Which particles could be waves?
Is the wave-particle duality a real duality?
How do TTL NAND gates work? This is supposed to be a simple NAND gate. I understand how the output is 1 if one of the inputs is zero but if both inputs are 1 then the base of Q1 is supposed to be zero. This is what I don't understand. I know that Q2 and Q3 will be in cut off so the base of Q1 is floating. If that is true, how is it zero then?When A and B are open does current flow through Q2  Q3 via R1 to turn on Q1? Checking if date is weekend PHP Is "The empty set is a subset of any set" a convention? How to format a USB flash drive? -Bash command not found appearing every time I start terminal every time I start my terminal, it always says "-bash:  .: command not found" twice.  Does anyone know how I can get rid of that? I'm about to start exploring the world of long exposure shots, using my Canon EOS M. The camera has a standard max exposure time of 30 seconds, but in bulb mode I can keep the shutter open indefinitely (using a wireless remote to control the shutter.)  How long can I leave the shutter open without running the risk of prolonged exposure to light damaging my sensor?  For the purposes of this question assume I'm shooting in summer daylight, so that we can go by the worst case. How do I put big brackets under different parts of an equation so that I can write, e.g., text specific to these parts? For example: f =  x^3 +  2     |___|  |__|        |     |    text 1  text 2 As linguistics student, I have to put more than one thing on a character every now and then. For example, I need to type ā̆. I thought I could simply do that by typing \={\u{a}}, but then the macron is placed above an empty space in front of the character.  How can I solve this? Thanks  P.S. I'm using MiKTeX 2.9, running on Windows 8; in case it might be of use. I'm currently working on building a predictive model for a binary outcome on a dataset with ~300 variables and 800 observations. I've read much on this site about the problems associated with stepwise regression and why not to use it.  I've been reading into LASSO regression and its ability for feature selection and have been successful in implementing it with the use of the "caret" package and "glmnet".   I am able to extract the coefficient of the model with the optimal lambda and alpha from "caret"; however, I'm unfamiliar with how to interpret the coefficients.    Are the LASSO coefficients interpreted in the same method as logistic regression? Would it be appropriate to use the features selected from LASSO in logistic regression?   EDIT  Interpretation of the coefficients, as in the exponentiated coefficients from the LASSO regression as the log odds for a 1 unit change in the coefficient while holding all other coefficients constant. I have installed the developer preview for Yosemite.  Huge mistake. Everything in my workspace is broken.  I don't have any sort of backup image. I was wondering if I could re-download Mavericks and run the installer - would that effectively downgrade me back to Mavericks? How to make an embedded question from "What time is it?" I am trying to display certain features in a shapefile-based layer using QGIS. I have found the subset function in the properties panel, which does exactly what i want, but is too tedious given that I have to manually sift through a large number of features. Is there a quicker way to do this?  I am using both shapefiles and postGIS best,  dietmar Did any Quidditch games ever end by agreement of the Captains? The game can only end when the Snitch has been caught, or by mutual agreement of the two teams' Captains; the latter is very rare, however, as one team would have to lose. (source: HP Wikia on Golden Snitch)   Is there an example from canon of this resolution to the game ever happening? LLC-SCorp to self - actually, does the corp pay payroll taxes? In the USA. Here are the two common scenarios for the self-employed:  A. Joe makes 100,000 over the year. It's paid to him as 1099 payments from his various clients.  Joe pays the many taxes on that.  B. Joe makes 100,000 over the year.  He has an LLC as SCorp (or maybe an SCorp per se).  The clients pay $100,000 to the entity JoeCorp.  JoeCorp pays Joe a certain salary (it might be the whole 100,000, or, it might be (let's say) half of that and the rest is taken as profit distribution, not relevant here).  So, JoeCorp (his LLC) pays Joe say $50,000.  