Based on Xkcd's Boat Puzzle At the riverbank, a sucession of people have given you a large lump of objects to transport across the river. These are: 101 cabbages 2 goats, one of which eats wolves 4 wolves, one of which can operate the boat alone A swarm of cabbage moths A colony of termites The...

There are some cases where a pilot may not be able to reach ATC directly due to lack of power or being below the radio horizon: On a handheld backup radio After a forced landing Over open water In high terrain What is the proper process and phraseology to request an airborne relay via an aircra...

Pedals It's pretty obvious that one of the two pedals needs be tightened counterclockwise, but which one? A brief reflection on the right pedal's sense of rotation (while pedaling forward) with respect to the crank would suggest that it is the pedal that needs to be tightened counterclockwise (so...

At KSLC (Salt Lake City International Airport) the ILS minimum RVR for runway 34L is 1800 ft. If the RVR equipment is inoperative and RVR is not reported how do you determine the minimum visibility for that approach? Can I interpolate between 1600 rvr visibility (1/4 mi) and 2400 rvr visibility ...

What is the difference in meaning between 事儿 and 东西. As far as I understand both mean "thing". All help is appreciated.

My character is trying to convince his girlfriend to let him keep his new puppy in their apartment. She opposes fiercely, because she doesn't like dogs and feels her space would be invaded. They have an argument, which ends with her saying: "There will be no further [word pertaining to dogs] in t...

My file compiled with siunitx 2 (TexLive 2020) but breaks with 3 (TexLive 2021). I can't find useful info in the upgrade section of the manual. MWE: https://www.overleaf.com/read/wmgnzhqhbfpy \documentclass{article} \usepackage{siunitx} \begin{document} \begin{table} \begin{tabular}{ r S[...

The Auto Tile Size add-on appears to to be missing in Blender Version 3.0. Is there any way to get it back? How can I use the Auto Tile Size in Blender version 3.0?

I have a flight next week from Ukraine to France with 1 hour connection in Germany. For the passengers arriving to France from Ukraine a covid test is mandatory. For the passengers arriving from the Germany to France no tests are required. There is also no need for tests from Ukraine to Germany. ...

Let $X=(X,\|\cdot\|)$ be a Banach space and suppose that $F\subset X$ is a finite-dimensional subspace. There is then an equivalent norm $|\cdot|$ on $F$ such that $|\cdot|$ is induced by an inner product on $F$ (i.e. $|\cdot|$ will satisfy the parallelogram law) and it follows that \begin{equati...

Text clues: Scratched (6) Snow sport (6) Maui and Oahu? (6 7) Pimento container (5) Celebrated singer (4) Guest (7) Old world warblers (9) English king, briefly (6 4) Stick (5) Cutting tools (4) Left (6) Moving slowly (7) Castle-dwelling neighborhood puppet (4 6 4) Self-referential (9) Document...

I am confused about why the light released from the moment when gas first formed was so dominant in comparison to the light released afterwards. Why isn't the CMB in interference with a series of cooling blackbodies as the universe continued to expand and cool?

I'd like to reproduce Panel A of Figure 7 (red curve) of this paper, which represents the steady-state solutions of four coupled ODE's, and verify this claim that the diagonal branch in the Z-shape part of the curve is the unstable branch. The governing equations for the model are: $$\frac{dF}{dt...

TLWR: How do I randomize any value in Geometry Nodes (Blender 3.0) Some versions before the Geometry Nodes fields update there was a node labeled "Attribute Randomize" which randomized whichever value. But now in 3.0 that node isn't there anymore, and trying to randomize a value with the "Random ...

Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be twice differentiable function. Suppose $a<c<b$ such that $f'(c)=0$ and $f''(c)>0$. Then $c$ is a local minimum of $f$. Does it follow that over $[a,b]$, $c$ is also global minimum? It seems no. By EVT, there exists $y\in[a,b]$ such that $f(y)\leq f(x)$ ...

