Challenge: Write a program or function that, given positive integers n, t, b, c, counts permutations of 1..n where: Exactly t numbers are in their original position Exactly b numbers are higher than their original position Exactly c numbers are lower than their original position Input: Four non...

A few years ago I did a brief undergraduate research apprenticeship in pure math, where I helped a professor come up with a novel construction, and it's in the works to get published. I think I helped come up with the "core idea of the solution", but I was missing many crucial details and the for...

I have a 10 month old bloodhound, and I want to train him to track deer and hunt coons or squirrels. Beyond the basic training any dog should have, whether a pet or a dog who will get specialized training for a specific purpose what, specifically, should I do to train my dog to track deer and hu...

The covariant powerset functor has a well-known monad structure, but is this monad structure unique? By the Yoneda lemma, there can be only two natural transformations $1 \Rightarrow \mathcal{P}$ and only one of those can work as the unit of a monad. But is the multiplication also unique? As an a...

Does anyone have a counter-example of the following statement : Let $f : [0;1] \to [0;1]$ a continuous function w.r.t. the usual topology. Let $A_n(x) = \frac{1}{n} \sum_{k=0}^{n-1} f^k(x)$ for $n \ge 1$, $x \in [0;1]$. Then $\forall x \in [0;1]$, $A_n(x)$ converges.

As far as I can tell from this wiki page, this note (B#6) is still playable on a flute, though it’s not easy: But how quietly can it be played? Can it be done in pp or p dynamics?

My lamp specifies that the bulb limit is "60w Incandescent / 10w LED" LEDs are more efficient and give off less heat. Shouldn't I be able to put in a higher wattage LED bulb? (regardless of the brightness difference)

How can I prevent the File Open dialog from grouping files and folders by date modified? Here I wish to navigate to one of many subfolder in Downloads, which conventionally appears at the top of the list when sorted by name or type. However as the contents of the folder are unhelpfully grouped into

I want to place a caption inside a minipage which is placed inside a tight fbox: \documentclass{scrbook} \usepackage{graphicx} \usepackage{caption} \setlength{\fboxsep}{0pt} \begin{document} \begin{figure}% \captionsetup{aboveskip=0pt, belowskip=0pt}% \fbox{The text here is in a tight box!}\\...

To start off, this is working fine but in doing some testing I am not sure WHY the open drain output is not going all the way down to GND. I am using a MAX16055 power monitor to drive the power on reset into a Zynq 7000 SOC, a reset LED (driven from a 74AC14 inverter), and some other external res...

Will it harm me or is it meaningless to chant OM NAMAH SHIVAAY without initiation? If initiation is needed, how to get initiated as I don't have any guru?

I am a 20 year old electrical engineering student who loves old tech. I recently got a new CRT to replace my old one for my setup but this one has a small 7 segment display at the bottom left of the monitor. The monitor is a Darius with the (I can only assume) model number HRN-14LR. Could someone...

When applying for a TT job in a cross-disciplinary humanities program, it seems important that I describe potential collaborations with current faculty members in the program. Should I refer to potential collaborators as "Prof. Firstname Lastname" or just "Firstname Lastname?" For example, "There...

I'm not musician, but I'm trying to help my song with a song for his School. I took this image from from https://musescore.com/user/39593079/scores/17210254 As you can see in measure 13: What is the name for under bar and the 3 number? Is is Triplet? How to create the same in MuseScore 3 withou...

Canada–India diplomatic row There has been a diplomatic standoff going on between India and Canada for some time now regarding the assassination of Canadian national Hardeep Singh Nijjar by some Indians. Even if the Indian government approved that assassination, what is Canada going to achieve ...

I've seen Spin Launch several times, a system where payload/rocket is spun up to a certain velocity in a vacuum and then "thrown" into the exosphere or space. I found this concept of "throwing" rockets quite interesting and potentially effective. I can't help but wonder if there's any other such ...

"Finger sandwiches" is another name for tea sandwiches, those crustless sandwiches served for afternoon tea: (Image: Wikimedia Commons, Payton Walton) In this ELL post there's a side-disagreement of whether the word "finger sandwich" is because it is eaten with your fingers ("finger food") or f...

In some Spanish language social media posts and websites the following poem is attributed to Anna Akhmatova: Mi vida ha transcurrido en algún sitio/ del que yo estaba ausente./ ¡Cuántas veces se levantó el telón/ y la escena vacía/ en vano ha esperado por mí!/ ¡Cuántas veces/ tendió el amor los ...

If we consider sequence $a$ where every $a_n$ is a rational number, then we can have a sequence, where: Every $a_n$ is a rational number Limit of $a$ as $n \to\infty$ exists Limit of $a$ is not a rational number A good example of that could be some "infinite fraction tower", like $1+\frac{1}{1+...

