I'm tring to prove the following statement: Suppose $f:\mathbb{R}^2\rightarrow \mathbb{R}$ is continuously differentiable, and for any $(x_0,y_0)\in \mathbb{R}^2$, we have $$ \frac{\partial f}{\partial x}(x_0,y_0)+\frac{\partial f}{\partial y}(x_0,y_0)\neq 0 $$ then show that: $$ E=\{(x,y):f(x,y)...

Example: % diff "/Volumes/New Volume/4kyoutube/" "/Volumes/New Volume/tmpmusic"| grep Distortion Only in /Volumes/New Volume/tmpmusic: ZAC & Bäkka - Distortion (Original Mix) [Sprout].mp3 Only in /Volumes/New Volume/4kyoutube/: ZAC & Bäkka - Distortion (Original Mix) [Sprout].mp3 % diff "/Volume...

A colleague and I are working with the Analog Devices AD74413R ADC for 4-20 mA current loop communications. On pages 15 and 16 of the datasheet, timing characteristics are presented. We encountered an unexpected specification, a maximum duration for reset pulse width, highlighted in green: We'v...

I am trying to reproduce the cyclooctatetraene isometrization process pulished here. In figure 3 of the paper, it shows the potential energy surface as a variable of the polar angle using the CAS(8,8) method. I am new to this field and I already learnt how to optimize the molecular geometry with ...

21 So one of the men who have accompanied us during all the time that the Lord Jesus went in and out among us, 22 beginning from the baptism of John until the day when he was taken up from us—one of these men must become with us a witness to his resurrection.” 23 And they put forward two, Joseph...

A friend of mine had an Amazing Tales-type anthology back in the mid-80's with this story. A traveller is sent back to an earlier time (early 20th century America?). He reveals innocently that he's "at least one-fourth" black, and is killed by an angry racist farmer. He's possibly developed a rel...

While investigating some Bitcoin coinbase transactions, I notice that a lot of them have an output of the form OP_RETURN OP_PUSHBYTES_36 b9e11b6d… where ‘…’ is 32 bytes, probably a hash of something. I know coinbase outputs can be used for whatever the miner likes, so could be arbitrary. However,...

When preparing a patent application for the USPTO, the patent lawyer I work with asks me for my "Full Residential Mailing Address" as I am one of the co-inventors. Is it required by the USPTO, and if so, why does the USPTO need my Residential Mailing Address? I only see the city, state and countr...

I have seen a few videos about Huygens' principle and I don't understand why a plane wavefront doesn't expand both vertically and horisontally. According to my understanding of Huygens' principle, each point of the wavefront forms a "centre of disturbance" from which it sends a spherical wave. Al...

I'm writing a crime/mystery YA novel and found that I accidentally gave my main character first and middle names from Mr. Darcy (the one from Jane Austen's Pride and Prejudice). My character's name is Fitzwilliam Darcy Claude Milton-Devereux, but for a large portion of the book, I first introduce...

Since only relative position of groups along a bond is considered while calculating torsional strain and considering "+" and "-" means clockwise and anti clock wise rotation, shouldn't any set of $\phi$ and $\psi$ angle say (x, y) satisfying the energy consideration have correspondingly (-x,-y) s...

I'm using STIX and I'd like to create this arrow: \congrightarrow editing the the \equalrightarrow, i. e., substituing the =-symbol with the $\cong$-one. Is it possible? Thank you so much My First Edit: I thought this (for the solution): \xrightarrow[]{\!\!\cong\textcolor{white}{W}} But my main...

I am reading a book Hausdorff Compactifications and I don´t understand the sentence in bold. It is part of proof of the Theorem above (claim 1). I dont undersand in particular, what is meant by "augmenting" the open cover with open set. Thank you for your help! Theorem 1.11 from Chandler´s book:...

Rey says to Kylo Ren, after healing him: Rey: I did want to take your hand, Ben's Hand. What does Rey mean by this statement?

After installing Ubuntu 22.04, I wanted to shut down the computer immediately when pressing the top right-hand button (rather than making 4 selections). On earlier versions of Ubuntu I think this was possible through shutdown options in System settings/Desktop settings/Startup and Shutdown/Deskto...

While trying to figure out how a civilization with 16-17th century technology could make airships I started to wonder how the wide availability of aluminum would affect a civilization. In our timeline aluminum started to become economically viable in large quantities in the late 19th century, one...

The book Sedra/Smith (Microelectronic circuits) tells in chapter 5 the following: My question: I found no statement on why the EOS is defined by the point where vc < (vb - 0.4V). Seems like other books just define saturation at where vc < vb, and I even saw vc < (vb-0.7V) somewhere else. Is the ...

