To express this question clearly I have to define positivistic logic. In positivistic logic you don't have to say "Snow is white" is true, you can just say "snow is white". It's essential to be clear that in any intelligible discourse on many valued logics the following 5 parameters must be tru...

I drew a curved shape using arc but I can't seem to fill this shape. \documentclass{article} \usepackage{tikz} \usepackage[active,tightpage]{preview} \PreviewEnvironment{tikzpicture} \setlength{\PreviewBorder}{10pt}% \usetikzlibrary{calc} \begin{document} \begin{tikzpicture} \coordinate (O) ...

Given $n$, consider configurations of n points on the sphere such that there is a finite subgroup of $SO(3)$ acting transitively on them. When $n$ is small, there are a few ways to do so which are related to platonic bodies. However, I suspect that when n is sufficiently large, the only way is to...

PDP11 doesn't provide an 'and' instruction - just xor. What is the usual pdp11 assembly code to implement an 'and' ie the pdp11 assembler equivalent of the c code 'a & b' please? What I'm looking for in particular is the pdp11 assembler equivalent to the c code 'if ( a == (a & b)) ...' My 'bit tw...

This philosophy often draws from the concept of duality, where opposing forces like good and evil are seen as inherent parts of the universe, constantly interacting and balancing each other out. In order to keep a state in which there isn't enough Good to bring about the switch to dominance of E...

Why are these meridian lines for longitude not arched lines following up and down from the poles of earth? Does it have something to do with making time zones easier to understand by country? Perhaps the earth isn’t a perfect sphere? I’m trying to navigate using a sextant and find time relative t...

Would it be grammatically correct to say: Two experts is always three opinions. Both parts of the sentence are plurals: "two experts" and "three opinions", so nothing indicates singular form here, except the assumed omitted part: Two experts is (a situation when you have) always three opinions. W...

The coordinates are right and I don't know how to avoid this, I tried using clip but it always makes the lines thinner as I have to make the clipping region an entire rectangle because it can't just be a line, so IDK what to do. \documentclass{article} \usepackage{tikz} \begin{document} \begin{t...

Consider a group G. There are huge studies on group homologies, K-theories of group rings, etc. (As an example of a difficult conjectures in a field one keep in mind conjectures on assembly map (quote:) "The Novikov conjecture is equivalent to the rational injectivity of the assembly map in L-the...

Wikipedia's UFO sidebar template contains the representative UFO image Flying_Saucer_-_NARA_NAID_303938034_cropped.png, which looks like this: This is a cropped version of an image from the National Archives, identified as https://catalog.archives.gov/id/303938034, with the following metadata: N...

I am trying to get a more intuitive understanding on the nature of centrifugal- and centripetal forces, which is my motivation in asking the following conceptual question so that I can deepen my understanding. Consider a rod that is being rotated around its center of mass with a very high angular...

I recently bought my first bike with hydraulic brakes, but the rear brake wasn't working. A friend and I bled it, which temporarily fixed the issue, but now it has stopped working again, clearly due to a leak somewhere. The M355 braking system seems to be obsolete and no longer in production, and...

I have a few questions regarding the metric in GR, if you wish to answer some of them, I would appreciate a detailed answer. (2) Under a coordinate transformation from x to x' the metric $g_{\mu\nu}(\mathbf{x})$ transforms as $$g_{\mu'\nu'}(\mathbf{x'})=\dfrac{\partial{x^\mu}}{\partial{x^\mu{'}}...

This is a Markov chain generator. It reads a file, reads all triples of words, and creates the Markov model. The model it makes is weighted, by which I mean that if "word1 word2 word3" occurs more frequently in the input, then it is also more likely to occur in the output. I think I'm more compet...

I understand that it has the root of 肉 because its related to the body, but why does it have 永.

I'm learning Russian using DuoLingo and in the lesson for Unit 2, something was left a bit unexplained for me. First I was told that verbs change based on the gender of the subject, which I was fine with and was told is as follows: Masculine: ОН УПАЛ Feminine: ЧАШКА УПАЛА Neuter: ДЕРЕВО УПАЛО The...

I want to define a \Limsup command that would work in the same way as \limsup, but with a capital L. However, I'm unsure how to achieve the correct spacing and behavior with \limits.

