The Holtzman Shield in Dune works by blocking the movement of objects faster than certain threshold. This has rendered projectile weapons obsolete in universe and combat has become primarily melee. The root mean square velocity of air molecules at 25 degree Celsius is about 500m/s. In the 2021 mo...

So the documentation is all mixed up and I can't find how to get unitaries, statevectors, etc. in the AerSimulator module. For an example, see e.g. this docs. In the old days, one would get this information using only the Aer module (as described in the previous link). But now, fresh qiskit insta...

Let's introduce a quark $SU(2)$ doublet. We are in the $m_u \approx m_d$ limit. So we have $$ q = \begin{pmatrix} u\\ d \end{pmatrix}. $$ Then we can construct the Nucleonic field $$ N := q q q = \begin{pmatrix} p\\ n \end{pmatrix}. $$ I expect this to transform as a $SU(2)$ doublet, which corres...

The Wikipedia article on Runge-Kutta Methods lists several examples of each order. My question is, are there any particular advantages using one particular scheme over another of the same order? I wanted to complete a convergence test of the Advection Equation, which is as follows: $$ \frac{\part...

I read something about the difference between suggest and recommend but I do not know if it's true or not. "The verb “suggest” is used to propose an idea or opinion. It is often used to offer a possible solution or to make a gentle or polite proposal. On the other hand, the verb “recommend” is us...

Let $M$ be a smooth manifold, and $L$ be a smooth real (non-trivial) line bundles over $M$, is it then true that $L\oplus L$ admits a non vanishing section? Intuitively, I feel like the answer should be yes, since I think I should be able to take a global section $s$ of $L$, and then obtain a new...

We make sure to ask Hashem for permission before we eat food and most of the blessings relate to the type of food being eaten. But when we eat a food that doesn't fit neatly into any other categories, we simply point out that Hashem gave us voices. We say בָּרוּךְ אַתָּה יְ‑יָ אֱ‑לֹהֵינוּ מֶלֶךְ ...

I mean to match (with ls, rm, etc.) files with names test10 to test18, test30 to test38, test22 to test23, with a single regex, in bash. I tried many variants around $ ll "test([1,3][0-8]|22|23)" but I couldn't make it work. What is the correct way to do this?

If the entire Taproot/Schnorr soft-fork was going to implement an entirely new signing scheme anyway that was completely independent from the previous ECDSA scheme, why did it use secp256k1? Couldn't it have used other curves, like Curve25519 and its signature schemes that are being used by many ...

During near field testing I encountered this thing I've never seen neither on the wild nor on the book. The board has an STM32F107 with an 8MHz crystal and no ferrites or choke whatsoever (I'm already crying.) The only other oscillating thing I could think of is the 24V to 5V switching regulator...

I am trying to add a wall sconce. I determined that there is wiring coming down from the attic crawlspace to receptacle low in the wall. I knocked a hole in the drywall as shown above, where it has easy access to the non-metallic cable running down to the receptacle box. However, if I tug on the ...

How to scale the weight of a RC model aircraft? If the scale of an model aircraft is 1/4, what should the scaled weight be?

Should it be "mis + took" or "misdook" (like the t in "mistake")?

Say I have an account with the following buying history: Date Symbol Price Quantity 01/01/2023 AAPL $300 3 shares 01/01/2022 AAPL $100 1 shares 01/01/2021 AAPL $100 1 shares If I were trying to sell some shares on 01/01/2024, am I able to sell all of these shares (5 shares) and qua...

If I read with he v argument a verbatim string, all newlines are replaced with a token ^^M (seems like it is a carriage return in latex). The problem is that when I write this down to a file, it actually writes ^^M instead of a new line. I tried to replace it with \tl_replace_all:Nnn {^^M} {^^J},...

I've heard that you don't have to use だ with いadjectives because it will be redundant since いadjectives already imply affirmation, then there is no need to use だ. And okay, i think i get it, but why… maybe the reason is just "they're affirmative" but why they're affirmative? maybe it's has a very...

I want to show that for all $x_i > 0$: $$\sum_{i=1}^{n}\dfrac{x_i}{x_1 + \ldots+x_n}\;\log(x_i) \geq \log\left(\dfrac{x_1 + \ldots + x_n}{n}\right)$$ I thought of Jensen's inequality but since $\log$ is a concave function, this seems to give me the opposite as for $x_i > 0, a_i \geq 0$, it holds:...

