Pic 1 is Eevee  Pic 2 is Cycles at exposure of 1  Pic 3 is Cycles at exposure of 5  Note that the backgorunds are of similar exposure in 1 &amp; 2, implying that while the 3rd may be nice and bright, that's only because the exposure is overkill. That actual background/world color is fairly close to black. Side note: I assume it's a 2.8 bug but the option to change the energy of the light disappears when you switch to cycles.
I get different lightning render with the same scene camera setup.  Cycles render (both experimental and supported feature set) gets weaker lightning and needs more energy.  How can I get the same lightning and reflection setup with EEVEE and Cycles?
"'void' type not allowed here" error (Java) I would like to know: How come that  $$\sum_{n=1}^\infty n x^n=\frac{x}{(x-1)^2}$$  Why isn't it infinity? How do I manage double-faced cards in Innistrad (MTG) tournament play? Hide parameterless constructor on struct Lower bound on energy is potential minimum Suppose we have a particle of mass $m$ that is in an eigenstate $|\psi\rangle$ of the Hamiltonian $\hat{H}=\hat{T}+\hat{V}$, where $\hat{T}$ is the kinetic energy operator and $\hat{V}=V(\hat{r})$ is the potential energy operator. If the potential has lower bound $V_0$, then is it necessary for the energy eigenvalue $E$ of $|\psi\rangle$ to be greater than $V_0$? Classically this is true, since we regard negative kinetic energy as physically unrealizable/meaningless. However, I don't know if I can necessarily say the same in the quantum case. For example, what I'm tempted to do is write  $$\langle\psi | \hat{T}|\psi \rangle = \langle\psi | E-\hat{V}|\psi\rangle$$  and say "If $E&lt;V_0$, then the RHS is necessarily negative, implying the LHS is as well, which we will regard as physically meaningless. If $E=V_0$, then $|\psi\rangle$ is trivial.", but I'm not sure if that's right.   Confused by that, I then wanted to show that, if $E&lt; V_0$, then a non-trivial $|\psi\rangle$ is non-normalizable. However, I'm not entirely sure how to do this. What is an observer in quantum mechanics? My question is not about (pseudo) philosophical debate; it concerns mathematical operations and experimental facts.  What is an observer? What are the conditions required to be qualified of observer, both mathematically and experimentally? Sequential Update of Bayesian I am currently reading Murphy's ML: A Probabilistic Perspective. In CH 3 he explains that a batch update of the posterior is equivalent to a sequential update of the posterior, and I am trying to understand this in the context of his example.  Suppose $D_a$ and $D_b$ are two data sets and $\theta$ is the parameter to our model. We are trying to update the posterior $P(\theta \mid D_a, D_b)$. In a sequential update, he states that, $$ (1) \ \ \ \ \ \ \ \  P(\theta \mid D_{a}, D_{b}) \propto P(D_b \mid \theta) P(\theta \mid D_a) $$ However, I am slightly confused as to how he got this mathematically. Conceptually, I understand that he is saying the posterior $P(\theta \mid D_a)$ is now a prior used to update the new posterior, which includes the new data $D_b$, and is multiplying this prior with the likelihood $P(D_b \mid \theta)$. Expanding the last statement out, I have, $$  P(D_b \mid \theta) P(\theta \mid D_a) = P(D_b \mid \theta) P(D_a \mid \theta) P(\theta) $$  but are we allowed to say $P(D_a \mid \theta) P(D_b \mid \theta) = P(D_a, D_b \mid \theta)$ in order to make the connection in (1)? How to recover a dropped stash in Git? I frequently use git stash and git stash pop to save and restore changes in my working tree. Yesterday I had some changes in my working tree that I had stashed and popped, and then I made more changes to my working tree. I'd like to go back and review yesterday's stashed changes, but git stash pop appears to remove all references to the associated commit.  I know that if I use git stash then .git/refs/stash contains the reference of the commit used to create the stash. And .git/logs/refs/stash contains the whole stash. But those references are gone after git stash pop. I know that the commit is still in my repository somewhere, but I don't know what it was.  Is there an easy way to recover yesterday's stash commit reference?  Note that this isn't critical for me today because I have daily backups and can go back to yesterday's working tree to get my changes. I'm asking because there must be an easier way! Using special auto start servlet to initialize on startup and share application data Proving there are infinitely many pairs of square-full consecutive integers So the question goes like this :  A positive integer $n$ is called square-full if for every prime $p$, $p \, | \, n$ implies $p^2 \, | \, n$, i.e. every prime power factor of $n$ occurs at least at the second power. This is equivalent to saying that there is no prime $p$ such that $p \, \| \, n$.  Show that there are infinitely many consecutive pairs of square-full numbers, i.e. infinitely many $n$ such that $n$ and $n+1$ are square-full.  The context of the question highly suggests that this can be proved by induction and it is the solution that I am looking for. It is not a homework, just something that caught my attention because I couldn't find any natural answer to it... I hope I'm not missing something trivial!  I've tried assuming $n_1, n_2, \dots, n_k$ were the first $n_k$ integers such that $n_i$ and $n_i+1$ are square-full, and then generate some polynomial in those $2k$ integers to get a new couple $n_{k+1}$, $n_{k+1} + 1$ but after a few natural tries I got nothing good out of it. Any ideas? What exactly is a photon? Consider the question, .  The answers say, "an elementary particle" and not much else. They don't actually answer the question. Moreover, the question is flagged as a duplicate of,  &ndash; the answers there don't tell me what a photon is either. Nor do any of the answers to  mentioned in the comments. When I search on , I can't find anything useful. Questions such as,  look promising, but bear no fruit.  say things like, "the photon is an excitation of the photon field." That tells me  nothing. Nor does the , which says:     The photon is the quantum of the electromagnetic four-potential, and therefore the massless bosonic particle associated with the electromagnetic force, commonly also called the 'particle of light'...   