What does a buffer do? In the given circuit,it is said that capacitors C1 and C4 act as buffer .What is their role here?Can't we just replace them with pull-down resisrors?
Just wondering if someone can give me an explanation for this capacitor layout - what is it's function? The chip to the right is an ADC.  Circled in blue.    I'm guessing it is well known but i don't know how to search for it.
the verb in plural with one company How can I remove the qed symbols from all lemma proofs? the following code will only make the qed not appear in the second proof. However, it it possible to make the qed symbol never appear at the end of the proofs without having to specify it locally every time?  \documentclass{article} \usepackage{amsthm} \begin{document} \begin{proof} This has the QED symbol. \end{proof} \begin{proof}\renewcommand{\qedsymbol}{} This hasn't. \end{proof} \begin{proof} And this has it again. \end{proof} \end{document} How to get object size in memory? I need to know how much bytes my object consumes in memory (in C#). for example how much my Hashtable, or SortedList, or List&lt;String&gt;. Which offences result in indirect free kicks? If a player commits a direct free kick offence in their own penalty area, this results in a penalty kick instead of a direct free kick. However, if the offence is an indirect free kick offence, it remains as an indirect free kick .  What offences result in an indirect free kick? How do you remove the axis multiplier? The value of $\lim_{n \to \infty}\int_{0}^{1}nx^ne^{x^2}dx$ is _____ I tried by taking the odd $n$ values as in that case, the integral I suppose was easier to calculate. So, denote $I_n=n\int_{0}^{1}e^{x^2}x^ndx$, then we have : $I_1=\frac{e-1}{2},\\I_3=\frac{3}{2},\\I_5=5(\frac{e}{2}-1),\\I_7=7(3-e)$ Then I tried calculating (random) values using calculator as integration was getting cumbersome. $I_{31}=2.488$, $I_{51}=2.57$. I do not see any kind of recurrence so that I can find a general term for odd $n$. I also tried the method given . The idea was that since integral doesn't depend on $n$ considering $I(n)=\int_{0}^{1}e^{x^2}x^ndx$, then $I'(n)=\int_{0}^{1}x^n\ln(x)e^{x^2}dx$, but this also doesn't lead me to any conclusion as well. I believe I couldn't get to a proper approach to tackle this question. Can someone please help with the idea that involves in solving these type of questions? Cannot find Underground Jungle Temple On my 1.2 Terraria Map I have been mining from left to right in my large underground jungle using my rocket launcher. Despite this, I have had no luck on finding the Underground Jungle Lihzahrd Temple. I have been searching the layer above where lava constantly spawns. Have I simply spawned in a world without one or am I searching in the wrong place? I have also considered using the clentimator with Dark Blue ammo to provide light, should I do that? How to make a declaration from a command? There are two forms of setting the type style: the declarative method e.g, \itshape and the command form, e.g, \textit. The command form takes an argument whereas the declarative form does not --- it just applies itself to whatever comes afterwards.  I would like to develop a declarative form, say \UppercaseIt, of the command form \MakeUppercase{&lt;text&gt;}. I have read, in source2e.pdf on CTAN the code for implementing \textit, \itshape and \MakeUppercase and can't claim that I understand any of them. I am after something like {\UppercaseIt some text} instead of \MakeUppercase{some text}.  I only have a code outline of what I'm after, since I don't know how to do it:  \documentclass{article}  \newcommand{\UppercaseIt}{%   %... magic }  \begin{document}  \MakeUppercase{some text}% Yields SOME TEXT  {\UppercaseIt some text}% Should yield SOME TEXT  \end{document} If we have two circles in the plane described by $(x_1, y_1, r_1)$ and $(x_2, y_2, r_2)$ we can determine if they are completely disjoint by simply:  $$(x_1 - x_2)^2 + (y_1 - y_2)^2 &lt; (r_1 + r_2)^2$$  Assume this is not the case, we now want to know if one completely overlaps the other.  (That is: if the second circles interior is a subset of the first circles interior.)  If $(x_1, y_1) = (x_2, y_2)$ than we can trivially compare radii, so lets assume their centers are distinct.  