TL; DR: Is this equation true, and how do I prove it? $$ \sum_{k=0}^n \binom{n}{k}(-1)^k(n-k)^n = n! \;\; \forall \;\; n \; \in N $$ Context: I came across this question while thinking about powers of natural numbers. Imagine you have a list of numbers like this: $$ 1^3 \;\; 2^3 \;\; 3^3 \;\; 4^...

Consider this type: export type ListenerToAll<Events> = <EventName extends keyof Events>(eventName: EventName, payload: Events[EventName]) => void This fails type CharacterEvents = { wait: {turns: number}, speak: {message: string} } const liToAll: ListenerToAll<CharacterEvents> = (even...

I would like to be able to evaluate a function based on multiple Slider values by pushing a Button that creates the function, produces the data, and also produces a plot in the same "GUI" window. This is like a Manipulate for a plot in many ways, but I want the update to be button-driven and not ...

I can easily find my way reading a book on homological algebra or algebraic geometry, but I tried once reading a book on statistics and... I felt dumb really: I simply do not understand the foundations of statistics, and it seems to me like reading Chinese. My ultimate goal is to understand in de...

In the Eric Bogle's anti-war song "Welcome Home" (about the Vietnam War) there is a line "I heard old war drums beat.". Is it grammatical or is it licentia poetica? I think I understand the meaning, but I do not understand how it can be grammatical. On the face of it, it appears to use this gramm...

I have been told that galaxies will never stop rotating because conservation of angular momentum But, there are planets inside of it can travel through dense nebulae and bodies of gas that would cause friction (and probably brake their travel speed through the Galaxy). Wouldn't that brake the gal...

Question: Prove or disprove the following statement. If $\{f_n\}$ is a non-decreasing sequence of Riemann-integrable functions on $R = [0,1] \times [0,1]$ so that $f_n(x) \to 0$ for almost all $x \in R$, then $\lim_n \int_{R} f_n \, dx = 0.$ I believe this statement is false. However, I am not ab...

I am confused about what gravitons exactly are. On the one hand it is said that gravitons are presumed to represent gravity (see Wikipedia "Graviton" : "In theories of quantum gravity, the graviton is the hypothetical quantum of gravity, an elementary particle that mediates the force of gravitati...

I’ve searched for this over and over but haven’t found a definite answer to my questions… It would be awesome if the answer(s) could contain links that support their sayings :) Say you are put to sleep by magic and can’t be woken up by your companions because reasons. You stay asleep for at lea...

In the end of this episode, after solving the crisis of the week on one world and moving on to another, the main characters freak out when they see a woman dangling her daughter from the upper floor of a two-story house. The mother lets go, and her child sprouts wings from her back and flies to s...

In a world where time travel in the past is possible but deletes the current future/ present, there is a person named Sarah does not worry about the ripple effects their actions might create. Sarah chooses to travel back in time by 5,000 or more years, to be one of the most powerful woman in the ...

I was trying to solve exercise III.10.6 of Hartshorne and found this post about it. My problem is that I am struggling to show that the morphism $f : X \longrightarrow Y$ (following notation of the post, $X$ is the étale covering and $Y$ the nodal curve) is flat. In the post it is said that we ca...

I'm making a t-shirt design in Blender texture painting. I'm planning on making a design with lines going down straight. Is there any way to do this in texture painting? Something like this below:

What is an experimental certificate? Is it just a certificate that is for aircraft that were built experimentally such as home-built aircraft? What is the purpose of the certificate?

To my understanding, most mathematical theories can be simply understood in the view point of Category theory and its derivative theories. But what exactly is the motivation to study infinity category theory? Why should one, for example, look at morphisms between morphisms and so on?

This quote is from Stranger Things season 4, episode 1, 43 minute 10 seconds mark by Fred Benson: Eh, I'm still rooting for my alt. What does 'alt' mean in this context? Maybe it has something to do with the paper, as he showed Nancy ‘The Tigers Lose the Championship Game’ paper while saying th...

