What can/do mixed second-order partial derivatives represent?
Geometric interpretation of $\frac {\partial^2} {\partial x \partial y} f(x,y)$
bash regex with quotes? The following code  number=1 if [[ $number =~ [0-9] ]] then   echo matched fi   works. If I try to use quotes in the regex, however, it stops:  number=1 if [[ $number =~ "[0-9]" ]] then   echo matched fi   I tried "\[0-9\]", too. What am I missing?  Funnily enough,  suggests this should work.  Bash version 3.2.39. I am trying to install a fresh version of Ubuntu in my computer without touching the windows 10 dual boot! In the Installation Type, the first option seems exactly what i wanted to do.  My question is, is this feature is safe to use? because i don't want to lose any windows files and other NTFS partitions on the hard-disk. Please eliminate my confusion. Note as that i dont need any files or media which are in the ubuntu partition, Thanks. What is the logic behind the timer of the Sojourner Badge? Does the 24 hours timer start:     when you hack a portal on a particular day     or     does it use the calendar days and check if you did hack a portal on a particular day   or     does it simply use a fixed international timezone to calculate the 24 hour cycle   or     does it use the agent's hacking cell's timezone to start it?   If it's the calendar days method than the explanation of the badge would be a little bit misguided because you could hack a portal on 00:01 on Saturday and then hack another one on 23:59 on Sunday and it would be practically two days between two hacks.  If it's based on the agent's last hack for a particular day then the explanation still would be problematic?  The third option would be a little bit unfair (or timezone racist) for the rest of the world.  The last option (the cell's timezone) would/could be both unfair for travellers and/or non-travellers.  Does anyone know any details about it? Norm is sup of inner products (proof). Let $V$ be a vector space with an inner product $\langle.,. \rangle$ and associated norm $|| . ||$ Then:    Could I have a proof of this fact? For any natural number $n\ge 1$, given pairs $(a_1,b_1),(a_2,b_2),...,(a_n,b_n)$ of integer numbers, there exist integer number $c$ and $d$ such that  $$\prod_{i=1}^{n}(a_i^2+b_i^2) = c^2+d^2$$    My initial approach is  Base Case: $(a_1^2+b_1^2) = a_1^2+b_1^2$ which is true. (Although it is trivial)  Prove the statement is true when $n=2$: We have $$(a^2+b^2)(c^2+d^2) = (ac-bd)^2+(ad+bc)^2$$ (Thanks André Nicolas for pointing it out)   So if $a,b,c,d$ are integers, $ac,bd,ad,bc$ are all integers and integers are closed under addition and subtraction. Hence $(ac-bd),(ad+bc)$ are integers.   Inductive Hypothesis: $\prod_{i=1}^{n}(a_i^2+b_i^2) = c^2+d^2$ is true  Inductive Step: $$\prod_{i=1}^{n+1}(a_i^2+b_i^2) = \prod_{i=1}^{n}(a_i^2+b_i^2)\cdot (a_{n+1}^2+b_{n+1}^2) = (c^2+d^2)\cdot (a_{n+1}^2+b_{n+1}^2)$$  Where $c$ and $d$ are integers.   But when we apply $n=2$, we have  $(c^2+d^2)\cdot (a_{n+1}^2+b_{n+1}^2) = (e^2 + f^2)$ where $e$ and $f$ are integers.  Hence, by the principle of induction, the statement we needed to prove is true. Rounded caps on a Bezier Curve pipe This may be a simple question.  Essentially I am procedurally generating random 3D figures using a bezier curve and bezier circle bevel object, however, one of the only things I can't figure out how to do is how to round the end caps of the object.   I have tried using a taper object like suggested  but have had only limited success.  This is about as close as I've gotten:   I should note that all of this is done through Python and I'm not modeling any of this by hand. So any suggestions for how I can make the rounded caps programmatically would be greatly appreciated. How do you remove the ability for a user to make a comment or post on a page? I am building a new website on Wordpress, and all my pages have the add comment box at the bottom. I wish fo rthis to be removed from pages such as Home, Contact Us, About etc etc, but want it to remain on the blogs and galleries.  I have read  but do not really understand what this means to do. is there an easier way to do it. I do not have  under Settings -> Discussions. I want to run a command when there are only 10 entities left. I know you can use /execute unless entity to detect when all matching mobs have died, but it doesn't work if you want to run a command when there are for example 10 entities left.  A command like /execute if entity @e[limit=10] does not work, it also triggers if there is only one entity.  Such a counting system could also be used to determine once there is only one player left in an arena, meaning they have won a battle or similar. I had posted a  last week about customizing a ToolValidator class and got some very good answers.  In working with the proposed solutions, I have created a custom module that performs queries on a db, and will be called by both the ToolValidator class (to provide values for the drop-down lists) and later in the geoprocessing script (to get other parameters based on items selected in drop-down lists).  However, I can't seem to actually call the custom module in the ToolValidator class.  I have been trying to append to path with no luck.  When I try to apply these changes to the script, I get a runtime error:  [Errno 9] Bad file descriptor.  If I comment out import line, no errors.  sys.path.append('my_custom_module_directory') import my_custom_module   Many of you may be asking why don't I just implement a custom tool with ArcObjects.  The reason is that my end users don't have the privleges necessary to register ANY dlls on their computer.  UPDATE:  This was happening to me in ArcGIS 10.  Interestingly enough, I was initially appending to the path inside of the initialiazeParameters function of the ToolValidator class.  