I am trying to create a custom "proof" environment that behaves as follows: \begin{proof}\end{proof} should produce \textit{Proof.}, while \begin{proof}{method}\end{proof} should produce \textit{Proof (method).}. Here's what I have right now: \documentclass[10pt]{article} \usepackage{xifthen} \ne...

Let $\mathfrak{g}$ and $\mathfrak{g'}$ be complex Lie algebras such that $\mathfrak{g}$ is a subalgebra of $\mathfrak{g'}$. Let $Z(\mathfrak{g})$ and $Z(\mathfrak{g'})$ be the centers of the universal enveloping algebras. Is there any relation between $Z(\mathfrak{g})$ and $Z(\mathfrak{g'})$? I...

Does glass undergo internal damage in a similar way to wood when struck hard, even if it doesn't visibly break, and is this damage accumulated gradually over time, or does it occur as a binary response, unlike wood.

Sketchy-ish information but I think it could have been Twilight Zone/Outer Limits. Earth is being overrun by killer somethings? Moths/butterflies. Astronauts go forward back or forward in time to destroy them. Only for closing scene to show pupae on outside of spacecraft ie. They brought

I am doing my mathematics homework on circles. One of the questions asks to find the equation of circle(s) given that it touches the x-axis, passes through $(1, 1)$ and has the line $x + y = 3$ as diameter. We may solve this question, but while drawing the diagram I asked if only one such circle ...

I want to add some opacity to draw several angles but the arrowheads (-latex and -stealth) are modified with fill opacity option. At the moment, I'm re-drawing all angles twice, with fill options and without, to keep the arrow heads plain. First : How can I keep the arrowheads without transparenc...

Consider the following puzzle: On the integer line from 1 to t (top, let's say 1000 for this example), you have two operators: uniform random on 1 to t, and subtract 1. What is the optimal algorithm to reach 1 with the least number of operators. For example, if you do one random sample and then a...

I may have hit the wrong button while trying to answer a radio How do I put this grenade away?

When I connect a multi meter across BC and AC I get the same reading, both show 5V, but isn't the resistor supposed to decrease the current/voltage? simulate this circuit – Schematic created using CircuitLab

I've been trying to design a circuit to control 23 LEDs dimming using a LED Driver, but I don't quite understand how they work. Put for example the model BCR420/1: Datasheet: BCR420/1 Datasheet I have 23 LEDs to controll, with Vf = 3.3V and If = 30mA. If I wanted to control all 23 leds in a sing...

What was the procedure for packaging SRC Osiris Rex after landing? How to keep it clean, with no dust or sand? Why was it not packed on a clean surface like a table?

Why my work like this Extrude Faces along Normals

I purchased this plant, and I don’t remember the name. At the time it had one or two vividly red, waxy flowers. The flower had a “tongue” part (excuse my ignorance) that looks like a hard, bumpy capsule? Anyway, the flowers lasted for at least a year. During that time, they remained extremely red...

I wanted to copy some code I have from Neovim to Firefox, but the stuff I yanked doesn't carry over outside Neovim. After I checked :checkhealth, this what it said: What should I do to handle this issue?

I have an electric car that I'd like to charge faster. I have a charger (EVSE) that will pull 24A. I have a detached garage with 30A service running to it (10-3 wiring, 30A breaker at the main panel). My question is: Am I allowed to have a 30A breaker in my garage subpanel with 30A service?

I'm not an electronic expert at all, but I'm keen on various electronics and stuff, and I like to watch videos where the different laptops are fixed. And in nearly every repair there is a multimeter used to test different components of the motherboard to see if their resistances/voltages are norm...

Hi Matter Modeling friend! I come today with a question regarding a "medium-large" (depending on who I ask) DLPNO-UCCSD(T)-F12 calculation. I have a ~250 electron system, an open-shell molecule inside a water droplet, and I'm trying to get the total energy, first using the default SCF and PNO set...

