I am on hard mode and I have been exploring underground jungle for 3 days.  I cant find any Bulbs, and I think I am prepared to kill it now.  How do I find the Plantera Bulb in the easiest way?
I have been playing on hardmode for a while and have beaten the three  a couple of times. But I have yet to find a . It's getting really frustrating.  Does anyone have any methods to finding a Plantera Bulb?
How to check if a string contains a substring in Bash What does "static" mean in C? Server 2008 Net Send or Msg? I have a Windows 2008 server running as a domain controller. The details are as follows:  Domain: corp Server Name: oxygen   The workstations are all running Windows XP SP3 and have fixed IP addresses.  I am trying to use the net send functionality to be able to send simple messages to either individual machines/users and also to all machines. This is so I can send a message to a user to alert them about something, or likewise alert everyone of something such as the server being rebooted.  Is this possible using Windows Server 2008? If so, what would the command be? Can I preemptively pay my credit card bill before a charge is posted? Factor analysis and regression Suppose $X, Y$ are independent random variables with $X\sim NB(r,p)$ and $Y\sim NB(s,p)$. Then $$X + Y \sim NB(r+s,p)$$  How do I go about proving this? I'm not sure where to begin, I'd be glad for any hint. How to attribute, give credit to creative commons/copyleft/public domain content for web/print? Edit:   To be extremely succinct: How to credit imagery used on a business card or ballpoint pen?      Inspired by  I started to think:  How do you attribute and give credit, when you use images and resources that are Creative Commons, copyleft; are in the public domain or have variation of "free" licensing?   (Some of the answers to the above questions grazes that question but it is not really the main issue in that question).  How do you attribute - say -:    a background tiled image for web? a background tiled image for print?   (the point here being tiny-weeny images)   an icon set web? an icon set print? To make it more fiddly: tiny images you might use for t-shirts, printed objects such as ballpoint pens, t-shirts, keyrings, letterheads?   For web; there seems to be divided between those who think that in the source code is fine and those who do not. For web you could make a link somewhere discreet that says "credits". This does not really work for print. If you enthusiastically stand on the shoulders of giants, and use what is legally yours to use, your printed leaflet would be bogged down in 6point text attributions.   (Yes, there are differences between countries; I am asking on a general note.)   Edit: I could add GNU licenses, but that is usually pretty straightforward, as it is mainly concerned with software, code, programming snippets, digital programmable objects etc. Came across this little practice exercise, and I couldn't properly convince myself of this relation:  Let $X,Y \subset \mathbb{R}^n$ and $g:X\times Y \rightarrow \mathbb{R}$. Show that $$\sup_{y \in Y} \inf_{x \in X}g(x,y) \leq \inf_{x \in X} \sup_{y \in Y} g(x,y).$$  My thinking was starting with $\inf_{x \in X}g(x,\overline{y}) \leq\sup_{y \in Y} g(\overline{x},y)$, but does that even hold for all $\overline{x} \in X$ and $\overline{y} \in Y$? I typed up an assignment with a lot of numbers in LaTeX and turned it in to my adviser.  When he returned it to me with some corrections, one of which was a lot of $ around my numbers.  I understand that $ are necessary around some mathematical formulas, but I was just using numbers like -2 and 4.  I did not see any change in the font of the numbers when I added the $ either.  Since my adviser did not want to give me an explanation, what is the rationale? Erdős-Straus conjecture The  (ESC), states that for every natural number $n \geq 2$, there exists a set of natural numbers $a, b, c$ , such that the following equation is satisfied:  $$\frac{4}{n}=\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\tag{1}$$  The basic approach to solving this problem outlined by Mordell [Ref1] is described below  By defining $t$ and $m$ as positive integers greater than zero and $q$ a positive integer greater than one we can observe that  a) There is always a solution for even $n$, since if $n=2^qt$ we have the trivial solution $$\frac{4}{4t}=\frac{1}{t}$$  In the remaining case $n=2(2t+1)$, a solution in the form of two Egyptian fractions can always be found  e.g. $$\frac{4}{2(2t+1)}=\frac{2}{2t+1}=\frac{1}{t+1}+\frac{1}{(t+1)(2t+1)}$$  b) If $(1)$ is a solution for some particular prime $n$ then all composite numbers $mn$ divisible by $n$ are also solutions, thus  $$\frac{4}{mn}=\frac{1}{ma}+\frac{1}{mb}+\frac{1}{mc}$$  will also be a solution. This means that we can simplify the analysis to the cases where $n$ is a prime greater than 2.  