Cayley's theorem says that any group embeds into $S_n$, the symmetric group, i.e. permutations of a set, i.e. $\operatorname{Aut}_{\text{Set}}(n)$, for some cardinal $n$. From general algebra, we also know that any abelian group embeds into $(\mathbb{Q}/\mathbb{Z})^n$ for some cardinal $n$, where...

This is a word division puzzle which uses cryptic clues. If you're unfamiliar with either or both of those, you can click the associated link. In order to solve the alphametic, you'll first need to fill in the dividend, divisor, and quotient by solving the cryptic clues. I've left the enumeratio...

I'm installing a ceiling fan into what has been confirmed by my electrician to be a fan-rated box. Before I got here, there was a blank plate installed over the box, of a type I was unfamiliar with, that had no screws, and was press-fit into this bracket installed on the box (with two ~1" grabber...

I am trying to change the font of a glyph inside a TikZ \pgftext block. However I get the error that appears to be a stack-overflow caused by \pgf@selectfontorig expanding to something that contains \pgf@selectfontorig. I've spent about half the day Googling and reading docs and source code, and ...

I'm planning a trip to Japan next year - Tokyo, Osaka and Kyoto. We would like to rent a bike in Kyoto, can you tell me your experience with parking them in front of temples?

What is the good way to pass remaining options to another class? \begin{filecontents}{main.cls} \ExplSyntaxOn \tl_new:N \l_cookbook_cls_option_tl \newcommand{ \selectedoptions } { color } \keys_define:nn { class / options } { theme .choices:nn = { bw, color, dark, draft } {...

An overall average grade is pts earned/total points possible, so if, for example, I have a 75% average in the class, or a $300/400$, why does getting 75% or above on any assignment bring this average up? I tried to solve for $$\frac{a+x}{b+y} > \frac{a}{b}$$ $$ab+bx > ab+ay$$ $$bx > ay$$ $$x > \f...

Is there a way to constrain transforms to faces? I am trying to move the selected vert in the image to the right a little (I am aware this can be accomplished with the knife tool, but I'd prefer to simply be able to directly nudge the vert).

Logical monism is often described in papers as the position that there is one "correct" logic (or consequence relationship; I have seen "genuine logic" and "true logic" in papers too). Pluralism gets described as the position that there are "multiple correct logics," and nihilism as the idea that...

Link to question Grandmaster Lev Alburt plays at least one game of chess a day to keep in shape and not more than 10 games in any consecutive seven-day period to avoid tiring himself out. Is it true that if he plays long enough there will be a series of consecutive days during which he will play...

I want to automate sending emails to Customer Community users that their password will expire in 7 days Our Customer Community users use several different profiles, each with their own Password Policies (90 days expiration, 180 day expiration, etc.) New Customer Community Profiles get created fr...

This was mentioned in a side conversation and this sounds interesting. Basically, it's a movie where humans (who are actually clones) are mining extraterrestrially. Whenever one of them dies, they're replaced by a clone of themselves. The clones aren't aware of them being clones. Memories are use...

I was surprised to run out of inodes on a filesystem that was formatted relatively recently. When I compared it to another filesystem that was formatted on an older version of Debian (unfortunately I don't know the precise versions used), the older filesystem had over twice as many inodes despite...

家の中心に中庭がある。 白い石が敷き詰められていて、遊ぶには滑るし足が痛かったから、彼にはただの空間であったのだが。 とはいえ居間の縁側や廊下は全て庭に面しており、見ない日は一日としてなかった。 The character is describing his childhood home. He says there is a garden but since he can't play in it for him feels like empty space. What I'm stumbled, is what is としてなかった。 here? "見ない日" is day he ...

My understanding is that the motor shaft is connected to the rotor using some sort of clutch so that if the engine shuts down the helicopter rotor can keep spining. However I've heard of some helicopter fatal accidents that happen after some sort of mechanical failure in the engine(like something...

Happy Halloween! This problem by Miguel Ambrona, 2024, has the following stipulation. We don't know which way round the board is, but we are told that one player retains castling right. Which side is White: the reds or the blues? This problem gives an example of a so-called "chess vampire", i.e....

I would like to plot the following function $$ f(m)=-2 \sum_{k=0}^{\infty}\binom{1/2}{k} \left(2^{2(k-1)}-1\right)\zeta(2 (k-1))\left(m^2-\frac{1}{4}\right)^k $$ I am only interested in $m$ between 0 and 1. I can't plot it with infinity as an upper bound; it appears as an error message: This co...

In Chernobyl Prayer (or Voices from Chernobyl), the widow of a clean-up worker talks to Svetlana Alexievich about the heroism they believed in before the demise of the Soviet Union and says, At one time, I envied heroes. Those people who had a part in great events, when everything was in the bal...

