I am writing a package that uses LaTeX2e loops like \@whilenum, \@whilesw and conditionals (switches) \ifx, \ifnum etc. I have not used package ifthen or expl3 so far and although I could, it seams odd to use it in just one loop at the end of coding process. So I would like a solution in the sty...

I learnt from egreg's elegant solution to typeset the below titlepage with authblk: \documentclass{article} \usepackage{authblk} \newcommand\CoAuthorMark{\footnotemark[\arabic{footnote}]} \title{this is an Example} \author[1]{AAA\thanks{Co-First-author}} \author[2]{BBB\protect\CoAuthorMark} \aut...

I read this short story back in the 1980's in a paperback which would've been in print by the 1970's. The giant 'trees' (asparagus-like?) filled their lower trunks and base with an explosive compound and acted much like a high velocity rifle with the evolutionary purpose of getting their seed-pod...

We have a Murray 1695539 snowblower. Problem is, while it runs fine, when we store it in our (attached) garage, it emits enough fuel vapor that the whole garage, and the breezeway between the garage and the house, reek of fuel, and we even have smaller quantities of fuel vapors entering the hous...

Let $ G $ be a group with a partition into conjugacy classes: $$ G = [g_1] \sqcup [g_2] \sqcup \dots \sqcup [g_r], $$ where the conjugacy class of an element $ a $ is defined as $$ [a] = \{g a g^{-1} \mid g \in G\}. $$ Suppose that for all $ i, j \in \{1, 2, \dots, r\} $, the elements $ g_i $ and...

Question Do the public and private keys contain the ip address? Scenario Suppose "Computer I" as client has a IP as 192.168.1.A and is generated for SSH purposes its respective pair of keys: The public key The private key Thus is possible do a SSH connection to "Computer II" as server where i...

When modeling I need to use Proportional Editing Mode. Then I realized that some vertices of the mesh should stay in place. Is it possible to completely prohibit the movement of certain vertices, while neighboring vertices move? Blender version 4.3.2.

Let $X$ be a separable metric space and let $\mathcal{P}(X)$ be the set of Borel probability measures. The topology of setwise convergence is the smallest topology that makes all maps $P \mapsto P(A)$ with $A \in \mathcal{B}(X)$ continuous. I know that this topology is not metrisable, and that it...

The frame door on my marble shower broke, so I installed a new all-glass frame. It looks great. However, when the metal shower frame was bolted to the marble at the door sill, it was removed, leaving a big stain where the glass shower door is. Any ideas on how to clean this off? I was thinking ...

My mother lives outside the USA, but is selling a property she has in the USA. I live in the USA. As she does not have a US bank account, she has asked if she can put the money from the sale in my bank account, and then have me transfer it out later to a location of her choosing. If I do so, will...

I'm trying to design a footprint in KiCAD for this P-Channel MOSFET. The datasheet seems to imply that the two central pads are connected to drain and source respectively, as are some of the outer pads: My question is, when designing the footprint, should I just have pads 1,2,5,6 and the centra...

As far as I know, the spell Tasha's Hideous Laughter differs from many other "named" spells in the D&D rules in that was not designed by or for a player character. Rather, Gygax one day received a letter from a young girl written in crayon, asking him to create a spell with laughter. Gygax also c...

I would like to visualize the derivation proof \documentclass[tikz,border=10pt]{standalone} \usepackage{amsmath} \begin{document} \begin{tikzpicture}[scale=2] % Parameters: Circle radius and number of segments \def\r{1} % Radius \def\n{8} % Number of segments \pgfmathsetmacro{\theta}{...

We read in Lk 7:31-32 (NKJV): 31 And the Lord said, “To what then shall I liken the men of this generation, and what are they like? 32 They are like children sitting in the marketplace and calling to one another, saying: ‘We played the flute for you, And you did not dance; We mourned to you, And...

I define multiple theorem environments by iterating over a clist, combining the environment name, displayed name, and background colour (rendered via tcolorbox). \documentclass{minimal} \usepackage{thmtools} \usepackage{tcolorbox} \tcbset{ thm/.style={ colback=purple }, ex/....

