The beginning of a PhD typically involves taking courses, and if you’re lucky, you might have close supervision throughout your PhD, where someone teaches you useful skills and shares knowledge. Above all, a PhD requires writing a thesis. However, the final phase of a PhD can also involve signifi...

I'm encountering an issue with the latest version of ConTeXt (ver: 2025.02.24 16:28) where the command \mathgreekupright does not seem to affect some Greek letters, depending on how they are input. For example, consider the following example: \startTEXpage[offset=5pt] \m{\alpha, \pi, π; \mathgr...

This is an extension of the question asked here: Colorizing Arched Words within a Tikzpicture Consider the code: \documentclass[12pt]{book} \usepackage{tikz,xcolor} \usetikzlibrary{decorations.text} \definecolor{cranberry}{RGB}{194, 79, 93} % Overlay Title \newcommand{\mytitle}[1]% #1 = title {\...

I am trying to run native QGIS functions through python (programatically) while exporting the output in two different ways : Exporting output into a physical file : processing.run("qgis:listuniquevalues",\ {'INPUT': vlayer,\ 'FIELDS' :'Rendement',\ 'OU...

To try and better understand the structure theorem of finitely generated modules over a PID, I wondered how exactly it would be possible to clarify finitely generated modules over a localisation of $\mathbb{Z}$, like $S^{-1}\mathbb{Z}$ where $S$ is the set of prime powers of $p$ for example. I kn...

The question Uncrewed Lunar Probe Transit Times.....Space Age Era vs Contemporary asks why uncrewed transit times are longer than crewed missions to the same destination. Comments mention that the added mass of consumables favors fast, inefficient orbits rather than longer, more efficient orbit...

I recently updated zsh and homebrew, and cannot determine where the error arose. When I launch vim, I see the usual syntax highlighting like this: The moment I interact with vim in any way (cursor movement, mode change, commands etc) the syntax highlighting changes to this: I've tried the follo...

I'm using the XCharter and upgreek packages. The \upmu is just a tad too small for my taste, and I want to define a command that prints a mu slightly larger (no more than a 10 pixel difference). Does LaTeX support this kind of fine adjustment? If fine size adjustment isn't possible, is it possibl...

It is well-known that $$\det(A) = \sum_{\sigma\in S_n}\mathrm{sgn}(\sigma)a_{1\sigma(1)}\cdots a_{n\sigma(n)}$$ for an $n\times n$ matrix $A$. I would like to understand what the double sum $$\sum_{\sigma\in S_n}\sum_{\sigma'\in S_n}\mathrm{sgn}(\sigma)\mathrm{sgn}(\sigma')a_{\sigma'(1)\sigma(1)}...

I'm looking for a theory that explains the price of a resource A, taking into account : that the producers of A, as individuals, are in competition with each other and will therefore tend to sell at a price that depends on the equilibrium between supply and demand. that the producers of A, taken...

I'm an American. Do I need a transit visa for a 2 hour layover in Reykjavik heading to Ireland?

I'm getting two different answers to a simple probability question that I can't seem to reconcile. You place three dots along the edges of an octagon at random. What is the probability that all three dots lie on distinct edges of the octagon? I first compute the probability directly as $\frac{8...

In a rectangular array of people, who will be taller – the tallest of the shortest person in each column or the shortest of the tallest person in each row? Source: World’s Greatest Riddles and Brain Teasers, by Edward Scarz. Bonus question: Let's say that there are m rows and n columns in the arr...

I am calculating formation enthalpies and the conversion from the eV output of most DFT software to the typical experimental kJ/mol is confusing me. Doing a Google search, I get that 96.485 is the conversion factor, but half the results say it is for eV to kJ/mol, while the other half say it is e...

How do I tell my direct report to stop kissing so much ass. Basically my question - it's weird, if I was a woman or both of us not straight, I' d think he was hitting on me. He's really good at his job and really competent and I let him know that but still, it's over the top. He's remote and in I...

I am trying to figure out how to evaluate this integral $$ \nabla_x \int_{B_R(x)} f(y) \,\Bbb dy, $$ where $B_R(x)$ is the ball of radius $R$ and center in $x\in\mathbb{R}^d$. Here, $f$ is an integrable function in $L^2(\mathbb{R}^d)$. Is there a simplification? Thanks in advance.

How can I find the average distance between two points randomly chosen (independent and uniform) on the surface of a unit $n$-cube. I am specifically interested in the closed forms of this average for a square and cube. The related problem of determining the average distance with two points in ...

In conjecture from this question exponential distribution, probably, is corner case among log-concave absolutely continuous probability distributions. Note that \begin{equation}\tag{1}\label{sum} a_0 + a_1\xi_1 + \ldots + a_n\xi_n \end{equation} is absolutely continuous and log-concave random var...

It looks like that in Wolfram Mathematica 14.2 (Windows, Linux, Mac) AllowInlineCells does not work as advertised. In the AllowInlineCells ref page the "Basic Examples" second NotebookRead[sel] is supposed to be different from the first one. But it is not. how to fix this, at least in a simple ca...

Let $\mathcal C$ be an $\infty$-category, let $K$ be a simplicial set, and let $G : K \to \mathcal C$ be a functor. Suppose that for each vertex $p$ of $K$, I have a monomorphism $F_p \to G(p)$, and for any edge $p \to q$ in $K$, the composite $F_p \to G(p) \to G(q)$ factors through the monomorph...

気が is キガ{LH} and 木が is キガ{HL} — you can clearly hear a difference. but what about when the words are pronounced in isolation, without a particle? as in それ、木 'that's a tree' or something like that. can you hear a difference between 木 and 気 in those contexts (so, キ{H} for 'tree', キ{L} for 'spirit')...

