Do neutrinos follow the Standard Model and get their mass via the Higgs Mechanism or we still don't know about the origin of their mass as neutrinos with mass are beyond the Standard Model?
I was reading the CernCourier, my favorite source of message on Higgs and friends. I was rather shocked, when I saw this:     "The mechanism by which neutrino mass is generated is not known."   What? Not known?  says: In Higgs-based theories, the property of 'mass' is a manifestation of potential energy transferred to particles when they interact ("couple") with the Higgs field, which had contained that mass in the form of energy.  Does this mean that neutrinos don't couple to the Higgs field?
Aligning three figures next to each other based on text width Problem:  I am trying to align three figures next to each other with text centered to each figure. This is going well until the box for the third box does not adjust after the text width.  Minimal Working Example (MWE):  \documentclass{article} \usepackage{graphicx} \usepackage{caption}  \begin{document}  \begin{figure}[!tbp]   \centering   \begin{minipage}[b]{0.2\textwidth}     \includegraphics[width=\textwidth]{icon-password.eps}     \caption*{Login system}   \end{minipage}   \hfill   \begin{minipage}[b]{0.2\textwidth}     \includegraphics[width=\textwidth]{icon-shopping.eps}     \caption*{Shopping cart}   \end{minipage}   \hfill   \begin{minipage}[b]{0.2\textwidth}     \includegraphics[width=\textwidth]{icon-clock.eps}     \caption*{Temporary information}   \end{minipage} \end{figure}  \end{document}   Outputs:   Desired outcome:  To get the width to adjust after the text so that "Temporary information" can be written out in one line instead of two. Subdivision Surface on curved mesh I'm trying to delete those ugly lines visible in the cylindrical shape of the lens. What is causing them is the added edge loops I made for the protruding detail with the switch. The problem is that if I delete those edges, it'll look even worse because of the n-gons. Any ideas? How to read a single character from the user? For $f :\mathbb{R} \rightarrow \mathbb{R}\displaystyle$ we have ${\lim_{n \to +\infty} f(x+n) =0}$ almost everywhere I want to show that for $f: \mathbb{R} \rightarrow\mathbb{R}$ Lebesgue integrable  $\displaystyle{\lim_{n \to +\infty} f(x+n) =0}$ almost everywhere.  It is clear to me that this statement is true and I have tried to prove it by contradiction, by assuming that either $\displaystyle{\lim_{n \to +\infty} f(x+n) =\infty}$ or$\displaystyle{\lim_{n \to +\infty} f(x+n) =K}$ with $K\in \mathbb{R}$ .  In the first case  we can follow that $|f|=\infty$ so that $\int_\mathbb{R}f=\infty$ and we have a contradiction.  In the other case we know that there must be an $a\in \mathbb{R}$ so that $\forall x&gt;a$ we have $f_+(x)&gt;K/2$ and by that:  $\int_{{\mathbb{R}}+}|f|&gt;\int_{\mathbb{R}_+}f_+=\int_{[0,a]}f_++ \int_{(a,\infty)}f_+&gt;\int_{[0,a]}f_++\int_{(a,\infty)}K/2=\infty$  Would this be enough to show the statement? Can I even make the assumption that the limit of $f(x+n)$ "exists"? Any hints would be great. We have no mention of Voldemort in Harry's sixth year. So, I was wondering- what could Voldemort have been doing? How to change background-color on text links on hover but not image links When / how should I ask about a manuscript's status in review? How to prove that 2017 divides $1^{2017}+2^{2017}+\dots+2017^{2017}$? How can I prove that $2017 \mid 1^{2017}+2^{2017}+\dots+2017^{2017}$? I tried proving it with the use of modulo, however it was to no avail. Afterwards, I  tried researching, for possible theorems, that may help, but that bore no fruit, either. Can you guys please help me proving it, as I am stuck? Thanking you in advance. I have a simular issue to the question asked in :  I have tried the solution provided by Jake. This makes that my picture fails to resize (scale) as i intend.  Whether i give Set scale=0.4 or Set scale=0.8 The size of the  picture remains the same  This is the code i use:  \begin{figure}[ht!] \centering \begin{tikzpicture}[Set scale=0.4, every node/.append style={transform shape},] % STYLES \tikzstyle{every node}=[rectangle,rounded corners, minimum width=100pt,     align=center,node distance=3cm,fill=black!10,inner sep=5pt,text width=3cm,minimum height=1.75cm,&gt;=stealth,text badly centered] % Draw forces \node [force, above of=rivalry] (top) {Firm strategy, structure and rivalry}; \node [force, left=1cm of rivalry] (left) {Factor conditions}; \node [force, right=1cm of rivalry] (right) {Demand Conditions}; \node [force, below of=rivalry] (bottom) {Related and Supporting industries}; %%%%%%%%%%%%%%%% % Draw the links between forces \path[&lt;-&gt;,thick]  (left) edge (right) (left) edge (top) (left) edge (bottom) (top) edge (right) (bottom) edge (right); \path[&lt;-&gt;,thick]  (bottom) edge (top); \end{tikzpicture} \caption{Porter's Diamond source:~\cite{Porter:1980}}% \label{fig:diamond}  \end{figure} Intuition behind using complementary CDF to compute expectation for nonnegative random variables I've read the proof for why $\int_0^\infty P(X &gt;x)dx=E[X]$ for nonnegative random variables (located ) and understand its mechanics, but I'm having trouble understanding the intuition behind this formula or why it should be the case at all. Does anyone have any insight on this? I bet I'm missing something obvious. Convergence in measure - product I'm trying to prove the following statements in Folland's book.  