proof that translation of a function converges to function in $L^1$
Continuity of $L^1$ functions with respect to translation
How to ask "If you have any problem then ask me" in polite manner I use a Full HD 24" external display besides my 15" MacBook Pro Retina, on which I use the option for most screen estate regarding the Retina display. In the display arrangement screen, the MacBook Pro is therefore a bigger rectangle than the external display. Is there a way to size these rectangles regarding their "real world size" instead of resolution? I'm annoyed by my cursor teleporting vertically whenever I move from one display to another. I'm going to submit form using cURL, where some of the contents is come from other file, selected using sed  If param1 is line matching pattern from other file using sed, below command will works fine:  curl -d param1="$(sed -n '/matchpattern/p' file.txt)" -d param2=value2 http://example.com/submit   Now, go to the problem. I want show only text between 2 matching pattern excluding the matching pattern itself.  Lets say file.txt contains:  Bla bla bla firstmatch It is a long established fact that a reader will be distracted by the readable content of a page when looking at its layout. secondmatch The point of using Lorem Ipsum is that it has a more-or-less normal distribution of letters, as opposed to using 'Content here, content here', making it look like readable English.   Currently, lots of "beetween 2 matching pattern" sed command won't remove firstmatch and secondmatch.  I want the result to become:  It is a long established fact that a reader will be distracted by the readable content of a page when looking at its layout. Was Yoda fully sane on Dagobah? Our (and Luke's) original impression of Yoda is by no means flattering. He looks like a crazy hungry green thing that unfortunately has the ability to speak. Yoda digs through Luke's stuff, eats Luke's food, and, obsessed with that awesome little flashlight, ends up stealing it. (He even goes so far as to fight with Artoo over it.)  So was Yoda slowly losing it during all those years as a hermit?  Perhaps going from fighting battles and conversing with others on a daily basis to living in total isolation with no one to speak with would play a part in that? Or could Yoda have been faking his apparent insanity for some reason? (If so, what is mentioned reason?) Evaluate $\int \frac{1}{(x^2+1)^2}dx$ $$\int \frac{1}{(x^2+1)^2}\mathrm dx$$ Look simple, but I stuck a little bit. What method is better in this situation? Please, help. Show OPs if someone is answering, live I ask a lot of question on SO, so this recommendation/idea comes from that experience. I'm not really sure how this would fit in with the current structure of SE.   Oftentimes after asking a question, maybe after an hour or so, I end up finding the answer I needed somewhere. And it comes time for me to answer the most difficult question of all: do I delete this question, or do I keep it in case someone answers and others may benefit from it. The problem is, if I don't delete it and no one answers, my acceptance rate goes down. So usually I'll just delete it.  However, sometimes I fear that someone is typing a really really long answer to my question since itäs only been an hour, and so I imagine the nightmare that person experiences when they find out their essay will be gone to waste. Overall, this never-to-be-seen-again answer could have benefitted many people had the question remained.  Since SE has gone "live-happy" lately, where answers and comments refresh live, I thought it might be interesting if the original asker of the question (or anyone else for that matter) could see how many people are currently responding to the question (just count, not necessary to display their names). This way, if I know someone is replying, I won't delete the question, and others can benefit from it. Why is a suspicious program draining my battery with GPS usage? Cycles settings missing This particular blend file is messed up. I'm not sure what I did or pressed. If I open a new blend file everything works fine but in this one the materials tab is missing and the render properties is also missing some things. I don't want to start over my project. I have tried a day and a half to figure this out. Featured On Meta section doesn't list MSE posts on meta sites Do we know why there is a speed limit in our universe? This question is about why we have a universal speed limit (the speed of light in vacuum). Is there a more fundamental law that tells us why this is? I'm not asking why the speed limit is equal to $c$ and not something else, but why there is a limit at all. EDIT: Answers like &quot;if it was not..