My Girlfriend and I have been forming an alliance as soon as possible when playing against AI... when we get to the end though, all other races wiped out we were hoping to have a shared victory.  In the end she gave me most of her planets and then the game gave me the victory, but if we had split the galaxy basically in half do we REALLY have to fight each other once there are no other contenders?
Question is pretty much in the title: is it possible for an alliance to win as one, instead of a single player being the winner?  And if there is such way, is there a difference between classic and disharmony?
I already found the radius of convergence of the power series $:$ $$\sum_{n=1}^{\infty} \frac {(-1)^n} {n} z^{n(n+1)}.$$ What happens at the boundary of disk of convergence?  I found that the radius of convergence to be $1$ and hence the disk of convergence is $|z|&lt;1$. Now I found at $z=1$ the series converges. Now how can I proceed? Please help me. Thank you in advance. Which variables should I transform, center, and/or standardize in my data for Principal Component Analysis? I have multiple datasets that I am attempting to use principal component analysis (PCA) on in order to infer the underlying structure of the data.  I'm attempting to predict growth increment of conifers (the response which apparently needed to be cube root transformed for my original linear models).  My predictor variables include: continuous (some log-transformed like size-related variables, some compositional, and some traditionally scaled); binary; ordinal; and nominal (of which I'm pretty sure I can order with respect to site productivity).  I'm mostly attempting to make inferences because some of my previous models from linear regression have not produced significant terms corresponding to categories like health or climate and I feel that they should have.  I've read in Joliffe (2002) that I might want to leave my compositional data uncentered.  Forgive my naiveté, but I'm wondering if I should also do this for my binary data.  It also seems that I might not want to scale these since they're already on a 0 - 1 scale but I'm not sure.  After only using my continuous predictors (including compositional variables), it appears that a size principal component makes up the largest portion of the variability and Joliffe also mentions that one might want to attempt a "double-centering" of the log-transformed data if this is the case.  I don't know if this is even possible since the log-transformed data only makes up a small portion of my datasets.  Finally, I should ask if having such a combination of data types will complicate analysis so much that it will make inferences unreliable.  I am currently using R for this analysis.  Thank you. Subject-verb inversion / verb-subject-object -- is this correct? I recently read the following in a schoolbook:     Wrote the researchers, "[...]"   I wonder if this is correct English. I have seen it a couple of more times. Is this just a matter of preference? English doesn't really have a very liberal word order, unless you're writing poetry or the like.  Can anyone tell me what this is called? I found some information on subject-verb inversion, but it only seems to be when the object is in front, but in this case, the word order is verb-subject-object. Understanding QGIS buffer tool units How can I create or use a global variable in a function?  If I create a global variable in one function, how can I use that global variable in another function? Do I need to store the global variable in a local variable of the function which needs its access? What does the term "BODMAS" mean? What is BODMAS and why is it useful in programming? I have a map of a city and a .csv-file containing 700 geographic coordinates pointing to locations within that city.  How can I plot these 700 locations on the map? Quick question about curly braces not showing up Ii am writing a short code, so I doubt anything else in the code is causing the problem. This is the problematic line of code:  \[ M_R := \max {|f(z)|: |z - z_0| = R }\le M\]   It doesn't show the curly braces. I've tried using \left{ and \right} but to no avail.  What should I do?  Thank you How to Sort Multi-dimensional Array by Value? Examples and further results about the order of the product of two elements in a group Let $G$ be a group and let $a,b$ be two elements of $G$. What can we say about the order of their product $ab$?   says "not much":     There is no general formula relating the order of a product $ab$ to the orders of $a$ and $b$. In fact, it is possible that both $a$ and $b$ have finite order while $ab$ has infinite order, or that both $a$ and $b$ have infinite order while $ab$ has finite order.   On the other hand no examples are provided. $(\mathbb{Z},+), 1$ and $-1$ give an example of elements of infinite order with product of finite order. I can't think of any example of the other kind! So:   What's an example of a group $G$ and two elements $a,b$ both of finite order such that their product has infinite order?     Wikipedia then states:     If $ab = ba$, we can at least say that $\mathrm{ord}(ab)$ divides $\mathrm{lcm}(\mathrm{ord}(a), \mathrm{ord}(b))$   which is easy to prove, but not very effective. So:   What are some similar results about the order of a product, perhaps with some additional hypotheses? Where do I put the code snippets I found here or somewhere else on the web? Many posts here or somewhere else contain code, but they do not say where to put it.  