First, I would like to verify is the circuit I drawn correct? Rin is consider large enough to be negligible in the equation. I tried using KVL to obtain 3 equation as below, considering to get vth and Isc so Ro=vth/Isc $$-v_i+i(R_1+R_2+R_{out})+A_{vo}V_d=0$$ $$-v_i+iR_1-V_d=0$$ $$v_{th}=v_o=iR_...

OP1 has a finite input resistance, but an infinite open loop gain (other parameters are also ideal). The other two op amps are ideal as well. Can I still assume that there is a virtual ground between the positive and negative terminals of OP1 and the input resistance (Rin in the schematic) is ac...

In my cryptography course I found the following problem: Find $|E(\mathbb{F}_{7^{100}})|$ where $E$ is given by $y^2=x^3+1$. I know how to do it for small numbers, using quadratic residues, but this doesn't work with $7^{100}$. My question is if there is a general method or algorithm that works ...

Recall that a poset $P$ is said to be continuous if, for every $p \in P$, the set $\{q \in P \mid q \ll p \}$ is directed with supremum $p$. Here $q \ll p$ is the "way below" relation (see the above nlab link for complete definitions). Following Scott, continuous posets are a widely used concept ...

Not sure if this is the right place to ask, but here goes .. I recently bought 2x WD Red Plus 8TB NAS hard drives, and while unboxing them I noticed that they have bumps on their sides, of varying intensities. Please take a look at the pictures below. Are these bumps normal, or are these hard dri...

I noticed some differences between UFC and street fights in terms of tactics after watching some recordings of UFC matches, and I wonder why such differences exist (since those two were kind of similar). Feints. Many self defence related websites recommends not using feints in street fights and ...

Seems like being inside a sand tent down inside a dune would act like a vibration amplifying chamber -- even the vibration of simply breathing, snoring. etc - much less any movements would be amplified nto the compacted drum-like sand (from the sand compaction tool) such that it would essentiall...

UPDATED: This question also helped me understand better. I have few apex method calls imperatively and its working as expected but I'm not sure if there is a better way to handle or has any pattern to follow. Is this okay to chain the calls like how I'm doing here? Here is my code: handleSaveMeth...

I am writing a document with several sections and subsections, using the amsart template. I would like the following: A short table of contents at the start of the document, which only includes the sections. Bookmarks on the generated PDF which includes sections and subsections, as is typically ...

first post ever here. I've read the guidelines, but please do let me know if I'm breaking any rule or doing something wrong. So, I am creating a magic system based on the energy of a star. More specifically, on certain wavelengths of the electromagnetic spectrum emitted by this star. It was relat...

I'm running Ubuntu 21.10 and have two identical monitors attached to my AMD 5700G system as "joined displays". When the monitors wake from sleep or are powered back on, it appears that Ubuntu doesn't realize that both monitors are coming back. Some apps that were located on one monitor are moved...

I have a pdf (having multiple pages) containing some colorful certificates, and need a black and white (grayscale) version of it. Is there any way to make it grayscale with a single command, or with any simple GUI program (preferably FOSS)? In principle, I can open all the pages separately in GIM...

My son just got his first guitar. I know NOTHING about guitars. One of the strings broke and we can’t figure out how to replace it. The videos I’ve found on YouTube make it look easy and spend about 5 seconds on the part that’s perplexing me. None of them look anything like my son’s guitar so the...

I have been dealing with the following issue related to the Schwarzschild geometry recently. When expressed as: $$ ds^{2}=-\left(1-\frac{2GM}{r}\right)dt^{2}+\frac{1}{1-\frac{2GM}{r}}dr^{2}+d\Omega_{2}^{2}$$ one can find a Killing vector $\xi=\partial_{t}$, since there are no components of the me...

I have a set of points $P$ and want to find the ellipse with the smallest area that covers at least a fraction $f$ of these points. How can I do this? These questions ask the same thing, but folks have only provided approximate answers. This question asks for the smallest ellipse that bounds all ...