It's well-known that if a cardinal is weakly compact, then it is weakly compact in $L$. Seems natural to ask if weak-compactness is preserved for arbitrary inner models. Since I've never heard this, I'm guessing the answer is no, but I'm having trouble finding a counterexample. I have something ...

Consider the following MWE: \documentclass{article} \usepackage{tikz} \usepackage{xparse} \ExplSyntaxOn \NewDocumentCommand{\answergrid}{ m m m }{ \begin{tikzpicture}[x=0.75cm,baseline] \seq_set_split:Nnn \splitted_seq{;}{#3} \newcounter{answer} \...

I have a bad leak in my bathtub faucet. The hot handle. I have a plumber coming but not until the upcoming week. I turned off the water supply to the electric hot water heater and it quit leaking. My question is, is it safe to leave it off, until I get the leak fixed? I obviously won’t have hot w...

Hero is a high school student trained in martial arts by his grandfather with a childhood friend. One day, he is summoned to another world (probably with his katana). His childhood friend is also summoned later, along with two police officers who came to investigate the hero's disappearance. The ...

I finally have my Apple //e booting from my SCSI2SD but I'm missing something regarding how ProDOS knows what program to 'startup' when it boots. As I understand it, ProDOS will look for the first .SYSTEM file and launch that, which seems simple enough. But what if you want to change a bad deci...

I've just added a 100A subpanel to a house with a 200A main panel, and would like to know if I did everything correctly and up to code before getting it inspected (I'm in WA state -- 2020 NEC). What I installed It's a Square D HOM2448L125PQGC 125A 24-48 panel with main lugs (but no main breaker)...

In continuation to What defines legitimacy of a DOI My paper was assigned a fake DOI, but they changed it to https://doi.org/10.5281/zenodo.8150058 which has the doi.org as the prefix. Is it allowed and is the new DOI legit?

I've found the following word transformation exercise in the book Cambridge English Proficiency 2 (page 51, exercise 17). All children occasionally ask why we should bother reading. Now, 500 years after Gutenberg’s printing press ___________ DEMOCRACY reading, recent technological advances mean ...

Could "going after strange flesh" mean the rape of strangers to the city? The Sodomites engaged in the practice of raping their enemies. It would be surprising if it was not mentioned in the Bible as being a sin. Jude 7 - just as Sodom and Gomorrah and the cities around them, having indulged in ...

I face this situation so often today. I have MacBook without M1 chip, and many simple apps on the AppStore for some reason require it. As I see this, they don't have any specific use to it, the app is just built the way it requires M1 for some reason. Specifically, I came across the SkyVPN MacOS ...

If I understand correctly, when a party to a contract breaches the terms in a material way (i.e., repudiation), the non-breaching party can, at its discretion, terminate it, cease performance under it and seek damages, if desired. If the innocent party expressly acknowledges the breach and consi...

Consider the Hamiltonian \begin{equation} H = \frac{p^{2}}{2m} + \frac{1}{2} m\omega^{2}x^{2} - \theta(t) qEx \end{equation} where $\theta(t)$ is 0 for t = 0 and 1 for t > 0. If at t = 0 the state of the system is the ground state, what exactly happens when t > 0? The energy levels are shifte...

I am looking for a variant of the knapsack problem in which the items are nodes in an undirected graph, and the knapsack must be filled with a connected subgraph. Formally: The input is an undirected graph $G=(V,E)$, where each node $v\in V$ has both a size and a value; and a knapsack capacity $...

In my current translation project I have a few lines where I would use a singular noun to refer to a group of people. For example, But be careful around the Fair Folk. They can be fickle, and you do not want to cross them. The Fair Folk rarely reveal themselves to travelers, and are seen only wh...

The Factor built-in function is usually idempotent, namely applying it twice gives the same result. However, in the following example it is not. Is that expected? Somehow the need to simplify Sin[x]Cot[x] to Cos[x] seems to confuse the code responsible for factoring, so that the result is not ...

