The Enestrom-Kakeya theorem states that all roots of the polynomial:  $$p(z):=\sum_{k=0}^n a_kz^k$$  lie outside the open unit disk if the sequence $(a_k)$ is positive and decreasing.  A proof can be found in Marden- Geometry of Polynomials.  I was wondering if the following idea of mine constitutes a valid proof as well:  $$(1-z)p(z)=a_0+\sum_{k=1}^n (a_k-a_{k-1})z^k-a_nz^{n+1}$$  so   $$|(1-w)p(w)|\geq a_0-\sum_{k=1}^n (a_{k-1}-a_k)|w|^k -a_n &gt; a_0-\sum_{k=1}^n (a_{k-1}-a_k) -a_n=0$$  for all $|w|&lt;1.$  (Using the reverse triangle inequality. The step at which strict inequality is introduced is only valid if some $a_{k-1}-a_k$ is nonzero. If this is not the case, our polynomial trivially has all roots on the unit circle.)
Let $P(z)=a_0+a_1z+\cdots+a_nz^n$ be a polynomial whose coefficients satisfy $$0&lt;a_0&lt;a_1&lt;\cdots&lt;a_n.$$  I want to show that the roots of $P$ live in unit disc. The obvious idea is to use Rouche's theorem, but that doesn't quite work here, at least with the choice $f(z)=a_nz^n, g(z)=$ (the rest).  Any ideas?
Someone mentioned it in the IRC as the slicing problem. I am trying to install Ubuntu 16.04 LTS on a Dell XPS 13 (9350). The laptop came with Windows 10 pre-installed. I am installing from a pendrive but I think the issue would be the same if I used e.g. a USB DVD drive.   Dude, where's my hard drive?  I am blocked because the installation program cannot find 8.6Gb of free space on my hard drive despite the fact that there are hundreds of Gb free according to Windows. Digging a bit into the problem, it seems that Ubuntu cannot see my hard disk at all.    This is the output of GParted:    I am not sure what that drive mounted at /cdrom is, but it seems the only device that exists in the system that is not a RAM disk or a loop device:   Content of /proc/partitions:   ubuntu@ubuntu:~$ cat /proc/partitions   major minor  #blocks  name     1        0      65536 ram0     1        1      65536 ram1     1        2      65536 ram2     1        3      65536 ram3     1        4      65536 ram4     1        5      65536 ram5     1        6      65536 ram6     1        7      65536 ram7     1        8      65536 ram8     1        9      65536 ram9     1       10      65536 ram10     1       11      65536 ram11     1       12      65536 ram12     1       13      65536 ram13     1       14      65536 ram14     1       15      65536 ram15     7        0     130048 loop0     7        1    1104188 loop1     8        0    1970239 sda     8        1    1953439 sda1   Summary of fdisk -l:   ubuntu@ubuntu:~$ sudo fdisk -l |grep Disk Disk /dev/ram0: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram1: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram2: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram3: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram4: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram5: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram6: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram7: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram8: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram9: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram10: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram11: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram12: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram13: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram14: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/ram15: 64 MiB, 67108864 bytes, 131072 sectors Disk /dev/loop0: 127 MiB, 133169152 bytes, 260096 sectors Disk /dev/loop1: 1.1 GiB, 1130688512 bytes, 2208376 sectors Disk /dev/sda: 1.9 GiB, 2017525248 bytes, 3940479 sectors Disklabel type: dos Disk identifier: 0x00000000   Result of fdisk of the only non-loop non-RAM device (not sure this is relevant):   ubuntu@ubuntu:~$ sudo fdisk -l |grep -A 50 sda Disk /dev/sda: 1.9 GiB, 2017525248 bytes, 3940479 sectors Units: sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disklabel type: dos Disk identifier: 0x00000000  Device     Boot Start     End Sectors  Size Id Type /dev/sda1  *      129 3907007 3906879  1.9G  c W95 FAT32 (LBA)   I am blocked at this point. Any help will be much appreciated.   Additional information (following comments):   Running dmesg |grep -i sata shows (among others) eight lines that suggest some kind of error:   ata1: SATA link down (SStatus FFFFFFFF SControl FFFFFFFF) ata2: SATA link down (SStatus FFFFFFFF SControl FFFFFFFF) ata3: SATA link down (SStatus FFFFFFFF SControl FFFFFFFF) ata4: SATA link down (SStatus 0 SControl 0) ata5: SATA link down (SStatus 0 SControl 0) ata6: SATA link down (SStatus 0 SControl 0) ata7: SATA link down (SStatus 0 SControl 0) ata8: SATA link down (SStatus 0 SControl 0)  I have "Restarted" windows instead of only "Shutdown" it to avoid problems with "fast startup", following some recommendations I have read of other users having problems installing Linux on Windows 10 laptops.ago   Regarding SATA, the BIOS says: "SATA Operation: RAID ON". The other two options available are "Disabled" and "AHCI".    