How did they light Magneto's plastic prison?
About the absence of metal in machinery and buildings of the past
Complex Exponent of Complex Numbers How does one find the algebraic solution of a Complex number raised to the power of another Complex number?  Here is the work I have done so far, if there are any mistakes please inform me.  A real number with a Complex Exponent: $$A \in \Bbb R, \space z \in \Bbb C,\space z = x + iy$$ $$A^z = A^{x+iy} = A^xA^{iy}$$ $$\implies e^{iy\ln A} = A^{iy}$$ $$\exp(iy\ln A) = \cos (y\ln A)+i\sin(y\ln A)$$ $$A^z = A^x[\cos (y\ln A)+i\sin(y\ln A)]$$  A Complex number with a Complex Exponent: [Using previous variables] $$C \in \Bbb C,\space C = a +bi\space|\space re^{i\theta}, \theta =\arg C$$ $$C^z = (a+ib)^z$$ [After previous mistake the following notes are inaccurate] $$C^z = a^x[\cos (y\ln a)+i\sin(y\ln a)] + ib^xib^{iy}$$  And this is as far as I could go as the expansion of $ib^xib^{iy}$ is being problematic. Could I have some help with this expansion? How do I drop an object to the sand? How to combine paths in Java? Is there a Java equivalent for  in C#/.NET? Or any code to accomplish this?  This static method combines one or more strings into a path. My wife wants a 4th baby, but I don't My wife wants a 4th baby, but I don't.  We have been talking about it for the last few days (talking strongly).   I have raised points such as:   We will get less time to spend with our current kids. The age gap between the first and the last will be too wide. It will cost more money. She will be out of work longer. We will need a bigger house. And we don't even have our own house yet (we are still renting). We will have to start again. Sleepless nights, nappies, feeding, new cot, car seat, etc etc.   She says:   She feels like she is missing something. She has always wanted a large family. Things will be the same regardless of having 3, or 4 kids. She agrees that money will be tighter, but wants to push through it.   Our current kids are 9 months, 2 years, and 4 years. We are young married couple (25), and I have a fairly decent job.  What would be the pros and cons of having another child?   How can we rationally talk to the other about having/or not having another child?  And what should we do if we cannot agree? What's the maximum length of the meta keywords tag? Could you please tell me that what is the maximum length for meta keywords? I am new to salesforce. I dont have coding background. Please let me know bst way to learn apex coding? Are there any universal rules in appropriating “_an,” “_sh,” “_es,” “_ch” for the demonyms of countries? Suffixes indicating people and language of country vary by country:  _an: American, German, Italian, Belgian, Australian, Russian, Ukrainian, Korean,  Mexican, Brazilian, Chilean, Argentinean, Indonesian, Malaysian, Iranian, Egyptian, Somalian, Palestinian  _sh: English, British, Polish, Danish, Swedish, Turkish,    _ch: French, Dutch  _ese: Chinese, Taiwanese, Japanese, Vietnamese, Portuguese  _no: Filipino, Latino  _i: Israeli  _: Thai  Among the above, _an seems to outnumber other suffixes.  Are there any simple rule to govern appropriation of suffix turning a country name into adjective, indicating people and language of countries in the world in terms of say, region, race, or cultural background? Or is it just discretional? How can I account for a nonlinear variable in a logistic regression? How can I account for a nonlinear independent variable in a logistic regression?  For example, consider this data set:  b1  b2  b3  b4  b5 1   1   0   0   20 0   1   0   0   20 1   0   0   0   13 1   1   1   0   8 1   1   0   1   5 0   1   0   1   4 1   1   0   1   5 0   0   0   0   8 0   0   1   0   13 1   0   0   1   20 1   0   0   0   29 1   1   0   1   40 1   0   0   0   53 0   1   1   0   68   Suppose I gathered some data like the above (suppose I had 10,000 rows) and I want to use them to predict future sets of similar data with an equation generated by a logistic regression. I get the above data. My independent variables are b1 through b5. By looking at the data, I can clearly see that independent variables b1 through b4 are binary (maybe they are male/female, rent/own, etc).   However I see that b5 is clearly not binary. Upon graphing it and looking at the numbers I determine that the b5 variable has a bathtub shaped U curve with an equation of b5=(x-4)^2+4.   I understand that using the b5 variable as it is would screw up my logistic regression - since any interval independent variables must have a linear relationship with the dependent variable.   Yet, I must account for the variable b5 in my data set while doing a logistic regression for it to be accurate and predict well (right?).  Given the above data, how would I go about making a predictive model with a logistic regression? Any references online or in books would greatly be appreciated as I am having trouble finding a good explanation of the above.  