It is written into halacha that we are not allowed to assist captives to escape, lest we encourage captors to be harsher with their victims, and watch them more closely. See SA 252:5 for example. It does not say that captives are not allowed to attempt their own escape, although the svara written...

Suppose you have some dataset $X \in \mathbb{R}^{n \times d}, y \in \mathbb{R}^{n}$ from some distribution $\mathcal{D}$ (if convenient to obtain a closed form formula, $\mathcal{D}$ can be a Gaussian distribution or something else that is tractable). You posit a linear model, and you compute the...

I'm sure this is a very silly question. But I saw a post here and other circuits on the internet, and I dont understand the difference between them. I have a pic microcontroller, and I need to use only 1 output for controlling two leds, if one it's ON, the other one it's OFF. Searching I found tw...

I am reading the Master Bitcoin book and came across the following: From a security perspective, the amount of entropy actually used for the production of HD wallets is roughly 128 bits, which equals 12 words. Providing more than 12 words produces additional entropy which is unnecessary, and thi...

I disassembled a cheap tweeter because I wanted to use only the inner part of it since it is just about 5mm tall (1/4 inch). I thought the coil that surrounds it was just a cheap inductor to "short out" low frequency and protect the tweeter. Turns out that when I connected only the piezo with the...

From a set-oriented point of view, a relation between sets $A$ and $B$ is a subset $\rho \subset A \times B$ of their product. By imposing further axioms (e.g. left-totality, right-totality, symmetry, transitivity, etc.) we may produce a number of useful concepts: (partial) functions, equivalence...

I wrote a small program that initializes a 3D array in C based on command-line arguments and prints it. I did my best to avoid undefined behavior and memory errors. I wrote comments as if I had an exported API. I don’t know if “owns” is standard terminology, I use it here to mean that a function ...

I'm novice TeX user who inherited 100 plain TeX files that I want to convert to PDF. I installed TeX Live 2013 on a Mac to do so. Before converting to PDF I would like to add each TeX file's date and time to the resulting PDF. I assumed that the \FIRST-LINE argument would allow me to do so since...

I'm trying to add a RJ45 connector to a Ethernet cable for a NVR system (Surveillance Cameras). The cameras comes with ethernet cables and I see that the only have 4 cables used and in different positions than RJ45 color coding T568A or T568B (image below) Seeing from bottom, the order is White O...

I do asset allocation: 10% in cash. 40% in equity mutual funds. 60% in bond mut funds. I've had the cash in Vanguard money market funds. Wondering about keeping some of the cash in HYS account to get ~5% interest.

I've been trying to input a video in a cubes on blender 3d software, somehow it seems right way but never worked out for me. please check the image below, i have few evidences for it.

I recently bought a 10 year old house and noticed the insulation on the outside HVAC tubing had deteriorated. I replaced it with Duck brand foam insulation about a month ago. Today I noticed that it seems to have melted down where the smaller tube has touched it (picture attached). The old tubing...

I want to do LC–MS analysis of the samples from a 384-well plate where each compound (at around 1–10 μM) is dissolved in 10–15 μL of DMSO. I am worried about the DMSO dwarfing the analyte’s signal, as well as the challenges from ion suppression caused by the DMSO. So, I’d like to evaporate DMSO a...

It was about two civilizations that were fighting each other, but, unknown to them they shared an origin on the same world. One civilization was obsessed with perfection which to them was pale skin, dark hair, etc. while the other just wanted freedom and love if I remember correctly and they had ...

I'm considering some non-cryptographic PRNG which uses multiplication of two 64-bit or 128-bit random numbers at some point. __uint128_t a; __uint128_t b; __uint128_t result; result = a * b; Is this constant time? I don't think so, especially since it takes less time to multiply two small numb...

I learned the Public Key Recovery algorithm for ECDSA, and wonder if we can use it in DSA. The answer seems to be no, but details are welcome.