I have followed the instructions of these two pages from Dell: , . What are the limits on how I can cast, change, and retract votes? What is the gradient of $f(x, y, z) = \sqrt{x^2+y^2+z^2}$? What is the gradient of $f(x, y, z) = \sqrt{x^2+y^2+z^2}$?  I know that $\nabla f = \left\langle\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z}\right\rangle$ or equivalently $\nabla f = \frac{\partial f}{\partial x}\mathbf{i} + \frac{\partial f}{\partial y}\mathbf{j} + \frac{\partial f}{\partial z}\mathbf{k}$.  Eventually, I am going to evaluate this gradient at a point and then dot it with some given unit vector to find a directional derivative. I think maybe what is troubling me is the radical in $f$. Will I have to use the chain rule in order to find the three partial derivatives?  I tried this:  $$\frac{\partial f}{\partial x} = \frac{1}{2}(x^2 + y^2 + z^2)^{-\frac{1}{2}}2x$$ $$= \frac{x}{\sqrt{x^2 + y^2 + z^2}}$$  That result looks ugly to me. However, if I did that partial derivative correctly, then I think I know what I am doing. I am pretty sure that most of us here, or at least those do graphic design for living, have found themselves in following situation:   You agree with a client to do the design, agree on price, schedules, formats etc… You work hard, make adjustments, collaborate with client; everything goes well in the beginning. At some point you realise that the client does not listen your professional advice regarding design and prefers his/her own ideas that might not look so professional (choice of fonts, colors, odd choices of elements, shapes etc…). No matter how hard you try, the client is persistent and will not accept the designer’s advice. You get back to work, try to make the best out of it, and the final result is not so good, mainly because you had to stick to the client’s wishes. Work is shipped, payment done, and you don’t want to include this work in your portfolio because it is not good. After all, it is not your work, it is something that was physically created by you as a designer, but the ideas, concept, story, and message came out as a result of nonprofessional person, your client.   Ok, they pay for it, and as long as they are happy this is fine. But, the more compromises you make, the more time you spend working on bad design. If you are a young designer on a quest to get recognition, you don’t want to work just for the sake of money and then face the lack of good design in your portfolio.   Maybe at the beginning of your career you don’t care that much, but later if life this might be a big issue. At some point you will be approached by a big client that might offer you long-term contract, but first they will want to see your work. No point explaining to them what you did and why you made so many compromises.   They will not be interested in that.  Every project is precious as your time and you want to do use it wisely and produce great work.   How would you deal with such a situation? Is $\mathbb{R}^\omega$ endowed with the box topology completely normal (or hereditarily normal)? Creating shapefile from Excel file in QGIS? I am using QGIS 2.6.1 and have worked in an Excel file database (which was actually converted from a Shapefile). I have managed to convert it as CSV file and load it into QGIS (displays data fine) but I have trouble to convert it to a shapefile.  I can view it but I can´t add or alter data in this file. I think I have to save it as a database.   Any clues how to convert the xlsl-data to a database and finally to a shapefile? Motivation for Ramanujan's mysterious $\pi$ formula The following formula for $\pi$ was discovered by Ramanujan: $$\frac1{\pi} = \frac{2\sqrt{2}}{9801} \sum_{k=0}^\infty \frac{(4k)!(1103+26390k)}{(k!)^4 396^{4k}}\!$$   Does anyone know how it works, or what the motivation for it is? Add field "tome" to biblatex entries I need to add a new field in the @book or @InProceedings entries: this field is "tome", for I have for instance the following title:  Francesco Bertolini, Società di trasmissione orale: mito e folclore, in Lo spazio letterario della Grecia antica, a cura di G. Cambiano, L. Canfora e D. Lanza, vol. I, tomo I, Salerno, Roma 1992, pp. 47--75.   So the following code is not enough:  @InProceedings{ bertolini:1992,   author                   = "Francesco Bertolini",   title                    = "Società di trasmissione orale: mito e folclore",   booktitle                = "Lo spazio letterario della Grecia antica",   editor                   = "G. Cambiano and L. Canfora and D. Lanza",   publisher                = "Salerno",   location                 = "Roma",   year                     = "1992",   volume                   = "1,   pages                    = "47--75", }   Using othes codes, I was able only to produce the "tome" field, but with a general trouble about the other fields:  \DeclareSourcemap{   \maps[datatype=bibtex]{     \map{       \step[fieldsource=tome,fieldtarget=usera]     }   } } \DeclareFieldFormat{usera}{tomo\space{#1}}   \DeclareBibliographyDriver{book}{%   \usebibmacro{author/editor}%   \setunit{\labelnamepunct}\newblock   \usebibmacro{title}%   \newunit\newblock   \usebibmacro{journal+issuetitle}%   \setunit{\bibpagespunct}%   \printfield{pages}%   \newunit\newblock   \printfield{usera}%   \usebibmacro{finentry}} \renewcommand*{\finentrypunct}{}   (useful for articles, but not for my case). By real, I'm not able to understand  which bibmascros I have to invocate...  