Property of a euclidean map
Problem about the definition of Euclidean domain
Can I use Google Maps as a layer in ArcMap?  Is it possible? Is there a convenient way to place a figure* at the end of the current page instead of taking up the entire next page in the twocolumn environment? Placement modifiers [Hb] do not work. Limit at infinity of $x^{1/x}$ I encountered a problem: calculate $\lim\limits_{x\to\infty} x^{1/x}$  My solution is quite weird and I find no document explaining whether I am right or wrong!  My solution:  As $\lim\limits_{x\to\infty} 1/x = 0$  then $\lim\limits_{x\to\infty} x^{1/x} = \lim\limits_{x\to\infty} x^0  = 1$  My question is: Whether I am right or wrong, and could you please explain why? 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? Answer draft is lost if you click to sign up Application-priority based automatic bandwidth distribution in Windows? Whenever my browser wants to download data, I want it to be granted as much of the bandwidth as it wants, while other applications must do with the leftover bandwidth; and when the browser is not transferring any data, other applications could be given the bandwidth. Something like the process priority in Windows task manager. Any method/software to accomplish this automatically? I mean to ask  that $7$ is an arithmetic  expression  but it can also  be  written  as $7x^0$.  which is a constant polynomial  expression.  Every polynomial  expression  is an algebraic  expression  so with  this logic is $7$ an algebraic  expression  or an arithmetic  expression.  Further $7=5+2$, is it an arithmetic  equation  or algebraic  equation  because  it can also be written  in  $7x^0 = 5x^0 + 2x^0$ form. please help.  Thank you. Purpose of hole in stove leading to oven I'm staying in a hotel and have access to a "electric coil stove" for one of the first times.  I accidentally turned on the oven light and saw that the light was shining up through only one of the stoves:    There's only a port from the oven into the top right stove, and note that the stove is not on.  Here's a view from within the oven:    Is there a hole here as a vent for the oven for some reason, or is this for the stove? I typically use a glass "flat-top stove" that doesn't have an oven underneath it. I've never seen a direct hole from a stove to the oven before, and have to wonder what the purpose is. Intuitive explanation for formula of maximum length of a pipe moving around a corner? For one of my homework problems, we had to try and find the maximum possible length $L$ of a pipe (indicated in red) such that it can be moved around a corner with corridor lengths $A$ and $B$ (assuming everything is 2d, not 3d):    My professor walked us through how to derive a formula for the maximum possible length of the pipe, ultimately arriving at the equation $L = (A^{2/3} + B^{2/3})^{3/2}$.  The issue I have is understanding intuitively why this formula works, and exactly what it's doing. I understand the steps taken to get to this point, but there's an odd symmetry to the end result -- for example, is the fact that $\frac{2}{3}$ and its inverse are the only constants used just a coincidence, or indicative of some deeper relationship?  I also don't quite understand how the formula relates, geometrically, to the diagram. If I hadn't traced the steps myself, I would have never guessed that the formula was in any way related to the original problem.  If possible, can somebody give an intuitive explanation as to why this formula works, and how to interpret it geometrically?    Here's how he found the formula, if it's useful:  The formula is found by finding the maximum possible length of the pipe by expressing the length in terms of the angle $\theta$ formed between the pipe and the wall, and by taking the derivative to find when $\frac{dL}{d\theta} = 0$, which is the minimum of $\frac{dL}{d\theta}$ and is therefore when $L$ is the smallest:  $$ L = \min_{0 \leq \theta \leq \frac{\pi}{2}} \frac{A}{\cos{\theta}} + \frac{B}{\sin{\theta}} \\ 0 = \frac{dL}{d\theta} = \frac{A\sin{\theta}}{\cos^2{\theta}} - \frac{B\cos{\theta}}{\sin^2{\theta}} \\ 0 = \frac{A\sin^3{\theta} - B\cos^3{\theta}}{\sin^2{\theta}\cos^2{\theta}} \\ 0 = A\sin^3{\theta} - B\cos^3{\theta} \\ \frac{B}{A} = \tan^3{\theta} \\ \theta = \arctan{\left( \frac{B}{A} \right)^{\frac{1}{3}}} \\ $$  At this point, we can substitute $\theta$ back into the original equation for $L$ by interpreting $A^{1/3}$ and $B^{1/3}$ as sides of a triangle with angle $\theta$ and hypotenuse $\sqrt{A^{2/3} + B^{2/3} }$:  $$ \cos{\theta} = \frac{A^{1/3}}{ \sqrt{A^{2/3} + B^{2/3} }} \\ \sin{\theta} = \frac{B^{1/3}}{ \sqrt{A^{2/3} + B^{2/3} }} \\ \therefore L = A^{2/3} \sqrt{A^{2/3} + B^{2/3} } + B^{2/3} \sqrt{A^{2/3} + B^{2/3} } \\ L = (A^{2/3} + B^{2/3}) \sqrt{A^{2/3} + B^{2/3} } \\ L = (A^{2/3} + B^{2/3})^{3/2} \\ $$  The equation for the formula for the maximum length of the pipe is therefore $L = (A^{2/3} + B^{2/3})^{3/2}$. Keep "Employee" on the profile of SE employees on meta Currently, SE employees are given diamonds wherever they need them. I agree with  on this to some degree, employees shouldn't be treated any different.  