I am noticing that equations when written inside the ``align" environment in the amsart class document come with a lot of white space around it. Particularly if there is a single line sentence between 2 instances of the align environment then there is a very conspicuous amount of white space around that single line.   Can someone suggest a fix for this?
I have a document I am trying to copy to learn TeX. Here is what I have encountered: How can I have the "or" in the equation. This is what I have right now:  \[ f = ma; \]  But $a$ is the change in velocity,  \[ f = m \frac{dv}{dt};\] \[ f = m  \frac{d^2y}{dt^2};\]   Edit: Trying out Stefan's answer
I'm learning Neural Networks and I grasped the algebra behind them. I'm now interested in understanding how normalization and centering of the input data affect them. In my personal learning project (Regression with NN) I've transformed my input variables to a range between 0 and 1 using the following function:  normalize &lt;- function(x) {return((x - min(x))/ (max(x) - min(x)))}   The NN model fits well and has an acceptable out-of-sample prediction error.   However, I read in other  that scaling the inputs to have mean 0 and a variance of 1 is advised for NN. I don't fully understand:   how this transformation works better for NN against the min-max normalization between 0 and 1. how can I assess which transformation to apply in my data? Prevent monitor from losing signal after screen saver / lock activates After the screen saver activates, or after I manually lock the screen via Ctrl+Alt+L, I see a blank black screen with just the date / time in the upper right corner. A few seconds after that, my HP flat screen monitor(s) lose the video signal and display ugly hopping "No Input Signal" boxes.  I'd like to keep the blank black screen (It's less distracting, consumes about as much power, and allows me to unlock faster, as the monitors don't have to re-sync), so Ubuntu should keep driving the video output while the screen is locked.  How can I configure this? I'm using Ubuntu 14.04.3 LTS with the Gnome Classic Fall-back. Graphics card is NVIDIA with the open source Nouveau driver, but I also see this with an external HP NL571AA USB graphics adapter. IllegalArgumentException or NullPointerException for a null parameter? I have a simple setter method for a property and null is not appropriate for this particular property. I have always been torn in this situation: should I throw an , or a ? From the javadocs, both seem appropriate. Is there some kind of an understood standard?  Or is this just one of those things that you should do whatever you prefer and both are really correct? I'm a US citizen and I've already gotten my Tier 4 visa to study in the UK in my passport, however, it looks like the start date on the visa and the letter to present to the Immigration Officer has allowed me entry an extra week on top of the usual month. My school starts on September 24th, but my visa states permission to enter on August 17th. I've read that you are only allowed a month before the beginning of school, but my visa is saying differently!  Should I assume its wrong and enter on the 24th or is it okay for me to enter on the 17th?   Thanks. Set String via String.prototype function without return What are the good ways to migrate a RAID array to bigger disks? Did the verb “fire a weapon” exist before the actual introduction of firearms on battlefields?  More specifically, does it make sense for a creative work to have archers (or whatever ranged weaponry) be told to “fire!”, when the world they live in has not yet seen firearms?  It seems some kind of an anachronism to me, since before firearms, “fire” would never propel any projectile...  I've seen several movies do it; I can't remember them all, but for instance I verified it in The Lord of the Rings trilogy (left), Kingdom of Heaven (top right), and more recently Frozen (bottom right):    The first two do it several times (with Kingdom of Heaven also using it on ballistae, and The Return of the King even having Aragorn ask Legolas to ), whereas firearms never appear on the battlefields they feature (Kingdom of Heaven is set in the 12th century; as for The Lord of the Rings, apart from one occurrence of a witchcraft-ish bomb, it's archery and medieval siege engines all the way).  Frozen may be debatable, happening probably somewhere in the 18th or 19th century, but since we only see swords, spears and the like, it made me flinch to hear crossbowmen use “fire!”.  