The way I have imagined is to create a parametric equation of the line that connects the two centers:  \begin{align} x_p(t) &amp;= x_1 + t(x_2 - x_1) \\ y_p(t) &amp;= y_1 + t(y_2 - y_1) \end{align}  Then we calculate the two line segments (represented as two pairs of t values) where the circles intersect this line.  One is a subset of the other if and only if the corresponding circles are subsets of each other.  Is there a simpler approach I am overlooking? Is it costly to do array.length or list.count in a loop I know that in JavaScript, creating a for loop like this: for(int i = 0; i &lt; arr.length; i++) is costly as it computes the array length each time. Is this behavior costly in c# for lists and arrays as well. Or at compile-time is it optimized?  Also what about other languages such as Java, how is this handled? Identical coefficients estimated in Poisson vs Quasi-Poisson model I'm studying for an abstract algebra exam and one of the review questions was this:     Let $X$ be a set, and $\mathcal P(X)$ be the power set of $X$. Consider the operations $\Delta$ = symmetric difference (a.k.a. "XOR"), and $\bigcap$ = intersection.   a) Does $\Delta$ and $\bigcap$ make $P(X)$ into a ring?   b) If so, is it a ring with unity?   c) Is the ring commutative?   d) Is it a field?   For parts a) and b), I think it does form a ring with unity, but I'm not quite sure how to get started on proving it.   For part c), it is a commutative ring since $\mathcal P(X)$ is closed under symmetric difference and intersection, right?  Not even sure how to get started on d).  I'd really like to understand this question fully, so any kind of input would be tremendously helpful. Thank you! Export each image from a collection in Google Earth Engine I am trying to export each image in a filtered stack of Sentinel-1 images and cannot seem to get it right.   suggests using imageCollection.map() and a custom function (such as a geometric clip).  // Create a geometry representing an export region. var roi = ee.Geometry.Rectangle([-63.0, 9.2, -63.1, 9.3]);   // Load the Sentinel-1 ImageCollection. var sentinel1 = ee.ImageCollection('COPERNICUS/S1_GRD');   // Filter by metadata properties. var IW_H = sentinel1   // Filter to get images with VV and VH dual polarization.   .filter(ee.Filter.listContains('transmitterReceiverPolarisation', 'VV'))   .filter(ee.Filter.listContains('transmitterReceiverPolarisation', 'VH'))   // Filter to get images collected in interferometric wide swath mode.   .filter(ee.Filter.eq('instrumentMode', 'IW'))   // Filter IWs to get High res.   .filter(ee.Filter.eq('resolution', 'H'))   // Filter IW-Highs to get 10m res   .filter(ee.Filter.eq('resolution_meters', 10));   // Filter to get images from different look angles  var DescCollection = IW_H.filter(ee.Filter.eq('orbitProperties_pass', 'DESCENDING'));   var ClipFunc = function(iImage, geom) {   var iClip = clip(iImage, geom);   return(iClip); };   imageCollection.map(ClipFunc(DescCollection, roi)); I'm having some trouble understanding the purpose of a salt to a password.  It's my understanding that the primary use is to hamper a rainbow table attack.  However, the methods I've seen to implement this don't seem to really make the problem harder.  I've seen many tutorials suggesting that the salt be used as the following:  $hash =  md5($salt.$password)   The reasoning being that the hash now maps not to the original password, but a combination of the password and the salt.  But say $salt=foo and $password=bar and $hash=3858f62230ac3c915f300c664312c63f.  Now somebody with a rainbow table could reverse the hash and come up with the input "foobar".  They could then try all combinations of passwords (f, fo, foo, ... oobar, obar, bar, ar, ar).  It might take a few more milliseconds to get the password, but not much else.  The other use I've seen is on my linux system.  In the /etc/shadow the hashed passwords are actually stored with the salt.  For example, a salt of "foo" and password of "bar" would hash to this: $1$foo$te5SBM.7C25fFDu6bIRbX1.  If a hacker somehow were able to get his hands on this file, I don't see what purpose the salt serves, since the reverse hash of te5SBM.7C25fFDu6bIRbX is known to contain "foo".  Thanks for any light anybody can shed on this.  