Let $A$ be a ring and let $A_{\frak{p}}=S^{-1}A$ with $S=A-\frak{p}$. I know that if $A_{\frak{p}}$ is a domain for every $\frak{p}$ prime ideal that doesn't mean that $A$ is a domain. However, I have a proof of the opposite statement (which is obviously wrong) but I don't know where my mistake i...

Buffalo Niagara International Airport (KBUF) does not have an associated VOR or VORTAC, yet it has a published frequency box that lists a VHF frequency (116.4) in parentheses. Why is this frequency in parentheses and what does it designate? See below:

According to Unitarian Christians, the identity of Yahweh is straightforward. Yahweh = the Father = God. Therefore, linguistic usage in the OT is fairly straightforward. Whenever Yahweh ('LORD') is mentioned, it is the Father. For Trinitarians, when Yahweh is used in the OT, what does it mean? Is...

I'm currently writing a paper and one of the points is about how overprotective parenting can cause anxiety in children. The results seem pretty clear cut in favour of the assertion (1). https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5007197/ However, there are individual studies (far fewer than th...

So I’m composing a song with “3” scales, G harmonic minor, A#/Bb Major and a set of notes that I can’t seem to find a scale for. C-D-D#-F#-G-A#-B I love how it sounds but don’t know much about music theory to modulate from this non existent scale I apparently made. It shares a lot of similar note...

Background I read (what I could understand of) this article in which authors Yuan and Steinle-Neumann "...use advanced quantum mechanical simulations on silicate and metallic melts showing that hydrogen becomes increasingly more incorporated in metal over silicate at high pressure and temperature...

Is there such a thing as a bit-level ASCII anagram, that forms a natural language word when the bits are interpreted as ASCII from left to right, but a different natural language word when interpreted in reverse? For instance, a test messsage "HELLO_WORLD" (Unicode or ASCII interpreted) is being ...

Due to environmental concerns (very cold winters) humans are concentrated into a few large cities all around the world; smaller isolated settlements die out quickly. These cities would form the basis for nations, and each nation would usually be composed of only one city. A typical city would spa...

look at this text: In example 3 The following map is discussed: $$w=-{{z+1}\over{z-1}}$$ The author claims that this linear fractional transformation maps the unit disk onto the right halfplane but does not prove it. How it can be proved? here is the graph of this mapping that has been drawn wit...

After the death of the universe’s first generation of stars, the clouds from which new stars form will include elements heavier than hydrogen. In the formation of a protostar from such a cloud, do heavier elements sink down toward the center? If so, does this sinking dilute the concentration of...

I realize the question of effectiveness of masks in preventing Covid has already been asked here several times, but no recent one seems to have a conclusive answer. This article from JustFacts (I know they have a center-right bias, but mediabiasfactcheck.com rates them as "mostly factual") states...

Answer is two words Hint 1 (very slight): Hint 2 (somewhat substantial): Hint 3 (major): Hint 4:

Say we have what we would call an 'object' made of many components, can these 'components' be named objects themselves? In the case do we have an object or many 'objects'? Do we define an object to be 'isolated' things? Is it a choice how we express whether we have one or many 'objects' if they f...

Given two normal random variables A and B with (mean, standard deviation) of (a,s) and (b,m) respectively, is there a scalar w in [0,1] that indicates how close A and B are?

When two surfaces are sufficiently close enough to each other, light travels through the remaining gap as if it did not exist. Effects like total internal reflection no longer occurs. If you look at this candle picture, you can see where the wax "touches" the glass and where it doesn't. https://w...

I am looking to plant hydrangeas pan bobo behind a mini hedge of boxwood green velvets. Should I elevate the soil for the hydrangeas so that they stand out more? I worry if I plant everything at the same height the boxwood hedge will simply hide too much of the plant. What do you think? Thanks!

This is a 90's aluminium frame with 130mm spacing between dropouts which originally had a 7 speed cassette. 2 years ago I changed the rear wheel for a standard 135mm and put a 9 speed drivetrain. The wheel is a bit off centred due to the larger cassette but the bike drives very well regardless. A...

Shift+RightClick a file on windows explorer and select 'copy as path', then ctrl+v paste to mathematica notebook, then apply FileExistsQ : ex1) FileExistsQ["C:\Users\Pi33\Desktop\FreeAlarmClockPortable"] True But the same method produces False sometimes : ex2) FileExistsQ["C:\Users\Pi33\Desktop\...

I recently watched this video: When the controller realized the pilot was hypoxic (at about 9m47s in the video) they said, Kalitta 66 if able descend and maintain FL260 but 26000 feet is still very high and provides insufficient oxygen. I (an ignorant student pilo...

My son is 7 and he is playing Pokemon Red Fire on-line. He was frustrated playing against a trainer's level 20 Butterfree. He ended up with most of his pokemon party paralyzed or asleep and with Pokemon Fire Red having a potion being a turn then you end up locked in the effect. I settled on Nido...

