SciFi book series about a guy surviving in three deadly planets
Trying to remember a book about a human male travelling to alien planet
Can I register a domain name that contains a company name or trademark? I wonder is it legal to register a domain name that contains a company name. For example cococola.cc (considering that this domain name is available). Can I buy and use any domain names that contain a name of a trademark? How to show $\lim_{n \to \infty} a_n = \frac{ [x] + [2x] + [3x] + \dotsb + [nx] }{n^2} = x/2$? This question came from the prelim exam I took last month. I have a proof that seems a bit unwieldy to me (posted as an answer), so I'm opening it up to ask if there are other ways of showing this.     Let $x$ be any positive real number, and define a sequence $\{a_n\}$ by   $$ a_n = \frac{ [x] + [2x] + [3x] + \dotsb + [nx] }{n^2} $$   where $[x]$ is the largest integer less than or equal to $x$. Prove that $\displaystyle{\lim_{n \to \infty} a_n = x/2}$. How to understand dot product is the angle's cosine? How can one see that a dot product gives the angle's cosine between two vectors. (assuming they are normalized)  Thinking about how to prove this in the most intuitive way resulted in proving a trigonometric identity: $\cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b)$.  But even after proving this successfully, the connection between and cosine and dot product does not immediately stick out and instead I rely on remembering that this is valid while taking comfort in the fact that I've seen the proof in the past.  My questions are:   How do you see this connection? How do you extend the notion of dot product vs. angle to higher dimensions - 4 and higher? What does (obj.length === +obj.length) compare? How do you parse and process HTML/XML in PHP? Create subdomains on the fly with .htaccess (PHP) I am looking to create a system which on signup will create a subdomain on my website for the users account area.   e.g. johndoe.website.com  I think it would be something to do with the .htaccess file and possibly redirecting to another location on the website? I don't actually know. But any information to start me off would be greatly appreciated.  Creating a sign up area is not the problem - I have done this many a time. I am just unsure where to start with the subdomain. How prove :         $$ {31}^{11}&lt;{17}^{14} $$       help please! Pressure inside a closed room If $a \cdot a = 1$ then $a = 1$ or $a = -1$ Let $F$ be a field.   And let $a \in F$ such that $a \cdot a = 1$.  Claim: $a = 1$ or $ a = -1$  Before, I begin with the proof I cannot understand what $ a = -1$ represents...  Is $a = -1$ representing the inverse of $a$?   I am capable of getting to $a = 1$ with no trouble, but how do you get the $-$ sign to show up in your proof?   Proof: This is my attempt at getting to $a=-1$.  If $a = 0$ then we have $0 \cdot 0 = 0 \neq 1$. Then this implies that $a \neq 0$ which implies that $ \exists b \in F,$ s.t. $a \cdot b = 1$, i.e. $b$ is the multiplicative inverse of $a$.  Knowing this fact prove as follows...:  $a \cdot a = 1 \implies$ $ (a \cdot a) \cdot b = 1 \cdot b \implies$ $a \cdot (a \cdot b) = 1 \cdot b \implies$ $a \cdot 1 = 1 \cdot b \implies$ $ 1 \cdot a =1 \cdot b \implies$ $a = b$.   But since $b$ is the multiplicative inverse of $a$ is this enough to say that $a = -1$? Distribution of $-\log X$ if $X$ is uniform. I can reproduce that every time now, I go to a site, open an article, then to the next site, open another article. The Feed page pops up for a second, the article page lays over this with some some transparent areas (see picture). The same app-version is ok on a Smartphone with Android 4.4.2. I also sent in some bug reports.    Edit  1.0.71 isn't the solution yet. I go to Meta SE, then to an article. When I want back to Meta SE again, it crashes. Much earlier than before. I already sent in a bug report for this.  Another Edit  I can describe it better now. From the questions-page of a site I go to a post. When I use the back button, everything is ok, I can go to the next site. When I try to go to the next site directly from the post, it crashes. This only happens on the Nexus 10 with Android 5.1.1, App version 1.0.71. Hope this helps.  Edit3  This is fixed in 1.0.73 now. Thanks again. I have two raster files that are the same cell size but I cannot get them to align properly. (I want the black to line up with the pink)    When creating the black raster file (from using polyline to raster), I imported the pink raster in the Snap Raster section in the Environments setting. I thought that Snap Raster was supposed to make it line up?  Am I doing something wrong or is it a bug in Arc (I remember reading that this was a problem about two years ago), and if it is a bug is there a work around?  