What is the probable mechanism for this ring expansion step: I expect $\ce{NaOH}$ would first deprotonate the acid group and the hydroxyl group(s), but I am unable to proceed further than this. What I could currently think of is that there has to be a decarboxylation step followed by dehydration...

I have an old stamp in my passport, as depicted below. My records says it should depict 23-Dec-2020. But there is a small c-like character, instead of 3 or any other digit, on the stamp right after the 2 associated with the day. What does this character mean?

I have this small code: Manipulate[ a1 = Annulus[{0, 0}, {1, 2}]; r1 = Rectangle[{-0.3, -0.3}, {0.3, 0.3}]; firstvec = a0*{1, 0}; secondvec = b0*{1, 0}; graphfirstvec = Graphics[{{Black, Thick, Arrow[Line[{{0, 0}, firstvec}]]}}]; graphsecvec = Graphics[{{Black, Thick, Arrow[...

I have a MBP M3. I attached an extrnal NVME SSD and I changed the folder file location of the brew --cask. I installed discord & figma with it on the external drive. Whenever discord has a new update, it gets wiped from the external drive which means I have to re-install it again. Same with figma...

I have a 1970s RCA CRT tester with some smoking resistors. They are brown with 8mm diameter , 17mm length and are rated 5.3 and 2 kohm. Doing some research, it appears based on diameter and length that I should replace with 10w resistors, but I read that dimensions on old resistors compared to to...

Before I use the Multiheaded Creature template in Savage Species, I want to make sure there isn't a more recent version somewhere that would supersede it. Is there?

How to make a amsmath-matrix inside a TikZ-matrix of math nodes look like a amsmath-matrix? % \documentclass{book} \documentclass[margin=5pt, varwidth]{standalone} \usepackage{amsmath} \usepackage{tikz} \usetikzlibrary{matrix} \begin{document} \begin{tikzpicture}[font=\footnotesize, ] % Matrix ...

There is a claim circulating, e.g. here on Mastodon: [...] in COBOL, if a date is missing [or "corrupt"] the program defaults to 1875 [...] The claim is sometimes "enhanced" by adding that it defaults specifically to 1875-05-20, the day the Treaty of the Metre was signed, and/or that this is so...

I've recently been awarded a postdoctoral fellowship by my country of residence, allowing me to work with a professor in the UK for two years. While the fellowship provides sufficient support, finances will be tight, especially since I have a family. I’m considering asking my future supervisor fo...

I have a tarmac sl7 dura ace di2 52/36 chain set with 11/30 sprocket Would you road bike climbing experts suggest the most effective/ efficient way to create an easier climb would be to simply swap the front chainrings for the 50/34 dura ace rings ? I realise that dura ace do not have a 32 or 34...

The digits from 1 to 9 are each used exactly once to write three one-digit integers and three two-digit integers. The one-digit integers are equal to the length, width and height of a rectangular prism. The two-digit integers are equal to the areas of the faces of the same prism. What are the dim...

I'm making a simple web service that (skipping other details) allows a user to upload a message that can be retrieved by another user but can be decrypted only with a certain key. The message is encrypted and decrypted on the client side and can't be decrypted on the server unless the key is some...

Looking for an animated (non-CGI) TV show, probably from the from 90s. It was about a weapon in the form of a boy, malfunctioning and revolting against its makers with befriended help. He can morph into almost anything with dangerous results, but is benevolent. We have already ruled out Astroboy

Until now, I have been using erewhon for my text font with \usepackage[utopia]{newtxmath} for my math font. However, I have started using merriweather as my main text font in my documents. I am now wondering which math font pairs well with merriweather. Any suggestions? I understand this is quite...

As I know the current flows momentary through the starter only when the bimetallic strip has bended and touched the other pin of the starter. As I understand when the 230V is applied between the starter pins the argon gas inside the starter is ionized and the bimetallic strip is heated up and ben...

