I have a charger light. It gets charged by 220V AC supply. It can light 5 LEDs. I know that it needs to make the supply 220V AC to DC of lower voltage nearly 5V to 10V. Then it can charge the small battery. But I found no transformer in the circuit. There are simply some diodes resistors and capacitors.   I want to know how the circuit works. I want to know how the small battery can be charged with so high voltage?
I have been using and making LED flashlights for years now and I am VERY familiar with all of the circuitry and technology inside of them, but I just got my first LED house light bulb that runs off of 110v AC electricity.  It is very similar to a flashlight - it has a large heatsink, and 1 or more LEDs inside of it (brand and specs of emitters, I do not know).  The part that I am most curious about is how the electricity from the socket gets to the emitter.  In a flashlight the power comes from a DC battery through a current regulator (LED driver) and into the LED itself.  This is not difficult because the voltage of common LED emitters is about the same voltage as Lithium batteries (3.7v, 7.4v, etc) which makes the current limiting relatively simple coming from a one or two cell light.  How does this work for a high voltage AC bulb?  Is there a transformer and rectifier inside of EVERY bulb (I sure hope not), or are the emitters manufactured to run off of 110v AC power and just use half of the wave cycle?
Do you capitalize both parts of a hyphenated word in a title?  "My Ex-Wife Hates Me"  or  "My Ex-wife Hates Me" Design simulates perfectly but won't work on FPGA How do I convert my PhD dissertation so that it can be published as a book? I have just completed a PhD by research, which I think has some merits in being available as a book (This is, of course, my personal opinion). The research cuts across several fields (e.g. sociology, public policy).  I am wondering what I need to do to take the next step.  In particular:   How do you turn an academic piece like the dissertation (which is written for the examiners) into a book (which is for the general public)? How do I find publishers who specialise in my field? How to partially hide content in beamer latex? Dobble card game - mathematical background In  there is a deck of 55 cards. Each of them has 8 symbols on it. There is a total of 50 different symbols and each two cards have one and only one in common.  I am wondering, given a total number of symbols N and a number of symbols on each card K, how do you find the biggest number of cards such that:   on each of those cards there are exactly K of the N symbols, every two cards have one and only one symbol in common. Let $V$ be a subspace of $\mathbb R^3$ generated by the vectors $\{(1,1,1),(0,1,1)\}.$ There are $3$ vectors $u_1=(0,0,1),u_2=(1,1,0),u_3=(1,0,1)$.Then which of the following sets are connected?  $1.\left(\mathbb R^3\setminus V\right)\cup\{(0,0,0)\}$  $2.\left(\mathbb R^3\setminus V\right)\cup \{tu_1+(1-t)u_3:t\in [0,1]\}$  $3.\left(\mathbb R^3\setminus V\right)\cup\{tu_1+(1-t)u_2:t\in [0,1]\}.$  $4.\left(\mathbb R^3\setminus V\right)\cup \{(t,2t,2t):t\in \mathbb R\}$  Now $V$ is generated by two linearly independent vectors so is like $\mathbb R^2.$ So $\left(\mathbb R^3\setminus V\right)$ will be disconnected but giving the $(0,0,0)$ with them will make it connected.  No. $4$, I think will be connected also because $\{(t,2t,2t),t\in \mathbb R\}$ is in $V$ and contains the point $(0,0,0)$ Now, any neighbourhood of this point will have points from both $V$ and $\left(\mathbb R^3\setminus V\right)$ and so the union is connected.I'm not sure about no. $2$ and $3.$ Managing multiple asynchronous NSURLConnection connections Why is the nucleus of an Iron atom so stable? Lighter nuclei liberate energy when undergoing fusion, heavier nuclei when undergoing fission.  What is it about the nucleus of an Iron atom that makes it so stable?  Alternatively: Iron has the greatest nuclear binding energy - but why? Show that the series $\sum(\exp(\frac{(-1)^n}{n})-1)$converges, but not absolutely. Show that the series converges, but not absolutely. $\sum_{n=1}^{\infty}( $exp$(\frac{(-1)^n}{n})-1)$.   My Try:  Let $a_n=$exp$(\frac{(-1)^n}{n})-1$. I was going to use alternating series test because the sequence $\{a_n\}$ is alternating. But $\{|a_n|\}$ is not decreasing to $0$. So, I am stuck now. Can anybody please give me a hint? If shuffle-playing playlist &times;100 resulted in [10 13 10  3  2  2] different songs being repeated [1 2 3 4 5 6] times, what is the estimate for the total number of songs? (assuming shuffle play was completely random)  Update: (R code)  k &lt;- 50 # k number of songs on the disk indexed 1:k n &lt;- 100 # n number of random song selections m &lt;- 20 # m number of repeat experiments colnum &lt;- 10 mat &lt;- matrix(data=NA,nrow=m,ncol=colnum) df &lt;- as.data.frame(mat) for(i in 1:m){   played &lt;- 1+floor(k*runif(n)) # actual song indices (1:k) selected    freq &lt;- sapply(1:k,function(x){sum(played==x)})   # = number of times song with index x is being played   histo &lt;- sapply(1:colnum,function(x){sum(freq==x)});   for(j in 1:colnum){    df[i,j] &lt;- histo[j]   } } df   Resulting in: e.g. 20 distributions (V1=number of single plays, V2=number of double plays, etc):     V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 1  15 13 11  1  2  2  0  0  0   0 2  15 12 10  1  4  0  1  0  0   0 3  12 14  7  6  3  0  0  0  0   0 4  17 16  6  4  2  0  1  0  0   0 5  17 10 12  5  0  0  1  0  0   0 6  13 15 11  6  0  0  0  0  0   0 7  10 14  9  3  2  1  1  0  0   0 8  12 17  5  6  3  0  0  0  0   0 9   9 19  8  3  1  2  0  0  0   0 10 13  9 11  6  1  0  1  0  0   0 11 16  9 12  5  2  0  0  0  0   0 12 15  9 11  6  2  0  0  0  0   0 13 19  9  7  4  4  1  0  0  0   0 14 17 11  4  7  3  1  0  0  0   0 15 11 20  8  1  3  1  0  0  0   0 16 14 12 10  5  0  2  0  0  0   0 17  9 12  8  7  3  0  0  0  0   0 18 10 15  9  4  2  0  1  0  0   0 19 14 11 12  7  0  0  0  0  0   0 20 16 14 11  3  1  1  0  0  0   0   Now I need to get from here to the Poisson modelling--my R is a bit rusty (?lmer)...--Any help would be appreciated...  Attempted Poisson modelling: disappointing fit?!  plot(1:colnum,df[1,1:colnum],ylim=c(0,30),    type="l",xlab="repeats",ylab="count") for(i in 1:m){   clr &lt;- rainbow(m)[i]   lines(1:colnum,df[i,1:colnum],type="l",col=clr)   points(1:colnum,df[i,1:colnum],col=clr) }  df.lambda=data.frame(lambda=seq(1,5,0.1),ssq=c(NA));df.lambda for(ii in 1:dim(df.lambda)[1]){   l &lt;- df.lambda$lambda[ii]       ssq &lt;- 0       for(i in 1:20){         for(j in 1:10){           ssq &lt;- ssq + (df[i,j] - n*dpois(j,l))^2         }       }       print(ssq)       df.lambda$lambda[ii] &lt;- l   df.lambda$ssq[ii] &lt;- ssq     }     df.lambda     lambda.est &lt;- df.lambda$lambda[which.min(df.lambda$ssq)] lambda.est # 2.4 points(x &lt;- 1:10, n*dpois(1:10,lambda.est),type="l",lwd=2)  100*dpois(1:10,3) n/lambda.est   the estimated lambda stays around 2.3, with an n estimate of around 43; the fitted curve seems very discrepant, and seems to worsen with rising n !?  Doesn't this have to do with the fact, that our repeats are different from the 'classical' Poisson distributions: it's not just ONE event that repeats itself x number of times, but the sum of repeats of different items (songs)?! Prove that there exist two integers such that i - j is divisible by n. Here's the full question:  Prove that, for any $n + 1$ integers, $\{x_0, x_1, x_2, . . . , x_n\}$, there exist two integers $x_i$ and $x_j$ with $i \neq j$ such that $x_i − x_j$ is divisible by $n$.  Now, the integers aren't necessarily consecutive, positive, or without repeats. I've tried breaking this into cases, such as "$x_i = x_j, \dfrac{0}{n} = 0$" etc. But I don't think it's possible to exhaust the cases.  I feel like there should be an easy way to contradict this one, by saying that $x_i - x_j$ isn't divisible by $n$. But I just wasn't getting anywhere with that one.  I thought about using induction, but I would have just as hard a time proving this for $n$ integers before $n+1$ integers, so I don't think it would be possible for me to do it that way.  If anyone could help out, that would be wonderful. I'm pretty stuck here. How do I format my code blocks? How do I post text so that it is formatted as code?  What do I need to do so that my code shows up properly &mdash; not escaped or removed &mdash; when posted? And how to get the correct syntax highlighting?     For more information, see "" in the . How can I render an edge only mesh as solid lines? Name of the book/series based on magicians who tap into computer grid? What is an ultra-wide lens? What is the point at which a lens is considered "ultra-wide angle" vs just wide angle? I have read many post about updating an iPad 1 (iOS 5.1.1) to iOS 8 but all I need at the moment is to update my iPad 1 to at least iOS 6. Is there any way I can update it to iOS 6? No jail breaking or anything, just a normal way of updating. Light Presets .exr I would like to install light presets for Blender to automate my lightning in my scenes. I have some .exr files (from Greyscalegorilla) but I don't know how to do it on Blender to make it work. Can someone help me? Thank you Is $0\,\mathrm{m}$ dimensionless? How do World of Warcraft referrals and the free month work? I sent the referral link to my boss and he bought the game and applied his CD key.  He now has a paid account linked to mine:    Yet when I view my World of Warcraft account, it seems they didn't give me the free month. It appears I only have the free month that came with my Battlechest purchase.  I just created and bought my account this morning. Would this affect the free referral month in any way?    We haven't seen each other or partied online in the game yet, do we need to do that first in order for me to receive the month? Force "low power mode" on mac