What is the rank of a matrix whose entries come from the set of integers? Is it still the number of independent columns? For instake, take the matrix $$\begin{bmatrix} 6 & 3 & 2 \\ 12 & 6 & 4 \\ 18 & 9 & 6 \end{bmatrix}$$ Is the rank of this matrix equals $1$ since the first column generates the ...

I have a question on detecting the outliers in a time series like PPI, CPI, inflation,...etc.) Which method should I use? How can I precisely detect these outliers in a test or a method? Please mention about all methods. Thank you.

For my ESP32 project I want to use a NCP1117 3.3V LDO and soon the question came, which capacitors are suitable if the LDO is driven either by USB or a 5V power supply while the cable length is about 2 meters. From what I understand, the output capacitor is more important than the input capacitor...

I am in a situation that might seems a bit odd. I published my research work in a pretty good journal. However, I believe that peer review wasn’t very strict (in my opinion). And this work is basically my supervisor’s best article ever published. Quite some time passed after publication and now I...

Let $X$ be a variety over a field $k$. The étale fundamental group of $X$ fits into the exact sequence: $$1 \to \pi_1^{\text{geom}}(X) \to \pi_1^{\text{arith}}(X) \to \text{Gal}(\overline{k}/k) \to 1,$$ where $\pi_1^{\text{geom}}(X) = \pi_1(X_{\overline{k}})$ is the geometric étale fundamental gr...

Can the functional form of $G$ in the expression $\frac{V}{\sqrt{gH}} = G(\frac{d}{H})$ be rigorously derived from first principles, where $V$ is the limiting wave speed of a line of falling dominoes, $H$ is the height of the dominoes, $d$ is the gap between adjacent dominoes, and $g$ is the acce...

Is there a way to prove there's only one viable definition of the connectives, which is their truth functional definitions?

I'm really trying find out more about how the early Church understood Communion, or the Eucharist, or the Lord's Table. One of the crucial aspects (for me) is whether they saw the Eucharist as a sacrifice/oblation (as the Catholic or Eastern-Orthodox do). If the Eucharist truly was a sacrifice, t...

I'm trying to create a specific kind of abstract line design that consists of parallel lines with a 3D look using Inkscape. Here's an example of what I'm aiming for: I've been experimenting with various techniques, but I haven't been able to achieve the desired effect. Here is what I have tried ...

The original sentence: The president of the association, spoke about how devastating it was to see something she has dedicated so much of her life to becoming unrecognizable in a matter of minutes. Alternate sentence: The president of the association, spoke about how devastating it was to see ...

I Believe the answer is when the set is closed in the sense of standard topology (we exclude $\mathbb{R}$) itself. Examples: Point sets have a minimum, and they are closed. Closed interval also have a minimum, which is simply the lower bound $[a,b]->a$ If my guess is right, how do I prove it,...

Classically, there’s discordance in the notation of the dual of a vector space over a field $K$. Of course we can all agree that the algebraic dual is the vector space of linear maps from $V$ to its base field. As such it can be represented as $$\operatorname{Hom}_K(V, K).$$ But notations are ple...

For an undirected graph with one connected component and distance matrix given by the shortest path between nodes, I would like to embed the nodes in a high dimensional Euclidean space where all distances are preserved. I have no requirement on the number of dimensions. Can classical multidimensi...

I have an Elops 100 bike from Decathlon, and I thought that perhaps it is possible to adjust the height of the steering column. I wanted to do this a few years after buying the bike, so the steering column has already become rusty. I tried loosening the steering column nut and removing the core b...

Let $(X, \mathcal{M}, \mu)$ be a measure space and denote the Lebesgue measurable subsets of $\mathbb{R}$ by $\mathcal{L}$. Assume $f : X \times \mathbb{R} \rightarrow \mathbb{R}$ has the following properties: (i) $f(\cdot, t)$ is $\mathcal{M}$-measurable for all $t$, (ii) the map $t \mapsto \int...

Am using LuaHBTeX and want to write Vinkel in the caption using bold small caps, but the command \sc{\textbf{Vinkel}} won't do it. \documentclass{article} \usepackage{graphicx} \begin{document} \begin{figure} \includegraphics[width=\linewidth]{boat.jpg} \caption{\sc{\textbf{Vinkel}}A boat.}...

