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...

In the context of general relativity, the Schwarzschild metric describes the spacetime geometry around a non-rotating, spherically symmetric massive object. The line element is given by: $$ ds^2 = -\left(1 - \frac{2GM}{c^2r}\right)c^2dt^2 + \left(1 - \frac{2GM}{c^2r}\right)^{-1}dr^2 + r^2d\theta^...

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....

Who is the subject of this mural at Novosadskog sajma in Novi Sad?

I am updating some LaTeX code, dragging it kicking and screaming to somewhere around LaTeX3. Most of it is my code, I am unlearning various old bad habits so that I can learn new and improved bad habits. :-) I found \IfBlankTF on page 8 of the LATEX for authors current version, 2024-10-22, usrg...

I have a method that returns an int[]. The array is made by filtering out only the even values of the array passed into the method. It works, but it's really ugly and inefficient. How can I condense this and do it more efficiently? import java.util.Arrays; public class SequentialSearcher { p...

I have a custometadata with a Long text Area field (LongTxtArea__c) which is exceed 255 characters long. Then I need to use replace method to replace the target by LongTxtArea__c value: Custom_MtDt__c customMtDt; [...] String target = 'sometarget'; textBody = textBody.replace(target, customMtDt.L...

A card shuffling machine always rearranges cards in the same way relative to the order in which they are given to it. The thirteen spades arranged in the order A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K are put into the machine, shuffled, and then the shuffled cards are put into the machine and shuff...

My goal is to make the following distinction: is my arg a one character or is it a \command like in these samples: {a} -> Yes {\AAllArrows} -> No. The problem of my code: it appends the string length to the output. I get {a} -> 1Yes {\AAllArrows} -> 12No. Here is my code \documentclass{articl...

I read this post: I'm wondering about the difference between "change into" and "change to" but I still don't get the rule in case of "changing name of file" or in case of programmers "changing class name". On the one hand the name may be something different and in this case I need to use "to". O...

I want to show a grid of parametric plots, which have a varying parameter a, with a caption under each plot, like this: The equations are x[t_] = Cos[t] * (Sin[t]^2 + a); y[t_] = Sin[t] * (Cos[t]^2 + a); I imagine I would need something like Grid[ ... (this is where the magic happens, as a func...

“If your hand causes you to sin, cut it off. It is better for you to enter into life maimed, rather than having two hands, to go to hell, into the fire that shall never be quenched—” ‭‭Mark‬ ‭9‬:‭43‬ ‭ Question: Does Jesus give a command/imperative to believers in this verse? If he does, doesn...

Say that judge Fern was the First to encounter a certain case where Law L could be considered relevant. Fern is more of a judicial activist and believes in an expansive interpretation of the law, so interprets L in a way that's borderline creating new law. Later on, a case that's essentially exac...

I'd like to talk a bit about the mind-body problem. We all know that intuitive dualism (Cartesian-style or its variations, aka "soul") is being firmly rejected by the academia on the ground of the so called "interaction problem", that is, because "we can't imagine how the physical can interact th...

As summer is coming to an end, I've noticed that my daisy plant that seemed to be doing very well earlier in the summer/ late spring, has begun to look very damaged. A lot of its foliage is crispy and is beginning to fall off. It gets a consistent water every day (double on hot days), so I'm not ...

How is the angle between two 4-vectors defined in special relativity? Consider two 4-velocity vectors: $$U^\mu=(1,0), \\ V^\mu=\gamma_{rel}(1,v_{rel})$$ Where the vectors are written in the frame of the particle with $U^\mu$. The dot product between these is $$U^\mu V_\mu=\gamma_{rel}$$ If we def...

This is clearly a very tough nut to crack, but there's no harm in trying. In December of the year before last, I came across a post by a girl in a Russian social network who was looking for two films. I recognized the first of them as "Creep" from 2004. She was incredibly happy about it. But I fa...

I have a pencil which has procedurally generated textures on it and I would like to bake these textures as a single image and place that image onto a duplicate pencil. I have made a duplicate pencil to bake the textures to. I have also UV unwrapped the duplicate pencil. But when I try to bake ...

I need to know the stabilizing capacitances for C5444548, because the datasheet does not indicate their values. 8MHz Surface Mount Crystal 20pF ±10ppm ±20ppm SMD3225-4P Crystals ROHS The link to the product is: https://www.lcsc.com/product-detail/Crystals_YXC-Crystal-Oscillators-XL2EL89CSI-111YLC...

I have a tex file where I manually repeat many commands of the same type \documentclass{article} \usepackage{amssymb} \newcommand{\bR}{\mathbb{R}} \newcommand{\bT}{\mathbb{T}} \newcommand{\bN}{\mathbb{N}} \newcommand{\bP}{\mathbb{P}} \newcommand{\bE}{\mathbb{E}} \newcommand{\bF}{\mathbb{F}} \new...

I tried the method in Derek's tutorial https://youtu.be/I-JvfzDTMZk?feature=shared&t=554 by adding a plane then turning "instances" on in object properties but it won't work and maybe also because the video is old and Blender has improved every since, do you guys have any method to stop the obje...

I often use Collect with a function in the third argument to manipulate the coefficient of the terms that match a given pattern. Sometimes I would like that function to be able to access the match of the pattern. Is there a native Mathematica function that can do that? Expample would be Collect[a...

I study French and I have run into this dialogue: – Vous me conseillez quel vin pour l’accompagner ? – Oh, un Côte du Jura ou un Riesling, ça ira très bien. – Le Côte du Jura ? Je ne connais pas... – Eh bien, c’est l’occasion d’essayer. Ça change un peu. Vous en trouvez des très bien à partir de...

I'm using the definitions from Napkin written by Evan Chen from Chapter 11: "Dual space and trace". Let $V$ be a $k$-vector space. Then $V^\vee$, the dual space of $V$, is defined as the vector space whose elements are linear maps from $V$ to $k$ Now defining functionals: Let $Hom(V,W)$ denote t...

I'd like to use coc.nvim for completion. However, this plugin requires the JavaScript runtime Node.js. Installing Node.js adds the following code to the shell rc file, (in my case .zshrc): export NVM_DIR="$HOME/.nvm" [ -s "$NVM_DIR/nvm.sh" ] && \. "$NVM_DIR/nvm.sh" # This loads nvm [ -s "$NVM_DI...

I was trying to create a basic differentiator which would convert a pulse into two spikes at the places where the pulse rises and falls. Instead of the desired result I got this presented very bad result. I was told to look at the data sheet plots 9 and 10 presented. Also, I have built mathemati...

I am not a Christian. In a second-hand bookshop I often visit, there are many Bibles for sale. These books are mostly in Chinese and Korean, sometimes English, piling up meters high (maybe 200 prints or more). The bookshop owner says many Chinese and Korean believers sold (or sometimes donated) t...

recently i change the battery of my Volkswagen and the radio cd ask me a code but i don't have it.. The serial no is: VWZ4Z4G7123412 Can anyone help me please?? Fortunately, i found this web page: https://radiocodess.com/volkswagen-radio-code Has anyone heard of him because i don't want to be ...

I implemented lock-free ring buffer from scratch. As I am a beginner in atomic features in C++, I wanted to hear your feedback and possible ordering issues if there are. #include <atomic> template<int size> class ring_buffer { static constexpr int buffer_size = size; char buffer[buffer_s...

Suppose X is a complete intersection in $\mathbb{P}^n$ of dimension at least 1. Write $X = N \cup L$, where $L$ consists of all linear components of X. If L has more than one components, is it possible that all the components of L are pairwise disjoint?