Is there a way of measuring components in circuit?
How to measure the component value on a PCB?
Why is foo.hasOwnProperty('__proto__') equal to false? I have 2 ADS1299 analog to digital converters(). I need to give them bipolar mode supplying but I must use a powerbank of 5V 3A. I wonder how can I create a bipolar supply of +2.5v -2.5v as mention in the datasheet from the 5V of the powerbank. I am new in this field. Thank you Paris has 3 airports (Orly, Roissy, Beauvais), what are the options to go to or to come from there?  (There is also Vatry (XCR) but there is very few flights and i see the shuttle system is currently off.) Mail vs. mail what is the difference Does mathematics become circular at the bottom? What is at the bottom of mathematics? I am trying to understand what mathematics is really built up of. I thought mathematical logic was the foundation of everything. But from reading a book in mathematical logic, they use "="(equals-sign), functions and relations.  Now is the "=" taken as undefined? I have seen it been defined in terms of the identity relation.  But in order to talk about functions and relations you need set theory.  However,  seems to be a part of mathematical logic.  Does this mean that (naive) set theory comes before sentential and predicate logic? Is (naive)set-theory at the absolute bottom, where we can define relations and functions and the eqality relation. And then comes sentential logic, and then predicate logic?  I am a little confused because when I took an introductory course, we had a little logic before set-theory. But now I see in another book on introduction to proofs that set-theory is in a chapter before logic. So what is at the bottom/start of mathematics, logic or set theory?, or is it circular at the bottom?  Can this be how it is at the bottom?  naive set-theory $\rightarrow$ sentential logic $\rightarrow $ predicate logic $\rightarrow$ axiomatic set-theory(ZFC) $\rightarrow$ mathematics  (But the problem with this explanation is that it seems that some naive-set theory proofs use logic...)  (The arrows are of course not "logical" arrows.)  simple explanation of the problem:  a book on logic uses at the start: functions, relations, sets, ordered pairs, "="  a book on set theory uses at the start: logical deductions like this: "$B \subseteq A$", means every element in B is in A, so if $C \subseteq B, B \subseteq A$, a proof can be "since every element in C is in B, and every element in B is in A, every element of C is in A: $C \subseteq A$". But this is first order logic? ($(c \rightarrow b \wedge b \rightarrow a)\rightarrow (c\rightarrow a)$).  Hence, both started from each other? Since it seems to me, that a lot of people still need sidebar workarounds, I would be interested to learn about the use-cases, experienced challenges and (most important) possible strategies to avoid them by using different approaches. This is related to the methods discussed here:   In my experience there are a few extremely important and constantly repeating patterns, which to my knowledge are still very hard to be solved using more official techniques. I will also contribute my own top-N use-cases, which are mostly related to UX and UI concerns. You are very welcome to add your own scenarios as answers and add comments on how you would avoid a workaround. My dream would be to team-elaborate strong and repeatable solution-patterns for the most common use-cases.  Finally I would be interested in the experiences of all of you who participate in the Aura pilot, which hopefully could make this kind of workarounds obsolete. $\operatorname{Aut}(V)$ is isomorphic to $S_3$ I'm currently working my way through Harvard's online abstract algebra lectures (if you're interested, you can find them ).  The lectures come complete with notes and homework problems.  Of course, since I don't actually go to Harvard, I can't hand in the homework assignments to find out if I'm doing them correctly.  So I've decided to try to crowd source the grading of my solutions.  I'll post individual questions as I finish them and wait for comments.  I would like to get critiques of not just my reasoning but the style of my write ups as well.  Also, any alternative approaches to the problem would be welcome.  I've looked for forums dedicated to these kinds of OCW courses but have not been able to find any.  This surprises me.  It seems like, with the advent of these free online educational resources, an online meeting place for those who take advantage of them would be a natural offshoot.  So this might be a bit of an experiment.  