I define a soft blockchain as a decentralized and distributed network that computes cryptography using a neural network for every peer, thus resulting in a soft hash instead of a hard hash like SHA-256. The application might solve social science problems, especially laws that are related to plagi...

Let $N$ and $K$ be nilpotent groups, and let $\varphi: K \to \mathrm{Aut}(N)$ be a homomorphism. I wonder if then the semidirect product of the groups $N$ and $K$, determined by $\varphi$, is necessarily a nilpotent group? I tried to prove this statement, but no luck. Any idea?

When we proved Cantor's theorem, we first showed that $|A| \leq |P(A)|$ by finding an injective function $A \to P(A)$. Then we showed that a surjection does not exist. Is the injection necessary? Doesn't the non-existence of a surjection already prove the theorem?

I'm in my final year of a three-year mathematics PhD in the UK. This is my second attempt at one; see here for details. In short, in the first attempt, I ran out of funding, the pandemic happened, and I developed schizophrenia, so I cut my losses and left with an MPhil. It was not a failed viva...

I would like two edits to the following code. The first is to have the figure rotated 15 degrees clockwise about the origin. I think that this can be most easily done with a scope environment. The second is to properly fill the region between the dashed line and the broken line with hatching. I w...

Currently the Juno mission is extended until September 2025. Originally it was supposed to be deorbited into Jupiters atmosphere in 2021. Is known if they will extend it again? It will be sad to see our spinning friend go.

Water bill jumped so I started investigating. Water meter showed constant .08/gal/min flow when all water was turned off in the house. Turned off the main and flow stopped. Turned main back on and and flow restarted. Did the dye test in all toilets. No dye transferring from tanks to bowls. I watc...

I have a bike with a basket of unknown material attached which was new two months ago but it's developing black spots after being out in the East Anglian winter, is this mould and how can it be treated or cleaned?

I am looking for a rigorous proof of the consistency and asymptomatic normality of an unbiased maximum likelihood estimator (MLE). Since a lot people from a lot of different academic backgrounds care about statistics, there is a great wealth of material on it on the internet, but it frequently ha...

We just had an ice and snow storm and everything is finally melting. I just noticed this on my ceiling. I have a roofer coming Monday but I didn't know if someone could tell if this looks like roof leak, problem with the attic or mold.

I have a couple of basic questions about visual hyperbolic metric spaces. A visual hyperbolic metric space $X$ is a hyperbolic metric space with the property that there exists an $o \in X$ such that any $x \in X$ is a distance $\leq K$ from a geodesic ray originating from $o$. If $X$ is the Cay...

Is it cheaper to get an eSIM for 2-3 weeks in Japan or buy a physical SIM upon arrival at the airport? Looking for the 5-10 GB range. My general impression is that eSIM is more expensive than physical SIMs (at least that was the case in more underdeveloped countries, but don't know the situation ...

What do people mean when they call music abstract? I’m confused because to me it seems that all music inherently abstract. However, if I write a 4 chord progression and slap some simple melody on top, that would not be called “abstract music” even if this piece is not “about” anything in particul...

My spouse has registered for a class which is required by the state license board to continue working in her field as a teacher. The professor returned her first assignment, which was mostly just a self-reflection on a short article, as the instructor complained it was "not creative enough". She ...

I use Chrome on Android. How can I configure Google Chrome or Android so that whenever I visit a given subdomain on a given site (e.g., www.reddit.com) it always redirects to another subdomain on the same site (e.g., old.reddit.com)?

In contemporary Russian, the plural is gender-neutral. However, pre-1918, Russian distinguished "feminine plural", as Polish, Spanish, some other languages do. For example: Не пой, красавица, при мне Ты песен Грузии печальной: Напоминают мне оне... "Оне", rather than "они", because "песня" is f...

I am writing notes for my students about the magnetic field $\mathbf{H}$ knowing that for the solenoid we have $$H = \frac{NI}{l}.$$ Hence $NI/l$ expressed in SI units, it refers to amperspire (or ampere-turns in English) per meter ($\text{Asp/m}$). In 1997, I remembered that this unit still exis...

