Newcommand with spaces after each letter How can I make a command \headline{COURSE PROJECT} that would result in   \textbf{C\,O\,U\,R\,S\,E\;P\,R\,O\,J\,E\,C\,T}
Increasing Letterspace for words in caps or small caps Some typographers say it's a good habit to increase the letterspace when writing words in caps or small caps. So my question is, how to do it with pdflatex and/or xelatex? And while we're at it, which words would you alter this way? Acronyms like USA, NATO, IBM, GNU, etc.? How about words like PCs, UdSSR, FreeBSD or TV-Station?
Problem: Suppose $f$ is continuous for $x\ge 0$, differentiable for $x&gt;0$, $f(0)=0$, and $f'$ is monotonically increasing.  Define $g(x)=\frac{f(x)}{x}$ for $x&gt;0$. Prove that $g$ is monotonically increasing.  Source: W. Rudin, Principles of Mathematical Analysis, Chapter 5, exercise 6. Why are the Degrees of Freedom for multiple regression n - k - 1? For linear regression, why is it n - 2? I'm reading a textbook and I see this question:    So there are 200 women, and the DF is 196, implying that the equation for DF is $n - k - 1$. There are 3 variables: bp, age, and type so $k == 3$. What's the intuition behind this?  Also, why is the degrees of freedom for linear regression n - 2? "I'm right, aren't I?" My dictionary reports that aren't is also an abbreviation for am not, when used in questions.  Is this use of aren't common? If it is common, are there any differences between the different English dialects?     Why aren't I being given a pay raise? I understand the difference between LET and LET* (parallel versus sequential binding), and as a theoretical matter it makes perfect sense.  But is there any case where you've ever actually needed LET?  In all of my Lisp code that I've looked at recently, you could replace every LET with LET* with no change.  Edit: OK, I understand why some guy invented LET*, presumably as a macro, way back when.  My question is, given that LET* exists, is there a reason for LET to stay around?  Have you written any actual Lisp code where a LET* would not work as well as a plain LET?  I don't buy the efficiency argument.  First, recognizing cases where LET* can be compiled into something as efficient as LET just doesn't seem that hard.  Second, there are lots of things in the CL spec that simply don't seem like they were designed around efficiency at all.  (When's the last time you saw a LOOP with type declarations?  Those are so hard to figure out I've never seen them used.)  Before Dick Gabriel's benchmarks of the late 1980's, CL was downright slow.  It looks like this is another case of backwards compatibility: wisely, nobody wanted to risk breaking something as fundamental as LET.  Which was my hunch, but it's comforting to hear that nobody has a stupidly-simple case I was missing where LET made a bunch of things ridiculously easier than LET*. Consider the blow-up of the plane in one point. Let $E$ the exceptional divisor. We know that $(E,E)=-1$. What is the geometrical reason for which the auto-intersection of $E$ is $-1$? In general, what does it mean, geometrically, that a divisor has a negative self-intersection or that the "right" number of divisors gives rise to a negative intersection?  Thanks. Why don't the zoom buttons work on my DSLR? I am a newbie to the new camera I just bought. It is a Nikon D5200 it has the original lens that came on the camera a 18-55 lens on it. My question is when I turn the lens to the 55 and then push the plus and minus buttons at the bottom of my camera to zoom in it appears to be zooming in and then I take the photo and the picture is not zoomed in at all.    I have a new Canon T3i and was able to take and capture zoomed in photos with the lens that came with the camera (EF-S 18-55mm) as well as a Canon zoom lens EF 75-300mm 1:4-5.6. Now when I zoom in with either lens and take a photo, when I review it, it shows original image before zooming. Is it a defect in the camera or inexperience of the operator?    (Two separate questions from separate users but with the same root cause.) Convert web page to image I don't understand this..maybe there is something wrong with my understanding of battery or electricity.  I am learning about electricity more deeply this time. So please bear with me.  So lets begin with what I know:   follow of current occurs when there is voltage drop. voltage drop happens when there is imbalance in charge. a battery is basically two separated chemicals. One side with electrons to spare and other side that needs electron to balance itself. which is imbalance in charge. When both sides are connected + side snatches electrons from - side. (And if there is a medium, conductor, then first electrons are taken from conductor that in turn snatches from - side, which not being able to keep electrons lose them and give up those electrons, we label it as excessive.)   The analogy i was taught with used marbles in pipe... When one side has excessive marbles And this pipe is connected to other side that has no marbles the marbles will instantaneously start falling out so even though marbles from container with excessive marbles haven't traveled there yet, they still start falling because filled side marbles are pushing marbles in pipe and which in turn push the last marbles in pipe out.   1st, Aren't electrons pulled by atoms that can use more electrons, and not move because one side is overfilled with electrons so they can't wait to push some out.  Questions:    if I connect a conductor to positive side of a battery, shouldn't it make all electrons/marbles fall into empty container as empty container will pull marbles as atoms need electrons? if I connect two batteries' only opposite sides to each other shouldn't they drain (balance the each other out, cancelling all - &amp; + charges)? Atmospheric pressure experiment using a cup with a fluid to hold a glass plate When I was in high school, my teacher did an experiment to show the power of atmospheric pressure.  