&quot; and answers explaining the consequences of having or not having a speed limit are not--in my opinion-- giving an answer to whether there is a more fundamental way to derive it from a law to explain this limit. Co-signed a loan and I need to have my name removed Recently I encountered a problem (the first exercise from chapter four of Atiyah &amp; McDonald's Introduction to Commutative Algebra) stating that if $\mathfrak{a}$ is a decomposable ideal of $A$ (a commutative ring with unity), then the prime spectrum of $A/ \mathfrak{a}$ has finitely many irreducible components. This follows easily from the recognition that the maximal irreducible subspaces of $\textrm{ Spec } (A / \mathfrak{a})$ are precisely the "zero loci" of the minimal prime ideals of $A /\mathfrak{a}$.   I'm curious about the converse - the proof isn't easily reversed since the notion of minimal ideals of $\mathfrak{a} $ doesn't make sense before we know what we are trying to prove. My intuition says that it is false based on the general premise that images are badly-behaved (and the fact that it isn't part of the exercise.) However, I've had some difficulty constructing a counterexample, so that the main purpose of this post is to ask for a reasonable procedure or heuristic for doing so (or, of course, proof that my intuition is false.)   If it helps, if $\textrm{Spec }(A / \mathfrak{a})$ is irreducible then the nilradical $\mathcal{R}_{A /\mathfrak{a}}$ is prime so that $r(\mathfrak{a}) = \rho^{-1} ( \mathcal{R}_{A / \mathfrak{a}} ) = \displaystyle\cap_{i=1}^n \rho^{-1} (p_i),$ where $p_i$ are the minimal prime ideals of $A /\mathfrak{a}$ and $\rho $ is the associated projection, is also prime. Thanks! How can slightly blurred photos be improved in post processing? cron.hourly sendmail errors even though my scripts do not involve sending mail How can I install a package without root access? Cocos2d-x supporting multi-resolution using density independent pixels Is there a way to use Density Independent pixels(dp) in cocos2d-x?  I am developing an Android game using Cocos2d-x 3.0.  The Android reference  tells me not to use pixels in code but use dp when supporting multi-resolution support. It also tells me to provide different images for different screen size groups and different density groups.  However, cocos2d-x tutorials use pixels for multi-resolution support. If I were to use pixels, I think it means I need to have images for all these different resolutions:  240x320, 240x400, 240x432 320x480 480x640, 480x800, 480x854 600x1024 640x960 1024x600, 1024x768 1280x768, 1280x800 1536x1152 1920x1152, 1920x1200 2048x1536 2560x1536, 2560x1600  Even if I don't support every screen resolutions, I think this requires more work than following the Android reference's best practice.  Am I missing something on how supporting multi-resolution works or do I indeed do need to do much more work using cocos2d-x? Visit the UK with an expired French identity card Many times I have read statements like, "the age of the universe is 14 billion years" . For example this wikipedia page .   Now, my question is, which observers' are these time intervals? According to whom 14 billion years? Which loss function is correct for logistic regression? I read about two versions of the loss function for logistic regression, which of them is correct and why?  From  (in Chinese), with $\beta = (w, b)\text{ and }\beta^Tx=w^Tx +b$: $$l(\beta) = \sum\limits_{i=1}^{m}\Big(-y_i\beta^Tx_i+\ln(1+e^{\beta^Tx_i})\Big)  \tag 1$$  From my college course, with $z_i = y_if(x_i)=y_i(w^Tx_i + b)$: $$L(z_i)=\log(1+e^{-z_i}) \tag 2$$    I know that the first one is an accumulation of all samples and the second one is for a single sample, but I am more curious about the difference in the form of two loss functions. Somehow I have a feeling that they are equivalent. Compound Adjectives and -ed A colleague asked me this question, and I couldn't come up with an answer that satisfied him, so I'm wondering if anyone can help:  Why does a man with a short temper become a short-tempered man? In other words, why do you need the -ed at the end?  Are there any special rules for this?