What is the time derivative $\frac{d}{dt}(\exp(\hat A))$ of operator exponential $\exp(\hat{A})$? Assuming that the operator $\hat{A}$ does not necessarily commute with $d \hat A/dt$, what is $$\frac{d}{dt}(\exp(\hat A))~?\tag{1}$$ Is it $\exp(\hat A(t)) \frac{d \hat A}{dt}$ or $\frac {d\hat A}{dt} \exp(\hat A(t))$ and why?  EDIT: Actually here is my original question: I was asked to show that  $$\frac{d(\exp{A})}{dt} \exp{(-A)} = \sum_{n=0}^{\infty} \frac{1}{(n+1)!} L^n_A(\frac{dA}{dt}),\tag{2}$$ with $$L_A(X) = [A,X], \qquad L^2_A(X) = [A,[A,X]],\qquad \ldots \tag{3}$$  I thought the Baker–Campbell–Hausdorff formula said  $$\exp{(A)} B \exp{(-A)} = \sum_{n=0}^{\infty} \frac{1}{n!} L^n_A(B),\tag{4}$$  and so comparing the two equations above, I would get  $$\frac{d\exp(A)}{dt} = \exp{(A)} \frac{dA}{dt}\tag{5}$$ (by plugging in $B = \frac{dA}{dt}$). Now that it seems that this is not true, does it mean that the identity I was asked to prove is also not true?
Derivative of the product of operators and Derivative of exponential I'm asked to show that  $$\frac{d(\hat{A}\hat{B})}{d\lambda} ~=~ \frac{d\hat{A}}{d\lambda}\hat{B} + \hat{A}\frac{d\hat{b}}{d\lambda}$$ With $\lambda$ a continuous parameter. Should I use the definition $$\frac{d\hat{A}}{d\lambda} ~=~ \lim_{\epsilon \to 0} \frac{\hat{A}(\lambda + \epsilon) - \hat{A}(\lambda)}{\epsilon}$$ applied to $\hat{A}\hat{B}$ like $$\frac{d(\hat{A}\hat{B})}{d\lambda} ~=~ \lim_{\epsilon \to 0} \frac{\hat{A}(\lambda + \epsilon)\hat{B}(\lambda + \epsilon) - \hat{A}(\lambda)\hat{B}(\lambda)}{\epsilon}$$ and do some algebra to get the RHS of the first equation, or I'm missing something? Another interesting derivative to pay attention to is: $$\frac{d}{d\lambda}\exp(\hat{A}(\lambda) )~?$$
How can i check if $remote_addr IP is NOT in CIDR range in nginx? I am using nginx latest web server. How can i check if the $remote_addr ip is NOT in specified CIDR range and return appropriate error code.  i would like to return specific error codes if IP is NOT in specific CIDR IP ranges.  how can i do this for CIDR IP range ?  e.g.    If remote_addr is not in 123.123.123.123/24 then return 444 code . It has come up in game a couple of times that a player might want to cast a spell that has a casting time of 1 bonus action using their "main" action (if they have another bonus action they also want to take on that turn, such as giving bardic inspiration, or controlling a Bigby's hand, etc.)  On the face of it, it seems obvious that something (a bonus action) that is usually much faster than a full action could be done as your full action.  Although the question comes up most often with respect to spellcasting, if I house rule this, I would rule that any bonus action can be taken as a regular action instead; however, I would not allow the same type of bonus action to be taken twice (so no giving bardic inspiration to two allies on the same turn, for instance).   Are there any abusive or overpowered combinations I should be wary of if I were to allow a character to take 2 bonus actions instead of one regular action and one bonus action on a turn?   The issue of casting two bonus-action spells would not come up because the rule against casting 2 spells on your turn unless one of them is a cantrip with a casting time of 1 action would still be in effect:  PHB p. 203 (under Bonus Action casting time)     You can't cast another spell during the same turn, except for a cantrip with a casting time of 1 action.   I know it's hard to prove/justify a negative answer to a question like this, but I'd be happy to get answers that say you don't think there would be any issues if you describe how you came to that conclusion. Can I use a spell with a casting time of "Bonus Action" as my action? Locking a vehicle bicycle rack We are planning a trip with a bike rack attached to our trailer hitch. What is the best way to lock the bikes while the vehicle is unattended? I see some racks have locks on the knobs but they don't seem very strong.   