Pretty straight forward my question.
How do you close windows/tabs in 2.8? I've tried a lot of stuff, but always end up opening up more.
Remove items from one list in another How does the built-in debugger decide what to highlight? Does this need a comma? I'm proofing a story, and at one point, as it is written at the moment, one the characters exclaims:     Prepare to die you fool!   Should there be comma after "die"? I've got a generic dictionary Dictionary&lt;string, T&gt; that I would like to essentially make a Clone() of ..any suggestions. Is it possible to accept the alternative hypothesis? I'm aware of several related questions here (e.g., , ) but I don't know the definitive answer for my question below.  Suppose a hypothesis test where we want to test whether a coin is fair or not. We have two hypotheses:  $H_0: p(head)=0.5$  $H_1: p(head)\neq0.5$  Suppose we use 5% significance level, there are two possible cases:   When we obtain the data and find that the p-value is less than 0.05, we say "With significance level 5%, we reject $H_0$."  p-value is greater than 0.05, then we say "With 5% significance level, we cannot reject $H_0$."   My question is:      In case 1, is it correct to say "we accept $H_1$"?   Intuitively, and from what I have learned in the past, I feel that "accepting" anything as a result of hypothesis testing is always incorrect. On the other hand, in this case, since the union on $H_0$ of $H_1$ covers the whole "space", "reject $H_0$" and "accepting $H_1$" look exactly the same to me. On another thought, I can also think of the following idea, which says it is incorrect to say "we accept $H_1$":     We have an evidence strong enough to believe that $H_0$ is not true, but we may not have an evidence strong enough to believe that $H_1$ is true. Therefore, "rejecting $H_0$" does not automatically imply "accepting $H_1$"   So, what is the right answer? I don't know how to solve $7^x-3^y=4$... I tried to see something $\pmod 7$ and $\pmod 3$ but it doesn't help at all. Can anyone give me some hints about it? Proving that $\sum\limits_{n = 0}^{2013} a_n z^n \neq 0$ if $a_0 > a_1 > \dots > a_{2013} > 0$ and $|z| \leq 1$ I'm going to teach a preparation course for the complex analysis qualifying exam from my university (which basically consists of me doing some problems from past exams) and I'm trying to solve some questions from previous exams. One of the questions is the following:           Prove that $\displaystyle{\sum_{n = 0}^{2013} a_n z^n \neq 0}$ if the coefficients  satisfy $a_0 &gt; a_1 &gt; \dots &gt; a_{2013} &gt; 0$ and $|z| \leq 1$.      I tried to approach the problem by using the reverse triangle inequality to try to isolate the leading term, which I thought should be the constant coefficient, as follows:  \begin{array} . \left|  \sum_{n = 0}^{2013} a_n z^n \right| &amp;= \left| a_0 +  \sum_{n = 1}^{2013} a_n z^n \right| \\ &amp;\geq |a_0| - \left|  \sum_{n = 1}^{2013} a_n z^n \right|\\ &amp;\geq |a_0| -  \sum_{n = 1}^{2013} |a_n z^n|\\ &amp;\geq a_0 -  \sum_{n = 1}^{2013} a_n |z^n|\\ &amp;\geq a_0 -  \sum_{n = 1}^{2013} a_0 |z^n|\\ &amp;= a_0\left( 1  -  \sum_{n = 1}^{2013} |z^n| \right) \end{array}  Then for $|z| &lt; 1$, we have that this last expression is equal to  $$ a_0\left( 1  -  |z| \frac{|z|^{2013} - 1}{|z| - 1} \right) $$  and my hope was to prove that this was always positive, nevertheless, after failing to prove it, I plotted the expression inside the parenthesis as a function of $|z|$, and found out that it changes sign in the interval $(0, 1)$.  Question  Can my approach somehow be made to work? And if not, how can I prove that the sum $\displaystyle{\sum_{n = 0}^{2013} a_n z^n \neq 0}$ under the given conditions?  Thank you very much for any help. Do individual rays of light lose energy via the inverse square law? Can wizards create their own spells? In the Harry Potter series, are wizards capable of creating their own spells, or are they limited to the spells that they're taught/learn?  I seem to remember something about Snape creating sectumsempra, but I'm not sure if that really is the case. Finding Radii of Convergence for $\sum a_n z^{2n}$ and $\sum a_n^2 z^n$ Setting: Let $\sum a_n z^n$ have radius of convergence $R$.  We have that  $$ R = \frac{1}{\underset{n \rightarrow \infty}{\limsup} \left|a_n \right|^{1/n}} $$  via Hadamard's formula for the radius of convergence.  Question: What are the radii of convergence for (i) $\sum a_n z^{2n}$ and (ii) $\sum a_n^2 z^n$?  Attempt for $\sum a_n^2 z^n$:   For ease of notation, let $R_1$ and $R_2$ denote the radii of convergence for power series $\sum a_n z^{2n}$ and $\sum a_n^2 z^n$ respectively. From Hadamard's formula, we then have  $$ R_2 = \frac{1}{\underset{n \rightarrow \infty}{\limsup} \left|a_n^2 \right|^{1/n}} = \left( \frac{1}{\underset{n \rightarrow \infty}{\limsup} \left|a_n \right|^{1/n}} \right)^2 = R^2 $$   But what about $R_1$? Creating shapefile from current dataframe extents in layout view of ArcMap? Where is the ArcGIS 10 tool for creating a shapefile from current dataframe extents in layout view?  Have looked around and the closet thing i can find is Toolbox's Grid/Strip Map Index tools under Data Drive Pages.  I just want to be able to create a single polygon rectangle shp file based on the data frame (in layout view) for any given scale / page setup. How do I minimize total cost of separate flights to the same destination plus optionally accommodation? My girlfriend and I are currently living in different countries, and meet occasionally for a few days every month or so. We don't really care all that much where we are going, as long as we don't need a visa (we're both in EU), just so we are at the same place and time for a couple of days.   