verify. To show that $\sum a_nb_n$ is absolutely convergent Assume that $\sum a_n$ is convergent and $\sum b_n$ is absolutely convergent.To show that $\sum a_nb_n$ is  absolutely convergent  My try::Consider the sequence of partial sums of $\sum |a_nb_n|$  $S_n=|a_1b_1|+|a_2b_2|+......+|a_nb_n|$  Now $(a_1b_1+a_2b_2+......+a_nb_n)\leq ( (a_1^2+a_2^2+..+a_n^2))^\frac{1}{2}((b_1^2+b_2^2+..+b_n^2)^\frac{1}{2})$  How to proceed from here? What does the plus sign do in '+new Date' How to set Windows bootloader as default bootloader? I have a Win 7/11.10 dual boot system with Grub 2 as the default bootloader. However, I want to make Windows bootloader the default bootloader (grub 'dos' like interface scrares the hell out of my sister) so when I start the PC I will have the following boot options: 1. Windows 7 2. Ubuntu  NB: A process to reverse this operation so Grub can be the default bootloader again will also be appreciated yum install error I can't run a yum command on my server without getting this:   CRITICAL:yum.cli:Config Error: Error accessing file for config file:///etc/yum.conf   This is what my yum.conf looks like:  # This is the fedorafaq.org yum.conf for Fedora Core 5. # # Note that you also need the rest of the configuration # as described at http://www.fedorafaq.org/#yumconf  [main] cachedir=/var/cache/yum keepcache=0 debuglevel=2 logfile=/var/log/yum.log exactarch=1 obsoletes=1 gpgcheck=1 plugins=1 metadata_expire=1800  # PUT YOUR REPOS HERE OR IN separate files named file.repo # in /etc/yum.repos.d   This is what my yum.repos.d looks like:  fedora.repo fedora-updates.repo fedora-updates-testing.repo   The permissions on those files are 0666 and it won't allow me to make them root:root How do I properly access Windows software RAID 0? I am a new Ubuntu user with a fresh installation, and am eager to get started with it. However, all of my important data is on Windows software RAID 0 array, and I need it to stay there as I'm also dual booting Windows. I need access to this data on Ubuntu, and can't really get anything real done until I have access.  I have already researched this subject as best as I could, and I managed to find a very helpful post:      The post describes how to get Ubuntu to see a Windows RAID 0 array that is made up of two drives. The main command used is sudo mdadm --build /dev/md0 --chunk=64 --level=0 --raid-devices=2 /dev/sdd2 /dev/sdc2. According to that user, and the other posters in the thread, it actually does work. That's great.  I have not tried following these instructions yet. Why? The post includes a warning about how you must not write to it if you enter the wrong chunk size; it's understandable how that could cause problems. My concern is that my setup is different to their example, and I am not sure that the commands should be entered exactly the same for my setup. I am afraid to break it by doing it wrong, and therefore wish to get the advice of somebody more experienced.  This is how my setup differs from their example:   I have three 1 TB drives, not two drives (of whatever size they used). I have two RAID 0 partitions spread across those three drives: one 500 GB and 2.3 TB. This means that I need to NOT use the full disks when creating the RAID array, but instead use just part of them. I used a non-default block size for at least one of my RAID 0 partitions when I set them up years ago. I have no idea if this block size is the same as the chunk size that they mention. My 500 GB partition has a block size of 4 kb (4096 bytes per cluster), and my 2.3 TB partition has a block size of 64 kb (65536 bytes per cluster).   The relevant output from sudo lsblk -o NAME,FSTYPE,SIZE,MOUNTPOINT,LABEL (for just those three RAID0 drives) is:  NAME   FSTYPE   SIZE MOUNTPOINT            LABEL sdb           931.5G             ├─sdb1            1M             ├─sdb2          127M             └─sdb3        931.4G             sdc           931.5G             ├─sdc1            1M             ├─sdc2          127M             └─sdc3        931.4G             sdd           931.5G             ├─sdd1        166.7G             └─sdd2        764.7G    The relevant output from cat /proc/partitions (for just those three RAID0 drives) is:  8       16  976762584 sdb 8       17       1024 sdb1 8       18     130048 sdb2 8       19  976631478 sdb3 8       32  976762584 sdc 8       33       1024 