In the tng episode Aquiel a Klingon Commander named Morag was suspected of killing a Stafleet officer aboard a subspace communications relay. He denied the killing but, under pressure, admitted to stealing multiple messages from the relay station's files- does anyone know if he faced consequences...

From this code. \begin{enumerate}[align=left,label=(\arabic*) :] \item x \item x \item x \item x \item x \item x \item x \item x \item x \item x \item x \end{enumerate} Will get this. How make the colon stay in the same align.

Moses is unique in the Hebrew Bible as the only Priest-King of Israel. There is also, of course, Melchizedek and probably some pagan Priest-Kings of other nations in the bible as well. Something that I've learned since I've started participating on this forum is that one traditional belief is tha...

I asked this question on the Philosophy StackExchange, as some belief systems have deep belief that everything is on a spectrum of polarity/opposites: What philosophies don't say things boil down to polarities (opposites)? What does Buddhism say about polarities/opposites? Does everything have ...

Lots of guitarists look at their fretting hand while playing. While this makes sense when learning, even very accomplished players do it and it just seems to be a bad habit. Those who play and sing or make eye contact with the audience or need to watch the drummer tend not to do it, or not much. ...

Bertrand Russell in 1903, in Principles of Mathematics, reflecting on the situation in the field of symbolic logic at the time, says that symbolic logic has three parts: The calculus of propositions, the calculus of classes and the calculus of relations. He also discussed an example demonstrating...

In plain.tex, insertion commands are defined as \newinsert\topins \newif\ifp@ge \newif\if@mid \def\topinsert{\@midfalse\p@gefalse\@ins} \def\midinsert{\@midtrue\@ins} \def\pageinsert{\@midfalse\p@getrue\@ins} \skip\topins=\z@skip % no space added when a topinsert is present \count\topins=1000 % m...

I have a 2 car garage that was either split at one point or it was always like that. There is an apartment above and I want to remove most of the wall between the 2. Is there a calculation I can do to determine how much of the wall I can take out and how big the beam needs to be. Concrete floor, ...

I'm teaching a student who is quite good - whenever we work on problems together, they tend to get most of the solution pretty easily. Occasionally they might need hints, but it's uncommon for them to make no progress on a problem. They are not a top student and will not be winning any competitio...

From Gradshteyn and Ryzhik, there's a formula that states for $a>0$ and $b>0$: $$\int_0^\infty \frac{x\tan(ax)}{x^2+b^2}dx = \frac{\pi}{e^{2ab}+1}$$ $$\int_0^\infty \frac{x\cot(ax)}{x^2+b^2}dx = \frac{\pi}{e^{2ab}-1}.$$ However, according to WolframAlpha these integrals diverges. Are these formul...

Fraktur was the dominant typeface in Germany for centuries until the Nazis suddenly stopped using it in WWII. I read citation needed that the Nazis, before they suddenly marked Fraktur as "Jewish" in 1941, tried to introduce Fraktur typewriters in 1933 but quickly gave up. That inspired my questi...

What is the probablity that any $4$ numbers arbitrarily selected from the set of natural numbers will have a product that ends with either $1$, $3$, $5$, or $7$. As the product yields an odd number, I considered all end digit cases for the $4$ numbers which are odd and subtracted those cases wh...

Currently reading David Graeber's Direct Action: an ethnography and he mentions "taking [...] the principle of moral autonomy seriously" (p 223). I wondered if anyone here could explain this principle in a more simplified way? Thanks.

So, coming across what QLStephen could do, I brewed it at once in the hopes of having the Quick Look functionality for most of the "text-based" files, as it advertises. However, to my disappointment, nothing was affected. I found temporary relief to find that the exact issue had been discussed he...

In a paper I am reading, the following seems to be claimed: Let $f:[0,\infty)\to [2,\infty)$ be a continuous, monotonically increasing function with $\lim_{x\to\infty}f(x)=\infty$ and let $\alpha>3/2$. Is it true that $$ \int_0^\infty \frac{f(x+1)-f(x)}{f(x+1)\big(\log(f(x))\big)^\alpha}dx $$ is ...

I'm trying to get selected objects from outliner running an operator from 3d view. In outliner 2 objects selected (one hided: 'eye' disabled). Running an operator from any other area (Text editor, Properties, Node editor) withing F3, get proper selection, but not from 3d view. What I'm doing wron...

Question Find values of m for which the below integral is zero. $$\int_0^{2\pi} \cos(x)\cos(2x)\cos(3x) ....\cos(mx)dx$$ My Approach By trial, I found $m=1,2,5$ but cannot find any method I know $2\cos(x)= e^{ix} + e^{-ix}$ but I want to apply it, how to apply it here? I applied King's too but it...

