I'm writing something about sets "life rules" like The Rules - The Way of The Cycling Disciple. I want to relate a proposed "set of rules" to existing "rules/sets of rules" like Murphy's Law or the Cycling Rules. For example, Over the years, I've developed a few __________ that I think are usef...

These seven cosmic circles appeared in the night sky: For some reason, I was reminded of something my great uncle gave me long ago. It was like a disk, but he called it a "celestial key". He told me to hold on to it and that I would know when and how to use it. Here, I found it: Starting fr...

I've seen how good neural networks and large language models can be at generating content based on textual input, so I asked someone to make me an algorithm to do that... My instructions were quite clear, but it's been less than successful. If I describe my inputs and outputs, maybe you can figur...

By the work-energy theorem, we can justify that the work on a particle due to the net force equals the change in kinetic energy of the particle. In compact notation, \begin{align}\tag{1} W_{\text{net}} = \Delta KE. \end{align} This seems very useful. However, there are other contexts where work i...

Craft is based on the PHP framework Yii2. I heard that this framework is less and less maintained. And yes, it seems to be the case if you go on contributor page : https://github.com/yiisoft/yii2/graphs/contributors Question to @pixeltonic : how do you think you will you manage it ? Thanks

John 14:27 New International Version says: 27 Peace I leave with you; my peace I give you. I do not give to you as the world gives. Do not let your hearts be troubled and do not be afraid. what does peace mean? what is the definition in the biblical context? by the way, is there references that...

What's idiomatical, 'a small quantity' or 'a little quantity? For instance: This ingredient has a little / small quantity in this product.

I'm now working on a new hobby project, an audio amplifier using TDA2050 ICs in bridge configuration, to be fed by phone or PC earphone output. I already made the amplifier, it sounds fantastic. Two of these per channel. When I started looking for tone control circuits, I find those using op-amps...

I'm new to Solidity and it's my first try to write a smart contract using Openzeppelin, Pancakeswap and BEP20 libraries basically to make a BEP-20 token. When i try to deploy the smart contract, i get the following error : "invalid opcode: opcode 0x5f not defined" and in my case i know that the O...

Is there a cubic polynomial $c(x,y)$ with exactly 3 saddle point critical points? In other words, can a cubic polynomial in two variables have three critical points, all of which are saddle points? Or could it have the maximum 4 critical points (as per Bézout's theorem), with only one of them b...

Consider 猫が3匹います 1匹で食べています from 2m50s of this video. DeepL translates the bottom sentence as "I'm eating one of them", which I'm pretty sure is wrong :] From context, it seems to mean "One of these cats is eating". (But in the video the photo shows all 3 cats eating?) Grammatically speaking, is...

I tried to adapt the answer to Automatically add a final period if argument of '\paragraph' does not end with a punctuation character as a way to automatically add a period to a caption when there is none. For reasons I don't understand, this does not work out of the box. What is wrong (see Fig. ...

Let's say we have $k$ real numbers $a_1, a_2, \dots, a_k$ and a positive real number $n$ that satisfy the following constraints: $\sum\limits_{i=1}^{k}a_i=n$, $\forall_{i\in\{1,2,\dots,k\}} \quad 0 \leq a_i \leq \sqrt{n}$. Can we prove that the sum of squares of these numbers it not greater tha...

Working through the freeCodeCamp JavaScript curriculum and I found this RegExp task surprisingly tricky (maybe I just don't use RegExp very much). The parameters are: Usernames can only use alpha-numeric characters. The only numbers in the username have to be at the end. There can be zero or mor...

We're working on a video conferencing platform that allows users to upload private and public files. What copy is typically used for public and private sections? Below are some ideas: Viewable by everyone / Only viewable by you Everyone can see this / Only you can see this Everyone can see files...

Near the beginning of Season 3 of the 2D Clone Wars series, Anakin is knighted onscreen: YODA: Step forward, Padawan. Anakin Skywalker. By the right of the Council, by the will of the Force, dub thee I do—Jedi, Knight of the Republic. Star Wars: Clone Wars — "Cha...

There is a conspiracy theory doing the rounds on the internet that a 7000 year old ostrich eggshell held at the Nubian Museum depicts a drawing of ancient Egyptian pyramids. Curiosmos An ostrich egg, dating back around 7,000 years, allegedly depicts the three pyramids at Giza and the Nile River ...

