Capitalization of "Subsection" I write a mathematical paper. Do you capitalize "subsection" when you refer to a specific subsection? For example, I would write:  "In Subsection 3 we show ..."   But I would write:  "In the previous subsection we showed that ..."   What is the consensus on that issue?
Capitalisation of "Section" and "Chapter" in a Ph.D. Thesis I am submitting a Ph.D. thesis fairly soon and my supervisor has flagged my use of capitalisation in "Section" and "Chapter" as possibly incorrect. I have googled about a bit and I see mixed opinions.  So my question is, when writing a computer science Ph.D. thesis, what is the correct way to capitalise "Section", "Chapter", "Appendix", "Figure", "Table", ... ?  For example, what is the correct capitalisation for the following:   "In Chapter 3, it was shown that..." "In the previous Section, a method was presented to..." "The graph in Figure 3 shows..."
Erase Windows Vista to Install Ubuntu new here. I have an old E-machine which as Windows Vista on it and I want to erase the Windows Vista, and install Ubuntu on it instead, but I am not sure where to start. Can I first install Ubuntu, and THEN erase Windows Vista, or is there a more sure method? I appreciate your help. Why do we say "try and" [verb] instead of "try to" [verb]? (E.g., "Try and call me tomorrow.") In written and standard semi-formal (and above) spoken English, one would use &quot;try to&quot;:  Try to be a better person. Try to get the fishhook out of my thumb, please. Try to find a pharmacy when you need one.  But in spoken English, we (Americans, at least) usually substitute &quot;try and&quot; for all those cases. &quot;Try to&quot; makes sense because the &quot;to&quot; begins the construction of an infinitive: &quot;try to be&quot;, &quot;try to do&quot;, &quot;try to act&quot; and so on. &quot;Try and&quot; on the other hand doesn't seem to make any sense. I'm curious how the &quot;try and&quot; crept in, and when. It's really tough to Google small words like these, so I'm not finding anything on the Web. Is it a contraction of something like &quot;Try hard, and ...&quot;? Note: I've seen  and it is somewhat related but doesn't tell me what I want to know. Edit Observe how, even on this site,  construction. Turning it on its head Note that you can't make a negative construction with &quot;try and&quot;:  It's raining. Try not to get wet. It's raining. Try not and get wet. [?]  Even adding do doesn't help. The following means something different from &quot;try not to get wet.&quot;  It's raining. Don't try and get wet.  Even use of to instead of and there means something else:  It's raining. Don't try to get wet.  &quot;Try not to get wet&quot; means try to stay dry. &quot;Don't try to get wet&quot; means avoid actively seeking out a soaking, and implies that a soaking might in fact be what you are looking for. MORE I just happened to notice a video from an editor for Merriam-Webster on this very topic, so I include the link here: . How to type "ç" when using USA intl as the keyboard layout? I asked  but I can't make that solutions work on Unity. I want to use the keys ´ followed by c and the output should be "ç". It works that way in Windows out of the box, and it did work in Ubuntu 10.10 following the solutions given in the question above. But in 11.04 it outputs "ć". How to change that? Is the Schrödinger equation derived or postulated? I'm an undergraduate mathematics student trying to understand some quantum mechanics, but I'm having a hard time understanding what is the status of the Schrödinger equation.  In some places I've read that it's just a postulate. At least, that's how I interpret e.g. the following quote:     Where did we get that (equation) from? Nowhere. It is not possible to derive it from anything you know. It came out of the mind of Schrödinger.    -- Richard Feynman   (from the Wikipedia entry on the Schrödinger equation)  However, some places seem to derive the Schrödinger equation: just search for "derivation of Schrödinger equation" in google.  This motivates the question in the title: Is the Schrödinger equation derived or postulated? If it is derived, then just how is it derived, and from what principles? If it is postulated, then it surely came out of somewhere. Something like "in these special cases it can be derived, and then we postulate it works in general". Or maybe not?  Thanks in advance, and please bear with my physical ignorance. If you run a code snippet, a hat still appears (hats are above snippets in the Z-order) Is there a formula for $(1+i)^n+(1-i)^n$? My model has a clear plastic (or glass) dome with objects inside.  The objects appear dark.  I've tried the glass shader with color 100% RGB, with very small IOR, and using just a refraction shader.    I know Cycles has problems with caustics, but I just want broad illumination to fall clean through the glass.  The light-to-column path can ignore refraction, but is blocked or tremendously attenuated. The camera-column path needs refraction, and seems to work fine anyway.  This demo image offers all optical paths of interest:   light upon object, seen directly light upon object, seen through glass (looks okay) light through glass onto object, seen directly. This is the shadow on the lit side of the column just below the glass tubing.  I expect full illumination, but there is shadow.  There is some light, but it's diffuse light from the floor. light through glass onto object, seen through glass. This     I did at one point try non-progressive rendering, and find extremely coarse light where there shouldn't be shadow, but this is not a practical way to make nice images. I've even tried cranking up certain sampling settings to many thousands, but still get bad noise though less, at the cost of long render times. I  would like to finish my creations sometime before "Star Trek, the Generation After the Next" becomes real life, if you know what I mean.  The next image is an example. I think Transmission in Sampling was 5000, but not sure.    