This table below in a 1 Form A SSR (VORA1010M4) datasheet is confusing me. It shows the max turn-on current as 2mA but then the forward voltage test current is 5mA. In the table for turn-on times I also see a test current of 5mA. In another 1 Form A SSR datasheet (CPC1017N) I see a max turn-on...

The usual baby step giant step algorithm has a complexity in $O(\sqrt n)$ in both memory and number of operations. I read several time that it’s possible to increase the memory complexity in order to decrease the number of computations : this something interesting in my case since I have enough m...

I'm attempting to use an NPN transistor as a switch in a 3.3V electrical circuit, and have been encountering some difficulties getting it to work properly. I have a basic understanding of electronics and transistors. As far as I understand it, an NPN transistor can let current pass from the coll...

This question is related to this one. COVID brought voting by mail into the spotlight. What would it take to have the absolute right to vote by mail? Is it as easy as just amending the constitution, which is not easy at all or is there another way to mandate that all states offer voting by mail?

I know that TLS MitM can get HTTP/S traffic decrypted when using certificates. I'm wondering if it has the ability to decrypt the Apple Airdrop protocol as well as it doesn't go through a server and uses WiFi Direct to create a peer-to-peer connection?

I'm trying to fit a rotated parabola with curve_fit, but it doesn't fit well as shown below: I'm already trying to fit the curve with respect to the cos(𝜃) and sin(𝜃) dependency as follows: def rotated_parabola(x, a, b, c, theta): # Original parabola y = a * x**2 + b * x + c # Rot...

Bus-connected devices almost always have a "high-impendance state", but I don't find where in the data sheet this is really defined. My question is this: what does an input see when connected to a Hi-Z output? I'm considering for concrete purposes 74HCT-series parts, but I'm trying to understand...

I'm trying to get numerical solutions to a double-well potential in regards to the inversion of an ammonia molecule. This has been done before, and I'm trying to replicate literature results with Mathematica's modern methods. According to the literature, the Manning-Rosen potential for ammonia is...

Let $I_n = [0, 1-\frac{1}{n}], n \in \mathbb{N}$ be a sequence of intervals. Is the statement (1) or statement (2) true? \begin{align} \lim_{n \rightarrow \infty} I_n = [0,1] && (1) \\ \lim_{n \rightarrow \infty} I_n = [0,1) && (2) \end{align} where the expression $\lim_{n \rightarrow \infty} I_n...

I am reading Introduction to Real Analysis by Robert G Bartle, and while reading it I was quite confused at the property of Completeness of real numbers. The author introduces the fields Q and R and compares them by saying that they both are fields and both of them are ordered, but √2 belongs in ...

My family will be moving to Russia in a few months. We don't know where yet. Though we have no interest in Moscow or St. Petersburg, if that helps. Where I live in Albania, local language courses cost a year's salary, per month. So no one can afford them. In the USA, and Japan, you can learn for ...

I'm working with the eval/dev-kit of the RA8D1 MCU and the external memory bus on their schematic has 4.7K pull-ups on the 16-bit SDRAM data-lines. (from https://www.renesas.com/en/document/sch/ek-ra8d1-v1-design-package?r=25452351) To be clear, these are pull ups and not series impedance matchi...

https://www.holy-bhagavad-gita.org/chapter/6/verse/27#:~:text=BG%206.27%3A%20Great%20transcendental%20happiness%20comes%20to%20the,and%20who%20sees%20everything%20in%20connection%20with%20God. प्रशान्तमनसं ह्येनं योगिनं सुखमुत्तमम् | उपैति शान्तरजसं ब्रह्मभूतमकल्मषम् || 27|| praśhānta-manasaṁ ...

Good time of day! As I think I have the following problem with Gen option in TD-DFT computations in Gaussian 16. I provided optimization with the following input successfully. %mem=16GB %nprocshared=8 %chk=TaOCl.chk #B3LYP/Gen pseudo=read opt freq IOp(5/13=1) scf=(XQC,maxcyc=40) P...

I've been thinking about calibrating a custom made potentiostat (essentially a multi-frequency impedance meter) that measures impedance of the test object under multiple frequencies with a four-terminal connection. The frequency range of tests are generally within 0.01 Hz to 10 kHz and the impeda...

I recently built two firewood stands, and I want a convenient way to hold tarps over the firewood. I have decided on carefully placed hooks to hook the tarp's grommets on. Hooks curved on a single plane are easily available. I'm after something more sophisticated - hooks curved in two planes. I...

How would I go about drawing an image behind the text of (sub, sub)section titles? I looked into various packages (e.g. background, tikz, tcolorbox), but every time got lost in overly complicated examples, that did something just slightly different. I expect any of those packages be able to do it...