If I take a piecewise linear function (piecewise affine) is it true that I can always write it as a sum of concave and convex functions? My understanding of this page https://mjo.osborne.economics.utoronto.ca/index.php/tutorial/index/1/cv1/t suggests that any linear function is both convex and co...

This is a follow up question from my question answered here: Why does a loop antenna not measure the differential magnetic field? Essentially I just found out today that we are actually measuring the derivative of the time varying electric field with an antenna, rather than its magnitude at a giv...

I have the following array. How can I produce a plot showing how fast A and B are accumulating? There are no options other than "A" or "B". votes = {"B", "A", "B", "B", "B", "B", "B", "B", "B", "A", "B", "B", "A"... Not certain if this is the correct approach, but the closest I have gotten is th...

I came across this joke while browsing the social medias of some piano dealers: I'm guessing it means the musician's New Year's Resolution is to remain the same as last year, but since I'm still lacking in music theory, I'm not sure to actually understand the joke.

I need help finding a short story I read in an anthology when I was very young (35-40 years ago.) I hope this rings a bell for someone. The story centers around a human who is revived from suspended animation by machines to pilot a space fighter in a war because (according to the story) computer...

In reading about brms, I came across the words "pterms" and "gterms" for "population-level effects" and "group-level effect". I was astonished. No, I was GOBSMACKED! Such sensible choice of terminology in statistics. How were they allowed to get away with it? More to the point, what makes "fixed"...

A lever and a fulcrum is able to to multiply the input force to the output force and trade moving distance for increased force. The same happens in automobile transmissions, taking advantage of high motor RPMs. What exactly is the physical mechanism behind this? I am very aware you can mathematic...

Let $u,v\in\mathbb{C}^2$. Let $u^\perp,v^\perp$ be vectors that are orthogonal to $u$ and $v$ respectively. Then $\{u,u^\perp\}$ and $\{v,v^\perp\}$ are two orthonomal basis of $\mathbb{C}^2$. Since the two are orthonormal basis, there is a unitary transformation $U$ such that $Uu=v$ and $Uu^\per...

When I plug in my guitar cable by itself in the amp (without the guitar attached) it makes a bad noise. I changed the cables and the noise is still there in the amp. Also, when I plugged just the jack without cable, it makes less noise. I tried different jacks to ensure that the fault is coming f...

Problem: I am trying to show that $$\frac1{3\pi}\int^\infty_{-\infty}\frac{dx}{\big(\frac89x^2+\frac23\big)\big(\frac{x^2}{3}+1\big)^{1/2}}=\frac13$$ This identity is link to the integral of the Airy function on $(0,\infty)$. I have made many attempts (substitution, contour integration ) to show...

When I do, say, a man zsh I get the zsh man page, parts of the text are in bold or underline, which makes it for easier reading. man is doing this for instance by inserting 0x08 control codes in its output, which then is interpreted by the Terminal for rendering underlined text. When I do a man ...

I'm using a hair particle system to spread objects over another but I want the object to be transparent or gone in the final render.

Bonjour, Je suis actuellement à la recherche d'une expression à peu près équivalente à I don't have a dog in this fight. [1] Je trouve (et là j'ai peut-être tort) que les expressions comme Ça m'est égal, ça ne me regarde pas, je m'en fiche/fous n'expriment pas ce que je veux. Plus précisément...

I am looking for a function $f: \mathbb{N} \rightarrow \mathbb{R^+}$ that satisfies these 3 conditions: There exist $c>0,k>0$ such that for all $n$, $f(n) \leq c \cdot n^k$ Let $b\in \mathbb{N^{\geq 2}}$. For any $d>0$, there exists $n_0$ such that for all $n\geq n_0$, we have $f(bn)\geq df(n)$ ...

Suppose I draw two sets of random integers from 1 to 100, one is size 50 and the other is size 25 (no repetitions within each set). How can I calculate the probability of the smaller set being a subset of the bigger one?

I have a setting I'm trying to get started on where the vast majority of mankind has been killed off, and all that is left is a speckling of small villages pieced together from the wreckage of society. The grown-ups in the setting were alive for the apocalypse. Most of them are pretty broken fro...

