In the 1930s almost 10,000 Jewish children arrived in Britain, escaping Nazi persecution. Britons rose to the occasion, quietly and without fuss. There is no reason why this could (NOT?) happen again, if only compassion WAS/WERE allowed back into public discourse.   Got from The Guardian. Can someone help me with the words I capitalized? Should "not" be there? Should it be "was" or "were"?
If I was... If I were...   When is it correct to use "If I was" vs. "If I were" in standard English?
Energy conservation of Virtual Particles - Quantum Fluctuation? I (as a middle-school student) was wondering how virtual particles even conserve energy of the entire system? I don't mean just the particle's energy, but conservation with respect to the surroundings?  Let me explain more, Einstein proved that $E = mc^2$ and equivalently, we can say $m = \frac{E}{c^2}$ . We however know mass causes curvature in space-time (gravity well). Now that statement being completely valid we can use Quantum Fluctuation, implying energy and time can be related by the relation:  $\Delta{E}\Delta{t}\approx\frac{\hbar}{2}$ and by that simple relation we can make the following points:   As the energy increases, the time allowed to be "borrowed" decreases, before it gives it back to the universe. As time increases, the energy allowed to be "borrowed" decreases.    These are completely satisfactory points I've made, I believe.  Now, I have read that the vacuum is filled with constantly bubbling virtual particles that get created from the energy "borrowed" by the above relation and is destroyed again, which satisfies the energy conservation laws.   This seems to imply that  in the short time the virtual particle exists, they must have a very small mass which is: $m_{1} = \frac{\Delta{E}}{c^2}$ and using basic classical mechanics rather than GR (for sake of simplicity) we calculate that the gravitational force mediated by this short-lived virtual particle;  $F_{g}= G\frac{m_1 * m_x}{r^2}$   where $m_x$ is an particle\mass in question. Nevertheless since we know the force set upon an object moves the object in a direction, we can say it would increase its kinetic energy by this factor: $F_g = \frac{1}{2}mv^2$ which is equal to $G\frac{m_1 * m_x}{r^2} = \frac{1}{2}mv^2$.  Surely, this implies that every time quantum fluctuations happen, energy of real-particles\masses increases and therefore violates energy conservation, but what prevents this violation from taking place?  If virtual particles are not really present and interact with objects like I thought, how can Hawking radiation (currently a large concept in black hole physics) then be accepted in physics community? What happens to matter in a standard model with zero Higgs VEV? Suppose you reset the parameters of the standard model so that the Higgs field average value is zero in the vacuum, what would happen to standard matter?  If the fundamental fermions go from a finite to a zero rest mass, I'm pretty sure that the electrons would fly away from nuclei at the speed of light, leaving positively charged nuclei trying to get away from each other.  Looking at the solution for the Hydrogen atom, I don't see how it would be possible to have atoms with zero rest mass electrons.  What happens to protons and neutrons?  Since only a very small part of the mass of protons and neutrons is the rest mass of the quarks, and since they're flying around in there at relativistic speeds already, and since the nuclear force is so much stronger than the electrical force with an incredible aversion to naked color, would protons and neutrons remain bound assemblages of quarks and virtual gluons?  Would they get a little larger?  A little less massive?  What would happen to nuclei?  Would they stay together?  If the protons and neutrons hold together and their properties change only some, then I might expect the same of nuclei.  Different stable isotopes, different sizes, and different masses, but I would expect there would still be nuclei.  Also the W and Z particles go to zero rest mass.  What does that do to the electroweak interactions?  Does that affect normal stable matter (outside of nuclear decay modes)?  Is the weak force no longer weak?  What happens to the forces overall? What is gravity and what causes objects to act against it? So I understand the concept of gravity, in that it's not actually a force, but more of a displacement in the spacetime grid. An object with a big enough mass will bend the spacetime, causing smaller objects to "attract" to it (not really, but good enough for what I am trying to figure out)   Ok so that makes sense, but what I am not understanding is, how come planets don't just get engulfed by the Sun? There must be something acting against the gravity for the planet to be a certain distance away from the sun. Am I not understanding this concept correctly? Split-like environment inside cases environment I'd like to have a cases environment with some cases that are too long to fit on one line. I tried this:  \begin{cases}   \begin{split}     long expression \\ second line of long expression   \end{split} &amp; condition \\   ...   but I get the warning     Package amsmath Warning: Cannot use 'split' here;   trying to recover with 'aligned' on input line 201.   It automatically replaces the split with an aligned environment, which looks like this:    Is there any way to get these long expressions to behave like they were in split or multline environments, with the top line flush left and the next line indented a little? Short story identification: society partitioned off by high wall Reading another question today reminded me of a short story I read in the early 90s (probably written in 60s or 70s though). A society is blocked off by a really high wall; the story follows a girl who tries to get over the wall. I think she manages it with a hot air balloon. When she reaches the other side she meets an older man who had managed to scale the wall in his youth - his solution had been to use a flock of birds to carry him.  