In all books about information coding theory, scientists describe shift registers of various configurations, but they always use the initial state "all 1" in any configuration and any bit depth. In practice, open sources of satellite and mobile communications also mention this initial state. But,...

The set-theoretic cardinal numbers form an abelian monoid under addition (ignoring size problems). Under the axiom of choice, given two cardinal numbers $c$ and $d$, there exists a cardinal number $e$ such that $c + e = d + e = e$. We now determine its groupification (or "Grothendieck group"): Co...

An approximation of the dimming of exoplanet transits can be obtained by dividing the areas of the disks of the exoplanet and star by each other. Taking the radii of Jupiter and our sun results in an area ratio of (69,911 km)^2 / (696,340 km)^2 = 0.0101, so a brightness change in the 1%-5% range ...

So, having rejected mind uploading in their quest for immortality, the people of my worldbuilding project now seek to develop brain transplanting. The main problem is immunorejection; if you simply chucked a brain into an donated body, then said body’s immune system will attack it and the brain w...

I am updating my Ubuntu distribution from 18.04 to 22.04. I exported the Ubuntu 18.04 instance with wsl --export Ubuntu-18.04 <file.tar> to a tarball and am trying to figure out how to effectively extract the files I need from it into my new 22.04 instance. I know I can... view the contents of t...

I’m writing a document in Swedish with Babel and feel that the hyphenation is rather strange. And I can’t seem to find any rules defined specifically for Swedish in either babel or polyglossia. Are there really no rules defined? (Or is it simply that I don’t know what I should be looking for.)

Dans Jean de Florette de Pagnol, Attilio écrit à Ugolin : Je t’ai pas répondu de suite pourquoi ma sœur s’est marié avec Egidio, celui qui la chaspait tout le temps. Mintenant, s’est son droit. The whole letter is full of amusing misspellings. But I find it hard to reconcile my best guess, chas...

In my city, in quite a few locations there appear to be wire jumpers from each phase to the earth(?) wire. They appear to have ceramic insulators, so I suspect they aren't just directly connecting phase to earth (notwithstanding that it doesn't work very well that way...) I'm not asking about the...

As an exercise for myself, I made a diagram where the goal is to solve for $w$ when $x$, $y$, $z$, and $k$ are known. I know this problem already exists but I'm having trouble locating it online: The circle at $D$ is touching the circles at $A$, $B$, and $C$ at a single point. To find $w$, I dec...

Coming from 5th Edition, the Weapon Finesse feat doesn't seem particularly useful for non-Rogues since it doesn't let you use your Dex mod for damage. Are Dex-based melee builds which don't get Sneak Attack just not very good in 3.5? If they are, what makes them so?

A sticker near the door inside a car said: Exposing a battery to intense heat may cause deterioration. Do not bake over 158F/30min or 176F/20 min in painting. I understand the first sentence, however, I can't see how words "bake" and "painting" are relevant in the context of batteries, can some...

Recall that SSSTriangle[a,b,c] is the symbolic representation of a triangle with sides $a$, $b$, and $c$. One can compute its area by (for instance): Area[SSSTriangle[3,4,5]] (* 6 *) Motivated by this problem, I'd like to find the triangle with the maximum area under the constraints $0 \leq a \...

One can consider a variant of the Dedekind-Peano axioms in which one replaces the assumption that every number has exactly one successor by the assumption that every number has at most one successor, leaving the other axioms the same (and in particular retaining the second-order induction axiom)....

From the article "Elon Musk's Appetite for Destruction" (archived version for posterity), published January 17, 2023 on the web and slated for publication in the January 22 issue of the New York Times Magazine: Slavik sent me one of the complaints he filed against Tesla, which lists prominent Au...

Could my rogue planet sustain/evolve complex multicellular life in its oceans? Details The planet is very volcanically/tectonically active. The planet is about 1.25 the size of earth. The planet has a very thick atmosphere of primarily nitrogen and oxygen with notable amounts of carbon dioxide. (...