I want to get the last element of a lazy but finite Seq in Raku, e.g.: my $s = lazy gather for ^10 { take $_ }; The following don't work: say $s[* - 1]; say $s.tail; These ones work but don't seem too idiomatic: say (for $s<> { $_ }).tail; say (for $s<> { $_ })[* - 1]; What is the most idiomat...

The All-Purpose Tool is a spellcasting focus for artificers printed in Tasha's. Among other things, it has the following property: As an action, you can focus on the tool to channel your creative forces. Choose a cantrip that you don't know from any class list. For 8 hours, you can cast that can...

My code is working but it is extremely long. So, I guess there is a way to make it shorter/more efficient. The problem solved here is from Advent of Code 2021, Day 3, Part 1: https://adventofcode.com/2021/day/3 binary_list = open("data.txt").read().split("\n") counter_1st_bit_0 = 0 counter_1st_b...

I am following the experiment in the popular electronics book - "Make: Electronics third edition". However, when replicating one of the experiments mentioned in the book (specifically Experiment 3 "Applying pressure", the part under the subheading "It's the law!", Pg 28), I am stuck. I believe th...

In the linear regression model we assume that the errors $ε_i$ are independent and identically distributed (i.i.d.) random variables. I am trying to understand what this assumption implies regarding the response variables $y_i$. As far it concerns the identitally distributed assumption, since $y_...

I've watched a few episodes of Amazon's new Wheel of Time series. It has its pros and cons, but something strange about it is that just about every single place has strong ethnic variety, as though it was a modern city with large immigrant groups from different countries, that we have these days;...

Apart from broke which acts as the past simple of break, we also have "broke" which is the obsolete past participle of break (v.) and still we use it as an adjective in sentences like "Now I'm broke!". So the verb break have to past participle in use which are actively used as adjective. What are...

Latin words like crematorium and vomitorium seem to be made from verb + -torium Is there a pattern to this I can follow for arbitrary verbs? Furor + -torium = furotorium Or Farcio + -torium = Farcitoroum Or is there something else to it?

A gynoid is just the term used to refer to female androids or “fembots”. Gynoids are typically female-styled robots and are usually more human-like compared to regular androids, with the accompanying body-proportions. While androids in general are sexless entities, gynoids have wider hips paired...

I don't need a completely formal explanation, just some intuition. My professor stated identifying antipodal points on $S^1$, yields the projective plane $P^2$. That means there exists a quotient map (and thus a surjective map) $q: S^1\to P^2$. Intuitively, this confuses me. How can identifying p...

Let me give you some context first: just a few days ago I found some intriguing references to Ricci flows in the setting of directed graphs. There are at least two versions of Ricci curvature in the discrete realm (one being the Ollivier-Ricci curvature, the other the Forman-Ricci, see here for r...

I notice that the metadata of custom objects (fields, sobjects) that I retrieve from my Dev org using the Org Browser (VS Code) have a <deprecated>false</deprecated> element in them. The documentation for CustomField simply says deprecated / boolean / Reserved for future use. Same for CustomObjec...

We know that in Oblique Parallel Projection Point $(x,y,z)$ is projected to position $(x_p,y_p)$ on the view plane.Projector (oblique) from $(x,y,z)$ to $(x_p,y_p)$ makes an angle $\alpha$ with the line (L) on the projection plane that joins $(x_p,y_p)$ and $(x,y).$ Line $L$ is at an angle $\phi...

Colonel James "Rhodey" Rhodes was present during Stark's kidnapping in Marvel Studios' Iron Man (2008) - in fact, he was in the Humvee behind him (dubbed the "Hum-drumvee" by Stark just minutes before the attack). However, it seems all members present were killed during the attack. Rhodes later c...

At 57:50 in Iron Man (2008), Obediah comes to visit Tony and is playing something on a piano. It sounds slightly classical. What piece is he playing?

Part of Advent of Code Golf 2021 event. See the linked meta post for details. The story continues from AoC2015 Day 24, Part 2. Here's why I'm posting instead of Bubbler To recap: Santa gives you the list of gift packages' weights. The packages must be split into multiple groups so that each grou...

