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Refused entry to UK, not sure what to do I'm a writer and theater/film director who has been traveling nearly all my life without incident. In February, I decided to pull up stakes in NYC and move to London. I am a freelancer and I'm working with three different organizations in NYC so I wasn't working illegally in the UK. I was, however, seeing if there might be some opportunities in London, ie. meeting with Artistic Directors of various theatre companies to see if they might be interested in producing my work.   In April, I was invited to a conference in San Diego and then a film festival in Switzerland. I didn't think it would be a problem if I went and then bummed around in France for a few days since I hadn't broken any laws and had left the UK well under my six month leave to stay. Well, when I tried to return to London, I was denied entry at Luton. The border control officer said I didn't have enough funds for a two month stay and put a black cross over a stamp in my passport. They put me in a detention room until the next flight back to Lyon, which was the following morning. I don't know anyone in Lyon so I ended up going to a friend's place in Paris.   After a few days of not knowing what to do, a friend suggested that perhaps I should try going back to London on the Eurostar since border control is in Paris. I wondered if I ought to go to the British Embassy but was deterred by something on their website that says that a visitors visa could take up to three weeks (I can't sit around here in Paris for three weeks) and anyway, the decision ultimately is with the border control, so I decided to take a chance on the Eurostar. I bought myself a return ticket in two weeks to Paris just so I had something to show.   Well, the UK border control denied me entry after giving me a third degree. They accused me of lying and seeking work in the UK. They also insisted that the amount of money I had was not enough to live on for two weeks. So I'm back at my friend's place in Paris, wondering what to do.   Is it possible for me to ever get back to the UK? I had to cancel one meeting and I'm wondering if I have to cancel going to the Sheffield DocFest. (Two of my projects were accepted to programs there.)   Should I apply for a visa from the British Embassy? Will this really take three weeks? When I started to say something about obtaining a visa, the border control officer cut me off and said, "Why are you going to the Embassy? This has nothing to do with the Embassy. We make the decisions." Which way is up? (electric outlet) Can we model gravitation as a repulsive force? This question is actually related to my earlier question ("").  The fact that objects move a lot in the universe and that the universe is expanding, can imply that gravity is a repulsive force that increases with distance.. so the farthest objects repel us more.  This can still explain several existing observations, e.g., why does the apple fall?   Motion is the result of such repulsion. Two objects unlucky enough not to be moving relative to each other get squished due to the repulsion of the rest of the universe  around them. The earth repels the apple less than the stars so it is pushed towards the earth.   Furthermore, it can explain the expanding universe without the need for dark energy.  This could be demonstrated in a thought experiment. If we take a lot of same-charge particles (with small mass) such as electrons and lock them in a large box at a low enough temperature. The mutual repulsion of the particles may cause similar motion as if due to gravitational attraction.   Another experiment would be to measure the slight changes in our weight during day and night when the sun and earth align (if their masses are large enough to detect the feeble change in repulsion).   [EDIT: the question in the original form may not have been clear. It is "can we model".. with a yes/no answer and why (not). If downvoting, please justify. Android Debugging, how? Inspired exercise Sheet from Indesign I would like to create this sheet which was made it by adobe indesign   Could someone create it with latex ?     Here's my code:  \documentclass[12pt,a4paper,twocolumn]{report} \usepackage[margin=0.5in]{geometry} \usepackage[french]{babel} \usepackage{fontspec} \usepackage{graphicx} \usepackage{amsthm,amssymb,amsfonts,mathtools} \usepackage[utf8]{inputenc} \usepackage{multicol} \usepackage{multirow} \usepackage{amssymb} \usepackage{array} \usepackage{graphicx} \setlength{\columnseprule}{0.5pt} \thispagestyle{empty} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} %%%%%%%%%%head%%%%%%%%%%%%%%%%%%%%%%% \twocolumn[    \begin{@twocolumnfalse}  \begin{center}  \fbox{\Large Exercise Sheets} \end{center}     \hrulefill \end{@twocolumnfalse}   ]  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  \fbox{ Exercise $1$:}\\  Compute the following limits \begin{multicols}{2} \begin{enumerate} \item $\lim_{x\to 2}\dfrac{4x^{3}-5x-22}{x^{2}-x-2}$ \item $\lim_{x\to 0^{+}}\dfrac{x-\sqrt{x}}{x+\sqrt{x}}$ \item $\lim_{x\to 1}\dfrac{\sqrt{x+3}+\sqrt{x}-3}{x-1}$ \item $\lim_{x\to 2}\dfrac{x^{2}\sqrt{x+2}-8}{4-x^{2}}$ \end{enumerate} \end{multicols}  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \fbox{ Exercise $2$:}\\ Let $n\in\mathbb{N}^{*}$ \begin{enumerate}     \item calculate : ${\displaystyle \lim_{x\to 0}\dfrac{1-\cos(x)\cos(2x)\ldots+\cos(nx)}{x^2} }$     \item b     \item c     \item d     \item e     \item f \end{enumerate} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \end{document} Usage of "second/third/fourth ... last" In German there is a pattern for counting items from the end of a list. The last item is "das letzte", the one before is "das vorletzte", the one before that is "das vorvorletzte" and for each other item there's just another "vor" added.  While searching for an English translation for the German word "vorvorvorletzte" I came across   and  but none of them showed any usage pattern. Furthermore I didn't find any indication of which variant ("to", "from", no preposition) is used most nor to what area of the world those translations apply.  So I am still wondering: When there are items 1, 2, 3, 4 and 5, how can/will item 2 be called?   third from last? fourth from last? anteantepenultimate? fourth-last? fourth to last? the last but three item? the last but four item?   Is this a question of dialect/local use? I have downloaded tar.gz files. But I don't know how to install it. How do I install this kind of file? Let $E_n$ be $$E_n:=\{f\in C[0,1]\mid \text{exist } x_f\in[0,1] \text{ such that } |f(x)-f(x_f)|\leq n|x-x_f|,\, \forall x\in[0,1]\}.$$  How show that $E_n$ is nowhere dense, that is, $\mathrm{int}\  \overline{E_n} = \emptyset$?  Can someone help me? How to remove the lines which appear on file B from another file A? Irrationality of sum of two logarithms: $\log_2 5 +\log_3 5$ I try to prove that the number $$\log_2 5 +\log_3 5$$ is irrational. But I have no idea how to do it. Any hints are welcome. "One of them was/were you" If I am talking to somebody about a certain group of people in the third person, and then want to refer to the person I am talking with as one of those people, which do I say?     One of them were you      One of them was you. Whenever I play a PC game with the directional keys, I can only press two buttons at a time.  For instance if I am playing a shooter like R-Type, I cannot hold down the fire button while moving diagonally at the same time.  The computer simply ignores the extra button press.  How do I remove this limit so I can shoot while moving diagonally?  This limitation seems to apply for every game.  I am running Windows 7 if it makes any difference.  