I'm trying to use a matrix in a foootnote, the text compiles but i'm getting this error ''... l.198 ...\sigma}^{i}$ son las matrices de Pauli.} The control sequence at the end of the top line of your error message was never \def'ed...'' Here is my code \footnote{ In Weyl's base ${\gamma}^{\mu} = ...

I'm setting a personal OKR for improving my communication with team mates, but I'm stuck because I don't know what measurable key results would demonstrate improvement. I'm doing this because it was pointed out as an area I need to work on in my recent performance evaluation. Specifically, a team...

I have a built in floating desk in my new house which the previous owners installed. The desk I believe is made from MDF with 2 brackets holding it to the wall, also wood but not sure what type. The desk is 3.30m in length, 62cm depth and 4cm thick. From what I can see the brackets are attached t...

l-o-n-g time searching for an old Chinese movie (english dubbed) about a man who accidentally entered a higher realm where flamboyantly-dressed 'gods' (much like Stargate Goa'ulds) were playing a board game and their board game moves were acted out in real life. each god controlled a region of pe...

I am studying the Quantum Fourier Transform and my question regards section 4 from this link. Specifically, I do not understand the step where they rewrite in fractional binary notation- could someone explain to me what that means? I tried to look it up but did not find anything relevant to this ...

Problem Let $X\sim f_X$, where $f_X$ is the probability density function of $X$. Let $g: \mathbb{R} \to \mathbb{R}$ a strictly monotonic (decreasing or increasing) mapping. I aim to prove or disprove: $$ g[\mathrm{median} (X)] = \mathrm{median}[g(X)] $$ Try Let $x_0 = \mathrm{median} (X)$, $Y=g(...

Why does the United Kingdom use strategic missiles made in the United States, such as Trident, instead of producing their own? It is understandable that they would import tactical missiles, but why would they need to import strategic missiles?

I’m looking for a book that I read when I was younger. It was a 90’s horror anthology book. The particular story that I’m looking for was about a group of teenage boys. They go to a local video rental store to rent a snuff movie. Whilst there, they come across another young boy who goes back to ...

Is it possible to smooth out the faces on the right shape to make it look similar as the shape on the left? As you can see, the shape on the right still has the edges visible and the shape on the left does not. I don't want to have edges on the shape on the right. I want a smooth surface just as ...

E: The repository 'https://ppa.launchpadcontent.net/flatpak/stable/ubuntu kinetic Release' does not have a Release file. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration det...

Thanks in advance for any advice - In 2018 we had the water main to a small apartment building replaced. Additionally, two exterior hose-bibs were installed. The plumbers installed the hose bibs without a dedicated shut-off valve. To shut off water to the bib in the Winter, we'd be shutting off t...

I live in Jackson County, Illinois. I failed to check if there was an easement before buying my house, and got saddled with a 50-foot-wide ingress/egress easement. I know this is unusual, but it really isn't a utility easement. The owner apparently gave himself the easement when he sold the land ...

I have two eigenvalues that are given as functions of two parameters $a$ and $b$ $$\lambda_1 = - a -\sqrt{ a ^2-b^2}, \lambda_2 =- a + \sqrt{ a^2-b^2}$$ I have a restriction that $a \gt b > 0$. I have been trying all sorts of things to determine places where the signs are the same (both negative,...

I am planning on dual booting a windows 11 laptop with an AMD Ryzen 5 processor, 8 GB RAM, and 512 GB SSD with Lubuntu. I planned on using Lubuntu because it is lightweight, and I wanted to use a distribution that is well-supported (I assume this since Lubuntu is an official flavor of Ubuntu). Ho...

A block on Bitcoin blockchain contains about 4000 transactions. Since a block is added approximately every 10 minutes, in 3 months, about 51 million transactions can be added (4000 x 6 x 24 x 90 = ~51 mil) A bad actor such as a government could post transactions for full capacity for 3 months wit...