There is a brown door, some flowers, a $100, an envelope

The Circle of Spores Druid gets the level 2 feature Symbiotic Entity, which does the following: As an action, you can expend a use of your Wild Shape feature to awaken those spores, rather than transforming into a beast form, and you gain 4 temporary hit points for each level you have in this cl...

A bit complex than a similar question, below is a minimal example, eqs1 = a b x'[t]^2 - ac x''[t] eqs2 = x''[t] - b x'[t] - c == 0 I want take x''[t] substitute in eqs1, where $eq1= a b \dot{x}^2- ac \ddot{x},~ eq2 = \ddot{x}-b\dot{x}-c$, the output should like $eq1 = ab\dot{x}^2 -ac(b\dot{x}+c)...

Defending FT public holiday, minister says ‘greatly pressured’ by KL folks after Malaysia Cup win A region in Malaysia recently declared a public holiday after their team won the Malaysia Cup, which is a national soccer competition. Has this happened anywhere else in the world? I haven't found an...

John 20:30 (ESV): 30 Now Jesus did many other signs in the presence of the disciples, which are not written in this book; 31 but these are written so that you may believe that Jesus is the Christ, the Son of God, and that by believing you may have life in his name. We are told that some signs t...

I'm an American who bought an antique chandelier from France on ebay. It has old cloth covered wires I'm guessing from the 1930s. I'm not sure which one is the hot wire. One wire is made up of 2 wires. Is one of these supposed to be be a ground? I'm assuming not. Each socket has the standard 2 wi...

My right brake lever (Shimano BL-M9020 to be specific) has attracted some dirt around the blade pivot area, and some parts look shiny. I suspect the master piston seals are starting to leak. Replacing the entire lever is the guaranteed safe solution, but I cannot afford to do so and I'm unsure ab...

Isn't the Equivalence principle not quite true, technically speaking? A gravitational acceleration and an inertial acceleration are communicated very differently. A gravitational acceleration is communicated throughout your body and its stress is spread out in your body, whereas an inertial accel...

I currently have a model that has a pretty large dataset (50ishMB) and was performing pretty well with a 80:20 split. However, when I tried changing it up to a 50:50 split, the model performed 28% better than the 80:20 split. Since I have evaluated the model to perform better in that data split, ...

This puzzle is part of the Puzzling StackExchange Advent Calendar 2021. The accepted answer to this question will be awarded a bounty worth 100 reputation.< Previous Door Next Door > What do we need to buy for our glorious Christmas dinner? Create a shopping list of all the things to get by decip...

I see kernel_task in Activity monitor. But I cannot find where the binary file is using Spotlight. Does anybody know where the binary is found on the disk? I am using Big Sur 11.4. But my question may not be related to the particular version of the OS.

I need a code/app/website that can receive a DNA sequence, for instance AATCT, and output a file with the atomic coordinates. I used to do this on this website http://www.scfbio-iitd.res.in/software/drugdesign/bdna.jsp#1 but the service is no longer working and I haven't mange to find a substitut...

J.K. Rowling has said in interviews that Luna married a character named "Rolf Scamander". No character of this name ever appears in the novels. Did Rowling just invent him for the interview? What happened to luna, did she get married who to? J.K. Rowling: Luna became a very famous wizarding natu...

The pronoun hic (this) is written with short i in many places, e.g. Oxford Latin Dictionary. But in Lewis & Short: Latin-English dictionary and Allen and Greenough's New Latin Grammar, it is written as hīc with a long i. Which is correct?

I've found my own solution to calculate the minimum radius of all points in the list, which runs on O(n) and is incredibly easy to implement, but I don't think that I'm the actual first "creator". So I want to find the scientist who invented it first. It is not described in Wikipedia. Basically s...

I have written a very simple nested If as follows atom = be; If[atom == li, lim = 5, If[atom == be, lim = 3, If[atom == b, lim = 2, If[atom == c, lim = 1, If[atom == n, lim = 0.5, If[atom == o, lim = 0.3, If[...

