i have created a dithered and stepped distance fading effect similar to lod transitions in video games. the parameter is controlled by the camera's texture coordinates. (basically a gradient attached to camera) this unfortunately results in vertices closer to the camera fading in first. see image:  is there any way to keep this &quot;distance to camera&quot; value consistent for the entire object? like calculate the distance of the object's origin from the camera? or sample the current texture coordinate system form one vertex for the entire object? one solution would be to use drivers. see image:  the issue with this is that drivers don't change for object instances, like geometry nodes scattering. any help or ideas would be greatly appreciated SOLUTION the second answer in the linked duplicate question, camera x, y and z position are added with a driver since there is only one camera.
I have a blender file where a sphere is orbiting a force field. I want it to be more red when it's closer to the center, and more blue when it's further. I already have the math figured out, I just need to know how to get x/y coordinates in nodes.  Here's the file:
How can the median number of sexual partners be 6.1 and 3.6? Median number of female sexual partners in lifetime, for men 25-44 years of age, 2006-2008: 6.1  Wouldn't it only be able to be x.5 or x.0? What is a single word in English which means to look down on others (due to their younger age, lower socio-economic position, lesser experience, etc)    Not look down upon everyone else in general, but look down upon some particular person due to a feeling of superiority of oneself over them ( this superiority may come from the fact that one feels has more money, talent, etc)?    By "look down upon" I don't mean just the feeling of having superiority over another, but acting to them in a manner that reflects this pride as well (for example, perhaps he acts very rudely to them, since he feels superior to them and feels he can get away with it, or he feels it doesn't matter at all due to his superiority) How to initialize all members of an array to the same value? Undo git pull, how to bring repos to old state about://(null) popup? I encountered a popup similar to this one this morning while checking the weather report at  in Safari, though I have not been able to reproduce it.  The title is "about://(null)" and the text "Why you no play Candy Crush!!"  The popup occurred twice.  I tapped Cancel both times.  I suspect the source of this is rogue JavaScript in an ad network, judging from the fact that the screenshot below shows it in an ad-supported application, and when I saw it, I was on an ad-supported website.  My phone is not jailbroken.  I'm wondering if anyone is able to identify the source of the popup definitively.  Speculation is running rampant on Apple's support communities and elsewhere, from push notifications (delete Facebook and all your games!) to carrier notifications (which don't work on iPod Touches…), and my gut tells me little of it is helpful.  But I could also be very wrong.  (This is not my screenshot; it comes from .)    UPDATE 1: The Candy Crush people have this to say, but I'm not (yet) convinced there's actually something installed that is to blame:   UPDATE 2: Just reproduced it in the iOS Simulator while clicking around woodtv.com, but I'm not sure how to track it down further from here. Why does my image have space underneath? Intel HD Graphics 620: Does my display adapter support HDMI 2.0 necessary for a 4k display? I want to connect my laptop (Inspiron 15 5000 Series) to a 4k display. When I read online about this it seems that HDMI 2.0 is a necessaity to handle the large resolutions / refresh rates involved to get full benefits of a 4k display.  Use case: I'm not going to use this to play games. Most of my use-case is editing documents, emails, spreadsheets and some engineering drawings and video (watching not editing).   The goal behind going 4k is to boost productivity by having more things open at once to read side by side.   I looked into the Dell specs and they only mention an HDMI without going into the details of what type or whether it will support HDMI 2.0 / 4K TV.     How do I tell whether my Dell Inspiron Laptop (i7 7500 U processor) supports this?  I looked under the Display Adapters and can see that I have an "Intel HD Graphics 620"  listed.   Will this suffice to tell me if this display adapter will support HDMI 2.0 / 4k display?   Or should I be checking out some other settings?  Thanks! Regex: match everything but specific pattern In the book Limit Theorems of Probability Theory by Valentin V. Petrov, I saw a distinction between the definitions of a distribution being &quot;continuous&quot; and &quot;absolutely continuous&quot;, which is stated as follows:  &quot;...The distribution of the random variable $X$ is said to be continuous if $P\left(X \in B\right)=0$ for any finite or countable set $B$ of points of the real line. It is said to be absolutely continuous if $P\left(X \in B\right)=0$ for all Borel sets $B$ of Lebesgue measure zero...