This question is a little on the softer and speculative side, so bear with me. Usually a measurable space is $(\Omega, \Sigma)$, a set $\Omega$ and sigma algebra $\Sigma$ of subsets. A measurable function $f:\Omega \to \Omega'$ is one such that for every $A\in \Sigma '$ we have that $f^{-1}(A)\in...

For example, if we really wanted to, could we, at least in principle, model electromagnetism just considering interactions between charged particles without using the EM field? That is, is it possible to predict all the same experimental results without bringing in the EM field (or the gravitati...

I travel to Europe once a year: It would be nice to be able to pay electronically in Euros. If one has amassed several thousand Euros. Is there an option (or a better option) than depositing Euros in an NYC bank and receiving a bankcard that spends in Paris / Rome / etc.? The goal is to keep th...

I am new to D&D, and my DM is letting me play the Mystic, as long as I am not a butt about it. I have chosen the Order of the Immortal subclass, which has unarmored AC calculated like a barbarian, but cannot use a shield: Immortal Durability [...] In addition, while you aren’t wearing armor or w...

I was riding home last night and heard a rhythmic noise from the rear wheel. On stopping I found this: The bead had parted company with the sidewall, and the inner tube was herniating out in a blister. The noise was this lump hitting a brake every wheel rotation. The tube is not punctured her...

Source Gita chapter 6 verse 8 jñānavijñānatṛptātmā kūṭastho vijitendriyaḥ yukta ityucyate yogī samaloṣṭāśmakāñcanaḥ Meaning :The YOGI who is satisfied with knowledge and wisdom, who remains unshaken, who has conquered the senses, to whom a lump of earth, a stone and gold are the same, is said ...

I've listened to many theravada buddhist sermons and something that is always mentioned is how everything that happens, happens for a reason. Does that mean that if we get sick, it's our karma to get sick, but then we get better because of our good karma as well? How does taking medicine fit into...

I am considering flying to the UK this summer with a small airplane. I heard that the daily use of the airspace is somewhere published by CAA (or NATS), including the activation of Dangerous / Restricted areas. I would like to be able to visualize them via a dynamic map (like the DABS in Switzerl...

My laptop is failing, but I know for sure the hard drive is okay and fine. I want to take the data inside it, I put my laptop's hard drive (open suse tumbleweed with btrfs filesystem) to my desktop pc motherboard (ubuntu 22.04.01 LTS with vfat filesystem) It could access the hard drive there is s...

If a probability density function (created using kernel density estimation) exhibits peaks (not necessarily the mode), can we infer the presence of clusters or subgroups in the data?

In this challenge, your input is an integer value. Your task is to find the sum of the range of the sum of the range of n. Examples: Input -> Output 1 -> 1 2 -> 6 3 -> 21 4 -> 55 5 -> 120 6 -> 231 7 -> 406 8 -> 666 9 -> 1035 10 -> 1540 This challenge should...

$\textbf{Nakayama's lemma.}$ Let $M$ be a finitely generated $A$-module, $I\subseteq A$ an ideal such that $I\subseteq \mathfrak{R}(A)$ Jacobson's radical of $A$. If $IM=M$, then $M=0$. I'd like to show that both the finitely generated hypothesis on $M$ and the inclusion hypothesis in the Jacobso...

I have written a python program for random password generation and as a newbie I would like my code to be reviewed by professionals and if they have any suggestions to improve it. import string import random letters = string.ascii_letters digits = string.digits special_chars = string.punctuation...

I wan to edit the totals of Invoice print in PDF format. If it was HTML page than its easy to inspect it. But I can't find where i can adjust the widht of a cell. As you can see the Discount text is overlapping. The file involved in printing is this. And here the code of my printing php file app...

I want to calculate, for each pixel, the proportions of returns between 0.5 and 5 m height above ground, compared to the total return count I have figured out how to do it for the entire las file, but how can I for each 10*10 m pixel? library(lidR) las = readLAS("C:/folder/lasfile.laz") #Normali...

