Localisation of the the roots of a polynomial
Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros
I have studied from Griffiths, the relativistic form of momentum is $$p = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} m_0v$$   Now when I evaluate the momentum for photon, I just insert $v=c$ and $m_0=0$ and I get $p= 0/0$. How does it make sense?   Can you tell me that where I am wrong? Remove blank attributes from an Object in Javascript Will yearly moderation statistics be published on all sites this year, and future years? Role of capacitors in amplifier What is the significance of a coupling capacitor in a common-emitter amplifier? What would happen if it is removed? What will be  the effect on AC amplifier gain on removing it? I am looking for an intuitive explanation as to why/how row rank of a matrix = column rank. I've read the proof at  and I understand the proof, but I don't "get it". Can someone help me out with this ?   I find it hard to wrap my head around the idea of how the column space and the row space is related at a fundamental level. Why is it "description" but "describe" (b and p)? I've just wondered by it is "description", but "to describe". It looks as if "to descripe" would be a more consistant choice. Is there any other explanation besides "this is how it is written for years"?  edit: Or alternatively "to describe" and "describtion". Need help with a question regarding the Big Oh In class we are currently covering upper/lower bounds, big Oh and omega and the like. I am pretty good on the "typical" functions one would do, but at a complete loss at "general" statements. This ons function, for example:  $$\forall f\in\mathcal{F}: \lfloor \sqrt{\lfloor f(n)\rfloor }\rfloor \in O(\sqrt{f(n)}).$$  the domain F by the same is all natural numbers that return a real positive number when inputted. My first instinct with something like this is to remove the floors, the general strategy I though to solve this is remove the outer floor, then get rid of the square root, and then the inner floor. But I have no idea how to go about this or if this is even the right way to do it.  Help please? Thanks in advance. Virtualbox: OS cannot use the new extended disk space (.vdi) I am running Virtualbox. I increased the size of my hard disk (.vdi) from 10G to 15G. Now when I start my Mint vm, the hard disk reports as 7.5g (df) even though i extended it (fdisk -l). I am not sure what is the problem. Can anyone point me the problem?  $ df -h Filesystem      Size  Used Avail Use% Mounted on /dev/sda1     &gt;&gt;7.5G&lt;&lt; 7.1G   61M 100% / udev            1.5G  4.0K  1.5G   1% /dev tmpfs           581M  888K  581M   1% /run none            5.0M     0  5.0M   0% /run/lock none            1.5G   88K  1.5G   1% /run/shm  $ sudo fdisk -l Disk /dev/sda: &gt;&gt;16.1 GB&lt;&lt;, 16106127360 bytes 255 heads, 63 sectors/track, 1958 cylinders, total 31457280 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 Disk identifier: 0x000c55a4     Device Boot      Start         End      Blocks   Id  System /dev/sda1   *        2048    15728639     7863296   83  Linux /dev/sda2        15730686    16775167      522241    5  Extended /dev/sda5        15730688    16775167      522240   82  Linux swap / Solaris  $ vboxmanage showhdinfo mint.vdi UUID:                 a94931b9-673c-440a-ab6b-2c3eedd0cf93 Accessible:           yes Logical size:         15360 MBytes Current size on disk: 7806 MBytes Type:                 normal (base) Storage format:       VDI Format variant:       dynamic default Location:             /opt/virtualization/vm/mint.vdi How do I create a master workbook in excel? In powerpoint we have something called a master slide.  I want the same idea for excel.  I want to create a template that I can work on with formulas and I want it to update all children files.  Example: I have a budget template.  This template has a budget listing all required equipments and their cost for a project.  We then have a formula that calculates the total cost of all equipment. I want to update only the template file with equipment and formulas, but I want the actual files (children) to contain the costs (because they might be different costs for different locations, but the rest of the budget and its formulas are shared).  Its pretty much exactly what a master slide in powerpoint is, if you've ever used that you should understand what I'm trying to do pretty easily.  One master file to store formulas, and a bunch of children files that store the data to be accessed by those formulas.  This way if a formula needs to be changed, the templates is adjusted and all other files update accordingly.  Any ideas?  I'd prefer not to have to use VB, and I'd also like a solution that works for both mac and windows.  Found  question but no answers.  I've already created a template, but that doesn't seem to update the other files when I modify it. I absolutely hate it when I watch a video on YouTube and it automatically loads another video page after it's done playing.  This is especially annoying when I'm in the middle of typing a comment as it will cause me to lose what I have typed.  I'd like the video to simply stop and for no further action to take place once it is finished playing.  Is there any way to accomplish this? Proof: Every convergent sequence of real numbers is bounded Should we use wheatstone bridges nowadays? For measuring strain gauges, the Wheatstone bridge is the historical choice.  In a quarter Wheatstone brigde (\$350 \Omega \$ typically (?)), with a high input impedance amplifier, and some bridge power voltage \$V\$, the ratio between the bridge output voltage w.r.t. any resistor is 1/4, which is the same ratio in a voltage divider between the output voltage w.r.t. any resistor, compared with a stable voltage reference of \$V/2\$.    A voltage divider with a voltage reference would have a voltage noise of about 35.16 nV/rtHz (from a voltage reference of 35 nV/rtHz plus two resistors), and the Wheatstone bridge a voltage noise of 4.86 nV/rtHz (from four resistors), which should be enough (?) for most ADC systems (i.e. for 24 bit, 0-5V range: 300nV resolution).  And a voltage reference (\$0.02\%\$ initial error, \$2 \ ppm/C^\circ\$, ), would be more stable and precise (?) about \$4\ ppm/C^\circ\$, than a precision resistor (\$0.005\%\$ error, \$2 \ ppm/C^\circ \$, ), about \$8 \ ppm/C^\circ\$.  Hence, why bother using Wheatstone bridges? What size should the HMAC key be with SHA-256? I'm trying to generate a secret key to be used for HMAC SHA-256 signature processing. I've seen many sample of keys with variable length from 32 characters to 96 characters.  What is the ironclad rule for this key size? Which is correct: "the below information" or "the information below"? I frequently see statements that refer to something later in the text that use a phrase such as "the below information". Is it more correct instead to say "the information below" (or "the following information")? Using a foreign driver's license in California when staying with a J-1 visa Updating entities in response to collisions - should this be in the collision-detection class or in the entity-updater class? How do I reset all progress in the game "just shapes and beats"? The game  has a very unique intro that I would like to show my friend again for the first time. I'm not sure how to reset all my progress on this game to achieve this though. Any thoughts? Display Animated GIF When is "EDIT"/"UPDATE" appropriate in a post? I often see questions edited into this form:     Lorem ipsum dolor sit amet blah blah blah paragraph paragraph original question.            UPDATE: The Lorem disappeared and left this message: "new information".   I find this format unaesthetic (since Stack Exchange posts are supposed to be useful in the long term and update boundaries are artifacts of the creation rather than the content) and feel that new information should, whenever possible, be incorporated into the original text “as if it had always been that way” if practical, and pointing out an update should be done mostly in comments.  Is this an appropriate writing style, and if so under what circumstances? If not, should it be removed or discouraged? After Factory Reset, In order to use Play store and Gmail I want to setup Google account on Samsung GT-S6802. When I tries to setup Google Account, In-spite of right user-name and password, following window appearers:    When I open gmail form browser, I've mail from google subject:Sign-in attempt prevented and says:     Someone just tried to sign in to your Google Account hidden@gmail.com from an app that doesn't meet modern security standards.     When I review, it shows unknown device but on browser it detects my device.  So, How do I face this issue and setup google account?