Earning reputation by downvoting? I found a way to earn reputation by downvoting. Specifically: If I downvote a post, then wait a while, then un-downvote the post, my net reputation count increases by 1.   Here's why it's happening. Two days ago, I posted an answer to  question on math.SE. It became a "hot" network question and I quickly reached my daily reputation limit. Thus, the question kept getting upvoted, but I wasn't earning reputation for it (as it should be).   Today, I once again reached my daily reputation limit. After reaching this limit, I downvoted a post on math.SE. So, my daily earned reputation was effectively 199. The next time somebody upvoted my question, I gained +1 reputation. But then, I retracted the downvote. To my surprise, I gained another +1 reputation.   Here is the data on the reputation I gained today:    Usually, I would have earned 215 in total: 200 reputation from upvotes and 15 from one accepted answer. But instead I earned 216 because I gained the extra +1 from retracting the downvote after already being "reimbursed".  Obviously, this trick isn't widely applicable. A user has to already have reached their reputation cap. And due to the limit of 40 votes per day, they would only be able to use this trick to earn a maximum of 40 bonus reputation points per day. I realize I'm not the first to point out inconsistencies in the voting system (see , , ). But as far as I can tell, this is the first instance where it is possible for a user to reliably game the system to earn 40 reputation per day without making any contributions.   Is this a bug? Should it be addressed?
Down vote changed to up vote caused reputation meter to pass daily maximum I just experienced a minor visual bug.  I had an answer that earned 2 down votes and 22+ upvotes, earning me the daily maximum of +200. Upon making some edits to the answer at the behest of the comments, one of the users who down voted changed their vote. Now my reputation meter shows that I gained +202 for the day.    This correctly did NOT affect my reputation, as I still only gained 200, so it is merely a minor display bug.  This appears in the achievements drop down and my reputation tab on my profile.
continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$ Let $g$ be a function on $\mathbb R$ to $\mathbb R$ which is not identically zero and which satisfies the equation $g(x+y)=g(x)g(y)$ for $x$,$y$ in $\mathbb R$.   $g(0)=1$. If $a=g(1)$,then $a&gt;0$ and $g(r)&gt;a^r$ for all $r$ in $\mathbb Q$.   Show that the function is strictly increasing if $g(1)$ is greater than $1$, constant if $g(1)$ is equal to $1$ or strictly decreasing if $g(1)$ is between zero and one, when $g$ is continuous. I have a very simple jQuery Datepicker calendar:  $(document).ready(function(){     $("#date_pretty").datepicker({      }); });   and of course in the HTML...  &lt;input type="text" size="10" value="" id="date_pretty"/&gt;   Today's date is nicely highlighted for the user when they bring up the calendar, but how do I get jQuery to pre-populate the textbox itself with today's date on page load, without the user doing anything?  99% of the time, the today's date default will be what they want. Are there perfect elastic collisions in Nature? How do I remove a property from a JavaScript object? In sampling without replacement the probability of any fixed element in the population to be included in a random sample of size $r$ is $\frac{r}{n}$. In sampling with replacement the corresponding probability is $\left[1- \left(\frac{1}{1-n}\right)^r\right]$.  Please help me show how this is proved. I read some articles, and seen some videos about a github project that do a sort of thing, but it's a little bit outdated things.I wanna see if this thing is possible to do, nowadays. Thanks Get steam to realize I have games already installed I uninstalled and re-installed steam. I didn't uninstall my games, and they still exist on my hard drive (I checked).  