Does there exists a function $f:\mathbb{\bar D}\to\mathbb{C}$ such that  (1) $f$ is holomorphic in $\mathbb{D}$ and $f$ is continuous in $\mathbb{\bar D}$ where $\mathbb{D}$ is the unit disk in the complex plane;  (2) for any $\delta&gt;0$, $f$ has no analytic continuation to $B(0,1+\delta)$.  Since I cannot prove whether there is such a function or not, I tried some constructions. My first attempt was to construct a power series that has convergence radius $1$ and continuous in the closure of the unit disk. But my results so far have at least one singularity on the boundary. Then I tried to find an entire function with infinitely many zeros, and then identify its domain with the unit disk by a conformal equivalence, for example,  $$\sin\pi\frac{1-z}{1+z}$$  Then there is a convergence point of the zeros on the boundary. But the singularity problem still remains unsolved.  Any help is appreciated.
So I need to find the Convergence Radius and Convergence Domain of the complex power series: $\sum\limits_{n=0}^\infty \frac{1}{2^{n}} z^{2^n}$  I've tried looking at the individual parts of the series and rewriting it somehow but couldn't find a way.  It can probably be solved, after a step or two, by the formula $R=\frac{1}{\displaystyle\limsup_{n\rightarrow \infty}\sqrt[n]{|a_n|}}$ .  Thanks.
If $(a,b)=1$ then prove $(a+b, ab)=1$. Is Mana Weaving ok if it's followed by a thorough shuffle? My friends and I are relatively new to MtG. At some point, one of them introduced us to the idea of mana weaving, and we'd do this to declump our decks prior to a very thorough shuffling. However, at the Theros pre-release, one of us was asked not to do this, and we learned it was frowned upon and ceased to do it.  I just now came across , and it sounds like mana weaving's only bad if you use it to leave your deck in an even distribution, and it's OK if your deck is then thoroughly shuffled. In hindsight, the judge may have simply thought my friend wouldn't have shuffled afterwards, but at the time I came under the impression it was frowned upon even if you did shuffle afterwards.  So: is mana weaving my deck OK, if I shuffle it very thoroughly afterwards? I've got some lenses of brand X, but I've just got a new camera of brand Y. How can I tell if it's possible to use my lenses on my camera? I accept that I may lose a lot of automatic functionality like autofocus, aperture control and metering when using an adapter to connect the two. Trying to find the original story (I read it in Russian translation, original was most likely English unless it was Lem).  The story plot had artificial birds designed to serve as cops. The birds started attacking humans who were percieved as being aggressive towards anything alive. So they created more advanced birds to protect against the first ones. This worked for a while until the second kind started attacking humans as well. It ended with the idea that they would need another generation to attack the second-generation birds.  The story wasn't very long. I read it a while back (mid-1980s, which means the original was written even earlier, probably before 1980).  Despite a somewhat Asimov-like "misbehaving robots" topic, I'm pretty sure it wasn't Asimov. Why isn't Force Speed used more often? Signed to unsigned conversion in C - is it always safe? Suppose I have the following C code.  unsigned int u = 1234; int i = -5678;  unsigned int result = u + i;   What implicit conversions are going on here, and is this code safe for all values of u and i? (Safe, in the sense that even though result in this example will overflow to some huge positive number, I could cast it back to an int and get the real result.) How to prevent any game from running on a PC I am looking for an unbreachable way to disable the games running on my PC. Even games which require quite a low amount of graphics say 256MB should not work. It is to put restriction on gaming on my PC. I have a graphics card of 1GB and  2GB RAM and a processor of 2.7GHz with Windows 7.  Can we prevent a process from running if it takes a certain amount of graphics memory greater than a value set by user? I mean can we put restriction on games on the basis of the amount of graphics memory they use. Also the method should be applicable to all games (ignoring the chess and other small games like that. Even if it gets blocked, then also no problem.  This is to prevent myself from playing games. But I need other software (non game) to run properly. What is the number of strings at size $n$ that is constructed from ${a,b,c,d}$ and there is an even num of $a$ What is the number of strings at size $n$ that is constructed from ${a,b,c,d}$ and there is an even num of $a$?  