EDIT:  Thanks for the help.  To summarize what I understand, the salt makes the hashed password more complex, thus making it much less likely to exist in a precomputed rainbow table.  What I misunderstood before was that I was assuming a rainbow table existed for ALL hashes. Run TTY script every time I open a GUI terminal When I log in to a TTY I get the following nice text:  Ubuntu 16.04.03 LTS Log-in: username Password: Last log-in date/time Welcome to Ubuntu 16.04.03 LTS   * Documentation:  * Management:  * Support:  9 packages to update 4 updates are security updates   I would like the last 2 lines repeated every time I open a GUI terminal for all users in the adm group (but will settle for having the entire thing displayed each and every time I open a GUI Terminal for all users)  I tried the obvious:  fab-root@fab-ux-predator:~ $ cd /etc/update-motd.d/ fab-root@fab-ux-predator:/etc/update-motd.d $ ./90-updates-available  fab-root@fab-ux-predator:/etc/update-motd.d $ cat /var/lib/update-notifier/updates-available cat: /var/lib/update-notifier/updates-available: Permission denied fab-root@fab-ux-predator:/etc/update-motd.d $   What am I missing?  P.S. Obviously I can chmod o+r the file, but how future-proof would that be? Implementing a PIVOT query How can I pivot the following SELECT statement:           SELECT sc.CID,                 sc.CodeName     as OverviewText,                 scRAG.CodeName  as RAGStatusText             FROM StatusCode      sc LEFT OUTER JOIN ProjectOverview po               ON sc.CID          = po.ProjectOverviewCID              AND po.ProjectId    = 180 LEFT OUTER JOIN StatusCode      scRAG               ON po.RAGStatusCID = scRAG.CID           WHERE sc.SCID         = 18   Such statement yields the result set that follows:  CID OverviewText    RAGStatusText --- ------------    ------------- 153 Cost            Green 154 Requirements    Yellow 155 Schedule        NULL 156 Technical       NULL 157 Testing         NULL   But, I want it to return one single row with 10 values, as shown bellow:   ----------------------------------------------------------------------------------------------  | Cost | Green | Requirements | Yellow | Schedule | NULL | Technical | NULL | Testing | NULL |  ----------------------------------------------------------------------------------------------   Can I pivot on CID? We have a few cases of chat accounts remaining without valid parent account:  and  for example. What should mods do when that happens:  delete the chat account notify the SE team so they can reattach or clean it up leave it as is: it's a normal situation Possible Duplicate:          I'm working on a website that displays distance to various locations to the nearest 1/10 mile. One of the developers (a non-native speaker) asked me an interesting question: If the distance is 1.0 mile(s), is that singular or plural? Clearly, anything other that 1.0 is plural, but is it:     1.0 miles away   or     1.0 mile away   The first option sounds more correct to my ear, but the voice of my elementary school language arts tells me that the latter option is correct.  Edit: Added the word 'away' to the example. It doesn't change the question, but might provide clarity for the answer. Also, regarding numbers between 0 and 1, after more thought, I'm not sure that the answer is as clear as I originally thought. See . Correlations with unordered categorical variables I have a dataframe with many observations and many variables. Some of them are categorical (unordered) and the others are numerical.  I'm looking for associations between these variables. I've been able to compute correlation for numerical variables (Spearman's correlation) but :   I don't know how to measure correlation between unordered categorical variables. I don't know how to measure correlation between unordered categorical variables and numerical variables.   Does anyone know how this could be done? If so, are there R functions implementing these methods? Identifying a quotient group (NBHM-$2014$) Let $\mathbb C^*$ denote the multiplicative group of non-zero complex numbers and let $P$ denote the subgroup of positive real numbers. Identify the quotient group.    My thought $$\frac{\mathbb C^*}{P}=\{P,-P,iP,-iP\}.$$ Is it right?