In a previous post I want to compare the last character of a string with other characters I asked how to compare the last character of a string with another char, and the solutions offered have solved my problem. However, I have observed that, if I import the strings from a .csv file, they fail. ...

I am studying this book: x64 Assembly Language Step-by-Step. Programming with Linux-Wiley (2024) JEFF DUNTEMANN If I understand correctly, 1 in hexadecimal is equal to 1 in decimal. However, the table shows, for example: 1H = 16^0 = 1 x 16 = 10H and that equality does not hold, I think. Am I...

I am trying to understand the actual purpose of the read-enable signal on synchronous FPGA Block RAMs. I do not see the actual need of it. But regardless of why it was put there in the first place, can read-enable being low during write operation or when we do not need to use output data actual c...

I am using a ZVS induction heater like this: Image Source The schematic looks akin to this (schematic has not been tested) Schematic Source I modified it with IRF3205 N-Channel MOSFETs for better heat dissipation and more efficiency (lower RDS(on)), and wound the 56 μH inductor on the same iron...

I am banging my head trying to simplify following expression to get rid of the nonessential "I" (I know, I can do it by hand, but this is only a toy example): I (Sqrt[-1 + a^2] - Sqrt[-1 + a^2 x^2]) To get: Sqrt[1 - a^2] - Sqrt[1 - a^2 x^2] Not even the following works: Simplify[I (Sqrt[-1 + a...

OS: Kubuntu 24.04 LTS Laptop: Lenovo IdeaPad 3 17IAU7 Hardware: running lspci command returns: 00:00.0 Host bridge: Intel Corporation Alder Lake-U15 Host and DRAM Controller (rev 04) 00:02.0 VGA compatible controller: Intel Corporation Alder Lake-UP3 GT2 [Iris Xe Graphics] (rev 0c) 00:04.0 Signal...

In a hypothetical advanced society with neurotechnology capable of directly modifying pain and pleasure pathways, one can imagine the specific pathways giving rise to sensations of pain or pleasure being manipulatable such that features like neurotransmitter sensitivity can be adjusted to arbitra...

It is general consensus that Cartesian product is distributive over set difference. However, I am unable to identify a flaw in this example. Let $A$ be a non empty set. Let $X=\prod_{i}^{\infty} A$, i.e. an infinite Cartesian product of A. Let $Y=A$ and $Z=A \times A$. Then, $Y - Z=Y$ and $X \tim...

I have a black sport trail all terrain Rockrider that I bought from Walmart for around 150 dollars. All was well for a few months, until I noticed a loud clunky sound with my pedals that made it hard to ride. The pedals would also feel like they were lighty stopping or fighting against me while r...

I am working through Maxfield and Maxfield's Abstract Algebra and Solution by Radicals, and the following exercise is included after discussing permutations and Cayley's Theorem: Two rows of a certain Cayley table are r q s 1 u v t w q s 1 u v t w r he rows show the eight distinct group members. ...

Both "боля" and "болея" are listed in wiktionary as present adverbial imperfective participle of "болеть". Is there any reason you would use one of these instead of the other, or are they always interchangeable?

Reading Bate Muller White and trying to find time dependency of angle and distance of Hohmann transfer orbit. Basically I'd like to plot how the vehicle flies from earth to mars and where it is in transfer during over time. I'd expect a function \nu(t) = ... or something but mostly see only t-t_0...

Let $S$ be a set of $n$ lines such that no two are parallel and no three meet in the same point. Show by induction that the lines in $S$ determine $\Theta(n^2)$ intersection points. I've read the definition of $\Theta(n^2)$, but when I draw these lines on a paper, I don't even get that it is corr...

I was looking at the definition of the imaginary unit $i$. We define it by $i^2=-1$. But what does square even mean in such context? It is easily proven that no real solutions exist to this equation. Then we say we define $i$ as a new type of number such that the equation is true. Then $i$ is not...

B"H Every chag has tashlumin, "make up time", to bring the required offerings on it, all 7 days. Even though shavuos is only 1 day, for 6 days after it, in the times of the Beis Hamikdash, people would be able to bring the necessary sacrifices. Nowadays, many Jewish communities that I'm aware of ...

I recently stumbled on the concept of thermoluminescence, specifically when minerals or stones emit visible light after being heated. However, information about one aspect seems a bit unclear: the color of the light. For instance, I found images of chlorophane fluorite emitting a green glow. Two ...