I've also noticed other movies avoiding this, using “loose!” instead, such as Troy (left) and Gladiator (right):    This makes me think it would be the right thing to say instead... although I'm still wondering why not use “shoot”, which seems simpler to me. I assume that the multimeter should read 2A, why is it only 0.358A? If this is how it is supposed to be, why? If I add a load, how do I measure that this load is being drawn, does the multimeter need to be in series? How to make a film in black and white and add color to some objects? How is a movie made to show selective colors. For instance, in  a sister and brother are transported to the universe of an old black and white TV show, and the movie switches to being B&amp;W. Then, as the protagonists cause the inhabitants to have 'real' emotions, like fright, anger, or love, things (people, places, etc.) start having color. In the middle of the movie, many objects are still B&amp;W, yet many more are now colorized.   also used this effect (the whole film was initially shot in full color, and was converted to black-and-white. Colorization is used on certain subjects in a scene), for example.  How is this effect achieved? Is it post-production editing? What techniques might a director employ to do this? Tips to extend battery life for laptops and notebooks What is the purpose of using a FIFO vs a temporary file or a pipe? From APUE     FIFOs can be used to duplicate an output stream in a series of shell   commands. This prevents writing the data to an intermediate disk   ﬁle (similar to using pipes to avoid intermediate  disk  ﬁles).       But  whereas  pipes  can  be  used  only  for  linear  connections   between processes, a FIFO has a name, so it can be used for   nonlinear connections.      Consider  a  procedure that  needs  to  process  a  ﬁltered  input    stream  twice.   mkfifo fifo1 prog3 &lt; fifo1 &amp; prog1 &lt; infile | tee fifo1 | prog2       We create the FIFO and then start prog3 in the background, reading   from the FIFO. We then  start prog1 and  use tee to  send  its  input    to  both  the  FIFO  and prog2.    How does a FIFO "duplicate an output stream in a series of shell commands"? Isn't this done by tee instead of a FIFO? In the example, mkfifo fifo1 creates a file in the current directory, and fifo1 seems replaceable with a regular file . So what is the point of a FIFO "prevent writing the data to an intermediate disk file"? What do "linear connections" and "nonlinear connections" between processes mean? What does it mean that a FIFO can be used for nonlinear connections, while a pipe can be only used for linear connections between processes?   Thanks. By default, all browser instances use the same cookie for the same site. Is there a browser that doesn't follow this?  Or is there a Firefox plugin that can "wear" different cookies for a specific site? How to influence the position of float environments like figure and table in LaTeX?   This is a general question and should collect useful answers for all users. I hope we can use this as a reference Proof a $2^n$ by $2^n$ board can be filled using L shaped trominoes and 1 monomino Suppose we have an $2^n\times 2^n$ board. Prove you can use any rotation of L shaped trominoes and a monomino to fill the board completely.  You can mix different rotations in the same tililng. I've seen this Kuratowski definition for ordered pairs, but can't fathom why it implies an order to $x$ and $y$  $(x,y):=\{\{x\}, \{x,y\}\}$  As I understand sets, $\{\{x\}, \{x,y\}\}$ is also $\{\{x,y\}, \{x\}\}$. Only when I think about the Axiom of Union does $\{\{x\}, \{x,y\}\}$ "collapse down" to $S = \{x, y\}$, but that doesn't give me much either. All I can see is some as yet hidden message in the set saying "I am the set $\{x,y\}$ and my order of $x$ first is indicated by having $\{x\}$ along for the ride." I am attempting to settle a friendly bet.  Would a pendulum swing indefinitely in a hypothetical vacuum (i.e. no air resistance) having a hypothetical frictionless bearing (i.e. no energy lost due to friction) assuming the following   The frictionless vacuum is on Earth (9.8 m/s^2). The pendulum is already in motion and no other external forces other than gravity act on the pendulum. Continuity of $L^1$ functions with respect to translation If derivative of function is less than or equal to 4, prove the existence of point $c$ so $f(c)=c^2$. I am struggling to construct a simple proof of the following.  Suppose $f(x)$ is differentiable for any real value $x$ and that $f'(x) \le 4$ for all real values of x. Prove there is at most one real value $c&gt;2$ such that $f(c) =c^2$.  I am completely lost on where to start on this proof and any help would be greatly appreciated! Why does the QGIS Server WMS layer not load in QGIS Desktop? Assume that $f(x),g(x)$ are positive and are in $L^1$. Moreover, they are differentiable and their derivative is integrable. Let $h(x)=f(x)*g(x)$, the convolution of $f$ and $g$. Does the derivative of $h(x)$ exist? If yes, how can we prove that $$ \frac{d}{dx}(f(x)*g(x)) = \left(\frac{d}{dx}f(x)\right)*g(x)$$  Thanks