I have a few polynomials. See below for example: polyList2 = { x^2*y + x*y^2 + 1, (* poly1 *) 2*x^2*y + 2*x*y^2 + 2, (* poly2 = 2*poly1, dependent *) x*y + 1 + 3/x, (* poly3 *) x^(-1)*y^2 - x*y (* poly4 *) }; vars2 = {x, y}; I want to find linearly indepen...

With the standard lexicographical ordering, consider the totally ordered sets $$\mathbb{Z}, \{0, 1\} \times \mathbb{Z}, \{0, 1, 2\} \times \mathbb{Z}.$$ Which pairs of these are order isomorphic? It's easy to see that the first set is not isomorphic to the other two: each segment $\left[ a, b \ri...

Report: https://web.archive.org/web/20140519113553/http://lessonslearned.faa.gov/PWA314/Cranbrook_B737_AccidentReport.pdf In the Cranbrook accident, the left thrust reverser deployed as the plane was lifting off of the runway. It crashed, and the voice recorder burned up in the fire. Some of the ...

We have a very new AC unit in the attic in northeast PA. It's cold in winters and the attic is cold and has air vents to the outside. The 8x12" AC vents in the ceiling are condensating severely inside in the winter when the heat is on in the home (so much that water runs out). Also, the inside of...

Mind blank Until the spell ends, one willing creature you touch is immune to psychic damage, any effect that would sense its emotions or read its thoughts, divination spells, and the charmed condition. The spell even foils wish spells and spells or effects of similar power used to affect the tar...

So i have this problem where I'm trying to find the Thevenin equivalent of a circuit, the load is resistance R4 and I'm trying to find the Thevenin outside the nodes A and B. I first open circuit R4 and and find Voc, then I short circuit R4 and find Isc, so the Thevenin equivalent would be a vol...

In a class that I think of as "Python for Poets," I occasionally come across student code that is syntactically valid, but isn't doing what the student thinks it's doing. For example, the student might be asked to write code to check whether a given year is leap. Here is what the student came up ...

The distance “400 parasangs” is mentioned quite a few times by Chazal, (and it’s almost always involved in a mystical sounding story). Some examples: Yoma 69b, The yetzer for idol worship- in the form of a fiery lion cub, lets out a shriek heard for 400 parasangs: אוֹתִיבוּ בְּתַעֲנִיתָא תְּלָתָ...

Republicans tend to win far more counties than Democrats. According to the Associated Press, in 2020, "Trump won 3,198 counties and New England townships, Biden won 1,380 and there were four ties." Can Republicans potentially award the election victory to the candidate who wins the most counties,...

What does 444 in the language options in 7-Zip mean? I use Windows 11 24H2 Pro and 7-Zip 24.09 x64.

Was just wondering why the Sonic Chaos Emeralds were named that, and found this reason. https://sonic.fandom.com/wiki/Chaos_Emerald/Miscellaneous#Trivia "Emerald" is [...] used in Japan as a generic term for jewels. If that's true, at least the Wiktionary isn't saying so, nor do I know where / ...

Are there other words where "eu" is pronounced like the letter u, or is "j'ai eu" an exception?

My wife and I speak languages A, B, and C. I am native at A and my wife is native at B. We are both highly proficient at C. We live in a B-speaking country. We want our upcoming child to be fluent at all three languages. Our plan is to alternate through the three languages on a daily basis. Meani...

Answer to Could space suits function underwater? by Jonathan Miller https://www.quora.com/Could-space-suits-function-underwater/answer/Jonathan-Miller-75?ch=15&oid=112651677&share=c86d354f&srid=C044h&target_type=answer This would most likely be due to differences in pressure inside the suit.

\documentclass{standalone} \usepackage{fp} \usepackage{tikz} \usetikzlibrary{automata} \newcount\nVal \newcommand{\drBinTNV}[4]{% \drBinTNV{x}{delta}{y}{n} % draw a row of n circles at a vertical level of y { \pgfmathsetmacro{\dx}{#2} \pgfmathsetmacro{\offx}{#1} \pgfmathsetmacro{\total}{(#4-1)...