Cheers =)  EDIT:  Sorry if my question is unclear.  Consider this: Suppose we had the following data on many people:  Y: Whether they had a stroke before the age of 50 or not 1. Whether they own a pet or not. 2. Whether they graduated college or not. 3. Whether they are male or female. 4. The number of hours they exercise every week.  We want to train a logistic regression model based on historical data to predict if someone in the future with the same data will be more apt or not to have a stroke before the age of 50.  The problem I am having is with the last variable. A continuous ratio variable like "number of hours exercised each week."  Exercising more each week may have diminishing returns on health and thus having a stroke. For example decreasing an increasing rate. Or maybe (totally made up) exercising a little bit is really good for you, exercising a moderate amount is really bad for you, and exercising a lot is really good for you again. We might have a U shaped curve like (x-4)^2+4 for example when plotting health to exercise.   I would image that having a curved, non-linear independent variable in a logistic regression like the one I described above would cause problems. Am I right? And if so, what kinds of things can you do to still include the variable in the logistic regression. Perhaps a transformation? Is that all? Mail App keeps popping up in the background in Mac OS Mojave Trying to find a Sci-Fi movie, probably from the 50's or 60's I’m trying to identify a movie I saw when I was very young.  It was a “Saturday Matinee” playing on one of the local stations, and I likely watched it in the late 60’s.  So I expect that the movie is from the 50’s or 60’s.  I watched it in black and white, but it could have been a color movie on a black and white set. I clearly recall a scene where scientists enter a lab and some see something move past them in a blur.  Later in the movie, they come upon themselves in the same lab where they appear to be frozen and not moving.  Then they notice that their “other selves” are moving, just almost inperceptibly slowly.  They are encountering themselves but at a completely different time scale. Unfortunately, I don’t recall much else about the movie, just the idea that they encounter themselves once with the others flashing past, and again seemingly not moving at all.  If this rings any bells with anyone, I’d love some pointers to try to track this movie down. Link2SD not working completely My Link2SD doesn't seem to be fully working. I noticed this when updating the Facebook application. Google Play prompted me of insufficient storage. I first uninstalled some apps but I got curious so I checked Link2SD's storage info, I got this:   (Click image to enlarge)  As you can see, the internal storage only has mere 70mb left. What's peculiar is, these are the only apps I have NOT linked:   (Click image to enlarge)  I tried moving one linked app (Amazing Alex) to the sd card (normal Android way) and sure enough, the free space on my internal storage got bigger by about an additional 20mb-ish.  Why is this happening? Why isn't Link2SD moving the data to my sdext2? How do I solve it? When would I need a SecureString in .NET? Why on-shell vs. off-shell matters? The definitions between on- and off-shell are given in .   Why is it so important in QFT to distinguish these two notions? My Minecraft app now only has the option of "play" and there is no "play on realms" to be found!  I downloaded - and paid for - the multiplayer app, but there doesn't seem to be a way to get to any realms on that app either. How can I make a bluish "white" LED less blue? An annulus in $\mathbb R^2$ is path connected Let $A = \{(x,y) \in\mathbb{R}^2: a \leq (x-c)^2+(y-d)^2 \leq b\}$ for given $a,b,c, d$ real numbers. I want to show that $A$ is path-connected.  How can I do that?  I know that every open subset of $\mathbb R^2$ that is connected is path connected. But this is obviously not open so I cannot use that. Then I thought of multiple cases. If we take arbitrary $x$ and $y$ and draw the line between them and they do not intersect with the circle centred at $(c,d)$ then we can obviously draw a line between the points which is still in the set, so we can then define the function. I am stuck on the other case. Reading string from input with space character? Capturing screenshots on the Mac has gotten very slow recently.  It used to be nearly instantaneous but now it is taking more than 10 seconds for the image to appear on the desktop.  I seem to recall having this problem years ago. The workaround was to delete a large accumulation of log files that the os had built up. After I deleted these log files, the screen capture worked very fast again.  Problem is that I cannot remember where these log files are. Searched for quite some time and could not find the information. Gauge fields and strings: Loop equations Are there any way to execute a query inside the string value (like eval) in PostgreSQL?