I have to write a post for my college website and it is the format of a "listicle". An introduction followed by short paragraphs with each paragraph getting a heading. My question is regarding these headings and the article title.  I am doing research on the listicle format and I see most have titles where every word is in the capital case. Even are headlines through the articles are given the same treatment.  For example,   20 Crushes Who Made Your Heart Soar In 2018 Who Said It: Harry, Ron, Or Hermione? Choose Your Dream Wedding And We'll Reveal How You'll Meet Your Soulmate Eat A Ton Of Food At A Buffet And We'll Tell You Which Disney Channel Star You Actually Are   Why is this done and more importantly is this correct?
Are there any concrete rules that say which words (parts of speech) in a title should start with a capital letter? What would be a correct capitalization for the title of this question?
Can a matrix have a null space that is equal to its column space? I had a question in a recent assignment that asked if a $3\times 3$ matrix could have a null space equal to its column space... clearly no, by the rank+nullity theorem... but I have a hard time wrapping my head around the concept of such a matrix, no matter what size, even existing. How could this be possible, and does anybody have an example of such a $m\times n$ matrix? Drop shadow for text in PGF/Beamer I want to really put an emphasis on some central piece of text I'm using in a Beamer slide.  I'm using tikz and overlay to put it, enlarged, on the center of the page, using the following code:  \begin{tikzpicture}[remember picture,overlay]   \node[at=(current page.center)] {     \scalebox{2}{\Huge\texttt{{This is important!}}}   }; \end{tikzpicture}   Can I add a drop shadow to the letter themselves, so they would look even more emphasized?  Is there some other decoration that can be added to the text itself, like a glow, etc.?  Or does PGF ignores node text altogether?  The text should be in typewriter style, so using special fancy fonts is probably not the solution. Dark matter and dark energy references I've been looking for questions about dark matter, and I've read some very interesting answers. However, I desire too look into it deeply.   This is not actually a question. I'm asking the community to recommend interesting references to understanding dark matter and dark energy.   I accept all sort of references: notes, books, scientific papers etc.  Let us assume some background on classical physics, thermodynamics and basics about quantum theory. Error propagation with asymmetric uncertainties I red the Wikipedia  on error propagation. I get into some trouble when I want to calculate the error propagation in a specific case. I have real numbers $A$ and $B$ with related upper ($\Delta A_u$, $\Delta B_u$) and lower ($\Delta A_l$, $\Delta B_l$) uncertainties. I have two functions calculated as follows: $$F = \sqrt{A^2+B^2}$$ and  $$G = \tan^{-1}\frac{B}{A}$$ What are the related upper and lower errors of $F$ and $G$?  I found general formulae for Gaussian error distributions ($\Delta A_u = \Delta A_l$ and $\Delta B_u = \Delta B_l$), for instance the first formula of the first answer on . Is there a way to generalize that formula for arbitrary distributions with asymmetric errors as in my example? What is the relationship between ISO, aperture, and shutter speed? I know digital cameras have ISO options, and that ISO is the camera's sensitivity to light, but if you set  higher ISO then you can get a noisy image. I also know there are two other camera options, shutter speed and aperture.   What is the relationship of between them? Is there any equation, or something like that?  For example, if I set the ISO to 640, then how should I set the shutter speed and aperture? Changing a CSS rule-set from Javascript Can you show me a continuous function $f \colon \mathbb{R}^n\to\mathbb{R}^m$ that satisfies $f(a+b)=f(a)+f(b)$ but is not linear?   We have that  $$f(0)=f(0+0)=2f(0)\implies f(0)=0\\ f(x-x)=f(0)=f(x)+f(-x)=0\implies f(-x)=-f(x)\\ f(nx)=f(x+x+\dots+x)=f(x)+\dots+f(x)=nf(x)\quad \forall n \in \mathbb{N}$$ But $$ f(-nx)=-f(nx)=-nf(x) $$ So: $$ f(ax)=af(x) \quad \forall a \in \mathbb{Z} $$ Why, historically, do we multiply matrices as we do? Multiplication of matrices &mdash; taking the dot product of the $i$th row of the first matrix and the $j$th column of the second to yield the $ij$th entry of the product &mdash; is not a very intuitive operation: if you were to ask someone how to mutliply two matrices, he probably would not think of that method. Of course, it turns out to be very useful: matrix multiplication is precisely the operation that represents composition of transformations. But it's not intuitive. So my question is where it came from. Who thought of multiplying matrices in that way, and why? (Was it perhaps multiplication of a matrix and a vector first? If so, who thought of multiplying them in that way, and why?) My question is intact no matter whether matrix multiplication was done this way only after it was used as representation of composition of transformations, or whether, on the contrary, matrix multiplication came first. (Again, I'm not asking about the utility of multiplying matrices as we do: this is clear to me. I'm asking a question about history.) How to decompose a unitary transform into two-level unitary matrices? Does one need a visa to transfer between two airports during a transit through the Schengen area? I am an Indian citizen travelling from New York to Delhi with a layover in Paris where I need to transfer between Paris Orly Airport (ORY) and Paris Charles de Gaulle Airport (CDG).  Do I need to have a visa to make this transfer?  I didn't notice that while booking the ticket. How to move my cube left or right using touch Inputs (C#) in unity I am trying to create a 3d game in unity. I have a cube in unity and I want it to move left or right on swipe . It should move to a distance till where user swipe or take their finger off of a screen. I want it to move fast or the cube should move fast on swipe and cube should flow smooth. Like in the gif there is a circle and the user use their finger to move the circle till wherever the user swipe it and it should be instant and I want my cube to move like that at a distance till where user swipe their finger and it should be instant and fast.  I don't know how to do it. Any help is appreciated! I've been reading through a lot of the rookie Java questions on finalize() and find it kind of bewildering that no one has really made it plain that finalize() is an unreliable way to clean up resources.  I saw someone comment that they use it to clean up Connections, which is really scary since the only way to come as close to a guarantee that a Connection is closed is to implement try (catch) finally.    