As I am studying ordinary (non-supersingular) binary elliptic curves in the Guide to ECC book by Hankerson (Section 3.1, page 81), for point doubling, the equations presented in the book are: $x_3 = \lambda^2 + \lambda + a = {x_1}^2 + \frac{b}{{x_1}^2}$ $y_3 = {x_1}^2 + (\lambda + 1) x_3 $ $\lamb...

I have disassembled two motor circuits that use a Hall sensor. One is a cooling fan blower and the other is a 230 VAC motor. The blower has a brushless motor and has its Hall sensor on the stator board with the coils. The rotor is a solid magnet cylinder encompassing the whole stator. The motor h...

Context: "enum" as an abbreviation/short for "enumeration" This question is about pronunciation of the letter "E", not about the 'num' part. I've heard people say both "æ-num" (like in "assign") and "/ˈinʌm/" (like alphabet "E") as it says on wiktionary. Which one is correct? Are both correct? No...

I'm trying to make a node style in which some extra decorations will be drawn on top of the node. However, I'm having trouble getting them to be drawn on top of the node rather than behind it, as the following MWE demonstrates. Is there a way to achieve this? \documentclass{article} \usepackage{t...

I asked this question some time ago in MSE but I didn't recieved any feedback. https://math.stackexchange.com/questions/4672664/diagonalization-of-symmetric-matrices-of-functions This problem arised to me when I was trying to find an analog to orthogonal reference frames for singular metric tenso...

I think that I've taken the Open-Closed and Single Responsibility principles too far. Previously, I had one huge static class containing every method that has C# talk to stored procedures on my SQL Server. Here is one such method. public static void DeletePerson(int PersonID) { CallCommandAndH...

I have a list with 150 colors, all representing a type of object in a scene (for example: walls, ceiling, grass, cabinet, painting, water, chair, table etc). you can see the list here I want to create a reusable node group to quickly change an objects color. What I have done in the past (if i had...

we failed security review of second-generation managed package because Lightning Message Channel (LMC) has isExposed=true. It should be false. The value of isExposed is not possible to change to false, that's why we created new LMC, refactored code to use new one and now we need to delete old LMC...

How to remove all files with a pattern except the recently created file ls -l total 655748 -rw-r--r-- 1 jetty jetty 120579643 May 10 19:59 2023_05_10.jetty.log -rw-r--r-- 1 jetty jetty 115205809 May 11 19:59 2023_05_11.jetty.log -rw-r--r-- 1 jetty jetty 102921116 May 12 19:59 2023_05_12.jetty.log...

Let the given set of points points = {{395.4416644777464`, 207.63931734339303`}, {391.15890276860114`, 240.47382378017346`}, {382.59337935031067`, 219.06001523444706`}, {378.3106176411653`, 209.0669045797748`}, {369.74509422287485`, 177.65998537937617`}, {361.179570804584...

Solving in 13.2.1 on Windows 10 Solve[Log[a] + Log[b] == 2 && 1/Log[a] + 1/Log[b] == 3, {Log[a],Log[b]}] , I obtain {{Log[a] -> 1/3 (3 - Sqrt[3]), Log[b] -> 1/3 (3 + Sqrt[3])}, {Log[a] -> 1/3 (3 + Sqrt[3]), Log[b] -> 1/3 (3 - Sqrt[3])}} , but Solve[Tan[a] + Tan[b] == 2 && 1/Tan[a] + 1/Tan[b]...

I have created a fork of a project that is releases under GPLv3 (As per LICENSE-file, GitHub and README). However, contributions that are from the community are licensed under MIT. Now since I want to continue this project as a standalone one, I want to understand how I need to treat the upstream...

As the title suggests, I wonder for how long one can hold postdoc positions after having done the PhD (specifically Mathematics, where I am currently a finishing PhD-student). In other words; is there any limitation on the length of the "postdoc-phase"? I know that in some fields and some Univers...

I downloaded an animation from Mixamo and I wanted to make this animation run really slow, like a slow motion video animation. I basically want to make the character run normally than at a certain point(at frame 100 for example) I want suddenly go slow motion but with the character animation only.

I have this table but I need more vertical space in the rows for fractions, they are very tight. \begin{tabular}{| c | c |} \hline \rowcolor{green} $x$ & $g(x)$ \\ \hline $0$ & \\ \hline $3$ & \\ \hline $-2$ & \\ \hline $\dfrac{3}{4}$ & \\ \hline $\dfrac{-1}{2}$ & \\ \hline & $0$ \\ \...