If I do the append outside (i.e., on top of) of the ToolValidator class, everything works as expected.  sys.path.append('C:/Working/SomeFolder') import somescript --------&gt;THIS WORKS  class ToolValidator:   """Class for validating a tool's parameter values and controlling   the behavior of the tool's dialog."""    def __init__(self):     """Setup arcpy and the list of tool parameters."""     import arcpy     sys.path.append('C:/Working/SomeFolder')     import somescript -------&gt; THIS DOESNT WORK     self.params = arcpy.GetParameterInfo()   UPDATE 2:  I think I found the true cause of my problem.  In the code snippets in this post, I have been appending what appear to be real paths (ex C:/Working/SomeFolder) to the sys.path.  In my actual ToolValidator class, I was constructing a relative path using os.path.dirname(__file__) +"\my_special_folder...".  I was anticipating that os.path.dirname(__file__) would return the path of the toolbox, since that contains the ToolValidator class.  I have come to find this is not the case.  As far as I can tell, the ToolValidator class is never actually written to a .py file, and I speculate the the this code is passed to the python interpreter in memory, so __file__ is useless, or some temp script is persisted and then execfile(path_to_script) is called, again rendering __file__ useless.  I'm sure there are other reasons I am missing as well.    Long story short, if I use a hardcoded path, the sys.append works anywhere, relative paths don't work so well in the ToolValidator class. I have a random sample of Bernoulli random variables $X_1 ... X_N$, where $X_i$ are i.i.d. r.v. and $P(X_i = 1) = p$, and $p$ is an unknown parameter.  Obviously, one can find an estimate for $p$: $\hat{p}:=(X_1+\dots+X_N)/N$.  My question is how can I build a confidence interval for $p$? Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$? I would like to use Zapf's Palatino font for the text in my document, which also includes a lot of maths. And I would like a good font for the maths. This is a snapshot of what I am doing.  \documentclass[10pt,letterpaper]{memoir} \usepackage{amsmath} \usepackage{amssymb} \usepackage{mathpple} \usepackage{upgreek} \usepackage{mathpazo} \usepackage{lipsum}  \begin{document}  \chapter{Demo}  Some regular text. \lipsum[1]  Now for some maths.  \begin{displaymath} P_{N-1 + m} = \frac{C}{N-{1} + m} \binom{N_{2} - N_{1}}{m}         \alpha^{m}\beta^{(N_{2} - N_{1}) -m} \end{displaymath}  The number 27 is the sum of the first 5 odd prime numbers: $27 = 1+3+5+7+11$  \end{document}   To me the text and math fonts seem a good fit but the text does not look like Palatino. Is this a grammatically correct line in a poem: “Will he roll the dice, and follow it to Vegas?”? I want to use the following line in a poem: "Will he roll the dice, and follow it to Vegas?"   A couple of things to note; firstly, obviously I'm using "roll the dice" in both a figurative/idiomatic sense (as in taking a risk), and in a somewhat more literal sense (painting the image of the person actually following the dice that have been rolled to Las Vegas). That being said, my confusion here is if I can get away with using "follow it" or if I need to say "follow them" .... As I've read online "dice" traditionally refers to more than one die (i.e., the plural of die), but in the modern usage, "dice" can also be used to refer to the singular (i.e., just one die).   So, it seems like if I was referring to the image of just one die, then the way I phrased it could be correct. However, the image I'm trying to paint is the one usually associated with the phrase "roll the dice" (i.e., rolling two dice)...   So could "follow it" still be considered acceptable in this sense... or would I need to use "follow them"?... And if not referring to the dice themselves, could using, could the "it" be taken to refer to the act of rolling the dice, or would that not work either? Thanks so much in advance!! How do I get the title of a .pdf document to appear as the page title? How do I add a Javascript library to a field formatter? I'm trying to include a Javascript gallery () on my new Drupal 8 site and wrote a field formatter for this purpose.   Now I need to add the jQuery lightGallery to pages using this field formatter and call the library when the page is ready. I am confused about how I am supposed to do this, though.   I defined the library in the module containing my field formatter, but I'm not sure how I attach it only on sites that contain the field.   The documentation of the library uses the jQuery $(document).ready function to call the libary, how would that work inside a Drupal module? How do I replace multiple spaces with a single space in C#? How can I replace multiple spaces in a string with only one space in C#?  Example:  1 2 3  4    5   would be:  1 2 3 4 5 Bookmark panel in Chrome/Chromium like in Firefox How can I find out if Ubuntu supports a particular hardware component, that is, if it works in Ubuntu?  I am going to put together a computer and I am choosing components.   How do I know if Ubuntu supports this or that motherboard, or this or that sound card, or this or that graphics card, etc? How do I know that there is no conflict in Ubuntu between this and that hardware component?   What resources are there to help with such situations?  I know that there are computers with Ubuntu pre-installed and that there are  for whole computers but this is not what I'm looking for. I'm looking for resources to find out support for particular hardware components and conflicts among particular hardware components. And when I tried the following commands /etc/hostnames and /etc/hosts, it says:  bash: permission denied. How to stop Mathematica 12.1 from chopping off the axes arrows?