In C#, what is the difference between Int64 and long?  Example:  long x = 123; Int64 x = 123;
Example (note the case):  string s = "Hello world!"; String s = "Hello world!";   What are the guidelines for the use of each? And what are the differences?
Community, please show some holiday spirit! Why does ? And more importantly: why does she not wear them?    Please, show some goddamn holiday spirit! Can we get Community to wear her hats, either randomly or through popular vote? After what speed air friction starts to heat up an object? I understand that air friction cools off an object at low speeds. For example, if you blow on a spoon of hot soup, it cools off. Or if you swing a hot frying pan in the air, it cools off faster.  But at higher speeds, the situation changes in the opposite. For example, consider a meteor falling on Earth. It is so fast that it heats up to such a high temperature that it burns into ashes.  What is the critical speed in which an object starts to heat up?  For example, consider a spherical object with radius of 1 meter. Let its density be 1 g/cm3 if needed. And let the air pressure be 1 atm. Assume that the temperature of the object is 400 K and the temperature of the air is 300 K. Also assume that the specific heat constant of the material is 1 cal/(gr.K). What is the critical speed for this object after which its temperature starts to rise above 500 K? There exist several implementations of the GBDT family of model such as:   GBM XGBoost LightGBM Catboost.    What are the mathematical differences between these different implementations?  Catboost seems to outperform the other implementations even by using only its default parameters according to , but it is still very slow.  My guess is that catboost doesn't use the dummified variables, so the weight given to each (categorical) variable is more balanced compared to the other implementations, so the high-cardinality variables don't have more weight than the others. It allows the weak categorical (with low cardinality) to enter to some trees, hence better performance. Other than that, I have no further explanation. Packed images used as background don't show up when reopening the file Launch apps full screen How to use stars and bars for solving number of integral solutions to an equality? How to use the  method?  Say I want to find number of combinations I can get with $x_1+x_2+x_3+x_4=22$,  where $x_i\in\mathbb{N}$.  Is this the correct time to apply the method?  This is being repurposed in an effort to cut down on duplicates, see here:     and here: Displaying row/column of point in raster using QGIS? Is it possible in QGIS to display column and row index of pixel in raster?   I mean something similar to value tool. Given 4 integers, $a, b, c, d > 0$, does $\frac{a}{b} < \frac{c}{d}$ imply $\frac{a}{b} < \frac{a+c}{b+d} < \frac{c}{d}$? Is copper piping required within a certain distance from a water heater? I have read that National Code requires you to use copper for 18 inches from your water heater.  How can I do this when everything existing is PEX?   I need to replace my existing low boy water heater next to my kitchen sink.  It was installed by the builder ten years ago. All the pipe in the house is PEX.  The existing water heater is connected using PEX as well.    The supply line comes directly thru the wall to the HW Heater. There is no space to run 18 inches of copper! The heater is under the kitchen counter, and the countertop is directly over it. Only about an inch clearance. Usage and origin of "sister" in expressions like "sister company, sister ship, sister site" etc How do I "un-roll" the viewport? "Give him a box that everyone knows what it contains." Particle speed and density I am using a Particle system to simulate falling dust / debris. The particle start and end fairly quickly. They should look like a short burst of falling dust.  I cant figure out how to get the particles to fall at slightly different speeds.  The particles should be falling downwards with very little Brownian motion.  The fact that the particles are falling at the same speed makes them look odd / too uniform (almost like a static image of some particles which is moving down rather than individual particles.  Also the particles end at a set frame so I get a uniform trailing edge (as below).   A bit of air drag helps a bit but not much.  Question 1. how to vary the downward speed of the particles?  Question2. Can the density of particles be animated so I can brake up the distribution?  Thanks Oliver Define the content of a polynomial (over an arbitrary commutative ring $A$) to be the ideal generated by its coefficients, denoted $c(f)$. I want to show that   $$c(fg) = c(f)c(g).$$      (I was told this is true.)    What I was able to show was that $c(fg) \subseteq c(f)c(g)$ (this is obvious), and that their radicals are the same. My reasoning for the latter was as follows: let $f = a_0 + \dotsb + a_nx^n,$ $g = b_0 + \cdots + a_mx^m,$ and consider the matrix  $$ \begin{pmatrix}  a_0 b_0 &amp; \cdots &amp; a_0b_m\\ \vdots &amp; \ddots &amp; \vdots\\ a_nb_0 &amp; \cdots &amp; a_nb_m \end{pmatrix} .$$  Then $c(f)c(g)$ is generated by the entries of this matrix, while $c(fg)$ is generated by the sums along the diagonals. Let $\mathfrak p$ be a prime ideal of $A$ not containing $c(f)$ or $c(g)$, and let $i,\,j$ be minimal such that $a_i,\, b_j \notin \mathfrak p$.  Then all the terms in the generator of $c(fg)$ corresponding to the coefficient of $x^{i+j}$ are in $\mathfrak p$ except for $a_ib_j$, so that $c(fg) \not\subset\mathfrak p$. It follows that $c(fg) \subseteq \mathfrak p \Longleftrightarrow c(f)c(g) \subseteq\mathfrak p$, and hence $\sqrt{c(fg)} = \sqrt{c(f)c(g)}$.     Can I go all the way and show that in fact $c(fg) = c(f) c(g)$? How to find users by name I am creating a custom form on a Salesforce Marketing Cloud Landing Page. This page will have information such as Email address, first name and last name pre-filled from an email, however there will be some cases where emails can be entered by the customer. What is the best way to validate email addresses on form submit? E.g. a regex to look at overall structure or is there a better way? Getting a better understanding of callback functions in JavaScript I understand passing in a function to another function as a callback and having it execute, but I'm not understanding the best implementation to do that. I'm looking for a very basic example, like this:  var myCallBackExample = {     myFirstFunction : function( param1, param2, callback ) {         // Do something with param1 and param2.         if ( arguments.length == 3 ) {             // Execute callback function.             // What is the "best" way to do this?         }     },     mySecondFunction : function() {         myFirstFunction( false, true, function() {             // When this anonymous function is called, execute it.         });     } };   In myFirstFunction, if I do return new callback(), then it works and executes the anonymous function, but that doesn't seem like the correct approach to me. Does light induce an electric current in a conductor? I know that electromagnetic waves induce electric currents in conductors and that's the basis for radio, wi-fi etc.  I also know that light is also an electromagnetic wave. So, can light induce a current in a conductor (like a metal wire? or a coil?). And, if the answer is yes, is the same visible for other high-frequency waves (X-rays, gamma)?  I heard about the photoelectric effect, but it seems related to the particle theory of light (photons transferring their energy to electrons).  So, do high-frequency electromagnetic waves generate electric currents? Is it possible to measure them? Is the skin effect relevant here? I'm trying to currently rename a large set of files and have been using quite kludgy methods to do so, such as:  rename 's:(.*)\.MOV:$1.mov:g' *.MOV rename 's:(.*)\.JPG:$1.jpg:g' *.JPG   What I'd really like to do is to be able to combine all of these commands using the . Evidently, using this operator, you can transform items to lower case. The problem is that I need to convert only the extensions. Is there a way to do this using this command? I need to essentially transform the capture group in the following expression to lowercase: ^.+\.(.+)$. Is there a way to do this? I'm kind of new to these kinds of transformations. I am new to Stack Exchange. I know there is a lot of discussion sites for Stack Exchange. I would like to know about there were any Stack Exchange site available for discussing and solving personal psychological problems.