Experiment: Prepare a glass bottle, fill with water, put a glass plate on the bottle, make sure there is no air in the bottle, just water. Hold the glass bottle and plate, and invert them. Slowly, release the hand which hold the plate. Because the atmospheric pressure, the glass plate will not fall down.    Question 1: As we know, if we didn't put water into the glass bottle, just air in the glass bottle the glass plate will fall down. So, If we use other liquid instead of water, this liquid has smaller density than water, like alcohol, the plate will not fall down. But, if we continue to chose the smaller density liquid until the liquid has density like air the plate will fall down. So, if there is a threshold density of liquid make the plate between falling  down and not falling down?  Question 2: If we put the bottle and plate into water slowly, when the plate and part of bottle are in the water but part of the bottle still above the water, will the plate fall down?  Question 3: Continuing question 2, when both bottle and plate are in the water I know the plate will fall down. So, how does the pressure of water and atmosphere change?  Is there a good description of this phenomena?  Why does the trick continue to work with lower density fluids and why does placing the plate in the water cause it to fall? Can't log in using Firefox in Stack Overflow When has Wonder Woman died? I know Wonder Woman has died in canon before, but in which issue did this happen? How many square meters "twenty feet square" is? One would assume it to be about 2 square meters, but this is obviously not the case. In fact, I'm reading Illium by Dan Simmons. A quote follows:     Much like the room they had faxed into, this space was windowless and about twenty feet square. But unlike the other room, this one was warm, lighted, and free of snow or ice. And unlike the other room, this one was almost filled with an oval metal machine about fifteen feet long.   By this description, "twenty feet square" seems to mean 20x20 feet aka 400 square feet or 40 square meters. Given that Dan Simmons is a renowned American writer, it's not likely that he just can't speak English correctly. So, who's right and who's wrong here? I am given $f,f' \in L^1(\mathbb{R})$, and f is absolute continuous, I want to show that:  $$\lim_{|x|\rightarrow \infty} f(x)= 0$$  Not sure how to show this, I know that $f(x)=\int_0^x f'(t) \, dt+f(0)$, and I can assume without loss of generality that $f(0)=0$, any help?  Thanks in advance. Many times when going through the Close queue I see that people are using the too localized reason.  Sometimes the reason for this is in the comments (like the syntax error being pointed out), but a lot of times it's in the answer, so then I have to click on the question and look at the answers to see if it is really too localized.  Could we please get the answers shown underneath the question in the Close review queue? Example 4.21 in Baby Rudin: Why is the inverse of this function not continuous at this point? Have we ever observed two drosophila lineages that evolved reproductive isolation in labs? Background  The standard definition of species refers to the concept of . If two lineages are found to be reproductively isolated, then we consider these two lineages to belong to different species. My question concerns evolved reproductive isolation in Drosophila sp. following labs due to experimental evolution.  Question  Have we ever demonstrated that two Drosophila sp. lineages that could initially interbreed (in nature or in labs) evolved through artificial selection (and drift and mutations) in labs to finally not be able to interbreed anymore either due pre- or post- zygotic isolation (see )? Or, in other words, have we ever demonstrated that two drosophila lineages evolved to become different species (reproductive isolation definition) in labs experiments?  If not, have we ever observed some partial reproductive isolation such as inbreeding depression for example?    Note: This question is motivated by @LotusBiology that could not receive the answers she/he was waiting for because he/she failed to ask questions that are possibly answerable! So I wanted to ask this question that somehow addresses  question he/she asked (now on-hold)  For more information about the concept of species, please have a look at How to run a command that requires sudo at login I have noticed that if you look directly at tubelight (I have only white ones in my home) and close your eyes little, you see little random shaped colourless things sometimes with slow speed and sometimes with falling down.   They are shaped like circles with something in between and in chains of random length.   My father has also seen them. So, I am sure I am not imagining things. What the hell are they? In my Java application, I want to run a batch file that calls "scons -Q implicit-deps-changed build\file_load_type export\file_load_type"  It seems that I can't even get my batch file to execute. I'm out of ideas.   This is what I have in Java:  Runtime.    getRuntime().    exec("build.bat", null, new File("."));   Previously, I had a Python Sconscript file that I wanted to run but since that didn't work I decided I would call the script via a batch file but that method has not been successful as of yet. I tried to search for similar questions, as I always do, but was not able to find one. I just created a new  on Data.Stack Exchange with my existing Google OpenID and it seems to be not associated with my regular Stack Exchange account. Is this by design? and if so, why?