I do struggle terribly to achieve the following: It does not need to be done inside bmatrix, but would be nice. Please note that I cannot provide much of my code as all my attempts ended like this as a result to this code: \documentclass[12pt]{article} \usepackage{amsmath} \begin{document} \b...

In SRP, an authentication exchange starts with the client and server generating nonces a and b, and sending their public variants (A = g^a % N and B = (v + g^b) % N) to the other party. However, reading RFC2945, it is quite adamant that The host MUST send B after receiving A from the client, nev...

I have a valid Schengen visa and i wish to travel soon. However there seem to be a few ink residue dots from the opposite pages where the entry and exit stamps were placed. Will this be an issue? Most of the information is intact. Also I have a micro tear on the USA B2 visa sticker page in my old...

My question is about a technique in proving that a statement is unprovable in some theory of first-order arithmetic. To make this definition, work in a nonstandard model $M$ of Peano arithmetic, and let $T$ be the desired theory of first-order arithmetic. An indicator function for models of $T$ i...

My situation: I have Nginx running on Ubuntu 24.04. It has a few configs on it where it acts as reverse proxy, terminating, for TLS domains local to the box (e.g. WordPress). For these, it has certificates, setup by Let's Encrypt. That is working well. These are e.g. https://blog.example.com/ I w...

I'm wondering about this for a speculative evolution project I'm working on. I know atmospheric oxygen concentration affects combustion and the maximum size of animals that breathe certain ways, but I've only ever heard this talked about in the context of an entire planet. Could different places ...

A router receives its IPv6 settings via dhcpv6 and ipv6-address: 2406:13a2:0:2:6013:6aa5:803:7ca4/128 ipv6-prefix: 2406:13a2:19b:2400::/56 Comparing the address and the prefix 2406:13a2:0000:0002:6013:6aa5:803:7ca4 2406:13a2:019b:2400:: Shouldn't the first 56 bits of the router IP and the PD b...

I have this simulated data in R with multiple variables: set.seed(123) n <- 100 x1 <- rnorm(n, mean = 50, sd = 10) x2 <- x1 * 0.7 + rnorm(n, mean = 0, sd = 5) x3 <- -x1 * 0.5 + rnorm(n, mean = 70, sd = 8) x4 <- rnorm(n, mean = 40, sd = 15) x5 <- x4 * 0.6 + rnorm(n, mean = 30, sd = 7) data <- dat...

The integration question $$\int_{0}^1 \frac{\ln(1+x^2+x^3+x^4+x^5+x^6+x^7+x^9)}{x}dx $$ The Above Integral Is of MIT BEE 2024 Quaterfinals 2 Problem#2. BY observing the question you can realize that the expression in the logarithm can be factorised as $$1+x^2+x^3+x^4+x^5+x^6+x^7+x^9 = (1 +x^2)+(...

I am on Python 3.10 and would like to upgrade to 3.13.1. I have been trying to figure out how to do this, and have managed to get it installed, but it uses the python3.13 alias instead of the python alias.

When the USSR acquired Kaliningrad at the end of WW2 they deported (or 'transferred') pretty much the entire German population out of there. (See for instance N. Eaton pp. 229-231) But around the same time, the Nuremberg trials made such (or very similar) deportations a crime. So, how did the USS...

Let $(X,d)$ be a metric space. We define the set that $(X,d)$ "produces" to be the set $$A(X)=\{d(a,b)|a,b\in X\},$$ i.e., the set that gives all the distances that $(X,d)$ "creates." We say that a set $A\subseteq\mathbb{R}$ is good, if $0\in A$, and if $x\in A$, then $x\geq 0$. For every $n\in\m...

We can check that $$\frac{1}{\sqrt{x}}-\sqrt{\ln\left(1+\frac{1}{x}\right)}\sim\frac{1}{\sqrt{x}},\quad x\to0,$$ $$\frac{1}{\sqrt{x}}-\sqrt{\ln\left(1+\frac{1}{x}\right)}\sim\frac{1}{\sqrt{x^3}},\quad x\to\infty.$$ How can I get this result by some general techniques? I tried to discuss the limit...