I was not schooled in CS, but I have been programming in Java professionally for close to a decade now and I have never seen anyone implement finalize() in a production system ever.  This still doesn't mean that it doesn't have its uses, or that people I've worked with have been doing it right.  So my question is, what use cases are there for implementing finalize() that cannot be handled more reliably via another process or syntax within the language?    Please provide specific scenarios or your experience, simply repeating a Java text book, or finalize's intended use is not enough, as is not the intent of this question. How to reconnect a logically disconnected USB device? It is possible for a USB storage device to become logically disconnected: the device is still plugged in, but is invisible from the operating system (e.g. it's not listed under /proc/bus/usb). Maybe this can happen to other kinds of USB or other removable devices as well. This can happen for example:   ; after VirtualBox has claimed a USB storage device (the device disappears from the Linux host when it is attached in the guest, and does not automatically reappear if it is detached from the guest).   What is going on in the driver or in the hardware, and most importantly, (how) can the device be logically reconnected (without physically plugging it out and back in)?  Note that this question is not about mounting. In the “logically disconnected” state, the kernel believes there is nothing on the USB bus (and so of course there is no entry under /dev). Overleaf does not compile after using Biblatex 3-manifold examples of homomorphisms between fundamental groups that are not induced by continuous maps I am looking for some examples of closed, orientable 3-manifolds $M$ and $N$ and a homomorphism $\phi : \pi_1(M) \to \pi_1(N)$ such that $\phi$ is not induced by any continuous map $f : M \to N$.  Are there examples of this occurring for lens spaces?  I do not believe that this phenomenon can occur for maps between surfaces. Background: I am currently employed by a start-up that, so far, is doing really well. As part of my contract, I have stock options that will come available on a typical vesting schedule. A quarter of my options are set to vest later this year. Also, the company is not public yet, and it may be several years before it is public / I could sell my shares of the company.  My question is, is there any reason I should exercise them as soon as they vest? As far as I know they don't expire as long as I work at my company (if I leave for any reason, then I only have 3 months to exercise).  I don't foresee leaving any-time soon, and if I did, I would have 3 months to make a final decision.  Is there any disadvantage to just letting the option stay an option for a while? Rotating a gyroscope's output values into an earth-relative reference frame For whatever reason, I seem to have gotten myself twisted into quite a confusion on how to process data from my 3 axis gyro and 3 axis accelerometer to get gyro rotation values related to the earth's reference frame. i.e. Given my accelerometer measures gravity (we assume it's stable) along the sensors (x,y,z) reference frame, how do I adjust the values of my gyro, measured along the sensors same (x,y,z) reference frame such that I am actually measuring the rotating about the Earth's frame x (North), y (West), and z (downwards) direction?  I just can't seem to wrap my head around the use of the rotation matrix. Do I simply employ a 3d rotation matrix, and multiply the vector, \$[gyro_x, gyro_y, gyro_z]^T\$, by a rotation matrix, R? I then assume the rotation angles, are somehow derived from the filtered accelerometer outputs, but I'm having trouble deciding on what those should be.  I have yet to find a concise reference on how to move the rotation and acceleration values from the sensor reference frame into the earth global reference frame. Perhaps someone can help? Thanks IINM my system is failing when bashing  for i in {0..10000000}; #   Seven zeroes. do     false; done #   `bash` exited and its `tmux` pane/window was closed.   or  for i in $(seq 0 10000000); #   Seven zeroes. do     false; done #   `bash` exited and its `tmux` pane/window was closed.   but not when  for i in {0..1000000}; #   Six zeroes. do     false; done #   Finished correctly.   Can you please briefly explain the internals of this behavior and prompt a workaround for getting the task done? What's a concise way to check that environment variables are set in a Unix shell script? Sci-fi story where all 'citizens' had shares in a global company Not everyone was a citizen though, there was a significant underclass who had no shares.  One character was a celebrity in some sort of combat game who was followed by camera drones &amp; used drugs to suppress puberty so he waa an eternal 'child', I have the impression that medical science allowed virtual immortality short of accidents.  One character (may have been the same one) had had a 'previous life' &amp; had committed personality suicide by some form of mind wipe bequeathing his worldly possessions to the new personality that would eventually develop in his old body.  I think the motive for this 'suicide' was essentially boredom, he'd lived a long time.  The mind wipe in question was pretty extensive &amp; all encompassing, he had to be cared for &amp; educated from scratch as if a newborn baby in an adult body, nappies &amp; all (but I'm pretty sure this was purely backstory in the book I read).  He also had miniature nano organisms (or bots?) like miniature worms or millipedes that complimented his immune system &amp; aided healing, they were self replicating, pretty sure they were some sort of bioengineered organism tailored to his DNA rather than bots  but not 100% on that.  There was an organism spanning a large area on the planet that absorbed (or consumed) anything that wandered into it but saved the DNA of anything it had previously absorbed &amp; might randomly reproduce any animal plant or individual it had previously absorbed fully formed.  One of the characters fell into this but got pulled out before the full effects took hold, as a result he grew leaves from his head &amp; his immune system was then constantly battling with the 'infection'.  When did I read this? probably some time in the 80's in the UK.  When was it written? I haven't a clue, sorry.  It was a paperback, probably something I had out of a library, because I never get rid of anything I've bought myself so I'd still have it &amp; be able to dig it out if it wasn't a library loan.  I have lots of fragments of world background &amp; 'colour' that seem to have stuck in my mind there, but a complete lack of any story arc to go with them.