I have an SSD and a HDD, and to save space I install programs (including steam) to C:\Program Files (x86)\Steam drive (SSD) and games to D:\Games\SteamApps (HDD). How to I let steam know the programs are installed there? SQL Servers has Traces and XEvents. These are used to capture and analyze what is going on with our SQL Server Instances. Events are stored in the stack for later analysis. For example,  If I decide to monitor any dead lock in the database, I just query the trace file to see the history of deadlock for a period of time. Here is my question:  While events occur, in our example deadlock event, is there a way to get an email notification using msdb.dbo.xp_send_dbmail? Show that $\arctan\frac{1}{2}+\arctan\frac{1}{3}=\frac{\pi}{4}$ Show that $\arctan\frac{1}{2}+\arctan\frac{1}{3}=\frac{\pi}{4}$.   Attempt:  I've tried proving it but it's not equating to $\frac{\pi}{4}$. Please someone should help try to prove it. Is anything wrong with the equation? If there is, please let me know. The arithmetic - geometric mean inequality states that $$\frac{x_1+ \ldots + x_n}{n} \geq \sqrt[n]{x_1 \cdots x_n}$$ I'm looking for some original proofs of this inequality. I can find the usual proofs on the internet but I was wondering if someone knew a proof that is unexpected in some way. e.g. can you link the theorem to some famous theorem, can you find a non-trivial geometric proof (I can find some of those), proofs that use theory that doesn't link to this inequality at first sight (e.g. differential equations …)?  Induction, backward induction, use of Jensen inequality, swapping terms, use of Lagrange multiplier, proof using thermodynamics (yeah, I know, it's rather some physical argument that this theorem might be true, not really a proof), convexity, … are some of the proofs I know. Why does HTML require that multiple spaces show up as a single space in the browser? I have long recognized that any set of whitespace in an HTML file will only be displayed as a single space.  For instance, this:  &lt;p&gt;Hello.        Hello. Hello. Hello.                       Hello.&lt;/p&gt;   displays as:  Hello.        Hello. Hello. Hello.                       Hello.  This is perfectly fine, as if you need multiple spaces of pre-formatted text you can just use the &lt;pre&gt; tag.  But what is the reason?  More precisely, why is this in the specification for HTML? If $l$ and $n$ are any positive integers, is there a  proof of the identity     $$\sum_{k=0}^{n}(-1)^{k}\binom{n}{k}(l-k)^n=n!\;$$   which uses the Inclusion-Exclusion Principle?  (If necessary, restrict to the case where $l\ge n$.)    This question is closely related to   and also Integral of $ 1 \, / \, (1 + a \, \cos(x) )$ Donating winning lottery ticket to 501(c)3 Private Foundation: cost-basis deduction + full tax free redemption for foundation? US 501(c)3 Private Foundations are typically controlled by the primary donator, so that is a nice perk, but in exchange for that perk I realize the tax deductions for donating are significantly lowered than for charities. Aside from being lower, the tax code doesn't recognize appreciated property and only allows for a deduction based on the donating taxpayer's cost-basis: ie. the price they paid for the property no matter its current market value.  When there is a significant delta of price paid vs current redeemable value, it seems this can still be a perk for the donating taxpayer in some circumstances, such as with lottery tickets that are known winners already.  If the donating taxpayer pays $1 for the ticket. Their cost basis is $1. If the ticket is now worth $100,000,000 but has not been redeemed, is it accurate that the donating taxpayer can donate this to their private foundation for a deduction at cost basis, and the private foundation can redeem the $100,000,000 ticket completely exempt from all lottery withholding income taxes?   (Other taxes unique to private foundations are known and outside the scope of this question.)  Most literature I can find is about appreciated marketable securities, and occasionally real estate. It doesn't seem that the tax code specifies any distinction between property, but it also doesn't seem the answer to this question is part of the general collective conscious even if it really is that obvious if my understanding is already correct. Can't redirect cut output I recently upgraded to 12.04 from 11.10 and since upgrading have been unable to log in to my user profile. The upgrade went okay and I can login to a guest session fine but whenever I try to login to my profile, after entering my password, I just return to the login screen.  