I'm trying to typeset the following (the part in green I'd like to add, but don't know how to:    Here's my sample code:  \documentclass{article} \begin{document} $$=F_j\underbrace{\frac{\partial G_j}{\partial x_i}}_{\substack{\text{derivative} \\ \text{acts} \\ \text{only} \\ \text{on} \: \vec G} }-F_j\frac{\partial G_j}{\partial a_j}$$ \end{document}   Any ideas?
There is a part of my paper where I use the distributive property and it might not be clear to the reader to see the operation result (I'm using in proposional logic for a proof). The logic equation (part of) is: $$ (l_{1}) \vee \big( (p \vee q) \wedge (\neg p \vee q) \wedge (p \vee \neg q) \wedge (\neg p \vee \neg q)\big) $$ $$ (l_{1} \vee p \vee q) \wedge (l_{1} \vee \neg p \vee q) \wedge (l_{1} \vee p \vee \neg q) \wedge (l_{1} \vee \neg p \vee \neg q) $$  So I was wondering if there is a way to represent this operation like a 'shower' (see another example in pic ). Maybe there is some hidden magic mathmode command or pkg for this. At last we can also rely on tikz.
What's the term in music, where the singer uses words without meaning? I've been searching for the word, which is used for describing parts of lyrics, where the singer sings for example the whole refrain only using words of syllables without any meaning. Maybe you could help? (here's one song with that type of refrain: ) Parenthetical pluralization of words ending in '-y' Why can I modify a read-only file? Short Question:  Why can we manipulate a read-only file in Vim using : + w + q + ! even without being an administrator?  Long Question:  I have a text file (myFile.txt) which is read-only for everyone:  navid@navid-ThinkPad-T530:~/ubuntuTest$ ls -l myFile.txt  -r--r--r-- 1 navid navid 26 Aug 22 21:21 myFile.txt   I can open it with Vim without having admin privileges:  navid@navid-ThinkPad-T530:~/ubuntuTest$ vi myFile.txt    I modify it and press: Esc + : + w + q + Enter and I see this error message:  E45: 'readonly' option is set (add ! to override)   So far, everything makes sense.  But when I press: Esc + : + w + q + ! + Enter, Vim saves the changes.  I'm using Ubuntu 16.04 and VIM 7.4. Package in Java Dynamically fill an Enum with a list I'm writting an addon with an UI. In my draw function in my UI class I've this   layout.prop(bpy.context.scene, 'activebone', text='active bone')   Wich create an enum in the UI.    And in my register class I've this:  bpy.types.Scene.activebone = bpy.props.EnumProperty(items=active_bone)   In my draw fonction I fill the active_bone list with the some data and but the enum don't refresh himself. I know that i can retype  bpy.types.Scene.activebone = bpy.props.EnumProperty(items=active_bone)   But the draw function is Read only so I can't. Is it possible to refresh my Enum item in the draw function or am I obliged to do it in an other class like a button? Why are two universal objects isomorphic? Browsing some , it is claimed that two universal objects are isomorphic because they admit the identity morphism on themselves. But from two identity morphisms, how would you get an isomorphism between the two? Cannot Delete Item "Could Not Find This Item" issue A friend sent a long a file (a .rar) he wanted me to check out for him before he installed it.  I downloaded it and unrared it with no problems, but it was full of .exe's instead of the intended contents (fonts) so I advised him to delete it immediately and not use.  I then proceeded to do the same, but the folder simply will not delete. Oddly the files went fine, and I never ran anything, but this is what I'm seeing:   Could not find this item  This is no longer located in C:\Users\This_User\Desktop. verify the item's location and try again.   I've tried the following things with no help:   Using "Unlocker" to Unlock and delete Using move on reboot and rebooting Using PendMoves (from sysinternals) and rebooting Elevating a cmd line, doing a dir /x to get the short name of the folder, and then del 'shortna~1' Moving the folder to a new folder and then trying to delete the parent folder   I'm on Windows 7 RTM, very fresh install. Any thoughts?  Update: Just to confirm, I've run Hijack this and half a dozen other malware detectors, and everything came back clean (no extra processes, no other obvious badness). Rebooting in safe mode didn't help either. I got a visa with my mother when I was 17 years old. On it was stated "Not valid unless accompanied by my mother".    Can I travel to the UK alone now that I am 18? Do you know a good way to compare PDF files side-by-side and show the modifications between the two?  I'm looking for Windows software to accomplish this. It would be great if you can post both free and not-free products. I would like to port Ubuntu Touch to a device that is currently not supported. What are the requirements for doing this and where do I begin? Is there any differences between      Try to do   And     Try doing   Thank you in advence. Maximum area of isosceles triangle with perimeter 6 cm I know that for continuous variable $P[X=x]=0$.   But i can't visualize that if $P[X=x]=0$, there is infinite number of possible $x$'s. And also why do their probabilities get infinitely small ? What made us think that Earth moves around the Sun? What is the difference between Reduce and Solve? How to prove $a_1^m + a_2^m + \cdots + a_n^m \geq \frac{1}{a_1} + \frac{1}{a_2} + \cdots + \frac{1}{a_n}$ A get() like method for checking for Python attributes This is an exam question I was practising. I have the general understanding of Linear programming, but how would you go about finding the Decision Variables, Objective function and Constraints for this?  My Opinions: Decision variables: $M_1$- # of Model $1$ to be produced $M_2$ and $M_3$(similar definition as $M_1$)  Objective function: I'd Multiple the Cost to make in house by cost to buy from subtractor  to get Minimise: $3900M_1+7500M_2+27300M_3$  Constraints: $3M_1+1.5M_2+2M_3\ge0$  $1.25M_1+2.5M_2+0.75M_3\ge8500$  $M_1,M_2,M_3\ge 5500$  No idea where number order would go? Do I use it in the Constraints and multiply by the Hours?  Now, am I on the right track? Where do the Python unit tests go? If you're writing a library, or an app, where do the unit test files go?    It's nice to separate the test files from the main app code, but it's awkward to put them into a "tests" subdirectory inside of the app root directory, because it makes it harder to import the modules that you'll be testing.    Is there a best practice here? Alternatives to one-way ANOVA for heteroskedastic data I have data from 3 groups of algae biomass ($A$, $B$, $C$) which contain unequal sample sizes ($n_A=15$, $n_B=13$, $n_C=12$) and I would like compare if these groups are from the same population.  One-way ANOVA would definitely be the way to go, however upon conducting normality tests on my data, heteroskedascity seems to the main issue. My raw data, without any transformation, produced a  ratio of variances ($F_{\max} = 19.1$) which is very much higher than the critical value ($F_{\rm crit} = 4.16$) and therefore I cannot perform one-way ANOVA.   I also tried transformation to normalise my data. Even after trials of various transformations (log, square root, square), the lowest $F_{\max}$ produced after transformation with a $\log_{10}$ transformation was $7.16$, which was still higher compared to $F_{\rm crit}$.  Can anyone here advise me on where to go from here? I can't think of other methods of transformation to normalise by data. Are there any alternatives to a one-way ANOVA?  P.S.: my raw data are below:   A: 0.178 0.195 0.225 0.294 0.315 0.341 0.36  0.363 0.371 0.398 0.407 0.409 0.432     0.494 0.719 B: 0.11  0.111 0.204 0.416 0.417 0.441 0.492 0.965 1.113 1.19  1.233 1.505 1.897 C: 0.106 0.114 0.143 0.435 0.448 0.51  0.576 0.588 0.608 0.64  0.658 0.788 0.958