I am using the fancy verbatim package and even though I set the font size to tiny, it still doesn't properly fit in a single slide. I was wondering is there a way to scale it down even further. Thank you \documentclass{beamer} \usepackage{graphicx} \usetheme{default} \usepackage{float} \usepack...

In the good old days, the space pirates used tractor beams to reel in unsuspecting merchant vessels before robbing them. Recently reports of them cohorting with the rebel army soon spread across the entire neighborhood stars systems, in the report they were specifically stated using military grad...

I have been trying to solve $$\exp\left(-\pi\frac {_2F_1(\frac12, \frac12, 1; 1-x)}{_2F_1(\frac12, \frac12;1;x)}\right)$$ Here the problem Is to find the above expression in terms of powers of x What I tried: I tried to find Taylor's series expansion but I'm still not able to go through this all

Ever since steel was created, it has been the go to material for swords since antiquity and into the modern era (for actual replicas and not wall hangers). Of course while being effective it is also, subjectively, boring for a sci fi setting. Many other sci fi works have recognized this and hav...

I am wondering if there is any literature on general formula of the Moebius function of subgroup lattices of any finite abelian group $G$? What I know is When $G$ is cyclic, the Moebius function is simply the classical number theoretic one. When $G=(\mathbb Z/p\mathbb Z)^r$, the formula involves ...

I want to know if it's possible to create keywords (similar to workflow keywords in alfred) for certain terminal commands. For example instead of typing: php artisan serve I want to type: pas while executing the above command.

It has always been my understanding that to use a disk or other storage device, it needs to have a partition which can then be mounted and used. Is this wrong? I inserted an nvme device in the machine and using the 'disks' gui utility chose ext4 and successfully mounted it to /mnt/nvme. My curren...

If I understand correctly polarisation of electromagnetic wave, two opposite phase wave of same polarisation can cancel each over, so the question is : As white light have all polarisation, all the wave are in equally direction around 360°, and as there is all phase, it should cancel all each ove...

I recently received an invitation to review a paper for publication in an MDPI journal. This is the first time I am being invited to review. I do feel qualified to do it since I have several publications relevant to this topic. However, in the invitation e-mail, I am greeted as Dr.- which reveals...

How can I color the words: "Figure and Table" with one color and their numbers with another color?(see attached figure). Thank you very much \documentclass{book} \usepackage{graphicx} \usepackage{capt-of}% or \usepackage{caption} \usepackage{booktabs} \usepackage{varwidth} \begin{document} \cha...

I have a simple lightning-vertical-navigation. I am trying to change the text color of the lightning-vertical-navigation-item but the css overide does not seems to works. Is there a way to do that? mycomp.html ...<lightning-vertical-navigation selected-item={selectedItem} onselect={changeHandle...

I would like to analytically integrate a function in Mathematica. However, I have found a problem with the final result when I compare it with the numerically integration of the same function. Here it follows an example Tex=1/(-1509.04 + 1/(-1.64387 - 1.05604 Cos[0.88 \[Theta]]) + 1/( 0.00062234...

I'd like to understand some more who the person behind the now famous scholar is. Unfortunately there is no hint whatsoever to be found anywhere, except that he is from Germany and ordained at the age of 33 about, as of his wikipedia article. Therefore I'd be grateful if anyone could provide some...

I'd like to ask if "to be" is a must in the sentences below: [1] She was the first female to be employed. [2] She was the first female employed. [3] I am the first person given the opportunity to go overseas. [4] I am the first person to be given the opportunity to go overseas. In the first two...

I was thinking of a way to prove this and I realised that for my approach the lemma from the title would be useful, and it´s an interesting question on its own. Obviously it is true if the manifold is compact or $\mathbb{R}^n$, but I don´t see it in general. This is the precise question: Let $M$ ...

