I read a series of books when I was in middle school about a kid who lived on a Mars colony, and since he was paraplegic (or handicapped in some way, I don't remember exactly to what extent, I'm pretty sure he was in a wheelchair), he was the only one who could control rovers on the exterior (I t...

Points $K$ and $L$ are chosen on the hypotenuse $AB$ of triangle $ABC$ $(\measuredangle ACB=90^\circ)$ such that $AK=KL=LB$. Find the angles of $\triangle ABC$ if $CK=\sqrt2CL$. As you can see on the drawing, $CL=x$ and $CK=\sqrt2x$. I don't know how to approach the problem at all. Since $\measu...

I have a Whirlpool LER7646EQ2 dryer. We moved recently and I had to change the cord from three prong to four prong to match the new outlet. It seemed to heat at first, but then four hours later I checked and the dryer was still spinning but not producing any heat. The timer wasn't moving. I check...

In Overleaf, I would like to show variable names with their equation behind them. To do so, I have tried: \begin{align} Entropy \quad 1 + \frac{\sum_{j=1}^{N} p_{ij}log_{2}(p_{ij})}{log_{2}n}\\ IDF \quad log_{2} \frac{n}{\sum_{j=1}^{N}b(tf_{ij})} \\ Normal\quad \frac{1}{...

I am trying to find a file that might be located in one of the folders in the $LD_LIBRARY_PATH. Basically I am trying to: find $LD_LIBRARY_PATH -name "*libdl*" However the above command fails because of multiple entries in the variable and separated my a :. I get the error: No such file or ...

I would like to know before the landing takes place, is there a way out for the pilot to know whether the doors or windows for the Front and Rear tires of the Aircraft will work 100%? If i am not wrong, the doors or windows are opened while landing for the Front and Rear tires to open. In case th...

I'm asking about my parents brick single family home that we are the original owners from around the late 50s. We were planning to sell the house and had the village come in to see what might need to be "updated" or corrected before selling. On the list was to label all breakers in the panel, as ...

I am fairly new to DM'ing and I am going to be running a simple one shot soon. I intend to start the players at level 3 so they can enjoy the more entertaining class features and not be so squishy that the chance of a PC kill is likely while still presenting a minor challenge. One of my equally n...

I found the ROC explanation at this link. It states that the ROC curve is TP vs FP. After the score has gone below 0.5. This makes all predictions negative. Thus, they are either TN or FN. Thus, how does it make sense to continue drawing as the axes are stated as TP and FP? I am really confu...

I want to drive a DC motor (linear actuator) rated at 12V with a 24V DC supply. Will using a driver IC that does current regulation (e.g. MP6515) be enough, or would I need additional measures in place? All other components would be properly sized (capacitors, etc.) DC Motor Overvoltage Operation...

I'm learning how to use a string trimmer before buying one. I know that it uses a line to cut the grass. But the line will wear and get shorter. Where does the line go? I guess into the grass and ground. Then it will be plastic waste into the ground, right? We know that plastic can't be decompose...

I planted a random collection of old unlabeled seeds. Most of what sprouted i recognised but what is this plant? The flower is about an inch across. The leaves and stems are very delicate. It also sprouted in a pale orange colour and a blueish colour

In the film The Fellowship of the Ring, Saruman says of Orcs: They were Elves once. Taken by the Dark Powers... tortured and mutilated... a ruined and terrible form of life. This origin of Orcs is explained in The Silmarillion, but I gather this book wasn't allowed to be used as a source due to...

I am trying to understand Bell's famous paper from 1964 on the EPR paradox. I stumbled over equation $(9)$ where it says $$\left.\begin{align}A(\vec a,\vec\lambda)&=\operatorname{sign}\vec a\cdot\vec\lambda\\B(a,b)&=-\operatorname{sign}\vec b\cdot\vec\lambda \end{align}\right\}\tag9$$ Apart from ...