Example:  I have found this post:  I'm a newbie with PHP. Where exactly should I place the code from the answer? Complete induction proof that every $n > 1$ can be written as a product of primes I'm not particularly fond of apps cluttering my $HOME directory with their own files or directories. It's rarely a problem, because most apps have the courtesy to hide their data by prefixing it with a dot or conforming to the ~/.config standard. But not snap.  Q1: Have I misunderstood this directory?  Is ~/snap really a directory which I'm supposed to enter and access on a daily basis on a par with ~/downloads, ~/pictures, ~/work, etc?  Q2: In any case: Can I move it e.g. ~/.snap?  I can't find anything like /etc/snap, /etc/default/snap, or ~/.config/snap to tweak things. I tried export SNAP_USER_DATA=$HOME/.snap but it didn't work. Fluid filled harmonic oscillator A vessel (preferably circular) filled with water is accelerating unidirectionally such that the level of water is higher on one end than the other. What I want to know is that if the vessel is immediately stopped, the water level will force itself back to the equilibrium point, but in doing so push the other end up. If water is an ideal fluid, what type of oscillation will occur in this situation.   I can tell that maybe the mathematical expression for this oscillation will be complex, but please do let me know if I am thinking this correctly.   I am considering, finding the oscillation equation for infinitesimally small u-tubes(considering a 2-d plane) and integrating it to get the final expression.  Thanks in advance How to select even or odd elements based on class name if you create html layout like so  &lt;ul&gt;      &lt;li class='a'&gt;&lt;/li&gt;      &lt;li class='b'&gt;&lt;/li&gt;      &lt;li class='a'&gt;&lt;/li&gt;      &lt;li class='b'&gt;&lt;/li&gt;      &lt;li class='a'&gt;&lt;/li&gt;      &lt;li class='b'&gt;&lt;/li&gt;      &lt;li class='a'&gt;&lt;/li&gt;      &lt;li class='b'&gt;&lt;/li&gt; &lt;/ul&gt;   and try to select odd elements with 'a' class like so $$('.a:odd') you will get empty array, and if you do $$('.a:even') you will get all four li elements with 'a' class.. It really strange.. But im new to mootools, maybe im doing something wrong..    So my question is how to select first and third li elements with a class. I know that i can do it with function like this  $$('.a').filter(function(item, index) { return index%2; }  but its too complicated for such small task as selecting odd or even elements.. What's the application extension? (aka .exe, .app, etc.) I'm new to Ubuntu. What's the application extension for development reasons? I know Windows is mainly .exe and Mac is .dmg or .app. Does Linux have an unique one? Where do I find the current C or C++ standard documents? For many questions the answer seems to be found in "the standard". However, where do we find that? Preferably online.  Googling can sometimes feel futile, again especially for the C standards, since they are drowned in the flood of discussions on programming forums.  To get this started, since these are the ones I am searching for right now, where are there good online resources for:   C89 C99 C11 C++98 C++03 C++11 C++14 C++17 How to know that your machine learning problem is hopeless? Imagine a standard machine-learning scenario:     You are confronted with a large multivariate dataset and you have a   pretty blurry understanding of it. What you need to do is to make   predictions about some variable based on what you have. As usual, you   clean the data, look at descriptive statistics, run some models,   cross-validate them etc., but after several attempts, going back and   forth and trying multiple models nothing seems to work and your   results are miserable. You can spend hours, days, or weeks on such a   problem...   The question is: when to stop? How do you know that your data actually is hopeless and all the fancy models wouldn't do you any more good than predicting the average outcome for all cases or some other trivial solution?  Of course, this is a forecastability issue, but as far as I know, it is hard to assess forecastability for multivariate data before trying something on it. Or am I wrong?   Disclaimer: this question was inspired by this one  that did not attract much attention. It would be nice to have detailed answer to such question for reference. Changing an element's ID with jQuery Is there an international taxonomy of academic titles/ranks? Looking at the  on Wikipedia shows that the same academic rank/title can mean quite different things in different countries. For instant, a "research assistant" in the US can stand for an undergrad student doing an internship, while in the UK it can stand for a postdoc. Similarly, the term "lecturer" might stand for a permanent position (e.g. in the UK) or for a teaching assistant position, open to graduate students.   However, when thinking about it, there are not so many kind of possible positions (permanent or not, with teaching or not, with research or not, with PhD supervision or not, with team responsibility or not, etc), and having a clear title could help a lot (for instance, in my case, I've been working in four different countries, with a different job title each time!).    Is there some kind of official taxonomy that one could refer to?  If not, who could be in charge to create it? (the EU, if only for intra-Europe mobility?)