When traveling through the vacuum, electromagnetic waves experience an increase of wavelength (redshift).   According to this equation:  $$E=\frac{hc}{\lambda}=h\nu$$  ( Where, as we know, h is the Plank constant, c is the light speed, λ is the wavelenght and ν is the frequency of the wave. )  An increment of the wavelength implies a decrement of the energy of the photon.  The question is, where does that energy go? Is it consumed during millions of years of movement of the EM or is there another explanation?
A photon emitted from a receding source (Doppler redshift) has less energy when detected at an observer's location. Please explain the energy loss from the perspective of energy conservation.
I have seen several answers and proofs here at MSE that a self-adjoint operator $T$ on a Hilbert space $H$ where $T^2=T$, implies $T$ being an orthogonal projection operator.   The thought struck me; what would happen if the condition $T^2=T$ is replaced by $T^3=T^2$ or instead by $T^4=T^3$ or why not more generally by $T^n=T^{n+1}$ for some $n\in\mathbb{N}$? Would this still imply $T$ to be an orthogonal projection operator?  I guess someone must have thought of this before me? In that case perhaps there is a reference in the literature for this or perhaps the proof is way simpler than I might expect? JAVA Bad variable reference? Receiving strange output - possibly memory address? What is the exact difference between an autoregressive (AR) and vector autoregressive model (VAR)?  I always thought that VAR would just be for more than two variables, until I learned that AR can also have more than two variables. I.e. I had a misunderstanding(?) that AR models are not always bivariate.  Before I write too much potentially false assumptions about the difference between AR and VAR, it would rather be interested to see if anyone can make provide a quick and good summary. Inspired by a StackOverflow question ().  Is there a DBMS that actually supports the = NULL syntax? PhD in Europe without scholarship from non-European homeland I earned my bachelors in Computer Engineering from my home country. I am now enrolled in a Physics masters program in the same university. Next year I plan to find a different university in Europe in which to enroll in a Computer Engineering PhD program.  However I doubt that I'll receive any scholarships from my homeland's government when studying abroad. Can I survive if I start to live out of my own my pocket? Is that enough to live in Europe just for a half year. Are there any available funds that can supplement my income such as a TA/RA's salary?  My main question is:   How to survive if I want to study PhD in Europe without any scholarship from my home country? Which country might provide sufficient support for a foreigner to study at graduate level?   I am interested to Germany and Finland but any European country would be acceptable! What happens when a moderator clicks 'leave open' in the close-vote queue? It takes  clicking "leave open" in the close-vote queue to remove the question from the queue.  How about diamond mods?  Do they remove it from the queue in one click, or not? Exporting Data From Salesforce - REST or SOAP? We have a requirement where we need to export records from salesforce tables into our application programmatically. I am reading on the various API's for data integration from salesforce mainly SOAP vs REST API's.  From what I understand, REST should be used when the web service requests are from mobile devices or browser based clients (since they understand JSON). Is that true? If that's the case how do Bulk REST API's fit the bill (since they are meant for bulk data transfers)?  I would like to get your thoughts on what are pros and cons in using SOAP or REST API's to export data records. Note that the requests are being made a java ee server application programmatically. After retrieving the records (probably in batches) from salesforce records we process (validate, filter etc) them and load them in our internal tables.  Thanks. What is the meaning of $\exp(\,\cdot\,)$? What is the meaning of the notation $\exp(\text{expression})$ ?  I think that it's something of the form $a^\text{expression}$ but does it mean that the base $a=e$ or can it be any base? Does anyone know where I can find cheat codes for Goldeneye 007 Wii? I know that the game hasn't even been out for a week, but does anyone know if any cheat codes have been released by Activision yet?  I know that they must exist since there is a cheat codes menu within the game. What can cause "Discovered - currently not indexed" in the new GWT What is it used for and why  doesn't it equal $\log{x^2}$? I am trying to use a  as input and then creating a query with it - so I need a .    I was surprised to find that it couldn't do the conversion implicitly or explicitly - but I don't even know how I would do this, as the Java API is still fairly new to me. Non academic career options for PhD in Math I am thinking of getting my M.S. in Computer Science. I chose C.S. because I enjoy programming and because its a solid choice, career wise.  Low unemployment, good pay, all that jazz.  But my real passions has always been math and lately I have been thinking about swapping and going for my graduate degree in Math. If I went the math route I would probably go full PhD (since I don't think there is much you can do with just a Masters in math).  But as much as I love math, I can't see myself being a math teacher. I would want to work in research or industry, applying math to solve real world problems.    What kind of non-academic jobs are there for someone with a PhD in math (or what is the best resource to see what jobs are out there)? Proficiency with specific weapons vs 'simple and martial'? In the PHB on pg. 146 it states that there are two weapon categories in which the players can be proficient: simple and martial.  