I've facing an interesting issue as a DM and don't know what can I do from my position to solve the problem. My players always argue with each other and are always disappointed by the other side, up to the point that they don't want to play any more. It seems like a social skills problem, but I s...

If my friend gives me a thousand dollars for 0.0001% of my "company", am I technically a Billionaire now?

Electrician told me a problem I was having was caused by a new arc fault breaker they installed. I was told you, "can't mix neutrals" Can you describe what that means? How would these neutrals get mixed?

In 1948 there was a Superman serial that starred Kirk Allyn as Clark Kent and Noel Neill as Lois Lane. Then in 1978 the first of the Superman films was released and had Allyn and Neill make a cameo as Lois Lane's parents. It has been suggested that this may be the first time starring actors were ...

I have been adding new Pokestops in my deserted town (PokemonGo perspective of view) for a month and I have never encountered what I have experienced recently. I nominated 2 stops and both of them got accepted. Two days passed and the Ingress portals are online, but the Pokestops in PokemonGo are...

I know that there is not a fully defined specification for the language used in jazz harmonic analysis, as it has grown slowly and organically and has many variations. I have seen some textbooks use the traditional way of marking minor chords with lowercase roman numerals and major chords with up...

Given a polynomial that is not constant, of course, it doesn’t contain a constant interval. But how can we prove it? Since the polynomial is differentiable over R, I came up with a solution that uses Lagrange mean value theorem n times and reduces the nth derivative to a constant. Since the leadi...

I hope this question is not too infantile: Falling into a Black Hole (intentionally or by accident) and thereby passing the Schwarzschild radius is very often said to be "nothing special" in the view of the falling observer. Tidal forces can be neglected when the mass is only big enough. But let’...

I am looking at a particle moving in a funny potential, described by the following differential equation. The solution should be just some kind of periodic trajectory, why is there a problem here? Edit: here is the code: k = NDSolve[{x'[t]^2 + 1/Cos[x[t]]^2 == 2, x[0] == 0}, x[t], {t, 0, 4}]

If Quantum fields are mathematical entities made up to explain nature,What they explain of is definitely something physical and is made up of something. So why can’t there be an answer to what these mathematical Quantum fields made up of? I mean if Physicists are making them up then they definite...

I am going through The Art of Electronics Third Edition. There is a note 12 unter Figure 2.10. Why Q3 would not switch if R3 = 100 Ohm?

I just finished my second year in a social science PhD program and have only one semester left to finish my coursework. Last semester my advisor A told me she was gonna take a job offer from another university and could not bring me because of lack of funding. I was her only PhD student, and she ...

Can a future UK government decide to rejoin the EU without a referendum or do they have to hold one?

Positioning inside \graph environment. Is it possible? What am I doing wrong? L 2 is not where it should be. \documentclass [border = 2mm] {standalone} \usepackage{tikz} \usetikzlibrary{ graphs, graphs.standard } \usetikzlibrary{ positioning, calc } \tikzset{ myVrtxStyle/.style = { circle, ...

I'm looking for a book that I've read maybe 10/15 years ago (it might be older though), and I think it was fantasy. The only element I remember is that at some point, the protagonist is given an amulet that has the power to make the wearer more likeable if the amulet is visible. People will help...

The English sentence being "I brush my teeth, wash my face, and have breakfast every day." My translation was 私は毎日歯で磨いて顔で洗って朝ご飯を食べます. The given answer was 私は毎日歯を磨いて顔を洗って朝ご飯を食べます. Given the context, I thought で could be used because I'm marking the location/tool/method/condition for an action. But...

May be some of you (moderators and custodians) would discard this question as opinion-based and requiring discussion, but I didn't want the effort to go to waste so felt compelled to ask. Please feel free to shut down/migrate/ignore this question. My question is "At what point does the complexity...

What if the LHC and further colliders can not find anything beyond the Standard Model? Nightmare scenario: LHC can not find anything beyond the SM-Higgs-like boson. VLHC, the linear collider or the muon collider can not find anything beyond the SM-Higgs-like boson. The 100TeV-1000TeV collider, l...