I am moslty a newbie to Mathematica, although I have used it for a short time before. I am trying to simplify the following expression in Mathematica. Assuming[{f, f1, Nn} \[Element] Integers, FullSimplify[Exp[(-I f (-2 + 4 n + (-1 + 4 f1) Nn ) \[Pi])/(2 f1 Nn)]]] The answer I get is: $$e^{-\fra...

Let $M$ and $N$ be smooth manifolds, then a continuous map $F:M\rightarrow N$ is a smooth map if and only if the induced morphism: \begin{align} F^\sharp_U:C_N&\longrightarrow F_*C_M \end{align} on sheaves of continuous functions given by pulling back, restricts to a sheaf morphism $C^\infty_N\ri...

Or is that only mission specific training after they've officially graduated into the astronaut corps?

Enlightenment - Exploration Age Science Legacy Path What strategies should I be employing in order to achieve the Enlightenment legacy path? I know in general I should be using Specialists on urban districts -- but are there other general tips / strategems I ought to be keeping in mind?

Pirkei Avot says The Torah went from God to Moshe, Joshua, Elders, Prophets, Men of the Great Assembly. The people Moshe appointed to handle the small cases are called "Sarim" and were appointed over 10's, 50's, 100's, 1000's. These guys aren't in the chain. By making rulings, weren't these guys...

The diagram shows a regular pentagram. Circles of the same color are congruent. Wherever things look tangent, they are tangent. Are the red and green circles congruent?

Lots of settlement agreements contain NDAs and non-disparagement agreements. In theory, could the creditor say/post anything they like about the debtor with no repercussions before agreeing to the settlement? If the settlement agreement contained a confidentiality term that the agreement itself i...

The 2024 version of the Bard's Magical Secrets says: You’ve learned secrets from various magical traditions. Whenever you reach a Bard level (including this level) and the Prepared Spells number in the Bard Features table increases, you can choose any of your new prepared spells from the Bard, C...

Let's say I have a mesh surface with parallel edge loops marked with an attribute(always closed circular strip, the loop number may vary): I would like to convert those edge loops to curves and also add many curves in between them that would interpolate from one curve's 3d shape to the next one...

For better or worse, I hooked up my VT320 to my Linux machine. I'm trying to run some software on, but the serial connection seems to end up in a crashed state whenever somes emojis are rendered. Not sure if it's important, but in this case it was the 🎲 (die) emoji. Instead, I get a mirrored qu...

I was looking through Théotiste Lefevre's Guide pratique du compositeur et de l'imprimeur typographes, vol. 1 (1880), when I came across a symbol I didn't recognize. Does anyone know what this notation was used to mean? (I refer to the symbol directly following the equals sign)

I'm asking what is the correct/best solution for SEO for my website. I don't want to waste having multiple pages of duplicate content (only different by one image) hurt me in the long run. How a particular part of my website is setup: I have a page (multiple pages actually (think "single.php" wh...

Niko is a student at the University of Strasbourg with a rather peculiar mental condition, they have an irrational need for cybernetic enhancements, an extreme discontent with their organic body to the point of violence (to get cybernetics), self harm (to make cybernetic enhancement mandatory), e...

I’m hoping you can help me identify a favorite childhood book I’ve been trying to remember. I read this book as a kid around 15 years ago, but it felt quite old even then. It became one of my favorites; however, I moved around too much and lost the book. The story involves schoolchildren in space...

So while redoing some flooring in my laundry room, I discovered that whoever built my house in 1995 got real lazy and used a flexible foil pipe to connect the dryer vent in the wall through the floor and out the back of the house. After opening up the floor in a couple spots to run a new pipe, I ...

When Jesus was tempted in the desert in Matthew 4, Satan told Jesus to turn the stones into bread. In the Sermon on the Mount in Matthew, Jesus said that when a child asks their father for bread, he will not give his child a stone. Then in Revelation 2:17, we have this: He who has an ear, let hi...

I have done my PhD in Chemistry in 2021. I am not working anywhere at the moment because I have to take care of my toddler. I can make out time to review papers of others. Is it possible to review research papers of others if I am not working anywhere or not doing any post-doctoral research? From...