In short:     I'm flying from airport AAA, she's flying from airport BBB, we need to find an airport XXX (not a euphemism!) which is cheapest to fly to overall.   Bonus task: Flights are first and foremost, and we could live with a somewhat more expensive accommodation as long as we can get in and out easily. Since the accommodation cost is comparable to flight cost for such a short stay, we'd like to have some sort of rough idea what we're going to pay for a certain type of accommodation, for example three-star hotel. Layers with same coordinate system should align/overlap in ArcMap but do not? Most games build on other games' successes and many are downright clones. Where is the limit of imitation before legal issues come into play? Is it down to literary or graphic work like characters and storyline that cause legal problems, or can someone actually claim to own gameplay mechanics?  There are so many similar clone games out there that the rules are probably very slack or nonexistent, but I'd like to hear the views of more experienced developers / designers. Number theory counting sums of squares modulus This is an extra question from an old examination paper:     VI. Let $n&gt;1$ in $\mathbf{Z}$ and let $r(n) = \#\{(a,b)\in \mathbf{Z}^{2};n=a^{2}+b^{2}\}$ Let also $n=n&#39;n&#39;&#39;n&#39;&#39;&#39;$ where $n&#39;,n&#39;&#39;,n&#39;&#39;&#39; \in \mathbf{N}$ and   $p|n&#39; \Longrightarrow p\equiv 1\mod 4 ; p|n&#39;&#39; \Longrightarrow p=2 ; p|n&#39;&#39;&#39; \Longrightarrow p\equiv 3 \mod 4$   for $p\in \mathbf{N}$ prime.   i) Show that if $n&#39;&#39;&#39;$ is not a square, then $r(n)=0$.  ii) Show that if $n&#39;&#39;&#39;$ is a square and $n&#39; = 1$, then $r(n)=4$  iii) Show that if $n&#39;&#39;&#39;$ is a square and $1&lt;n&#39;=p_{1}^{e_{1}}\ddots p_{k}^{e_{k}}$ where $p_{1},...,p_{k}$ are different primes in $\mathbf{N}$ and $e_{1},...,e_{k} \in \mathbf{N}$, then it holds that $r(n)=r(n&#39;)=4(e_{1}+1)\ddots (e_{k}+1)$    I am completely dumbstruck and can't see how to begin (and neither did an older student who took this exam and whom I asked for hints). Help is greatly appreciated. What is the reasoning behind restricting the number of migration paths? On the religion and culture stackexchange sites, many, many users will initially ask a question in a place that's kind of off-topic there, but are fully on-board elsewhere.    Christianity.SE, for example, gets a lot of general philopsophical questions that would be better on Philosophy, historical questions that might be better on History.SE, and hermenutical questions that are better on BH.SE.  It is, however, unreasonable in my mind for a user with a question to be required to have domain expertise on which sub-site each has. Indeed, even amongst users with a high amount of knowledge, there can be disagreement.  Likewise, , but as just about every one of those is in beta, the user would have to be very saavy (or would have to find that post) in order to nail it every time.  That said, recommending that a question be moved is much harder than it needs to be.  I have seen business rule logic that says, for example,    migration paths only exist to graduated sites (ergo politics, money, history, and quantitative finance wouldn't qualify) migration paths seem to be limited to 5.   Anything not on a migration path requires a moderator (and not just a high rep user) to get involved.  So, what is the reasoning behind this?  Note, I'm not asking for a solution (although the obvious solution would be to allow migration paths to any established site, beta or not, i.e. a VTC as off topic b/c it belongs on another site should allow you to pick any other site) - I just want to understand the business purpose in restricting migration paths to a small, predefined number for everyone other than a mod. How can I move my /home directory to another partition if it's already part of the / partition? I have a wonderful running Maverick Meerkat install going on right now. I want to move my /home to another partition as per many suggestions.   How can I go about doing this without reinstalling the entire Ubuntu system? Can I simply create the partition with gparted and then change the mount point of /home in fstab to reflect it or is it a bit more difficult? cp -r is meant to copy files recursively, and cp -R for copying directories recursively. But I've checked, and both appear to copy both files and directories, the same thing. So, what's the difference actually? Relativistic Mass and Dark Matter In a question  Ron Maimon comments that "relativistic mass makes gravity, not rest mass."  If so, does that mean that the faster that stars orbit the galaxy the larger the relativistic mass of the galaxy therefore more gravity therefore the stars orbit even faster therefore the gravity gets even more therefore the stars keep on getting faster ...  So the speed of stars and mass of galaxy would be correlated with age and history of the galaxy or galaxy clusters and that's why calculations of galaxies' masses don't add up. Let $X$ and $Y$ be topological spaces. A function $f: X \rightarrow Y$ is defined as continuous if for each open set $U \subset Y$, $f^{-1}(U)$ is open in $X$. This definition makes sense to me when $X$ and $Y$ are metric spaces- it is equivalent to the usual $\epsilon-\delta$ definition. But why is this a good definition when $X$ and $Y$ are not metric spaces?  How should we think about this definition intuitively?