I'm struggling to think of one that doesn't. Utilitarianism obviously does, but even others seem to. Take Kant's categorical imperative for example. What is the point in performing one's perfect duties? For instance, in the example given by wikipedia, theft is immoral because if everyone did ...

If I have a list of numbers as (the number of elements in this list is even) list={1,23,32,54,65,76,87,98,109,110,...} How can I ask Mathematica to subtract each adjacent pair, and then, sum them, i.e. compute this value $sum=(...)+(110-109)+(98-87)+(76-65)+(54-32)+(23-1)$

I'm trying to develop a matriarchal Empire for a story, but the main issue I'm having is that I don't want the women to all be warriors or magically physically stronger etc. The setting is essentially medieval-esque europe and asia, though there are differences that aren't really relevant to this...

Suppose, we're (I and my wife) asked by people how long is my marriage since I got married, which tense should I use? Past tense or perfect tense or else? We were married for 15 years. We've been married for 15 years. Since a marriage is a status and it occurs once (each marriage) but the sta...

Can a rocket use just enough fuel to reach an area wherein it has escaped a planet's gravitational pull and then turn its engine off? Supposing there is nothing else with a gravitational pull that the rocket would get caught in, would the rocket keep on moving since there is nothing to slow it do...

Background An interval graph (Wikipedia, MathWorld, GraphClasses) is an undirected graph derived from a set of intervals on a line. Each vertex represents an interval, and an edge is present between two vertices if the corresponding intervals overlap. The following is an example interval graph wi...

The English word, “scarecrow,” spontaneously came to mind the other day, and I realized just how similar this word is to other words and phrases in other languages. For example, there are many commonly used nouns in Spanish that are formed by conjoining a transitive verb with its object (with the...

How many positive integers, not exceeding 100, are multiples of 2 or 3 but not 4? Hello, I was wondering how to solve problems like these. My thoughts are to count the number that are multiples of 2 but not 4, multiples of 3 but not 4, and then multiples of 6 but not 4, then use Principle of Incl...

I was reading Jeffrey Archer's Kane and Abel, where on page 191 I found this line: William began to be aware of his housemaster's wife during his last two terms at St. Paul's. She was a good-looking woman, a little slack around the stomach and hips perhaps, but she carried her splendid bosim wel...

The orbitals of an atom can be thought of as being formed from the probability of finding electrons in those orbitals. If the orbital is 1s (n = 1, l = 0), then it has a certain "volume" for which the electron can be at any position, and in some radial distances from the nucleus, it will be at th...

I want a box created by tcolorbox to make a theorem without numbering. This is my code while setting up: \usepackage{tcolorbox} \tcbuselibrary{theorems} \newtcbtheorem{theorem}{} {colback=green!5,colframe=green!35!black,fonttitle=\bfseries}{th} I've searched online and one tip that I got is usin...

A city was built in a location that's generally difficult to access (floating in the sky, on a remote island, on top of a mountain or something similar). The primary way of accessing it is by teleporting inside. In this world, skilled mages can teleport from anywhere, but only to a previously built

Given a triangle ABC with sides a=|BC|,b=|CA|,c=|AB| a diamond is circumscribed around the triangle's incircle. The diamond and the triangle share the corner C along with (part of) sides a and b. Derive an expression for the diamond's side length d in terms of a,b and c. Prettiest solution wins...

The kind of full-face veil I'm thinking of is the Niqāb - it covers the entire face except the eyes. I don't have any ideological objections to people who choose to wear the full-face veil. However, by its very nature, the veil makes it hard to hear what the student is saying since it muffles the...

Follow-Up to this question: How can the wealthy prevent the illegal propagation of their genetic code? The rich and fabulous in today's world have the significant problem of how to protect their wealth. Technology has advanced to the point in which the genetic structure of an individual can be co...