What do you suggest? Profile picture cannot have transparent background User cards are no longer showing reputation or badges across the network iOS navigation bar item image size Add a link to the timeline of a post For the past year I have been quite active on SO and a bit on meta, but I had never heard of the timeline of a post until today in a comment on meta.  There was an  two years ago of this feature as "experimental". ( for that question).  This feature was , answer: this exists, but the link has to be built manually.  I think this could be quite interesting sometimes and I would like to use this, but I will not do so if I have to build the link each time by myself.  This feature has existed for two years and is still "experimental"? Who is using it? Who knows about it?  My feature request: Implement a link in the posts to their timeline. I am sure this nice feature will be used. Quick question to anyone who has used this LaTeX template:    Any ideas on how to change the left margin to get more words onto one page? I need to use filter to sort calendar months in mmm format.  Data &gt; Sort &gt; Custom will do it but I cannot make filter work. Months are in a column eg SEP, APR, JAN, APR, etc.  Filter just does an alphabetical sort so it puts all the APR first. Too long in Primary Fermentation? What's the maximum amount of time for primary fermentation, assuming the beer is going straight to bottles next? Will it over ferment and then fail to carbonate, if left too long in a carboy? I am trying to solve a 2 part question, the first part is to expand $\sqrt{1-x}$ up to and including the term $x^2$ which I did.  This gives me $1-(0.5)x-(0.125)x^2 + ...$  However, the 2nd part of the question says that by taking $x=(1/64)$ in the expansion of part (i) -> which refers to the one above, deduce that $\sqrt 7 = 10837/4096$. How do i do this part?  EDIT (After Hint Given By SimpliFire):  $$ \sqrt{1-\frac1{64}}=\frac{\sqrt{63}}8=\frac38\sqrt7 $$ $$ =\frac83\sqrt{1-\frac1{64}}\;=\sqrt7 $$ $$ =\frac83\left(1-\frac12\left(\frac1{64}\right)-\frac18\left(\frac1{64}\right)^2\right)\; $$ $$ =\frac83\left(1-\frac1{128}-\frac1{32768}\right)\; $$ $$ =\frac83\left(\frac{32768}{32768}-\frac{256}{32768}-\frac1{32768}\right)\; $$ $$ =\frac83\left(\frac{32511}{32768}\right)\; $$ $$ =\frac{260088}{98304} $$ $$ \frac{10837}{4096}\;\approx\sqrt7 $$  I'm not sure if I can present it like this, if it is okay i will post it as my answer :X How to use Redstone dust in Minecraft PE? I have Minecraft Pocket Edition and I have collected a lot of redstone dust. For some reason, I couldn't use it for things such as iron doors. Why? querying Recently account viewed I'm doing a masters course at a different university than I did my undergrad (both in maths). I did well in my undergrad but now I'm finding it very difficult. The shock of the change is hard to cope with.  I'm not just finding it very difficult, but I get zero feedback: we don't have any tests and I was not able to make friends so I don't know how others are finding it. I'm starting to think that I might be an idiot.   How can I build some confidence in my abilities at the same time as I rush and struggle to keep up with the massive rate of new material I need to learn? How might I get myself some reassurance that I can actually pass, or stop worrying about this so much? (I feel terribly guilty using so much money from my family to be here) It's possible that I don't really have a chance at all but knowing that would be fine. sliding a tangent line along a curve How can I run a specific command for each find result? How would one run a specific command for each file that was found by using the find command? For the purpose of the question lets say that I would simply like to delete each file found by find. Redirect all requests to HTTPS, except for one subdirectory Scorched3d will not launch Scorched3d worked then stopped. Unistalled and reinstalled did not help. Running Ubuntu 16.04.04LTS. I think it was after installing new release.  