I am arriving in the UK one day before canary islands are on the safe travel list on Sunday 4pm. Do I have to self-quarantine for the full 14 days or just until Sunday 4pm?
From 8th June there's been a  period for people entering the UK. From 10th July, travellers from  via a travel-corridor. If more countries are added to the list of exemptions then the date for each country will be later than the 10th July. If a traveller entered the UK from a country that is not on the exempt list and that country is added to the exempt list prior to the end of the 14 day self-isolation period does the self-isolation period end early? For example, if an individual entered the UK from France on the 5th July, should they remain in isolation for 14 days or does the isolation end on the 10th when France is added to the list of exempt countries?
Show that any set in a metric space can be written as the intersection of open sets Show that any set contained in the metric space $(X, d)$ can be   written as the intersection of open sets.   Definitions: A set $A \subseteq X$ is open if $\forall x \in A$, $\exists \varepsilon&gt;0$ such that $B_{\varepsilon}(x) \subseteq A$. A set $C \subseteq X$ is closed if and only if $X \setminus C$ is open.   I also know that the intersection of a finite collection of open sets is open and that any open ball contained in $X$ is open. How can I prove this question? If-else working, switch not I want to learn to use biper and biblatex in Lyx. This is how I would do it in LaTeX traditionally with biblatex and biber  \documentclass[12pt,a4paper,oneside,pdftex]{report} \usepackage[backend=biber]{biblatex} \addbibresource{minCuts.bib} ... \printbibliography \end{document}   The error is apparently originating from the \bibliographystyle command and biblatex package getting mixed, by . But I have no \bibliographystyle command in Preamble so they should not be mixed unless Lyx is somehow importing the \bibliographystyle.   How to resolve the biblioraphystyle error in Lyx with Biber and Biblatex?    Settings by the instructions  and Error        Document > Settings > Bibliography > Biber                  In Document > Settings > LaTeX Preamble                   Insert > List / TOC > BibTeX Bibliography...                        Package biblatex Error : '\bibliographystyle' invalid. If electrons were positive and protons were negative, would life be different? This was a question on a worksheet during my first week in a class on Electromagnetism. The answer is essentially:     No. Life would be no different if electrons were positively charged and protons were negatively charged. Opposite charges would still attract, and like charges would still repel. The designation of charges as positive and negative is merely a definition.   But how would we have negative charges within the nucleus? Taking a look at the , it seems that down quarks are required in this new "negative proton" to help with creating the pion to "transmit a residual part of the strong force even between colorless hadrons".  I tried to set out and try to find a particle with (-1) charge with a down quark (by going through this ) but all the particles are not stable with the exception of two unknown:   Bottom Xi Baryon Double Bottom Xi Baryon   Assuming one of the above are stable, could the strong force act between one of them and a neutron, implying its alright to have a negatively charged nucleus?  Edit: If it wasn't clear, my question concerned whether or not there existed stable baryons of $-1$ charge with down quarks that could "replace" the proton. Python Split String Lets Say we have Zaptoit:685158:zaptoit@hotmail.com   How do you split so it only be left 685158:zaptoit@hotmail.com Like the subject: short sci-fi story about Earth blockaded by other human colonies.  The best humans have colonized some stellar systems. But they begin to treat humans of earth like inferiors. A war began, colonies won the war and blockaded the earth, but despite this the earth won. Who is the author? What is tail recursion? The residue at $\infty$ I am stuck on the following problem :      $\,\,\,\,$*Problem*$\quad$The residue of an entire function at $\infty$ is $0$.      Solution: True. This follows from the definition of the residue at $\infty$ together with the Cauchy-Goursat Theorem. Another way to see this is to take the Taylor expansion for $f$ at $0$ $\displaystyle f(z)=\sum_{n=0}^\infty a_nz^n$ and replace $z$ with $1/z$ to get the Laurent expansion for $f(1/z)$ at $0$: $\displaystyle f(z)=\sum_{n=-\infty}^0a_{-n}z^n.$ Then we have that the residue at $\infty$ is given by the negative coefficient of the $1/z$ term of    $$ \dfrac1{z^2}f\left(\dfrac1z\right)=\sum_{n=-\infty}^{-2}a_{-n-2}z^n, $$   which is clearly $0$.   I am having trouble to understand the last few lines (in italic) in the given solution. Can someone give lucid explanation? Thanks and regards to all. I've recently embarked on my PhD studies (cancer, structural biology) and have yet to publish. Currently, there are some 200 papers in my name and several thousand under my surname. Because of this, I am considering switching my surname to an old, rare, surname in my family, which is only used by one active researcher.  My question is this: are there any reasonable alternatives that does not include legally changing my name? I personally don't mind changing it, but the old surname happens to be "noble", and may come off as quite pretentious. I would be able to change to another, less pretentious, surname, but in terms of rareness, no alternative comes close.   