Confused about time dilation/length contraction
Does the sign of $\Delta x$ matter in this time dilation calculation?
Combining randomForests in R, why are the err.rate, mse and rsq components NULL From ?combine in :     The confusion, err.rate, mse and rsq components (as well as the   corresponding components in the test compnent, if exist) of the   combined object will be NULL.   Why are the err.rate, mse and rsq components for the combined NULL? Is there an efficient way to re-calculate these metrics?  I ask because I would like to figure out a way to use the oob re-sampling method with the parRF model in . I know about beamer's  feature \setbeamercovered{invisible} and \setbeamercovered{transparent} to hide or grey out upcoming item's . But is there some way to have past items greyed (transparent) and future items hidden (invisible), so that only the current item is black/highlighted? And the best would be if on or 1 slide after the last all the item's could be visible highlighted. Something like this:   [grey] past 1 [grey] past 2 current [hidden] future 1 [hidden] future 2 [hidden] future 3   Is there any easy way of doing this? Why does Captain Antilles in a New Hope say they're on a diplomatic mission? Here's what is happening; everytime I go to Stack Overflow (stackoverflow.com, NOT meta) with Firefox, it gives me the "Welcome back" tab that pops up from the top. Whenever I click in the "click here to refresh the page" link, all it does is refresh the page without logging me back in.  Even if I try to log in using the "log in" button at the top, all it does is pop up the tab that says "Welcome name here, you're being redirected." The problem is I'm not being logged in, not to mention that it keeps refreshing the page over and over again without giving me a choice to log in with Facebook.  For some reason, I was capable of logging in to Meta Stack Overflow using Firefox. I am still unable to log in to Stack Overflow. Any ideas? Is it possible to create a counter just with wiring? With the new logic gates in the 1.3.1 update, is it possible to create some wiring circuit that counts how many times a trigger was activated? In other words, is it possible to make a circuit that outputs a trigger every two input triggers?  I've done some experimenting but the nature of wires and there being no intrinsic on/off state in Terraria makes it pretty counter-intuitive compared to real world logic circuits. How does pointing a CNAME on my domain to a service-provider's server enable them to offer customized services? infinite monoid H that is not a free monoid and contains a free monoid as a submonoid Let $H= \langle h_1, \ldots , h_n \rangle$ ($n&gt;1$) be an infinite monoid that is not a free monoid. Does $H$ contain an isomorphic copy of a free monoid as a submonoid? EDIT. It is a natural question. The corresponding question for groups is the Burnside problem. "Have you seen her?" or "Did you see her?" I already knew that we use the present perfect for an action in the past with a result now. Consider the following questions:   "I'm looking for Paula. Have you seen her?" "I'm looking for Paula. Did you see her?"   Is there any difference between these two questions for this specific action (verb)? What is the result of "seeing" action which can't be represented by simple past? Fundamental particles identical or just differences very small? I have read that all electrons are identical and I assume the same for protons, etc. That is, all electrons are of the exact same mass and charge.  But do we really know this? Could there be slightly heavier electrons with slightly higher charge or is there a reason why such particles could not exist or would be unstable? Convert hex string to int in Python How do I convert a hex string to an int in Python?   I may have it as "0xffff" or just "ffff". Polygon intersection using turf js I have given this code for intersection: function intersectPolyByPolyFC(poly,fcPoly){         var fgp=[];//variable for feature group         var bbPoly=turf.bboxPolygon(turf.bbox(poly));//polygon representation of the bounding box of a reference polygon         for(var i=0;i&lt;fcPoly.features.length;i++){//loop through the feature collection of polygons             var bb=turf.bboxPolygon(turf.bbox(fcPoly.features[i]));//variable bb represents each polygon for feature collection             if(turf.intersect(bbPoly,bb)){//condition to check if the two bounding boxes intersect                 var int= turf.intersect(poly,fcPoly.features[i]);                 if(int){                     int.properties=fcPoly.features[i].properties;                     fgp.push(int);                 }             }         }         return turf.featureCollection(fgp);     }  and the function definition I have given as var bufline=turf.buffer(line,0.05,{units:&quot;kilometers&quot;}); var intBUOWL= intersectPolyByPolyFC(bufline, lyrBUOWL.toGeoJSON()); L.geoJSON(intBUOWL,{style:{color:'red',weight:5}}).addTo(mymap);  When I am drawing a line over a polygon for intersection I am getting this error Uncaught TypeError: Cannot read property 'map' of undefined     at Object.t.collect (turf.min.js:1)     at summarizePointsByLine (buffer.html:440)     at NewClass.