I've changed my password in Root (passwd &lt;username&gt;) and can log in to tty1 with no issues, it's just in GUI I'm having problems.  I'm using a HP dv7 laptop, 32-bit Ubuntu install, Intel® Core™2 Duo CPU P7350 @ 2.00GHz × 2, Nvidia graphics.  Any help would be appreciated. I was naively validating my binomial logit models by testing on a test dataset. I had randomly divided the available data (~2000 rows) into training (~1500) and validation (~500) datasets.   I now read a post in another thread ( Frank Harrell) that causes me to question my approach:     Data splitting is not very reliable unless you have more than 15,000   observations. In other words, if you split the data again, accuracy   indexes will vary too much from what you obtained with the first   split.   How serious is this worry and what are ways around it? The OP speaks of "resampling" but not sure how that works here for validation.   Edit: Adding context as per @Bernhard's comment below: Show that $\frac{X-\mu}{\sigma}\sim N(0,1)$ using moment functions Let $X\sim N(\mu,\sigma^2)$. Show that $Z=\frac{X-\mu}{\sigma}\sim N(0,1)$ using moment generating functions. \begin{align*} M_Z(t)&amp;=M_{\frac{X-\mu}{\sigma}}(t)\\ &amp;=M_{X-\mu}\left(\frac t\sigma\right)\\ &amp;=e^{-\mu t}M_X\left(\frac t\sigma\right)\\ &amp;=e^{-\mu t}\cdot e^{\frac{t\mu}{\sigma}+\frac{t^2}{2}}\\ &amp;=e^{-\mu t+\frac{t\mu}{\sigma}+\frac{t^2}{2}} \end{align*} I'm not sure how to conclude that $Z\sim N(0,1)$. How do we initialise unpacked arrays in Verilog? Suppose I declare an unpacked array of size say 8 bits wide. reg b[7:0];  If I want to assign b[7] = 1,b[6] = 1, b[5] = 1, ......b[0] = 1, then apart from assigning value to each bit is there a way to assign any combination of bits say 8'bA8, to b? For instance if I execute this code(below) in verilog: module tb();     reg [7:0]a;     reg b[7:0];     initial begin         $monitor(&quot;a = %b,b = &quot;,a);         a = 8'hA8;         b = 8'hA8; // Line 7     end endmodule  I get this error: C:\iverilog\bin&gt;iverilog -o a test.v test.v:7: error: Cannot assign to array b. Did you forget a word index? 1 error(s) during elaboration.  I am using Icarus Verilog on a command prompt on Windows 10 operating system. Minkowski Metric Signature When I learned about the Minkowski Space and it's coordinates, it was explained such that the metric turns out to be $$ ds^{2} = -(c^{2}dx^{0})^{2} +(dx^{1})^{2} + (dx^{2})^{2} + (dx^{3})^{2}   $$ where $ x^0,x^1,x^2,x^3 $ come from $ x^{\mu} : \mu = 0,1,2,3 $, and $ c $ is the speed of light. The first resource I had access to--I have to do a bit of digging for the exact paper--of course addressed that this invariant takes the tensor form: $$ ds^2 = g_{\mu \nu}dx^{\mu}dx^{\nu} $$ as well. This two things I've seen in all of my texts and online resources regarding resources. The element in question that varies between authors, is the time coordinate, $ x^0 $. When it was first explained to me, it was using the standard Cartesian representation for the spatial portion of the coordinates, and the time coordinate was labeled as $ x^0 = ict $. Squaring gives $ (x^0)^2 = -c^2t^2 $, and applying differential calculus, we get $ (dx^0)^2 = -c^2dt^2 $. Sensible and expected to have the tensor formula spit out the Minkowski Metric. The author then later explicitly states the coordinates are $ x^0 = ict, x^1=x,x^2=y,$ and $x^3 = z$.  My questions is then, why is it most authors on the subject omit the imaginary unit on the time coordinate? For example, .   The only reason I can fathom omission is if the author is using metric signature $ [+,-,-,-] $, where I started off learning the theory with signature $ [-,+,+,+] $ which may be the reason seeing the time coord with no imaginary unit seems dissonant to me. All help appreciated!  Edit: After reading the other answers, my questions is now one of why and how (mathematically) do we obtain the Minkowski Metric Signature. More specifically the one element with a different sign.