The second halves of the first two seasons of A Certain Scientific Railgun seem to contain content not seen in the manga. Are they considered filler and thus not canonical to the overall plot of the Raildex Universe? In particular, I am asking whether the Silent Party Arc and the Poltergeist Arc ...

Let $P$ be the set of all polynomials with integer coefficients, one variable, and deg $n \ge 1$. A number is said to be algebraic, $\mathbb{A}$, if it is real and the solution to an element of $P$. For a given $a \in \mathbb{A}$, let $f_a(x) = c_1 + c_2 x + c_3 x^2 + \dots$ be the (not necessari...

"Scientists discover emperor penguin colony in Antarctica using satellite images" This is the title of an article in the Guardian newspaper today: Guardian There must be some clever penguins down there? I appreciate that this is ambiguous because of a slip in punctuation, but it is only truly a...

So, in the relatively-far future, humans, in their endless quest for immortality, develop a form of mind uploading. This involves scanning the brain, cell by cell, and creating an electronic model of the neurone patterns in which all the information about the subject, their memories, likes and di...

I recently inherited an old 4” PowrKraft jointer, from the early 50s. I measured the old blades with digital calipers and found that they are 4” x 0.71” x 0.11”. I can’t find a reliable source on what size the blades should be, let alone a supplier. Is it generally safe to use shorter blades? Are...

Is it possible for a living creature to have no need to breathe? So this question came to mind when I was pondering the plausibility of space-dwelling life forms. I did some research and I came to the conclusion that living creatures as we know them need oxygen (or in a grander scale some sort of...

So, a group of mine made this doubt pop up: do huge creatures have reach just because of their size? From what I understand, a creature has reach on a melee attack only if it's written as this one (an adult red dragon used as an example) jaws +29 / +24 / +19 (fire, magical, reach 15 feet) The d...

I listened to a recent episode of the podcast Conan O'Brien Needs a Friend where Conan off-handedly refers to Superman being able to crush a piece of coal into a diamond. Instead of simply enjoying the content of the podcast, I immediately combed the recesses of my memory to see if I could rememb...

Consider a complex sequence $\{a_n\}$ defined as follows: $$a_0=0 \text{ and }a_n=\frac{1}{2i+a_{n-1}}, \text{ for }n\geq 1.$$ I am interested in showing whether this sequence converges or not. My attempt: I made use of the fact that if a limit, say $L$, of the given sequence exists, then it must...

Let $M$ be the Mandelbrot set. Question: Is the interior of $M$ dense in $M$? My intuition is that this is true, and moreover that hyperbolic components of the interior are dense in $M$ as well, and moreover that this is known (as it is not very close to the Hyperbolicity Conjecture and thus not ...

I've loved Shostakovich's 8th quartet for ages but only just now looked at the score. I imagined the second movement would be a sea of black notes given its breakneck pace and was shocked to see that it's mostly whole, half, and quarter notes. The indicated tempo is whole note = 120 (quarter not...

The Flash always goes by the moniker of "The fastest man alive" , but there have been many villains who have shown they are faster. So who's the definitive fastest person in terms of running speed in the DC Universe? I don't care if it's a villain, a hero or an anti-hero and answers from the comi...

I have a directory of FASTA files, some of which are empty (placeholders that were output from a pipeline) and I would like to delete the empty files using a for loop on the command line. From what I have seen so far I can use the wc -l [file] approach to see "if there are lines present, delete t...

In Acts 26, Paul offered his defense before Festus and Agrippa. Afterwards, they both realize that he's innocent. From verses 30 - 32, The king rose, and with him the governor and Bernice and those sitting with them. After they left the room, they began saying to one another, “This man is not do...

To whom or what is Jesus referring in this passage when he speaks of “something greater than Solomon”? The queen of the South will rise up at the judgment with this generation and condemn it, for she came from the ends of the earth to hear the wisdom of Solomon, and behold, something greater tha...

