How to use sha1() login
Secure hash and salt for PHP passwords
Typically Apt packages are served over bare HTTP and the downloaded contents are verified with GPG signatures. This makes it easy for  to proxy the HTTP connections and add the downloaded packages to its cache. apt-cacher-ng is unable to directly MITM an HTTPS connection created by Apt. It is possible to  apt-cacher-ng, but then the contents are not cached--they are re-downloaded from the remote server every time. This quickly gets annoying when rebuilding Docker containers that install many packages from Apt repositories served over HTTPS. Is there a way to get apt-cacher-ng to cache packages downloaded from HTTPS repositories? $(U\cap W)^0 = U^0 + W^0$ Let $V$ be a finite dimensional vector space and $U^0$ and $W^0$ denote the annihilators of subspaces $U$ and $W$, respectively.  Then I need to show that $(U\cap W)^0 = U^0 + W^0$.  I can show that $U^0 + W^0 \subseteq (U\cap W)^0$ like so: Let $f\in U^0$ and $g\in W^0$.  Then, because $U^0, W^0 \subseteq (U\cap W)^0$, we see that if $f\in U^0$ and $g\in W^0$, then for any $v\in U\cap W$ and $a,b \in \Bbb F$, $(af+bg)(v) = af(v) + bg(v) = 0$.  Thus $af+bg\in (U\cap W)^0$.  But because $f$ and $g$ were arbitrary, this implies that any linear combination of elements of $U^0$ and $W^0$ is an element of $(U\cap W)^0$.  I.e. $U^0+W^0 \subseteq (U\cap W)^0$.  But I haven't had any luck proving the other direction.  Obviously I should start with $f\in (U\cap W)^0$.  But then it looks like I need to somehow break that function into two to show its in $U^0 + W^0$.  That's throwing me off. NEWID() In Joined Virtual Table Causes Unintended Cross Apply Behavior My actual work query was an inner join, but this simple example with cross join seems to nearly always reproduce the problem.  SELECT * FROM (     SELECT 1 UNION ALL     SELECT 2 ) AA ( A ) CROSS JOIN (     SELECT NEWID() TEST_ID ) BB ( B )   With my inner join I had many rows for which I added to each a GUID using the NEWID() function, and for about 9 out of 10 such rows the multiplication with the 2-row virtual table produced the expected results, just 2 copies of the same GUID, while 1 out of 10 would produce different results. This was unexpected to say the least and gave me a really hard time trying to find this bug in my test data generation script.  If you take a look at the following queries using as well non-deterministic getdate and sysdatetime functions, you won't see this, I don't anyway-I always see the same datetime value in both final result rows.  SELECT * FROM (     SELECT 1 UNION ALL     SELECT 2 ) AA ( A ) CROSS JOIN (     SELECT GETDATE() TEST_ID ) BB ( B )  SELECT * FROM (     SELECT 1 UNION ALL     SELECT 2 ) AA ( A ) CROSS JOIN (     SELECT SYSDATETIME() TEST_ID ) BB ( B )   I'm currently using SQL Server 2008 and my work around for now is to load my rows with GUIDs into a table variable before finishing out my random data generation script. Once I have them as values in a table as opposed to virtual table, the problem goes away.  I have a workaround, but I'm looking for the ways to workaround without actual tables or table variables.  While writing this I tried without success these possibilities: 1) placing the newid() into a nested virtual table:  SELECT * FROM (     SELECT 1 UNION ALL     SELECT 2 ) AA ( A ) CROSS JOIN (     SELECT TEST_ID     FROM (         SELECT NEWID() TEST_ID     ) TT ) BB ( B )   2) wrapping the newid() within a cast expression such as:  SELECT CAST(NEWID() AS VARCHAR(100)) TEST_ID   3) reversing the order of appearance of the virtual tables within the join expression  SELECT * FROM (     SELECT NEWID() TEST_ID ) BB ( B ) CROSS JOIN (     SELECT 1 UNION ALL     SELECT 2 ) AA ( A )   4) using uncorrelated cross apply  SELECT * FROM (     SELECT NEWID() TEST_ID ) BB ( B ) CROSS APPLY (     SELECT 1 UNION ALL     SELECT 2 ) AA ( A )   Just before finally posting this question, now I tried this with success it seems, a correlated cross apply:  SELECT * FROM (     SELECT NEWID() TEST_ID ) BB ( B ) CROSS APPLY (     SELECT A     FROM (         SELECT 1 UNION ALL         SELECT 2     ) TT ( A )     WHERE BB.B IS NOT NULL ) AA ( A )   Anyone have any other more elegant, simpler workaround? I really don't want to use cross apply or correlation for a simple row multiplication if I don't have to. How do we know Dark Matter isn't simply Neutrinos? Live USB for Ubuntu 13.10 does't recognize Windows 8 OS What does each AMS package do? In my view, any document with a substantial amount of mathematics should load the packages from AMS-TeX. Hence, most of my document's preambles contain  \usepackage{amsmath, amsthm, amssymb, amsfonts}   (I could add to that the non-AMS mathtools, etc.). What do each of those packages do? Do I really