I have keypair (u,r), and two pieces of data, X and Y.  I reveal X publicly but keep Y secret. Y has high entropy.  I then combine X and Y, into c(X,Y) = Z.  I encrypt Z, into "encrypt(Z,u) = Q".  r is needed to decrypt Q back into Z.  Can I prove (including interactive zero-knowledge proofs) that Q contains X, without revealing r or Y?  Please help! Thank you very much.
I have keypair (u,r), and two pieces of data, X and Y.  I reveal X publicly but keep Y secret. Y has high entropy.  I then concatenate X and Y, into Z.  I encrypt Z, into "encrypt(Z,u) = Q". r is needed to decrypt Q back into Z.  Later, (when it doesn't matter), r will be revealed and everyone will decrypt Q into Z. At that point, everyone will know that, all along, Q "contained" X. Can I prove that Q contains X before r is revealed (including interactive zero-knowledge proofs)?
What is the purpose of a Windows Workgroup? In Microsoft Windows, what is the purpose of a Workgroup? I understand that a Domain allows the administration of security (user names, passwords, file access, etc.) to be centralized. But what does a Workgroup give you? I recently made changes to my fstab file and, upon reboot, noticed I had an error in it. I get the typical mount error on boot. I went to try and modify it by entering the read-only mode but then, since it's read only, I can't access it. Is there a way around this or some way to delete the file so I can use the backup (which I'm pretty sure works)? Can the notion of vector space or algebra over a field be meaningfully extended to fractional dimensions, so that for example $\mathbb{R}^{-2/3}$ makes sense? Has this been explored somewhere?  I know that super vector spaces can be thought of as one way of generalizing vector spaces to negative integer dimensions. Is there a similar concept for dimensions that are rational numbers? I'm not talking about Hausdorff dimension, because it doesn't allow for negative rationals, and I'm rather looking for extensions from a more algebraic point of view (dimension as the trace of the identity map), without recurring to a given metric. How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$? How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$? Almost all standard sources on the existence of Majorana spinors (e.g. Appendix B.1 to Polchinski's "String Theory", Vol. 2) do so in a way I consider inherently ugly:   A priori, we are dealing with an irreducible complex representation $(V,\rho)$ of the Clifford algebra of signature $(p,q)$, i.e. generalized Dirac spinors. That Majorana spinors exist means abstractly that there is a  on $V$, i.e. a conjugate-linear map $\phi : V\to V$ with $\phi^2 = \mathrm{id}_V$ that commutes at least with the $\mathfrak{so}(p,q)$ action.  Every single source I can find for Majorana spinors uses operations like the transpose, complex conjugation and Hermitian adjoint on the $\Gamma$-matrices to obtain matrices acting on the same space. This is abstractly wrong, the transpose acts on the dual, the complex conjugation on the conjugate, and the Hermitian adjoint needs an inner product we have no reason for choosing. Of course, since $V$ is finite-dimensional, one can pick a basis and define the uncanonical isomorphisms to its dual and its conjugate, but I find this inelegant, particularly since the standard derivations require us to make a particular such choice with respect to the signs the $\Gamma$-matrices have under e.g. ${}^\dagger$. Finally, the Majorana spinors are usually defined by some equation involving an unnatural and arbitrary-looking product of $\Gamma$-matrices, which varies from source to source according to different sign conventions and sign choices made in the course of the derivation.  It's inelegant because the rest of the theory of spinors can be developed without making such uncanonical choices. Both the uniqueness of the dimension of the irreducible Dirac representations (there are two of them in odd dimensions) and the existence of the Weyl spinors in even dimensions can be derived purely from the abstract properties of the Clifford algebra, no choices made, no transpose, adjoint or conjugate occuring. The (admittedly slightly subjective question) is: Is there a way to show in which dimensions Majorana spinors exist that neither requires an uncanonical choice of basis nor arbitrary choices of signs?  Some partial results:   In even dimensions, the Dirac representation is necessarily self-conjugate since it is the only irreducible representation of the Clifford algebra, so all that is left to show is that a conjugate-linear $\mathfrak{so}$-equivariant map on it squares to $\mathrm{id}_V$ and not to $-\mathrm{id}_V$. However, I can't seem to exhibit any particular equivariant map on it that one could simply check for its square. In odd dimensions, one first needs to figure out whether the two inequivalent Dirac representations are conjugate to each other or self-conjugate.     As further motivation that a clear proof using only canonical properties of the Clifford algebra itself is required, consider the confusing and contradictory claims in the literature:   Polchinski, "String Theory", Vol. 2, p.434: $\mathrm{SO}(d-1,1)$ has Majoranas for $d = 0,1,2,3,4 \mod 8$, corresponding to a special case of $p-q = d-1-1 = 6,7,0,1,2 \mod 8$. Fecko, "Differential Geometry and Lie Groups for Physicists", pp. 651: $\mathrm{Cliff}(p,q)$ has Majoranas for $p-q = 0,2\mod 8$.  This clearly conflicts with Polchinski's claims e.g. for $d=3$. Figueroa-O'Farrill, , pp. 18: We have Majoranas for $p-q = 0,6,7\mod 8$ and "symplectic Majoranas" for $p-q = 2,3,4\mod 8$.   Note that these results conflict simply by the number of possible $p-q$ regardless of whether I've correctly taken care of the differing conventions of whether $p$ or $q$ denotes timelike dimensions. The Bash Manual says   { list; }        Placing a list of commands between curly braces causes the list to be executed in the current shell context. No subshell is   created. The semicolon (or newline) following list is required.      