I am trying to fit my data to the function: a + (b*(c/2)^2)/((T - d)^2 + (c/2)^2) I entered nlm = NonlinearModelFit[data, a + (b*(c/2)^2)/((T - d)^2 + (c/2)^2), {a, b, c, d}, T] However it returned [0.747-533.437/(260.512+<<1>>^2)] How can I know the best fit value of each parameter? data = {{1.,...

How can I create the following table in latex? I am not sure what concept is used to create this table. Are these two independent sub-tables combined in one? Any pointers or suggestions are appreciated.

Below is a dialog between two girls - Maddie and London - talking about a man called Lance: London: So how did it go with the lifeguard? Maddie: Well... London: What's the matter? Didn't he love your outfit? Maddie: Yah but, I don't think it's going to work. London: Why not? He loved your outfit...

It seems like topology is used to model spacetime, but outside of cosmology, it seems like topology has absolutely no use in philosophy. Is topology used to create models that relate to abstract and non-physical concepts in philosophy? I was looking for evidence of this, but couldn't find anything.

I am working a few problems in my textbook for practice and I came across this problem: $y' = \frac{x}{y+2}$ Proceeding as usual: $\frac{dy}{dx} = \frac{x}{y+2}$ Separating the equation: $(y+2)dy = xdx$ Taking the integral of both sides: $\frac{1}{2}y^2 + 2y = \frac{1}{2}x^2 + C$ Simplifying slig...

My cat is a 12-years old American short-hair male. I think I have to take him to a vet for a medical check-up because he is quite old. The inspection items may vary by a vet, so I wonder what are 'must-do' items for a health examination.

Usually, I just enter special characters with the Esc key and hence am not familiar with their real code in plain text. But this seems troublesome in the search box opened by Ctrl+F since Esc simply quits the box. Although some plain text \[Omega] seems to work, I was wondering if any other worka...

Is doing 10 min meditation 6 times same as doing 1 hour meditation? Or is doing 30 mins 4 times same as 2 hour meditation ?

The old english letter Æ/æ in various words have been modernised to either A (Æthelstan to Athelstan); E (Ælf to Elf, Æthelræd to Ethelred) and sometimes both A and E in the same word (Ælfræd to Alfred), sometimes the Æ is most commonly spelt as Ae (Æthelwulf to Aethelwulf according to the Britan...

Is there a way to prevent babel from hyphenating words shorter than five letters? While still allowing the parts on either side of the hyphen to be a minimum of two letters?

Electronics books often use Laplace to analyze circuits, while in physics we use Fourier, most of the times... if not always: from complex impedances to electromagnetism, quantum mechanics, Green functions, etc etc. Various sources maintain that Laplace is somehow necessary to properly analyze ci...

As far as I know, a rail-to-rail op-amp is capable of providing output up to the power supply rails (i.e. from +VDD to -VDD.) I've been using a TLC2272 op-amp to understand this concept. According to the datasheet, the maximum allowable input voltage is VDD - 1.5 V. My input is 0-5 V, but the out...

This has happened to me at least half a dozen times before but I never found a really great solution so this time when it happened I thought to ask here. If I've stayed in one place for a while or been between trips for a while, my backpack and daypack get little attention in storage. Several tim...

Let $x_1,\dots, x_n$ be $n$ variables. For brevity I'll use the following notation: for $I \subset \{1,\dots , n\}$ define $$ x_I := \prod_{i \in I} x_i. $$ Let $e_k(x_1,\dots, x_n)$ be an elementary symmetric polynomial. That is $$ e_k(x_1,\dots, x_n) = \sum_{\substack{I \in \binom{[n]}{k}}} x_I...

I would like to use case-ignoring completion in the file arguments I pass to (n)vim in the internal command prompt: For example, :edit case<tab> should suggest caselower.txt and Caseupper.txt. Or :edit some-<tab> should offer completions including some_underscore.txt in addition to some-dash.tx...

