Proof of conservation of information
Why is information indestructible?
Wires do not connect in Circuitikz I've been trying to use relative coordinates to make my drawings more precise but it seems I don't know how the command \node works since I've been having this problem while connecting a circuit element to another:    I'm trying to eliminate the blank between the two wires.  This is the minimal code:  \documentclass{book} \usepackage[siunitx,RPvoltages]{circuitikz} %Circuit Schematics/Diagram \usetikzlibrary{arrows,shapes,calc,positioning} \begin{document}     \begin{circuitikz}             \path (0,0) coordinate (C);             % Comparatore             \path (C) + (0,-1) + (1,0) coordinate (com) node[above]{};             \path (com) + (1.5,-1) node[op amp] (comp) {};             % Collegamenti Comparatore             \node (G1) at ([shift=({-1.3cm,0cm})]comp.-) {};             \draw (G1) -- (comp.-);             \node (G2) at ([shift=({-1.3cm,0cm})]comp.+) {};             \draw (G2) -- (comp.+);             \draw (C) -- (G1); % Collegamento Rettificatore - Comparatore         \end{circuitikz} \end{document}   Thanks for any help! Convert object string to JSON Calling delete on variable allocated on the stack How to check if list item already exist when adding it with how to check Title( Country) if exists in the list. if exists it is necessary to do the update if not it is necessary to add it ?  function AddListItem() {      var listTitle = "Test";     //Get the current client context       context = SP.ClientContext.get_current();     var airportList = context.get_web().get_lists().getByTitle(listTitle);          //Create a new record       var listItemCreationInformation = new SP.ListItemCreationInformation();     var listItem = airportList.addItem(listItemCreationInformation);      //Set the values      var country= $("#Country").val();     var client= $("#Client").val();     // var nb1 = $("#nb1").val();      // var nb2 = $("#nb2").val();       // var nb3 = $("#nb3").val();      // var nb4 = $("#nb4").val();       // // var nb5 = $("#nb5").val();        listItem.set_item('Country', Country);     listItem.set_item('Client', Client);     listItem.update();     context.load(listItem);     context.executeQueryAsync(AddListItemSucceeded, AddListItemFailed); } function AddListItemSucceeded() { } function AddListItemFailed(sender, args) {     alert('Request failed. ' + args.get_message() + '\n' + args.get_stackTrace()); } ViewPager and fragments — what's the right way to store fragment's state? How can I upgrade Ubuntu LTS to the next one offline? I'm using Ubuntu 12.04 on my computer and I want to upgrade to Ubuntu 14.04.  I do not have internet at home, so I need to do the upgrade offline.  On openSUSE there a way to make the upgrade offline simple and effective way is by using  the iso DVD.  My question is: Is there any way to make Ubuntu upgrade offline as in openSUSE ? How do I add more categories to Mac OS X Finder's sidebar? My Finder sidebar has two categories: Favorites and Devices. How do I add more categories? Capital letters in "Theorem", "Conjecture" etc This is my first post and as you can probably guess I am a mathematician so I have no clue about grammar. I am writing a mathematical document at the moment and I would appreciate some advice on my usage of capital letters. Can somebody please confirm if the following are correct?  1) "We know by T​heorem 4.6.1 that..."   2) "the following c​onjecture, due to..."  3) In order to prove the "Mckay-Stevens $k$-covering C​onjecture, once needs to show that..."  I'm particularly confused about 3).  Many thanks for any help Low budget alien movie about the Earth being cooked I’m looking for an alien movie I watched years ago, mid to late 2000’s about the Earth being cooked or heated up by aliens. The poster is a reflection of the Earth heating up with an orange glow on an aliens eye. It was a low budget movie and I think the one I watched was pirated from China. Again low budget, bad quality and the name could’ve been something worthy he word scorch or something like that. The alien in the movie had legs with knees that went inwards and it had red eyes. Python setup, install one module as a sub module of another module? Computing $\mathrm{Hom}(\mathbb Z_n,\mathbb Z_m)$ as $\mathbb Z$-module Find and replace multiple values within selected cells I want to run a find and replace on multiple values within a range in excel with values from 2 columns: A with the original word; B with the translation. I already found the VBA code to get this working for 50%, but this code runs it on the whole worskheet.  Ideally I would like to be able to run it on just the range I selected. An added bonus would be if I could also select the lookup range.  This is what I'm using this far. Thanks for your help!  