As per  answer to another question, being proficient in either category makes the players character proficient in using all weapons of the respective category.   However in the race descriptions the players are given proficiency for specific weapons. Dwarfs, for example, have the trait Dwarven Combat Training giving proficiency with battleaxes, handaxes, throwing hammers and warhammers.   How do the two types of proficiencies interact with each other? LaTeX/BibTex not arranging citations by order of appearance I am having an issue with LaTex/Bibtex presenting my citations in order of appearance. I know there a plenty of questions on this and I have read some of them, but the solutions posted don't seem to do me any good. I am using MacTeX and TeXmaker.  I am writing a large document, like a Thesis. Chapters are split between individual Tex files and included using the \include command.  I have a large .bib file that is maintained by Mendeley (program I use for storing my references and producing a BibTex file).  I am using the package, cite (mainly for doing references like [1-3,6,9])  I have a pretty standard looking document.  \documentclass[11pt,a4paper]{report} \setcounter{secnumdepth}{3} \setcounter{tocdepth}{3} \newcommand{\doubleSignature}[3][Alex Mason]{% \parbox{\textwidth}{ \centering #3 \today\\ \vspace{2cm}  \parbox{7cm}{   \centering   \rule{6cm}{1pt}\\    #1  } \hfill \parbox{7cm}{   \centering   \rule{6cm}{1pt}\\   #2 } } } \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} %\usepackage[sorting=none]{biblatex} %\bibliography{Alex} % Where journals.bib and phd-references.bi \usepackage[pdftex]{graphicx} \usepackage{enumerate} \usepackage{nomencl} \usepackage{wasysym} \usepackage{booktabs} \usepackage{cite} \usepackage[left=1in,right=1in,top=1in,bottom=1in]{geometry} \graphicspath{{./Diagrams/}} \usepackage[labelfont={sf,bf}, margin=1cm]{caption} \usepackage{subcaption} \renewcommand{\figurename}{Fig.} \renewcommand{\tablename}{Tab.} \renewcommand{\bibname}{References} \author{NAME (MEng)} \title{TITLE} \date{\today} \makenomenclature %------------------------------------------------ \begin{document} \maketitle \pagenumbering{roman} %-----------------------------------------------certificate of originality----------------      -------------------------------------------- \input{CertofOrigin} \begin{abstract} ABSTRACT \end{abstract} %-----------------------------------------------contents------------------------------------------------------------ \tableofcontents \listoffigures \addcontentsline{toc}{chapter}{List of Figures} \listoftables \addcontentsline{toc}{chapter}{List of Tables} \chapter*{Acknowledgements} \addcontentsline{toc}{chapter}{Acknowledgements} ACKNOWLEDGEMENTS \printnomenclature[1.5in] \addcontentsline{toc}{chapter}{Nomenclature} \pagebreak \pagenumbering{arabic} \include{2ndYearReport_CHAP1} \include{2ndYearReport_CHAP2} \include{2ndYearReport_CHAP3} \bibliographystyle{unsrt} \bibliography{Alex} %\printbibliography \end{document}   The goofy looking part at the top (\newcommand{doubleSig.....) is just for when i input a special page I made containing a certificate of originality spiel with two boxes for signatures and my university logo.  As you can see I am using the standard bibtex way of doing bibliographies by stating the style then the stating the bib file to use right at the end of the document. I have tried biblatex but can't get it to work. It says it hasn't produced the bib file but doesn't really state why.  As far as I am aware everything was working A-OK until I started on the second chapter and began adding citations in there. Now my citations are all messed up and won't correct. My first citation starts with [9]!!!  [1] appears in a figure caption later down the page, after 10, 11 and 12 have been called!  I have tried deleting all the working files (bbl, aux, log etc) but nothing happens. I get the same result. IIRC I used to have this problem with MS Word and is part of the reason why I switched to LaTex...yet it seems to have followed me!   bibtex does through a few warnings when it runs stating that some references are missing journal names or volume numbers. Would that be a reason?  What have I done wrong with my code? Orthogonal matrix and orthonormal columns Forgotten the pattern and phone not showing the "forgot pattern" button. I upgraded my Moto G2 to Android Lollipop using over-the-air upgrade. It was awesome but I set a pattern lock which I forgot. Usually after 5 wrong attempts it shows the "forgot password" button but it is not showing that button even after 100 wrong attempts. How to unlock the phone? Are there any published details of Kenobi's communication with Lars family on Tatooine before ANH? I am using cURL to insert data into salesforce. It works with single record but I need to insert multiple records at a time. Is it possible to do so and is it possible via a REST interface? The characteristic and minimal polynomial of a companion matrix of a monic polynomial $f \in \mathbb F\left[x\right]$ in $1$ variable $x$ over a field $\mathbb F$ plays an important role in understanding the structure of finite dimensional $\mathbb F[x]$-modules.  It is an important fact that the characteristic polynomial and the minimal polynomial of $C(f)$ are both equal to $f$. This can be seen quite easily by induction on the degree of $f$.  Does anyone know a different proof of this fact? I would love to see a graph theoretic proof or a non inductive algebraic proof, but I would be happy with anything that makes it seem like more than a coincidence!