What is the difference between partition function for two-boson system and two-fermion system?
I have two atoms, both of which are either bosons or fermions, with four allowed energy states: $E_1 = 0$, $E_2 = E$, $E_3 = 2E$, with degeneracies 1, 1, 2 respectively.  What's the difference between the partition functions of a pair of two bosons and that of a pair of two fermions?
I heard a lot about in-body image stabilization recently and I wonder how this technology works. I don't mean the mechanical part (I understand how the sensor moves along different axes to compensate), but the technique in principle:  When I take my 5D III and a lens like the 70-200 2.8 II IS USM with activated stabilization, the IS will constantly move one glas element within the lens in such a way that it directs the cone of light exactly onto the sensor, so that you can always use the full sensor area.  When the cone of light goes through an unstabilized lens and you need to move the sensor - how can it capture the same amount of light at all? The light enters the lens down a fixed axis right through the center of the lens. When the sensor currently moves down, for example, to compensate for a shake, I can't see how it then is still able to capture the full resolution? When a part of the sensor is below default/calm position, then there must be missing the same part on the opposite site?  There's only one way I could image IBIS to work without resolution reduction: if the sensor area was significantly bigger than the area exposed to light, so that there's still sensor available when it currently moves out of its initial position. But wouldn't this (partly) be the same as digital stabilization because the final image gets calculated from the full sensor area minus the not exposed area?  I really would like to understand this and it would be great if someone could "shed some light on this". Fantasy/scifi combo - band of travelers who must get from "sphere" or domain to domain - each geographic area is ruled by a magician - it turns out later these are people who are unwittingly tapping into the computer grid they all live on to alter their own reality? Estimate the population variance from a set of means Command for creating a directory and navigating into it directly? Can .exe and .msi files (Windows software) be installed in Ubuntu? Alternative of `route -n` of Linux in Mac How can I see the list of routes and its corresponding gateway in a Mac ? The command in linux is route -n .  For a particular IP address, I am able to get the routes for an particular IP address via route get 10.0.0.0. Help with proof of $|x+y| \geq |x|-|y|$ Granting access only to standby database One of the physical standby databases in my environment is open in read-only mode and used for reporting purposes . I want to give users access only to this particular standby, not to primary db.   The best approach I found so far is to create AFTER LOGON ON DATABASE trigger which checks v$instance (or maybe v$database), and throws error for depends on  values of host_name/instance_role columns  .   I wonder if there is a better way to do it. If a function returns no value, with a valid return type, is it okay to for the compiler to return garbage? The Wikipedia  has a derivation of the Klein-Gordon equation.  It gets to this step:  $$\sqrt{\textbf{p}^2 c^2 + m^2 c^4} = E$$  and inserts the QM operators to get  $$\left( \sqrt{ (-i \hbar \nabla)^2 c^2 + m^2 c^4 } \right) \psi = i\hbar\frac{\partial}{\partial t} \psi$$  The article then says     This, however, is a cumbersome expression to work with because the differential operator cannot be evaluated while under the square root sign. In addition, this equation, as it stands, is nonlocal.   To fix this, the first equation is squared instead to get  $$\textbf{p}^2 c^2 + m^2 c^4 = E^2$$  after which the QM operators are inserted and the expression is simplified to get  $$-\hbar^2 c^2 \nabla^2 \psi + m^2 c^4 \psi = -\hbar^2 \frac{\partial^2}{\partial t^2} \psi$$  A couple things I don't understand.  First, are the solutions to this differential equation not exactly the same as the solutions to the first differential equation?  Both sides of the starting equation were squared, so it seems to me that regardless of the particular form of the resulting differential equation, both of them should have the exact same set of solutions.  Secondly, why is the first differential equation cumbersome to work with?  It seems like it would in fact be easier to work with, since the operator under the square root could be expanded in terms of a Taylor series and then you have an equation that is first order in time.  