I think the problem is the Ubuntu 16.04.4LTS. The newer version has no Scorched3d in the Ubuntu Software Center. I have 3 systems. After updating to new version. Scorched3D will not install and work after updating.  ron@RonsComputer:~$ sudo objdump -p $(type -p scorched3d) | grep NEEDED  NEEDED libwx_gtk2u_adv-3.0.so.0  NEEDED libwx_gtk2u_core-3.0.so.0 NEEDED libwx_baseu-3.0.so.0 NEEDED libfreetype.so.6 NEEDED libz.so.1 NEEDED libSDL-1.2.so.0 NEEDED libSDL_net-1.2.so.0 NEEDED libexpat.so.1  NEEDED libstdc++.so.6 NEEDED libm.so.6 NEEDED libgcc_s.so.1 NEEDED libpthread.so.0 NEEDED libc.so.6   ron@ron-desktop ~ $ objdump -p $(type -p scorched3d) | grep NEEDED | awk '{print $2}' | xargs -n 1 dpkg -S  libwxgtk3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_gtk2u_adv-3.0.so.0.2.0 libwxgtk3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_gtk2u_adv-3.0.so.0 libwxgtk3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_gtk2u_core-3.0.so.0.2.0 libwxgtk3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_gtk2u_core-3.0.so.0 libwxbase3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_baseu-3.0.so.0.2.0 libwxbase3.0-0v5:amd64: /usr/lib/x86_64-linux-gnu/libwx_baseu-3.0.so.0 libfreetype6:amd64: /usr/lib/x86_64-linux-gnu/libfreetype.so.6.12.1 libfreetype6:i386: /usr/lib/i386-linux-gnu/libfreetype.so.6 libfreetype6:amd64: /usr/lib/x86_64-linux-gnu/libfreetype.so.6 libfreetype6:i386: /usr/lib/i386-linux-gnu/libfreetype.so.6.12.1 zlib1g:i386: /lib/i386-linux-gnu/libz.so.1.2.8 zlib1g:amd64: /lib/x86_64-linux-gnu/libz.so.1 zlib1g:i386: /lib/i386-linux-gnu/libz.so.1 zlib1g:amd64: /lib/x86_64-linux-gnu/libz.so.1.2.8 libsdl1.2debian:amd64: /usr/lib/x86_64-linux-gnu/libSDL-1.2.so.0.11.4 libsdl1.2debian:i386: /usr/lib/i386-linux-gnu/libSDL-1.2.so.0 libsdl1.2debian:i386: /usr/lib/i386-linux-gnu/libSDL-1.2.so.0.11.4 libsdl1.2debian:amd64: /usr/lib/x86_64-linux-gnu/libSDL-1.2.so.0 libsdl-net1.2:amd64: /usr/lib/x86_64-linux-gnu/libSDL_net-1.2.so.0 libsdl-net1.2:i386: /usr/lib/i386-linux-gnu/libSDL_net-1.2.so.0 libsdl-net1.2:amd64: /usr/lib/x86_64-linux-gnu/libSDL_net-1.2.so.0.8.0 libsdl-net1.2:i386: /usr/lib/i386-linux-gnu/libSDL_net-1.2.so.0.8.0 libexpat1:i386: /lib/i386-linux-gnu/libexpat.so.1.6.0 libexpat1:amd64: /lib/x86_64-linux-gnu/libexpat.so.1 libexpat1:amd64: /lib/x86_64-linux-gnu/libexpat.so.1.6.0 libexpat1:i386: /lib/i386-linux-gnu/libexpat.so.1 libstdc++6:amd64: /usr/share/gdb/auto-load/usr/lib/x86_64-linux-gnu/libstdc++.so.6.0.21-gdb.py libstdc++6:i386: /usr/lib/i386-linux-gnu/libstdc++.so.6 libstdc++6:amd64: /usr/lib/x86_64-linux-gnu/libstdc++.so.6 libstdc++6:amd64: /usr/lib/x86_64-linux-gnu/libstdc++.so.6.0.21 libstdc++6:i386: /usr/lib/i386-linux-gnu/libstdc++.so.6.0.21 libstdc++6:i386: /usr/share/gdb/auto-load/usr/lib/i386-linux-gnu/libstdc++.so.6.0.21-gdb.py libc6:amd64: /lib/x86_64-linux-gnu/libm.so.6 libc6:i386: /lib/i386-linux-gnu/libm.so.6 libgcc1:amd64: /lib/x86_64-linux-gnu/libgcc_s.so.1 libgcc1:i386: /lib/i386-linux-gnu/libgcc_s.so.1 libc6:i386: /lib/i386-linux-gnu/libpthread.so.0 libc6:amd64: /lib/x86_64-linux-gnu/libpthread.so.0 libc6:i386: /lib/i386-linux-gnu/libc.so.6 libc6:amd64: /lib/x86_64-linux-gnu/libc.so.6 ron@ron-desktop ~ $ Trigger Task Scheduler in Windows 7 when computer wakes up from sleep/hibernate I don't want task scheduler or whatever to wake the computer, but when I open the laptop back up and the machine wakes I'd like that to be the trigger that task scheduler or something uses to run an app.