\documentclass{standalone} \usepackage{tikz} \begin{document} \begin{tikzpicture} \foreach \x in{0,0.1,...,0.5}{ \node[] at (20*\x,0) {\x}; } \end{tikzpicture} \end{document} However, as follows: \documentclass{standalone} \usepackage{tikz} \begin{document} \begin{tikzpi...

In the Gospel of John we read what seem to conflicting admissions by Christ's Jewish audience, one on the verse of stoning Him: John 8:39-41: "They answered and said to Him, 'Abraham is our father.' Jesus said to them, 'If you are Abraham’s children, do the deeds of Abraham. 40But as it is, you ...

I mean this punctuation mark: ! I've been puzzled recently by the use of the exclamation point in German. I recently received a message from a work colleague using a couple of exclamation points at the end, which made him sound angry. And we also got one from our landlord, though in this case ...

I found a transaction on bscscan in which a burn address sends some tokens. The transaction: https://bscscan.com/tx/0xa03e1803eff745227865f4f58dc50847b1afc1c5628a323603db01a2e5bcaf06 I'm new here. can anyone explain that to me? thanks.

I have heard that no known long term shelf stable form of vitamin C is known. I find this surprising, is it really true? What are the best options for astronauts to have vitamin C for long term (>1 year missions) ex: traveling to Mars. I did some research on this site and found that they have suc...

For verbs that typically use に in the dative sense (indirect object) like 送る (for example 手紙を先生に送った), is there any ambiguity in the function of に when the verb is used in the passive? For example, take the following sentences? 手紙が先生に送られた。 手紙を先生に送られた。 Can sentence 1 mean either "The letter was...

I have some simple experience with TTL logic and Arduino, but I'm only a hobbyist and am bit stymied by my current project, which is attempting to read the data from an old Intel 1702A EPROM. The actual reading part should be simple: set the address lines and look at the data lines. But this EPRO...

I've been playing Pokemon Go for a few months now. I live in a major metropolitan area in the US, and pretty much since I started I have 4-5 pokestops in range of me when I'm sitting in my apartment. In the past two weeks, I got super busy and didn't log in. Today, when I logged in, all the same ...

I am designing a PCB using the QSC15024S28. It is an isolated DC-DC converter. This is the first time I am using an isolated DC-DC converter. They have provided some kind of application circuit and table which has component values. C3 and C4 should 4700pF. Why are these capacitors used? What ar...

I've been asked to prove that if $f$,$g$ are uniformly continuous functions, then their composition $g\circ f$ is also uniformly continuous. This is my attempt: Since $f$ and $g$ are uniformly continuous, we have, For a given $\epsilon_1>0$, $\exists\ \delta_1>0$ such that $|x_1-x_2|< \delta_1\im...

I found a paper in a top journal in my area here. I have a question regarding the inconsistency in citation displaying. For example, somewhere they use (author year), somewhere they use author (year) within a single paper cited as below: The breakdown of collusive activities that involve higher ...

I have an arduino UNO recently whenever I connect an MQ-9 sensor or an ESP8266MOD wifi chip, the LCD backlight drops that it doesn't display anything, the red LEDs on the arduino board reduces and the voltage regulator begins to get hot, I am using a 12V -- 1.5A DC supply to power the arduino, as...

Trying to request all the records from a contract. The etherscan.io solution offers a 5k records but the total is 120k+. Any API endoint or solution can go through it all? What I tried: ethslurp, limited to 10k (Dont remember the exact number). Etherscan.io (didn't find an API that provide as in...

Psychic Blades The Soulknife from Tasha's Cauldron of Everything gains the Psychic Blades feature at level 3. These are described as "shimmering blades of psychic energy . . . that you can manifest . . . from your free hand." Their description goes on to say [TCoE, pg. 64-65]: This magic blade...

So I was looking through models on a Discord server, and I stumbled across this picture. While looking at the picture I wanted to see how I would make my edges look like that in the picture, as if they where white. I tried searching everywhere and couldn't find it, I think this is a Matcap but I...