I am curious why the only person who wrote a commentary on the Talmudic tractate Hashanah is the Rosh, Rabbi Jacob Ben Asher. This question is Purim Torah and is not intended to be taken completely seriously. See the Purim Torah policy.

Recently I found this line adapted by Kierkegaard from the Aeneid. In this case "Regina" is a bit of a grim pun as K's fiance (the engagement with whom he had recently broken off) was called "Regine." The website I found it on says, "Queen, the sorrow you bid me revive is unspeakable," but transl...

As in, is it safe to consume the leftover beaten eggs in an egg wash to make scrambled eggs? Today I made buttermilk fried wings. I overestimated the amount of eggs needed for the egg wash and ended up with a relatively large amount of egg wash left after prepping all of the fried chicken. As a...

I'm doing research on the effect of strategic video game play on students' mathematical ability. My independent variable is the number of hours spent playing strategic games daily, but my data is not continuous; rather it goes by interval range (e.g., <1 hours, 1+ hours, 2+ hours, 3+ hours). Mean...

When my husband was alive, we did not have inordinate difficulty in guiding small mammals and birds out of the house. Open the windows, open the doors, employ a coordinated pincer movement wielding brooms or (for birds) light fabric, and after the animal ran or flew past the opened doors and win...

If one was to combine two different variations of sport in a manner that has not been done before, can this new hybrid sport be patented?

I am currently designing a circuit that includes a solid state relay, the CPC1125 . I chose it because it is one of the faster normally closed solid state relays I found. I want it to be optical because I want to isolate the two parts of the circuits which are linked by the relay. The problem is ...

Positive and negative feedback circuits : let the following circuit I want to prove that this system is stable (meaning the op-amp isnt getting saturated) if and only if \$ k_+ = \frac{R_{1+}}{R_{1+}+R_{2+}} < k_- = \frac{R_{1-}}{R_{1-}+R_{2-}} \$ Here is what i tried to do, since \$ V_s = A_0 \...

I'd like to run a function/set of functions when I open a specific file. Just like file type hooks, but for a specific file. For instance, when I open foo.bar, I'd like some functions to run. Maybe those functions are specified on my init.el or in the file itself; I don't mind either. Is there so...

Let k be a field of characteristic 0, but not necessarily algebraically closed. Let P be a prime ideal of $k[X]$ (where $X$ is an n-tuple of variables), and $V := \{x \in K^n: \forall p \in P\ p(x) = 0\}$ be its zero set. Is V irreducible over k? Equivalently: let $I(V) := \{q \in k[X]:\ \forall ...

I am transcribing the Sentimental Tango for four hands by Vasha Azarashvili. And I'd like to obtain this: But my code (in Italian, but surely you get the point) \language "italiano" <sib re sol>8_. r16 <sib re sol>_. produces this: How can I get the former?

I had always heard it as "Yeddo", but then the other night the Japanese actors in the new Shōgun series seem to favor the un-glided "Edo," and looking it up on jisho.org I find that the furigana give it as えど, though they quote Wikipedia in saying that "Yeddo" was used for purposes of romanizatio...

I am trying to solve this question: Your brother-in-law asks you to lend him $100,000 as a second mortgage on his vacation home. He promises to make level monthly payments for 10 years, 120 payments in all. You decide that a fair interest rate is 8% compounded annually. What should the monthly pa...

I am a PhD student in mathematics in the US, scheduled to graduate this year. Last fall, I applied for postdoc positions. My situation is a bit complicated: in late January, I was offered a postdoc position in China. I wasn't particularly thrilled about this opportunity because there's no one wor...

I have two small tribes which are in a similar, small geographical location. One of the civilisations is a group of warriors, called Wolves, who have trained to be warriors since children. The others, which is more numerous is called Sheep, and they are pacifist, so do not fight. The Wolves are r...

I'm considering recommending, in a short timeframe, some sort of CRM that integrates as natively as possible with Drupal. Salesforce is probably overkill for our needs. CiviCRM, and most CRMs, could probably meet it, to the extent they integrate. Monday is currently in use but likely able to redi...

Math Stack Exchange! I am trying to figure out how to prove that the value of the infinitely nested radical $$x = \sqrt{2^0 + \sqrt{2^2 + \sqrt{2^4 + \sqrt{2^8 + \ldots}}}}$$ is 2. I have already established that this expression converges based on Herschfeld's Convergence Theorem, but I am now in...