In fact: does JoeCorp have to pay "payroll taxes" on that??  Does it perhaps make a difference if it is an LLC with S-Corp election v. S-Corp?  (I realize there are many questions on here about "1099 v. corp" .... but I've never really understood this and can't seem to google it up.) As i am new to blender i decided to learn by recreating some animations which have some interesting problems, and gain more knowledge about how tv intros are being done, collecting some parody intros to videos. I came across a simple yet troublesome effect , found no answer by googling or getting through tutorials and testing methods on this case led me to nowhere.     I attempted to recreate the animation above, especially  the extending/appearing/drawn white strip with "randomly" placed gaps , strip which travels just above surface , casting shadow.   Tried dynamic paint,( with alpha channel) image sequence texture but although effect was very similar, whole invisible strip was casting shadow being Z transparent, in places where white color haven't reached yet.  I tried bezier curves as well(vector mode) but it appears that taper cant profile part in squary way, or maybe i am missing something here.  Shape keys seem to hard way to go , while keeping whole animation of stripe "unrolling" at constant speed.  I tried as well putting an array of planes on the path but it is completely not what i attempt to achieved.   I will edit post and add some pictures tomorrow. For the Quadratic Form $X^TAX; X\in\mathbb{R}^n, A\in\mathbb{R}^{n \times n}$ (which simplifies to $\Sigma_{i=0}^n\Sigma_{j=0}^nA_{ij}x_ix_j$), I tried to take the derivative wrt. X ($\Delta_X X^TAX$) and ended up with the following:  The $k^{th}$ element of the derivative represented as  $\Delta_{X_k}X^TAX=[\Sigma_{i=1}^n(A_{ik}x_k+A_{ki})x_i] + A_{kk}x_k(1-x_k)$  Does this result look right? Is there an alternative form?  I'm trying to get to the $\mu_0$ of Gaussian Discriminant Analysis by maximizing the log likelihood and I need to take the derivative of a Quadratic form. Either the result I mentioned above is wrong (shouldn't be because I went over my arithmetic several times) or the form I arrived at above is not the terribly useful to my problem (because I'm unable to proceed).  I can give more details about the problem or the steps I put down to arrive at the above result, but I didn't want to clutter to start off. Please let me know if more details are necessary.  Any link to related material is also much appreciated. Suppose I have a function $f$ that is analytic on the unit disk $D = \{ z \in \mathbb{C} : |z| &lt; 1 \}$ that is also continuous up to $\bar{D}$. If $f$ is identically zero on some segment of of the boundary (e.g. $\{ e^{it}, 0 \leq t \leq \pi/2 \}$ ), is it then true that $f$ is identically zero on the entire boundary?   I know that analytic functions that are zero at an accumulation point inside the domain of analyticity are identically zero throughout the entire domain, but I don't know what (if anything) can be said if something similar occurs on the boundary of the domain. Proving Pascal's identity So I came across Pascal's identity: Prove that for any fixed $r\geq 1$, and all $n\geq r$, $$ \binom{n+1}{r}=\binom{n}{r}+\binom{n}{r-1}. $$  I know you can use basic algebra or even an inductive proof to prove this identity, but that seems really cumbersome. I was wondering if anyone had a "cleaner" or more elegant way of proving it. For example, I think the following would be a decent combinatorial proof.   Proof: Let $S$ be a set with $n+1$ elements, and consider some fixed $x\in S$. There are $\binom{n+1}{r}\;\; r$-subsets of $S$--count them according to whether or not they contain $x$: there are $\binom{n}{r}$ not containing $x$, (each formed by choosing $r$ of the remaining $n$ elements in $S\setminus\{x\}$), and there are $\binom{n}{r-1}\;\; r$-sets containing $x$, (each formed by selecting an additional $r-1$ elements in $S\setminus\{x\}$).   Is that right? Are there any other efficient ways of doing it? I have a rather long footnote which breaks a listing in two parts, unnecessarily.  Since the listing is more important then the footnote I'd rather lake to have the footnote split.   Can I customize (one or all) footnotes to have a maximal length before they are continued on the next page? Or can I manually split a footnote in two to get the effect? Differences between LuaTeX, ConTeXt and XeTeX