Assumed we have a fuel flask that is made of titanium. The bottle will be filled with white gasoline when used. At the bottleneck there is a standardized thread manufactured into the titanium. Are there any dangers of (contact-)corrosion between the materials if the screwed-in bottle cap is made ...

The question seems suspicious but no, I'm not planning on smuggling any drugs. I ask because I share a house with two other people, both of whom are drug users. They use cocaine, ecstasy and weed when they party and I regularly see some trace amounts of drugs on the floor, table etc.. I'm travell...

From an examplary plot plot = ParametricPlot[{1 Cos[s] , 2 Sin[s]}, {s, 0, 2 Pi}] I know how to get the plotted points pi = Cases[plot, Line[p_] :> p, Infinity][[1]]; Additionally I would like to get the parametervalues s (automatically used by ParametricPlot) of the plotted points pi: {s[i],...

Currently if I select a group of object and change the Z value it only move the object I originally selected. Is it possible to change the coordinates of a certain selection of objects of different Z values to all the same Z values without changing the x or y values. In addition to this can you c...

Is it possible to have a capacitance in a system of two point charges? Since there is a potential energy between them and they both have charges then we can divide the charge by the potential and get capacitance. However, capacitance is supposed to depend only on geometry so should therefore be z...

I got job in one of uk universities. When I got the offer, the working hours were 38h per week then when they send the contract to sign, it says, minimum of 38h and university will ask from time to time to work extra hours without further remuneration Is this normal in UK? Should I discuss this w...

I'm joining a US university as a tenure-track assistant professor in January. I was previously told that I will teach 1 undergraduate course in the spring semester which will start in the 2nd week of January. Despite sending multiple emails, I was unable to find out which course I would be teachi...

The university I'm attending for gradaute school offers programs that give you official certification in university teaching. The program consists of taking teaching workshops, participating in teaching sessions, and things like this. My question is, how much attention would a hiring committee pa...

I am working on a beamer file that has a a lot of slides as an "appendix". Hence, when I introduce the command \setbeamertemplate{footline}[frame number] to display the page progress in the footer I get the outcome 1/200. I would like to know if there is a command that can fix the count to stop w...

So I'm reading the Gas Turbine Engine Fundamental, and suddenly come across the airflow passes through one axial compressor stage. I wonder why the Resultant Rotor Inlet Velocity is pointing downward, while the Rotor Speed vector is pointing upward. The Resultant Rotor Inlet Velocity is the sum...

Over on the German Language StackExchange, RDBury asks Is Gandalf really on 'du' terms with the Balrog? (Odd 'duzen' example) I don't speak German, but I get the impression from their question: Gandalf says "Du kannst nicht vorbei!" [...] The grammars say that the 'du' form is used for friends a...

In Lingua Latin per se Illustrata: Chapter 32, Line 158: Sed frūstrā hoc optō, nam iam illī pīrātae eam spem mihi ēripient, idque eōdem diē quō ab amīcā meā dēsertus sum. dēsertus sum seems to be the verb of the quō-clause (the same day in which I am deserted by my girlfriend), and where is the...

Should a wheel user that was created to disable root login and secure SSH have the same ownership as root from a security point of view?

In Macbeth, at the end of Act 2, Scene 3 Macbeth reveals that he killed Duncan's servants: O, Yet I do repent me of fury That I did kill them However, doesn't this appear as a plot hole when we take Lady Macbeth's reaction into account ("Help me hence, ho!")? I see two interpretations: Macbeth...

Can salesforce functions be released as part of Salesforce managed package on AppExchange? We build Salesforce package which connects to ruby application. We want to establish some Web Sockets connection from Salesforce to that external application. Looks like this is not possible per se since Sa...

I am using the "Edition Peters" and there are notes which have a staccatissimo sign under some notes. Should these be observed? It seems to me that it disrupts the overall tonal quality of the piece. Copies of the pieces I am playing have to be provided to the examiners. Would appreciate some adv...

The primary meaning is You are so strong. But is it possible to translate it as You are so loud, too ? What are the other ways to say You are so loud in French?