I have tried to answer it as recursion formula in the following logic:  In order to build $ A(n) $, I will split into several cases:   if the string starts with $a$, then I will need another $a$ to make an even number of $a's$. so we get $aa[A(n-2)]$ meaning 2 $a's$ at the start + a valid string at the size of $n-2$. if it starts with $b,c,d$ we get $b[A(n-1)]$ + $c[A(n-1)]$ +$d[A(n-1)]$, meaning a one of the letters + a valid string at the size of $n-1$.   So we will get a recursion formula that looks like that:  $A(n) = A(n-2) + 3A(n-1)$  I'm not 100% on my answer, am I right to approach it in that direction? I added this to /etc/crontab on a few different linux &amp; freebsd systems:  # monthly reboot: 3rd Tuesday of every month 56 07 15-21 * 2 root /sbin/shutdown -r now   I want a reboot on the 3rd TUESDAY of every month.  However, all the systems rebooted on the 3rd Wednesday of this month (the 19th).  What am I doing wrong?  Update: Thanks to Ranon's answer below, looks like the below revision will work, can anyone confirm or is there an even better way of doing it?  # monthly reboot: 3rd Tuesday of every month 56 07 15-21 * * root test $(date +\%u) -eq 2 &amp;&amp; /sbin/shutdown -r now How do we control web page caching, across all browsers? Connect iPhone to Mac Without Charging I am developing iOS apps and I hate, that always when I connect my iPhone to my Mac to install and test an app, the iPhone gets charged. Is there any possibility to connect my iPhone to my Mac without charging the phone?    My Environment: -  iPhone 4S (No Jailbreak) -  MacBook Air3,2 (Late 2010) Isomorphism between complex numbers minus zero and unit circle How do we show that $\mathbb{C}^{\times}$ and $S^{1}$ are isomorphic as groups? How should a family with young children apply for UK visas? I am trying to achieve something like this:     This image is linked from .  also provides a solution and seems simpler. Both answers deal with the algorithmicx package however. I am interested in the solution for the algorithm2e package.   I read the documentation of the algorithm2e package but didn't find an answer.   How can I achieve the colored effect?  EDIT:  Here is sample code to create a minimum working example.  \documentclass{article}  \usepackage[ruled]{algorithm2e} % http://www.ctan.org/pkg/algorithm2e  \begin{document}  \begin{algorithm}[h]  \caption{Evolutionary algorithm}   initialize population \;  \For( \emph{Evolutionary loop}){$g := 1$ to $G_{max}$}  {     do things \;     evolve population \;  }  celebrate \; \end{algorithm}  \end{document} How do I stop my rim brakes making a squeaking/squealing sound? I bought a Schwinn Frontier Sport few months ago and started riding happily. After a few weeks my front rim brakes started creaking. It's so annoying in public places. My rear brake doesn't produce any sound but isn't as powerful as the front brake.  The retailer says cleaning would solve the front brake's issues and I got it cleaned, but nothing changed. Is there something I can do something myself to fix this? If $X$ takes on a Gamma Distribution, how can I find $X^2$, $X^3$, etc? Here is a sentence excerpted from ,     Teen suicide is a growing health concern. It is the third-leading cause of death for young people ages 15 to 24, surpassed only by homicide and accidents, according to the U.S. Center for Disease Control and Prevention.   I've heard people use both "people aged from X to Y" and "people ages from X to Y" quite often, but I've always been believing that only the former is grammatically correct, whereas in the latter the "ages" doesn't seem to serve as any grammatical component of this sentence. So when I see an APA paper use "ages" in that way, I am just quite surprised: I just can't believe such an authoritative and rigourous academic institution will let such an explicit (and indeed naive, even to a non-native speaker's eyes) grammatical mistake survive in their publications. I'm aware that in daily language usage one ought not to become so fussy over insignificant matters like this, but I do wonder whether it should be paid attention to in academic writings.  