I buy gay lea butter and lately especially there have been water pockets in the butter. I eat it daily then half way through I hit a pocket and it squirts me. The butter tastes fine and smells fine etc. Just this water. This has happened often lately. Can I eat this butter anyway without hav...

Did Johnathan Edwards apparently misunderstand Jesus' point in John 8:23? In the sermon titled "Sinners in the hands of an angry God" Johnathan Edwards says that sinful man deserves judgement (certainly), has been condemned by God in the law (that's true), then he says this as well: So that ever...

Every problem has multiple possible solutions, some better, some worse. Therefore to have a solution to a problem, it must be chosen. Every choice is made for a set of reasons, to achieve a desired result. Therefore every choice is a solution to a problem: "How to achieve this result with least n...

I am looking for a scene in an episode where Data is reading something on the bridge off of the computer. He repeatedly asks the computer to speed up. I believe he says "Faster, please" a few times.

I need to write code for wye-delta transformation of square resistor grid. I found a paper from 1988, where this algorithm is given , using propagators to get rid of diagonal elements. I started with 3x3 grid, where each resistor has resistance of 1 Ohm and if I run such system on the circuit si...

Say I'm running OLS on a dataset $D$ and a linear regression model $y = \beta_0 + \beta_1x + \epsilon$. If I now duplicate my dataset to obtain $D'$ and run OLS again I get $y = \beta_0' + \beta_1'x + \epsilon$. It is to my intuitive understanding that $Var(\beta_1') = \frac{1}{2} Var(\beta_1)$. ...

I watched this movie between late 2014 and 2016 when I was a kid. It was on a CD, but I don't remember if my mom got it for me or if my older sister had it when she was young. If it was my sister’s, that would mean the movie is from around the 2000s, which might explain the poor quality of the an...

In stabilizer codes, usually, a code state is defined to be a simultaneous +1 eigenstate of all stabilizer operators. In many simulations of QEC, we first prepare physical qubits to the tensor product of $|0>$ states, for example. Then, we encode the qubits to the code state by measuring all stab...

I have a C1 Visa for transit through the U.S. and intend to fly from South America to Fiji. Tickets to Fiji are considerably cheaper if I book a flight to the U.S. on an local airline, then a flight from the U.S. to Fiji on Fiji Airlines (which do not operate in South America). Would it be permis...

I'm trying to separate geometry based on material. The materials are retrieved from a vertex group input. I first separate the vertex group based on Face, to get the faces of those vertex. Then, if I capture the Material Index, I get a range of integers which are all the materials on that vertex ...

I have a nul-terminated char * (may be NULL). For logging purposes, I want to write a function inspired by python's repr() for it: it should return a string such that if the string is interpreted as a C++ expression, it evaluates to a copy of the original. By "copy" I mean that the contents of th...

You are trapped in a room with one door. There are 3 guards in the room. The guards all look identical, and all of them have the same weapon. They're not guarding the door, but the door is locked anyway. You can ask them questions, but yes/no questions only, each time to only one guard. There is ...

I am second year PhD student in neuroscience and imaging. It is a multidisciplinary PhD as it is attended by students with different background (from psychologist to engineers). In such environment, I am a physicist. In the physics world, I knew that authors in an article are listed in alphabetic...

When the plot starts the main character and his sister don't have a good relationship. The protagist's sister went to hang out with her friends at a mountain (or something) then got isekaid, along with main character by accident. He was greeted by the gods of that world and was informed that his ...

The HDMI port for my Acer Nitro ANV15-51 is unable to output any signal. From my research, I believe this is due to the port being directly tied with the GPU. I've tested and used it with windows and the HDMI works properly with that OS. Selecting any of the listed RTX 2050 drivers in the Additio...

So I was reading a children’s book (using the word 風 and using it with many particles), and in explaining ばかり, it uses this: I found a similar expression online, 問題ばかりおこる人, which means “people for which nothing but problems occur,” but I struggle to transfer this definition to “nothing but wind....

Let $S_{n}$ be the $n$-th symmetric group. I want to know why the symmetric product $$(\mathbb{P}^{1})^{(n)}=(\mathbb{P}^{1}\times\cdots\times\mathbb{P}^{1})/S_{n}$$ is biholomorphic to $\mathbb{P}^{n}$. I constructed a map from $(\mathbb{P}^{1})^{(n)}$ to $\mathbb{P}^{n}$, given by $$([x_{1},y_{...