And finally, can someone elaborate on what nonlocal means? The linked article on the Wikipedia page didn't entirely help me understand it. How do I install pillow in Ubuntu 16.04 LTS? How do I know if a laptop will work with Ubuntu? I want to buy a laptop at some point in the near future, but not knowing beforehand whether it works with Ubuntu makes the whole operation risky and tiresome. I would like to know if there is some kind of official hardware database where I can enter the name of the laptop I'm interested in and see if it's 100% compatible out of the box, or in case it isn't what is it exactly that doesn't work (ideally also if there is a way to fix it).  Does Canonical have a project along these lines? How should you interview for QA *Automation* positions? Why multiplicative group $\mathbb{Z}_n^*$ is not cyclic for $n = 2^k$ and $k \ge 3$ How to show $(a^b)^c=a^{bc}$ for arbitrary cardinal numbers? One of the basic (and frequently used) properties of cardinal exponentiation is that $(a^b)^c=a^{bc}$.  What is the proof of this fact?  As Arturo pointed out in his comment, in computer science this is called . brute force password guessing on SSH server isn't going to work? I'm running an SSH server on my personal computer. The log had many people(or bots?) repeatedly trying to log in to my server (that is before I changed the default port), which made me a little freaked out. I was worried about their dictionary attacks or brute force password guessing.  But then if you type wrong password (or wrong username), the server waits for about 2 seconds before it asks for password again. So an attacker can try one password per 2 seconds. So I concluded that these attacks aren't that great a threat (as long as your password does not consist of dictionary words.) Am I correct? Convert and redirect URL in uppercase to lowercase using .htaccess I would like to redirect a URL with uppercase characters http://localhost/A/B to a lowercase version http://localhost/a/b using the .htaccess file. Using regex I can capture A and B but is it possible to convert them to lowercase? Why is "be" here? People be like 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? Which Wifi Channel should I use? Very confused.  I'm using inSSiDer, WiFi Overview 360 and Wifi Analyzer apps to try to determine the best wifi channel to use. Assuming all channels are in use and there are about 20 different users in close proximity...  Q1: Signal Strength    If all channels are in equal use, do you select a channel where others that use it have the lowest signal strength?  I'm guessing that a higher signal strength means that it's from a router from your closest neighbour and you want to avoid that.  Is that the case?  Does lower signal strength mean the person using it is further away and therefore less likely to interfere with your signal? If 2 people are on channel 1 and have high signal strength and 2 people are on channel 11 and have low signal strength, do you choose channel 11?  Assume 6 cannot be used.    Q2: Signal Strength Weighted Against Number of People    What is the impact of signal strength compared to number of people using channel?  If 1 person is on channel 1 with very high signal strength and 2 people are on channel 11 with low signal strength, do you choose channel 11 over 1?  Assume 6 cannot be used?    Q3: Channel Overlap    If, for example, I had 11 routers sitting on top of each other, each set to a different channel, I'm guessing channel 1 and 11 would be the least interferred.  Is that right?  People go on about the fact that only channel 1, 6 or 11 should be used (in US) as they don't overlap but surely that statement is wrong.  Yes, if only 3 people were using Wifi, the best channels to use would be 1, 6 and 11 as they don't overlap but in practice, there are about 20 people using the channels in the same area.  What do you do in that scenerio.  Do you go for the shoulder channels if all channels are being used equally with equal strength?    Q4: Auto Channel Select    Do routers set to auto channel select only choose between 1, 6 and 11?  How do they make the choice?  Do they select by choosing channel with lowest other routers and do they factor in signal strengths.  My router auto chooses channel 1 but my closest neighbour is on that channel.  Is that correct.      Q5: Baby Monitors and Wireless Phones    What channels do 2.4 GHz baby monitors and wireless phones use?  No useful info on the internet for them.  Do inSSiDer, etc. pick them up?    Q6: I have access to channel 13.  All other things being equal, am I better to use this over channel 11 as it is further away from the other channels?    Those questions have puzzled me for a number of years and Google is not helping!!  Would really be grateful if someone could give sensible answers to one or all of them.  Thanks, Mike.