I am confused over the habitable zone, as I calculated the expected temperature of Earth (minus greenhouse effects), and it would be -17 C. Which is below the freezing point of water. I also made a fictional A-type star with a luminosity of 20, and its habitable zone would be 4.26401432711 to 6.1...

$G$ is a topological group and $H$ an open subgroup of $G$ I want to show that the quotient topology of $G/H$, $\tau_{G/H}$ is equal to the discrete topology $\tau_{\text{discrete}}$. I mean clearly we know that $\tau_{G/H}\subseteq \tau_{\text{discrete}}$ since $\tau_{\text{discrete}}$ is the...

I've been looking all over for a source to buy Amiga OS 3.9. My A1200 has Workbench 3.2.2 and it would be nice to get OS 3.9 since I'm also adding an 68060 card and lots of RAM. Anybody have any idea where I might find OS 3.9 install media? I have Cloanto "Amiga Forever" but it doesn't seem to ha...

A Wikipedia page on filters claims: if $(X, \mu)$ s a measure space, then the collection $\{A : \mu(A) > 0\}$ is a filter. I assume that the implied poset is the $\sigma$-algebra on $X$ partially ordered by set inclusion, so $A$ in the above definition is a measurable subset of $X$. Assuming th...

Permission is hereby granted to all parties to copy, distribute copies of this license... Should I use and here instead, or is omitting it more clear?

I often cook a typical frozen pizza like this in a typical mini-oven like this I go with a nominal 420° indicated on the small over for 13 minutes. ("12-14 mins" suggested on the packaging.) TBC I very simply sit the naked pizza on the metal wires of the mini oven (no stone, foil, or anything e...

I have a frame+fork that had old style locknuts on the wheels. I used those wheels for a project. Now I want to put wheels back onto this frame, but I only have quick release wheels in the same size. My question is can I install the quick release wheels on this bike that previously had locknut on...

There are statutes in the Immigration Nationality Act that punish willful material misrepresentations/fraud and false claims to citizenship in connection with any benefit under the law (See https://www.law.cornell.edu/uscode/text/8/1182 - INA 1182(a)(6)(C)(i) and INA 1182(a)(6)(C)(ii)). However, ...

I playing am a Shifter (Wildhunt), Druid (Circle of the Shepherd) with a Gruul Anarch background. I am not sure how many Proficiencies I should have. Please help me get the right number.

Let $S^2$ be the 2 dimensional sphere embedded in $\mathbb{R}^3$. It is well known, using the Euler characteristic, that it is not possible to tessellate $S^2$ with all congruent regular hexagons. My question is, would be it possible to partition $S^2$ with congruent regular hexagons, and only a ...

The discriminant of variables $x_1, \dots, x_n$, $$d=d(x_1, \dots, x_n)=\prod_{i<j}(x_i-x_j)$$ is a classical example of a polynomial whose square $d^2$ is symmetric in its entries. This turns out to be very useful for understanding what do some field extensions look like. So the question is: Doe...

My school laptop has an option called "Secure_Printing" where the documents can be printed out on any school printer after inputting the student card number. Here is the configuration in the System Report: Is there a way to replicate the configuration on my personal Mac so that I can use the pri...

I've never seen 𢧜 in any other character before, so I'll take that 𢧜 is exclusively for 鐵 (just like 邊 and 微 which I've asked before in the past). So where does 𢧜 come from? It seems to be a combination of relatively unrelated components, and none of them sound like 鐵.

OpTeX has the macros \begmultiand \endmulti to split a text into multiple column, but since it becomes inner vertical mode, the \mark command does not have any effect anymore. Compare \headline={\botmark} hello \mark{lorem ipsum} \bye and \headline={\botmark} \begmulti 2 hello \mark{lorem ips...

I just got this 23 year old, small tablesaw from a friend of mine. I know it’s nothing great, but if it can be made to work, it will suit my needs. It’s been stored indoors and seems to be in good shape generally. But, he said he hasn’t used it in the last 12 years or so. What do I need to do an...