I just installed a bathtub, one of those cheap, lightweight enamel-coated steel ones from Lowes. But I didn’t find out about the trick of placing it in a bed of mortar til it was done. It’s just sitting on the subfloor (actually, two layers of the old linoleum). It’s held in place by the tile fla...

I found the following in man bash as a definition of interactive shell: An interactive shell is one started without non-option arguments (unless -s is specified) and without the -c option whose standard input and error are both connected to terminals (as determined by isatty(3)), or one starte...

An experienced, competent road cyclist and MTB rider said: I plan to do a pine cone lap of short bays with a back pack one day. and I have no idea what he meant. He's not available to ask for clarification - what is a pine cone lap ? Short Bays is a popular local cycling route with two climbs...

I noticed that it's a bit finicky to tension the chain, get my rear wheel straight in and don't damage the fender on my 20 inch transporter bike with an IGH. In the past I've used chain tensioners on a single speed that allow for very fine adjustments of chain tension by pulling the rear axle bac...

Given arguments arg1 and arg2 and function f I want the output to be result. (arg1 and arg2 are of the same length, in the example of length 4) f[#, x1] & /@ {y1, y2, y3, y4}; f[#, x2] & /@ Rest[%]; f[#, x3] & /@ Rest[%]; f[#, x4] & /@ Rest[%]; result = {%%%%[[1]], %%%[[1]], %%[[1]], %[[1]]} {f...

In story by Pu Songling I learn that 水莽/shui3 mang3 is a deadly herb, and people who die from it may become 水莽鬼/shui3 mang3 gui3. I believe that tone sandhi for three successive third tones does not have any universal rule, but depends partly on what you are saying. My question: Could 水莽鬼 be pro...

Let $A$ be some set in $\mathbb{R}^m$ with the property that it is easy (polynomial-time computation) to generate random elements $r\in A$. Is it then also easy to compute $$P_A(x)=\mbox{arg}\,\mbox{min}_{y\in A} \;\|y-x\| ,$$ that is, the set of elements in $A$ nearest $x$? You may assume $A$ is...

Consider the following curves which plot: NevVal[x_, y_, z_] = If[x < 5.3, Evaluate[ 10^20 Sqrt[1 - x^2/5.3^2] y^2*(Exp[-10^10*x^3*y^2*z] - Exp[-2*10^10*x^3*y^2*z])], 0]; reg[z_] := Block[{}, RegSens = RegionPlot[ NevVal[10^x, 10^y, z] >= 2.3, {x, Log10[0.02], Log...

I am writing a section in a literature review for an honours thesis on the use of 3D printed PLA sprockets. The only academic sources involving this topic don't do much in the way of analysis, essentially just mentioning they exist. There is a study by high school students that I have examined, m...

The Gauss-Wantzel theorem states that a regular $n$-gon can be constructed with ruler and compass if and only if $n$ is a power of $2$ times a product of distinct Fermat primes. Most known proofs rely on algebraic number theory, particularly Galois theory and field extensions. However, is there a...

I have this MWE: \documentclass{article} \usepackage{enumitem} \begin{document} \noindent \textbf{lorem} ipsum \textit{textblock 1}. \begin{enumerate}[label=\roman*.] \item $s_1 \rightarrow$ lorem ipsum \item $s_2 \rightarrow$ lorem ipsum \end{enumerate} \begin{enumerate} \item \tex...

[Lev 1:17 YLT] [17] and he hath cleaved it with its wings (he doth not separate [it]), and the priest hath made it a perfume on the altar, on the wood, which [is] on the fire; it [is] a burnt-offering, a fire-offering of sweet fragrance to Jehovah. Is Leviticus 1:17 about God-pleasing perfume?

Adhesive (Object Form Only). The mimic adheres to anything that touches it. A Huge or smaller creature adhered to the mimic has the Grappled condition (escape DC 13). Ability checks made to escape this grapple have Disadvantage. Say you shove a mimic away and it fails the save, does that break ...

General background on extended affine Weyl group: Fix integer $n>1$. Let $\widetilde W = S_n\ltimes \mathbb Z^n$; this is the extended affine Weyl group for $GL(n)$. It has generators $s_1,\dots,s_n,\tau$, where $s_i=((i\hspace{10mu} i+1),0)$ for $i<n$, $s_n=((1\hspace{10mu}n),(-1,0,\dots,0,1))$,...

Let me first explain what I do, it is simple: I design small projects (PCBs) often using ESP32 and ATtiny microcontrollers. I use relays, optocouplers, ICs, LEDs, microSD cards – the total power consumption of these devices is always below 1 A, often not more than 50 to 250 mA (excluding peaks), ...

In Perl, /a/i matches both A and a, so I don't have to write /A|a/. What is the easy way to write /４|4/ ? Yes, I'm talking about $ unicode ４ 4|grep U+ U+FF14 FULLWIDTH DIGIT FOUR U+0034 DIGIT FOUR Must I repeat each line, if (/大茅埔段３２(７|８|９).地/ || /大茅埔段32(7|8|9).地/) {...} or is t...

I have run into a trouble with Integral when I am reading the book Relativistic Quantum Mechanics and Field Theory by Franz Gross. The integral is on page 377, (12.5). The background is to evaluate the scattering amplitude for a bound state, where we have to evaluate a one-loop process within a Q...

According to Catholic doctors or Fathers of the Church, if Adam hadn't sinned, would we wear clothes? Or are clothes a consequence of Original Sin? St. Thomas Aquinas asks such speculative questions regarding the condition of Adam's offspring had he not sinned (Summa Theologiæ I q. 99, q. 100, q....