Plotting phase diagram for the velocity vs position graph. Interpolation as a possible solution?
Plot construction for a velocity vs position graph. Interpolation for phase-diagram construction?
Vote for Tag Synonyms Directly on the Page Before:  After:   The pros:  Speeds up the tag synonym voting process. Easier to locate (as opposed to navigating to each individual tag wiki page). Encourages users to vote on more than one at a time.  The cons:  Serial up/downvoting. But this really isn't even an issue because, (1) only experienced users can vote on tag synonyms, and (2) more than one vote is required to approve a tag synonym, so the occasional serial up/downvoter won't significantly impact the overall process. Disable the guest user completely in El Capitan without having to disable 'Find My Mac' I know it should be straight forward but unfortunately, it  isn't.  I did disable the guest user in the System Preferences by unchecking the checkbox for Allow guests to login in to this computer, but it still shows up on the login screen.  I have heard that disabling 'Find My Mac' would fix it for OS X Lion, but I want to keep it.  Is there a way to do this? What I am working with: I am running my self-made Arduino board (in the sense that I use the Arduino bootloader and code editor) at 3.3V, and powered from a Lithium ion battery, which is USB-charged by a corresponding Microchip charger IC.  What I am trying to achieve: I want to measure battery capacity once every minute or so. I have an LCD attached, so the idea is that the overall setup lets me know how the battery is doing at a given moment. The datasheet of the battery has a voltage versus discharge-level curve, and so by measuring the voltage of the battery, I can estimate the remaining capacity (very roughly but enough for me!).  What I did:   (EDIT: Resistor values updated and P-MOSFET switch added based on @stevenvh and @Jonny's suggestions).  I connected a voltage divider from the battery V_plus, with the larger "portion" going to an analog-read-pin (i.e., ADC) on the Arduino/Atmega chip. The divider is 33 KOhm-to-10 KOhm, thus allowing measurement up to 4.1 Volts maximum of the Li-ion battery from my 3.3V level microcontroller. Also, using one of the I/O pins connected to an n-channel MOSFET, I can switch the current through the divider only when I need the measurement. Here is a rough schematic (updated for a 2nd time based on suggestions of @stevenvh and @Nick):     My question:   How is my current setup? My only constraints are: (1) I would like to make a rough measurement of the battery capacity based on the voltage reading, as described above. (2) I would like to prevent the voltage divider from interfering with my charging IC's reading of battery presence (in my original setup, the divider sometimes caused the IC to misread presence even when the battery was absent). 50 hertz sine wave in oscilloscope when I touch it I bought a new PicoScope USB oscilloscope and noticed that when I touch the tip of the probe with my hand I see a 50&nbsp;Hz signal of 2 volts on the screen. What is causing this? (Or rather, how is the mains 50 Hz sine wave getting through me to the scope?) Finding the maximum likelihood estimator (Theoretical statistics) Let $X_1, X_2, ..X_n$ represent a random sample from this pdf:  $$f(x|\theta)= \frac{3x^2}{\theta^3}, 0\leq x\leq \theta$$ (with 0 elsewhere)  Could someone explain how I would find the maximum likelihood estimator (MLE) of this pdf? I know I have to get the likelihood function L, then the log likelihood function, then differentiate, but I am getting lost in the calculations. Thanks! I am currently thinking about open-sourcing a project of mine and am in the process of preparing the source code and project structure to be released to the public. Now I got one question: how should I handle the signature key for my assemblies? Should I create a new key for the open-source version and publish it along with the other files to the SVN repository? Should I leave the key out and everyone who wants to compile the code should generate his own key?  How do you handle this? I feel a little bit uncomfortable with releasing a signature key to the public. Which set is unwell-orderable? In textbook it says that every well-orderable set is equipotent to an initial ordinal number. However, of course unwell-orderable cannot equipotent to any ordinal number, but is there any set is unwell-orderable? By axiom of regularity we know that every set is well-founded, so can we conclude that every set is well-orderable? If not, which set is unwell-orderable? Should I use the singular or plural verb in mathematical formulae ("Two and two make/makes four")? Cannot replace a packed image in the uv image editor I was trying to replace an image in my UV image editor, but the image defaults to a different image. how do I fix this? Invoking JavaScript code in an iframe from the parent page Basically, I have an iframe embedded in a page and the iframe has some  routines I need to invoke from the parent page.  