Background As part of the Advance Passenger Information (API) for an upcoming flight from my country of residence (Country R) to my country of citizenship (Country C), the airline is asking me to indicate the following: Field Response Citizenship I know that that has to be Country C Cou...

Stephen Haber ("professor of political science, professor of history, and professor of economics" at Stanford) claims in a 2014 podcast: the state of Iowa has more farmland suitable for growing corn and wheat than the entire country of Canada. From some quick Googling: Statistics Canada: In 2...

I am experimenting with basic logic gates on multisim. From my understanding in digital logic the 0/1 represent output voltages of 3.3 - 5 and 0 V. My logic gate pictured conducts a current when 5 V is applied to the base terminals but nowhere in the output do I measure a voltage in the high rang...

I am using the siunitx package and the documentation is a bit mind-blowing. I'm using it with no options and no sisetup. There is zero spacing my units. I have tried to add sisetup with inter-unit-product = \, but there is no change. I believe this is meant to be the default anyway. Here is an ex...

There are $n$ people and $m$ jobs. We would like to assign at most one job to each person. For each person,job pair, there is a positive value determining the fitness of this person to that job. The goal is to find an assignment that maximizes the total value. So far, it is exactly the problem of...

This is from the BBC Tomato shortage "Tomato shortage: How far is Brexit to blame?" At first I could not quite decide what exactly the question is focusing on. I thought people have not yet understood that the problem was actually caused by Brexit, so it still seems a little bit far away for peop...

I replaced the Vehicle SpeedSensor that’s on the tail shaft of gear box nothing changed. I would like to know if there is another sensor that affects the speedometer possibly inside the transmission ( 4L60E ) ? Also thought about the wheel speed sensor does it affect the speedometer ? The truck ...

I always wondered since my late high school years, how increasing the voltage can simply be proportional to the flowing current in a resistance. Given $$\ dU = Eds = \frac{F}{q} ds \implies U \propto v^2 \ ,$$ also the electrical current should be proportional to the speed $v$ of the electrical c...

I'm trying to understand the scoring mechanics for breaking bubbles in the original 1989 arcade version of Pang (aka Buster Bros. or Pomping World) because I'm implementing it myself for fun in PyGame. I don't have my own copy of the game. From this YouTube video, I've figured out that, in descen...

Some background you can happily skip Twenty years ago or so, when navigating the web costed a lot, when I was a Windows-only user, and when CDs/DVDs were a large storage means, and when sharing video files with a friend or relative would sometimes require to split the file over multiple CDs/DVDs,...

If I have both wifi on and am also connected via ethernet to my modem. Which is my system using? I am curious because I want the ability to SSH into other devices on my local network, but I also want the 1 GB connection I have with my hard line. So I am curious when I have multiple internet con...

It seems that in a tikz-foreach-loop mathematical expressions are not evaluated correctly: \documentclass{minimal} \usepackage{tikz} \begin{document} \begin{tikzpicture} \foreach \c [count=\i] in {0,1,...,{floor(9/4)}} \node at (\i,0) {\c}; \end{tikzpicture} \end{document} This yields the str...

I have an binarized image and a center cvx = Import@"https://i.sstatic.net/1QoEo.png"; center = {258.19137417775005`, 150.8459811782782`}; HighlightImage[cvx, center] gives I want to rotate this white triangle by 180 degree around this center point and keep the original image dimension. If...

I was recently in the cafeteria with a friend, and while having lunch I explained to him why the tangent bundle of a manifold is good at encoding geometric information of the manifold. My second example was Foliations and the Frobenius theorem. I described to him the tangent sub-bundles etc. Afte...

I have two blue bones that move freely along the x axis. I have mulitple red bones that are ment to only move when they are between the blue bones the red bones when they are inbetween the blue bones have a location limit of 0 to 0.1 and they have an even distribution value from 0 to 0.1 accordi...

I lined up the ranks for British, New Zealand, and Rhodesian armies. No OF-9 in Rhodesia. Is Wikipedia mistaken? Why did the Rhodesian Army have Lieutenant Generals and Major Generals, but no Generals? The lack of the General rank feels illogical!

