I'm trying to create a warped space curve like examples here. Any ideas? I can't seem to get my plane to dip.
I want to create a animation like those "spacetime deformation" ones, but I am stuck on creating "spacetime".  (a mesh/plane).  I created a plane, gave it a soft body, collisions, and a passive rigidbody.    A cube with a rigidbody and collisions will land and deform the mesh, but it snaps right back.  How can I make it so the cube lands, and then leaves the plane deformed, and the cube just sits there?  I googled around and searched this site, nothing comes up.  An image of what I want (after it settles):    The ball depressed the mesh, creating an indentation.
The characteristic and minimal polynomial of a companion matrix Defining my own None-like Python constant Best Place to put Feature Requests? The only place I am aware of is the . I have a Macbook and an iMac, generally I work on my Macbook, but sometimes I need that information on my iMac. My OS is Mac OSX Snow Leopard. Did Snape ever commit murder? It's well known that Severus Snape was, in one way or another, a Death Eater since he was at Hogwarts. He hung out with the likes of Avery and Mulciber who became well known Death Eaters, he joined Voldemort right after he left Hogwarts, and he basically became Voldemort's right hand man until the very end.   However, in his time as a Death Eater did he ever kill anyone? We know that he was a Death Eater for around 3 years before Voldemort fell; Lily and James died at 21 and they were the same age as Snape, so it would have been 3 years since they left Hogwarts. Then after Voldemort came back in book 4, Snape would have been a Death Eater again for around 3 years. That's a total of around 6 years of Death Eaterhood with Voldemort.  So, in either of these periods, did Snape commit murder as part of his job as Death Eater? I'm not counting a certain death at the end of book 6 for reasons which are obvious if you've read book 7.   Clearly it's much more likely he killed before Voldemort fell since that roughly correlated with the period when he pledged allegiance only to Voldemort, before he became a teacher at Hogwarts. But did he ever do it? How the `\alignat` works in ams package I have read the related question(), which had detailed answer but still don't know what the meaning of the \alignat's argument. It is said in  that      This environment takes one argument, the number of “equation   columns”: count the maximum number of &amp;s in any row, add 1 and and   divide by 2.   What is the meaning of adding one in &amp; number and divide by two? I presumed the argument is given by the user, not automatically generated by the system? It would seem that LIGO measures wibbles in the metric (not manifold) of spacetime:    It would seem that the expansion of the universe is an expansion of the metric of spacetime:    Imagine for a moment that LIGO is not an interferometer. (So, it just plain times speed changes, rather than using phase shift of orthogonal directions.)  If the ends of one of the arms was indeed receding away from each other, at a speed consistent with the expansion of the universe, is the sensitivity of real-world LIGO of the needed sensitivity of a machine which could measure that shift?  On other words: ideally I'd like to know these two meters:  (A) The left arm of LIGO is about 4km. It was stretched/shrunk (a few times) for roughly .01 seconds by the gravitational wave.  How many meters was it stretched/shrunk in .01 seconds?  (B) Assuming the same abstract LIGO arm was affectable and affected by the expansion of the Universe. How many meters is it stretch/shrunk every .01 seconds?    Note - of course, an interferometer is an ingenious device to measure extremely small changes in speed - assuming the changes are orthogonal. Of course, an interferometer, per se, can't at all measure the expansion of the universe since that is uniform in both directions. The sense of my question is, can something that measures distance changes > as accurately as &lt; the LIGO does, measure the expansion of the universe?  How big or small is the ongoing expansion of the universe compared to the wibble from the black hole system in question? Why do we need sigma-algebras to define probability spaces? We have a random experiment with different outcomes forming the sample space $\Omega,$ on which we look with interest at certain patterns, called events $\mathscr{F}.$ Sigma-algebras (or sigma-fields) are made up of events to which a probability measure $\mathbb{P}$ can be assigned. Certain properties are fulfilled, including the inclusion of the null set $\varnothing$ and the entire sample space, and an algebra that describes unions and intersections with Venn diagrams.  Probability is defined as a function between the $\sigma$-algebra and the interval $[0,1]$.  Altogether, the triple $(\Omega, \mathscr{F}, \mathbb{P})$ forms a probability space.  Could someone explain in plain English why the probability edifice would collapse if we didn't have a $\sigma$-algebra? They are just wedged in the middle with that impossibly calligraphic "F". I trust they are necessary; I see that an event is different from an outcome, but what would go awry without a $\sigma$-algebras?     The question is: In what type of probability problems the definition of a probability space including a $\sigma$-algebra becomes a necessity?       provides a plain English accessible explanation. The idea is a spinning pointer rotating counterclockwise on a circle of unit perimeter:       We begin by constructing a spinner, which consists of a circle of unit   circumference and a pointer as shown in [the] Figure. We pick a point   on the circle and label it $0$, and then label every other point on the   circle with the distance, say $x$, from $0$ to that point, measured   counterclockwise. The  experiment  consists  of spinning the pointer and    recording the label of the point at the tip of the pointer. We let the random   variable $X$ denote the value of this outcome.  The sample space is   clearly the interval $[0,1)$.  