Is there a way to extend the length of wires for I2C connection?
Can I use I2C over 2m cables?
"Add/show 1 other comment" bug strikes again Moving a doorbell transformer Can a doorbell transformer that is on the outside of a wall be place inside the wall behind the drywall. I’m concerned about it getting too hot. Mine is in the kitchen by the ceiling lights Existence of elements of order $p^k$ in a finite group By Cauchy's theorem, if a prime number $p$ divides the order of a group $G$, then there is an element $g$ in $G$ whose order is $p$. In addition, if $|G|$ admits a prime decomposition with a factor $p^k$, then Sylow's theorem tells us that a subgroup of order $p^k$ must exist.   My question is the following. If $|G|$ admits a prime decomposition with a factor $p^k$, does this imply that an element of order $p^k$ must exist in $G$?   Update: As explained in Mindlack's answer (among others), the implication does not hold and simple counterexamples exist. In the comments, Mindlack discusses special cases where such an element exists. Ubuntu 18 - how to ungroup apps in dock? I want to make Ubuntu dock like Windows taskbar  Ubuntu:    Windows:    (as you see Windows has three Explorer icons and Ubuntu has only one Files icon  Is it possible to uncombine/ungroup apps in Ubuntu? Best way to find a point on a circle closest to a given point Given a point (pX, pY) and a circle with a known center (cX,cY) and radius (r), what is the shortest amount of code you can come up with to find the point on the circle closest to (pX, pY) ?  I've got some code kind of working but it involves converting the circle to an equation of the form (x - cX)^2 + (y - cY)^2 = r^2 (where r is radius) and using the equation of the line from point (pX, pY) to (cX, cY) to create a quadratic equation to be solved.  Once I iron out the bugs it'll do, but it seems such an inelegant solution. "They are quite full up this year." How to get the ASCII value of a character After I deleted my Ubuntu partition, I rebooted my computer and I only get a prompt:   grub rescue &gt;   The command ls lists   (hd0) (hd0,msdos5) (hd0,msdos3) (hd0,msdos2) (hd0,msdos1) (hd1) (hd1,msdos1)   I check them one by one:  ls (hd0,msdos5)/ ls (hd0,msdos1)/   But I cannot find the right partition. I am trying to understand the sentence  the mean minimizes the mean squared error.   from wikipedia .  From a previous post  I can see a formal proof which according to the authors prove that the mean minimaze. But my objection on that prove is that is you substitute m with median all the reasoning still stands.  Therefore, I restricted myself to one dimension and built the following example :   MSE = 1/n[SUM(Y_hat_i - Y_i)**2]   Given the following distribution Y = [5,3,2,7,4], minimizing MSE I intended as in the following: I should find a function Y_hat such that when it is applied to the MSE formula (more specifically to each element of the Y distribution), we are sure that we obtain the minimum value. For simplicity, I could consider the Y_hat as any measure or function for the central tendency, including, mean, median, mode, etc.  Lets suppose, Y_hat = mean (=4.2 for our distribution), therefore, I did all the calculations such as:  1/5 [(4.2-5)**2 + (4.2-3)**2+ (4.2-2)**2 + (4.2-7)**2  + (4.2-4)**2 ] = 2.96   Let's suppose, Y_hat = median (=4 for our distribution), therefore, I did all the calculations such as:  1/5 [(4-5)**2 + (4-3)**2+ (4-2)**2 + (4-7)**2  + (4-4)**2 ] = 2.8   If I did all the calculation correctly, the result shows that for this case, the median is minimizing better than the mean.  I am sure, I am doing something wrong and missing important aspects of the overall reasoning.  Please, could you provide any clarification on the above topic? I would really appreciate it.  Many Thanks in advance, Best Regards, Carlo In chapter 2 section 7 (pg 151) of Hartshorne's algebraic geometry there is an example given that talks about automorphisms of $\mathbb{P}_k^n$. In that example Hartshorne states that $\mathcal{O}(-1)$ has no global sections. However, we know that $\mathcal{O}(1)$ is generated by global sections. This is stated at the first of the section that if $\mathbb{P}_k^n = Proj k[x_0,...,x_n]$ then the $x_0,...,x_n$ give rise to global sections $x_0,...,x_n\in\Gamma(\mathbb{P}_k^n,\mathcal{O}(1))$.  I guess I don't understand this twisted structure sheaf very well, or to be honest I don't think I understand structure sheaves in general as well as I would like. The twisting part seems simple at first- you shift the grading of Proj over and then take the structure sheaf.  Admittedly I don't feel comfortable using the structure sheaf other than using the basic facts about it that Hartshorne gives when it is introduced. If anyone could give some insight as to what's going on here or how I might be able to understand this better it would be much appreciated. Thanks. Explicit vs implicit SQL joins Is there any efficiency difference in an explicit vs implicit inner join? For example:  SELECT * FROM table a INNER JOIN table b ON a.id = b.id;   vs.  SELECT a.*, b.* FROM table a, table b WHERE a.id = b.id; Allow only alphanumeric characters for a UITextField Asynchronous shell exec in PHP Profile tab hyperlink should match name change What's the starting wealth for higher levels? The PHB only gives starting wealth for Level 1 PCs. Based on my experience in other games, specifically Pathfinder, I would expect to get more at higher levels. Where can I find an appropriate table or calculation? Energy-momentum tensor transformation Common lines between two files I updated the chrome to version 61, and the auto-scroll stopped working, it is necessary to scroll down the page manually. The problem does not occur in the previous version or in firefox.  Also, the reply icon no longer working when the message replied to is not in the current chat page. (Middle click still works and opens the link in new tab.) Reverse String order Are the units of the quotient ring $\mathbb{F}_2[x]/\langle x^k+1 \rangle$ known in general, where $\mathbb{F}_2$ is the finite field with two elements? I'm specifically interested in the case where $k$ is divisible by two, such as say $k=8$, or $k=12$.  If so, can they be constructed easily? I'd be grateful if you could provide a few examples.