&quot;  The concept I am familiar with is:  &quot;If a random variable has a continuous Cumulative Distribution Function, then it is absolutely continuous.&quot;  My questions are: are the two descriptions about &quot;absolute continuity&quot; in (1) and (2) talking about the same thing? If yes, how can I translate one explanation into the other one? How do I run an executable file with a double click? I'm trying to run an executable (testdisk) but double click doesn't work. The only way is to run:  sudo ./testdisk   from terminal. But I'd like to open executables with double click in future. How can I do this? Say we have a rod with a fixed axis of rotation. If we give it a push at some point other than the axis, it will start to rotate. Say our force is $F$, then we might write: $\Delta P=F\Delta t$. I’m wondering how to incorporate angular momentum here. We know that for a single particle it holds that $L=r\times p$. And for an extended object with a fixed axis of rotation, we generally might write $L=I\omega$. However, can I write $L=r\times p$ too for the extended object? I would think that I would need to integrate. So we have $p_\alpha=m_\alpha v_\alpha=m_\alpha r_\alpha\omega$, where we consider an infinitesimal mass $\alpha$. So should I write $L=\int r^2\omega\,dm$? I’m confused whether to work with this integral, or just use $L=r\Delta P$ at once.  The reason I'm asking, is because I'm trying to calculate the sweet spot of a baseball bat. So this is my attempt at solving the exercise. Prove that the power set of an $n$-element set contains $2^n$ elements Theorem. Let $X$ denote an arbitrary set such that $|X|=n$. Then $|\mathcal P(X)|=2^n$.      Proof. The proof is by induction on the numbers of elements of $X$.      For the base case, suppose $|X|=0$. Clearly, $X=\emptyset$. But the empty set is the only subset of itself, so $|\mathcal P(X)|=1=2^0$.      Now the induction step. Suppose $|X|=n$; by the induction hypotesis, we know that $|\mathcal P(X)|=2^n$. Let $Y$ be a set with $n+1$ elements, namely $Y=X\cup\{a\}$. There are two kinds of subsets of $Y$: those that include $a$ and those that don't. The first are exactly the subsets of $X$, and there are $2^n$ of them. The latter are sets of the form $Z\cup\{a\}$, where $Z\in\mathcal P(X)$; since there are $2^n$ possible choices for $Z$, there must be exactly $2^n$ subsets of $Y$ of which $a$ is an element. Therefore $|\mathcal P(Y)|=2^n+2^n=2^{n+1}$. $\square$      From the above explanation, I don't understand why the set that contains $\{a\}$ will contain $2^{|n|}$ elements when it should clearly be $2^{|1|}$.  The construction of a new set $S$ is the union of the old set with cardinality $n$ and an new element $\{a\}$, therefore the set that do not contain $\{a\}$ still has cardinality $n$ and the set that contains $\{a\}$ is just $\{a\}$, one element...  Can someone please elucidate? Converting string into datetime I've got a huge list of date-times like this as strings:  Jun 1 2005  1:33PM Aug 28 1999 12:00AM   I'm going to be shoving these back into proper datetime fields in a database so I need to magic them into real datetime objects.   This is going through Django's ORM so I can't use SQL to do the conversion on insert. Why did this edit get attributed to the community user? It seems that  by the OP of  was attributed to the community user.   I'm assuming that the edit was by the OP from the edit summary:     updated my question   and from the actual update. Both texts are speaking in the first person. In my question's preview, the attached image looks rotated. So, assuming you are able to see it in the real orientation, can anyone determine what is that dust flake type thing on the top, slightly towards the left?   One looks like a dust flake and there's another dot to the left of it?  Note: I wont have physical access to the camera until the weekend.  Is it just a dust flake on the lens or can it be some problem with the sensor? Its a 3 month old Canon 1500D. Confused at + and ++ in TikZ I can't seem to figure out the difference between + and ++ relative coordinates in TikZ.   I understand ++. ++ specifies delta coordinates that are added to the last current point, the current point is then set to the new absolute current point (correct?):  \draw (0,0) -- ++(1,0) -- ++(0,1) means:  set Current Point to (0,0) add (1,0) to Current Point = (1,0) set Current Point to (1,0) add Current Point (1,0) to (0,1) = (1,1) set Current Point to (1,1)   I can't seem to figure out that + does, when I try it out it looks like the coordinates in the +(x,y) are absolute coordinates rather than delta coordinates, but the manual says otherwise Let $A$, $B$ be two reduced $k$-algebras. Then if an element of the form $$\sum a_{i}\otimes b_{j}$$ is nilpotent, we can compose it with any $k$-homomorphism $f$ from $A$ to $k$ to get a homomorphism from $A\otimes B$ to $B$. This map's image is $$\sum f(a_{i})\otimes b_{j}$$must be nilpotent as well. So if we assume $b_{j}$ is linearly independent in the first place, we may reason that $f(a_{i})=0$. This showed that $a_{i}$ are in the Jacobson radical of $A$. However, we only know $\mathrm{Nil}(A)=0$, and it is not clear to me how to pass from the Jacobson radical to the nilradical without using some commutative algebra machinery.   