I'm writing a paper about Ruth and I found a midrash that describes Boaz as being an infertile man (there are others that put the opposite). From Ruth's prayer, he is allowed to conceives. My question is: is there any explicit reference to another man in the TANACH as being infertile? Or is Boaz ...

Are there any images from the surface of the moon during lunar night? Preferably taken by Apollo astronauts, but otherwise by rovers etc showing "earthshine" on the lunar surface? I found this example from Apollo, but it is from the CSM, and I think it's from before landing? https://en.wikipedia...

I invested small amount of money 5 years ago and then panicked and withdrew it all, 10Trading was the company and I believe they were closed down, however periodically I receive emails suggesting I still have an investment of bitcoin that needs refunding to me as 10Trading is shut, Is this just a...

I am trying to teach myself real analysis but I faced some difficulty understanding this lemma. I can't understand why the sequence $$x_n >n$$ is defined isn't that enough to simply say assume that one point $$f(x_0)> n$$ then the any sequence that converge to this point in the domain of the fun...

When I've edited the child stylesheet for my site I'm encountering a problem where anyone who has already browsed my site will not see the correct version because their browser cache is using an old version of the same stylesheet. I have put some code in my functions file that's in the same fold...

I stumbled across this Reddit post which is a joke on the following code snippet, void f(int& x) { if (x != 1) { x = 1; } } void g(int& x) { x = 1; } saying that the two functions are not equivalent to 'the compiler'. I was convinced that any of the major C++ compilers would ...

I want to say if "field1" is (this or this or this) And "field2" is (this or this or this) then Z. What is wrong with my Expression? (There are more lines after the first, but I excludet them because they follow the same scheme). I tried replacing When with IN but that don't work either. CASE WHEN "

I am looking for a "thick" book on complex analysis, which also has historical details such as the motivation behind it. Which problem lead to the creation/discovery of a certain topic. E.g. what is the reason behind fundamental groups how is it in connection with topology. Thanks in advance.

I am trying to deploy The Hive 4 on a VMware Workstation 17 player VM to test Splunk integration with The Hive. I am following the guide at this link, but I encountered an error at one of the stages, namely when launching cassandra using the cqlsh localhost 9042 command: Connection error: ('Unabl...

In War 1.650ff, Josephus describes a confrontation between the Herod and the people over a statue of an eagle that he had put up over the entrance to the temple. What was the significance of this eagle? The eagle was a complex symbol in the ancient world. It was a Greek symbol of Zeus (an Egyptia...

I was thinking about getting some unleaded to a Rotax engine, and realized I could ferry some UL94 in the tip tanks of a Bonanza. Not that it really matters in real life, but let's say that I were ramp checked on my way out of the airport and I didn't have an STC for said UL94 (although it could ...

How can I improve this code? I would like to know if there is a better way of doing this. Also, is there some way that I can change the dimensions of the circuit diagram without needing to manually change the numbers? \documentclass{article} \usepackage{circuitikz} \usepackage{amsmath} \begin{do...

Dear all, I found this equation to estimate a RDD in a paper. $(f_i-f_z)$ is the running variable, hence $\alpha$ should be the slope to the left of the cutoff and $\lambda$ the variation in the slope between the left and the right of the cutoff for the function. But what does it mean the term as...

I have a knot about the "secondary" colours and its spectra. So If I look the spectra of white light, I can see that yellow, which is between R and G, has some wavelength. If I do an addition of light of Red and Green, I get yellow. Ok. Now If I do an addition of light of Red and Blue, I get Mage...

In some educational materials on bitcoin P2PKH transactions, I'll see 2 digits included in the front of what would be considered the ScriptSig. For example, what is the 8b in the front of the ScriptSig below representing? 8b483045022100a8205f5879952c6a931affae66519c4a4bda0d912dd166d89e7b671efddfd...

Manchester Airport UK goes to sleep at night. All public transport stops and all car rental depots are closed. If my flight arrives, say, at 2 AM, and I have only a small personal bag and no luggage to collect, where in the airport can I sleep for around 3 hours in a chair while waiting for the f...