I am looking for a closed form for the following integral. If that's not feasible, an expression in terms of a series or integral is also acceptable. $-\frac{1}{4}\int_0^1\frac{ln(x)}{\bigl(\frac{x+1}{2}\bigl)ln\bigl(\frac{x+1}{2}\bigl)}dx$ What follows is an attempt at a solution. Consider I(s)...

Was looking at anthologies and found out that Michael A. Stackpole had two stories whose titles start with "Field": Field Test and Field Trip. I wasn't sure if they're related, but looking for more info about the latter found me Field Trip (In Hero Years Book 3). Are both Field Trip-s the same st...

I am simulating a basic inductor circuit 120V AC of 60Hz Voltage source with 2.65H inductor it has default of 1mOhms of series resistance. reactance should be (2 pie F L) = 999 Ohms or 1K the current should be 120V/1K = 120mA My problem: the current waveform is not showing the negative half but i...

https://www.youtube.com/watch?v=iYdQiW5YHFc In this video, the author argues that via the three upcoming special elections (1 in New York and 2 in Florida) Democrats could take the House back by winning just 2 of them. This would imply that Democrats are only 2 seats behind Republicans. But, when...

I am working on a geometry problem involving two circles, $O_1$ and $O_2$, with the following properties: Center-to-center distance: The distance between the centers of $O_1$ and $O_2$ is 5 units. Radii: The radius of $O_1$ is 2 units, and the radius of $O_2$ is 1 unit. Condition: There exists a ...

The following question is taken from JEE practice set. Three smallest squares are chosen randomly on a chess board. Find the probability that these squares have exactly two common corners but no common side. Given Solution: (Seems like they had a figure in mind but forgot to attach.) If the sha...

Is there a simple physical argument why lattice structures involving 3 and 4 fold coordinations as in graphite and diamond are not stable in radially symmteric pair potentials? I read in the bond order potential molecular dynamics literature as motivation that simple Lennard-Jones potentials do n...

Consider the transverse field ising model on a 1D line (or any sign changes or alternative variables that you prefer) $$ H=-J\sum_{<i,j>}Z_iZ_j-h\sum_i X_i \,. $$ Here X, Z are the usual Pauli matrices. Given an initial computational basis state $|\psi_0>=|b_1,\dots b_N>$ how do I efficiently sol...

I'm trying to modify the \section number color by modifying the \@seccntformat command. I'm trying to use \@ifnextchar to check if the next token after \section is the \textcolor command. If so, I want to change the section number to red, else, I want to keep it black. The following code illustra...

In the Dune novel, the word "literjon" is used to describe single liter of water. (As far as I can tell.) Many words in Dune have origin in old languages, or just mix of languages, however just adding "jon" to existing common word in English look, well, too "simple". Can anyone tell the origin of...

When I try to download the full installer for macOS Monterey 12.7.4 with softwareupdate I get the following error: softwareupdate --fetch-full-installer --full-installer-version 12.7.4 Scanning for 12.7.4 installer Install failed with error: An internal error occurred How should I diagnose thi...

Here's the poem "在西国怀王舍城" by 义净: 在西国怀王舍城 游， 愁。 赤县远， 丹思抽。 鹫岭寒风驶， 龙河激水流。 既喜朝闻日复日， 不觉颓年秋更秋。 已毕耆山本愿城难遇， 终望持经振锡住神州。 And this is my translation: Thinking to Rajagriha while being in the Western lands Roaming, in sorrow. The Red Country is so far: this is my only thought. The Vulture Peak’s cold wind...

This proof is from Terence Tao Analysis I, 4th ed. page 317, App. A: The Basis of Mathematical Logic. Proposition A.2.2. If 2+2=5, then 4=10-4. Proof: Assume 2+2=5. Multiplying both sides by 2, we obtain 4+4=10. Subtracting 4 from both sides, we obtain 4=10-4 as desired. My question is, for thi...

In the chapter "At Dawn" of Jhumpa Lahiri's novel Whereabouts, the narrator recalls "the words of a great writer underlined in one of my books": I flee, after a moment, terrified, from the great flame to the shadows; I fear the flame will consume me, that it will seize me and reduce me to an ele...

