If I use red eyes dmd effect to bring a dragon from the graveyard then send red eyes dmd to the graveyard and then bring it back in the same turn, is it treated as a new monster resetting it so I can re-use its effect to special summon another monster?
So here is one I wish to know:   I use Tri-Gate second effect, which allows me to target and banish one card on the field. Then I link that with another monster to bring out another link. Tri-Gate would be in the graveyard but then I use transcodes effect (1 of the 3 co-links) to bring it back from the graveyard.   Can I use the second effect again?
I am trying to prove that:  Let $f$ be analytic in the closed unit disc with $f(z)\leq 1$ for $|z|\leq1$.  For a given $0&lt;r&lt;1$ and $|z_1|,|z_2|\leq r$, $z_1\neq z_2$ then,   $$\left|\frac{f(z_2)-f(z_1)}{z_2-z_1}\right|\leq \frac{1}{(1-r)^2}.$$  My attempt is: part a  of the question asks to prove $$\left|\sum_k^\infty a_nz^n\right|\leq \frac{ |z^k|}{1-|z|}.$$   So, \begin{eqnarray*}  \left|\frac{f(z_2)-f(z_1)}{z_2-z_1}\right|&amp;=&amp; \frac{|\sum_1^\infty a_nz_2^n-\sum_1^\infty a_nz_1^n|}{|z_2-z_1|}\\  &amp;\leq&amp; \frac{\frac{ |z_1 |}{1-|z_1|}+\frac{ |z _2|}{1-|z_2|}}{|z_2-z_1|}\\  &amp;\leq&amp;\frac{1}{(1-r)^2} \frac{   |z_2| ({1-|z_1|})+  |z _1| (1-|z_2|) }{|z_2-z_1|}\\ \end{eqnarray*} But could not prove that the last term is controlled by 1. How to typeset a primed vector I write a vector with an arrow above the letter using \vec{p} and sometimes the vector needs to be primed using ' (or ^{\prime}, equivalently).  However, neither  \vec{p}'     nor  \vec{p'}     looks satisfactory (first option: prime dash overlaps with vector arrow, second option: arrow looks misplaced).  How would one write a primed vector? Forgive the stupid simplicity of this question, and please feel free to refer me to an older answer. I'm not quite familiar enough with LaTeX terminology to have found it.  All I want to do is set a different default format for my section titles. Instead of just being bolded and slightly larger than the main text, I'd like them to be of normal weight, the same size as the main text, and all caps.   I'm using the article class. What to do with random effects correlation that equals 1 or -1? Not so uncommon occurrence when dealing with complex maximal mixed models (estimating all possible random effects for given data and model) is perfect (+1 or -1) or nearly perfect correlation among some random effects. For the purpose of the discussion, let's observe the following model and model summary   Model: Y ~ X*Cond + (X*Cond|subj)  # Y = logit variable   # X = continuous variable   # Condition = values A and B, dummy coded; the design is repeated  #             so all participants go through both Conditions   # subject = random effects for different subjects    Random effects:  Groups  Name             Variance Std.Dev. Corr               subject (Intercept)      0.85052  0.9222                              X                0.08427  0.2903   -1.00                      CondB            0.54367  0.7373   -0.37  0.37                X:CondB          0.14812  0.3849    0.26 -0.26 -0.56 Number of obs: 39401, groups:  subject, 219  Fixed effects:                  Estimate Std. Error z value Pr(&gt;|z|)     (Intercept)       2.49686    0.06909   36.14  &lt; 2e-16 *** X                -1.03854    0.03812  -27.24  &lt; 2e-16 *** CondB            -0.19707    0.06382   -3.09  0.00202 **  X:CondB           0.22809    0.05356    4.26 2.06e-05 ***   The supposed reason behind these perfect correlations is that we have created a model which is too complex for the data that we have. The common advice that is given in these situations is (e.g., Matuschek et al., 2017; ) to fix the overparameterized coefficients to 0, because such degenerate models tend to lower the power. If we observe a marked change in fixed effects in a reduced model, we should accept that one; if there is no change, then there is no problem in accepting the original one.  