Prove that for positive integers $m, n$ and two positive numbers $p, q$ satisfying $p+q = 1$ we have  $$(1 − p^n)^m + (1 − q^m)^n \ge  1.$$  Using binomial theorem, we have $1-C^m_1*p^n+C^m_2*p^2n-\cdots $ for $(1 − p^n)^m$. And same logic for the second term of the equation but they don't cancel each other out.  Is there anything I am doing wrong? (this is a practice from a probability class)
Let $p, q \in \mathbb R$ be positive reals for which $p + q = 1$. How to prove that for any two natural numbers $n, m$ the following inequality is true?  $(1 - p^n)^m + (1 - q^m)^n \ge 1$  I don't have a big knowledge about solving inequalities, so I tried to use cauchy-schwarz inequality, binomial theorem and some other baisc techniques, but it lead me nowhere. I've been thinking about it for a long time and now I'm completly stuck.
Rollback Committed transaction in SQL Server Is it possible to rollback a committed transaction?  I have deleted all the data in a table. The delete statement is inside Begin Transaction and I have committed the transaction with a commit transaction command. Now is it possible to rollback and get the data back? Tony's suit is an engineering marvel, and they explain many facets of the technology to help give legitimacy to the special powers, abilities and weapons it has.  I never read the Iron Man comics, but in the movie they really don't have a technological explanation for how he miraculously seems to be unaffected by crushing G-forces of sudden acceleration, the inertia of sudden stops and hair-pin turns, and especially the blunt force trauma from getting smashed in the face with Thor's hammer.  Certainly it appears the suit takes punishment, but Tony always remains unscatched, never a collapsed lung, broken bone or even a bloody nose.  In my infantile understanding of theoretical physics, the same technology that would be used to counter G-forces and sudden blunt force trauma to the body inside would be the very same technology used for  which in my honest opinion would be a much more stunning technological achievement than his heralded Arc Reactor.  Was their ever an explanation proferred for this and if so was it indeed attributed to Anti-Gravity? How to demonstrate that there is no all-prime generating polynomial with rational cofficents? Eliminating non-integer solutions to $ab / (2\sqrt{ab} + a + b)$ I am unable to find the link for downloading Ubuntu 16.04 onto my   desktop/laptop. I am able to see the link only for 18.04, but I need 16.04. How to install a list of packages using apt-get? This post is an expansion of  For many graduated sites (eg Physics), moderators do not want to apply the unilateral close vote in all cases--it is better to let some community votes pile on first.  We only use the unilateral in obvious cases then. This renders the CV queue useless to us. If we &quot;skip&quot; something, we can't get back to it. If we say &quot;do not close&quot;, it's removed from the queue and our community can't see it. If we use &quot;close&quot;, we are using a unilateral mod vote--we don't want to do that. What I propose is a set of &quot;next/previous&quot; buttons, that let us navigate the queues, looking for closeable questions, and coming back to the others later. Thoughts? Update and bounty reason Due to the recent Great Flag Overhaul, mods no longer see close flags in the flag queue. Which means that the only way to get to them is via the review queue 1 Shog's solution is ideal in this case; let mods view the close queue as a list. (In fact, a list similar to the old flag queue -- which shows a list of mods who have seen the post and what mod actions have already been taken -- would be great) On Physics, the majority of the flags that we get are VTC flags. And the community isn't always able to close things on their own, so we have to step in. However, powering through the close queue isn't an option; because &quot;skip&quot;ing a post2 leads to it being dumped into the void (I can't get back to it unless I have a link). Extremely inconvenient. Could the workflow here be improved? 1. The /tools listing for posts with outstanding close votes doesn't work because it doesn't list posts which have been flagged but not VTCd 2. which I may want to take a closer look at later; gotta be careful with the binding votes. Why does my Task Manager window outline keep disappearing? Possible Duplicate:          I'm not sure what the proper term for the window outline is (chrome, I think?), but it keeps disappearing.    As you can see, theres no File->Exit or buttons that allow me to minimize or close this dialog. So instead it stays on top of everything else (unless I 'Switch To' another window). There is also no Processes tab or anything.  Since you cant right click the toolbar or bring up another instance of Task Manager, the only way to actually kill this dialog seems to be restarting. However the next time I bring up Task Manager, it will still refuse to go away.  Anyone know whats going on? I'm running 32-bit Vista SP1. What is a word for someone without allegiance? Is stopwatch benchmarking acceptable? Does anyone ever use stopwatch benchmarking, or should a performance tool always be used?  Are there any good free tools available for Java?  What tools do you use?  To clarify my concerns, stopwatch benchmarking is subject to error due to operating system scheduling.  