I am using PublishManager.PublishSmart to auto publish items from master db to web db. New items which are in final workflow state are getting published as expected but for the existing items if I make the changes and reset the workflow state other than final, after auto publish runs this existin...

What is the inner/outer or mid radius of the 45 degree arc the following element makes? https://www.bricklink.com/v2/catalog/catalogitem.page?P=65473 I tried to align several of the elements in 90 and 180 degree arcs in stud.io, the end of the arc never seems to align with any modules, so I'm in...

(source) When they saw in neutral hydrogen wavelength they saw a neutral hydrogen bridge, while the Hubble Space Telescope concluded that the light from the quasar was redshifted. So if it's redshifted, how can a quasar be so near to earth? When the distances were measured the quasar was 1 billi...

We define the dot product of two vectors (A and B) as : a * b * cosθ which usually just says that it is the projection of A vector on B vector multiplied to give a scalar value. Although, I am not able to digest this idea completely and have these doubts: What does it actually mean to multiply t...

I want to use a custom font for emacs on arch linux. Therefore, I installed the package ttc-iosevka. Then I added the following line to my init.el: (set-frame-font "/usr/share/fonts/TTF/iosevka-medium.ttc") This file however, can't get loaded.. Running emacs with --debug-init: Debugger entered--...

I have searched quite a bit, but following points remains unclear. (1)Is it alpha maltose or beta maltose? (2)In other words, if we cleave amylopectin with amylase (α-amylase or β-amylase), which form of maltose is the ultimate result? I think, Maltose, which has axial anomeric hydroxy group w...

A response to a previous question indicated, “In a helicopter, aft cyclic (“pitching up” in a plane) will only serve to make the helicopter climb and slow down until it reaches equilibrium in the new attitude.” I understand that is not the same thing as a “retreating blade stall.” My question is:...

How can I execute a command only if a certain file exceeds a defined size? Both should at the end run as a oneliner in crontab. Pseudocode: * * * * * find /cache/myfile.csv -size +5G && echo "file is > 5GB"

How can I alias ... to ../.. in Bash? I am aware that other answers allow alias '...'='cd ../..' but I'd like to be able to address the directory two levels up with other commands, allowing for: cd ... ls ... realpath ... I have tried alias '...'='../..' but when trying to use this I get the fol...

I want to perform a loop (type within) on all the paths of a text. I tried to build a picture with btex ... etex but it seems that this kind of picture has only one element (length gives 1). I want something like the glyph example of mpman.pdf, but for a whole word. Is there a way? picture mots[...

In his answer to a recent question of mine, @egreg advised \newcommand instead of \NewDocumentCommand to define a container for a text. And I'm aware of this (10 years old!) question where: Joseph Wright answers “Conceptually, \NewDocumentCommand is intended for 'package authors' to define comma...

I've noticed that some cave icons on my map have checkmarks next to them while others don't. What does the checkmark symbol mean?

I think 100 dollar bills are common both in US and outside but not sure about euro. Seems like no? Asking because apparently having a 500 euro bill makes you look shady and cause hassle according to reports of some people which I find weird.

I am having a hard time solving this triple integral: $$\int_0^1 \int_0^x \int_y^x x e^{-z^2} \ dz\ dy\ dx$$ I tried doing u-substitution but I it repeats the same process as I solve. Another thing I did is to find the new bounds for the whole integral but I am not sure about it. I graph the orig...

Imagine a rock in the shape of a chessboard with pieces in a certain configuration. Throw the rock down a particular hill. The hill is shaped in such a way that, given the correct throw, the chessboard-rock will be chipped and flinted in a deterministic way as it rolls and bounces down. At the en...

Is there any documented difference between 10- and 11-speed GRX cranksets FC-RX600-10 and FC-RX600-11? Net search gives "closer chainring spacing", but I'm looking for a proof. Also interested in how the corresponding chaingings - WP-Y0K798010 and WP-Y0K698010 - differ; similarly, looking only fo...

From Nielsen and Chuang, the error correction criteria is $$P E_i^{\dagger} E_j P=\alpha_{i j} P$$ $P$ is the projector onto the correct codespace, $E_{j}$ are error operations and $\alpha_{i j} $ is a Hermitian matrix. Using this, how do I show that, the three-qubit repetition code can only corr...