When camping, I often need to tension a rope between two points, and it starts by tying the rope to the first point. It can be a tree. In this situation, I can use a bowline, or a siberian hitch, or a clover hitch for example, which are respectively a loop knot, a slip knot, and a hitch knot. Is ...

Languages, natural like English or French, or subject to specification like the mathematical language or formal logic itself, do not make any assumption, and this for the obvious reason that assumptions are made by logical beings which have a language, not by the languages themselves. Someone s...

I drew a ruler using the MWE below then I realized that It draws each medium (5 mm step) vertical line over the small ones (1 mm step) and each large (numbered) vertical bar over both medium and small ones. So, my question is: how to use conditionals to prevent overlapping? \documentclass[tikz, b...

I need to write a document using the dgruyter template. When I include an algorithm environment I get the following error. Undefined control sequence. <write> ...\protect \numberline {\plist@algorithm 1}{\ignorespaces Alg\relax... l.32 \end{docu...

California house built in the 1960s. Here's the existing junction box for the ovens. Ovens are busted and needed to be replaced Right away, I am confused: Red looks like 8 AWG Black, White look like 10 AWG Bare wire (ground?) looks like 12 AWG Jacket for the 4-wire is plastic/polymer, not met...

Today I look at my electrical panel and I realized it doesn't have a main breaker, but the ground bar and neutral bar are connected by a metal on the top (As I remember the ground bar and neutral bar need to be separated if it's a sub panel). I'm wondering if this electrical panel is a main panel...

Should instant yeast be at room temperature when used to make bread? I store mine in the freezer but I was wondering if it should be allowed to warm up a little before use.

Simply as the heading states. What is the most recent version of AmigaOS?

Given the following code: ClearAll[names, vl, el, ew, community, vName, vRule, g, evc]; names = { "agr: Agriculture, hunting, forestry, fishing", "min: Mining and quarrying", "ma1: Food, beverages, tobacco", "ma2: Textiles, textile products", "ma3: Leather, leather products, foot...

I want to prove by definition that the following sequence of functions $${f}_{n}= {1 \over 1+n^2x^2}$$ $x\in [0, 1]$, $n\in \mathbb{N}$, converges uniformly in the interval $(0, 1]$ We can find the pointwise limit $\lim \limits _{n\to \infty} f_n(x_{o})=\lim \limits _{n\to \infty} {1 \over 1+n^2x...

While attempting to typeset a piece of baroque vocal music, I've come upon this issue where lyrics cause uneven spacing of the notes in other voices in the score. For example, the 2nd violin on the final beat of bar 2 here (notice how the final eighth note is quite further from its neighbour than...

I have a Python command line application that needs to ask the user for confirmation at some point. I want to add a --assume-yes/--assume-no command line flag to skip the confirmation. I have several ideas how to handle this flag and am not sure which is good/best/terrible. Initial code # main.py...

Is it possible to plot the general solutions of the following pde: pde = \!\(\*SubscriptBox[\(\[PartialD]\), \({t}\)]\(u[x, t]\)\) == t (u[x, t] + ( 2^(1/3) u[x, t]^2)/(-2 u[x, t]^3 + A + Sqrt[-4 u[x, t]^3 A + A^2])^( 1/3) + (-2 u[x, t]^3 + A + Sqrt[-4 u[x, t]^3 A + A^2])^(1/3)/2^( 1/3)) ...

The Law of Identity is one of the fundamental principles in classical logic, stating that an entity is identical to itself, meaning that A is A, and nothing can be other than itself. Without the Law of Identity, it's challenging to create a coherent and consistent system. A logical system that en...

The Analytic representation of a signal has no negative frequencies. Does this mean that everywhere, it's instantaneous frequency is positive?

I read a sci-fi short story many years ago but can't recall the title. It is about a person that has to run across country to get to a place of sanctuary within a period of time, somewhere about 10 minutes. He is aging drastically as he is exposed to the elements.

