Anyone who's played with bar magnets knows that if you bring a bar magnet close to another tilted at some angle off axial to the other magnet, the one you're not holding will immediately flip to line up with the other that you're holding.   This would mean that every single tiny magnet sent in to the SG apparatus no matter the angle would immediately flip in to a vertical orientation in line with the applied field and be sent in a straight line through the apparatus, resulting in a single clump at the center.  Yet in most animations of the Stern Gerlach experiment (like this one here ), and indeed in explanations of the classical expected outcome of the experiment, we see the tiny magnets maintain their orientation throughout the trajectory through the magnetic field, and this is used as an argument as to why the tiny magnets are evenly distributed at the other end.  This has always bothered me why this is not reconciliated with our childhood experiences of playing around with bar magnets. Please note that I am NOT talking about the actual result of the experiment wherein the electrons formed two clumps one at the top and one at the bottom. I'm asking about the part where they explain the classical expectation of an even distribution.  My classical expectation is for only a single clump, right in the center because they all rotate line to up immediately entering the field and have equal magnetic forces up and down.   What is wrong with my expectation?
My understanding of the Stern–Gerlach experiment is that neutral (0 total charge) particles are sent through a non-homogeneous magnetic field, with the expectation that the field will push that particle's path higher or lower on a detector because of the collective spin of that particle. While the detector can detect particles in a two-dimensional surface, the results of the experiment are that particles appear in only two localized areas directly above the path of the particle stream, or directly below the path of the particle stream - spin up or spin down. The conclusions from these measurements are that the particle, when measured, will always have about the same magnitude.  Why does this not follow from classical mechanical theory related to magnetism? If you shot a magnet through a similar apparatus, I would expect the magnet to be rotated to align with the magnetic field in some way which, at high enough field strengths relative to the mass of the magnet, would cause us to measure basically the same magnitude as if the magnet entered the apparatus pre-aligned with the field.  How is my explanation incorrect?
Create backup iPhone with forgotten encryption password I'm trying to make a backup from my iPhone, however it's set to be password protected. I do not know the password, as I've never set one. I've tried all the passwords I know, which I've ever used to make sure I didn't set it.  I've also tried the default 0000 and 1234 codes.   I want to uncheck the encryption checkbox in iTunes, but it requires me to type a password. What else can I try?  I have no problems in removing all backups and start from the scratch somehow, however - I do not want to restore my phone as new and remove all those settings. Plot points:   I think the man was one-armed or had one damaged/withered arm. He is an artist when we meet him. He's picked up by aliens to represent earth in a galactic armada. Put in a ship with other aliens only there so a representative of their species can be said to be present - but not expected to actually contribute much to the coming fight. Fight is to protect against invaders from another galaxy. Somehow or other, their ship and crew become integral to winning the war. Trouble trying to use Windows Search to search for file with a question mark in the content It seems that Windows Search is having trouble when I specify a question mark character as the content that I'm searching for within my files.  I've tried:   content:? content:"?" content:"\?" content:\? content:%3f content:"%3f" content:\3f content:"\3f" content:\00\00\00\3F   but each of these yield no results when I do indeed have files that contain ? within the scope of the search. If I instead search for something like content:happy it will indeed find all files with the phrase "happy" within those same files.  My assumption is that Windows Search is treating some characters such as the question mark as a special character likely for the purpose of wild card expressions. To test this theory I've also searched for files containing an asterisk * and indeed I have the same issue as when searching for content of question mark. What I'm wondering is whether there is any way to get a search to work where I can search for a literal expression without any type of wildcard matching or at least a way to escape the special characters within the expression.  By the way I'm using Windows 7 Enterprise. How is double negation interpreted in English? I want to use input from a user as a regex pattern for a search over some text.  It works, but how I can handle cases where user puts characters that have meaning in regex? For example, the user wants to search for Word (s): regex engine will take the (s) as a group.  I want it to treat it like a string &quot;(s)&quot; .  I can run replace on user input and replace the ( with \( and the ) with \) but the problem is I will need to do replace for every possible regex symbol. Do you know some better way ? Bounded sequence in a metric space The question is:     Show that there are an infinite number of pairs $(m,n): m, n \in \mathbb{Z}^{+}$, such that: $$\frac{m+1}{n}+\frac{n+1}{m} \in \mathbb{Z}^{+}$$   I started off approaching this problem by examining the fact that whenever the expression was a positive integer, the following must be true:  $$\frac{m+1}{n}+\frac{n+1}{m} - \left\lfloor\frac{m+1}{n}+\frac{n+1}{m}\right\rfloor = 0$$  However, I was unable to do much more with this expression, so I abandoned it and started the problem again from a different angle.  