I have this piece of code: int foo(){ return 0;} int main() { int (*float_function)(float) = foo; } Compile using x86-64 gcc 12.2, with -Wall, it produces the warning (Link): warning: initialization of 'int (*)(float)' from incompatible pointer type 'int (*)()' [-Wincompatible-pointer-types]...

In Mathematica 13.2, while defining a function for manipulating and animating a plot of multiple functions, I'm unable to generate a legend for the second and subsequent functions in my list. I've narrowed down the problem to the use of ReplaceAll(/.). Here is a simplified demo: The first Plot[]...

I have a discrete time Solow model and need to derive the golden rule for the economy by setting maximization problem. How can I do that, if I can’t take derivative? Note: required investment can’t be approximated.

From my understanding, lipid membranes in biological systems are made mostly of phospholipids, which have a hydrophobic chain region and hydrophilic head group containing a phosphate. In the membranes, these head groups then all come close together to prevent water from reaching the bilayer's int...

When using the style rules in GURPS (Martial Arts, Shooting Styles, Magic Styles) do points spent on perks provided by the style count toward points spent on "components" of that style in order to gain more slots for style perks or is it only skills, techniques, and spells that count? If so, doe...

The mana from the giant Rosheen Meanderer can only be used for spells with X, but it does not have to only pay the X cost. So, for instance, you can tap an island and the giant and cast Stroke of Genius for X = 2. I'm pretty sure it works like that, just need confirmation.

I am currently studying for my exams in Analysis, and came across a problem that I am not quite sure how to solve. It asks to check whether a given series converges or not, and if it does, what value it converges to. The specific series I am having troubles with is $$\sum_{k=1}^\infty \frac{k^k}{...

I bought a 1977 Gracia Color Video Game TVG 432 (not much to be found online), image from 20th Century Video Games: And the unit works, but the video signal is kind of sketchy. It is not very strong, and when I fiddle with the board, it changes in quality (up to near perfect image). My TV's aut...

I'm a student from germany and currently preparing for some exams. I got an email from one of the professors that contains information about the cheat sheets you are allowed to write and use in the exams. These consist of 4 DIN A4 pages (so default writing paper) you can write your "Formelsammlung"...

I have found, unintentionally, that if you write $\mathcal{P_1}$ you obtain the same as $\mathcal{P}_{\infty}$ , i.e., Is this a bug or a Latex functionality unknown to me?

This is part 8 of the puzzle series Around the World in Many Days. Each part is solvable on its own. Deаr Puzzling, The name of the game here is printer’s devilry, with an added definition part in each clue. In each clue, you must find a single nine-letter word which can be inserted somewhere in...

Say we have a ball. We throw it at the wall at an angle. The ball hits the wall with a force and a direction away from you. The wall then applies a force equal in magnitude and opposite in direction. So the direction was away from you at an angle and now the opposite of that should be back at you...

I'm trying to develop my intuition about when something likely has, or does not have, a closed form expression. So I would like to ask: Have you ever been very surprised that something has, or doesn't have, a closed form? For example: I was once surprised that $\sum\limits_{k=1}^n \sin k$ has...

Introduction So, I recently completed a chess game with a GUI in Python, using Pygame. Upon research, I learned that Pygame is built on SDL, and since I wanted to practice C++ more, I decided to code chess again in C++. I have 5 source files and 6 header files. Since this is a large project, fee...

⚠ It doesn't make much sense to answer this question if you are not acquainted with Gabriel's work and do not even read the linked interview. I always thought that common sense is fundamentally different from the information-gathering systems we have, like the sense of sight. Sounds ironic, but a...

The US government has run a deficit budget every year since 2002. As per this answer, in FY2012, the budget deficit was $1.12 Trillion while revenue was $2.47 Trillion. That was a budget deficit of over 45%, a full four years after the financial crisis started. After that, the budget deficit dec...

In the equation environment, the equation is centered, but the equation number is right-aligned. I would like to have, locally, a list of equations (think enumerate), where similarly the equations themselves are centered but the labels are not. Ideally they should be left-aligned but a bit indent...