The title was a bit too short for me to fit the full details, so here's the scenario I have. Prove that two triangles are congruent if in two triangles, the median from the common vertex and two sides is congruent with the corresponding median and the two sides in the second triangle. Trying to f...

The norm in my field is for every job advert to require 3 letters of reference. From my point of view, this is a massive waste of effort. I am going to put out my first ad for a postdoc, and I am considering not asking for reference letters unless the candidate reaches the shortlist. What are the...

I have a resident permit of Schengen country X. I entered Schengen directly from X with stamp from X. I take a bus to another Schengen country and leave Schengen from there without a stamp. I come back to X from a Schengen country that doesn't stamp. There are no other stamps on the passport for ...

Why does breaker keep tripping when I try to use my flaps 1965 Cessna 172G? It’s 15amp breaker.

Relevant Context: Redirect standard out command > file command 1> file Redirect standard error command 2> file Redirect standard out and standard error to separate files command 2> error.txt 1> output.txt Redirect standard out and standard error to the same file command > file 2>&1 command &>...

If we built an orbiting platform of sufficient mass (let's say, made from harvested asteroids) that was anchored at both poles of the planet it surrounded, would such an addition to the planet's mass affect its orbit? Further to this, if the sun in this hypothetical system was dying and lowering ...

I would like to plug in my outside nest camera to the outside GFCI circuit. It is a weatherproof outlet but I can't get the flaps/holes on the bottom or side to open. How to do that? Here is a picture: Thanks

I recently watched the Casy vs July match from 2006-2007 OSL Season 3. This was game 3 from round 1 of the elimination bracket. The game is notable for being very short and including a deception that tricks July into believing that Terran has expanded when they are actually massing units for an a...

How to wrap a text selection to a certain column width using AppleScript? For e.g., let's say the following text is selected: AppleScript is a scripting language created by Apple Inc. that facilitates automated control over scriptable Mac applications. First introduced in System 7, it is currentl...

In the 80’s and 90’s the Intel x86 and Motorola 68000 families are the two leading microcomputer architectures in the 16bits/32bits personal computer scene. 68000 are even preffered by the purists because of it’s orthogonal instruction set. intel X86 family, although always the market leader, has...

It was stated at the beginning of my lecture notes that the Taylor expansion of the sine, cosine, and exponential function converge, i. e. we have $$\sin{x} = \sum_{\nu = 0}^\infty (-1)^\nu \frac{x^{2\nu+1}}{(2\nu+1)!}, \quad \cos{x} = \sum_{\nu = 0}^\infty (-1)^\nu \frac{x^{2\nu}}{(2\nu)!}, \qua...

The following code will print "a"s up to the terminal width and then a tab character and then a "b". I've tested both Ubuntu's default Gnome terminals and Terminator and they display all the "a"s and the "b" on one line as a single word with no tab character. Copying them results in no tab charac...

From https://www.treasurydirect.gov/savings-bonds/i-bonds/i-bonds-interest-rates/#cerates Composite rate formula: [Fixed rate + (2 x semiannual inflation rate) + (fixed rate x semiannual inflation rate)] "fixed rate" is an annual rate. "semiannual inflation rate" is a 6-month rate. I feel like I ...

It is required to replace the == in equation 2b==E ^ x0- x0 with ->, becoming: 2b ->E ^ x0- x0 My personal attempt was like this, but it didn't achieve the goal eq1 = E^x0 - x0 - 2 b == 0 eq2 = eq1 /. k_ + m_ - 2 b == 0 :> 2 b == k + m eq3 = eq2 /. Thread["==" -> "->"]

When you enter your rage, you can choose one weapon that you are holding and infuse it with one of the following damage types: acid, cold, fire, thunder, or lightning. While you wield the infused weapon during your rage, the weapon’s damage type changes to the chosen type, it deals an extra 1d6 ...

