I need to drive several indicator LEDs at &lt;2mA.  Each LED has a nominal Vf between 3.2V and 3.3V (Vf max up to 4V).  In the past I've had the luxury of (a) current-limiting resistors or (b) constant-current power supplies.    But what do I do when my entire circuit has to run off a single 3.3V SMPS, and the microprocessor outputs are limited to 25mA? Here solution A isn't applicable, and the budget doesn't allow solution B (unless maybe all the LEDs can share a single current-limited supply--they don't all have to be on at the same time--and yet I still get to control the LEDs from a microprocessor directly, without external transistors.)  Background:     I have a microprocessor with a few PWM outputs, but not enough for every LEDs.  (yes, multiplexing is possible) This is an ultra-low-power, portable application. BOM cost has to be low, low, low.
Modern electronics industry has developed very efficient LEDs with nice and fancy colors (“true green” , “cyan”, and “blue”) based in InGaN technology, or similar. Some of these LEDs are specified as having forward voltages of 3.2 to 4.2 V. Here are examples of such LEDs, , or surface-mount .  But the usual MCUs are powered from 3.3 V supply, and the GPIO output is usually at 3.1-3.2 V, which seems to be barely enough to drive these LEDs . How can I use these LEDs as indicators of some signal statuses, or power rail status? Do I need a series resistor R1 here?    If yes, how do I choose its value?  DISCLAIMER: This "question-answer" comes as elaboration of the original question , to address the particular use case of LEDs as logic state indicators.
Virtualbox: OS cannot use the new extended disk space (.vdi) I am running Virtualbox. I increased the size of my hard disk (.vdi) from 10G to 15G. Now when I start my Mint vm, the hard disk reports as 7.5g (df) even though i extended it (fdisk -l). I am not sure what is the problem. Can anyone point me the problem?  $ df -h Filesystem      Size  Used Avail Use% Mounted on /dev/sda1     &gt;&gt;7.5G&lt;&lt; 7.1G   61M 100% / udev            1.5G  4.0K  1.5G   1% /dev tmpfs           581M  888K  581M   1% /run none            5.0M     0  5.0M   0% /run/lock none            1.5G   88K  1.5G   1% /run/shm  $ sudo fdisk -l Disk /dev/sda: &gt;&gt;16.1 GB&lt;&lt;, 16106127360 bytes 255 heads, 63 sectors/track, 1958 cylinders, total 31457280 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x000c55a4     Device Boot      Start         End      Blocks   Id  System /dev/sda1   *        2048    15728639     7863296   83  Linux /dev/sda2        15730686    16775167      522241    5  Extended /dev/sda5        15730688    16775167      522240   82  Linux swap / Solaris  $ vboxmanage showhdinfo mint.vdi UUID:                 a94931b9-673c-440a-ab6b-2c3eedd0cf93 Accessible:           yes Logical size:         15360 MBytes Current size on disk: 7806 MBytes Type:                 normal (base) Storage format:       VDI Format variant:       dynamic default Location:             /opt/virtualization/vm/mint.vdi Destroying a spammer does not delete their comments Does the series $\sum \limits_{n=2}^{\infty }\frac{n^{\log n}}{(\log n)^{n}}$ converge? Primes dividing $11, 111, 1111, ...$ Does Android keep the .apk files? if so where? Export Track Markers to csv I am trying to export markers from the Blender motion tracker and found the following script that will do exactly that:  for clip in D.movieclips:     for track in clip.tracking.tracks:         fn = 'data/tr_{0}_{1}.csv'.format(clip.name.split('.')[0], track.name)         with open(fn, 'w') as f:             frameno = 0             while True:                 markerAtFrame = track.markers.find_frame(frameno)                 if not markerAtFrame:                     break                 frameno += 1                 coords = markerAtFrame.co.xy                 f.write('{0} {1}\n'.format(coords[0], coords[1]))   It works but I have two questions:   How can I save the data on my Desktop rather than in folder in MacOS blender content where it saved right now. The following won't work:   fn = '/User/me/Desktop/data/tr_{0}_{1}.csv'.format(clip.name.split('.')[0], track.name) The resulting values I get do not represent the more user friendly marker values in den Blender GUI. Instead of x/y coordinates in screen coordinates, I get a value between 0/1. How can I convert them to those screen coordinates ?    Thanks for your help How many "polygons" does my model have? I have my model and in the info bar its show this   May I need to know how many polygons it has, but  there is no option to find polygons. Verts, Edge and Faces nothing polygon option there. In the website its say that the upload limit is 400,000 polygons. I did not get over that limit or how many polygons my model has? I've got about a billion rows of data in a table with a name and an integer in the range 1-288.  For a given name, every int is unique, and not every possible integer in the range is present--so there are gaps.  This query generates an example case:  --what I have: SELECT * FROM ( VALUES ('foo', 2),               ('foo', 3),               ('foo', 4),               ('foo', 10),               ('foo', 11),               ('foo', 13),               ('bar', 1),               ('bar', 2),               ('bar', 3)      ) AS baz ("name", "int")   I'd like to generate a lookup table with a row for each name and sequence of contiguous integers.  Each such row would contain:  name   --  the value of the name column start  --  the first integer in the contiguous sequence end    --  the final value in the contiguous sequence span   --  end - start + 1  This query generates example output for the above example:  --what I need: SELECT *  FROM ( VALUES ('foo', 2, 4, 3),               ('foo', 10, 11, 2),               ('foo', 13, 13, 1),               ('bar', 1, 3, 3)      ) AS contiguous_ranges ("name", "start", "end", span)   Because I have so many rows, more efficient is better.  