Evaluating $\int_0^\infty \frac{dx}{1+x^4}$.
How can I compute the integral $\int_{0}^{\infty} \frac{dt}{1+t^4}$?
Rewriting a custom-post-type permalink with taxonomy term? What was missing in Dirac's argument to come up with the modern interpretation of the positron? Why do the $n \times n$ non-singular matrices form an "open" set? Creating an index of quality from multiple variables to enable rank ordering I have four numeric variables. All of them are measures of soil quality. Higher the variable, higher the quality. The range for all of them is different:  Var1 from 1 to 10  Var2 from 1000 to 2000  Var3 from 150 to 300  Var4 from 0 to 5  I need to combine four variables into single soil quality score which will successfully rank order.  My idea is very simple. Standardize all four variables, sum them up and whatever you get is the score which should rank-order. Do you see any problem with applying this approach. Is there any other (better) approach that you would recommend?  Thanks  Edit:  Thanks guys. A lot of discussion went into "domain expertise"... Agriculture stuff... Whereas I expected more stats-talk. In terms of technique that I will be using... It will probably be simple z-score summation + logistic regression as an experiment. Because vast majority of samples has poor quality 90% I'm going to combine 3 quality categories into one and basically have binary problem (somequality vs no-quality). I kill two birds with one stone. I increase my sample in terms of event rate and I make a use of experts by getting them to clasify my samples. Expert classified samples will then be used to fit log-reg model to maximize level of concordance / discordance with the experts.... How does that sound to you? On what systems is //foo/bar different from /foo/bar? Throughout the POSIX specification, there's provision (, , ...) to allow implementations to treat a path starting with two / specially.  A POSIX application (an application written to the POSIX specification to be portable to all POSIX compliant systems) cannot assume that //foo/bar is the same as /foo/bar (though they can assume that ///foo/bar is the same as /foo/bar).  Now what are those POSIX systems (historical and still maintained) that treat //foo specially? I believed (I've now ) that POSIX provision was pushed by Microsoft for their Unix variant (XENIX) and possibly Windows POSIX layer (can anyone confirm that?).  It is used by Cygwin which also is a POSIX-like layer for Microsoft Windows. Are there any non-Microsoft Windows systems? OpenVMS?  On systems where //foo/bar is special, what is it used for? //host/path for network file systems access? Virtual file systems?  Do some applications running on Unix-likes —if not the system's API— treat //foo/bar paths specially (in contexts where they otherwise treat /foo/bar as the path on the filesystem)?    Edit, I've since  about the origin of //foo/bar handling in the spec, and the discussion is an interesting read (from an archaeology point of view at least). Why Listen to Music, why not Listening Music Maximum time I face this problem by saying listening music. Is there any traditional cause behind this?  Can we use listen music or listening music?  Seems there is only a slight difference, but why is listen to music the right way to say it? How to make specifics apps password protected even after passcode in iPhone? Is there really a way to make a true toon shader material in Cycles? Can we switch terminals at Heathrow (LHR) for shopping only? Are the tags shown in a particular order? I noticed that, sometimes, the tags I add to a question are not shown in the same order I wrote them, when the question is saved. Are they shown in a particular order? If they are, in which order they are shown? Assumptions of linear models and what to do if the residuals are not normally distributed I am a little bit confused on what the assumptions of linear regression are. So far I checked whether:  all of the explanatory variables correlated linearly with the response variable. (This was the case) there was any collinearity among the explanatory variables. (there was little collinearity). the Cook's distances of the datapoints of my model are below 1 (this is the case, all distances are below 0.4, so no influence points). the residuals are normally distributed. (this may not be the case)  But I then read the following:  violations of normality often arise either because (a) the distributions of the dependent and/or independent variables are themselves significantly non-normal, and/or (b) the linearity assumption is violated.  Question 1 This makes it sound as if the independent and depend variables need to be normally distributed, but as far as I know this is not the case. My dependent variable as well as one of my independent variables are not normally distributed. Should they be? Question 2 My QQnormal plot of the residuals look like this:   That slightly differs from a normal distribution and the shapiro.test also rejects the null hypothesis that the residuals are from a normal distribution: &gt; shapiro.test(residuals(lmresult)) W = 0.9171, p-value = 3.618e-06  The residuals vs fitted values look like:   What can I do if my residuals are not normally distributed? Does it mean the linear model is entirely useless? Here is the blender window I have:    As you see, it doesn't have the menu that is usually displayed at the top of the screen.  How can I get the menu back? JavaScript property access: dot notation vs. brackets? Postfix SMTP banner show multiple hostnames We have a Postfix SMTP server that's bound to two IP addresses and serves mail for two different domains. We can't change the domains to both use the same, single IP. Both IP addresses have reverse DNS   1.1.1.1 reverses to mail.domain1.com 2.2.2.2 reverses to mail.domain2.com   In our Postfix config I have  myhostname = mail.domain1.com myhostname = mail.domain2.com  inet_interfaces = 1.1.1.1, 2.2.2.2  smtpd_banner = $myhostname Mail Server   (And some other stuff, which I think is irrelevant)  Using , running the smtp test command on mail.domain2.com returns everything as OK, however running it on mail.domain1.com returns an error because Postfix is identifying itself as 'mail.domain2.com' in the SMTP banner, how do I get it to return the correct banner based on the external IP address used? To prove that $f_n(x) = \frac{nx}{1+n^2x^2}$ does not uniformly converge to $f(x) = 0$ on $[0,1]$ In Windows there’re perhaps only a couple of important folders (by important I mean important in my logical picture of the Windows file system) in the installation drive (in my case C:\). Namely Program Files and Windows. I simply stay away from Windows folder and the “add remove program files” is good enough to handle the program files folder of Windows. Of course there’s a folder named Users where the users (who are not admins) can access only their folders.  Thus there’s a clear picture at some level in my mind of the Windows file system. In Ubuntu, when I reach the location /, there’s a huge list of folders, most of which I have no clue as to what they contain. The /bin folder seems to be the equivalent of the Windows folder in windows. The /usr folder seems like it’s the equivalent of the Users folder in Windows. But even the /home folder looks like it can fit the bill.  Please understand that I do understand, that Ubuntu (Linux) has a different character than that of Windows, i.e., there need not be exact equivalent of Windows functions, in Ubuntu. All I am looking for is a bit more clearer picture of the Ubuntu file system.   This question is a part of a bigger question which I am splitting up to make it more answerable. The original question can be found here: When is $\sin(x)$ rational? Where will my bus be at the Port Authority Bus Terminal in New York? TikZ: Having circle borders only grown to the outside The Complete Rate-Limiting Guide