UPDATE  I seem to recall that it splits off an elite group of people - getting over the wall is like a rite of passage. Most people don't even bother to get over it (or even be concerned by its existence at all), but a few try. There might be some magic involved (on the other / better side), or they might just be more advanced technologically.  FINAL UPDATE  As pointed out in the answer, and confirmed by me re-reading the story, I was mistaken in a few details. The main protagonist is not a girl, it's a boy called Porgie. He doesn't use a balloon, it's a glider he made, assisted with a broom. Magic is involved, but it's on the inside, with technology on the outside. Footnotes in tables? 2D inhomogeneous biharmonic equation I need some help in relation to this exercise    "Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$."  I'm not allowed to use quotient groups in the proof, because the exercise is in the chapter before.   I tried by induction on $n$. The case $n=1,n=2$ are obvious, but even  the case $n=3$ is giving me trouble so I give up studying the general case of the inductive step.  My other approach was studying left or right coset of $G$. But I only proved that if $g \in aH$ then $g^2 \notin aH$ if $a \notin H$, and I can't find a way to demonstrate that $g^n \in H$. (my starting idea was to prove that every power of $g$ is in a different coset but then I realize that in this way I don't handle several case, for example $g$ has period strictly lesser than $n$ and in conclusion it doesn't prove the exercise)  Maybe I'm missing something about indexes, and this is why I asked here for some help,  (I can't use quotient groups because they are introduced later than this exercise, forgot to add this info in the beginning) Thanks in advance :) Lipschitz Condition and Optimization I am reading paper on . I am trying to understand the following statement:     I would like to ask how the Ball doesnot contain the minimum of f? I would appreciate if this could be graphically shown something like following taken from Bayesian Optimization and Data Science Complete Statistic: Uniform distribution Take a random sample $X_1, X_2,\ldots X_n$ from the distribution $f(x;\theta)=1/\theta$ for $0\le x\le  \theta$.  I need to show that $Y=\max(X_1,X_2,...,X_n)$ is complete.  Now, I know I should multiply the sample distribution of $Y$ and multiply it with a function of $Y$, then integrate over the range of $\theta$ and equate them to zero. But how do I get the sampling distribution of $Y$? Why I cannot unpin some directories from file explorer in windows 10 I am a non-EU national, permanent UK Resident. Recently, my work issued me with a multiple Schengen visa with Norway as the first (main) point of entry. Now I want to go on holidays to Greece - do I need to apply to Schengen visa again, as Greece is not Norway and I am not going there for work? Prove that : $\displaystyle \lim_{n\to \infty} \frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+\cdots+\frac{1}{2n}=\ln 2$    the only thing I could think of is that it can be written like this :  $$ \lim_{n\to \infty} \sum_{k=1}^n \frac{1}{k+n} =\lim_{n\to \infty} \frac{1}{n} \sum_{k=1}^n \frac{1}{\frac{k}{n}+1}=\int_0^1 \frac{1}{x+1} \ \mathrm{d}x=\ln 2$$  is my answer right ? and are there any other method ?(I'm sure there are) Pretty new to Blender, I'm trying to learn how to make a studded wall.  How do I use the array modifier to use imperial units? For example, I would like to create a stud, and have them spaced 16 inches on center a set distance.  Thank you much!  Edit I've accepted the below answer, however, I had another issue I had to fix. The culprit was that when I scaled the initial object, I didn't apply the scale. Because I didn't apply the scale before the modifier, it wasn't working as expcted. Thank you much to  for helping me through this issue! Ubuntu 18.04 No WiFi adapter found [Dell Inspiron 3542.] Compactness and Hausdorffness Is it possible to have a topological space having all compact subsets closed, but the space itselt is not Hausdorff?  I couldn't find any counterexample. I tried $\mathbb R$ with cofinite, point inclusion and point exclusion topologies, but these didn't work.  Any suggestion in this context will be helpful for me. Explaining two-tailed tests I am looking for various ways of explaining to my students (in an elementary statistics course) what is a two tailed test, and how its P value is calculated.  How do you explain to your students the two- vs one- tailed test? I have a problem with this file tex:  \begin{document} \begin{figure} \begin{center} \begin{pspicture}(0,0)(1,3.8) \psline{-&lt;}(0,0)(0,.2) \psline{-}(0,.2)(0,.4) \psline{*-&gt;}(0,.4)(0,.9) \psline{-*}(0,.9)(0,1.4) \psline{-&lt;}(0,1.4)(0,2.4) \psline{-}(0,2.4)(0,3.4) \psline{*-}(0,3.4)(0,3.6) \psline{&gt;-}(0,3.6)(0,3.8) \rput(1,.4){$y=0$}%testo \rput(1,1.4){$y=1$} \rput(1,3.4){$y=3$} \end{pspicture} \end{center} \caption{} \end{figure} \end{document}   but I don't understand where is the error. Math.cos() gives wrong result I'm able to get a list of the field types with the following code.  $defs = \Drupal::service('plugin.manager.field.field_type')-&gt;getDefinitions();   I want to get the field type of a specific field. How do I get it?  For example, I'd like to check if the field type of field_image is _image. Is there code similar to the following one?  $fieldType = \Drupal::service('plugin.manager.field.field_type')-&gt;getDefinition('field_image');