I'm using Cycles in Blender 2.67 on a quad core Linux machine, 16GB RAM. Machine limits have never been a problem for 3D rendering.  Possibly, I screwed up some setting when I made my startup file, and just need to fix it. OTOH maybe this is just a limitation of path tracing, or of the way Cycles does it. If that's the case, what to real-world Blender artists do when they need to produce images on a budget and schedule?  What is the practical real-world fix? What are Java command line options to set to allow JVM to be remotely debugged? Idempotent of closure and other properties A composite integer n is a Carmichael number if the only Fermat   witnesses for $n$ are those $a \in \mathbb Z_n^+$ which are not   coprime with $n$. The smallest example of such a number is $561 = 3 ·  11 · 17$   I think I understand the definition, but I don't quite understand why is the smallest Carmichael number is the above mentioned number. Please clarify. I tried to follow the new Blender 2.8 tutorial from Blender Guru.   When entering "Sculpting" with the icing there were suddenly alot of holes in it. Why is this? Example of mailmerge package with an Excel spreadsheet I am looking for an example for using the  package to write a cover letter, with names and addresses on a spreadsheet. The package comes with an example, but you have to manually enter all the data. QGIS Atlas generation for multiple map extents? In a theoretical physics homework problem, I have to show the following: $$\partial_\nu T^{\mu\nu} = - j_\nu F^{\mu\nu}$$  Where $T$ is the Energy-Momentum-Tensor, $j$ the generalized current and $F$ the Field-Tensor. We use the $g$ for the metric tensor, I think in English the $\eta$ is more common.  I know the following relationships:   Current and magnetic potential with Lorenz gauge condition: $$\mathop\Box A^\mu = \mu_0 j^\mu$$ Energy-Momentum-Tensor: $$T^{\mu\nu} = \frac1{\mu_0} g^{\mu\alpha} F_{\alpha\beta} F^{\beta\nu} + \frac1{4\mu_0} g^{\mu\nu} F_{\kappa\lambda} F^{\kappa\lambda}$$ Field-Tensor: $$F^{\mu\nu} = 2 \partial^{[\mu} A^{\nu]} = \partial^{\mu} A^{\nu} - \partial^{\nu} A^{\mu}$$ d'Alembert operator: $$\mathop\Box = \partial_\mu \partial^\mu$$ Bianchi identity: $$\partial^{[\mu} F^{\nu\alpha]} = 0$$   So far I have set all the definitions into the formula I have to show, but I only end up a lot of terms from antisymmetrisation and product rule. I also drew all what I have in , but I still cannot see how to tackle this problem.  Could somebody please give me a hint into the right direction? How do I resize/change resolution of pictures easily? Why does the SARS-CoV2 virus not remain infectious forever? Or does it? Given that the majority of biologists do not currently consider viruses to be alive, a virus can never die.  It can, however, get destroyed by long exposures to soapy water, alcohol, and apparently certain frequencies of UV light.  Why is an individual SARS-CoV2 virion not infectious forever?  Or is it? Problem printing LaTeX from lua in lualatex Upgrading straight handlebars to drop handlebars I have a two-and-a-half year old  (with a road-bike-like frame and thin tires; it's somewhere in the loosely-defined "hybrid" range) that I use to commute to work, twenty-five miles round-trip, once or twice a week. The bike has straight handlebars, and having gotten used to the idea of commuting via bike, I'm interested in upgrading to drop handlebars. It looks like I'd need new break/shift levers to go with the handlebars; the whole upgrade looks like it'd run a couple hundred dollars. This is a sizable fraction of the original cost of the bike, which leads me to wonder if I'm better off saving my money for a new bike that's a little better adapted to my use.  Is upgrading my bike's handlebars a reasonable investment? Bibliography in Texmaker I'm having some problems with my bibliography in Texmaker. My code is:  \documentclass[11pt, a4paper]{article} \usepackage{graphicx} \usepackage{amsmath} \usepackage{natbib} \usepackage[utf8]{inputenc}     \usepackage{natbib} \usepackage[usenames,dvipsnames]{xcolor} \usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry} \begin{document}  ....  \cite{Johnson} \bibliographystyle{plain} \bibliography{mybib}  \end{document}   I also created a new file (File > New) that I saved as mybib.bib:  @Article{Johnson, author = {Edgar G. Johnson and Alfred O. Nier}, title = {Angular Aberrations in Sector Shaped Electromagnetic Lenses for Focusing Beams of  Charged Particles}, journal = {Physical Review}, year = {1953}, volume = {91}, number = {1}, }  @phdthesis{Zoran, author = {Zoran Racic}, title = {\'Etude et essais du spectromÃ¨tre Ã  plasma {DYMIO} de la  mission {MARS 96}}, publisher = {UniversitÃ© Pierre et Marie Curie}, year = {1996} }   When I compile my .tex file, I only have a [?] appearing.  Could you tell me what my mistake is? In  is a proof of Stirling's formula.  I really like most of it, but at a crucial step he uses the integral identity  $$n! = \int_{0}^{\infty} t^n e^{-t}  dt$$  , coming from the Gamma function.  I have a mathematical confession to make: I have never "grokked" this identity.  Why should I expect the integral on the right to give me the number of elements in the symmetric group on $n$ letters?    (It's not that I don't know how to prove it.  It's quite fun to prove; my favorite proof observes that it is equivalent to the integral identity $\int_{0}^{\infty} e^{(x-1)t}  dt = \frac{1}{1 - x}$.  But if someone were to ask me, "Yes, but why, really?" I would have no idea what to say.)  So what are more intuitive ways of thinking about this identity?  Is there a probabilistic interpretation?  What kind of random variable has probability density function $\frac{t^n}{n!} e^{-t}$?  (What does this all have to do with Tate's thesis?)  As a rough measure of what I'm looking for, your answer should make it obvious that $t^n e^{-t}$ attains its maximum at $t = n$.  Edit:  The kind of explanation I'm looking for, as I described in the comments, is similar to  of the beta integral.