Why would a file show up surrounded by double quotes with a character surrounded by single quotes within it? "insight_automation.log'.'2024-03-13" I am using Ubuntu Server 22.04.3 LTS. A service desk management program (Atlassian Jira Data Center 9.12.4 if that is relevant) installed on the serv...

I recently learned that the word "tholian" is an Old English word meaning "to suffer, endure." Is it known whether Judy Burns and Chet Richards knew this fact, and deliberately created a "Web of Suffering," or is this a coincidence that I'm overinterpreting?

If I understand correctly, an acid corrodes things because the hydronium ion attracts electrons away from whatever it is reacting with. Do bases corrode things in a similar manner? with the metal cation operating in the same way as the hydronium ion (taking electrons)?

I'm trying to experiment with SOLID in order to get a better grasp of its' concepts. With that in mind, I'm making a card game project. There's a GameUtils project that contains the following classes: IPlayer, ICard, and IDeck. Then there are projects for each game, such as Hearts, GoFish, and W...

I discovered my house kitchen vent doesn't actually vent anywhere. Since I cook a lot of Chinese food, it means the air is always oily. I bought a brand new high-powered ceiling fan, pulled out the old unit and and installed this with the help of an electrician. The plan was to drill a 6" hole di...

There's a question on math SE (question 4879248) about this integral: f = (z-a)/Sinh[z-a] (z+a)/Sinh[z+a] Integrate[f, {z, -Infinity,Infinity}, Assumptions->{a>0}] The integrand f is positive and real and free of singularities on the entire real axis, the integral converges, and the ans...

I want a 3km buffer from a coastline but only on the seaward side. How would I accomplish this? I tried using difference but it didn't work I initially got a geometry error which I fixed and still no good. The new layer (after using difference) just replicates the initial buffered layer as far as...

Disclaimer: Post contains rantish tone, possibly even sarcasm! Lazy designers or those with feelings that bruise easily may take offense. 🤣 I see it all over the place. Like 9 out of 10 gear icons (where there is more than one gear) the teeth of the gears don't touch properly! We all know how g...

E.g., is the following sentence ok? We term this prompting technique as SuperPrompting. If not, how can one use the verb term in this case? I believe one could use: This prompting technique is termed SuperPrompting. However, I'd like to convey the meaning that the term was defined by us. I kn...

If I want to type the string aaa, the least keystrokes I can type it in is 3: a a a. But if I want to type the string aaaaaa, I can do it in 5: a a a ctrl-c ctrl-v, where the ctrl-c refers to copying aaa and the ctrl-v refers to pasting it. Specifically, starting with an empty "buffer" and an empty

My ex-PhD-advisor submitted my paper to the journal I explicitly stated I don't want to submit to. I believe the ex-advisor is busy with other things and doesn't want to bother with submissions, so they are taking a very easy path to publish my work, while not replying to my inquries. If I contac...

I'm new to C, and made this program that parses a string expression into a linked list post-fix expression, and then evaluates it, without parsing the string beforehand. Wondering if there is anything to improve/fix (I feel like my implementation is kinda big...) main.c #include "util.h" #include <...

A potentially controversial issue that can jeopardise the career of one or more people, so I am treading lightly while protecting the concerned persons as much as possible, save a few details for context. This is taking place at a government funded research institute in Singapore (something akin ...

I have a speculative zoology world with large sea creatures. The astrobiologists don't have a submarine, but they have hi-tech scuba suits. I'm wondering about the reasons for why such large creatures would attack one small potential prey item. It wouldn't necessarily have to be out of predation....

X is very clever, even the cleverest in the class, so sharp-mouthed that no one can beat him in speaking. He makes all silent. One day, a new man Y enters the class and makes even X silent. A student wants to say: Even the most powerful can come across someone more powerful than them. What is the...

Hello people smarter than me! I've created a sort-of-a-queue table system, but it seems too simple to be safe from race conditions. Am I missing something or is the following race condition safe? The Schema I have a table, let's call it ProductQueue: CREATE TABLE dbo.ProductQueue ( SerialId B...

I keep looking around on databases like EBSCO and JSTOR and google scholar, but I can't find anything conclusive on the total army strength of the Byzantine empire under Justinian. The Wikipedia article on the Byzantine army has the following to say: The size of Justinian's army is unclear. Bury...