sdc1 8       34     130048 sdc2 8       35  976631478 sdc3 8       48  976762584 sdd 8       49  174763008 sdd1 8       50  801865728 sdd2   The "Disks" program in Ubuntu displays the following partitions for my drives:  /dev/sdb:   GUID Partition Table . /dev/sdb1:  1.0 MB, Microsoft LDM metadata. /dev/sdb2:  133 MB, Microsoft Reserved. /dev/sdb3:  1.0 TB, Microsoft LDM data. /dev/sdc:   GUID Partition Table partitioning. /dev/sdc1:  1.0 MB, Microsoft LDM metadata. /dev/sdc2:  133 MB, Microsoft Reserved. /dev/sdc3:  1.0 TB, Microsoft LDM data. /dev/sdd:   Master Boot Record partitioning. /dev/sdd1:  179 GB, Unknown. /dev/sdd2:  821 GB, Unknown. /dev/sdd:   136 MB, Unallocated space.   I hope I've provided enough information here. So now, my question is this: what is the proper command for me to enter with my setup, so that I can access both of my Windows RAID 0 partitions from Ubuntu?  Thank you very much in advance. Cases environment compresses fractions? what should I do to stop the cases environment compressing the first line of the following? \begin{equation} \alpha_{mn} = \begin{cases} \frac{16\mu^2}{mn\pi^2\left[\pi^2(m^2/a^2 + n^2/b^2) - \mu^2\right]} &amp;\mbox{for } m \mbox{ and } n \mbox{ odd;}  \\ 0 &amp;\mbox{for } m \mbox{ or } n \mbox{ even;} \end{cases} \\[1ex] \end{equation}  I'm not sure to do tex on this site, but if anyone tries it they see the first case is compressed because it's a fraction. If every compact set is closed, then is the space Hausdorff? Is there a rule for pronouncing “th” at the beginning of a word? Consider the th in thistle versus the th in this: the former is unvoiced, while the latter is voiced.  Is there a rule or reason for the differences? Exact Duplicate:        I was reading an article on MSDN where I found a mention to google-fu. It says, “To search for C++ delimeters and code snippets is going to take a little Google-fu on the reader's part.” what does google-fu mean? How to perform hard / cold reboot of iPhone or iPad? I understand that when I press and release the power button on the top of my iPhone or iPad, it stays on but turns off the screen.  Whereas if I press and hold the power button, a "slide to turn off" control appears on the screen.  Sliding this, as I was told, does turn the unit off, but it does so by suspending the RAM to disk (flash memory, actually.) So, when turning on the iPhone or iPad, it isn't so much rebooting the OS as it is resuming it from flash storage.  How to force the OS to completely reboot on these devices? Call to a member function on a non-object So I'm refactoring my code to implement more OOP.  I set up a class to hold page attributes.  class PageAtrributes  {   private $db_connection;   private $page_title;      public function __construct($db_connection)      {         $this-&gt;db_connection = $db_connection;         $this-&gt;page_title = '';     }      public function get_page_title()     {         return $this-&gt;page_title;     }      public function set_page_title($page_title)     {         $this-&gt;page_title = $page_title;     } }   Later on I call the set_page_title() function like so  function page_properties($objPortal) {         $objPage-&gt;set_page_title($myrow['title']); }   When I do I receive the error message:     Call to a member function set_page_title() on a non-object   So what am I missing? Bachelor thesis or Bachelor's thesis Can I use the Twig template engine? I do a lot of  development and I like their templating language. , the , looks very much like it.  How can I use Twig in Drupal 7 or even Drupal 6? Where do I use delegates? What are some real world places that call for delegates?  I'm curious what situations or patterns are present where this method is the best solution.  No code required. prove that $24 \mid a(a^2-1)$ If $a$ is an odd integer, prove that $24 \mid a(a^2-1)$.  I proved in my class that $a^2=8k+1$ for some $k$, provided $a$ was odd.  So $$a(a^2-1)=(2k-1)(8k+1-1)=8k(2k-1)$$ but I can't pull a $24$ out of it. Our high-school teacher told us that the Earth pulls us with some force $F$ and we pull the Earth with the same force $F$. Within Newtonian physics this is true because of , but let’s consider . My mass is small; so I don’t warp space-time much. But Earth’s large mass warps space-time to a far greater extent.  So do I pull Earth with the same force it pulls me? If yes, how?