I know its Four Bar Mechanism. While rotating I can't get desired results. Lets say the rest length is 1m. Please refer to the graphics for the details. Chebyshev linkage

I've been through all the troubleshooting, it's a hardware issue. It appears something in my g key is broken. I won't be able to get into town to buy another keyboard for at least 2 days, but I can't figure out how to remap it properly. Nothin I change it to has the same effect that it did. Stres...

I'm trying to create a template for my lecture handout. I'm using Segoe UI as the main font for the presentation and I want to use BaskervilleF (https://tug.org/FontCatalogue/baskervillef/) for the handout part that appears right below the slide. Since Segoe is a system installed font and must be...

This is a cryptic crossword. Each clue contains an extra letter which must be removed before the clue is solved, leaving real words in place. Solvers may find a use for these letters. Each corrected clue consists of wordplay for itself, and a definition (not necessarily in that order) for a di...

I’ve been reading up on approaches to pitch shifting, and have found some common approaches use fourier transforms to achieve a change of pitch. I’m curious, is fourier transform technology used in the “guts” of digital equalizers? Any suggestions for references to gain an understanding on how di...

In the following paragraph, does the author mean Linux distributions finally adopted ZFS or, they are reluctant/refuse to adopt ZFS? Additionally, after a bit of an hiatus it’s once again possible to install Ubuntu using ZFS (Zettabyte File System). Nice to see this interesting, featured file sy...

I am expected to start my first semester in college next spring as a math major. While preparing for undergraduate studies I heard from my peers that I should study this language/program called LaTeX which is basically the MS Word of natural sciences. I went through the math department's curricul...

I work at a bank in the United States. Every month we have a two hour department meeting and the head of Loan Operations talks first and gives a run down of the past few weeks activities. What bothers me the most about these meetings is that it is hard to follow what she is saying because she says "

So I had found two question based on the title one was talking about momentum operator in bound state and the other was a more general. Where in the first bound state calculation they had related $\langle p \rangle \sim \langle[H,x]\rangle $ and then further proved $$\langle [H,x] \rangle = \lang...

According to manual I thought that systemd-remount-fs.service is responsible for parsing and applying /etc/fstab entries. So I tried to test it: I removed ExecStart part (ExecStart=/lib/systemd/systemd-remount-fs) and rebooted the system. After booting and logging in I still had fstab entries in ...

Both Kolagan Warmonger and Recruitment Officer have an ability that says to look at the top 6 and 4 cards from the library, then you can show a card matching a condition from among them and put it in hand, and finally put the rest at the bottom of the library. If I don't show any card, because th...

This was a book I read in the ‘70’s about a deserted futuristic city under the ocean floor that appears to be abandoned but is discovered by two teenaged scuba diving boys. They find a statue in an underwater cavern of an amphibious man. Things get blurry here, but somehow they awaken one of the ...

I have a 5 V embedded circuit where a 10 kΩ pot controls the duty cycle of an LED. I noticed that when the duty cycle is only 0.39% (or 1/255 bits), the LED is still perceptibly bright. I'm looking at the PWM signal on an oscilloscope and can see that the +5V fraction takes up only 65 us of a 16....

Can priests be on capital punishment juries, or is this interdicted as an irregularity by canon law?

I'm just starting to learn CNN (Convolutional Neural Networks), and I'd like to ask if the test data also needs to be divided into batches, similar to how it's done with the training data.

I am trying to generate a triangular wave of frequency ~ 100 kHz and V(p-p) = 4.5 V. Additionally, I also have a tight specification that the value of the peak of triangular wave generated in each cycle should be very precise. It is aimed to achieve a 12-bit performance, by which I mean that the ...

I'm trying to prove the following result: Let $(X, \|\,\cdot\,\|_X)$ be a normed space and $Y$ a subspace of $X$. If $\|\,\cdot\,\|_{YY}$ is an equivalent norm to $\|\,\cdot\,\|_Y$ (the inherited norm from $X$) in $Y$, then there exists a norm $\|\,\cdot\,\|_{XX}$ in $X$ which is equivalent to ...