A friend of mine recently had a test during one of her English classes and there was a task to choose the correct word that best fits the sentence: "Few of the students knew ___ of the answers". And the options were: no, none, any, some. I, personally, never learned grammar in a formal way, so I ...

XP (Experience Point) is a term particularly used in gaming. Should I use much or many in this context? Adam: 'I killed the boss! I got 100 XP!' Alex: 'Great, how ___(many/much) XP have you got?' Google says to use "how much". According to the app version of the OALD, it has another form: XPs (...

Given random varaible X with distribution $$ \begin{cases} \mathbb{P}\left(X=1\right)=\alpha\\ \mathbb{P}\left(X=-1\right)=1-\alpha \end{cases} $$ Where $ \alpha $ is a given parameter($X$ is a binary signal), and noise $Z$ with normal distribution $ Z\sim\mathcal{N}\left(0,\sigma^{2}\right) $, w...

Some of the best bread makers often work with a secret ingredient - e.g. a yeast starter that has been passed down for generations. Jesus told his disciples to beware of the “yeast of the Pharisees” - i.e. their teachings (Matt. 16:6, 11; Mark 8:15; Luke 12:1). The conventional interpretation is ...

I would like to reproduce the following figure using Tikz: So far, I have done this: using the following MWE: \documentclass[a4paper,12pt]{report} \usepackage{lmodern} \usepackage[T1]{fontenc} \usepackage{tikz} \usetikzlibrary{calc,intersections} \begin{document} \begin{center} \begin{tikzpic...

I have made this a long time ago in Photoshop 3D when it had more support for some effects and was easier to customize. I've been playing around with Blender for the first time now and i'm trying to make something alike but it's difficult, I managed to create the object from a .svg, extrude it a...

How can we describe this way of shaking hands? The men are using both hands to shake hands. This doesn't sound coherent. But I'm unable to find another construction.

Lemma. Let $y \in [0,1] \setminus \mathbb{Q}$, $\epsilon > 0$ and $N \in \mathbb{N}$ such that $\frac{1}{N} < \epsilon$. Then one can choose $\delta > 0$ small enough such that $$ \frac{p}{q} \in (y - \delta, y + \delta) \Rightarrow q > N, $$ where $\frac{p}{q} \in \mathbb{Q}$ and $gcd(p, q) =...

I want to tell a command or mapping to advance to the next non-blank line before executing - but to do this only if the current line is not blank. Ultimately, I intend to apply this to a command to collapse blank lines in a given range, replacing the blank lines with tabs. This must be done from ...

The font size is 12 pt, tracking (aka line spacing) is 18 pt, and 18 pt between guides: I want the lines to be aligned at the bottom of their line spacing instead of their top. What is the proper way to do this? Do I need to shift the baseline (that is, to open the basic paragrah settings, select "

In Ouroboros, the more ADA you have the bigger the chance to get elected to mine the next block and get the rewards. Apart from other parameters and up to the saturation level for a single poole this incentivizes high net worth entities to run several stake pools and/or to provide pledges. At fir...

I have a data set with two items that potentially measure the same latent variable: personal well-being. Can it be useful to run a factor analysis (Principal Axis Factoring Analysis) on them, or does a factor analysis require more items?

The question states: Let us consider the field $GF(2^4)$ with multiplication modulo $x^4+ x^3+1$ Find all y such that $1010(y + 0011) = 1111$, in other words find y that satisfies $(x^3+x)(y +x+1) = x^3+x^2+x+1$ I tried to find the inverse for element $1010$ to multiply both sides of the equation...

this is my first posting here. I am an IT engineer which does some work on electronics also, partly hobby, partly for innovations at work. I have a working stepper FOC prototype with current sensing and magnetic encoder (AS5147, max. 14bit). The stepper has 50 pole pairs. The software I use is ca...

There is a way to write this \begin{tikzpicture} \draw (0,0)--(10,0) node[midway,above] {top}; \draw (0,0)--(10,0) node[midway,below] {bottom}; \end{tikzpicture} drawing only one line?