In short, what are my alternatives? Field that is a subfield of own of its subfields Let $K$ and $L$ be fields. We have homomorphisms $f: K \to L$ and $g: L \to K$. Are $K$ and $L$ necessarily isomorphic? Some people use a term for a popular special case in place of a generic term.  (Often this popular special case is a particular product in that category.)  I think that this is a common phenomenon.  Is there any word/phrase for it?  For example, “Coke” officially refers to a  (I think), but some people seem to call any carbonated soft drinks “Coke.”  In Japanese, famikon is the Japanese name for , a video game console which was extremely popular in 1980s and early 1990s, but some Japanese people call any video game console famikon even if it is not really a famikon.  (As an aside, calling a video game console famikon when it is not really a famikon is even a stereotype of a “mother unfamiliar with technology” in Japan.)  I am looking for a term which refers to this kind of usage of words. A function $f : I \rightarrow \mathbb R$ on an interval $I$ is convex   if $f((1-t)x+ty)\le (1-t)f(x)+tf(y), \forall x,y \in I, t \in [0,1]$      Assume now that $I$ is an open interval.  Show that if $f$ is convex   then for each $c \in I$ there exists $m \in \mathbb R$ such that $m(x  − c) + f(c) \le f(x)$ for all $x \in I$ , and if in addition $f$ is   differentiable at $c$ then $f'(c)$ is the unique $m$ that works. In   general, must m be unique?   (we have previously shown that convex functions are continuous)  I think I'm missing the point of the question.  Surely, by the mean value theorem we can find some $y\in (x,c)$ such that $f'(y)=\frac{f(x)-f(c)}{x-c}$ setting $m=f'(y)$ we get $m=\frac{f(x)-f(c)}{x-c}, m(x-c)+f(c)=f(x)$ such an $m$ fits the inequality we're asked to show.  I also cannot see why $f'(c)$ would be the unique solution or why we would ever get a unique solution of the inequality at all for that matter.  Clearly I'm misunderstanding the question, so if someone could point out where I would appreciate that.  Thank you Overflow: Visible on SVG How can I attack an enemy's weapon? I want to hit enemy's axe to break it. How this is properly played in D&amp;D 5e? And what about shield or armor? Can I attack these items to break it? How to prove $a^3 + b^3 +c^3 - 3abc =1 $, If a,b,c are infinite series as given in the description box below? How do I prove that $$ a^3+b^3+c^3−3abc = 1 $$ if   $ a = 1+\frac{x^3}{3!}+\frac{x^6}{6!}......$ , $b=x+\frac{x^4}{4!}+\frac{x^7}{7!}....$ , $c=\frac{x^2}{2!}+\frac{x^5}{5!}+\frac{x^8}{8!}......$ ?  I have tried the following :-  I discovered that $a+b+c=e^x$ and that $a=\frac{d(b)}{dx}$, $b=\frac{d(c)}{dx}$, $c=\frac{d(a)}{dx}$ . But I am unable to proceed further with these information. What's the function like sum() but for multiplication? product()? Python's  function returns the sum of numbers in an iterable.  sum([3,4,5]) == 3 + 4 + 5 == 12   I'm looking for the function that returns the product instead.  somelib.somefunc([3,4,5]) == 3 * 4 * 5 == 60   I'm pretty sure such a function exists, but I can't find it. Does a logistic regression maximizing likelihood necessarily also maximize AUC over linear models? Is it possible to change the color of a single bar when the bar plot is based on symbolic values? I am beginner in LaTeX, trying to use it for industrial documents. I wonder if there is a way to change the color of only one bar of the plot below, ie "TestDetails", to illustrate it is a local macro and not a LaTeX keyword. I have been trying to experiment with point meta, but could not find a way.  \documentclass{article} \usepackage{filecontents}  \usepackage{pgfplots}  \usepackage{pgfplotstable} \pgfplotsset{width=.95\textwidth, compat=newest}   \begin{document}  \begin{filecontents}{data.csv} {Occurences}, {keyword} 215, item 159, SI 134, subsubsection 106, TestDetails 58, caption \end{filecontents}  \pgfplotstableread[col sep=comma]{data.csv}{\datatable}  \begin{tikzpicture} \begin{axis}[ /pgf/number format/.cd,1000 sep={}, width=0.8\linewidth,height=6cm, xbar, xmin=30, xmax=250, xtick=\empty, enlarge x limits={value=0.1, upper}, enlarge y limits=0.1, ytick=data,  y dir=reverse, xlabel= {}, y tick label style={major tick length=0pt}, yticklabels from table={\datatable}{[index]1}, nodes near coords, nodes near coords align=horizontal, ] \addplot [draw,fill=blue!50]table[ y expr=\coordindex, x index=0]{\datatable}; \end{axis} \end{tikzpicture}  \end{document} How should I type author names in a bib file? Can someone please explain in a clear and concise way how am I supposed to enter the names of authors in a BibTeX file? I have entries with something like   @article{someid,    author = {Juan A. Navarro P\'erez, Ra\'ul de la Garza and Andr\'es Espinoza},    ...   but somehow the output seems kind of wrong! Given a matrix $A \in R^{n \times n}$ which is normal ($AA^H=A^HA$ where $A^H$ is hermitian of $A$) and nilpotent ($A^k=0$ for some $k$). Now we need to show that $A=0$. (This is essentially exercise 5(b) in sec. 80 on p.162 of Paul R. Halmos' Finite-Dimensional Vector Spaces.) I tried to show in the following way, we know that, $AA^H=A^HA$ pre-multiply by $A^{k-1}\implies A^kA^H=A^{k-1}A^HA$ Now, we have $0 = A^{k-1}A^HA$, since $A$ nilpotent. I am not sure how to proceed from here to show $A=0$. Can someone help me in this problem?