Next I re-arranged the expression to state that:  $$\frac{m^2+m+n^2+n}{mn} \in \mathbb{Z}^{+} \implies \frac{m(m+1) + n(n+1)}{mn} \in \mathbb{Z}^{+}$$  And therefore:  $$mn \mid (m(m+1) + n(n+1))$$  However, I'm unsure how to demonstrate there are infinitely many occurances of $(m, n)$ for which this is true. So I'd appreciate any help.   Thanks in advance Is it possible to save a Diablo 3 chat session or save some in game notes Ubuntu 20.04 on DualBoot fail 90% of tries - Initramfs unpacking failed: Decoding failed I just installed Ubuntun 20.04 on a Dell Latitude 7400 on DualBoot. I had to remove the RST as mentioned on this post :  It works but now I need to test 5 or more times to boot. After the grub screen, most of the time i have a black screen. Sometimes I have this error : Initramfs unpacking failed: Decoding failed And then it starts.  here is a file called initramfs.conf cat /etc/initramfs-tools/initramfs.conf MODULES=most  BUSYBOX=auto  COMPCACHE_SIZE=&quot;&quot;  COMPRESS=lz4   DEVICE=  NFSROOT=auto RUNSIZE=10% I have an object already created in blender, a tree, or a human, or a pipe.. and I need this to be drilled with multiple holes.   The holes are painted in an image, that is, it is an image that has a repeating an images pattern (they can be circles, squares, or any form).  Here are some examples for drilling-pattern: $f$ holomorphic on $D\setminus \{0\}$ and takes no values in $(-\infty,0],$ then $0$ removable If $f$ is holomorphic on $D\setminus \{0\}$ and takes no values in $(-\infty,0]$ then $0$ is a removable singularity.   I thought to prove this by elimination, but I can't really tell anything about the behavior of $f$ around $0$. How can one translate the information about the definition of $f$ in semi-open interval $(-\infty,0]$. How to show GRUB after install Ubuntu over Windows 8? I installed Windows 8 and after that I installed Ubuntu. This are my partition now:   70Gb --> Windows 8 50Gb --> Ubuntu 12.10 100Mb --> UEFI 300Mb --> Recovery   I installed the GRUB on /dev/sda. Then, after GRUB not showing up and booting directly into Windows 8, I turned the laptop off and booted again into Ubuntu LiveCD and ran the Boot-repair utility, it give me  but it didn't solved the problem.  My Laptop still boots directly into Windows 8, without GRUB or Ubuntu even showing up. Why does pluralization of compound words typically occur in the middle as opposed to the end of the word? As I understand, correct plural versions of passerby and attorney general become passersby and attorneys general.  But why?  With passerby, the the preposition "by" has been combined with the noun "passer" to become a one word noun "passerby".  So why shouldn't this be passerbys?  If I am an attorney general, and you are an attorney general, why are we not attorney generals?  As an American I have always heard it as attorneys general, however  suggests British English does use "attorney-generals" (as well as an interesting 2nd paragraph that further probes my question).  Are there hard rules to this topic?  Or merely generally accepted practices based on locale? I have multiple characters linked to a blender file, but i moved the original character files and now blender is sating they're missing.  Is it possible to get blender to find the missing blender files like it finds missing image files so that i can preserve the previously made animation?  On a side note is there a way to also view a list of all the missing files? How can I replace Windows with Ubuntu? Let $x&gt;0$, $y&gt;0$ and $z&gt;0$. Show that   $$x^3y+y^3z+z^3x\ge xyz(x+y+z).$$   I known we can't WLOG: $x\ge y\ge z$, if this, I can use rearrangement inequality, But other I can't it. Thanks? I have written below Wrapper class.  global class BI_VA_AutomationWrapper {      global class BI_VA_AutomationRequest {      webservice String userName;     webservice String emailId;     webservice String buinessUnit;     webservice String orgName;     webservice String country;     webservice String environment;     webservice String myShopNumber;     webservice String BidsId;//for testing     webservice String Type; //for testing  }  global class BI_VA_AutomationResponse {      webservice String responseStatus;     webservice String myShopNumber;     //webservice list&lt;Error&gt; errorMessages;     webservice String  errorMessages;//for testing   } global class BI_VA_Error {      webservice String type;     webservice String message;    }}   And test class is,  @isTest public class BI_VA_AutomationWrapperTestClass  { public static testMethod void unitTest(){      BI_VA_AutomationWrapper.BI_VA_AutomationRequest wrap= new BI_VA_AutomationWrapper.BI_VA_AutomationRequest();        wrap.userName='Test@test.com';     wrap.emailId='Test@test11.com';     wrap.buinessUnit='AH';     wrap.orgName='ORD';     wrap.country='US';     wrap.environment='QA';     wrap.myShopNumber='123456789';     wrap.BidsId='123';     wrap.Type='ResetPassword';              BI_VA_AutomationWrapper.BI_VA_AutomationResponse res= new BI_VA_AutomationWrapper.BI_VA_AutomationResponse();     res.responseStatus = 'Success';     res.myShopNumber = '987654321';     res.errorMessages = 'Test error';      BI_VA_AutomationWrapper.BI_VA_Error error = new BI_VA_AutomationWrapper.BI_VA_Error();     error.type = 'Test';     error.message = 'Test';  }}   Code coverage is 0% only. What are the differences between "to talk" and "to speak"? StandardSetController with History records Possible to have the default landing page of my Sharepoint Site be an applicaiton page? So basically when someone goes to:   http://mysite.com   I would like to show an Application Page that I have created, without the giant URL.  Example of the giant URL :  http://mysite.com/_layouts/ap/myAppPage.aspx   Is there any way for me to do this?