Planning a design that has a 12V voltage source connected to a physical part that rotates. I need to conduct electricity from the rotating part to a fixed part which is connected (electrically isolated) to free-standing structure like a pole or a tower. I'm imagining the matching 'rotating' and '...

I am using the unicode-math package with XeLaTeX. It works well, but it is making some of my characters look weird. Specifically, the code f \colon x \mapsto x^2 looks different from normal. Normally, it looks like this: However, when I use unicode-math, it looks like this: In the second imag...

Solve[{TrigExpand[Tan[2 α]] == Cos[α]/(2 - Sin[α]), tanα == Sin[α]/Cos[α], 0 < α < π/2}, tanα, {Sin[\[Alpha]], Cos[\[Alpha]]}] It returns {{t -> ConditionalExpression[Tan[\[Alpha]], 0 < \[Alpha] < \[Pi]/4 || \[Pi]/4 < \[Alpha] < \[Pi]/2]}}, which is incorrect. the correct answer...

In the (unweighted) minimum k-cut problem, the goal is to partition the nodes in a given graph to at least $k$ subsets, such that the number of edges between different subsets is as small as possible. I am interested in a variant in which the number of subsets is not fixed in advance, but there c...

i'm trying to wrap a cylinder in a torus, the best i've done is the following code: Manipulate[ParametricPlot3D[{(2 + Cos[v]) Cos[u/(6 - gamma)] - 2, (2 + Cos[v]) Sin[u/(6 - gamma)], Sin[v] + 1}, {u, 0, 2 Pi}, {v,0, 2 Pi}, ImageSize -> 500, Mesh -> None, BoxRatios -> {2, 1, 1}, PlotRange -> {{-2 ...

How do Zsh distinguish utility/file if it's executable either binary or script, or just file, or shell builtin, etc, etc ?

How to prepare a list of the items in the following manner: i. Question ii. List item iii. Next item i. New list ii. Next question Below is the MWE of my attempt. The second item prints as '1. ii.' while I want the output to be simply `ii.' The margin for roman numerals should be aligne...

Let $p_i=x_1^i+x_2^i+\cdots+x_m^i=\sum_{k=1}^mx_k^i$ be the power sum polynomials. Then, the determinant of the $m\times m$ Hankel matrix $M_m=(p_{i+j-2})$, for $1\leq i,j\leq m$, has a neat evaluation $$\det M_{\color{blue}m}=\prod_{1\leq a<b\leq {\color{blue}m}}(x_b-x_a)^2.$$ Notice the number ...

The eigenvalue map in question is $\sigma: {\mathfrak gl}(\mathbb{C}, n) \to S_n \backslash \mathbb{C}^n$, from $n$ by $n$ complex matrices to $\mathbb{C}^n$ vectors modulo permutation of entries by $S_n$, and is known to be continuous. This map can be constructed by first considering the root ma...

I'm building a static webpage with php and Javascript. I have setup all my data in craft cms entries. I want to use ajax to retrieve the data from craft and just display it on my webpage. How do I do this?

Inverted: To the east of the building is the car park. Someone said my sentence was wrong. I want to explain to her that the sentence is inverted. I put the bold part ahead. Is the bold part called the adverbial? I put the adverbial ahead and therefore the verb should also be put ahead. Normal...

I am running a PHP app using FastCGI and in the Handler Mappings I see the following: Name | Path | State | Path Type | Handler | Entry Type -------------------|-------|---------|----------------|-----------------...

I have a shell function that looks like this: rebar3 () { set -o localoptions -o localtraps trap '/bin/stty sane' INT command rebar3 "$@" } How do I find out where command rebar3 is finding the rebar3 binary? I've tried the following, none of which work: % which rebar3 rebar3 () { ...

I want to create a Tex file to create something like the image below. Basically a letter underneath a cell. I don't really want to use a table. Any suggestions?

While calculating air pressure and temperature during cruise of jet engines, we consider that air comes into the jet engine inlet with our flight velocity. But why? In fact, air stops stagnant in atmosphere and aircraft moves with a flight velocity into air. During calculations, we say: "Static p...