What is this sci-fi movie about a guy who wakes up from a truck accident, has lost his memory, and anybody who gets within 150 yards of him drops dead? Then he meets a woman who nullifies his toxicity, and then there's a twist I won't divulge and ruin it.

So Sakurai in their QM book defines the propagator in wave mechanics as: $$K(x'',t;x',t_0)=\sum_{a'}\langle x''\vert a'\rangle \langle a'\vert x'\rangle \exp\left[\dfrac{-iE_{a'}(t-t_0)}{\hbar}\right].$$ Since the exponential terms are the eigenvalues of $\vert a'\rangle$, you could write this ex...

On a geological map legend is it possible to automatically add a label (eg. formation abbreviation) inside their respective boxes of map layout legend?

While I was looking up some origins regarding the character 失, I happen to come across three theories for the character. The most common one a lot of sources say about this character is that it was composed of 手 and 乙 (which from what I've heard is also sound component) and it depicted a hand loo...

I consider myself an Orthodox, and I'm from Eastern Europe (Not Russian, nor Ukrainian) and I discovered that we, Orthodox Christians, are very permissive regarding consuming alcohol. Of course, we believe that being a chronic alcoholic is a sin, however even if our official position regarding al...

We know that 1-wire devices, such as the DS18B20 temperature, sensor have 1 64 bit address, of which 8 bits is 0x28 and another 8 bits is the CRC. We know that the address is burned into the chip at manufacture. But where does the manufacturer obtain these IDs? Presumably there are multiple manuf...

I have products such as gaming tables and chairs I want to add two prices to them Price with carton and price without carton how can I do that

It is not hard to prove the following lemma: LEMMA: Let $(G_i)_{i \in I}$ be a chain of simple groups. Then $G = \bigcup_{i \in I} G_i$ is a simple group. Let $N$ be a normal subgroup of $G$ and define $N_i = N \cap G_i$ (all $i \in I$). $(N_i)_{i \in I}$ is a chain such that $N = \bigcup_{i \in ...

In English, I would say: You can not be serious! But, in German, one could either say: Du kannst es nicht ernst meinen (ernst as adjective) or, Das kann doch nicht dein Ernst sein. (ernst as noun) When I check reverso, it seems to me that the noun form of Ernst is used more often. Is this a...

$$ cos(h)= -tan(\delta)tan(\phi) $$ $$ \Theta = h + \alpha $$ if these two equations are the correct equations to solve the following question why doesnt it yield the same answer for the sideral times at rising on June 22 and December 22 (for part a) Declination ($\delta_{june}$) of the sun on...

Question: what is the geometric interpretation of the subject of machine learning and/or deep learning? Being "forced" to have a closer look at the subject, I have the impression that it all boils down to approximately reconstruct the characteristic function that decides about set-membership of...

If $G$ be the geometric mean between two quantities $A$ and $B$, show that the ratio of the arithmetic and harmonic means of $A$ and $G$ is equal to the ratio of the arithmetic and harmonic means of $G$ and $B$. $A, G, B$ are in geometric progression. Therefore $\dfrac{B}{G}=\dfrac{G}{A}$, or $G^...

Well, recently I'm working on a program which is able to sync files between different folders. However, as a fresh man, the algorithm I worte seems feasible, but looks really disgusting, and inefficient as well (bruh~) The following lines are the related things I wrote, I really hope there would ...

1 Peter 1:6-9 NASB “In this you greatly rejoice, even though now for a little while, if necessary, you have been distressed by various trials, so that the proof of your faith, being more precious than gold which is perishable, even though tested by fire, may be found to result in praise and glor...

I am attending Boston University in Massachusetts this fall and flying from India to Hong Kong to LAX to Boston on an F1 Visa. I have a long layover of 20 hours at LAX and, since the US considers my Port of Entry to be my first entry port, I'll have to go through the Port Of Entry Process at LAX....