Problem I am trying to typeset a tcolorbox (documentation) called solutionbox which has two distinct parts: the upper section is for the solution, and the lower section is for the explanation. I've defined a separate sectionbox (it's an inline \tcbox{} environment) which is used by the section ti...

I'm using the following code to draw a spiral using TikZ. \documentclass{article} \usepackage{pgfplots} \usepgfplotslibrary{polar} \begin{document} \begin{tikzpicture} \begin{polaraxis}[ width = 100pt, height = 100pt, axis lines = none, no marks, samples = 200, ...

I've written the following program that uses requires without parentheses. The program compiles with msvc but not with gcc and clang. I want to know which compiler is right here. Demo #include <type_traits> template<typename T> requires !std::is_enum_v<T> void foo(T) { } int main() { foo...

If we consider the claim that it would be wrong for Facebook to partake in social engineering to influence election outcomes, we may ask, to what extent are people already swayed by this or that social force, influencing how they vote? What might be an insightful ethical analysis of this? For exa...

Let $A, B$ be Morita equivalent $\mathbb{E}_1$-ring spectra. Fix an an $(A, B)$-bimodule $P$ and a $(B, A)$-bimodule $Q$ such that $P \otimes_B Q \cong A$ and $Q \otimes_A P \cong B$. If $A$ is bounded below then $B$ is bounded below, because $P, Q$ are perfect $A$-modules (hence bounded below) a...

I am using nucleo-f401re board for my project and I want to write sensor data to SD card. I am writing data when sensor interrupts occur, and that happens at 408 Hz, so I have around 2 ms to write data. I am using SPI at max frequency to communicate with SD card reader, I am using micro SD card r...

We know that AI is rapidly growing. do we have any large language models (LLMs) to process images, pdf documents directly (fine-tune approach) for text generation tasks?

Is there a way of using custom hdris in material preview mode, whether it be by going into the program files or is there a way of doing it inside blender?

When translating it from Vietnamese (my mother tongue) to English, it is "it's as easy as eating candy". That is a common expression in Vietnamese. I couldn't find this phrase "** as easy as eating candy**" in any English dictionary. Interestingly, I see about 15 phrases containing it from Google...

Let $f:\mathbb{D}\to\mathbb{D}$ be a holomorphic function s.t $0$ is a zero of order $k\geq 1$. Prove that $f(z)=z^kg(z)$, in which $g:\mathbb{D}\to\mathbb{D}$ is holomorphic. My attempt: Since $f$ is holomorphic on $\mathbb{D}$, then by Taylor's expansion we have $$f(z)=\sum\limits_{n=0}^{\in...

I wished to know how to make a curve normal follow the normals of a nearby geometry. I saw they have asked that already, but slightly different from what I wish I guess... Because in other cases, they input a tilt value, and I don't want that, I want the normals to follow the geometry, only that...

A recent spacetime video about Kerr's objection to the existence of singularities has made want to clear up something about geodesics towards the origin in the Schwarzschild solution. It is said that null geodesics of this kind always terminate at the singularity - but what about the worldlines o...

SpaceX is about launch IFT3 and during IFT2, the booster exploded probably due to sloshing and an engine having something block its fuel supply. What has SpaceX changed to avoid fuel sloshing?

Paperback novel from late 70s or early 80s. Cover shows a door shaped portal with an alien (whom I believe had a canine shaped head, but looked and dressed human in appearance.) exiting the portal in place of who they were expecting to exit. [Some error caused this alien to arrive instead of the ...

What does enclitic mean in Learn to Read Greek, by Keller? In Attic Greek the word tis, ti may function either as an indefinite pronoun or as an indefinite adjective. Its forms are identical with those of the interrogative pronoun/adjective except that the indefinite pronoun/adjective is encliti...

So we all know what happens when there is no liquidity at all; it's impossible to buy or sell a token with no liquidity. But what would happen in the reverse scenario; if 100% of a token's supply was provided to the liquidity pool? I imagine necessarily this would mean that the price is capped at...

There are rules of inference, e.g. in natural deduction they are listed. These rules follow the same rules than the logic language. If we see Modus ponens, a → b, a ⊢ b We can write for the same purpose, ((a → b) ∧ a) → b. So, I don't understand what we gained by constructing the inference ru...

I want to perform various calculations in a document, but I want the result of these calculations to be displayed at the beginning of the document. I have the following approach, but unfortunately the output is always 0. \documentclass{article} \usepackage{fp} % Paket für die Berechnungen \usepac...