need to list all of them, or do some of them load others? In particular, does any package load all of them, so that I can simply type  \usepackage{ams-everything}   shorter than the current list? For $p,q$ prime and $p \neq q$ show that $C_p \times C_q \cong C_{pq}$ Here are my thoughts so far:    $C_p = \langle x \mid x^p =e\rangle$ $C_q = \langle y \mid y^q =e\rangle$ $C_p \times C_q$ has elements of the form $(x^a,y^b)$ There are $p$ possible values for $x^a$ and $q$ possible values for $y^b$. So there are $pq$ possible elements in $C_p \times C_q$. $C_{pq} = \langle z\mid z^{pq} = e\rangle$ and there are $pq$ elements in this group. For an isomorphism from $C_p \times C_q$ to $C_{pq}$ we send $(e,e)$ to $e$ to ensure that the identities are mapped to each other. However, I'm not sure how to define an isomorphism for the other elements. What are the rules for China's visa-free transit programs? Assuming one wants to travel through China, what are the rules for visa-free access? To be more specific:   How does the 24-hour visa free transit work? How does the 72-hour version work? What does a person ineligible for either of these programs have to do to transit China? Do the programs apply to flights only or do they also work for transit on land? Would a visitor save much hassle by using visa free transit instead of just getting a visa?      NB: this is intended as a canonical question on transiting China Let $a,b,c$ real numbers. Prove the inequality $|a-b| \leq |a-c| + |c-b|$. Prove that equality holds if and only if $a \leq c \leq b$ or $b \leq c \leq a$.   I've tried starting with just $a \leq c$ and using field properties to reconstruct the inequality, however I haven't been able to make it work. I also tried making the negatives positive and stripping the inequalities and making something happen but again I don't know if that's a proper rule and it didn't seem to get me anywhere. Pumping Lemma for $L=\left\{0^i 1^{j} \mid \gcd(i,j) = 1\right\}$ Let $L=\left\{0^i 1^{j} \mid \gcd(i,j) = 1\right\}$ I want to prove that this is not a regular language, but I am having trouble finding a string I can pump resulting in the string not being in the language. Ideally, rather than a full solution, I'd like suggestions for a string that I could use in this proof. I've played with the idea of setting $j = 2$ and $i = 2n+1$, but I don't think that would work. If $n = 51! +1$, then find number of primes among $n+1,n+2,\ldots, n+50$ If $n = 51! +1$, Then find no of primes among $n+1,n+2,\ldots, n+50$  Really speaking, I don't have any clue ... Why don't we read ''k'' here?  Know → /nəʊ/   Knotty → /ˈnɒt.i/   Knockout → /ˈnɒk.aʊt/ I'm writing a script which shows the git log for a directory when I cd into it. Such a log can be overwhelming, containing hundreds of lines. So far I have been limiting that to a hard-coded 20 lines (... | head -n 20), which is fine on the screen at work, but too much on the smaller MacBook screen at home.  I would prefer the log to take up about half the (vertical) screen on either terminal. And "terminal" also changes: it's Gnome terminal at work, but iTerm2 at home. And I do not use screen or tmux.  How do I find the number of vertical lines available in a terminal from command line? Pretty-print a Map in Java Official reasons for "Software caused connection abort: socket write error" I once heard the late John Ciardi (NPR's "A Word in Your Ear") try to explain that the 1920s idiom, "copacetic" (meaning completely satisfactory), entered into the African-American vocabulary in Harlem from the days when Jews and African Americans lived there together.  He argued that copacetic has the same meaning as the Israeli idiom "kol b'seder" which literally means "all is in order."  The problem with that, said my Harlem-raised father-in-law, is that the Jews in Harlem spoke Yiddish and kol b'seder was not used in Yiddish.  The dictionary I've got is not helpful. Can someone come up with a better explanation? How to set date format when manually inserting date on excel, without changing regional settings? What's the difference between MathOverflow & Mathematics.SE? If I have a maths question, on which site should I ask:  or ? Refresh Icon Cache Without Rebooting Normally, to refresh the icon cache in Windows, we have to reboot.  Is there a way to refresh the icon cache in Windows 7/8 without rebooting? Some speculation here:   Is there a possibility it would pass 'undetected' through your hand, or is it certain death?  Can you conclude it to be vital, or only loose your hand?  Would it simply make a small cylindrical hole through your hand, or is there some sort of explosion-effect?  Assume your hand has a cross section of 50cm², and a thickness of 2cm, how much of the beam's energy would be transferred to your hand?