Is it better to say argumentum a/ab contrario or e/ex contrario? It seems that both are acceptable but in most Romance languages it is a contrario. The movement out/from is not clear/explicit/graphic and it is a concept/mental abstraction that "moves", not a physical object. EDIT secondary questi...

I found this "video game legends" poster by Patrick Brown, which features a whole bunch of characters which appeared in video games: I recognize some of the characters, but many are obscure to me. Observe that some of them originated from a video game (e.g. the Portal protagonist), and some of t...

I would like to search a text in multiple files (within a directory) at a certain line number. Example: I have ~100 Script Files in a directory (C:\Scripts) and I would like to scan all of these files for the term "getId()" in line number 31. Considering I am working on Windows 10, what can I do ...

I deleted all the lights in my scene. However even without light some of my textures are uniformily "lighted up", or at least visibleas you can see on the picture. The visible textures are psd files I put via texture nodes. This makes my textures very flat looking. Any idea what causes this and ...

I have a Whistle B-Race 7.1 e-bike that's about 3 months old. Recently the front disc brake has started touching the brake pads when not braking, when it does you can hear a "zing" sound. It does so during hard turns or when i'm riding without hands on the handlebar, but when i try to willingly r...

I'm just starting with Qiskit and I would like to reproduce basic results about spin measurements. For that I want to prepare multiple spins each in arbitrary directions and measure them in arbitrary directions to get the probabilities. What is the suggested way to do that in Qiskit?

I am currently trying to make a special symbol in QGIS My best idea is to use Geometry Generator but I can't seem to find any good tutorials besides converting geometry to various types. Is there any way how to draw this in Geometry Generator? EDIT: I do not need to use the Geometry Generator if...

I have text data, and want to transform a column values $ cat infile Mark father Jason SOn Jose son Steffy daugHter I want to search for (father|son|daughter) case insensitively and substitute any father combination to Father, any case of son to Son, any case of daughter to Daughter So outfile s...

I have received some email notifications from Azure, containing this: Activity log alert Alert [Server Name] Health Status Properties { "title":"Reboot initiated from inside the machine", "details":"A reboot was triggered from inside the virtual machine. This could be due to a virtual ...

How to create the curved firework which is at the end of the Disney's movie-intro? I am talking about this (video link): https://youtu.be/k9bUTfFF3_4?t=20

When I draw a polygon in QGIS that overlaps an existing polygon from the same layer, QGIS automatically clips the overlapping area from the new polygon. Is there a setting to preserve the shape that I have draw with the overlapping part?

With the following Simplify[Abs[-1 + x], {-1 + x < 0}], I expect Mathematica to return 1-x, but it instead gives the same Abs[-1+x] back. Why is it so?

I was hoping someone could clarify this for me. I have used OLS regressions using the PISA dataset where most of my outcome variables are categorical in nature and measured on 4 point Likert scales, ranging from "Strongly disagree to strongly agree" with observations spread across all answer cate...

Reading this news article and some related references, I learned that mercury’s liquidity is due to relativistic effects in Hg, where "the electron approaches about 58% of the speed of light." I do not see how this can be reconciled with the Fermi velocity of Hg being $1.58 \times 10^6$ m/s, a...

For the year 1909 in my Great Grandfathers Civil Guard records there are four entries. Here is the second one: The transcribed text so far: El Excmo. Señor Director General del Cuerpo en común no. 197 de 29 de Agosto xxx por el Señor Coronel Subinspector del xxx en 29 del mismo manifiesta se ha...

Acidic hydrolysis of alkyl isocyanide gives rise to primary amines and formic acid. But alkyl isocyanides do not undergo hydrolysis in basic medium. Why?

I have some other devices, Philips Sonicare Toothbrush, Xiaomi Powerbank, and Bose Headphones. Can I use iPhone's 5W power adapter and/or USB cable to charge these devices? Is it safe for their batteries?