However, let's presume that we are not interested only in fixed effects controlled for RE (random effects), but also in the RE structure. In the given case, it would be theoretically sound to assume that Intercept and the slope X have non-zero negative correlation. Several questions follow:   What to do in such situations? Should we report the perfect correlation and say that our data is not "good enough" to estimate the "real" correlation? Or should we report the 0 correlation model? Or should we maybe try to set some other correlation to 0 in hope that the "important" one will not be perfect anymore? I don't think there are any 100% correct answers here, I would mostly like to hear your opinions. How to write the code which fixes the correlation of 2 specific random effects to 0, without influencing the correlations between other parameters? How prove that $\lim\limits_{x\to+\infty}f(x)=\lim\limits_{x\to+\infty}f'(x)=0$ if $\lim\limits_{x\to+\infty}([f'(x)]^2+f^3(x))=0$? Question:     Let $f$ be differentiable on $[0,+\infty)$, such as$$\lim_{x\to+\infty}\left([f'(x)]^2+f^3(x)\right)=0$$show that $$\lim_{x\to\infty}f(x)=\lim_{x\to\infty}f'(x)=0$$   I think this problem is similar to  and (the  background)  For my problem I guess that if  $$\lim_{x\to+\infty}\left([f'(x)]^{2m}+f^{2n+1}(x)\right)=0,m,n\in N^{+},n,m&gt;1$$ then we have $\lim_{x\to\infty}f(x)=\lim_{x\to\infty}f'(x)=0$. Interfaces with static fields in java for sharing 'constants' I'm looking at some open source Java projects to get into Java and notice a lot of them have some sort of 'constants' interface.  For instance,  has an interface called , and most other core classes implement this interface. The interface is riddled with static members. Is there a reason for this approach, or is this considered bad practice? Why not use enums where it makes sense, or a static class?  I find it strange to use an interface to allow for some sort of pseudo 'global variables'.  public interface PConstants {    // LOTS OF static fields...    static public final int SHINE = 31;    // emissive (by default kept black)   static public final int ER = 32;   static public final int EG = 33;   static public final int EB = 34;    // has this vertex been lit yet   static public final int BEEN_LIT = 35;    static public final int VERTEX_FIELD_COUNT = 36;     // renderers known to processing.core    static final String P2D    = "processing.core.PGraphics2D";   static final String P3D    = "processing.core.PGraphics3D";   static final String JAVA2D = "processing.core.PGraphicsJava2D";   static final String OPENGL = "processing.opengl.PGraphicsOpenGL";   static final String PDF    = "processing.pdf.PGraphicsPDF";   static final String DXF    = "processing.dxf.RawDXF";     // platform IDs for PApplet.platform    static final int OTHER   = 0;   static final int WINDOWS = 1;   static final int MACOSX  = 2;   static final int LINUX   = 3;    static final String[] platformNames = {     "other", "windows", "macosx", "linux"   };    // and on and on  } In the sentence     What’s funny is Cat’s dry humour.   Wouldn’t it be better to put a comma after “funny”:     What’s funny, is Cat’s dry humour.   This question entails a (at the time of writing) heated discussion in the . Is my mobile AMD card being used? I have a new Sony E Series Vaio with an intel i5 and an AMD 7xxx mobile card. Despite making sure sure my app (game) is set to High Performance in switchable gfx and choosing high performance power plan I'm not entirely convinced the gfx card is being used over the CPU's HD4000 chipset. Is there anyway I can prove for sure the AMD card is being used?  thanks for reading  (OS is Win8 64bit) Subsetting a 2D numpy array When were the 'and' and 'or' alternative tokens introduced in C++? I've just read this  from Reddit.  They mention and and or being "Alternative Tokens" to &amp;&amp; and ||  I was really unaware of these until now. Of course, everybody knows about the , but and and or? Since when? Is this a recent addition to the standard?  I've just checked it with Visual C++ 2008 and it doesn't seem to recognize these as anything other than a syntax error. What's going on? What do viruses do? There are those big green spiked things that my friends call viruses. I don't know what they do and I want to know. Do the viruses do something to the device you are playing on? Are they good or bad? I'm more of a math guy than a physics guy so bear with me....  