I am using JsonRpcProvider in ethers V6. I am sending requests to node like getBlocknumber, getBalance ,sendTransaction etc through JsonRpcProvider. I want to set the response timeout for the requests I send to the node through the provider. I have found and tried many methods but all of them fai...

In the 1930s and subsequently, Lucas supplied a car voltage regulator of the twin bobbin type. A detailed description of how it operated can be found here, but in summary, one solenoid operated a cut-out to prevent reverse current from the battery discharging through the dynamo, and the other co...

Context: I have a managed package and I removed a field from the latest version of the package. Now Although the field is not part of package the customer org still has the field and relevant data in it. Requirement: Since the deprecated field contains sensitive data and has security risks, so I ...

I'm watching a video on ratio test proof and am confused about a statement. For an infinite series $$\sum_{n=1}^\infty a_n$$ $a_n > 0$, and $$L = \lim_{n\to \infty}\frac{a_{n+1}}{a_n}$$ If $L>1$, pick $\epsilon$, such that $L - \epsilon > 1$. The video states that by definition of limit, there mu...

I'm watching the 1987 James Bond movie, The Living Daylights, with Russian subtitles. In the scene where Bond first spots the main female character, he says, in English: "Sniper. Two floors up, center window." In the Russian subtitles, this has been translated as: "Снайпер. Двумя этажами выше,...

I was curious about why the pins on my Raspberry Pi didn't have a positive and negative pole, but positive and ground. I read about it on various web pages, but each article I read seemed to answer a different part of the question. I think I got it, but I'd like to have confirmation. I will use a...

This is a problem that happens to persist for 2 days now. It feels like a ticking time bomb knowing that this happens again after one hour. The error message that appears says it is a kernel panic: "panic(cpu 3 caller 0xfffffe002ea90028): userspace watchdog timeout: no successful checkins from lo...

How would I be able to explain a city that is underwater, floating in place and such. Without it constantly moving. Basically, how can I explain how it stays in place and doesn't get pushed? The city is deep underwater, around 400 meters at the shallow end, and is basically a bunch of passages co...

It seems reasonable to me to conjecture that the weak derivative is a special case of Radon-Nikodym derivative between measures. Recall that (missing some technical details): Weak derivative: given a function $f:I=(a,b) \rightarrow \mathbb{R}$, $f'$ is called its weak derivative if for every $\v...

Background Numeric Mahjong is a hypothetical variation of Japanese Mahjong, played with nonnegative integers instead of Mahjong tiles. Given a list of nonnegative integers, it is a winning hand if it satisfies the following: its length is \$3n+2\$ for some nonnegative integer \$n\$, and it can b...

I'm thinking about implementing a race of flying creatures into my current setting, specifically, an earth-like planet with a breathable (enough) atmosphere. Now the easiest way to do this is just creating a race of bird-analogs, but i stumbled across a specific picture which made me love the ide...

I want to know what exactly state preparation means in a quantum computing. Are preparing a quantum state by applying different operations on it or we are preparing by some other methods?

I want to upgrade my headset to a different one. As I was researching my frame specifications, it says: Steerer headset: 1-1/8 Ahead" I don't understand if something like this would work. Basically, I couldn't put my finger on what the "ahead" specification enforces me to choose. Would appreciate...

I am trying to understand consumer behavior in microeconomics. Consider a market basket of food and clothing. Utility / Satisfaction of 200 gram food + 2 shirts is always supposed to be greater than that of 100 gram food + 1 shirt, because 'more is better'. So the 1st combination lies on an indif...

Ural Airlines flight 1383 had to land in a field due to hydraulic problems and fuel shortage. The airline does not dismantle it, but repairs and is going to fly it. A320 landing gear is not suitable for soft surface. How are they going to make it run and take off?