The air molecules near the ground, are at higher temperature and tend to go up. However, in the air pressure context, is the density of air near the ground, much higher than the sky?

I'm learning Natural frequencies for circuits and i found out that the application of it is in circuit design. Basically, we want to avoid to give an input to a circuit (or drive the circuit) with the same frequency as its natural frequency because the circuit exhibits unstable behavior and compo...

Question- see Compiler Explorer If I create an std::vector<int> and initialize it two ways, both call the std::initializer_list constructor. std::vector<int> v1{1, 2, 3}; // Calls vector(initializer_list< int >) std::vector<int> v2 = {1, 2, 3}; // Calls vector(initializer_list< int >) But...

This question was sparked from the fact that, using the mean value property, you can bound the value of $u(1/2)$ given that $u$ is a positive harmonic function on $D(0, 1)$ and $u(0)=1$: \begin{align*} u(0) &= \frac{1}{\pi} \int_{D(0,1)}u \\ &\leq \frac{1}{\pi}\int_{D(1/2, 1/2)}u \\ &=4u(1/2) \en...

So I'm currently writing a RPG campaign with a spacefaring species and I was wondering if you could genetically engineer cells to be able to use electricity instead of ATP as an energy source? Energy storage would be assured by implanted battery or a bioengineered battery-like organ. The goal of ...

I'm just a high school graduate, with no prior knowledge about the psychology field and research. Additionally, I don't have access to professionals. Basically, I had a hypothesis, which lies in psychology field, and I have searched the hypothesis, keywords and similar researcher. I couldn't find...

I'm thinking about a certain issue now and I'm confused so I'm asking a question. Let $A$ be a commutative ring which is a finite direct prodcut of fields. Let $M$ be a $A$-modue. Then, by Every $A$-module is projective if and only if $A$ is a finite direct product of fields., $M$ is projective (...

Let $\Omega \subset \mathbb{R}^n$, $n \ge 2$, be a bounded convex domain. Suppose $x_0$ is the centroid of $\Omega$. Then do we have $$\text{dist}(x_0, \partial\Omega) \geq C \text{diam}(\Omega),$$ where $C$ is a positive constant which is independent of $\Omega$

I have a MediaWiki template in which I want to display or hide a MediaWiki table based on a parameter (showtable=1, it’s an integer). <includeonly> {{#ifeq: {{{showtable|}}} | 1 | <div id="tableContainer"> {| class="wikitable" |- ! Name !! Alter |- | Max || 25 |- | Anna || 30 |} </div> }} </in...

If all 10 stones from pile $A$ weigh 10kg, and all but 1 stones from pile $B$ weigh 1kg, and the last stone weighs 100kg. The greedy approach would not work because it is possible to compare $9\times 10>9\times 1$ and $10<100$ but it's impossible to determine that actually $|A|<|B|$. How?

I don't understand the use of "see" in this sentence because it has "see" lots of meanings. Can you tell me what it means? 75 mins Quiet spell. West Ham are seeing a lot of the ball just at the moment, but they're struggling to do anything meaningful with it.

Must companies keep records of internal messages (emails, Slack messages, MS Teams chats, etc.) in case some court later asks for it, and if so, for how long do they have to keep it? I'm mostly interested in the United States.

In the following theorem and proof from Linear Algebra Done Right by S.Axler See image The author proves the first direction of the theorem but I fail to understand it fully. I have 2 main areas of doubt that might stem from the way I think of the first direction. That's how I see it : "If the op...

I had a 25% belief that Alan was Bertie. Alan then posted a pic of someone that looked very much like Bertie, say 80% sure. The chances of it being Bertie if Alan is Bertie seems very likely, as good as 100%, if you need that information. Alan is often misleading etc., and it is far from certain...

The easiest way to understand this task is to look at this graph, which you can change interactively. It defines a sequence n -> a(n) like this: a(0) = 0; thereafter a(n) is the least integer (in absolute value) not yet in the sequence such that the absolute difference of a(n-1) and a(n) is a sq...