On a given run of your program the OS might schedule another process (or several) in the middle of the function you're timing.  In Java, things are even a little bit worse if you're trying to time a threaded application, as the JVM scheduler throws even a little bit more randomness into the mix.  How do you address operating system scheduling when benchmarking? I need a graduate level, mathematically rigorous textbook on multivariate analysis and inference to enhance myself. I've been reading the  and doing the problems within, but I need a book with other focuses. Topics like famous distributions (Wishart, Wilks lambda, etc.), hypothesis testing, some theory on estimation (point, interval), and other more modern materials are welcome. I've checked , but the OP there was looking for something useful for his psychological analysis, which is not exactly what I want here. Currently I have the , so I would also like to hear the comments about this book and its exercises. Thank you. Can somebody explain "leveraged debt investment positions" and "exposures" in this context for me, please? "The strong bond performance has led to a surge in leveraged debt investment positions that are ultimately funded by the banks' interbank exposures and WMPs. But nobody really knows how levered these positions are, who has financed them, and by how much," S&amp;P said. "The contagion risks for the financial sector could be high."  source: Another question I am struggling with:  Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be defined in a neighborhood of $a$ (except maybe $a$ itself) and suppose that, $\lim_{x \rightarrow a}\left(f(x)+\dfrac{1}{\left|f(x)\right|}\right)=0$. Find $\lim_{x \rightarrow a}f(x)$, and prove by definition, that this is indeed the limit.    Thank you all for your answers!!  But.. How can I prove by definition that this is indeed the limit? take $\epsilon&gt;0$, I have to show that there exists a $\delta&gt;0$ such that, $|x-a| \leq \delta$ implies $|f(x)+1| \leq \epsilon$. now, I do know that there exists an $\delta_1&gt;0$, such that $|f(x)+\frac{1}{|f(x)|}|&lt; \epsilon$.Or, $\frac{\epsilon}{k}$ for some constant $k$ But, how can I continue from there? Plot Details/Summary I only watched an episode or two of this one, so I can't recall a whole lot about it.  The protagonist is a former astronaut of some sort, who makes it his mission to clean up the crime in his city.  He might have been a police officer in his &quot;new life&quot; or he might have decided to become a sort of quasi-superhero.  In either case, I distinctly recall his space suit being the gimmick that makes him an effective crime fighter in the show.  I seem to recall the protagonist being a young, dark-haired man, and I think he had a friendship or an alliance with a young woman (maybe a fellow cop, or someone from the space program?).  I don't think there were alien beings in the show.   The criminal threats were all quite terrestrial, IIRC. Timeframe and other Publication Details This was a syndicated tv show I saw on American television, probably around the late 90s to early 2000's.  I believe the show was filmed in Canada, though I'm not certain.  I don't think it lasted very long - it was pretty dreadful.  I can say for certain the show is not Space Cop or Gerry Anderson's Space Precinct. Is $D_n$, the dihedral group of order $2n$, isomorphic to a subgroup of $S_n$ ( symmetric group of $n$ letters) for all $n&gt;2$? CLI path to ftp network connection I've setup a connectio to an FTP server in Nautilus / Nemo / Caja, the file manager. Now I can browse the contents via this file manager.  How can I browse these files via the command line? What is the path to this network connection? Is this possible, is this a system connection, or specific to the file manager, and do I have to setup a separate FTP connection to do that? If I open this connection in Caja, I see it in Nemo as well, so it seems like a system connection. The category Set has the property that any morphism f can be decomposed into an epimorphism $e$ and a monomorphism $m$ with $f$ = $m\circ e$. (The intermediary set object is the image of $f$.)  Is there a name for this construction?  Is there a name for this property of categories?  In Set, the intermediary object is unique up to isomorphism. Is this the case for all categories with the property? It's not difficult to show that  $$(1-z^2)^{-1/2}=\sum_{n=0}^\infty \binom{2n}{n}2^{-2n}z^{2n}$$  On the other hand, we have $(1-z^2)^{-1}=\sum z^{2n}$.  Squaring the first power series and comparing terms gives us  $$\sum_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}2^{-2n}=1$$  that is,  $$\sum_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$$  My question: is there a more direct, combinatorial proof of this identity?  I've been racking my brains trying to come up with one but I'm not having much success. How do I create files using the lines in a .txt file? For example I have a file called fileNames.txt.  cat &gt;fileNames returns  abet  able  abacus   How do I use fileNames to create abet, able, and abacus as .txt files?  I tried using pipes with cat and touch. With a macro such as:  \def\naive{na\"{\i}ve}   I find that the space which I would hope to follow it, is absent. So, with  the \naive approach   I get     the naïveapproach   in the output. How do I bring back the space?