Which of these phrases is more correct? I am trying to express that the campsite stewards are trained in first aid and are stationed on site. on-site first-aid trained campsite stewards on-site first-aid-trained campsite stewards on-site first aid-trained campsite stewards (I think it should be ...

I know it has been asked several times, but there is always one step that I don't see. My argumentation goes as it follows: Given the set $\mathbb{V}$ set of all sets, then $V \in V$. Because of the Axiom of Schema of Specfication we can define a certain property $P(x) = x \not\in x$, and prove ...

I have this optimisation problem: $$f(x, y, z) = 2xy + yz \qquad \text{subject to} \qquad \begin{cases} x+y+2z \leq 1 \\ x \geq 0, y \geq 0, z\geq 0 \end{cases}$$ I solved it with "a certain writing of KT conditions" but with "the usual KT" conditions I cannot solve it. The point that gives the m...

Find the real solutions of the following equation $$\frac{4x-1}{x^2-2x+2}+\frac{4x+7}{x^2+2x+2}=\frac{4(2x+3)}{x^2+2}.$$ I think the problem was given in a junior olympiad. My best idea was to denote $x-1=a$, $x+1=b$ and after adding $2$ the LHS becomes $$\frac{(a+2)^2}{a^2+1}+\frac{(b+2)^2}{b^2+...

I have a big project were the package floatrow are used. I discovered that when this package are used, the caption put inside my tables are now show outside. I can't find any way of getting it back inside. Here is my MWE: \documentclass{article} % Document class \usepackage{hyperref} % For hyperl...

If you receive stock as apart of your company compensation is it insider trading to sell covered calls on your stock? What if your spouse who literally doesn't know anything about the company is in charge of the account? Its normal for companies to do a vesting schedule to show they aren't buying...

In terms of UTXO management, I have the following extreme example to illustrate my question. Let's say I have 1 BTC with 100 million UTXOs of 1 sat each (or even 10 million UTXOs with 10 sats each). My question is - is the entire 1 BTC balance unspendable in a higher fee environment OR is it spen...

I have found a statement online saying that there must be an eigenvalue of the Hamiltonian inside the range $(E-\Delta H,E+\Delta H)$. Where the mean value and variance are defined for a random wave function $| \psi \rangle $, so $E \equiv \langle \psi |H|\psi \rangle$ and $\Delta H \equiv \sqrt{...

Last week I was reading this post about a famous Muppet's sketch with Fozzie and Kermit (featuring in episode 110), so I watched it (the video can be easily found on several streaming service, and, even more easily, on the internet). I must admit that my English is quite bad, and in fact, even af...

In my set theory course, we introduced the Axiom of Union. For any set $x$ there exists a set $y$ s.t. all elements of $y$ are elements of some $z\in x$. Notation for this set is $y= \bigcup x$. $\forall x\ \exists y \ \forall z (z\in y \leftrightarrow \exists w \ (z\in w \land w\in x))$ My pro...

I'm new to woodworking and I'm in the process of building myself a workbench for my garage. The workbench is divided into three sections. Each side will have space for storage and the middle will be left empty as I intend to be able to sit at the workbench. This space leaves space for my legs whe...

Why is the footnote text repeated several times at the bottom of the page? How to get the footnote text only once? (and not 6 times as in the following example) \documentclass{article} \usepackage[a4paper,margin=1mm]{geometry} \usepackage{lipsum} \usepackage{tabularray} % https://tex.stackexcha...

Especially at lower altitudes, can we asume that if the tide looks high that there would be more turbulence and vice versa?

Pregnant Egyptian mother who converts to Judaism, what status does the child have at birth?

Today a few questions popped up in my head, and I'm curious to know the answers. a). Let $C$ be a disk of radius $R$ centered at the origin. Given a point on the disk $P = (x,y)$, what is the expected distance between $P$ and $P'$, where $P'$ is a point chosen uniformly at random somewhere on the...

I would like to use quotes with left indents only. The standard \quote command creates both right and left indents. I have been using instead the following: \begin{enumerate}\item[] "place quotation here" \end{enumerate} which has the same effect. I would like to create a command that does the...

This command: sudo chown -R root:root directory will remove the SUID bit and reset all capabilities for files. I wonder why it's done silently and it's not mentioned in the man page. Weirdly the GUID bit is not removed. And it doesn't matter who the file or directory belonged to prior to running...