In fractal geometry, fractals are considered to have fractional dimension. For instance an object such as the Koch curve has a fractal dimension of around $1.2$. You can also define a concept called fractal extent (which is the experimental version of hausdorff measure). This extent is a measure of how large a fractal is. It's even been used to more accurately model the distribution of coastline bird nesting.   Even though fractals work as an interpretation of geometrical units, I don't think they would describe things such as $kg^{1/2}$ very well. In addition, I've heard about white Gaussian noise that has square root time units.   What is the physical meaning of fractional units such as the above? (Since it obviously has little geometric meaning) Prove that the derivative of an even differentiable function is odd, and the derivative of an odd is even. Do we have name for these kind of "flat graphics" images? "approach to address" or "approach to addressing"? Depending on our point of view, we offer different approaches to address(ing?) a same issue.   Should I use &mdash;ing in this context, and if yes, why? Domain Controller etiquette after a crash between Server 2003 & Server 2008 I have 2 domain controllers on a non-Internet connected network running Windows Server 2008 R2. They running RAID 5 on a 8 Hard Drive server. Sometime last week the Boot Sector became corrupt on DC1 and I was unable to recover the server. I am not going to have to rebuild the server. I have been reading about the changes from Server 2003 to Server 2008. DC1 was the main domain controller and now that it won't but it is all falling to DC2. I know that in previous versions of Windows Server you had to make on the primary and one the secondary. Since DC2 does not see DC1 anymore is there anything I need to do to DC2 as it is now the one in control? I am thinking some kind of meta data clean up but I can't find any hard information on what procedure to do. I understand as of Server 2008 domain controllers are on an equal footing and provide replication to each other so they should be the same correct? Can't get unicode symbols in math mode I am trying for about a week to launch unicode-math package with XeLaTeX and got nothing. PDF is created well but all Cyrillic symbols in math mode are skipped. I tried using different math fonts - no progress at all. In log file, I found low-level error:  Missing character: There is no [cyrillic letter from input] in font cmmi12!   But all fonts used in document are Unicode ones.  Here is a file I want to be processed well (of course it is UTF-8).  \documentclass[12pt]{book} \usepackage{polyglossia} \setdefaultlanguage[spelling=modern]{russian} \setotherlanguage{english} \defaultfontfeatures{Ligatures={TeX}} \setmainfont{CMU Serif} \setsansfont{CMU Sans Serif} \setmonofont{CMU Typewriter Text}    \usepackage{amsmath, amssymb} \usepackage[russian]{hyperref}  \usepackage{unicode-math} \setmathfont{Latin Modern Math}  \frenchspacing  \begin{document} Просто буквы % Plain letters $$Память: M_{доп}(n) = \Theta(N)$$ % Memory: M_add(n) = \Theta(n) \end{document}   Looking for your help. Movie/TV series with a scene of spiky, black goo growing out of a lab container? There was a scene from a sci-fi horror video, not animated, don't know if it's a movie or TV series, where there was this black goo in a glass container and some scientists were looking at it under a microscope.   The pitch black goo grew and grew so fast, eventually breaking out of the inner box and the scientists that were inside the "inner lab" were begging to get out but the scientists outside that inner lab refused to open the door. The black goo was spiky (had spikes).  It's not any of the "Alien" movies, "The Blob", "Life", or "The Thing". It's not vintage. It was made after 1990, I'm pretty sure. "Within" and "in" when referring to time In Ubuntu, applications can be opened from a terminal. But sometimes it isn't clear what the appropriate command is to do this.  So, having an application open, how can I get the command used to launch it, without having to search anywhere (just by looking at it)?