Using a subjunctive form correctly
Past Subjunctive vs Future Subjunctive form
why $1+\frac{1}{1+\frac{1}{\frac{1}{1+\dots}}}$ cannot be equal to $\frac{1-\sqrt{5}}{2}$  I know that some of you will answer because it is positive.I know it but I don't know how to prove it.Maybe the second part is positive how do you know that?Thanks in advance. Short story that takes place off planet, involving sun and rain I read this short story about 20 years ago, and I'd love to find the title and author. This is what I can recall about the story:   It takes place in a classroom full of kids (around 10 years old?) The planet always gets rain The kids lock the main character (a girl, I think) in the closet during the very rare occurrence of sunlight and she misses the entire event.    I know it's not much to go on, but I hope it rings a bell for someone! How to select the rows with maximum values in each group with dplyr? Add bst file with LaTeX / MiKTeX I'm trying to use elsarticle-num-ident.bst, an exact copy of  C:\Program Files (x86)\MiKTeX 2.9\bibtex\bst\elsarticle\elsarticle-num.bst    but every time I run LyX, I get the bibtex error  I couldn't open style file elsarticle-num-ident.bst   This is despite reconfiguring LyX and restarting, and despite running MixTex's Settings/Options' "Refresh FNDB" as Administrator.  It also doesn't work if I put the .bst file in the same folder as the .lyx file.  How should I help lyx/bibtex/Mixtex find the .bst file?  Once I get the identical copy to work, I plan to edit it to not print URLs, as suggested .  Related questions: With constant travel, is it possible to not have a tax residence? Why can't variables be declared in a switch statement? I've always wondered this - why can't you declare variables after a case label in a switch statement?  In C++ you can declare variables pretty much anywhere (and declaring them close to first use is obviously a good thing) but the following still won't work:  switch (val)   {   case VAL:     // This won't work   int newVal = 42;     break; case ANOTHER_VAL:     ...   break; }     The above gives me the following error (MSC):     initialization of 'newVal' is skipped by 'case' label   This seems to be a limitation in other languages too.  Why is this such a problem? Why doesn't the percentage of oxygen in Earth's atmosphere diminish significantly with altitude? According to numerous sources online, the percentage of oxygen is approximately the same at sea level and 10,000 meters. Since oxygen is heavier than nitrogen, shouldn't the percentage of oxygen decrease with altitude? Compactly supported continuous function is uniformly continuous Novel in which the protagonist fades out is forgotten by, and can't interact with, the rest of the world Trying to identify a novel I read years ago (probably in the '80s) in which the protagonist (late teens, early 20s?) is gradually forgotten by and ceases to be able to interact with the rest of the world (all of which gradually fades to gray).  In the beginning, as he is slowly fading out (not realizing it) he goes down to breakfast with his parents, and his mother has only set out two plates (one for his father and one for herself) — she'd forgotten to set one out for him.   He reminds her.  Foreshadowing, eh?   But gradually everyone forgets about him and ceases to be able to hear or see him, and fade to gray.  Some other things apparently similarly get "forgotten" however — e.g., occasionally he finds colored, not gray, cans of food in grocery stores, which he can interact with and eat — so he survives.  He then meets a girl who has similarly been forgotten by the world, and they spend time together and fall in love.  At the end,       he is gradually starting to fade back into the world (she isn't) and she puts writes a note about them and puts it in his pocket, in the hope it will fade back into the world with him.  It does, and he sees it one day — but has no idea what it is or any memory of her.  Sad. Home Electric Panel Questions I’m having a pool put in and the pool guys said they need a 20 amp breaker for the pool equipment. My outside panel says 100 amps (see picture). But my panel inside adds up well over 100 amps. Is this normal?  