Here is what I think that might work. If $A$ is of finite type, then by Nullstellensatz we can assert the above is true. But if $A$ is not of finite type, then I can write $A=k[x_{1},...,x_{n}][X]$, where $n$ is the transcendence degree of $k(A)$ and $k[X]$ is finite over $k$. Then I should be able to pass from $k[X]$ to $A$ by inductive argument on the transcendental degree of $k(A)$, since prime ideals are maximal in a UFD (I am working with $k[x]$ by introducing $[x]$).   The proof I have for the case of finite type is not satisfying. Given $I\subset k[X]$, using Nullstellensatz one can show that $$I_{X}V_{X}[I]=\sqrt{I}$$ where $V_{X}[I]$ is the set of all points in $X$ on which $I$ vanishes, and $I_{X}(V_{X}[I])$ be the ideal in $k[X]$ which vanishes on $V_{X}[I]$. Granting this, let $I=(a_{i})$, then we want to show $I=0$, which is $V_{X}[I]=X$. This follows since if $U\subset W$, then $V_{X}[U]\supset V_{X}[W]$. Since $V_{X}[I]\supset V_{X}[m_{x}]$ for all maximal ideal corresponding to points, it must be $X$. This proof is unnecessarily winding by using the ideal-variety correspondence. Ideally I should be able to construct a pure algebraic proof.   The thing not clear to me is whether the above strategy really works. Namely I am not sure if I can really induct on the transcendental degree of $k(A)$. To make matters simple assume we showed the statement holds for $A$ with transdental degree $&lt;n$. For $A$ with transdental degree $n$ we can thus write it as $k[A'][x]$. Then any maximal ideal $m'$ of $k[A'][x]$ must correspond to a maximal ideal $m=m'\cap k[A']$ in $k[A']$. But it seems not possible to show that any prime ideal is maximal. Indeed considering the simple example of $k[x,y]$, where $(x)$ is a prime ideal but not maximal since $k[x,y]/(x)=k[y]$ is not a field. The problem is in the inducting process the base ring is not neccessarily a field, and so this strategy cannot work.   I am thinking maybe I can show $m'=m[f(x)]$ with $f(x)$ some irreducible polynomial in $k[A'][x]$. Because we know $k[A'][x]$ is noetherian by Hilbert's basis theorem, so in particular $m'$ must have a finite generating set. And we can reduce the number of irreducible polynomial to 1 since $m'$ is a maximal ideal. But I still do not know how to use this to finish the proof. @future method: Unsupported parameter type I am trying to copy records from one org to other via web services. I am calling a class which has logic written into a trigger. But @ future method is not taking sObject  list as a parameter. Can someone suggest me an alternative?  The Code:  public class webServicesTriggerClass   {     @future public static void webServicesMethod(list&lt;MyFriend__c&gt; mfList)     {         partnerSoapSforceCom.Soap sp = new partnerSoapSforceCom.Soap();       partnerSoapSforceCom.LoginResult lr = sp.login('hitesh.kumar.singh@accenture.com.varun','4Rajyavardhan');      soapSforceComSchemasClassNiralaapp.SessionHeader_element ses = new soapSforceComSchemasClassNiralaapp.SessionHeader_element();      ses.sessionId = lr.sessionId;       soapSforceComSchemasClassNiralaapp.MyFriendsDetailSoapApi vNapp=new soapSforceComSchemasClassNiralaapp.MyFriendsDetailSoapApi();      for(MyFriend__c mf:mfList)       {        string  s1= mf.myEmail__c;        string  s2=mf.friendName__c;         string  s3=mf.friendEmail__c;        string  s4=mf.aboutFriend__c;        integer i1=Integer.ValueOf(mf.age__c);        boolean result=vNapp.addFriendDetails(s1,s2,s3,s4,i1);        system.debug('################' +result);           }     }    }     Trigger-->  trigger webServicesTrigger on MyFriend__c (after insert)     {      webServicesTriggerClass.webServicesMethod(trigger.new);    }     Error--    Error: Compile Error: Unsupported parameter type LIST at line 3 column 30 Can anyone please tell me whether the following function $d:\mathbb{R}^2 \times \mathbb{R}^2 \to  \mathbb{R}$ is really a metric or not on $\mathbb{R}^2$.  $$ d((x_1,x_2),(y_1,y_2))= \begin{cases} |x_1-y_1|, &amp;\text{ if } x_2=y_2\\ |x_1|+|y_1|+|x_2-y_2|, &amp;\text{ if } x_2 \neq y_2. \end{cases} $$  If it really is indeed a metric, please give the proof of triangle inequality.(I'm OK with the other two conditions). What is the first movie to show this hard work message at the very end? What is the first movie to show this hard work message at the very end?