Need shapefile for worldwide bathymetry
Detailed Bathymetric/Bathymetry contour data (0-200M)
Geometric series for two-point function In deriving the expression for the exact propagator  $$G_c^{(2)}(x_1,x_2)=[p^2-m^2+\Pi(p)]^{-1}$$   for $\phi^4$ theory all books that i know use the following argument:  $$G_c^{(2)}(x_1,x_2)=G_0^{(2)}+G_0^{(2)}\Pi G_0^{(2)}+G_0^{(2)}\Pi G_0^{(2)}\Pi G_0^{(2)}+...$$  wich is a geometric series so the formula for the exact propagator.Here  $$G_0^{(2)}$$   is the free propagator and   $$\Pi=X+Y+Z+...+W$$  is the sum of all irreducible diagrams.Here the irreducible diagrams is represented by $X,Y,Z,...,W$.  Using the path integral i can see, that  connected diagrams $D$ can be written in the form  $$D=G_0^{(2)}XG_0^{(2)}Z...G_0^{(2)}W$$  Question: But how to prove that there is no constant $C$ so that instead we have  $$D=G_0^{(2)}XG_0^{(2)}Z...G_0^{(2)}W$$  we would have  $$D=CG_0^{(2)}XG_0^{(2)}Z...G_0^{(2)}W~?$$  In the last case we would not have a geometrical serie. Can someone explain me i t please  or give me another way to derive it. For equal cost, why would you select the MacBook Air over the MacBook Pro? I can see that the 13" version of MacBook Pro and MacBook Air is same $1199, but the Pro is more feature-loaded than Macbook Air. Why would anyone buy MacBook Air? What's the catch in this?    I was thinking of buying a MacBook for development purposes, and worried if there's any problem in the Pro version, because it comes with more features (like more storage).  Edit:    Thanks for the answer guys, I bought a MacBook Pro a week ago and already loving it. Chrome asks for password to unlock keyring on startup In Google Chrome, when I go to a login page, a window pops up asking to "Enter password for keyring 'default' to unlock". In most cases, whether I click Cancel or enter my password, the login form gets auto filled anyway.  How do I get rid of the popup? I want it to auto login each time, not ask for my system password. The dialog box never appears for any other apps. Commutator Subgroup of Direct Product equals the Direct Product of the Commutator Subgroups I need to prove that $(G_{1}\times G_{2})^{\prime} = G_{1}^{\prime} \times G_{2}^{\prime}$, where $G^{\prime}$ denotes the commutator subgroup of $G$ - i.e., $G^{\prime}=[G,G]$, the subgroup generated by all commutators of elements of $G$.   Recall that the commutator of two elements $x$ and $y$ in a group $G$, denoted $[x,y]$ is defined to equal $x^{-1}y^{-1}xy$.  I have posted my proof as an answer below. Could somebody please take a look at it and let me know if it's okay? If not, please let me know what I need to do in order to fix it. Thank you. :)    Edit: I have been informed that my answer given below actually shows only equality of the set of commutators, and that $G^{\prime}$ consists of products of commutators. So, this question is no longer a proof check, but I am asking specifically how to fix what I have written below in order to make it actually answer the thing I set out to prove. I am having a bit of trouble understanding some of the hints given me thus far, and am going to need more detail in any answers given in order for them to be helpful. PostgreSQL multi-column unique constraint and NULL values I have a table like the following:  create table my_table (     id   int8 not null,     id_A int8 not null,     id_B int8 not null,     id_C int8 null,     constraint pk_my_table primary key (id),     constraint u_constrainte unique (id_A, id_B, id_C) );   And I want (id_A, id_B, id_C) to be distinct in any situation. So the following two inserts must result in an error:  INSERT INTO my_table VALUES (1, 1, 2, NULL); INSERT INTO my_table VALUES (2, 1, 2, NULL);   But it doesn't behave as expected because according to the documentation, two NULL values are not compared to each other, so both inserts pass without error.  How can I guarantee my unique constraint even if id_C can be NULL in this case? Actually, the real question is: can I guarantee this kind of uniqueness in "pure sql" or do I have to implement it on a higher level (java in my case)? I was rewatching the Breaking Bad episode S04E08 (Hermanos) and I didn't quite understand why exactly Don Eladio killed Gus's partner, but he let Gus live. He says:     The only reason you're alive and he's not, is because I know who you are.   