Unless I'm the 873rd person to post something like this here.  If that's the case, sorry for being so long winded.  Anyway, on with the question.  This one is assigned in the 4th lecture.     Let $V$ denote the Klein 4-group.  Show that $\operatorname{Aut}(V)$ is isomorphic to $S_3$.   (I've moved my solution below to keep this question from showing up in the unanswered list.)  Thanks... Suppose a book consists of three sections:     The book is/was divided into three sections.   I am thinking the past tense option "was" should be used, because the act of dividing the book into three sections happened at the time of writing. Is my analysis good? Let $T,S$ be linear transformations, $T:\mathbb R^4 \rightarrow \mathbb R^4$, such that $T^3+3T^2=4I, S=T^4+3T^3-4I$. Then S is:   one-one but not onto onto but not one one invertible non-invertible   (One or more correct options)  My attempt: $S=T^4+3T^3-4I=T(T^3+3T^2)-4I=T(4I)-4I=4T-4I$  How do I go about proving or disproving my options?   My thoughts on options # 1. and 2.: I'm guessing $S$ is one-one if $Ker(S)=\theta$ is one way to go, but how do I obtain the kernel when I don't know what the transformation is? $Ker(S)=\theta$ if $T=I$, which does satisfy $T^3+3T^2=4I$. But so can other $T$s.   My thoughts on options # 3. and 4.: $S$ is invertible if $det(S)\neq0$, which is possible $det(T-I)\neq0$, i.e. $T\neq I$. How do I show that?  Please help! Since a while, 2 weeks, Dropbox does not startup anymore on my laptop running Ubuntu 12.04 LTS with GNOME shell.  When I run dropbox start -i in the console I get the following output.    Starting Dropbox...Traceback (most recent call last):   File "/usr/bin/dropbox", line 1387, in &lt;module&gt;     ret = main(sys.argv)   File "/usr/bin/dropbox", line 1376, in main     result = commands[argv[i]](argv[i+1:])   File "/usr/bin/dropbox", line 1247, in start     if not start_dropbox():   File "/usr/bin/dropbox", line 731, in start_dropbox     stderr=sys.stderr, stdout=f, close_fds=True)   File "/usr/lib/python2.7/subprocess.py", line 679, in __init__     errread, errwrite)   File "/usr/lib/python2.7/subprocess.py", line 1249, in _execute_child     raise child_exception   OSError: [Errno 8] Exec format error   I already removed Dropbox and reinstalled it. What should I do to fix this? The proof of shrinking coefficients using ridge regression through "spectral decomposition" I have understood how ridge regression shrinks coefficients towards zero geometrically. Moreover I know how to prove that in the special "Orthonormal Case," but I am confused how that works in the general case via "Spectral decomposition." NOT IN vs NOT EXISTS How close would you have to be to the merger of two black holes, for the effects of gravitational waves to be detected without instruments? How to auto populate with conditions? Can I force an iPhone user to upgrade an application? An incorrect answer for an integral As the authors pointed out in  (p. 2), the following evaluation which was in Gradshteyn and Ryzhik (sixth edition) is incorrect (and has been removed). $$ ''\int_{0}^{\infty}\frac{1}{\left(1+x^{2}\right)^{3/2}} \frac{1}{\sqrt{1+  \frac{4 x^{2}}{3\left(1+x^{2}\right)^{2}}+\sqrt{1+  \frac{4 x^{2}}{3\left(1+x^{2}\right)^{2}}}}} \mathrm{d}x = \frac{\pi}{2\sqrt{6}}'' \qquad (*) $$ A numerical evaluation gives $0.6663771 \cdots$ on the left hand side and $0.64127491 \cdots $ on the right hand side.  I have not succeeded to correct $(*)$.  Do you have any idea on how to evaluate the above integral? How do I integrate the following? $\int{\frac{(1+x^{2})\mathrm dx}{(1-x^{2})\sqrt{1+x^{4}}}}$ Removing Ubuntu from a dual-boot setup with Windows SQL JOIN - WHERE clause vs. ON clause After reading it, this is not a duplicate of . The answer may be related (or even the same) but the question is different.    What is the difference and what should go in each?  If I understand the theory correctly, the query optimizer should be able to use both interchangeably. I am trying to run a buffer tool as part of script that I will both use as a standalone script and import into ArcToolbox. I'm just wondering, if I use GetParameterAsText for the buffer distance, how do I set the linear units? E.g. I want it preset so they only have to type 300 and the script takes that to be meters? Here is what I have so far:  # Buffer the Thames feature class to create the Flood Risk Area in_features = "Thames" out_feature_class = "Flood_R_A" # Run the Buffer Tool arcpy.Buffer_analysis (in_features, out_feature_class, arcpy.GetParameterAsText(5),    "FULL", "ROUND", "ALL", "")