Show that a complex polynomial of degree $n$ doesn't have zeros in a unit ball
Showing that the roots of a polynomial with descending positive coefficients lie in the unit disc.
Theorem numbering Wake screen after scheduled task wakes computer apt-get update, unlinking In plain English, how does casting spells and using creature abilities work with the stack and priority? I'm a relatively new player to Magic: the Gathering. I was reading  to try to understand exactly when it's okay to cast instants (e.g. ) and use some abilities (e.g.  should be tappable sometime during other peoples' turns), but I don't seem to be making much progress: as I come to understand some things, others make less sense.  My confusion is boundless  For instance: to cast  one needs priority. Spells go on the stack, and priority gets passed at some points (I have no idea when), and effects on the stack are resolved when both players have passed priority. But when is that? I can't find any mention of when the other player gets the priority to cast an instant, except on their own turn. Furthermore,  states that during the Main Phase:     505.4. Second, the active player gets priority. Players may cast spells and activate abilities. The active player may play a land.   So players (plural) may cast spells, but only the active player has priority, so only the active player can cast an instant. The turn rules, and the rules on , never mention any point at which the other player gets priority, so when can they possibly Cancel?  In addition, you can only cast a spell when the stack is empty, so the entire stack must be able to be resolved in your turn at some point.  I need an explanation!  I could go on a bit more. There is also  which can be overloaded to "Counter each spell you don't control", which seems like it could only possibly work with an understanding of the stack.  Could someone explain, in simple English:   When can Instants be cast? When can tap abilities be used? What do Instants and abilities have to do with the Stack and Priority? Access Java / Servlet / JSP / JSTL / EL variables in JavaScript How can I install WhatsApp in Ubuntu? Related: scheduled event Xdotool using "DISPLAY=:0" not works in Crontab Determining true mean from noisy observations I have a large set of data points of the form (mean, stdev). I wish to reduce this to a single (better) mean, and a (hopefully) smaller standard deviation.  Clearly I could simply compute $\frac{\sum data_{mean}}{N}$, however this does not take in to account the fact that some of the data points are significantly more accurate than others.  To put it simply, I wish to preform a weighted average of these data points, but do not know what the weighting function should be in terms of the standard deviation. How do I set environment variables? I'm trying to set up Apache Tomcat on my pc, and it wants me to set up an environment variable for CATALINA_HOME.  Does any know how to do this? Show Console in Windows Application? Is Borden's true identity real, or another ruse? Towards the end of , it's revealed that Borden accomplishes his Transported Man trick by using his twin brother, Fallon, as a double. It then becomes clear that he has been doing this in his personal life as well as on stage - each brother leads 'half a life', sometimes appearing as Borden and sometimes as Fallon. This is how he completes the illusion: one Borden goes into the first door, the other Borden emerges from the second door a moment later. Angier doesn't know how Borden does the trick, and doesn't believe Borden uses a double despite being told as much by Cutter. He follows what he believes to be a clue in Borden's notebook and travels to Colorado to meet Nikola Tesla, who Angier believes can build a machine that can help him perform the trick. Angier believes that Tesla built a similar machine for Borden. However, the final pages of the notebook reveal that Tesla was merely a red herring, designed to get Angier out of Borden's way for a long time. Tesla, it turns out, had never built such a machine before. At this point, Tesla agrees to build Angier's machine anyway. Instead of building a machine that transports matter, he builds one that duplicates it. Angier uses this machine in his act, but in order to avoid having to deal with multiple clones (the &quot;prestige materials&quot;), one of them must die as part of the act. This all makes sense, so far, but I find it hard to believe that Borden's use of the word 'Tesla' as the key to his cipher is random. It's too coincidental that he sends Angier on a wild goose chase, but Angier returns with a working machine. A film that is otherwise so tightly plotted shouldn't rely on coincidence to move the narrative forward, so there must be something else going on. Is it possible that Borden cloned himself using Tesla's machine? Power series of a function I am wondering if there are any functions $f(x)$ such that it cannot be expressed as a power series of $x$? This might turn out to be a silly question, but I can't think of one at the moment.   Thanks! How to see the full date on macOS Big Sur? Is there a (La)TeX distribution running on iPad? I am non-EU citizen working in Germany. Can I travel to UK without a visa? Conclusively stop wake timers from waking Windows 10 desktop When does a complex matrix have a square root? What is the neccessary and sufficient condition for a matri$A \in C^{n  \times n}$ so that it has a "square root" , that is there is a matrix $B \in C^{n \times n}$ such that $A=B^2$.  I am not quite sure but I was thinking that it would be that A and B are similar. Do there exist an infinite number of 'rational' points in the equilateral triangle $ABC$? Let's call a point $P$ which satisfies the following condition 'a rational point'.  Condition: Each distance $PA, PB, PC$ from a point $P$ to three vertices $A, B, C$ of an equilateral triangle $ABC$ which has edge-length $1$ is rational number.  I'm interested in this point because I found the following three:  1. There exist an infinite number of rational points on an edge of the equilateral triangle $ABC$.  2. There exist an infinite number of rational points on the circumference of the circumscribed circle of the equilateral triangle $ABC$.  3. There exists a rational point in the equilateral triangle $ABC$.  Supposing that $A(0,\frac{\sqrt3}{2}), B(-\frac12,0), C(\frac12,0)$, one example for the above 3 is the following: $$P\left(\frac{61}{2058},\frac{220}{1029}\sqrt3\right), \left(PA, PB, PC\right)=\left(\frac{73}{147}, \frac{95}{147}, \frac{88}{147}\right).$$  I found this example by using computer. I found the other examples, but I don't know there exist an infinite number of rational points in the equilateral triangle $ABC$. Then, here are my questions.  Question 1: Do there exist an infinite number of rational points in the equilateral triangle $ABC$ ?  Question 2: Can we find all rational points in the equilateral triangle $ABC$ ? Using setminus notation with set elements The "correct" way to write a set without a specific element is as follows: $S \setminus \{s\}$  But in some contexts this is cumbersome to write/type or read, and it detracts from the flow of the writing. Is it acceptable to just use $S \setminus s$?  Edit: By "cumbersome" i mean they look bad when you're trying to inline formulas in LaTeX.