bounded julia set $f(z)=z^2 + c$
For $x$ and $\lambda$ complex, if $|x| \gt \frac{1}{2} + \sqrt{\frac{5}{4} + |\lambda|}$ then $|x^2+\lambda| \gt |x| +1$
Consider I've set variable site and needs to be printed by echo or printf, but If I use single quote to write something and want to use variable then how?  Example:  $ site=unix.stackexchange.com $ echo "visit:$site" visit:unix.stackexchange.com   But If I use single quote:  $ echo 'visit:$site' visit:$site   Then we know that '' is strong quote and will not expand the variable   I've tried something:  $ echo 'visit:"$site"' visit:"$site"   but do not succeed. So, I am looking for way to print value inside variable while using single quote. I have seen a few  here on Meta&nbsp;Stack&nbsp;Exchange that cover parts of this, but they are often too local, and none of them seem to cover all the relevant scenarios.  I will break it up into multiple parts in order to make this more specific:     When should I vote on a question:   What are the qualifications for a question to be deserving of being up-voted? When shouldn't I vote up on a question? What are the things that would cause a question to need to be down-voted?   How should I go about down-voting the question (do I wait a little while to give the OP a chance to change it, or do I down-vote it immediately)?  When shouldn't I vote down on a question?  When should I vote on an answer:   What are the qualifications for an answer to be deserving of being up-voted? When shouldn't I vote up on an answer? What are the thing that would cause an answer to need to be down-voted?   How should I go about down-voting the answer (do I wait a little while to give the OP a chance to change it, or do I down-vote it immediately)?  When shouldn't I vote down on an answer?  When should I vote on a comment:   While votes on comments do not affect reputation points, it might be useful to new users to know when to up-vote them.    It seems that a full, comprehensive list of these would be invaluable to new users looking to figure out how the voting system works, but this list seems to be missing from the meta site. Based on , I figured that there might be multiple questions for distinct locales. Why do the most common transactions to or from bank accounts in the US require waiting one or more days before they are completed? In the information age, it seems like we should be able to transfer money instantly (or nearly so). Imagine you're trapped inside a free falling elevator. Would you decrease your impact impulse by jumping during the fall? When? XML attribute vs XML element Club filter of $\kappa$ is $\kappa$-complete I'm trying to show that club filter of $\kappa$ is $\kappa$-complete for uncountable regular cardinal $\kappa$:  Let $\kappa$ be uncountable regular cardinal, let $C(\kappa)$ be the club filter generated by $\kappa$.  To show that $C(\kappa)$ is $\kappa$-complete it is enough to show that for every sequence $\langle \alpha_i\mid i&lt;\gamma\rangle$ with $\gamma&lt;\kappa$ and $\alpha_i$ club of $\kappa$ the set $\alpha=\bigcap_{i&lt;\gamma}\alpha_i$ is a club of $\kappa$.  Showing that $\alpha$ is close is easy:     If $\beta_n$ is a sequence in $\alpha$ then for every $i$ we that $\beta_n$ is a sequence in $\alpha_i$, because $\alpha_i$ is a club it is close hence $\lim \beta_n$ is in $\alpha_i$ for every $i$ so it is also in $\alpha$   But I have a problem with unboundedness, my guess will be for each $\lambda&lt;\kappa$ to find a sequence for each $\alpha_i$ such that all of the sequences converge to some $\mu&gt;\lambda$, that way $\beta&lt;\mu\in\alpha$. I think I'll have to use the fact $\kappa$ is regular, but I don't know how to proceed and prove my idea.  So, is my idea correct, and if yes how can I proceed? Is there an ideal PWM frequency for DC brush motors? I was curious about how other people use the this keyword. I tend to use it in constructors, but I may also use it throughout the class in other methods. Some examples:  In a constructor:  public Light(Vector v) {     this.dir = new Vector(v); }   Elsewhere  public void SomeMethod() {     Vector vec = new Vector();     double d = (vec * vec) - (this.radius * this.radius); } How to solve "Unable to find expected entry 'restricted/binary-1386/Packages' Wrong sources.list entry or malformed file"? How to show $\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$ I have been asked by a client to implement some views for reporting purposes, the views will be accessed via PowerBI, Excel and SSRS. The designated user will only have access to the view and no underlying tables must be available to the user.  