Is there any special bash reserved characters in bash regex expression? ex: eg: if [[ $url =~ ^https:\/\/www\.youtube\.com\/playlist\?(.+&)?list= ]]; then echo "URL matches the regex"; fi This is just a normal regex test. problem: Do I need to be careful about special case where: I have th...

I want to plot the new parliamentary boundaries for the upcoming general election. This will use an NIHR API to grab the map location of the FID=3, the 3rd parliamentary constituency in alphabetical order - Altrincham and Sale West. response = URLExecute[ "https://nihr.opendatasoft.com/api/ex...

The Wikipedia page on the Larmor formula says that the Larmor formula makes the unavoidable assumption that the charged particle is orbiting in a circle. This quoted sentence isn't true, correct? I just reread the derivation of the Larmor formula in a couple sources and never saw any assumption...

God is described as Father passim in the New Testament, but where in the Old Testament is God described as a Father?

Setting is modern day Earth. North Korea has been secretly mentally corrupted and assimilated into the collective consciousness of the Chthonic Hivemind. Wishing to manifest itself into Earth for further assimilation, it needs to conduct a ritual that must minimize potential foreign attention. In...

Theorem. Let $X$ be an infinite complete metric space. Then there is an injective convergent sequence in $X$ or there exists $\varepsilon>0$ and an infinite $\varepsilon$-discrete subset $A\subseteq X$. (I.e., a subset such that $(\forall x,y\in A) d(x,y)\ge\varepsilon$.) I'll mention that we can...

In fairy chess a Gnu moves like both a Camel and a Knight. A Camel moves three squares in one direction (either horizontally or vertically) and then one square perpendicular to that direction. A Gnurider is a combination of a Nightrider and a Camelrider. A Nightrider is a fairy chess piece that m...

Many questions on this site ask a question of the form: assuming X committed offence Y, why did the prosecution not charge X with offence Y? E.g. (paraphrasing): Why would the U.S. Attorney focus on civil-rights law, rather than laws specific to homicide? For example, why not focus on 18 U.S. ...

For example in this image, This node is labeled as Background but I think this is an emission node from the parameter it has. But in general, if the name has been altered , How can I find out which type of nodes it is ?

Bitcoin script number encoding follows sign-magnitude according to BIP62, while most of programming language uses two's complement for signed integer(i.e. Rust format hex representation of signed integer following two's complement). As it's just encoding and the number of hex digit is not fixed, ...

If a United States Federal judge credits critical testimony without fully explaining him or herself, is it subject to appeal? For example, suppose a judge awards an amount to the winning party because "I found witness C's testimony on X to be credible", would there be grounds to appeal if there a...

If my map is in EPSG:4326, the text annotation is normal. However, if the projection is transformed, such as EPSG:102017, the text label does not change. I want the text label information to be labeled in the direction of the latitude, like in the image below. What should I do? This gis.stacke...

I have this folder containing only two files. If I use root and cd to that folder, ls would get stuck. However, ls runs correctly when I log in as a common user, or ls from parent folder like ls file_ffmpeg/. If I moved these two files to another folder, the destination folder could not be listed...

everyone ! I have a question that is beyond my knowledge and I would like to ask the community for help. I am testing my web server for response speed, these are VPS servers (AlmaLinux 9, Apache, Let’s Encrypt SSL certificates), and i am optimizing some laravel apps, html pages, php apps, rest AP...

'We’re looking forward to spreading this new lust for life we have,’ he told Rolling Stone, doing his best to sound confident. ‘There’s a new strength in Metallica that’s never been there before. There are still fearful parts, too. But I’m pretty well set up. And I’m really proud of the new musi...

I recall a movie I watched more than 10 years ago with this scene in it: A young and an old man are observing a far away gate through a telescope. The younger one is going to pass the gate and the older one is explaining about the gate to him. The gate is guarded by two statues. A person is seen ...

this is my first question, so please bare with me. I am new to Latex and are using it to create a investigation I have conducted on Snells law. I need assistance with creating a results table. I am unsure on how the results table should be formatted as my teacher has not specified or alluded to. ...

The sentence is: "Could we have found a buyer who would continue operations, I would have certainly preferred to sell the business rather than liquidate it." I can guess the meaning of "could we have" as "if we could have". So the questions are: Is it grammatically correct to use "Could" at the ...