I'm trying to find the variance of the following random variable with density function $$f(x)=\begin{cases} \frac{3}{2}x(1+x),& \text{ $|x|\leq1$ } \\ 0& \text{ } o. w \end{cases}$$ First, we find $\displaystyle E(x)=\frac{3}{2} \int_{-1}^{1}x^2(1+x)dx=1$ and $E(x^2)= \displaystyle \frac{3}{...

Can someone suggest a way to specify per-function MeshStyle when plotting multiple functions? An example is below, I'm trying to show two contours, with black and red/dashing style. The Plot3D only displays a single style a = {{1, 0}, {0, 2}}; b = {{3/2, 1}, {1, 6}}; f1[x_, y_] = {x, y}.a.{x, y};...

The emptiness problem for Context Free Grammars is decidable. Does the same hold for Parsing Expression Grammars (PEGs)? That is, is it decidable given a PEG $G$ to find whether $L(G) = \emptyset$ or not. My intuition says no, as PEGs are closed under intersection, allowing one to construct hard ...

It appears that I will have to appeal the decision of an examiner, and if I could do so without waiting for a final rejection, I might be able to catch the tail end of the Fast-Track Appeals Program, which may have a limited number of slots each year (it did last year). But this rests on the mean...

I'm a self-taught/hobbyist electronic engineer, and I enjoy taking apart old scrap electronics both to salvage components and to try to study design patterns (and as a challenge!). I've recently extracted a nice 1.5" 4-digit 7-segment display from an old slot machine (I'd guess from the early 199...

I learned that we should use present perfect while talking about things which happened in the past but which still hold. However, it sounds weird when I think about using "I have lost my bag" when I tell a police officer about the missing bag. I feel "I lost my bag" is more appropriate. I feel th...

Looking for an English book based on Torah ideals, that helps quell the bad midda of anger. The book can be specific to anger but can also be a book on how to better all of your middot. Note: this doesn’t have to be a classical book/Sefer, it can be something modern or recently written. Just some...

I have been looking at using Goedecker-Teter-Hutter (GTH) pseudo-potentials and I came across the abbreviation PADE. I was wondering what this abbreviation actually stood for and how it is related to LDA?

Why is this mantra called a “mahamantra”? Is it described so only by Karshnavs/Vaishnavs?

I have my own detection of the file indent settings based on the file contents. All good and works ok for my needs but... When I open a c source file of the vim itself it overrides options set by modeline: /* vi:set ts=8 sts=4 sw=4 noet: * * VIM - Vi IMproved› by Bram Moolenaar * * Do ":hel...

The following Latex document shows this equation: \documentclass{article} % \usepackage[document]{ragged2e} \usepackage{ parskip % Makes formatting nicer } \begin{document} $\lim_{x \to c}(f(x) - f(c)) \\ = \lim_{x \to c}(x - c)\frac{f(x) - f(c)}{x - c}$ \end{document} I'm very happy with how...

Like this sample picture: If I add a huge lake, internal sea, like the Caspian sea for example, can I avoid that the middle of a continent would turn into a desert or dry spot due to dry high pressure? EDIT: Thanks for the answers so far. Just forgot to tell that those red arrows around the cont...

So I have a designer building out a logo and they're having a hard time coming up with a concept, but the attached is the best design that they have sent over so far. I want to get your honest opinion on what could be improved and what should go/stay/etc.. About the logo: I'm building an app cal...

I'm curious about the grammatical reason for saying "Io ho fame" vs "Io sono fame". In most instances where you are saying "I am" the verb sono is used. Example: "Sono stanco" (I am tired). The verb "ho" means "I have" so the literal translation of "Io ho fame" to English is "I have hunger" vs "I...

Your final answer(s) should be thematic.

I'm trying to use basic colors of the package xcolor from standalone documents, but the following error is returned: main/filename.tex|29␣error|␣Package␣xcolor␣Error:␣Undefined␣color␣`MAGENTA'. The main document has this: \documentclass[10pt, b6paper, twoside, openright]{memoir} \setlrmarginsand...