I'd say that's less than helpful because it gives the impression that photons are forever popping into existence and flying back and forth exerting force. This same concept is in the  too - but it isn't true. As , "Virtual particles only exist in the mathematics of the model." So, who can tell me what a real photon is, or refer me to some kind of authoritative informative definition that is accepted and trusted by particle physicists? I say all this because I think it's of paramount importance. If we have no clear idea of what a photon actually is, we lack foundation. It's like what :     Photons seem to be one of the foundation ideas of quantum mechanics, so I am concerned that without a clear definition or set of concrete examples, the basis for understanding quantum experiments is a little fuzzy.   I second that, only more so. How can we understand pair production if we don't understand what the photon is? Or the electron? Or the electromagnetic field? Or everything else? It all starts with the photon.   I will give a 400-point bounty to the least-worst answer to the question. One answer will get the bounty, even if I don't like it. And the question is this:    What exactly is a photon? Get e-mail addresses from Gmail messages received I want the QED symbol to be 1 line lower at the end of proof Just as my title says, I would prefer to have my qed symbol to be 1 line lower than the last line of my proof. By default its on the same line and aligned to the right.   How can I achieve this?  EDIT: See below code for an example:  \documentclass[11pt,a4paper]{article} \usepackage[margin=3cm]{geometry} \usepackage[english]{babel} \usepackage{amsmath, amsthm} \begin{document}  \begin{proof}     Hello there good chap! I'll put in another line here just to be sure its clear what I mean. \end{proof}    \end{document} Division rules for other number systems? How could we make the same division rules for other number systems, like in our decimal system: a number is divisible with 2 if it's last digit is 0,2,4,6,8, by 3 if the sum of digits is divisible with 3, and so on.  Can we do the same rules for g-based number systems too, where g is not 10, and greater than 1? How small a quantity should be added to x to avoid taking the log of zero? I have analysed my data as they are. Now I want to look at my analyses after taking the log of all variables. Many variables contain many zeros. Therefore I add a small quantity to avoid taking the log of zero.   So far I've added 10^-10, without any rationale really, just because I felt like adding a very small quantity would be advisable to minimize the effect of my arbitrarily chosen quantity. But some variables contain mostly zeros, and therefore when logged mostly -23.02. The range of the ranges of my variables is 1.33-8819.21, and the frequency of zeroes also varies dramatically. Therefore my personal choice of "small quantity" affects the variables very differently. It is clear now that 10^-10 is a completely unacceptable choice, as most of the variance in all the variables then comes from this arbitrary "small quantity".  I wonder what would be a more correct way of doing this.  Maybe it's better to derive the quantity from each variables individual distribution? Are there any guidelines about how big this "small quantity" should be?  My analyses are mostly simple cox models with each variable and age/sex as IVs. The variables are the concentrations of various blood lipids, with often considerable coefficients of variation.  Edit: Adding the smallest non-zero value of the variable seems practical for my data. But maybe there is a general solution?  Edit 2: As the zeros merely indicate concentrations below the detection limit, maybe setting them to (detection limit)/2 would be appropriate? Is exponential map locally a diffeomorphism w.r.t. base point? Let $M$ be a riemannian manifold and $\exp_p: T_pM \rightarrow M$ the exponential map at $p \in M$.  At each point $p\in M$, $\exp_p$ can be restricted to a neighborhood $V$ of $0\in T_pM$ so that $\exp_p|_V$ is a diffeomorphism. Let $U\subset M$ denote image of $V$ under this map.  Choosing an orthonormal basis $\{E_i\}$ for $T_p M$ and using the isomorphism $E: \mathbb R^n \rightarrow T_pM$, where $E(x^1, \dots, x^n)= x^iE_i$, gives normal coordinates $(U, \phi)$, where  $$ \phi := E^{-1} \circ \exp^{-1}_p: U \rightarrow \mathbb R^n $$  My question is: can we fix some $z\in \mathbb R^n$ (small enough) and take some small neighborhood $\widetilde{U}$ of $p$ so that the function $\widetilde \phi$, defined as $$ \widetilde{\phi}_z (p) := \exp_p ( E(z)) $$ is a diffeomorphism when restricted to  $\widetilde{U}$?  (In the definition of $\widetilde \phi$, the isomorphism $E$ will also vary with $p$.) Calculate work done by a hovering helicopter over time This is likely to be very simple, but...  How does one calculate work done by a hovering unmoving aircraft over time?  As in work in Joules.  In this scenario, to remain hovering the aircraft has to exert a force that counters gravity (which would be its mass times G, pointing in opposite direction of gravitational pull).  However, work is defined as newton per meter, and the aircraft does not move.  Meanwhile the battery charge or fuel is going to be expended, so the energy is spent.  The other question here:   is dealing with conservation energy and not calculating drain/work performed by hovering. I have designed a circuit where I want to give a pulse of very short duration using a switch. How can I implement it in spice. Signed to unsigned conversion in C - is it always safe? How to influence the name of the pdf file created with pdfLaTeX (from within the source code)? I have a source file called 2011-05-27_Myfilename.tex and I'd like to create a PDF file from it called only Myfilename.pdf.  Can this be configured from within the .tex file itself?  (It seems to be possible with    pdflatex -jobname=Myfilename.tex 2011-05-27_Myfilename.tex   However, as many different files are concerned, It would be easier to have an option like output=Myfilename in the LaTeX source code.)