I have two chips that I don't really know what they could be. The chips with the Z253 marking are connected to a connector, micro and some other things; whereas the N1 marked chips are connected to an op amp. The N1 chip I think could be a transistor, just because of the way it looks. The Z253 I ...

Leviticus 20, 18 says If a man lies with a woman during her menstrual period and uncovers her nakedness, he has made naked her fountain, and she has uncovered the fountain of her blood. Both of them shall be cut off from among their people. where the last part is translated in German as "shall ...

As I understand it, once a character successfully rolls a Dexterity (Stealth) ability check, they are successfully hidden and moving stealthily. Others will need to succeed on a Wisdom (Perception) check or have a high enough passive perception to detect them. The rules also declare that you cann...

Imagine a fiend casting Enemies Abound on a creature within a Hallowed area Enemies Abound A creature automatically succeeds if it is immune to being frightened. On a failed save, the target loses the ability to distinguish friend from foe, regarding all creatures it can see as enemies until the...

I am an EU citizen living in the UK with indefinite leave to remain. My EU passport expired recently and I seem to have no luck getting an appointment with my embassy in London. There is the theoretical option to use VFS Global, which seemingly provide visa and passport services on behalf of many...

Can you connect the Lego Power Functions M motor to a computer with USB?

I have stumbled across these papers 1 and 2. I can't seem to work out how they are defining a 2 way quantum computer other than an analogy and then they jump to something that seems vastly more powerful than a regular quantum computer (in that it can run 'Grovers' In a single query). Is this a di...

This plane passed over our house in Doncaster England and we’d like to know more about it please:

Help me to understand how this oscillator works. Although I mostly want the vintage computer to work, I also want to understand how this circuit functions. I attempted to recreate the oscillator on a breadboard, but did not get it to oscillate. I verified the crystal works by connecting it to a s...

can someone explain me, why the gap between the caption and the table is so huge? \documentclass[a4paper,12pt]{scrartcl} \usepackage[ngerman]{babel} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{ltablex} \usepackage{siunitx} \usepackage{booktabs} \keepXColumns% Bitte in der...

HMMT 2009 Problem 20 : A positive integer is called Jubilant if the number of 1’s in its binary representation is even. For example, $6=110_2$ is a Jubilant number. What is the $2009$th smallest jubilant number? There is 1 two digit Jubilant number 2 three digit Jubilant numbers 4 four digit ...

(Note: This question emerged out of mere curiosity in the definition of a normal subgroup.) Let $(G, \cdot )$ be a group, and let $H$ be a subgroup. Now, for each coset in the set of (left ) cosets, $G/H,$ pick a representative element$^{1}$. Define a binary operation $*: G/H\times G/H \to G/H$ b...

This is first order homogeneous ode from undergraduate textbook, which can be solved using standard $y=u x$ change of variables. But DSolve can't. Could someone figure out why? I show below that using Mathematica's DSolveChangeVariables it gives the correct solution. ClearAll[y, u, x] ode1 = (x^...

I'm trying to build a quadcopter with and Arduino, and I'm facing a problem, that is the RF receiver of the quadcopter freezes (not the Arduino) when I turn on the brushless motor. setup: Controller: ->arduino ->nrf24l01 -> 2 joysticks quadcopter: ->arduino ->nrf24l01 ->4 brus...

Playing harmonics on a stringed instrument is an acknowledged technique which involves placing a finger at a certain point on the string to damp a node that would otherwise sound. Is there a counterpart technique to playing a wineglass with a wet finger? Can you damp a node by touching it at part...

The phrase on the right, next to is theres some context. From what I found it means x處化 but idk what the 1st one means. Any help appreciated :)

I have a data table and I want to center the data values underneath the heading "Angle of incidence", so rather than the numbers 0, 15, 30, 45, 60, 75 being situated left I want them to be centered like those found underneath the sin i and sin r headings. This is my code \documentclass[10pt]{arti...

I first saw this challenge when a user posted it to SO about two years ago without a shred of code. The post's plea, "How do I get started?" meant the user's post didn't survive long on that site. This is, it seems, a well-known challenge, with lots of Google-able demonstrations of solutions. Spo...

From the Genki II textbook, 3rd edition page 297 (a reading passage about Doraemon): 「これは『アンキパン』だよ。覚えたいことをこのパンに写して、食べてみて。覚えられるから。」のび太くんはパンに写して、全部食べました。もうテストは大丈夫です。 I'm confused about the exact meaning & best translation for this last もう. My best guess is that it translates like "anymore", but for...