I noticed the same problem back when I used Windows XP. Let $f:[0,+\infty)\to\Bbb R$ be a function bounded on each finite interval. I want to show that if $\lim\limits_{x\to+\infty}[f(x+1)-f(x)]= L,$ then also $\lim\limits_{x\to+\infty}\dfrac{f(x)}x = L$ If G is a group, prove that $(ab)^n =a^nb^n$ implies G is abelian. I need to prove the equivalence of the following two statements, if $G$ is a group:     $G$ is abelian $\Leftrightarrow$  for each $a,b$ in $G$: $(ab)^n = a^n b^n$ for each integer $n$   I have done the $\Rightarrow$ implication, but I have no idea how to approach $\Leftarrow$, any hints are very welcome. No notification was received for an edit to a post Special package combination gives "No room for new \write." How to split strings into text and number? Boundary conditions for calculus of variations in phase space and under canonical transformations This might be a stupid question, but I just don't get it. In Hamiltonian mechanics when examining conditions for a $(\boldsymbol{q},\boldsymbol{p})\rightarrow(\boldsymbol{Q},\boldsymbol{P})$ transformation to be canonical one starts with $$ \dot{q}_ip^i-H(\boldsymbol{q},\boldsymbol{p},t)= \dot{Q}_iP^i-\bar{H}(\boldsymbol{Q},\boldsymbol{P},t)+\frac{d}{dt}W(\boldsymbol{q},\boldsymbol{Q},t)$$ where $\bar{H}$ is the transformed Hamiltonian, and $W$ is the generating function (now a function of $\boldsymbol{q}$ and $\boldsymbol{Q}$). This term shouldn't break Hamilton's principle, since $$ \delta\int_{t_1}^{t_2} dt\frac{d}{dt}W(\boldsymbol{q},\boldsymbol{Q},t)=\delta W(\boldsymbol{q},\boldsymbol{Q},t)|_{t_2}-\delta W(\boldsymbol{q},\boldsymbol{Q},t)|_{t_1}=0-0=0 .$$ But I don't see why the variation of $W$ should disappear at the endpoints (say at $t_1$). Expanding leads to: $$ \delta W(\boldsymbol{q},\boldsymbol{Q},t)|_{t_1}=\left(\frac{\partial W}{\partial q_i}\right)_{t_1}\underbrace{\delta q_i(t_1)}_{=0}+ \left(\frac{\partial W}{\partial Q_i}\right)_{t_1}\delta Q_i(t_1)=\left(\frac{\partial W}{\partial Q_i}\right)_{t_1}\delta Q_i(t_1).$$ $\boldsymbol{Q}$ is itself a function of $\boldsymbol{q}$ and $\boldsymbol{p}$, so $$ \delta Q_i(t_1)=\left(\frac{\partial Q_i}{\partial q_k}\right)_{t_1}\underbrace{\delta q_k(t_1)}_{=0}+\left(\frac{\partial Q_i}{\partial p_k}\right)_{t_1}\delta p_k(t_1)=\left(\frac{\partial Q_i}{\partial p_k}\right)_{t_1}\delta p_k(t_1). $$ It seems as if we also needed the variation of $\boldsymbol{p}$ to vanish at the endpoints, and I don't get this because (at least in cartesian coordinates) $\boldsymbol{p}=m\dot{\boldsymbol{q}}$ and the velocity can be different along the original and the varied orbitals even at the endpoints (they can point in totally different directions), so in general $\delta \dot{\boldsymbol{q}}(t_1)\neq 0$. What am I doing wrong? Can someone help me with this, please? Does the full quarantine period have to be observed for short trips of less than 14 days to England? I am planning to go to England for 2 days in preparation of moving (I already have a place rented and would be staying there) a few weeks later. I am coming from a country where I would need to do a 14 day quarantine as soon as I enter England. Does this mean that I have to stay in England for 14 days or can I leave the country before the end of the 14 day quarantine without facing a penatly? I have found no information about what the rules are for planned stays of less than 14 days on the , while  seems to say that short trips are OK. Official sources would be appreciated. Does the fact that matrices $A, B$ are similar imply that $A+cI$ is similar to $B+cI$? Let $A, B$ be similar $n \times n$ matrices over (say) $\mathbb{R}.$  Is it the case that $A+cI$ is similar to $B+cI$?    Here is an argument (which seems too good to be true...)  Since $A, B$ are similar, they have the same Jordan form. So we can write $PAP^{-1}=QBQ^{-1}=J$ for $P, Q$ invertible matrices.   Hence we have $P(A+cI)P^{-1}=PAP^{-1}+cI= J+cI.$ Similarly, we find $Q(B+cI)Q^{-1}=J+cI.$  Hence $A+cI$ and $B+cI$ are both similar to $J+cI$ and hence similar to each other.   Is this correct?