The ultimate teaching of Buddhism is that of anatta or that there is no permanent soul or self as is there no creator Godhead. However across the vast tapestry of spiritual traditions, there are many which not only actively assert the God/soul beliefs but also have many individuals who say they h...

In order for many valued logics to make sense the following five parameters must be true. The logic is positivistic. One of the many truth values is 'true'. One of the many truth values is 'false'. 'and' has the same meaning it has in two valued logic when 'A and B' is asserted. 'not' has the sa...

This image is taken from the textbook Physics for Scientists and Engineers: A Strategic Approach - Randall D. Knight: Using circuikiz package I obtained this \documentclass[a4paper,12pt]{article} \usepackage{circuitikz} \begin{document} \begin{tikzpicture} % Paths, nodes and wires: \dra...

In the answer to exercise 8.7 in The TeXbook, it is mentioned that if \lq and \rq were to be defined as \let\lq=` and \let\rq=', they will no longer work with constants, aka getting the ASCII code of a character or converting octal to decimal, because "\lq will not expand into a character token, ...

I need the bitwise XOR (exclusive-OR) of a list of integers (a function that is to ^ as sum is to +). The following code works, but I suppose the loop is not efficient. def variadic_bitwise_xor(integers): result = 0 for n in integers: result ^= n return result Edit: It is a l...

I often use what we call a 10ms (50Hz half-wave) buffer at work - a circuit to backup input power for at least 10ms. Now I bought a fan-less power supply with 4pin Molex (PC 5V+12V) to power a optical drive. The supply states 4A on each line, the optical drive states it need 2A. I also have a old...

Ephesians 6:13 Therefore take up the whole armor of God, that you may be able to withstand in the evil day, and having done all, to stand firm. Paul urges believers to put on the whole armor of God to withstand "in the evil day." The word for day used here is the singular ἡμέρα. What exactly do...

See the question in the title. I could not yet come up with a counter example, but I strongly doubt that this holds for bag semantics (bag semantics for join and union). What do you think?

Consider a product of (sigma finite) measure spaces $(X,d\mu_X), (Y,d\mu_Y)$ and a measurable function $f:X\times Y\to\mathbb{C}.$ Suppose that for each $x,y,\,$ $f(x,\cdot)\in L^1(Y)$ and $f(\cdot,y)\in L^1(X).$ Suppose further that for all $x,$ $$\int_Y f(x,y)\,d\mu_Y(y)\ge 1\,.$$ Is it possibl...

I am trying to plot the following function versus r for two values of q=1 and q=2: h6[r_, q_, \[Lambda]_, \[Theta]_, g_] := 1 - 2/r + r^2/10^20 - ((-1 + 3.12` g^2) q^2 r^(-1 - \[Lambda]) (-1 + \[Lambda]^2) \Csc[\ [Theta]]^2)/(2 \[Lambda] (3 + \[Lambda]) 10^20) The first two terms of the functi...

Here's the circuit: simulate this circuit – Schematic created using CircuitLab Usually when we build coilguns, they're so inefficient we can reasonable assume the projectile has no effect on the electric circuit. Obviously the energy comes from the circuit so there must be an effect, but I can...

I am looking for textbooks on QFT in curved spacetime that contain a lot of exercises, since Birrell & Davies does not seem to contain any, and the chapter in Wald is very short. What are some good references for someone who has a solid background in GR and QED, and some idea about gauge theory?

I have read a lot of articles and questions/answers on this site about sessions. I understand what they represent (source) : A collection of process groups established for job control purposes. Each process group is a member of a session. A process is considered to be a member of the session of ...

There is a classical theorem due to Whitney that says that for any closed subset $C \subset \mathbb{R}^n$, there is a smooth function $f: \mathbb{R}^n \rightarrow \mathbb{R}^1$ so that $C = f^{-1}(0)$. See A result attributed to Whitney. One way to reformulate this result is to say that if there ...

We’re installing drop ceiling to a 12.25 feet wide room and at one end it is 12 feet 1 inch (they framed the wall crooked (sigh)). With sketching grid we end up with a tiny 3” piece of tile required at the sides meaning we need a whole extra row of tiles cut with an extra piece of cross t. Trying...