Using Mordell's approach we have just shown that we only need to consider the cases where $n$ is prime and where $n \equiv 1 \pmod{2} \;\;[meaning \;\;n=2t+1]$  The argument continues...  Mordell goes on to show in turn that the search can be reduced further to the cases when $$n \equiv 1 \pmod{4} \;\;[meaning \;numbers \;\;n=4t+1]$$ $$n \equiv 1 \pmod{8} \;\;[meaning \;numbers \;\;n=8t+1]$$ $$n \equiv 1 \pmod{3} \;\;[meaning \;numbers \;\;n=3t+1]$$ $$n \equiv 1,2,4 \pmod{7} \;\;[meaning \;numbers \;\;n=7t+1,n=7t+2 \;or\;n=7t+4 ]$$ $$n \equiv 1,4 \pmod{5}  \;\;[meaning \;numbers \;\; n=5t+1 \;or\;n=5t+4]$$  Assembling these results together, Mordell showed that the conjecture can be proved in this context except for the cases when $$n \equiv 1,11^2,13^2,17^2,19^2,23^2 \pmod{840}$$  Mordell stated that since the first prime meeting this condition is 1009, this is proof that the conjecture holds for $n&lt;1009$.  This basic approach can be pursued further. Other workers have shown that the conjecture holds for much higher values of $n$ using similar methods as can be seen on the above Wikipedia page.   Note that other intermediate results can be constructed from the above congruence's, e.g. $n \equiv 1 \pmod{24}$.  The question is:  Are there any other elementary approaches to solving this problem than the one outlined by Mordell (and described above)?  [Ref1] Louis J. Mordell (1969) Diophantine Equations, Academic Press, London, pp. 287-290. Why do we get the same differential equations from both principles? Surely there is a fundamental connection between them? When written out, the two seem to have nothing in common.   $$\sum _i ( \mathbf F _i - \dot{\mathbf p}_i) \cdot \delta \mathbf r _i = 0$$  $$S[q(t)] = \int ^{t_2} _{t_1} \mathcal L (q,\dot{q},t)dt$$  After playing with d'Alembert's principle  we find that we can rewrite the whole thing as $$\sum _i \left[ \frac{d}{dt} \left( \frac{\partial T}{\partial \dot{q}_i} \right) - \frac{\partial T}{\partial q_i}-Q_i\right] \delta q_i$$  This can further be rewritten under certain conditions so we get the exact form of the E-L equation.   It seems to me that both ways of arriving at the result are fundamentally different.   A function must obey the E-L equations in order to minimize the action over a path, but when we look at the virtual work, it appears that they come from the fact that (quoting Goldstein) "particles in the system will be in equilibrium under a force equal to the actual force plus a 'reversed effective force'."  I think I understand the principle of stationary action, I can see how it leads to the E-L equations, but d'Alembert's Principle seems so arbitrary, I can't see any motivation for it. Is there a way to find comments you made on YouTube? Call to a member function on a non-object So I'm refactoring my code to implement more OOP.  I set up a class to hold page attributes.  class PageAtrributes  {   private $db_connection;   private $page_title;      public function __construct($db_connection)      {         $this-&gt;db_connection = $db_connection;         $this-&gt;page_title = '';     }      public function get_page_title()     {         return $this-&gt;page_title;     }      public function set_page_title($page_title)     {         $this-&gt;page_title = $page_title;     } }   Later on I call the set_page_title() function like so  function page_properties($objPortal) {         $objPage-&gt;set_page_title($myrow['title']); }   When I do I receive the error message:     Call to a member function set_page_title() on a non-object   So what am I missing? Reading the question posted  left me with a more general question:  Given the professional title and name: Dr. (First Name)(Last Name), is there some way to differentiate between the holder of a philosophical doctorate and a medical doctor? Wouldn't it be more appropriate for a PhD holder to have the title (First Name)(Last Name), PhD? Why are second order linear PDEs classified as either elliptic, hyperbolic or parabolic? Is there a geometric interpretation of second order linear partial differential equations which explains why they are classified as either elliptic, hyperbolic or parabolic, or is this just a naming convention? That is, do they have any relation with actual ellipses, hyperbolas and parabolas? Memory layout of a .NET array What is the memory layout of a .NET array?  