But I still have yet to fully understand. Can I open Microsoft Word and Excel files with Ubuntu? Browse for Servers does not display local instance Do I need an airport transit visa through Switzerland if I have no Schengen visa? Am traveling from Cairo to Moscow via Swiss Air Virtual vs Real image How do I install drivers for Realtek RTL8812BU? So I've been experimenting with Ubuntu on and off for a while, but I honestly have no idea what the hell I'm doing. So I have a realtek RTL8812bu WiFi dongle that I'm hoping to get working. I did some research, and came across  that a couple people across two threads said worked for them:  At the bottom it said there is a new version . So somewhere it said it was confirmed to work on kernels up to 4.16, so I checked and I'm on 4.15.0. But the problem I'm having, is what am I supposed to do? There is some installation guide at the bottom that is about as clear as mud to me since I don't know much. How do I find playtesters? Obviously the first tester group would be your own group. But beyond that? It would seem to make sense to have at least more than one group test out your game, as different groups want different things and play differently. Fresh eyes find different bugs, etc. etc.  Are there resources out there to help aspiring game designers without a lot of contacts find people willing and eager to test out their game?  Or is this in essence a "" issue?  To clarify my own situation:  I have the mechanics finished. The setting is still under development, but in accordance with the motto "fail faster" I want to go ahead and test the mechanics (in a different setting for now) to see if they work and are fun or if I need to go back to the drawing board. I have a sort-of group, but I don't know them very well and they don't meet often, and so I'm not excited about the prospect of presenting the mechanics to them right now (as I'm sure there are a dozen issues I've overlooked). Also, I'd like to test the game (including the setting, later) on more than one group, as mentioned above. I've put out some feelers among my current friends and acquaintances, but nobody's really been excited about playtesting or even really giving in-depth feedback, and I don't want to be that person who's always shoving their project in your face. I'm willing to run something online as well. I'm also interested in having others run a game without me present, and giving me their feedback.  Also, I'm looking for something of a guide-type answer that might help someone besides just me. Why an R-module is an R/I-module precisely when it is annihilated by I? Let $I$ be an ideal of $R$ and let $M$ be an $R$-module. Prove that the formula $(r + I) \cdot m = r \cdot m$ for $r + I \in R/I$, and $m \in M$ makes $M$ into an $R/I$-module if and only if $i \cdot m = 0$ for all $i \in I, m \in M$.   I don't quite understand why we must have $i \cdot m = 0$ instead of $I \cdot m \in M$. This is for proving the only if part. Wifi not working in Ubuntu 14.04.3 Non-Exchange address in Exchange GAL We just made the switch to Google Apps for part of our domain. We disabled the accounts that are now on Google Apps and mail routes correctly. Our problem is that now we have no way of seeing those users in the Global Address List.  So we have these users in our Active Directory, they have no mailbox on Exchange, and we want to be able to see/search for their addresses in the GAL. Is there any way to do this?  This is Exchange 2007, if that matters. Why does work depend on distance? How to find original community description Before joining a community you can easily see the community description. For example, for example before joining the Programming Puzzles &amp; Code Golf Stack Exchange you see the description:     Programming Puzzles &amp; Code Golf Stack Exchange is a question and   answer site for programming puzzle enthusiasts and code golfers.   However, after joining I can no longer see this description. I can go to the on-topic page and see a different description:     Programming Puzzles &amp; Code Golf is for programming contests and   challenges. We welcome questions from beginners and experts alike.   Yet, I cannot seem to find the original description anywhere. Is there a way to find the original description while being logged into a Stack Exchange site?  Based on Rene's answer, I can click the Tour link on each site, but StackOverflow (and maybe other sites) do not have a tour link. Instead, I'd have to go there by manually typing it in the address bar. Is there a reason that this has been removed from the Stack Overflow page? I've been given a proof that shows the following:  If $f:[a,b]\to \mathbb C$ is a continuous function and $f(t)=u(t)+iv(t)$ then $$\left| \int_a^b f(t) dt \right| \leq \int_a^b \left| f(t) \right| dt$$ The proof begins by letting $\theta$ be the principle argument of the complex number $\int_a^b f(t)dt$ and there is one step in the proof I don't understand; can anyone explain to me why $$\int_a^b e^{-i\theta}f(t) dt=\Re\bigg(\int_a^be^{-i\theta}f(t)dt\bigg)$$  Would this not imply that the imaginary part of the left hand side is equal to $0$? I'm not sure why the LHS and RHS would be equal here. Combining two covariance matrices Is there a way to format a UTC time into any arbitrary string format I want in java?  Basically I was thinking of having some class take the timestamp and I pass it is string telling it how I want it formated, and it returns the formatted string for me.  Is there a way to do this?