The braces are reserved words, so they must be separated from the list   by blanks or other shell metacharacters.       The parentheses are operators, and are recognized as separate tokens   by the shell even if they are not separated from the list by   whitespace.   If I remove the semicolon, like this:  $ { date } &gt;    Why does it expect stdin input? A metacharacter is a character that separates words.  The semicolon and whitespace are both "shell metacharacters". Why can't whitespace separate words date and }? Why do we need a semicolon instead of a whitespace for separating the words? I'm getting "jumpy" loadings in rollapply PCA in R. Can I fix it? Undo apt-get remove open* ubuntu 12.04 Find all integral solutions of $y^2=x^3+7$ Find all integral solutions of $y^2 = x^3+7$.  I tried to use many different moduli, but it never works. With modulo $9$, you can get $x$ is divisible by $3$. I am pretty sure that most of us here, or at least those do graphic design for living, have found themselves in following situation:   You agree with a client to do the design, agree on price, schedules, formats etc… You work hard, make adjustments, collaborate with client; everything goes well in the beginning. At some point you realise that the client does not listen your professional advice regarding design and prefers his/her own ideas that might not look so professional (choice of fonts, colors, odd choices of elements, shapes etc…). No matter how hard you try, the client is persistent and will not accept the designer’s advice. You get back to work, try to make the best out of it, and the final result is not so good, mainly because you had to stick to the client’s wishes. Work is shipped, payment done, and you don’t want to include this work in your portfolio because it is not good. After all, it is not your work, it is something that was physically created by you as a designer, but the ideas, concept, story, and message came out as a result of nonprofessional person, your client.   Ok, they pay for it, and as long as they are happy this is fine. But, the more compromises you make, the more time you spend working on bad design. If you are a young designer on a quest to get recognition, you don’t want to work just for the sake of money and then face the lack of good design in your portfolio.   Maybe at the beginning of your career you don’t care that much, but later if life this might be a big issue. At some point you will be approached by a big client that might offer you long-term contract, but first they will want to see your work. No point explaining to them what you did and why you made so many compromises.   They will not be interested in that.  Every project is precious as your time and you want to do use it wisely and produce great work.   How would you deal with such a situation? How can you tell when a roast is done? How can you tell when a roast is done?  How long should they roast for? filling area between 2 functions, with shading How to extract a number from a string Im a newbie in Apex and im developing a page using Visualforce.  My string format is always like this "xx-xx-999999". In this format I need to get only the integer. For example the string is  "RO-W1-445567". I want to get only the integer 445567 in the string. Can someone willing to share a piece of apex code in my problem.  Your help is vey much appreciated.  Thanks in advance!  Ferdie Banu When editing a post and using the image uploader, any unused link references are completely removed.  For example, this post has three image references, only one of which is used ([3]) in the body of the post:        After uploading a fourth image, references [1] and [2] are completely removed (and the remaining references are renumbered to become [1] and [2]):        I sometimes write link references before using them in the body of the post and sometimes remove images temporarily before reinserting them elsewhere in the post so this is inconvenient.  (Note: this also applies for the iOS app, having the same behavior) I have several thousand nodes of a particular content type. Using the web interface (example.com/admin/content), I can only delete about 50 at a time. How can I quickly delete them? Let $V,W$ be nonzero normed spaces over $\mathbb{K}$ such that $V$ is finite-dimensional.  Let $E$ open in $\mathbb{K}$ and $p\in E$.  Let $f:E\rightarrow W$ be Gâteaux-differentiable at $p$.  Is $f$ necessarily Fréchet-differentiable at $p$ in this case?  I think this is not true in general, but cannot find a counterexample. What would be a counterexample? As I navigate through physics stackexchange, I noticed .  Electrons radiate light when revolving around nucleus? Why is it so obvious?  Note that I do not know anything about quantum mechanics - and I just want classical stories. At college we use ArcGIS Desktop 10, but that does not function on my Mac so I have QGIS there instead.  I want to do my exercises with QGIS, but in ArcGIS Desktop we use .lyr files with ArcMap and .lyrx files with ArcGIS Pro, and they are not supported by QGIS.  Does anyone know, how I can connect the *.lyr files to my *.shp files to use them on my Mac with QGIS? What is data blending? This term appears frequently in the .  Is blending a specific method in data-mining and statistical learning? I cannot get a relevant result from google.  It seems blending is mixing up outcomes from many models and resulting in a better result. Is there any resource that helps me knowing more about it? pgfpages and section I'm making a Beamer presentation. I need to show some notes on a second screen, so I'm using pgfpages.  Whereas, when I put a section, it appears 2 times :/ Here, it's a minimal code with the problem. Have you any idea ?  \documentclass{beamer} \usepackage[latin1]{inputenc} \usepackage[T1]{fontenc} \usepackage[francais]{babel}  \usepackage{pgfpages} \setbeameroption{show notes on second screen=right}    \begin{document} \begin{frame} \tableofcontents \end{frame}  \begin{frame} \section{test} toto \end{frame}  \end{document}   Thanks !