Characterize units in formal power series $R[[x]]$
Prove $\alpha \in R[[x]]$ is a unit iff $a_0 \in R$ is a unit
Server 2012 deduplication: run on Hyper-V host or guest VM? I have a Windows Server 2012 Hyper-V host with VMs on a dedicated RAID-5 volume. One VM is also running Server 2012 and is being used to serve files. The other VMs are smaller and mostly used for temporary testing scenarios.   The main file server VM has two dynamically expanding VHDX files - one for the OS and one for storage. The VHDX being used for storage has quite a few duplicated files on it.  Should I run Server 2012 deduplication on the volume containing the storage VHDX file on the host, or within the file server VM itself? I understand that running it within the VM will not decrease the size of the VHDX file on the host, but my goal is to enable as much storage capacity within the VHDX file itself. I also understand that if I run it on the host, I will have to take the VM offline to do it. Downtime isn't a concern in this instance, just the best way to do this. Completing a 3x3 correlation matrix: two coefficients of the three given I was asked this question in an interview.  Lets say we have a correlation matrix of the form \begin{bmatrix}1&amp;0.6&amp;0.8\\0.6&amp;1&amp;\gamma\\0.8&amp;\gamma&amp;1\end{bmatrix}  I was asked to find the value of gamma, given this correlation matrix. I thought I could do something with the eigenvalues, since they should be all greater than or equal to 0.(Matrix should be positive semidefinite) - but I don't think this approach will yield the answer. I am missing a trick.  Could you please provide a hint to solve for the same? What are Ctools plugin (content type, access, etc), and how does one create them? What are Ctools plugins, and how does one create them? How do servlets work? Instantiation, sessions, shared variables and multithreading Should the personal/research statement be technical? Related:   I know I must describe my past and current research in my personal/research statement or statement of purpose. But do I use technical terms?  I was given the advice that since the people reading my statement are mathematicians (I am applying to US for applied mathematics), they should know what I am talking about.  Although I am applying to applied mathematics, it would also be nice to hear from other fields (biology, computer science, engineering etc) about this. I set /usr/bin, /usr/lib, and /usr/share to be owned by my regular user and now I am getting interesting errors After running this command - sudo chown -R $(whoami) usr/{lib/node_modules,bin,share} I am not able to run sudo anymore: sudo: /usr/bin/sudo must be owned by uid 0 and have the setuid bit set. How do I fixed that?  I read  but I am not sure what advice to follow and if it's applicable to my case. How I would go about getting the current users username or first and last name?  I have been looking at this for the last couple of hours - I was just wondering how I would go about getting their name and then displaying it on the page.  For example the current user is 'John Smith' and in the lightning component I want to output John Smith's name like:     Welcome to our community John Smith! PuTTY inserts random characters during a session I recently started renting space on a remote server so that I could work on a project. I found that a relatively painless way to access it on a windows machine is through PuTTY. However, there is one thing that has always irked me when using it: for seemingly no reason random characters are sometimes inserted at the cursor.  Most of the time it is just a single tilde, but rarely it spits out what looks like some escape sequence ([[^8 or the like). It will only occur when I am focused on the window, whether I am typing or 20 feet away from the keyboard. If left for long enough, it will spit tildes at random intervals (average is about 1 minute).  Finally, this behavior seems to be inconsistant when running programs such as nano or the mysql interface: in nano, instead of inserting tildes, it will set marks (ctrl-^); in mysql, lines will become un-editable.  My question is this: Has anyone else experienced this sort of behavior in PuTTY? And if so, what can be done to prevent/correct this behavior? Find a recurrence relation for the number of $n$-digit binary sequences with no pair of consecutive $1$s Find a recurrence relation for the number of $n$-digit binary sequences with no pair of consecutive $1$s.  I know my base case:$$a_1 = 2$$ for either $1$ or $0$. Normally to construct the recurrent relation I would say fill in $n-1$ spaces then add a $1$ or $0$, which is simply:$$a_n = 2\cdot a_{n-1}$$However, I don't believe this is right, because this doesn't take into account that there can't be any consecutive $1$s.  Even when I use the base case of $2$ digits:$$a_2 = 3$$for either $01$, $10$, or $00$, I still get the recurrence relation of:$$a_n = 3\cdot a_{n-2}$$which also does not account for $01$ and $10$ occurring consecutively.   So how would I express this? Is $G^{(X, Y)} = (G^X)^Y?$ ($A^B$ just means that $B$ is mapped to $A$) Sum of First $n$ Squares Equals $\frac{n(n+1)(2n+1)}{6}$ I am just starting into calculus and I have a question about the following statement I encountered while learning about definite integrals:  $$\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}{6}$$  I really have no idea why this statement is true. Can someone please explain why this is true and if possible show how to arrive at one given the other? Is there a way to add a timer to a Beamer presentation? Is there an elementary proof that $\sum \limits_{k=1}^n \frac1k$ is never an integer? There is a statement that maximizing the likelihood is equivalent to minimizing the cross-entropy.  Are there any proof for this statement? Does eating infected flesh have an effect? I don't remember what actually happends when people eat infected flesh. I have in mind :  Gareth and the cannibals eating bitten Bob's leg in . It seems that the cannibals survive for a while after eating Bob's flesh and they seem OK.  The Saviors eating pigs that ate walkers in . We don't know for how long this process has been on, but  has his routine and looks used to doing that. Can we assume that Saviors are eating infected pig flesh for a while now ?  Does it have negative effect in long term ? Convert continuous numeric values to discrete categories defined by intervals Why are mirrorless cameras much slower than DSLRs? This is a follow-up to a .  I've been comparing cycle times (or shot to shot times in single shot mode) of mirrorless cameras with interchangeable lenses with traditional DSLRs and all of them, even the highest end ones (like the Olympus OM-D EM-5 or Panasonic GH3) are slower than even entry level DSLRs.  How's that possible? The electronics should be the same and they don't have the burden of a mirror going up and down between each shot. I think that there must be a technical reason for that (maybe some cpu time is going to feed the live-view before the image is encoded?), because from a commercial point of view it does not make sense.  I've seen the cycle times under the performance tab in the reviews pages of .  The average CSC has cycle times around 0.7~1.2s, the flagship ones around 0.5s. The average DSLR has cycle times around 0.4s and the flagships around 0.25s. I have a mathematical problem with the following formula. The goal is to transform this equation to have a seperated real and imaginary part. I have already done this with several other equasions, but for this particualar one I don't know where to start.  I dont expect you to do the complete work of transforming for me, it would already be very nice if you could give me a hind on how you would start.  Thank you in advance!  C||RLC      This is my current progress:    My question is:  How can I get rid of the imaginary part jωC2*R?  When the denominator is completely real I can just split up the formula and have an imaginary and a real part. How can I change some pages into document into landscape mode, while leaving the others in portrait mode (or vice versa)? How do simulacra behave?