That said, I only have to run this query once, so it isn't an absolute requirement.  Thanks in advance!  Edit:  I should add that PL/pgSQL solutions are welcome (please explain any Fancy Tricks--I'm still new to PL/pgSQL). Difference between deportation and removal As I understand it, there are two mechanisms for throwing somebody out of the UK: deportation and removal. Informally, people seem to call both of these "deportation".  What are the differences between them? Who do they apply to? Do they have different effects on the person's ability to return to the UK later? Minimum value of $\left(a+\frac{1}{b}\right)^2+\left(b+\frac{1}{c}\right)^2+\left(c+\frac{1}{a}\right)^2$ Given $a,b,c \in \mathbb{R^+}$ such that $a+b+c=12$   Find Minimum value of $$S=\left(a+\frac{1}{b}\right)^2+\left(b+\frac{1}{c}\right)^2+\left(c+\frac{1}{a}\right)^2$$  My Try: By Cauchy Schwarz Inequality we have  $$\left(a+\frac{1}{b}\right)+\left(b+\frac{1}{c}\right)+\left(c+\frac{1}{a}\right)\le \sqrt{3}\sqrt{S}$$  $\implies$  $$\sqrt{3S} \ge 12+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}$$  Now by $AM \ge HM $ inequality we have  $$\frac{a+b+c}{3} \ge \frac{3}{\frac{1}{a}+\frac{1}{b}+\frac{1}{c}}$$ $\implies$  $$\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \ge \frac{3}{4}$$  hence  $$\sqrt{3S} \ge 12+\frac{3}{4}=\frac{51}{4}$$  hence  $$3S \ge \frac{2601}{16}$$  so $$S \ge \frac{867}{16}$$  is this approach correct and any better approach please share. How to copy the complete folder structure one location to another location include all files and sub folders I have folder structure like in Shared documents/East using CSOM and C# Main Folder   Folder1   Folder2      File1      File2  I have to copy all folders with files to Shared documents/West .... Continuously copy all file changes from one folder to another on change (Windows) I'm working on a massive Java web application which is kept under centralized version control, but the source files are used to build and run the actual server, which then copies all the files I work on into a random temporary directory while it's running.  My problem is that I need to either rebuild this huge application to see any changes to my files, or keep track of all my changes and copy over the files I've changed back to their source location before committing them back to source control.  My question is: is there a command line script I can run that will monitor any changes in the source folder and automatically copy changed files across to temporary folder X?  The idea is to remove the human point of failure in having to manually mitigate the two-locations problem. UEFI machine doesn't boot Ubuntu through NVRAM bootcatalog. How to fix? How does similar_text work? Create violine plots I use pgfplots for most of my plots. Now I need to add a . Is this possible with pgfplots or any other package? What software can I use to view epub documents? What software can I use to view .epub documents? I have a question about the corollary to theorem 5.12 in Rudin's Principles of Mathematical Analysis (page 108):  Suppose $f$ is a real differentiable function on $[a,b]$ and suppose $f'(a)&lt; \lambda &lt; f'(b)$ then there is a point $x \in (a,b)$ such that $f'(x) = \lambda$ Corollary: If $f$ is differentiable on $[a,b]$ then $f'$ cannot have any simple discontinuities on $[a,b]$.  Can someone help me to show how he uses the result in the &quot;main theorem&quot; in the corollary?  (There are two cases of simple discontinuities  $f(x+) = f(x-) \neq f(x)$ and $f(x +) \neq f(x-)$ Make sure only a single instance of a program is running Is there a Pythonic way to have only one instance of a program running?   The only reasonable solution I've come up with is trying to run it as a server on some port, then second program trying to bind to same port - fails. But it's not really a great idea, maybe there's something more lightweight than this?    (Take into consideration that program is expected to fail sometimes, i.e. segfault - so things like "lock file" won't work) TikZ externalization with absolute path and MiKTeX distribution This code:  \documentclass[11pt,openright]{book} \usepackage[T1]{fontenc} \usepackage[latin9]{inputenc} \usepackage[british]{babel}  \usepackage{tikz} \usetikzlibrary{external} \tikzexternalize[prefix={"C:/Users/MyName MySurname/Documents/LaTeX/Figures/"}]  %\tikzexternalize[prefix={Figures/}]   \begin{document} \begin{tikzpicture}     \draw (0,0) circle (1cm); \end{tikzpicture} \end{document}   gives me the error:     ! I can't write on file `"C:/Users/MyName   MySurname/Documents/LaTeX/Figures/MyMWE-figure0.md5"'.   I'm working with Windows 10, MiKTeX 2.9 distibution.  Following the advice Tarass gave me on a comment of this question:  and as indicated here:  I've registered a user-managed TEXMF directory but I still get the same error.  With \tikzexternalize[prefix={Figures/}] all works perfectly but, since I'm using LyX, the files are stored in a LyX temp dir, hence I loose them when I close the program (making externalization useless), so I need to use an absolute path. One page website - Effect on SEO I'm considering re-designing my personal website to promote my web services in my local area.  My issue is whether to do a one page website with a scroll-to navigation system. What effect does this have on SEO. As i understand it, you set stuff like h1's and meta description on specific page content. How does this work when all of your different content is on one page?