The problem I have encountered in that the SQL within the view touches 3 different schemas (All within the same database):   Pupil Provider  Security   The view is:  CREATE VIEW dbo.vTestPermissions AS SELECT a.Column1,        b.Column1,        c.Column1 FROM Pupil.Table1 a JOIN Provider.Table2 b ON a.Column1 = b.Column1 JOIN Security.Table3 c ON a.Column1 = c.Column1   The owners of the Tables/View are as follows:   Pupil.Table1 - Owner Pupil Provider.Table2 - Owner Provider Security.Table3 - Owner Security vTestPermissions - Owner dbo   When I select from the view I get an error:     The SELECT permission was denied on the object 'table3', database   'TEST', schema 'Security'   I have tried giving SELECT permission with and without the GRANT option to the schema, and the tables, but that makes the underlying tables available to the user.  Any help on this will be greatly appreciated. Why will Ubuntu no longer measure file size unit as byte, megabyte, gigabyte, etc? I read on  that Ubuntu will no longer use the familiar file size units we all know by now (kB, MB, GB, TB) and switch to a different IEC standard (KiB, MiB, GiB, TiB). If this is true, I would like to know what's the reasoning behind this change, and the impact (if any) this change has, especially with multiplatform applications or applications run with Wine. When should I use an em-dash, an en-dash, and a hyphen? I generally know how to use a hyphen, but when should I use an en-dash (–) instead of an em-dash, or when should I use a hyphen (-) instead of an em-dash (—)? What terminal command or program can list an SSD's Power On Hours? I'm looking to script using the unix shell the retrieval of SSD (and HDD) data that disk utility shows in the information window.    I'm immediately interested in the Power On Hours and Power Cycle, but if all the data comes from one data structure or tool, so much the better. The usual tools diskutil info disk0 and ioreg -l are not producing the "of interest" values listed in the screen shot above.  Is this information available from any of the built in OS X terminal tools or do I need to locate an open-source package that makes the same API calls to get this level of detail about a Mac drive? Is it a weakness to use a single shared secret for protecting messages using a Encrypt-then-MAC scheme?    Assuming a system is using AES-256-CBC and a SHA1-HMAC and the same secret key for both operations.  Upon intercepting one of these messages and attacker could brute force this secret key by trying to solve the HMAC or by successfully decrypting the first block of the ciphertext.  Performing  a decryption on a single block of AES-256 should be a lighter operation than performing a SHA1-HMAC on a potentially large message.  Therefore AES-256 is ideal for a massively parallel brute-force attack and the use of the SHA1-HMAC doesn't hurt the system.  Is this approach sound, or is there an attack that has not been taken into consideration? I've seen lots of examples of making an entire regular expression case-insensitive.  What I'm wondering about is having just part of the expression be case-insensitive.  For example, let's say I have a string like this:  fooFOOfOoFoOBARBARbarbarbAr   What if I want to match all occurrences of "foo" regardless of case but I only want to match the upper-case "BAR"s?  The ideal solution would be something that works across regex flavors but I'm interested in hearing language-specific ones as well (Thanks )  Edit  The link Espo provided was very helpful.  There's a good example in there about turning modifiers on and off within the expression.  For my contrived example, I can do something like this:  (?i)foo*(?-i)|BAR   which makes the match case-insensitive for just the foo portion of the match.  That seemed to work in most regex implementations except Javascript, Python, and a few others (as Espo mentioned).    The big ones that I was wondering about (Perl, PHP, .NET) all support inline mode changes. What to do with bounty on question which is no longer relevant? When using zero as a quantifier, is it correct to use the singular form on the object of the quantifier, or the plural form?  It sounds confusing when I put it that way, but what I mean is: Which is correct?   Your password expires in 0 days. Your password expires in 0 day.   Essentially I suppose I'm asking, does "singular" mean "one" or "the opposite of more than one", as zero is not "plural" in the traditional "more than one" sense?  I'm pretty sure "days" sounds correct, but I can't be sure. ! LaTeX Error: Undefined color `BLACK' i have written all the text in black color, but i get this error several times in the same page:  ! LaTeX Error: Undefined color `BLACK'.   i tried to solve it by writting this: \definecolor{black}{gray}{0,0,0} but it didn´t work.   what should i do? What are recursive triggers? How can recursive triggers be controlled? What are recursive triggers? How can we control them, or prevent infinite recursion?  Are these any risks inherent in them, and any limits that we should be aware of?  Please explain with an example.