The breakers never trip even with the dryer, AC, and other appliances running. I used MiKTeX 2.9 on windows. I have downloaded a package I want to install from the internet (manually, not through MiKTeX). The archive (*.lmza) containing the package was saved to a directory on my C:\ drive. Through MikTeX -> Maintenance -> Settings -> Packages -> Change... I can select the directory in which I have saved the archive containing the package. However, if I choose Packages shall be installed from a directory and choose the location of the package, I get this error message: C:\my\package\is\here does not seem to be a local package repository. What does it take for a directory/folder to become a local package repository? Why are there $1 / 1.602176634 \times 10^{-19}$ electrons in a coulomb? Why that exact number of electrons in one coulomb? who decided it? there is nothing wrong with the number, it just seems slightly messy. Why didn't the scientific community just settle on an easier number, such as $1\times10^{-19}$ for example? Do I have to do something "special" to get the Color -> Color to alpha menu option to work in GIMP? I am trying to convert a background color on a GIF image to transparent by converting the background color to an alpha channel but the Color to Alpha menu option is not selectable.  I've gone through the GIMP documentation and it looks pretty simple :-) I must be missing something rather obvious here! finding $\int_0^\infty \dfrac{dx}{1+x^4}$ through complex analysis I'm trying to compute this integral, $$\int_{0}^{\infty}\frac{\ln x}{x^{a}(x+1)}dx \hbox{ where } 0&lt;a&lt;1$$ I drew a typical Pacman contour with branch cut at positive real axis. Then, we have $$\int_{\Gamma}\frac{\ln z}{z^{a}(z+1)}dz=\left(\int_{L_{1}}+\int_{L_{2}}+\int_{C_{R}}+\int_{C_{\epsilon}}\right)\frac{\ln z}{z^{a}(z+1)}dz$$ The function has a pole at $z=-1$. Then, by residue theorem, the whole integral becomes  \begin{align*} \int_{\Gamma}\frac{\ln z}{z^{a}(z+1)}dz&amp;=2\pi i\text{res}(\frac{\ln z}{z^{a}(z+1)};-1)\\&amp;=2\pi i\lim_{z\rightarrow-1}(z+1)\frac{\ln z}{z^{a}(z+1)}\\&amp;=2\pi i\lim_{z\rightarrow-1}\frac{\ln z}{z^{a}}\\&amp;=2\pi i\frac{\ln e^{i\pi}}{e^{i\pi a}}\\&amp;=2\pi i\frac{\ln1+i\pi}{e^{i\pi a}}\\&amp;=-\frac{2\pi^{2}}{(e^{i\pi})^{a}} \end{align*} On $L_1$, $z=xe^{i\epsilon}$ where $\epsilon\leq x\leq R$  On $L_{2}$, $z=xe^{i(2\pi-\epsilon)}$ where $\epsilon\leq x\leq R$  On $C_{R}$, $z=Re^{i\theta}$ where $\epsilon\leq\theta\leq2\pi-\epsilon$  Lastly on On $C_{\epsilon}$, $z=\epsilon e^{i\theta}$ where $\epsilon\leq\theta\leq2\pi-\epsilon$  So I tried to compute them separately and I anticipate the curves will both go to $0$ by ML inequality, and two linear integrals will consist of the term $\int_{0}^{\infty}\frac{\ln x}{x^{a}(x+1)}dx$ and hence simply solve for it. But I'm having trouble physically solving it out. I think the log is throwing me off. Can anybody please help me? What does first authorship really mean? In my field (theoretical computer science), authors of any paper are always listed alphabetically; our papers .  (Well... hardly ever.)  In most other disciplines, at least within science and engineering, the ordering of authors is a signal about their relative contributions to the paper, with the first author indicating the most significant contributor.  Hiring and promotion committees do give extra weight to "first-author papers" (and sometimes have to be reminded that not all areas have them).  As an outsider, I find this practice confusing.  What does first authorship actually mean in your discipline? I understand vaguely that the first author is supposed to be the one who "", but what counts as "work" in this comparison?  Does "most" mean "more than all the other coauthors together" or just "more than any other coauthor"?  What happens when the comparison is unclear?   How often is "did the most work" the actual truth, versus a cover story for a more complex political decision?  I realize that the precise answer is different for every paper.  I'm looking for general guidelines for how an outsider (like me) should interpret first authorship in your field.  Pointers to guidelines from journals or professional societies would be especially helpful.  Please give only one answer per discipline. I'm applying for B1/B2 visa. In DS-160, it asks for      Monthly Salary in Local Currency (if employed)   However it doesn't mention anywhere if this should be gross (before tax deductions) or net (after tax deductions, whatever is credited into my account every month).  What should I fill here? How can I change Blender's theme? I just downloaded blender and its very bright. I want it darker. How can I change the color of it? How do I calculate the power consumed by a lightbulb? I'm studying a lightbulb and its variable resistance, given by the expression:  $R(T) = Ro[1 + α(T-T_0)]$, where $R_0$ is the resistance of the lamp at $T_0$.  In this case, $R$ is not given by Ohm's law ($V=Ri$). So, which expression can I use to calculate the power consumed by a lightbulb?   $P = R\cdot i^2$ $P = \frac{V^2}{R}$ $P = V\cdot i$ (I don't think I can use this one)   I have measured the current and the e.p.d. at the bulb using instruments. How to fix very slow Ubuntu booting?