Let $\mathbb{F}_q(T)$ denote the function field over $\mathbb{F}_q$, where $q$ is a prime power. The norm in this field is defined by $ \left| \frac{f}{g} \right| = q^{\deg(f) - \deg(g)}, $ where $f, g \in \mathbb{F}_q[T^{-1}]$. Consider the field of Laurent series over $\mathbb{F}_q$, denoted by...

Please see the attached photo. The two switches on the left are blocking screwdriver access to the screw in the blue circle, any solutions? This type of setup is commonly found with Legrand switches, so I assume there must be a proper way to handle this. Thanks!

For now, I have only implemented a simple I2C protocol where only the master transmits the data. Also there is ack_bit for the I2C Address only. For state 5, i.e., data_byte its always acknowledged. I am just starting with Verilog, and this is my first big project so, please review my code and ...

Is there a way to declare an enumeration that has multiple representations, for example a numeric and a string? The intent here is to create an enum class with multiple values, each of which has 2 different representations, a numeric and a string. Either representation is valid and unique across...

Right clicking in ext4.vhdx file, selecting properties and security shows thousands of unknow accounts with full rights: Computer has only single user. User accounts are not created or modified manually . Why those accounts are created? Used icacls "full path to your file" /reset to remove the...

I published a mathematics paper on arXiv. Now I have found a much more elegant way to prove the theorem, although there is no error in the paper I have uploaded. There is much difference between the new and the old (ugly) proof, so I have to rewrite lots of lemmas (and the abstract). I have not s...

In the MWE below, I am not getting the result I would expect. \documentclass{article} \usepackage{fvextra} \def\a{} \def\b{\gdef\a{a}} \begin{document} \begin{Verbatim}[commandchars=\\\{\},breaklines] 1. \a 2. \a\b 3. \a \end{Verbatim} \end{document} The letter a should not appear on line ...

I wrote this code: n = 8; U = RandomSample[Range[0, n-2]]; V = Table[{Sin[2π k/(n-1)], Cos[2π k/(n-1)]}, {h, 0, n-2}, {k, -h, n-2-h}]; W = V /. Thread[V[[1]] -> U]; The code does exactly what I expect. On the other hand, I would like to get W directly from U, without passing through V, for examp...

In Frankel, Geometry of Physics, section 16.4e, he notes that the wave function of an electron over punctured space is given as a section of a nontrivial complex bundle - called the monopole bundle - over the punctured space. He then further notes: Finally, we wish to emphasise one point. If the...

Due to data loss, I have lost some keyfiles to access some fully encrypted drives. As always there is very important data on the drives and information I better not lose. The drives have been encrypted using only keyfiles, no additional passwords or whatsoever. The drives have been encrypted with...

A proficient LilyPond user recommends the following: Another essential practice is to notate voices separately. Never use \parallelMusic. [...] I started using LilyPond with \parallelMusic. That was a big mistake. It took a very long time to convert all of that music to separate voice blocks. \p...

I live outside North America, and am eligible for both the ESTA (US) and eTA (Canada). I would like to visit Canada followed by the US as a tourist, and in total I might stay for more than 90 days in North America, even though I will be staying for at most 60 days in each country. Most flight it...

I used align* environment to align the equations in two columns as shown in the photo. In addition to that, since the last equation is long, I would like the other equations to "ignore" its length to eliminate the awkward space. That is, I would like to "merge" the two "columns" in the last row. ...

In a school level text book I came across the definition of calorific value. It is defined in both ways: in per kilogram and in per unit volume at STP. The unit mentioned for per unit volume at STP was: kilocalorie/cubic metre. Is it correct? As the unit of energy is in calorie (cgs system) and ...

Assume that $X,Y$ are complex varieties and $f:X\dashrightarrow Y$ is a dominant rational map, that is $\overline{f(X)} = Y$. Is then $f(X)$ Zariski open in $Y$? Or at least does $f(X)$ contain a Zariski open subset of $Y? If $f$ is a morphism do we have that $f(X) = Y$? I think the assumption th...