I tried to write a biblatex-tome.dbx:  \ProvidesFile{biblatex-tome.dbx}   \DeclareDatamodelFields[type=field,datatype=literal,skipout=false]{tome}   \DeclareDatamodelEntryfields{tome}   Inside the main .tex file I put just this code:  \DeclareFieldFormat{tome}{\mkbibacro{tome}\addcolon\space #1} \newcommand*{\patchmoretome}[1]{   \xpatchbibdriver{#1}%     {\printfield{tome}}     {\printfield{tome}%           \newunit\newblock      \printfield{tome}}%     {\typeout{patching #1 to include more tome succeded}}%     {\typeout{patching #1 to include more tome failed}}% } % patch all drivers \patchmoretome{article} \patchmoretome{book} \patchmoretome{collection} \patchmoretome{inbook} \patchmoretome{incollection} \patchmoretome{inproceedings} \patchmoretome{manual} \patchmoretome{periodical} \patchmoretome{proceedings} \patchmoretome{report} \patchmoretome{thesis}   but it doesn't print the field in bibliographic entry. So I'm very confused about a (re)writing of driver Purpose of hole in stove leading to oven I'm staying in a hotel and have access to a "electric coil stove" for one of the first times.  I accidentally turned on the oven light and saw that the light was shining up through only one of the stoves:    There's only a port from the oven into the top right stove, and note that the stove is not on.  Here's a view from within the oven:    Is there a hole here as a vent for the oven for some reason, or is this for the stove? I typically use a glass "flat-top stove" that doesn't have an oven underneath it. I've never seen a direct hole from a stove to the oven before, and have to wonder what the purpose is. My internet connection is very slow. I suspect someone in the network is using a BitTorrent client which takes huge amount of bandwidth.  Is there a way to detect who is using my bandwidth (network sniffing tools etc)?  I should have pointed out that I have no access to the router, what I am looking for is a way of detecting someone's MAC/IP if she uses Bittorrent. Username and Password not recognized when logging into Minecraft We just got a new laptop (ASUS) though we did have a mac.  We are trying to log onto Mojang to download Minecraft and it keeps saying, "The username and password are not recognized."   We have done all the usual procedures; we have reset the password, we are using the email, not the username to sign in, and it looks like the minecraft login servers are working etc. etc.  We quit Minecraft on the old computer and shut off that computer thinking that was the issue.   Still, we can't get onto Mojang.  We are accessing mincraft through firefox and trying to download it to the new computer but we can't get into the account to do that!  What in the world could be the issue? New post formatting Update 3 It took me longer than I wanted, but I’ve got some updates for you on our s-prose component. You can see the  with my thinking over at our design system’s repo. It does the following:  Spreads s-prose headers out from paragraphs for better grouping. Tightens up s-prose paragraphs a bit, and made sure spacing under headings are more consistent. Replaces all s-prose margins internal to the component with a CSS variable var(--s-prose-spacing) so our users can more easily tinker with it in their browsers and user scripts. Kills trailing margins in s-prose  You can see  of content at our Stacks documentation.  Update 2 I’ve split the difference between the original 1.3 line-height and the proposed 1.6 line-height. We’re now at 1.5, with additional refinements to spacing between elements. I’ve also reduced line height within code blocks back to near the original value.  Update 1 This is now live.  We’re doing a bit of refactoring on our post formatting. Currently, we apply a single class with both layout and styling called .post-text. Our first goal is to separate layout from our text styles. Simple enough! However, our current post styling has a few missing spots and areas for improvements. Using our  as a sandbox, we’ve beefed up our styling and created a new component called .s-prose. It’s designed to offer styling for everything the  spec allows. This should allow us to add Stack Overflow-flavored styling anywhere we need to consume Markdown—questions and answers, of course, but also things like user profiles. Our .s-prose component adds:  Proper formatting for   Further header support and better spacing there  Additional blockquote refinements.  