Take for instance this array:  Int32[] x = new Int32[10];   I understand that the bulk of the array is like this:  0000111122223333444455556666777788889999   Where each character is one byte, and the digits corresponds to indices into the array.  Additionally, I know that there is a type reference, and a syncblock-index for all objects, so the above can be adjusted to this:  ttttssss0000111122223333444455556666777788889999         ^         +- object reference points here   Additionally, the length of the array needs to be stored, so perhaps this is more correct:  ttttssssllll0000111122223333444455556666777788889999         ^         +- object reference points here   Is this complete? Are there more data in an array?  The reason I'm asking is that we're trying to estimate how much memory a couple of different in-memory representations of a rather large data corpus will take and the size of the arrays varies quite a bit, so the overhead might have a large impact in one solution, but perhaps not so much in the other.  So basically, for an array, how much overhead is there, that is basically my question.  And before the arrays are bad squad wakes up, this part of the solution is a static build-once-reference-often type of thing so using growable lists is not necessary here. Problem:  Let $A_{n.n}$ be square complex matrix. Prove the following: $$\left \| A \right \|=\left \| A \right \|_{HS}\Leftrightarrow  rank(A)\leqslant 1$$. Where $\left \| . \right \|_{HS} $ is the Hilbert Schmidt Norm.  Please read my solution and tell me whether it is correct. If not, let me know where the mistake is.  Proof of the implication $\Leftarrow $:   If $rank(A)=0$, then in this case $A=0$. It follows that $\left \| A \right \|=\left \| A \right \|_{HS}=0$ If $rank(A)=1$, than: $ A=\begin{pmatrix} A_{1}\\  \alpha _{2}A_{1}\\  ...\\  \alpha _{n}A_{1} \end{pmatrix}$ where $A_{1}$ is the first row of $A$   and in this case: $\left \| A \right \|=\left \| A \right \|_{HS}=\left \| A_{1} \right \|\sqrt{1+\alpha _{1}^{2}+...+\alpha _{n}^{2}}$  Proof of the implication $\Rightarrow $   We know that $\left \| A \right \|=max_{\left \| x \right \|=1}\left \| Ax \right \|$  On the other hand: $ A=\begin{pmatrix} A_{1}\\  A_{2}\\  ... \\ A_{n}  \end{pmatrix}$. So, $$\left \| Ax \right \|=\left \| \begin{pmatrix} \left \langle A_{1},x \right \rangle\\  \left \langle A_{2},x \right \rangle\\  ...\\   \left \langle A_{n},x \right \rangle\end{pmatrix} \right \|=\sqrt{\left \langle A_{1},x \right \rangle^{2}+\left \langle A_{2},x \right \rangle^{2}+...+\left \langle A_{n},x \right \rangle^{2}} $$  Where $ \left \langle A_{i},x \right \rangle$ is the inner product of $A_{i}$ and $x$  Using the Cauchy-Schwarz inequality: $\left \langle A_{i},x \right \rangle^{2}\leq \left \| A_{i} \right \|^{2}\left \| x \right \|^{2}$, we get: $\left \| A \right \|=max_{\left \| x \right \|=1}\left \| Ax \right \|\leq max_{\left \| x \right \|=1}\left \| x \right \|\left \| A \right \|_{HS}=\left \| A \right \|_{HS}$. In order to have the equality: $\left \| A \right \|=\left \| A \right \|_{HS}$, we should have: $\left \langle A_{i},x \right \rangle^{2}=\left \| A_{i} \right \|^{2}\left \| x \right \|^{2} $ which occurs only if $A_{i}=\lambda _{i} x$. So, the rows of A are dependent, which implies that $rank(A)=1$. Note that the case $rank(A)=0$ happens when $A=0$  Please let me know if my solution makes sense. Dynamic grid with Atlas generation How can Cooper communicate with his daughter before the time he went to space? We are in the early stages of development of the official Stack Exchange Android app and we need your help with testing. To set a few expectations: there will be bugs, crashes, and missing features, all of which will be fixed in .    We are initially targeting Android devices running  (Android 4.1 or higher) starting with phones (up to ~5 inch) and eventually moving our way to tablets.    To register for alpha testing .  After you register we will send you an invite to a private Google community where you can find a link to download our app directly from the  store. The invitations will be sent out in waves, so if you don’t get an invite immediately, be patient.  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