From "Address to a Haggis" by Robert Burns: The groaning trencher there ye fill, Your hurdies like a distant hill, Your pin wad help to mend a mill In time o'need, While thro' your pores the dews distil Like amber bead. I think I've managed to get my head around most of the poem, but this line ...

A party's making me question everything. I couldn't find an official quote about the wounded value being added to your dying value everytime you increase (not dropping to 0 HP, but taking damage while down already) the dying value. So is the wounded value added to the dying value every time you i...

Every year in the United States, there is usually a disagreement regarding the raising of the debt ceiling, which was especially noticeable in 2013 when it caused a government shutdown. Why is raising the debt ceiling the only option to solve this issue? Why is it seen as controversial to reduce ...

I want to use tikz or pgf plots to sketch the following figure. I don't know how I can do this. I am new to tikz any help is much appreciated.

0I have the following code where I want to maximize a stochastic function based on two variables. The code is taking a very long time to evaluate but still not giving answers. Can anyone help? Clear["Global`*"] C1 = 100; C2 = 150; P = 500; M = 10000; n1 = 140*(1 - Exp[-0.1*a1]); n2 = 40*(1 - Exp[...

Baker's theorem in transcendental number theory states that $$ \left|\beta_0 + \sum_{i=1}^n \beta_i \log \alpha_i\right| > H^{-C} $$ where $\beta_0, \ldots, \beta_n$ are algebraic numbers, not all zero, $\alpha_1, \ldots, \alpha_n$ are algebraic numbers whose logarithms are linearly independent...

In this wikipedia article there is a description of the difference between the Maxwell-Faraday equation $$ \vec\nabla\times\vec E = -\frac{\partial\vec B}{\partial t} \tag{1}\label{uno} $$ and the Faraday law of induction $$ \mathcal E = \frac d{dt}\Phi_\Sigma(\vec B), \tag{2}\label{due} $$ where...

I'm referring to the incident at Purdue detailed here https://www.ams.org/journals/notices/202302/rnoti-p196.pdf?adat=February%202023 The head of the Purdue math department tried to pressure an older tenured faculty member to leave by setting his salary to 0 (among other things). I actually don't...

I have found that numerals are written separately from a million. So is this transcription correct then: 56.353.829.543 in Worten: sechsundfunfzig milliarden dreihundertdreiundfunfzig millionen achthundertneunundzwanzigtausendfunfhundetdreinundvierzig ?

My goal is to design an encryption scheme for the application so that the backend stores encrypted data and the whole process of encoding and decoding happens on the frontend. And you can be sure that even if the backend database gets compromised the data is impossible to decrypt. I'm in no way a...

I got 200 computer CD games here and I think checking them for viruses would be inappropriate. Also, when I bought software on CD I was always sure there is no virus. I wonder if there ever was software or a game containing a virus on the optical disc? If this happened by accident or with intent,...

So there's this dungeons and dragons themed question where you're a wizard facing 6 trolls. The trolls spawn with 1d4 health (meaning that their health points are chosen randomly from 1-4) and the wizard is able to attack all of them with a fireball that deals 2d2 damage (the damage is calculated...

Some URLs include unicode characters. For example https://en.wikipedia.org/wiki/Durbin–Watson_statistics. All (most?) webbrowsers are able to handle such URLs but some PDF viewers (like Mac's Preview and Skim) aren't. How would one show such a URL in a LaTeX document? You can obviously use \href{...

I would like to restructure my "knowledge" part in the resume (skill level). From the structure I would like to make it similar to this one, only with "flat" rectangles: In-line graphics in text to represent a loading Unfortunately, I didn't manage to adjust the points to a flat rectangle. Second...

I need to replace a switch. When I first took off the panel, I noticed two terminals plus a neutral so I assumed a single pole switch. However, when I went to replace the switch, I found two wires going into one of the terminals, see picture. The top switch is the one that was already installed, ...