Refinements for revealing spoilers. We now reveal this on click / tap for a more consistent experience across devices—fewer accidental reveals as well, since it’s no longer a :hover interaction. Clicking again does not hide the spoiler. We also now add a badge to the top right corner. You can see how these work on our . It looks something like this:   This is a spoiler  It has two lines   General refinements to spacing including nested lists, images within lists  Sizing variations for different contexts. We offer xs, sm, and md variations of the .s-prose component.   As with everything, our prose component is a work in progress. We think we’ve got a heck of a start to a reusable component. We plan on going live with the new component network wide on Thursday, August 27, 2020. We’ll edit this post if that changes. If you see something funky, let us know. Some things are intended but might feel like regressions—images have a slightly different baseline—but others may have slipped through the cracks. Do I need a transit visa for a layover in the United Arab Emirates? Do I need a transit visa for a layover via airports in the UAE, such as Dubai International Airport or Abu Dhabi International Airport? If so, what are the requirements for such a visa? Can I get the transit visa on arrival? To run programs as sudo without password, I edited /etc/sudoers with wrong content.   Then I re-edited it with Mac's default text editor(course sudo cannot be used when /etc/sudoers is wrong).  I tried to run sudo agin, and get this error:   sudo: /etc/sudoers is owned by uid 501, should be 0 sudo: no valid sudoers sources found, quitting   What should I do? I cannot remember the root password (maybe I haven't ever set root password before). Problem with a sequence with multiple integrals The use of "exact same" Importance of Representation Theory Representation theory is a subject I want to like (it can be fun finding the representations of a group), but it's hard for me to see it as a subject that arises naturally or why it is important. I can think of two mathematical reasons for studying it:   The character table of a group is packs a lot of information about the group and is concise. It is practically/computationally nice to have explicit matrices that model a group.   But there must certainly be deeper things that I am missing. I can understand why one would want to study group actions (the axioms for a group beg you to think of elements as operators), but why look at group actions on vector spaces? Is it because linear algebra is so easy/well-known (when compared to just modules, say)?  I am also told that representation theory is important in quantum mechanics. For example, physics should be $\mathrm{SO}(3)$ invariant and when we represent this on a Hilbert space of wave-functions, we are led to information about angular momentum. But this seems to only trivially invoke representation theory since we already start with a subgroup of $\mathrm{GL}(n)$ and then extend it to act on wave functions by $\psi(x,t) \mapsto \psi(Ax,t)$ for $A$ in $\mathrm{SO}(n)$.   claims that if our physical system has $G$ as a symmetry group, then there is a correspondence between particles and representations of $G$. I'm not sure if I understand this correspondence since it seems to be saying that if we act an element of G on a state that corresponds to some particle, then this new state also corresponds to the same particle. So a particle is an orbit of the $G$ action? Anyone know of good sources that talk about this? There is a problem 3.3 in :     Ambiguities in the energy-momentum tensor:      (a) If you add a total derivative to Lagrangian ${\cal{L}} \rightarrow {\cal{L}} + \partial_\mu X^\mu$, how does the energy-momentum tensor change?      (b) Show that the total energy $Q = \int d^3x \; {\cal{T^{00}}}$ is invariant under such changes   Given the definition of energy-momentum tensor:  $$ {\cal{T}}^\mu{}_\nu = \sum_n \frac{\partial{\cal{L}}}{\partial \left( \partial_\mu \phi_n \right)} \partial_\nu \phi_n - g_{\mu\nu} {\cal{L}} $$  It changes as:  $$ \delta {\cal{T}}^\mu{}_\nu =  \sum_n \left( \partial_\rho \frac{\partial{X^\rho}}{\partial \left( \partial_\mu \phi_n \right)} \right) \partial_\nu \phi_n - g_{\mu\nu} {\partial_\rho X^\rho} $$  $T^{00}$ changes as:  $$ \delta {\cal{T}}^{00}= \sum_n \left( \partial_\rho \frac{\partial{X^\rho}}{\partial \dot{\phi_n}} \right) \dot{\phi_n} - \partial_\rho X^\rho $$   From this point I’m stuck. The first term doesn’t seem to disappear at all after integration over space, and the second disappears only partially:  $$ \int d^3x \; \dot{X^0} $$  So even if I’d have assumed that $X$ depends on position, and not on the fields - the total energy doesn’t seem to be invariant under it.  What is the best way to proceed forward with this? Any good application for data usage monitor? I was wondering if there are any good applications to monitor how much data I use on my laptop in a month. My net connection has a restriction of how much data I can use after which the speed goes down considerably. I saw ntop, but I just wanted to ask if there are any other good options or suggestions regarding this. Regards.