In an isosceles right angled triangle, vertex opposite to the hypotenuse which has $90^\circ$ is always on the perpendicular bisector of the hypotenuse. So my question is, if we consider a sides of length $a$ and hypotenuse as $c$, then how to prove that length of segment $c$ is not a rational mu...

How can we prove the above theorem using synthetic geometry.

Given the four-dimensional metric tensor $g_{\mu\nu}$, written in the perturbed form as: $$g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu \nu}, \qquad |h_{\mu \nu}|<<1$$ In deriving the linearized Einstein's equations in Braneworld models, I got terms like: $$\partial_{\mu}\partial_{\nu}h \ \ \ \ \mathrm{and} \...

I'm on a cross-Canada trip from BC to Newfoundland. I noticed a problem which sounds like a wheel bearing going. I took it to a dealer in New Brunswick, and they claim the rear diff is bad (metal shavings in oil etc), so they quoted me a price for the work. They assumed I wouldn't be getting the ...

Farquaad is interrogating Gingerbread Man: Gingerbread Man: You are a monster. Farquaad: I'm not the monster here. You are. You and the rest of that fairy tale gang, poisoning my perfect world. Now, tell me! Where are the others? Gingerbread Man: Eat me! (spits on his face) Farquaad: (cleaning h...

I'm upgrading from FusionDrive to a regular drive (or a dual-drive setup). Is there any difference as compared to regular HDD -> SSD upgrade specifically in terms of inheriting pre-upgrade set of Time Machine backups and using the same Time Machine volume for future backups incrementally? In case...

In Ch 19 of Peskin & Schroeder, they discuss spontaneous symmetry breaking (SSB) at low energies in massless (or nearly massless) QCD, given by \begin{equation} \mathcal{L}_{\text{QCD}} = \bar{Q} (i\gamma^{\mu}D_{\mu}) Q - m\bar{Q}Q, \end{equation} where $Q = \left( \begin{matrix} u \\ d \end{mat...

There are various absorption lines that correspond to the difference in energy levels between electron orbits. E.g. the https://en.wikipedia.org/wiki/Lyman-alpha_line correpsonding to the difference in energy between an electron orbiting a hydrogen atom in its ground state and the $n=2$ orbital. ...

I have two accounts on my phone institutional google managed workspace - [email protected] private gmail - [email protected] The institution that manages ([email protected]) ended relationship with Google and switched to Microsoft instead. I am no longer able to use that email address as my Google Account. I ...

I am facing some spacing issues in LaTeX. Using this code: \documentclass[numbers,sort&compress]{IntechOpen-Book}%%OPTIONS are numbers, authoryear, sort&compress,sectref \usepackage{physics} \usepackage{caption} \usepackage{subcaption} \usepackage{svg} \usepackage{graphicx...

I have done a symbolic integration in mathematica 13.2 as follow Integrate[-((Sqrt[-r(r - 2 l)] l)/(r(r - 2 l) (-r + l))), r] // Simplify[#, r > 0] & Integrate[-((Sqrt[-r(r - 2 l)] l)/(r(r - 2 l) (-r + l))) /. {l -> \[ScriptL]}, r] // Simplify[#, r > 0] & All that I have done is simply the rep...

In the 1989 movie, Family Business, Jessie McMullen, his son Vito, and Vito's son Adam plan a heist from a lab. They go inside, retrieve plasma (it has color) and place them in a hard case and go out. The youngest realizes they didn't retrieve the book that is essential for their 1 million dollar...

I'm using OpenLayers 7.4.0 to create a webapp that allow users to add a vector tile layer by providing a URL via an input field. When the user hits an import button, the map should be centered on the features and I need to extract the geometry_type of the features for further processing. I found ...

In gatomic.c of glib there are several function declarations that look like this: gboolean (g_atomic_int_compare_and_exchange_full) (gint *atomic, gint oldval, gint newval, ...