We know in detail the clothes of the kohen gadol, which he wore specifically for service in the Temple, which he could not wear outside of it. Did the kohen gadol have specific clothes that he wore outside the Temple? The kings of Israel, for example, wore crowns. Did the kohen gadol wear anythin...

I listened to this audiobook story about 2019 as part of an anthology. It may have been Mars where they lived or possibly the moon. The two boys were about twelve. One was the son of the heavy vehicle driver. His dad has a stroke or similar medical emergency so the boys have to drive them all hom...

While reviewing the stabilizer formalism in Nielsen and Chuang, I could not understand why the Toffoli and the $\frac{\pi}{8}$ cannot be described as normalizers, even though they map Pauli group elements to other Pauli group elements. I've attached the screenshot from Nielsen and Chuang as refer...

Is it possible to copy an individual file and preserve its comment? Here is what I have tried. Nothing here works for me on macOS 14.3.1 and Zsh 5.9 (x86_64-apple-darwin23.0). cp file.txt file-copy.txt cp -a file.txt file-copy.txt rsync file.txt file-copy.txt rsync -E file.txt file-copy.txt The ...

In Im Westen nichts Neues (All Quiet on the Western Front), Remarque uses the phrases "fünf Tage Dicken" and "fünf Tage Kahn." Can anyone explain those phrases?

On a recent trip to Egypt, the hotel required - either for obvious economic-situation or legislation reasons - that the payments for my room and booked tours be paid in US Dollars. The payment was made via an online portal that seemed legitimate (it went via MasterCard's portal site at least), a ...

What optimal strategy can I apply to earn this achievement?

I recently had the opportunity to study some (very basic) model-theory, and that made some theorems in ring theory become immediately more interesting. For example, one characterization of the Jacobson radical of a ring $R$ makes it possible to express the formula "$x \in J(R)$" as a first-order ...

I have a folder with the name "Mexico" and inside I have pictures in .jpg . How do I copy the folder name into the filename. thats current: Mexico(folder) 1.jpg 2.jpg thats what I want: Mexico(folder) Mexico1.jpg Mexico2.jpg And afterwards cut out the picture files and send...

While the Gemara usually sides with Rava, there are famously 6 places where we say the Halacha is like Abaye, known as יע"ל קג"ם (as explained by Rashi) יאוש שלא מדעת - אביי אמר לא הוי יאוש (Bava Metzia 21b) עד זומם - אביי אמר למפרע הוא נפסל (Sanhedrin 27a) לחי העומד מאליו - אביי אמר הוי לחי (Er...

We found this device in our school. Does anyone know what this can do exactly, and how it could work? We managed to input values into the bit storage on the top, but nothing more. Can we calculate things by using the registers? It would be already helpful to know what the symbols like AD, EX, A...

We usually have need for a Map<Id, Integer> counter which does the following: for (thing t : things) { if(thingCountMap.containsKey(t.id)){ thingCountMap.put(t.id,thingCountMap.get(t.id)+1); } else{ thingCountMap.put(t.id,1); } } Is there an apex built-in or s...

Let be $X$ and $Y$ two random variables such that, for any event $A$, $P( X \in A \mid Y) = P(X\in A)$ with probability 1. Can I conclude that $X$ and $Y$ are independent ?

I've been reading through the Deck of Many Things and Skull got my attention. It says the Avatar of Death appears and attacks you, warning all others that you must win the battle alone and If anyone tries to help you, the helper summons its own avatar of death The battle should proceed until ...

I was thrilled to watch the 3rd test flight of SpaceX Starship today. One thing I noticed watching the video was that debris came off the ship. This was more noticeable during its coasting phase. Some of the chunks looked fairly large. In this video, you can see a few nice examples between about ...

1 fruit is missing, are you able to find it?

More than a dozen Earth-like planets have been discovered around nearby stars based on observations of changes in the brightness of their sun as they pass across its disk (transit events). If an Earth-like planet has a satellite like our Moon, its trajectory is slightly perturbed. Is this disturb...

Consider two discrete binary random variables A and B. If $P(A=1,B=0) = P(A=1)P(B=0)$, can we conclusively say that A and B are independent? My response is we cannot conclusively say they are independent because the $P(AB) = P(A)P(B)$ should hold for all possible values of A and B.