Let $(X,\mathcal{M},\mu)$ be a measure space. If $f_n\to f$ in measure and $g_n\to g$ in measure, then $f_n+g_n\to f+g$ in measure and $f_ng_n\to fg$ in measure (in this last case, assume $\mu(X)&lt;\infty$).  The first one is already done, but the second one is giving me trouble.   My attempt: We can take subsequences $f_{n_k}$ and $g_{n_k}$ such that $f_{n_k}\to f$ a.e. and $g_{n_k}\to g$ a.e. In this case, we know that $f_{n_k}g_{n_k}\to fg$ a.e. Note that $\mu(X)&lt;\infty$, so we can use Egoroff's theorem to conclude that $f_{n_k}g_{n_k}\to fg$ almost uniformly. Finally, almost uniform convergence implies convergence in measure, therefore $f_{n_k}g_{n_k}\to fg$ in measure.   The problem is that I just have convergence in measure for some subsequence of $f_ng_n$ and I need convergence in measure for the whole sequence. Also I don't know if using Egoroff's theorem is unnecessary, if this is the case, I would appreciate to see some more elementary prove.  Detail: We say that $f_n\to f$ almost uniformly if for every $\varepsilon &gt; 0$ there is some $E\subset X$ measurable, such that $\mu(E) &lt;\varepsilon$ and $f_n\to f$ uniformly on $E^c$.  Thank you! How can I calculate magnification ratio I get by reversing a lens? I am looking for a way to mathematically determine the maximum magnification ratio that is possible/practical to achieve by reverse mounting a non-macro lens, prior to purchasing the lens.     See related questions: Is it possible to search for punctuation/special characters? I tried to find a related question here, but was unsuccessful.  Someone on SO asked ... I tried searching SO and was presented with the search options page. Even Google fails at this search.  So my question is, is there some way to search for an exact word (in quotes) that won't cause it to fail? In English, I sometimes hear a phrase like green is the new black.  Literally, this makes absolutely no sense whatsoever.  What does it mean when someone says X is the new Y, when this makes no sense when taken literally?   gives plenty of examples:          I've found definitions online for specific examples, such as , but overall I don't understand what X is the new Y means, and I can't find it explained anywhere.  What does X is the new Y mean?  As far as I'm aware, this phrase exists only in English. How to use mysql JOIN without ON condition? Alternatives to "and/or"? Package Listings Warning: Text dropped after begin of listing when calling function I'm trying to this:  \newcommand{\code}[1] {\begin{lstlisting} {#1} \end{lstlisting} }   But I keep getting this error:  Package Listings Warning: Text dropped after begin of listing   I'm calling \usepackage and all so, do any of you knows how to solve this? How many squares on a 5-foot grid does a 5-foot radius spell affect? We had a situation come up regarding this term and how it affected spells.  In the spell Moonbeam, for example, it says a 5-foot radius cylinder appears. Does this mean that from the center of square it extends 2.5 feet into the next square hypothetically hitting up three squares or does this mean from the edge of one the target square to the five feet and five feet the other direction effectively covering only two squares for a total of 10 feet between total range of both squares?  I understand that radius means half the distance of a circle from the center point. The spell is not the issue but the understanding of radius as it pertains to the spell, as there are other spells that are worded similarly such as Fireball, etc.  Essentially we are asking, does the spell in the example effect one square or three? This would be saying the edge of the initial square is the point of origin and not the center of the square for the total distance of ten feet.  I had been working under the understanding that the radius is half of the distance and therefore dragging a ruler from the center of where I want the spell to take effect would get me the area of effect.  It's much easier to do this with Fireball, due to the larger area to effect, but this one has such a small area and therefore sparked the debate. We are using a grid system to mark the distance, etc. We play within the digital realm of roll20.com. How can you programmatically tell an HTML SELECT to drop down (for example, due to mouseover)? How can you programmatically tell an HTML select to drop down (for example, due to mouseover)? we have been using the Find Nearby Accounts app from appexchange for a while now. The app uses the Google Maps API vs 2 which is now deprecated and hence has rendered the app ineffective. I have tried migrating the Google maps API version for the app from v2 to v3 by generating a v3 API key. The URL for my salesforce instance was included in the creation of the Client ID under API Access. After all these steps, I still get the error "Problem with Address. I know the address is right.   Has anyone been able to get this working? Thanks.