We consider the category of endofunctors of finite sets with natural transformations. Is there an infinite chain $F_1, F_2, \ldots$ of endofunctors such that there is a natural transformation from $F_i$ to $F_{i+1}$ for all $i\in \mathbb{N}$ but no natural transformation from $F_{i+1}$ to $F_i$ f...

We want to take a 1-week trip to England with my wife in November. We will land at London STN airport on Monday and we have a flight from London STN airport the following week. It's our first time coming to the UK and we're a little confused about planning. We roughly made a plan like this, but I...

I'm in the process of redesigning my network and have a few questions about LACP configuration: Can LACP be set up to connect to two different firewalls? In the diagram I provided, there are three lines representing LACP. Can this be consolidated into a single line, especially given that the swit...

Wikipedia writes The tau was independently anticipated in a 1971 article by Yung-su Tsai.[8] Providing the theory for this discovery, the tau was detected in a series of experiments between 1974 and 1977 by Martin Lewis Perl with his and Tsai's colleagues at the Stanford Linear Accelerator Cente...

C++20 added concepts, and the standard library includes quite a few of them. One concept in particular caught my eye: std::invocable which validates that a functor can be invoked with a set of arguments. std::invocable is just syntactic sugar for std::is_invocable. However, the standard library f...

On Windows 11 is there a way to confirm if a background is transparent on a PNG file without having to install a photo editing program like GIMP or Photoshop?

Let $\bf Rel$ be the category whose objects are sets and whose morphisms are relations. What is an epimorphism in this category? I have a sufficient condition, which is: $R$ is epic if the associated non-deterministic map $A \to 2^B$ is 'surjective on singletons'. Another sufficient condition is ...

As far as I know, there are 2 main ways to add rules in firewalld, normal "zone" rules and rich-rules. Also, I understand that when we set target="DROP, all new incoming connections will be dropped unless we add rules to allow selected incoming traffic. I want to ask is there any standard pattern...

I am reading Les foules by Guy de Maupassant and I find this sentence: Toutes ces personnes côte à côte, distinctes, différentes de corps, d’esprit, d’intelligence, de passions, d’éducation, de croyances, de préjugés, tout à coup, par le seul fait de leur réunion, forment un être spécial, doué d...

Let's assume I have n identical resistors. I can connect them either in series or in parallel (let's disregard bridge connections for now). Now, I want to list all possible connections along with their equivalent resistances. For example: "pp" represents a parallel connection. "ss" represents a s...

Is there a simple way to conclude whether the following series converges or diverges using the ratio test? $\sum_{n=1}^\infty \frac{1}{n^n}$ My level is multi-variable calculus. (Note: I know this can be easily found with the root or comparison tests)

An element $a$ of a ring $R$ is nilpotent if there is an integer $n$ such that $a^n = 0$. Every element in a ring must have some $n$ that makes this true (the order of the element). So why is every element in a ring not a nilpotent?

I'm reading Ανάβασις by Xenophon. Here Klearchos has basically said: "someone else might want to command at this point". ὡς δὲ τῷ ἀνδρὶ ὃν ἂν ἕλησθε πείσομαι ᾗ δυνατὸν μάλιστα, ἵνα εἰδῆτε ὅτι καὶ ἄρχεσθαι ἐπίσταμαι ὥς τις καὶ ἄλλος μάλιστα ἀνθρώπων. It's this word ᾗ that mystifies me. From Perseu...

Tofu is always being touted as a "flavour sponge" due to its texture. Yet, I have never been able to get it to actually absorb any flavour. People talk about marinating it, searing it, invoking sacred incantations, yet nothing works (for me). Is there a genuinely tried and tested method that work...

I am not very bash-fluent, but I really need to comprehend what does the following mean and what is the explanation? The code is not mine, but I trust the source I am especially bothered by the expression in the if clause, what's the benefit of having DISABLE_CUSTOM_CREDS twice? if [[ -z "${ENA...