Sub abbrev()             Dim abvtab() As Variant             Dim ltsheet As Worksheet             Dim datasheet As Worksheet             Dim lt As Range              'Change Lookup to the sheet name with your lookup table.             Set ltsheet = Sheets("Lookup")              'Change Data to the sheet name with your data.             Set datasheet = Sheets("Data")              'Change A2 to the top left cell (not the header) in your lookup table.             'Change B2 to top right cell.             Set lt = ltsheet.Range("A1", ltsheet.Range("B1").End(xlDown))              abvtab = lt              For i = 1 To UBound(abvtab)                 datasheet.Cells.Replace What:=abvtab(i, 1), Replacement:=abvtab(i, 2), LookAt:=xlPart, _                     SearchOrder:=xlByRows, MatchCase:=True, SearchFormat:=False, _                     ReplaceFormat:=False             Next i End Sub Why Process Builder doesn't work on Delete Scenario? How to get address of cell which calls a VBA Functions in a Excel sheet Smart Phone's camera socket I just want ask how the socket in the image is called?   I couldn't really find and the closer I could get is only Raspberry's module. Is it possible to play D&D 5e solo? Is it at all possible to run a solo game where you act as the DM/GM for yourself? I know there was a 4th edition adventure published in an old issue of one of the D&amp;D magazines but recently I read somewhere (Reddit I think) that the games Outbreak: Undead and Eclipse phase were good games to play solo.  Can anyone with experience with running a game of D&amp;D 5e for themselves explain how to do so? What is the smallest (installed size) ubuntu based distribution? For ridiculously small hard drives (8GB), what Ubuntu Based (although not necessarily official) distribution offers the smallest installed size?  Let me clarify: I still want a certain amount of personal file space, preferably a few gig. I also don't have a problem with performance, while it is mediocre, a 2.6GHz single-core and 1GB of ram suffice to run ubuntu fine, but i find that it  uses 6-7GB of space. I am aiming for closer to 4GB. Compute the (multiplicative) inverse of $4x+3$ in the field $\frac {\Bbb F_{11}[x]}{\langle x^2+1 \rangle}$? So I am finding a polynomial $px+q$ ($p,q \in \Bbb F_{11}$) which is multiplicative inverse of $4x+3$ in $\frac {\Bbb F_{11}[x]}{\langle x^2+1 \rangle}$.  i.e. $[(4x+3)+\langle x^2+1 \rangle][(px+q)+\langle x^2+1 \rangle]=1+\langle x^2+1 \rangle$   $\Rightarrow$  $(4x+3)(px+q)+\langle x^2+1 \rangle=1+\langle x^2+1 \rangle$  $\Rightarrow$  $4px^2+(4q+3p)x+3q+\langle x^2+1 \rangle=1+\langle x^2+1 \rangle$.  We see that the remainder,when $(4x+3)(px+q)$ is divided by $x^2+1$, is $1$. So by Division algorithm,  $$ \require{enclose} \begin{array}{r} 4p \\[-3pt] x^2+1 \enclose{longdiv}{4px^2+(4q+3p)x+3q} \\[-3pt] \underline{4px^2+4p} \\[-3pt] (4q+3p)x+(3q-4p) \\[-3pt] \end{array} $$    So I equate $(4q+3p)x+(3q-4p)=1$ and solve the simultaneous linear equations  $4q+3p=0, 3q-4p=1$. I get $p=6,q=1$  Hence $6x+1$ is the required inverse.  I am pretty sure that the answer is correct but is the method to achieve it right? "An operator is hermitian". Implications? Alastair Rae states that there are 4 postulates of Quantum Mechanics in his text on the subject matter.  The first part of his second postulate can be stated as:      Every dynamical variable may be represented by a Hermitian operator whose eigenvalues represent the result of carrying out a measurement of the value of the dynamical variable...   My question is: just how much can we deduce from saying that the some of the operators involved in Quantum Mechanics are Hermitian?  When I use the word Hermitian, I am referring to the property that $A=A^+$ where $A$ is an operator and $A^+$ is the adjoint of $A$.  Does an operator being Hermitian automatically imply that there will exist eigenfunctions and eigenvalues corresponding to this operator?  Does being Hermitian imply that, should there exist eigenfunctions corresponding to this operator, they will form a complete and orthonormal set?  That any wavefunction can be expanded in terms of these eigenfunction?  Just how much is hidden in the word "Hermitian"? Irreducibility of a polynomial if it has no root (Capelli) Let $F$ be a field of arbitrary characteristic, $a\in F$, and $p$ a prime number. Show that $$f(X)=X^p-a$$ is irreducible in $F[X]$ if it has no root in $F$.   This  to a related question mentions the result is due to Capelli.  I can prove the result if $F$ has characteristic $p$ as follows.  Suppose $f$ is reducible: $f(X)=g(X)h(X)$ with $g(X)$ an irreducible factor of degree $m$, $1\le m&lt;p$. Then if $\alpha$ is a root of $g$ in some extension field $K$ of $F$, we have $$f(X)=X^p-\alpha^p=(X-\alpha)^p$$ so its divisor $g(X)$ must be of the form $(X-\alpha)^m$. Since the coefficient of $X^{m-1}$ in $g$ is in $F$, we have $m\alpha\in F$.  So $\alpha\in F$ because $m$ is invertible modulo $p$.  How would you show the result in other characteristics?