OR, using "ages" in that way is no longer considered a grammatical mistake? Honestly I don't think this'd be true, but if it really is, I'd be grateful to be informed. Thanks! E: Could not get lock /var/lib/dpkg/lock-frontend - open (11: Resource temporarily unavailable) I'm trying to run this command in the terminal:  sudo apt install software-properties-common   This is the error message I get:  E: Could not get lock /var/lib/dpkg/lock-frontend - open (11: Resource temporarily unavailable)   E: Unable to acquire the dpkg frontend lock (/var/lib/dpkg/lock-frontend),     is another process using it? Elsevier has started circulating  as a consequence of the  to the editors of their journals:     Subject: US editors and reviewers can no longer handle submissions by   authors employed by the Government of Iran            Dear Dr Bruno Granier,      The Office of Foreign Assets Control (OFAC) of the US Department of   the Treasury administers and enforces economic and trade sanctions. As   a result of OFAC sanctions we have been made aware that US editors, US   Elsevier staff and US reviewers are now unable to handle scientific   manuscripts where any of the authors are employed by the Government of   Iran. This includes the research departments of the various oil and   gas companies which are deemed to be entities of the Government of   Iran. We realize that this OFAC regulation will cause some   inconvenience in your role as an editor but Elsevier is legally   obliged to ensure that all reasonable efforts are made to avoid   submissions from Iranian government agencies and companies being   handled by US editors, US Elsevier staff and US reviewers. Please be   aware that editors, Elsevier staff and reviewers from outside the US   may still handle these manuscripts and that this OFAC regulation does   not pertain to manuscripts where the authors are based at Iranian   academic and research institutes. Manuscripts originating from a   clinical setting that are not government run, for example, a hospital   or clinical practice are also exempt from this regulation.      To view the official OFAC regulation, please click here. In practice   the result of these sanctions will mean that:      • Submissions where any author is based in Iran, and is not at an   academic and research institution, cannot be handled by US-based   editors, US Elsevier staff, US reviewers, or any US citizens based   outside of the US.      • If an Iranian author has dual affiliations (eg. university and   government), their submission cannot be handled by US-based editors,   US Elsevier staff, US reviewers, or any US citizens based outside of   the US.      • Affiliations of Iranian authors should therefore be checked, and any   manuscripts which fall under this OFAC regulation delegated to a   non-US editor, before handling.      • When assigning reviewers, affiliations of Iranian authors should   also be checked, and any papers which fall under this OFAC regulation   should only be sent to non-US reviewers. (As an editor you should do   what is reasonable to determine the nationality of a reviewer e.g.   check their email address. This check does not extend to emailing   reviewers directly to confirm their nationality or location). Unless   there is specific knowledge that a non-US-based reviewer is a US   citizen, editors can send such submissions to reviewers based outside   the US.      • If your journal workflow involves all submissions being handled by   US-based Elsevier staff, they will reject these manuscripts outright   before they reach you.      • Should there be no suitably qualified editor or reviewer, please   reject the manuscript outright.      When rejecting manuscripts which fall under this OFAC regulation   please use the new EES Decision Term "Reject - OFAC Sanctions" and the   following text:      "As a result of OFAC sanctions all editorial staff who are US-based/US   nationals are unable to handle scientific manuscripts which are   authored by Iranian scientists, employed by the Government of Iran.   Based on this OFAC regulation we are unfortunately unable to handle   your manuscript. We wish you success with your submission to another   Journal."       We apologize for the inconvenience this may cause. If you do have any   questions please contact your Publisher.       Sent on behalf of Dan Lovegrove      Cretaceous Research   Has there been any public response, by US editors or reviewers, stating whether they will obey (or not) the instruction? Also, does this letter conflict with the  of the  (all Elsevier journals are members of COPE as of January 2008)? Is there a way of moving unwanted villagers out faster? Is there any way to speed up this process or indirectly 'force a villager to move out'?  I know they move out if it's time for a new one to move in, and I know you can't actually 'force' them persay.  I have a villager who has caused nearly all my other villagers to wear his.. rather hideous 'kiddie shirt'. ((the character's default shirt)) Aside from that his home blocks the perfect spot, very close to my river, for building a convenient bridge...  I've taken to pushing him, hitting him with a net, and I've been trying to find a Toy Hammer... He wanted to leave once and I told him to go, but then he said he wouldn't leave until I, "made an effort to get to know him" or some BS..  Are there any other ways I can get an unwanted, 'pesty', villager to leave town?