I have also read there is a Raster Shift, but I'm not sure what to enter in the X Coordinate and Y Coordinate. Since I only want the black raster to shift down, I know that the X Coor = 0 and the Y Coor should be negative something, but what are the units?  Thanks. Where can I find delay/cancelation statistics for a given airline route? My flight got canceled yesterday and I am currently waiting for the delayed next flight.   Is there any website that keeps records of airlines being delayed/canceled? I would like to know my chances. I did find some sites through google (flightaware, flightstats), but they focus on us flights only and I am currently in the azores. Why do I need multiple sites for the same property in Google Webmaster Tools? In researching the best practice for adding sites to the Search Console, I've often seen it suggested to add separate properties for different versions of the same website. Even in  it states:     "Similarly, if your site has http:// and https:// versions, you should   add each as a separate site."   I've seen the same suggested for www/non-www. So if a site is accessible at all the variations of http/s and www/non-www we should have four properties.  But what if the site is only accessible at one variant? i.e. https and www are forced via htaccess, so only  can ever be accessed - should we still add all the variants?   In essence, the problem is that I don't know why Google wants us to do this, so I can't work out if it'll be ok just to have one instance. I always use lm() in R to perform linear regression of $y$ on $x$. That function returns a coefficient $\beta$ such that $$y = \beta x.$$  Today I learned about total least squares and that princomp() function (principal component analysis, PCA) can be used to perform it. It should be good for me (more accurate). I have done some tests using princomp(), like:  r &lt;- princomp( ~ x + y)   My problem is: how to interpret its results? How can I get the regression coefficient? By "coefficient" I mean the number $\beta$ that I have to use to multiply the $x$ value to give a number close to $y$. natbib: combining chicago style and sorting by appearance Is $\int_{-\infty}^{\infty} \sin x \, \mathrm{dx}$ divergent or convergent? I was determining whether   $$\int_{-\infty}^{\infty} \sin x \, \mathrm{dx}$$  was divergent or convergent. So, I did the following steps:  $$\begin{align} \int_{-\infty}^{\infty} \sin x \, \mathrm{dx} &amp;= \int_{0}^{\infty}\sin x \, \mathrm{dx}+\int_{-\infty}^0\sin x \, \mathrm{dx} \\ &amp;=\lim_{t\rightarrow\infty} \left(-\cos x |^{t}_{0}\right) + \lim_{a\rightarrow-\infty} \left(-\cos x |^{0}_{a}\right)\\ &amp;=\lim_{t\rightarrow\infty} -\cos (t) + \cos 0 + \lim_{a\rightarrow-\infty} -\cos 0 + \cos a\\ &amp;=\lim_{t\rightarrow\infty}1 - \cos t + \lim_{a\rightarrow-\infty} -1+\cos a \end{align}$$  Now, at this point, it would be reasonable to say that both the limits are undefined and therefore, the integral is divergent but then if I try something like the following   \begin{align} \quad\quad&amp;=\lim_{t\rightarrow\infty}1 -\cos t + \lim_{a\rightarrow\infty} -1+\cos a \\ \quad\quad&amp;=\lim_{t\rightarrow\infty}-1 -\cos t + \lim_{a\rightarrow\infty} \cos a+1 \\ \quad\quad&amp;=\lim_{b\rightarrow\infty}-1 +\cos b - \cos b+1 \\ \quad\quad&amp;= 0 \end{align}  So, as you can see, it was shown before that the integral is divergent but with some manipulation, we came at an answer of $0$ but is that valid? I assume, a similar technique can be applied to $\int_{-\infty}^{\infty} \frac{1}{x} \, \mathrm{dx}$. Crossroads / Second Chance / Choices I am trying to find a short story involving an alien race of 'Intellectuals.' They possess no opposable thumbs or other limbs to control their world.  I think the basis of the story is their discovery of a way to influence another unintelligent species that can manipulate objects.  This leads to a new start for them.  They may have been at risk of breeding beyond available resources.  The story ends with explorers returning from sea. They may have discovered a new land into which they can expand. The last few scenes have a darker flavor where one character has been presented with a rock that glows in the dark. He considers it for a period before being called away to greet the explorers. The author then takes over and makes some comments about most species passing one crossroads only to meet another.  The story could have been written at any time from the Golden Age though to the 1970's. Getting text from the Resource file in asp.net 4 Does anyone know of any interesting subsets of the Cantor set? When I first started thinking about this, I thought that since the Cantor set $C$ is the intersection of disjoint unions of closed sets, those particular closed sets would be subsets of $C$. Those sets, however, happen to be intervals! The Cantor set contains no isolated points nor (open) intervals, so then what subsets does it contain besides $\varnothing$ and itself?