What are the differences in mathematical notation around the world?
Mathematical notation around the world
In the special relativistic action for a massive point particle, $$S=\int_{t_i}^{t_f}\mathcal {L}dt,$$ why is the Lagrangian $$\mathcal {L}=-E_o\gamma^{-1}$$ a negative number? How to forbid a specific package to be installed? More than 9 hundred as hundreds? In German, we often use "Elfhundert" (literally, "eleven hundred") for 1100 or "neunzehnhundert" ("nineteen hundred") for 1900; but is this correct in English? I've heard that you need to get a Mac if you want to develop iPhone apps. Is this true?   Is it possible to develop iPhone apps using Linux? If yes, what do I need and where do I download the necessary tools? When does a Möbius transformation map $\Im(z)>0$ to itself? Show Möbius transformation which maps $\Im(z)&gt;0$ to itself iff  $$ f(z)= \frac{az+b}{cz+d}\,,\,\,ad-bc&gt;0$$ and $a,b,c,d$ are real. Why should a CTE start with a semi-colon? states that if $a, b \geq 0$, $p, q &gt; 0$, and $\frac{1}{p} + \frac{1}{q} = 1$, then $$ab\leq \frac{a^p}{p} + \frac{b^q}{q}$$ (with equality only when $a^p = b^q$).  Back when I was in my first course in real analysis, I was assigned this as homework, but I couldn't figure it out.  I kept trying to manipulate the expressions algebraically, and I couldn't get anywhere.  But every proof that I've seen since uses calculus in some way to prove this.  For example, a common proof is based on this  and integration.  The proof on Wikipedia uses the fact that $\log$ is concave, which I believe requires the analytic definition of the logarithm to prove (correct me if I'm wrong).  Can this be proven using just algebraic manipulations?  I know that that is a somewhat vague question, because "algebraic" is not well-defined, but I'm not sure how to make it more rigorous. But for example, the proof when $p = q = 2$ is something I would consider to be "purely algebraic":  $$0 \leq (a - b)^2 = a^2 + b^2 - 2ab,$$ so $$ab \leq \frac{a^2}{2} + \frac{b^2}{2}.$$ Complete beginner here.  I'm trying to follow  tutorial on Anisotropic shaders, but my property panel looks nothing like the property panel in the tutorial.  For example, when creating a material, this is what his property panel looks like:    But this is what mine looks like, if I follow the same path:    I'm sure I'm missing something obvious.  How can I see the property panel shown in the tutorial? The suffix -phobia means fear of, often irrational fear of.  For example, according to Wikipedia:       or ophiophobia is a particular type of specific phobia,   the abnormal fear of snakes.   Is there a suffix attachable to ophidio- which would describe a person who is not afraid of snakes, except for, say, a coiled rattler encountered on a trail, but who dislikes them and would not willingly share space with one?  Similarly, an  (don't click here if you are at all arachnophobic) is someone who loves spiders.  Is there a suffix for someone who likes spiders but does not love them?  These are Greek suffixes, and the Greeks, theoretically, were in favor of moderation.  So, are there suffixes in use in English, derivable from Greek or not, for moderate like and moderate dislike?    Edit to explain why the question:  "Is there a suffix for loathing" does not answer my question.  My question is NOT about fear and/or loathing.  My question is about moderate dislike (and moderate like).  I can watch a snake cross my driveway with interest, but would not want it in the house or lounging on my patio.   A person who loathed snakes would not be able to admire the smooth motion of the snake as it glided over the rough gravel and disappeared into the woods.  Loathe is very different from moderate dislike; Phobia is very different from caution. What's the difference between scaling text via transform and changing font size? Is there a difference between using Transform commands to scale text and altering the size of the font via Character panels?   I'm working in Photoshop CC What is the best way to randomize the order of a generic list in C#? I've got a finite set of 75 numbers in a list I would like to assign a random order to, in order to draw them for a lottery type application. How to get a variable name as a string in PHP? Say i have this PHP code:  $FooBar = "a string";   i then need a function like this:  print_var_name($FooBar);   which prints:  FooBar   Any Ideas how to achieve this? Is this even possible in PHP? I am having trouble finding the derivative of the following:  $$y = x^x+x^3+3^x+3^3$$  $$\frac{dy}{dx}= x \times x^{(x-1)}+3x^2+3^x\ln3+0$$  I think the $x^x$ part is wrong. Any help would be appreciated. PHP replaces spaces with underscores Typically Apt packages are served over bare HTTP and the downloaded contents are verified with GPG signatures. This makes it easy for  to proxy the HTTP connections and add the downloaded packages to its cache. apt-cacher-ng is unable to directly MITM an HTTPS connection created by Apt. It is possible to  apt-cacher-ng, but then the contents are not cached--they are re-downloaded from the remote server every time. This quickly gets annoying when rebuilding Docker containers that install many packages from Apt repositories served over HTTPS. Is there a way to get apt-cacher-ng to cache packages downloaded from HTTPS repositories? Contacting prospective advisors before graduate school applications - courtesy or annoyance? Last year, rather late during the MSc application cycle (after one round of funding was allocated - tardiness due to an abrupt change in my life situation), I emailed two professors from two schools that I most wanted to go to. I had perused their webpages and decided these professors had the specific research interests closest to my own.  My reason for contacting them before finishing my applications for their respective schools was that the applications included a large section for specific research questions that I wanted to investigate. So, I emailed these professors asking a bit about their work, because their webpages of course featured surface-level stuff.  One professor was very receptive and invited me to Skype with her so she could better explain herself and I could ask her questions. With her support, I was able to write an application that met her standards quite quickly.  The other professor told me - paraphrasing, of course - that he was too far into the process of choosing a new student for his research group to spend time helping me finish the application.  Let me be clear that the latter professor didn't say any harsh words and I have nothing bad to say about him. That said, the purpose of my question is to decide whether it's better for me as a prospective MSc student to email professors ahead of time like this. Was the latter's rejection likely due to my tardiness rather my emailing him? The more receptive professor made the point that she always wanted to have prospective MSc students write their own research proposals and get her approval before submitting the application. Is this common? If so, then I guess reaching out beforehand is a good thing to do, but earlier in the application cycle?  Thank you. pdfTeX error (font expansion): auto expansion is only possible with scalable Can quarks be considered real and elementary? I read that this is because the mean and variance completely specify a normal distribution. However, e.g. for a Poisson distribution the mean, variance and third moment can all be expressed with the same parameter lambda. Is this not what it means to 'completely specify' a distribution?  What is an example of two Poisson distributions having the same mean, variance and different higher moments? If we treated weak stationary as if it was strict stationarity, what would happen when we try to do time series analysis? I read an essay about prime numbers. In it the author suggests that a natural first question to ask is,      What is the probability of a random natural number being prime?   but proceeds to dismiss it as "not making sense". I wonder what's wrong with the question. Is its meaninglessness related to the fact that there is an infinite number of naturals?