&lt;anonymous&gt; (buffer.html:155)     at NewClass.fire (Events.js:190)     at NewClass._fireCreatedEvent (leaflet.draw.js:8)     at NewClass._fireCreatedEvent (leaflet.draw.js:8)     at NewClass.completeShape (leaflet.draw.js:8)     at HTMLAnchorElement.handler (DomEvent.js:92)  How can I resolve this error? Could I replace headphones NIMH battery with Lithium Ion phone battery of the same voltage? Problem: Let $f$ be defined for all real $x$, and suppose that   $$|f(x)-f(y)|\le (x-y)^2$$  for all real $x$ and $y$. Prove $f$ is constant.  Source: W. Rudin, Principles of Mathematical Analysis, Chapter 5, exercise 1. Why isn't an infinite, flat, nonexpanding universe filled with a uniform matter distribution a solution to Einstein's equation? How do I use itertools.groupby()? I haven't been able to find an understandable explanation of how to actually use Python's itertools.groupby() function.  What I'm trying to do is this:  Take a list - in this case, the children of an objectified lxml element Divide it into groups based on some criteria Then later iterate over each of these groups separately.  I've reviewed , but I've had trouble trying to apply them beyond a simple list of numbers. So, how do I use of itertools.groupby()?  Is there another technique I should be using?  Pointers to good &quot;prerequisite&quot; reading would also be appreciated. Is it possible to use the animals that are summoned using Conjure Animals as mounts?  As an example: Summoning Giant Eagles to carry a group up the mountain or over a wall. Mining cryptocurrencies with Ubuntu and sgminer What are the steps for setting up a Ubuntu machine for mining of crypto-currencies?  I am looking for a full guide to follow - from installing Ubuntu to how to config and start the miner itself. If $(A-2I)^3(A+2I)^2=0$, then what are the possible Jordan canonical forms of $A$? Here is the exercise:     Let $A$ be a $5\times5$ complex matrix such that $(A-2)^3(A+2)^2=0$, where we define $A-\mu:=A-\mu I$ for scalar $\mu$. Assume that $\lambda=2$ is an eigenvalue of $A$ and its geometric multiplicity is at least $2$. What are the possibilities for the Jordan canonical form (JCF)?   What I know so far from the assumption is that    the minimal polynomial of $A$ is of the form $f(x)=(x-2)^i(x+2)^j$ where $1\leq i\leq 3$ and $0\leq j\leq 2$.  The number of blocks in the Jordan segment $J(2)$ is at least $2$.    One can write the possible minimal polynomial one by one, which gives the information of the size of the largest block in each Jordan segment, and use the possible geometric multiplicity of $\lambda=2$ to find JCF.   Here are my questions:   Is there an alternative approach?  Can we use the characteristic polynomial of $A$ here? I use Lasso logistic regression in order to identify a smaller subset of important variables. I start with N=51 (28/23) and 32 predictors.   So far it looks pretty promising, because I can identify four important predictors in my optimal model.   Now I would like to take those four predictors and examine them along with some control variables in a standard logistic regression.   My question is, does that analysis strategy make sense? Is there a better way to include controls or other variables that might be interesting?  For a better understanding:   Identify important variables via Lasso logistic regression Do further analysis including identified predictors and other control variables using standard logistic regression (using AIC to check model fit) Prove or find a counterexample: For all real numbers x and y it holds that x + y is irrational if, and only if, both x and y are irrational. The following is a Homework Question that I've been working on and I would like some feedback on my answer: Prove or find a counterexample: For all real numbers $x$ and $y$ it holds that $x + y$ is irrational if, and only if, both $x$ and $y$ are irrational.  So I've got (or at least like to think I've got) a counter example.  Let $x = 1$ and $y = \sqrt{2}$.   Thus $x$ is rational and $y$ is irrational. Adding $x$ and $y$ gives us $1 + \sqrt{2}$ which cannot be simplified any further (right?) and is an irrational number.  Thereby proving that $x + y$ can be irrational without both x and y being irrational.   Is this okay? Any feedback is greatly appreciated thank you!