I am told that I must use 5V, 1A charger to charge power bank. If I will use 5V, 2A charger then will it burn power bank?  Is that possible?  \$I = V / R\$  Charger give constant voltage and current depends on resistance. That is why I think only Voltage is important and charger must be able to give enough current.  But battery bank may have some smart impulse chip like charger have. It may play with its resistance and voltage may jump.   Also I do not understand if I can plug battery bank in PC's USB to charge power bank.
Power supplies are available in a wide range of voltage and current ratings.  If I have a device that has specific voltage and current ratings, how do those relate to the power ratings I need to specify?  What if I don't know the device's specs, but am replacing a previous power supply with particular ratings?  Is it OK to go lower voltage, or should it always be higher?  What about current?  I don't want a 10 A supply to damage my 1 A device.
Differences between longtable and xtab I have a pretty simple table that needs to span multiple pages. This seems like a job for either the / package or the  package.   The voting on the answers to this  suggest that longtable is the preferred package, yet xtab is much newer and has been revised since that question was asked.  What are the differences between xtab and longtable and when is one preferable to the other? Selecting one every n frames from a video using ffmpeg Why should events in C# take (sender, EventArgs)? It's known that you should declare events that take as parameters (object sender, EventArgs args). Why? Cleaning ‘staining’ off bottom of MacBook screen A couple months ago, I started to see some very small stain spots on the bottom of my MacBook Pro early 2015 screen. It's very annoying to see while I'm using it. When the screen is turned off, I see it as in the picture below. But when it's turned on, I see it as very small water-ish drops. I tried to clean it using water, screen cleaner, and even alcohol, but it didn't go away.  Also that area doesn't feel as smooth as the unaffected area. So, I think it's on the outside of my screen not inside.  Have you ever seen this before? Any suggestions on how to remove it without the need of replacing the whole screen? Say I have 12 and have to factorize it in 2 factors. Now possible factors are 1, 12 2, 6 3, 4   Now 3,4 is such that value of maximum factor i.e. 4 is minimized among all pairs.  How to find the solution in generic case where a number N is to be divided in K factors minimizing maximum value. Let $D \subset \mathbb{C}$ be the open unit disk, $f:D \to \mathbb{C}$ a holomorphic function and $d=\sup \{|f(z)-f(w)|:z,w\in D \}$. How can I show that $|f'(0)|\leq \frac{d}{2}$?  I tried using Schwarz's lemma on the function $g:D \to \mathbb{C}$ defined by $g(z)=\frac{f(z)-f(0)}{d}$, but I am only getting $|f'(0)|\leq d$. Game Theory and Uniform Distribution question? In an Auction , two players are  bidding. Their bids will be a unknown fraction of their valuations. The valuations come from a uniform distribution $$[0,1] $$  If Player 2 bids $$ v/2 $$  and Player 1 bids $$b1&lt;1/2$$   What is the probability player 1 wins ? Clearly for player 1 to win,players 2 bid has to be less than player 1 bids. $$P(v/2 &lt; b1)$$  $$P(v &lt; 2b1)$$ I follow the question up to this stage. Now it says since its uniformly distributed the probability player 1 wins is $$2b1$$ Im confused how can you just get 2b1 from the inequality ?  Thanks in advance What is the Physical Meaning of Commutation of Two Operators? I've just started to learn about the tensor product and I want to show: $$(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}.$$  Can you tell me if my proof is right:  $\mathbb{Z}/m\mathbb{Z}$ and $\mathbb{Z} / n \mathbb{Z}$ are both finite free $\mathbb{Z}$-modules with the basis consisting of one single element $\{ 1 \}$. So $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z})$ has the basis $\{ 1 \otimes 1 \}$.  Therefore, any element in $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z})$  is of the form $(ab) 1 \otimes 1$ and any element in $\mathbb{Z}/ \gcd(m,n)\mathbb{Z}$ is of the form $k 1 = k$ where $k \in \{ 0, \dots , \gcd(n,m) \}$.  