But... on meta, employees are different. They have the power to dole out official responses, and thus we should be able to differentiate between an employee and a normal user. Currently, only some employees have a diamond on MSO (see , ). This makes it confusing, especially when you see official-sounding posts like .  Now, giving diamonds to all employees on meta may not be the best solution to this. I don't think all employees want their precious inboxes spammed with all the suspensions that are doled out on meta, and other mod stuff. They won't really need the diamond powers either (though it wouldn't hurt).  So, I propose this:  Similar to how moderators have "Moderator" clearly on their profile    display "employee" on an employee's profile, along with the diamond if they have one. At least on meta.    It would imho be even better to display it on their usercards in some form, but that has already been shot down.  It would be even even better if non-MSO mods had greyed out diamonds, similar to , but that's just me wanting more shiny stuff ;-) Is there a number whose absolute value is negative? Why doesn't the T-800 run? I just re-watched the first two films in the Terminator series. The T1000 (Robert Patrick) does a lot of running, and is quite fast.  I didn't see many scenes where the T800 (Arnie) ran. Is it because he's really heavy? Is he mainly designed as a heavy "stand your ground" machine?  The only scene I could see him running is in T2 in the mental hostpital where the T1000 morphs through the metal gate and his gun gets caught. Then the T800 does a little jog to get into the elevator following John and Sarah. (anybody know of any other running/jogging scenes?) (EDIT Arnie also breaks into a run while pursuing Reece and Sarah down the alley after the NOIR nightclub attack.)  If he can at least jog though, why wouldn't he do this throughout the entire film? You would think that from a "chance of survival" point of view, if he could get a John even the slightest bit faster then he'd do so.  Of course, maybe I am overthinking this... Arnie walking around slowly is a lot more badass than Arnie jogging around.  Edit: Just watched T3 again, the T800 also ran towards the end when the big hangar door was closing and he ran over to slow it down. Interested in other examples of the T800 running too. I would like to determine the operating system of the host that my Java program is running programmatically (for example: I would like to be able to load different properties based on whether I am on a Windows or Unix platform). What is the safest way to do this with 100% reliability? In almost every canon (that is, visual) source, Force users typically wave a hand to invoke the Force to move or manipulate objects, people and thoughts. I get out-of-universe this is a visual cue that the Force is being used, but in-universe is it strictly necessary?  (The only exception I can think of is when Luke is training on Dagobah and is balancing rocks while standing on one hand with Yoda on his foot. He doesn't appear to be waving his hand to move the rocks.)  Is this addressed anywhere in-universe, even in Legends? If the topology of a space  has a countable base, then each base contains a countable subfamily which is also a base. Points disappear when zooming past certain scale in ArcMap? My points are disappearing when I zoom in past 300,000 in ArcMap.  I tried to repair geometry, but it doesn't fix anything?    I also checked the scale extents and those are turned off.  I can export the points to a new shapefile/feature class, but I'd like to not have to do that.    I'm using 10.1 on Windows 7 x64. I'm new to Blender and am having a few hitches.  Each time I use box select on a group of vertices it extends the selection from what was previously selected.  I can avoid this by hitting A to deselect all before using Box Select but I was hoping there was a way to have this happen by default.  Isn't it the desired workflow to select groups of objects and move them independently and only extend the select with Shift?  I must be doing it wrong. How do I draw the graph of inequalities in the coordinate plane? I want to graph the following inequalities (done in desmos) in latex. I need the code. I am an undergrad in economics and really want to get a helping hand as I get from math and stats from a Stack Exchange site for economics. Where can I post my questions on economics topics? I installed an Ubuntu alpha or beta and have been keeping it up to date.   So, Should I presume that my system has automatically updated to the next alpha or beta, and will be running the official release when it's finished?