I'm a poetry learner looking for a platform that allows me to share my work securely with a small group for feedback while preventing plagiarism. Specifically, I need a platform that: Allows controlled access (so only selected people can view my work). Provides tools to prove authorship and det...

I need to loop over a directory. I found this code from (here): \documentclass{article} \usepackage{l3sys-shell} \ExplSyntaxOn \NewDocumentCommand \inputfiles { m } { \sys_shell_split_ls:nN {#1} \l_tmpa_seq \seq_map_inline:Nn \l_tmpa_seq { \input {##1} } } \ExplSyntaxOff \begin{docume...

I did a project on compilation of few results in reverse mathematics few weeks back and had given an example of Group Axioms stating that those are independent of each other i.e. we can get a well-defined structure even though any one or two of the axioms aren't considered. For instance, the loop...

(cross-post) I’m transcribing (almost) every program from the People’s Computer Company magazines. In V2N6, Greg Yob begins providing his listings in a new dialect. Previously he used HP TS-BASIC, and the only mention of this change is a single REM statement that says “datapoint”. It is bizarre. ...

We read in Lk 7:19-23 (NKJV): And John, calling two of his disciples to him, sent them to Jesus, saying, “Are You the Coming One... Jesus answered and said to them, “Go and tell John the things you have seen and heard: that the blind see, the lame walk, the lepers are cleansed, the deaf hear, th...

Castle Greyhawk was the focus of the original D&D playtest campaign. In the new 2024 PHB, its location is to the North of Greyhawk, West of the Selitan river: But in the short story Expedition into the Black Reservoir (El Conquistador Magazine, 1975) Gygax described the location thus: To the ea...

I've checked this post where it is asked about the condition number for OLS as well. However, my question is more direct and conceptual, and less numerical. When reading the first pages of the paper TNT an expression of the condition number ($k$) was confusing to me. Below I expand and explain th...

I am renting a small cabin. The owner built it with the intention of using it for weekend guests. Not as a home to rented. I am trying to track down why a 15 amp breaker keeps tripping. Sometimes I have 3 space heaters going. One is 1650 watts. Another is 1500 watts.(Quartz) and the other is also...

Let $V,W$ be two n-dimensional inner product space, $F:V\to W$ an arbitrary map (not assumed to have any condition) such that $|F(x)-F(y)|=|x-y|$ and $F(0)=0$, with usual norm defined by inner product. I want to show that $\langle F(x),F(y)\rangle=\langle x,y\rangle$. It seems that polarisation i...

Ambrosia and Janiya are going to play a game of dominoes with all the usual rules, except that they have agreed that, at all stages of the game once a domino is placed, the total number of spots on display on the table must be a prime number. What is the longest (i.e. largest number of dominoes p...

My car was broken down yesterday. My car broke down yesterday. Are these two sentences the same?

For context, I work in an Aluminium smelter which has an enormous magnetic field, including in the tea break room. I'm trying to use a laptop (Dell Inspiron) here so I can get other work done, but my laptop only functions when the keyboard is oriented vertically. I understand/believe that the iss...

I'm trying to schematize a graduated pipette: I've already made the body of the pipette. I would now like to be able to add the graduations to look like this model (http://labo.pablo.free.fr/images/pip.jpg) but I don't see how I can proceed. Thanks \documentclass{standalone} \usepackage{tikz} \b...

In general, I have this initial data: n = 8; a = Range[0, n - 1]; b = RandomChoice[a]; c = RandomSample[a]; d = Partition[c, 2]; where n must be an even positive integer. Since I have to give an example now, let's assume it is: n = 8; a = {0, 1, 2, 3, 4, 5, 6, 7}; b = 7; c = {0, 7, 2, 6, 1, 4, 3...

I am a beginner user of the R programming language. I have a panel dataset that includes the number of males at a lek (Males), the number of fights per male (Fights), and several different lek sites (Lek = index number for lek sites 1-20), about 150 observations together. The aim is to test how t...