In the gravitational redshift, the frequency of photons radiated from some source is reduced. As the energy of a photon is given by $\hbar\omega$, if the frequency is reduced where is the lost energy?
I think the title says it. Did expansion of the universe steal the energy somehow?
Within 300 km of Tokyo: Where for flora, landscape, nature? I plan to visit Japan for 10 days and apportion 5 days to Tokyo. For the remainder, I want to escape the megalopolis and enjoy picturesque backwoods or countryside. Please recommend? Criteria:   No dangerous animals or untamed boondocks. No  or snakes. I won't drive, and must rely on public transport and walking less than 5 km in total.  No shrines, temples or any religious edifice. OPTIONAL: I fancy  , the more  the better.   This instantiates, doesn't duplicate, . Can I play against or with Xbox 360 players through my Xbox One? Is it possible to play against and with Xbox 360 players through my Xbox One? How to grep a specific line _and_ the first line of a file? How to dynamically change a web page's title? I have a webpage that implements a set of tabs each showing different content. The tab clicks do not refresh the page but hide/unhide contents at the client side.  Now there is a requirement to change the page title according to the tab selected on the page ( for SEO reasons ). Is this possible? Can someone suggest a solution to dynamically alter the page title via javascript without reloading the page? What is the correct way to punctuate the end of a sentence before a quote that directly supports the statement? I assume either a colon or a semicolon, but I have no idea which is correct.  For example:     Waldo is a better hide-and-seek player than Clem; "Waldo was   the winner of the past ten annual hiding awards" (Where's Waldo 13).      Waldo is a better hide-and-seek player than Clem:  "Waldo was   the winner of the past ten annual hiding awards" (Where's Waldo 13).   (Excuse the silly example, but I didn't have a better one.) How can I convince new players to read and learn the basic rules before sitting down to play? Everyone in this story works mostly together. Some work friends and my wife were talking about playing D&amp;D, and I was appointed the DM. I've played the game once 20 years ago, so I've spent the past few months buying the resources and learning as much as I can about the game so I can make it as enjoyable for then as possible, we are yet to have our first session.  But to make it easier so I don't have to teach them literally everything I asked them to read the Basic Rules so they have some idea of what they are in for and the expectations of them and me are.  But they came back with "its too hard to read it, I learn by doing, that's what we have you for".  I'm super pissed by this, I've spent so much time and effort learning this game and they can't be bothered to put any effort in.  My question is should I let them know how much it's annoyed me, and reiterate they need to know stuff, or just ignore it and carry on? To show that Fermat number $F_{5}$ is divisible by $641$. How can I show that  $F_{5}=2^{2^5}+1$ is divisible by $641$. Deriving the conditional distributions of a multivariate normal distribution I have a powershell script that I am trying to add in to a sql agent job, but the job step is failing with the following error      A job step received an error at line 1 in a PowerShell script. The corresponding line is 'import-module SQLPS  -DisableNameChecking'. Correct the script and reschedule the job. The error information returned by PowerShell is: 'Could not load file or assembly 'file:///C:\Program Files (x86)\Microsoft SQL Server\130\Tools\PowerShell\Modules\SQLPS\Microsoft.SqlServer.Management.PSSnapins.dll' or one of its dependencies. This assembly is built by a runtime newer than the currently loaded runtime and cannot be loaded.   I assumed that the error was being caused by differences in the module path, so I explicitly set the path via $env:PSModulePath to match the path of my powershell session where the code runs fine.  I am pretty new to powershell, so any help you could provide would be appreciated  I am just doing some testing right now, so everything is running locally on my desktop.  I am running SQL Server 2012. Double dispatch in C#? I have heard/read the term but don't quite understand what it means.  When should I use this technique and how would I use it? Can anyone provide a good code sample? What's the equivalent of the "cls" command from Windows/DOS? How to replace the domain name in a Wordpress database? I have a Wordpress database which was installed in a development environment... thus, all references to the site itself have a fixed IP address (say 192.168.16.2). Now, I have to migrate that database to a new Wordpress installation on a hosting. The problem is that the SQL dump contains a lot of references to the IP address, and I have to replace it with: my_domain.com.  I could use sed or some other command to change the that from the command line, the problem is that there are a lot of configuration data which uses JSON. So what? Well, as you know, JSON arrays uses things like: s:4: to know how many chars an element has, and thus, if I just replace the IP with the domain name, the configuration files will get corrupted.  I used an app for Windows some years ago that allows to change values in a database and takes care of the JSON arrays. Unfortunately, I forgot the name of the app... so the question is: do you know any app that allows me to do what I want? How, on a physical level, does ATP confer energy? When ATP is used as the energy currency to make, say, reaction X + Y → Z happen, is what happens on a physical level down at the molecular scale that during the reaction    ATP + H2O → ADP + Pi &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ΔG˚ = −30.5 kJ/mol (−7.3 kcal/mol)    that 30.5 kJ/ mol is conferred by ATP molecules physically bumping around the reactants X and Y, the kinetic energy of the above reaction being what does it?  I mean, is the energy coin of ATP conferred to reactions by molecular collisions, or is it an electric field effect in the spatial geometry the way the ATP molecule tends to break apart? I'm planning a trip to recover a motorcycle from a distant city. The ideal trip would be flying to that location and coming back riding the bike, but that would require me to transport my riding gear with me in the plane: Leathers, boots, gloves, back protector and crash helmet.  All this is bulky and expensive stuff, and a crash helmet may be damaged if dropped or hit hard.   I don't expect any airline to allow me a crash helmet as hand luggage; and wearing it all the time is out of the question :-)   To complicate things, I would be coming back riding the bike, so any hard suitcase would have to be left behind.   How do people normally transport that kind of stuff? Anti-Cheat for MMOs issues and solutions? Most online games suffer for this problem and there are some  out there to cover this but recently from what I've seen most companies are trying to avoid those programs creating their own system (blizzard with warden, aion with their own checking, etc...) but it is a very difficult case to prevent such ...  Just wanted to say i made another question topic as community wiki specific for posting applications and it is features and the ideas behind this question here is not to list those but instead to know more about what were your attempts, issues along the road and possible solutions, piece of codes if application and so forth.  What sort of protection do you guys use in order to (try to) prevent such acts:   Anti-cheat Software ? (please state which, why and possible problems you faced, for example aion stopped using GameGuard at beta stage due to a huge amount of compatibility problems and complains from their users) Your own code ? (what sort of verification do you usually run to make sure of the bad-faith players, for example speedhack, verify new location against speed+last location, etc...) None, i dont care ? (any personal reason or input you did like to share ?)   Any interesting piece of code related to the issue you would like to post ?  Feel free to rework my text my english inst that great  ?** I have come across this .  Has anyone tried anything similar or does it work for you? Can you tell if an email customer / user enters is correct &amp; exists? Argue that there exists a continuous function $g: \mathbb{R} \rightarrow \mathbb{R}$ which satisfies $g(x) = \frac{1-e^{-2x^2}}{x^2}$ for $x \neq 0$ How to store credit card info on iphone? How to show  that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal? Is it possible to find the cardinality of $\mathbb{Z}[i]/I$ as well?  I know how to show that it is an integral domain, because that follows very quickly. I just checked my server's /var/log/auth.log and found that I'm getting over 500 failed password/break-in attempt notifications per day! My site is small, and its URL is obscure. Is this normal? Should I be taking any measures?