Consider a triangle $ABC$ and a point $T$. Given that $∠ATB=∠ATC=∠BTC=120°$ and $AC=3$, $BC=4$, $∠ACB=90°$, find $(9BT + 7CT)/AT$. From the question we can imply that the point $T$ is the Fermat-Torricelli point of the triangle. The question wants us to basically find the distance from the vertex...

In story I'm considering writing, a branch of hominid that had been trapped on another alternate earth after being crossing over through rifts are able to return to our earth after these rifts started appearing again. These hominids which split from homo sapiens 200,000 to 100,000 years ago are d...

Why is the work done on a spring independent of the amount of applied force acting on it? Why does it only depend on the spring constant and the amount of stretch or compression? For example: $k=2$ N/m, $x(\mathrm{stretch})=10$ m. Case-1: Applied force $F=50$ N. $$\mathrm{Total \ work \ on \ the ...

TLDR: given a sensing device that produces a varying resistance, how does a "sensor" change this into a 4-20 mA current flow from a 24 V supply? Various sensors (flow, fluid depth, ...) use a 4-20 mA output to convey their measurements: you put +24V into one of the two sensor wires, feed the othe...

talking to a colleague who is more skilled than me in English I asked this: can you provide information about the bear out term origin? and he said I should have written: Can you provide information about the origin of the term 'bear out'? I agree his way is better, but I can't see technicall...

Does air in the atmosphere suffer friction in some way due solely to the planet's rotation?

I was reading East of Eden by John Steinbeck, where I came across the sentence: A man’s mind vagued up a little, for how can you remember the feel of pleasure or pain or choking emotion? You can remember only that you had them. An elder man might truly recall through water the delicate doctor-te...

I couldn't find this in the documentation, but what is max Level number of accounts in an Account Hierarchy. Thanks.

As part of a larger remodel, my contractor installed new sidelights by our kitchen patio doors. But the outdoor side of the threshold on which the sidelights sit seems to be cracked and not filled. Is this okay? Apart from the obvious aesthetic issue, I mean, is there a structural issue with havi...

As can be seen in the image, some composers mix the note types used in tuplets. In this case, there are two eighths and a half note (equal to 4 eighths). The total duration is 6 eighths in triplet time. Thus, ignoring the last four eighth notes in the bar, the first part of the phrase could b...

Been working in games development professionally now for about ~5 years, but have only been doing OOP & haven't worked with multi threading before as I'm mostly a gameplay programmer. Wrote this small program as an exercise in DOP & multi threading. Please ignore my "physics" equations if you can...

I am interested in generating a Bitcoin address by hand for security's sake. After I choose/generate a private key, how do I generate the public key? From there, how would I double check my work? Essentially, I am interested in not exposing my private key to any hardware, including my own. Please...

Denys Fisher, the creator of Spirograph, sold his company, bought an estate in Scotland and started working on his next creations, or at least so is narrated in a BBC's documentary, broadcast as part of "Tomorrow's World" in May 1977. I know because a clip of the documentary was posted on YouTube...

I will be travelling from Vienna to Bratislava via train, however i am not clear on 2 points: I have booked a specific journey on a particular date however when I look at my date it says "valid: Day 1 until: Day 2". Does it mean that if I miss my train then same ticket can be used over period of...

I have booked a ticket (Sparpreis Europa, class 1) via Dbahn website from Munich to Vienna and there are 2 points I wanted to clarify: My ticket says "München+City ->Wien". Does it mean that on the day of departure from Munich, i can use all local transport as well with my ticket? If yes then ho...

I want to estimate the effect of a grouping variable (5 groups) on an outcome variable that is an integer and a scale from 0-10. So, for the outcome only scores of 0,1,2,... etc. are possible. This dependent variable is most comparable to a Likert scale, it is not a count. It specifically is a ps...

I have an Apple Watch 1st gen that does not power on anymore. I want to dispose of it. If I just recycle it (at a recycling center), can someone recover data off it? Should I try to destroy it first (maybe by hitting it with a hammer like a hard drive)?