We would like to construct a   probability model in which each outcome is equally likely to occur. If   we proceed as we did [...] for experiments with a finite number of   possible outcomes,  then we must assign the probability $0$ to each   outcome,  since otherwise,  the  sum  of  the  probabilities,  over    all  of  the  possible  outcomes,  would not equal 1.  (In fact,   summing an uncountable number of real numbers is a tricky business;    in  particular,  in  order  for  such  a  sum  to  have  any  meaning,   at  most countably many of the summands can be different than $0$.)    However, if all of the assigned probabilities are $0$, then the sum is   $0$, not $1$, as it should be.   So if we assigned to each point any probability, and given that there is an (uncountably) infinity number of points, their sum would add up to $&gt; 1$. How to customize the Ubuntu Live CD? Panasonic Lumix G 25mm f/1.7 ASPH vs Olympus M. Zuiko 25mm f/1.8 How exactly do I install Minecraft Mods and what is Forge? I'm having a really, really hard time figuring out how to install mods on Minecraft. I've looked everywhere I can think of for help but the information is almost always outdated or unhelpful.  I've seen on several sites about the use of something called Forge. The Mod I want to use requires 1.6.4 Forge and I have both Forge and the Mod folders sitting in my downloads folder.  I haven't installed any kind of mods for any game prior to this and I have little clue to the technical side of Minecraft, so please keep this in mind when you give me an answer please!  Things that might help you figure out how to help me:   I want to play this mod  and am using the 1.6.4 Forge given on a link that website gives Is there a rising trend in Number Series I am trying to build a stock screening utility.   What  I am trying is to find if there is a rising trend in a time series of profit margins of a company. I know there can be dips in some years but I want to find if mathematically that overall there is a rising trend as well as towards the recent years there is higher margins as compared to previous years.   Is there any way we can find it mathematically?          Profit Return Year,Company A,Company B,Company C 2005,38.97,20.44,22.01 2006,22.4,20.59,20.63 2007,22.4,20.59,20.63 2008,21.56,22.01,23.87 2009,25,20,23.52 2010,25,22.38,18 2011,30,24.13,24.85 2012,32,25.43,27.47 2013,30,20,22 2014,35,27,20 How to Convert 0 to 10V analog signal to 0 to 2.5V for ADC input? I have an analog signal which ranges between 0V and 10V.  I want to linearly scale it down to 0 to 2.5V for my ADC.     I'm concerned that using a resistive voltage divider will affect signal quality.  Is this true?  If it's not true, what value resistor should I use for voltage divider? Checking if Ubuntu package contains desired update Prove that $\text{rank}(X^TX)=\text{rank}(X)$ Prove, for real $X$, that $\text{rank}(X^TX)=\text{rank}(X)$.  Could anyone please help me with this problem? I've tried to use full-rank factorization and rank-related theorems mentioned in my book but still failed to solve this. I am learning linear algebra by myself and my book has no solutions manual so I find it really hard to get used to solve linear algebra problems.    Many thanks in advance for your help! Layover at Narita, Japan. Do I need a transit visa? I will be transferring between two international flights at Tokyo Narita airport. I'm scheduled to depart the same day I arrive. I am planning to stay within the airport during the layover. Does anyone know if I will require a transit visa at Narita? A group is generated by two elements of order $2$ is infinite and non-abelian Let $z \in\Bbb{C}^{\times}$ such that $|z^3+\frac{1}{z^3}|\leq 2$. Prove that $|z+\frac{1}{z}|\leq 2$. Problem :  Let $z \in\Bbb{C}^{\times}$ such that $|z^3+\frac{1}{z^3}|\leq 2$. Prove that $|z+\frac{1}{z}|\leq 2$.  My approach : Since : $(a^3+b^3)=(a+b)^3-3ab(a+b)$ $\Rightarrow z^3+\frac{1}{z^3}=(z+\frac{1}{z})^3-3(z+\frac{1}{z})$ Now I don't know further about this problem whether or not this will help here. Please guide to solve this problem will be of great help, thanks. Here is a DOM-based XSS flaw reported by SalesForce Security Review team in our code:   RootComponent  &lt;aura:component extensible="true" abstract="true" access="global"                 description="Root template component"&gt;     &lt;!-- ... lot of other code ... --&gt;     &lt;aura:attribute name="label"                     type="String"                     access="global"                     description="Label of the form input element" /&gt;     &lt;!-- ... lot of other code ... --&gt;  &lt;/aura:component&gt;   SubComponent  &lt;aura:component access="global" extends="c:RootComponent"                  description="Child extension of RootComponent"&gt;     &lt;!-- ... lot of other code ... --&gt;     &lt;label&gt;{!v.label}&lt;/label&gt;     &lt;!-- ... lot of other code --&gt;  &lt;/aura:component&gt;   According to SFDC, "any app can extend SubComponent component and pass in  as a label and trigger a DOM-based XSS attack." The solution would be to "sanitize" label global attribute to avoid such attack. What is meant by sanitization of global attribute?  I tried to reproduce the so-called security flaw , but as label attribute is of type "String" , when we send it HTML, it is displayed as a string, not as interpreted HTML ... so I don't see where the security flaw could be :/  &lt;aura:application &gt;     &lt;aura:handler name="init" value="{!this}" action="{!c.doInit}" /&gt;      &lt;c:SubComponent aura:id="TestXSS" label="DOM-based XSS attacks" /&gt;  &lt;/aura:application &gt;   JS Controller  ({     doInit: function(component, event, helper) {         var XssAttack = '&lt;img src=x onerror=alert(1) /&gt;';        component.find('TestXSS').set('v.label',XssAttack);     } })   Output    We have global attributes everywhere. Our components are packaged and meant to be extended by client implementation. Do we actually need to sanitize them? Eclemma not offering report exportation option