I think I am okay here but would be really good to triple check! My current cassette: Shimano 105 5800, 11-speed, 11-28t My front chain ring: 52-36t My rear/front derailleur: Shimano Ultegra 6800, 11-speed I would like to change my cassette to Shimano 105 R7000 11 Speed Cassette (11-34t). I've ha...

Consider the minimal example RegionPlot[{x^2 < y^3 + 1, y^2 < x^3 + 1}, {x, -2, 5}, {y, -2, 5}] Then I can use PlotStyle -> {Red, Yellow} BoundaryStyle -> {1 -> Green, 2 -> Blue} to, for example, set the red and yellow the first and second region, respectively. And also turn the boundaries green...

I am trying to understand how to use a MOSFET as a switch. I want to use a microcontroller to control a load using an AOI508 MOSFET as in this schematic: simulate this circuit – Schematic created using CircuitLab Now, if this were using a mechanical switch instead of a MOSFET, we could determi...

This has been bothering me for years and I never finished reading the book. When I was younger (around 1994-1996) I read a young adult book about a youth who finds a ring in graveyard. They put on the ring and spin it causing them to go back in time (if I remember correctly the youth only goes ba...

From all the files in a directory, the method shiftFilenamesOffset is to increment the numeric part (int) of the alphanumeric filename by offset each time, and rename the files. A negative offset is also allowed. Example: offset: -2 Old filename: New filename: Textdokument (neu) ...

I heard that wheat and bajra came very late in India while many other crops were there much before.

Is there a way to start a Windows Terminal Preview process? I know you can start the regular Windows Terminal using wt.exe, however, I am using the preview version and would like to open a terminal preview instance from a program. I have searched Google, but I always just seem to find how to open...

I try to compile the following code with luatex \documentclass[a4paper,11pt,latvian]{article} \usepackage[margin=2.5cm]{geometry} % for margins on a A4paper \usepackage[shorthands=off,bidi=basic]{babel} \usepackage[skip=5.5pt]{caption}[2020/09/12] \usepackage[Export]{adjustbox} % #124 \usepackag...

I have 5 pictures and want to align them that three pictures are on the left side above each other and two on the right side. I have tried it like this \begin{figure} \centering \begin{subfigure}[h]{.48\textwidth} \centering \includegraphics[width=0.9\textwidth]{pictures/deltaphi_09_21.png} \capt...

If both houses of Congress vote to grant a letter of marque and reprisal, does the President need to sign it (or have a veto overridden) in order for it to be valid? (I do understand that this power of Congress is mostly obsolete, but I believe they do still have the power. As far as I know, it i...

Let G be a group. Let n be a fixed natural number. Consider $S=\{g^{n}|g\in G\}$. Is this set a subgroup of G? For n=1 it is the trivial subgroup, for $n\geq 2$ we need the condition that G is abelian to say that this is a subgroup. But I was unable to find a counter example for non- abelian case...

When I first started studying modular forms, I was told that we can consider any congruence subgroup $\Gamma\subset\operatorname{SL}_2(\mathbb{Z})$ as a level, but very soon the book/lecturer begins to focus on the three types which are usually denoted by $\Gamma(N),$ $ \Gamma_0(N)$ and $\Gamma_1...

In the schematics at the end of this document, there are a bunch of resistors. The author says in a footnote: Part Notes, All Pages: Unless noted: Resistors are 5%, 0.12 W, or better, for standard 5% values. Resistors are 1%, 0.25 W, or better, metal film, for standard 1% values. Resistors ar...

Here are a few first measures of "Pomp and Circumstance, March 1"'s score: What puzzles me is that in both the oboe and clarinet staves, we can clearly see two instruments indicated, yet there are instances where only one note is specified. Should this note be played by the higher-voiced instrum...

Any insights into the historical rationale for using the term 'Edges' to describe connections between vertices...as distinct from the term 'Lines'?