I'd like to generate realistic sample data in javascript for monetary donations. I've chosen to model them as following the log normal distribution. I think a fairly intuitive way for a lay person to specify the parameters of a function that generates this data is by giving a median and 99th perc...

Here is the code I'm trying to run. #include <functional> int doFunc(std::function<void()> someFunc) { someFunc(); return 1; } int doFunc(std::function<bool()> someFunc) { someFunc(); return 2; } int main() { return doFunc([]() -> bool {return false;}); //return doFunc(...

The Bracha the Kohanim recite for Birkat Kohanim is (Sotah 39a): אשר קדשנו בקדושתו של אהרן וצונו לברך את עמו ישראל באהבה who has sanctified us with the sanctity of Aaron and commanded us to bless Your nation Israel with love. What is the reason for saying the word באהבה (with love), given that ...

Context I have a software RAID5 array (mdadm) on 3 disks. Last week, one disk started to get reading issue: # dmesg ata3.00: exception Emask 0x0 SAct 0x30000001 SErr 0x0 action 0x0 ata3.00: irq_stat 0x40000008 ata3.00: failed command: READ FPDMA QUEUED ata3.00: cmd 60/08:e0:40:0b:c6/00:00:a1:00:0...

In any variant of chess, played either online, or over the board, are there any pieces that can, and are allowed to take multiple other pieces in one move?

Anyone know what this IC is? Trying to find a datasheet for it. Best I can make out from markings is: LB 21 Package SOT-89-3

I'm trying to define a memoir's \fancybreak taking a vertical space of, say, 2\baselineskip (or any other exact amount of \baselineskip). But I have a problem with the height: if I do \documentclass[twocolumn]{memoir} \usepackage{lipsum} \parindent=0pt \begin{document} \lipsum[1-4] \vbox to 2...

In $SomeCorpo there is a policy that passwords must never be stored anywhere else except employees' heads. Paper notes, password managers, storing passwords in browsers, etc, are all forbidden. To facilitate this they are even willing to relax a little bit password strength requirements, as long ...

I am not able to understand what significance phase margin would hold in case of open loop. Shouldn't it be just phase? If it was loop gain I'd understand specifying phase margin to denote stability. Why then, do the datasheets of some op amps like the TLV365 specify it as below:

I am curious about the algorithm used by Mathematica's FindSequenceFunction to identify patterns in sequences. This function is powerful in finding closed-form expressions for a wide range of sequences. I would like to know the details of the algorithm it employs to achieve this. Furthermore, I a...

I came up with a C++17 (I cannot use C++ >= 20 in my project) implementation of a python-like range function (class). The Code "range.hpp" #include <stdexcept> namespace stdx { namespace details { template<typename T> struct RangeIterator { constexpr RangeIterator(T cursor, T stop, T step)...

How can I change the data values underneath the angle of incidence heading from being center and change to left. Currently this: I want this: This is the code I have \documentclass[10pt,twoside]{article} \usepackage[labelfont=bf, skip=5pt, font=small]{caption} \usepackage{subcaption} %for table...

I have read from What's the difference between an entangled state, a superposed state and a cat state? that an entangled state is one that cannot be expressed as product state. Suppose we have the following state $$ |\psi\rangle = |\alpha\rangle_1 |\beta\rangle_2 $$ which can be seen as a produc...

Ok, this is my reasoning. I am probably making some wrong assumptions here, pls tell me where I am going wrong. Spin as a quantum phenomenon: Quantum phenomena disappear as plank constant goes to zero and since the intrinsic spins are proportional to Planck constant, it is a quantum phenomenon. S...

One year ago, we discovered that one of our papers published in IEEE Transactions on Smart Grids (https://ieeexplore.ieee.org/abstract/document/9122589) was plagiarized by another paper published in the International Journal of Electrical Power Systems & Energy Systems (https://www.sciencedirect....

I am in the process of writing a paper for one of my PhD test series. As the test series was extensive, with many different materials and specimen, there are quite a lot of figures: images of the different specimen, graphs of the results for each type of material, images of failure analysis for e...

My 20 year old heat pump gave up the ghost. With summer here, I need something soon. I've had companies give me bids over the weekend, both with great reviews on yelp and Google. Guy #1 was selling me on a $22k unit. It's a high end model with maximum energy efficiency and all the variable speed ...