Matthew 22:1-14 "For many are called, but few chosen". ESV I think there are on this site at least three questions about aspects of this story but none asking about its conclusion at v14. The 14 verses end with the word "chosen". If the point of the story is to illustrate the difference between "...

In the following example, compiling with -Wall, some of the unused variables are not warned about: #include <tuple> struct Foo { int a, b; }; struct Bar { ~Bar() {} int a, b; }; int three() { return 3; } int main() { Foo f0 {1, 2}; Foo f1 {three(), 2}; Bar b0 {1, 2}; ...

I'm looking to use a P-channel high-side MOSFET to enable/disable some sensors and peripherals connected to an ESP32. The peripherals use 3.3V and the ESP32 runs on a 3.3V logic level. I'm not an electrical engineer, and I'm probably a bit out of depth on selection of the parts in this schematic....

When I run the below code each line aligns on the right. How do I change this to align on the left instead please? I haven't gone into detail about what each equation represents as this is purely a formatting question and don't believe this to be necessary. Any help would be much appreciated. \do...

I am learning a bit of Evans Gambit theory lately, and when exploring a Master level games database, I have found this surprising line. [FEN ""] 1. e4 e5 2. Nf3 Nc6 3. Bc4 Bc5 4. b4 Bxb4 5. c3 Bc5 6. d4 exd4 7. O-O After it concludes, Black doesn't take the free pawn on c3 that allows them to b...

Matthew 22:8-9 8 Then he said to his servants, "The wedding feast [ho gamos] is ready, but those invited were not worthy. 9 Go therefore to the main roads and invite to the wedding feast [tous gamous] as many as you find. ESV Why does the singular, ho gamos, become plural, tous gamous? Is ther...

/dev/sda5 is mounted at / and it's my filesystem piotr@thinkpad:~$ sudo mkdir /home/mpoint piotr@thinkpad:~$ sudo mount /dev/sda5 /home/mpoint so now I can do: piotr@thinkpad:~$ cd /home/mpoint/home/mpoint and when I'm in second mpoint directory, it's empty. My questions are: Why is it possibl...

I'm currently researching GPS signals and am trying to fully understand the path of a signal from satellite to receiver. I understand that mixed into the GPS signal is a C/A code as well as a PRN which aids in the process of CDMA that the receiver preforms. However I'm a bit lost on how the recei...

Many books define the language of set theory only based on $\in$. What about the binary relation '$=$'? Why is it not mentioned as a symbol of the language? Yes, it is part of first-order logic, but to me its meaning seems to depend on the interpretation which in turn depends on axioms (like exte...

Problem: If $\alpha+\beta+\gamma=20$, then what is $\max(\sqrt{3\alpha+5}+\sqrt{3\beta+5}+\sqrt{3\gamma+5})$? My attempt: Assume $\alpha \geq \beta \geq \gamma$. Then $\alpha+\beta+\gamma \leq 3\alpha$ so $25 \leq 3\alpha+5$. Also $\sqrt{3\alpha+5}+\sqrt{3\beta+5}+\sqrt{3\gamma+5}\leq 3\sqrt{3\a...

Let $f: \mathbb R \to \mathbb R$ be a $C^1$ function. We say a point $c \in \mathbb R$ is a mean value point of $f$ if there exists an open interval $(a,b)$ containing $c$ such that $f’(c) = \frac{f(b) - f(a)}{b-a}$. Question: Is it true that (Lebesgue) almost every point in $\mathbb R$ is a mea...

In Archie Armstrong's Banquet of Jests (1641), the following passage occurs: A Gentleman and a Parson. Some pleasant Gentlemen riding by the High-way, espyed a Countrey Parson before them. Sayes one of them, yonder is a Scholler, let us mend our pace, and you shall heare me pose him with a ques...