Now the opposite is quite simple as you only need to call parent.functionName(), but unfortunately, I need exactly the opposite of that.  Please note that my problem is not changing the source  of the iframe, but invoking a function defined in the iframe. What is the best program for image optimizing for the web? What programs besides Photoshop are good for saving and optimizing images for web? How to input open intervals I want to write open and half-open intervals using the following notation:  ]a, b[ ]a, b] ]-∞, b]   When writing them just like that in the LaTeX source, the spacing doesn't come out right. For example, for this equation:   \(X = ]-\frac{π}{2}, +\frac{π}{2}[\)   the minus sign is typeset as a binary operator. I can solve this by surrounding the whole value in braces, but then the spacing around the equal sign is still not correct. For other combinations of intervals and operators, different spacing inconsistencies arise.  What is the correct and easy  way to input intervals in order to avoid having to take care of this at all? apt: how to be sure that a specific package gets installed/updated from specific repository and not from the default one? Question: If $R$ is a finite boolean ring, then show $R \cong \mathbb Z_2 \times \mathbb Z_2 \times \cdots\times \mathbb Z_2$.   I know that   $\mathrm{char}(R) =2$  $R$ has $2^k$ elements for some $k$  (this is because, if $p\neq 2$ is a prime with $p\mid|R|$, then there exists a non-zero $x \in R$ s.t. $px=0$ and $p $ is odd $\implies x=0$, contradiction).   Does this suffice to answer my question? Moment of inertia of a cylinder about its base I've tried to find the moment of inertia of a cylinder rotating about an axis parallel to its base (i.e about the 'End diameter') as one can see  . But when I checked my results with different references ,I've found that it's incorrect!.I need a help to figure out where I did it wrong. since $$I=\int\limits x^2.dm$$ $$dm = \rho.dv$$ where $$dv= r.d\theta . dr .dh$$ &amp; $$\rho=\frac{M}{\pi R^2 H}$$ $M$:cylinder total mass. $H$:total height of cylinder. $R$:the radius of the cylinder. The distance of each infinitesimal element from the axis of rotation would be : $$\sqrt{r^2+h^2}$$ Therfore, $$I= \frac{2M}{ R^2 H}\int\limits_{0}^{R} \int\limits_{0}^{H}\, r(r^2+h^2)dh\,dr$$ and this gives a result of : $$\frac{M~H^2}{3}+\frac{M~R^2}{2}$$ Which is obviously wrong since the second term should be multiplied by a factor of $1/2$. Computation of a limit involving factorial $\lim_{n \to \infty} \sqrt[n+1] {(n+1)!} - \sqrt[n] {(n)!} = \frac{1}{e}$ When a star becomes a black hole, does its gravitational field become stronger? Given a collection of sets $\mathcal{C}$ and $E$ an element in the $\sigma$-algebra generated by $\mathcal{C}$, how do I show that $\exists$ a countable subcollection $\mathcal{C_0} \subset \mathcal{C}$ such that $E$ is an element of the $\sigma$-algebra, $\mathcal{A}$ generated by $\mathcal{C_0}$?    The hint says to let $H$ be the union of all $\sigma$-algebras generated by countable subsets of $\mathcal{C}$....although I don't know why. Can we model gravitation as a repulsive force? This question is actually related to my earlier question ("").  The fact that objects move a lot in the universe and that the universe is expanding, can imply that gravity is a repulsive force that increases with distance.. so the farthest objects repel us more.  This can still explain several existing observations, e.g., why does the apple fall?   Motion is the result of such repulsion. Two objects unlucky enough not to be moving relative to each other get squished due to the repulsion of the rest of the universe  around them. The earth repels the apple less than the stars so it is pushed towards the earth.   Furthermore, it can explain the expanding universe without the need for dark energy.  This could be demonstrated in a thought experiment. If we take a lot of same-charge particles (with small mass) such as electrons and lock them in a large box at a low enough temperature. The mutual repulsion of the particles may cause similar motion as if due to gravitational attraction.   Another experiment would be to measure the slight changes in our weight during day and night when the sun and earth align (if their masses are large enough to detect the feeble change in repulsion).   [EDIT: the question in the original form may not have been clear. It is "can we model".. with a yes/no answer and why (not). If downvoting, please justify. What is the name of this kind of character illustration?