How to Recover Lost Website/ blog data with no backup?
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How do I show that $\sum_{cyc} \frac {a^6}{b^2 + c^2} \ge \frac {abc(a + b + c)}2?$ Let $a, b, c$ be positive real numbers, show that  $$\frac {a^6}{b^2 + c^2} + \frac {b^6}{c^2 + a^2} + \frac {c^6}{a^2 + b^2} \ge \frac {abc(a + b + c)}2.$$  I think this is likely to turn out to be proved by Hölder, but I can't see how. Any hints will be appreciated. What happens when a moderator clicks 'leave open' in the close-vote queue? It takes  clicking "leave open" in the close-vote queue to remove the question from the queue.  How about diamond mods?  Do they remove it from the queue in one click, or not? Trace of a commutator is zero - but what about the commutator of $x$ and $p$? Operators can be cyclically interchanged inside a trace: $${\rm Tr} (AB)~=~{\rm Tr} (BA).$$ This means the trace of a commutator of any two operators is zero: $${\rm Tr} ([A,B])~=~0.$$ But what about the commutator of the position and momentum operators for a quantum particle? On the one hand: $${\rm Tr}([x,p])~=~0,$$ while on the other hand: $$[x,p]~=~i\hbar.$$ How does this work out? What term refers to those who adhere to scientism? The "Select your next badge" dialog box is not displaying correctly. It looks like this:    Freehand circles, as requested:    It seems to be an issue with box-sizing, because when it's content-box, it looks fine. I think the width and height rules for .popup-badges .all-badge-progress .badge-progress should be increased a little, for example:  .popup-badges .all-badge-progress .badge-progress {   width: 214px;   height: 96px; }   Tested on the latest Chrome and Firefox on Linux Mint. Is there a criterion to differentiate "thriller" from "horror"? Which groups have precisely two automorphisms Which groups $G$ have precisely two automorphisms, i.e., precisely one non-trivial automorphism?  Examples: $G= C_3, \mathbf{Z},\ldots$.  I think $G$ has to be abelian. In fact, we have $ \vert G\vert \geq 3$. Therefore, if $G$ is not abelian, we have at least two non-trivial inner automorphisms.  If we can show that $G$ is cyclic the above examples are all of them. Is it possible to insert multiple records in Salesforce using cURL at the same time? "the better" vs "the best" of two players Can a character escape the  (DMG p. 177, listed in the SRD as the ) with the  spell? To clarify, I am not asking if the bands prevent teleportation. I am asking whether the bands are teleported with the character as he teleports using misty step. Folland, "Real Analysis", Chapter 5.3, Exercise 36. Folland, "Real Analysis", Chapter 5.3, Exercise 36:     Let $\mathcal{X}$ be a separable Banach space and let $\mu$ be   counting measure on $\mathbf{N}$.  Suppose that   $\left\{x_n\right\}_1^\infty$ is a countable dense subset of the unit   ball of $\mathcal{X}$, and define $T \colon L^1(\mu) \to \mathcal{X}$   by $Tf = \sum_1^\infty f(n) x_n$.  (a)  $T$ is bounded.  (b)  $T$ is   surjective.   I have proved (a).  I would like help on (b).  Here are my ideas so far.    Say we want to show $y \in \mathcal{X}$ is in the image of $T$.  Reduce to the case $||y|| = 1$ and let $x_{n_m} \to y$.  My thought is to produce for each $N$ a function $f_N \in L^1(\mu)$ such that $||y - \sum_n^\infty f(n)x_n|| &lt; 1/N$ and also such that the $f_N$ converge in $L^1(\mu)$ to some $f \in L^1(\mu)$.  Then use the continuity of $T$ to conclude $T(f) = y$.    The way I have been setting up my inequalities is as follows. Pick $M_N$ such that for all $m &gt; M_N$, $||y - x_{n_m}|| &lt; 1/N$.  Then I want to define $f_N$ so that $$\sum_n^\infty f_N(n) = \sum_{m &gt; M_N}^\infty f_N(m) = 1, $$ hence $$||y - T(f_N)|| = ||\sum_{m &gt; M_N}^\infty f_N(m) y + \sum_n^\infty f_N(n)x_n|| \leq \sum_{m &gt; M_N}^\infty f_N(m) || y - x_{n_m} || &lt; \frac{1}{N}. $$  Presumably, if the $f_N$ are appropriately chosen, then I can find a dominating function and apply the Dominated Convergence Theorem to finish up.    However, getting all these hypotheses to hold simultaneously has been difficult.  In essence, the difficulty seems to be in requiring that the $f_N$ be "normalized" as well as possess a dominating function.  If this method is feasible, at least it seems to require a bit of analysis to show the desired series all converge.  Perhaps I am missing something cleaner.  If so, a simpler solution would be much appreciated.    -Thanks. Plotting a 3d surface in tikz, with a limit to the infinity According to this question:  entire ruSO site shouldn't become hot. But I just saw the following while searching MSE:        Direct link to the question on ruSO:   Perhaps the HNQ filter works on question title (in the current case there are no non-Latin symbols) instead of site origin. Hence, according to the post mentioned before this behaviour should be interpreted as a bug.   However, I suggest to fix such "bug" by taking another feature request in mind: Equivalent conditions for a preabelian category to be abelian Let's fix some terminology first. A category $\mathcal{C}$ is preabelian if:  1) $Hom_{\mathcal{C}}(A,B)$ is an abelian group for every $A,B$ such that composition is biadditive,  2) $\mathcal{C}$ has a zero object,  3) $\mathcal{C}$ has binary products,  4) $\mathcal{C}$ has kernels and cokernels.  A category $\mathcal{C}$ is abelian if it is preabelian and satisfies:  5) every monomorphism is a kernel and every epimorphism is a cokernel.  Define the coimage of a map to be the cokernel of its kernel, and the image to be the kernel of its cokernel. We have the following commutative diagram:    where $\overline{f}$ is the only existing map (because of universality of kernel and cokernel).  I'm having trouble proving the following:     A preabelian category $\mathcal{C}$ is abelian iff $\overline{f}$ is an isomorphism.   The converse is easily shown, I'm having trouble proving $\Rightarrow$... Debian : Verify disk encryption password for already mounted system I am working on our Debian server on which we have a Raid drive encrypted with 2 devices. I did this around 1.5 years back and have never rebooted since. Now, we want to reboot for some reasons, but I have to make sure that the password I have is the correct one, or we will be stuck.   How can we verify the password for an encrypted-raid? Thank you.  Raid details :    mdadm --detail /dev/md0    /dev/md0:         Version : 1.2   Creation Time : Thu Feb 11 14:43:40 2016      Raid Level : raid1      Array Size : 1953382336 (1862.89 GiB 2000.26 GB)   Used Dev Size : 1953382336 (1862.89 GiB 2000.26 GB)    Raid Devices : 2   Total Devices : 2     Persistence : Superblock is persistent      Update Time : Fri Mar 10 10:37:42 2017           State : clean   Active Devices : 2 Working Devices : 2  Failed Devices : 0   Spare Devices : 0             Name : HOSTNAME:0  (local to host HOSTNAME)            UUID : 5c450558:44a2b1e9:83cb4361:9c74df8e          Events : 49      Number   Major   Minor   RaidDevice State        0       8        1        0      active sync   /dev/sda1        1       8       17        1      active sync   /dev/sdb1   Thank you.   Update  dmsetup table --showkeys CryptVol: 0 Large_Number crypt aes-cbc-essiv:sha256 RANDOM_TEXT  0 253:0 4096 RaidVG-LVMVol: 0 Large_Number linear 9:0 2048 Ignore compile errors How can I set up a permanent compile loop that keeps trying even when there are errors? I'm using latexmk with a remote compile setup as discussed  and . However, if I save a document with a bug (either a legitimate bug, or I save it before closing a tag), then latexmk halts. Any suggests how I can have it pause, try again, and keep trying again, for ever and ever? What blocks can Endermen pick up and what blocks they can't? I am wondering if there is away (possibly a better way) to order by the order of the values in an IN() clause.  The problem is that I have 2 queries, one that gets all of the IDs and the second that retrieves all the information. The first creates the order of the IDs which I want the second to order by. The IDs are put in an IN() clause in the correct order.  So it'd be something like (extremely simplified):  SELECT id FROM table1 WHERE ... ORDER BY display_order, name  SELECT name, description, ... WHERE id IN ([id's from first])   The issue is that the second query does not return the results in the same order that the IDs are put into the IN() clause.  One solution I have found is to put all of the IDs into a temp table with an auto incrementing field which is then joined into the second query.  Is there a better option?  Note: As the first query is run "by the user" and the second is run in a background process, there is no way to combine the 2 into 1 query using sub queries.  I am using MySQL, but I'm thinking it might be useful to have it noted what options there are for other DBs as well. How do I audit my reputation? If I am concerned that my reputation score is incorrect, how can I audit it, or get a report of a detailed breakdown of my reputation? how to get full path from fileupload using Javascript