I would like to construct an isomorphism that maps $ab$ to some $k$. Let this map be $ab (1 \otimes 1) \mapsto ab \bmod \gcd(n,m)$.  This is a homomorphism between modules: it maps $0$ to $0$ because it maps the empty sum to the empty sum. It also fulfills $f(a + b) = f(a) + f(b)$ because there is only one element, $a = 1$.   It is surjective. So all I need to show is that it is injective. But that is clear too because if $ab \equiv 0 \bmod \gcd(m,n)$  then both $a \equiv 0 \bmod n$ and $b \equiv 0 \bmod m$ so the kernel is trivial.  Many thanks for your help!! Computing the cardinality of a combinatorial set Define two sets: $S_1$ and $S_2$ where we have that $a$ is an odd natural number and $b\in \mathbb{N}$, $S_1 = \Big\{ \frac{2}{a},\frac{2}{a-2},\frac{2}{a-4},...,\frac{2}{a-(a-1)},$ $\frac{2+4}{a+2},\frac{2+4}{a},\frac{2+4}{a-2},...,\frac{2+4}{a-(a-1)},$ $\frac{2+8}{a+4},...,\frac{2+8}{a-2},...,\frac{2+8}{a-(a-1)},$ $\vdots$ $\frac{2+4\lfloor\frac{b}{2}\rfloor}{a+\lfloor\frac{b}{2}\rfloor},\frac{2+4\lfloor\frac{b}{2}\rfloor}{a+\lfloor\frac{b}{2}\rfloor-2},...,\frac{2+4\lfloor\frac{b}{2}\rfloor}{a-(a-1)},$ $\frac{2+4(\lfloor\frac{b}{2}\rfloor+1)}{a+\lfloor\frac{b}{2}\rfloor},\frac{2+4(\lfloor\frac{b}{2}\rfloor+1)}{a+\lfloor\frac{b}{2}\rfloor-2},...,\frac{2+4(\lfloor\frac{b}{2}\rfloor+1)}{a-(a-1),}$ $\frac{2+4(\lfloor\frac{b}{2}\rfloor+2)}{a+\lfloor\frac{b}{2}\rfloor-2},\frac{2+4(\lfloor\frac{b}{2}\rfloor+2)}{a+\lfloor\frac{b}{2}\rfloor-4},...,\frac{2+4(\lfloor\frac{b}{2}\rfloor+2)}{a-(a-1)}$ $\vdots$ $\frac{2+4b}{a},\frac{2+4b}{a-2},...,\frac{2+4b}{a-(a-1)} \Big\}$ and $S_2 = \Big\{ \frac{2}{\lceil\frac{a}{2}\rceil}, \frac{2}{\lceil\frac{a}{2}\rceil-1},\frac{2}{\lceil\frac{a}{2}\rceil-2},...,\frac{2}{1}$ $\frac{2+2}{\lceil\frac{a}{2}\rceil+1},\frac{2+2}{\lceil\frac{a}{2}\rceil},\frac{2+2}{\lceil\frac{a}{2}\rceil-1},...,\frac{2+2}{1},$ $\vdots$ $\frac{2+2(\lfloor\frac{b}{2}\rfloor-1)}{\lceil\frac{a}{2}\rceil+(\lfloor\frac{b}{2}\rfloor-1)},\frac{2+2(\lfloor\frac{b}{2}\rfloor-1)}{\lceil\frac{a}{2}\rceil+(\lfloor\frac{b}{2}\rfloor-2)},...,\frac{2+2(\lfloor\frac{b}{2}\rfloor-1)}{1}$ $\frac{2+2\lfloor\frac{b}{2}\rfloor}{\lceil\frac{a}{2}\rceil+\lfloor\frac{b}{2}\rfloor},...,\frac{2+2\lfloor\frac{b}{2}\rfloor}{1},$ $\frac{2+2(\lfloor\frac{b}{2}\rfloor+1)}{\lceil\frac{a}{2}\rceil+\lfloor\frac{b}{2}\rfloor-1},...,\frac{2+2(\lfloor\frac{b}{2}\rfloor+1)}{1},$ $\frac{2+(\lfloor\frac{b}{2}\rfloor+2)}{\lceil\frac{a}{2}\rceil+\lfloor\frac{b}{2}\rfloor-2},...,\frac{2+(\lfloor\frac{b}{2}\rfloor+2)}{1}$ $\vdots$ $\frac{2+2b}{\lceil\frac{a}{2}\rceil-1},...,\frac{2+2b}{1} \Big\}$ The question is, how do I determine the cardinality of the intersection of these two sets i.e. how would I compute the value $|S_1 \cap S_2|$? Note that duplicates may appear within both sets such as $\frac{1}{2}=\frac{2}{4}$ etc. Therefore we must make sure that for each fraction $\frac{n}{m}$ we have $\text{gcd}(n,m)=1$. I am aware of the existence of , but not entirely sure if that identity would be useful here. Difference between standard error and standard deviation I'm struggling to understand the difference between the standard error and the standard deviation. How are they different and why do you need to measure the standard error? How can we change root password? Syntax to transfer from remote to local scp by leapfrogging onto another host? I always see commands like this  apt-get -y install    What is the -y tag for and what is the difference between apt-get install with and without the -y tag? Getting tabular statistics from table using QGIS? The question is based on my theory from the recent manga chapter (Naruto 661):     Sasuke, when stabbed by Madara is the effect of Tsukuyomi from Sasuke.   Now, to prove my theory, is there an episode in manga/anime that Sasuke used Tsukuyomi? How does Spider-Man climb walls? Does the order in which I set properties using the object initializer syntax get executed in the exact same order?  For instance if I do this:  var s = new Person { FirstName = "Micah",                      LastName = "Martin",                      IsLoaded = true                    }   will each property get set in the same order? Where do I put item tags on items inside a chest or your inventory? Where are icons stored? I want to change an icon of a specific theme. Where do themes save their icons?