I am trying to recursively convert all .mkv files in a folder structure with subfolders to .mp4. I got a standard line that works in just the present folder for video in *.mkv; do ffmpeg -i "$video" -acodec aac -ac 2 "${video%.*}".mp4; rm "$video"; done So I thought I would make something like f...

What forgetful functors are equivalences? The motivation here is understanding when some part of a structure can be 'safely' forgotten, even if remembering it might make our lives easier. There is some ambiguity as to what constitutes 'a forgetful functor', but I am open to any answers that are...

I have often read that radicals are electron deficient and are therefore stabilized by things like electron donating groups and hyperconjugation. However, today I learned that electron withdrawing groups can also stabilize radicals. Does this mean that radicals are not truly electron deficient? I...

I can see intuitively why this graph will not have a Hamilton path, but I can't seem to write up a convincing proof. Are there any tips on how to prove that a graph does not have a hamilton path?

I think in the current system the reviewers are not properly rewarded. Yes there are outstanding reviewers awards (even gift cards), but that's only a small fraction of reviewers, and the majority of reviewers spend a significant amount of their time without getting any rewards. Some reviewers ma...

Context: 10 Finally, be strong in the Lord and in the strength of his might. 11 Put on the whole armor of God, that you may be able to stand against the schemes of the devil. 12 For we do not wrestle against flesh and blood, but against the rulers, against the authorities, against the cosmic pow...

When I was young I had the seeming ability to "feel" metal objects in the dark, or with my eyes closed, from a spot deep in the center of my forehead behind the bridge of my nose. Yeah, I know, weird. And I can't do it anymore, I got glasses with metal frames in 7th grade and after a year of head...

Before the advent of Lempel-Ziv family compression algorithms, there was an algorithm for "Information compression by factorising common strings" by A. Mayne and E. B. James (1975), based on Mayne's dissertation "Data Base Compression and Retrieval on Significant Substrings" (1972). Were there an...

I am installing a package called nvhpc from a third party repository. To do that I use the recommended method that consists on: $ apt-get update && apt-get install --no-install-recommends -y --quiet ca-certificates $ echo 'deb [trusted=yes] https://developer.download.nvidia.com/hpc-sdk/ubuntu/amd...

Flashes of UV light can create electron-hole pairs in transistors. Or at least reports of the "UV flash bug" claim this happens in microprocessors. People observed raspberry pies reset when subjected to a bright flash. I'd like to do a demonstration of triggering generic transistors (e.g. 2n3904)...

I'm trying to create a 3D model of a key in blender made from a single cylinder object only. But I'm having trouble to think of a way of how to extend a round handle from the cylinder as seen from the image. I'm still a beginner and I haven't learned all the modifiers yet so maybe there is a tech...

For example, Alice and Bob have two numbers $a$ and $b$, respectively. They want to calculate the multiplication $a\cdot b$ without Alice knowing $b$ or Bob knowing $a$ and send this multiplication $a\cdot b$ to Carol. Carol will use this $a\cdot b$ to do further application. Carol will not collu...

I've been trying to draw these squares using Inkspace, but I'm having trouble exporting it to LaTex. Now I want to draw it using Tikz but I'm learning Tikz. Does anyone have an idea how to draw it?

As early as Mahasamghika schools of Buddhism there was a view that there are countless Buddhas in the ten directions, that all Buddha's have one body (dharmakaya), and that they are just manifestations (nirmanakaya). The last part says how Buddhas, including Gautama, didnt and dont actually ever ...

Ok I’m no electrician but I’ve wired many plugs but 220v I’m hesitant unless it’s a direct change out wire for wire my question is my plasma cutter is a 3 prong 220v power cord I’m wanting to make an extension cable that I can plug into my dryers 4 prong 220v outlet on one end and I have a 3 pron...

Years ago I watched a movie about a time traveler arriving at Earth, picking someone, and bringing them back to his own time. I have searched and searched for the movie, but can't find it. What I remember: I watched the movie on Danish television in the mid 90s, so I guess the movie is from the ...

I have 13 errors all ending with \end{align*}. Here is my code \begin{align*} e(\underline{a})x_1=& \ \ \alpha_1\prod\limits_{j=2}^{n}q^{-a_j} \e(\underline{a})\\ \forall \ \ 2 \leq i \leq n, \ \ \ e(\underline{a})x_i=& \ \ \prod\limits_{j=2}^{i-1}q^{a_j}~e\left(\underline{a}+e_i).\\ e(\u...

So bear with me on this So I'm working on constructing a world for a DnD game that I am going to be running. I have a general idea of the world that I would like to develop, but am getting stuck on fleshing out some details. The general setting is the usual Tolkienesque high fantasy set in a dark...

I came across many gaudiya Vaishnavas saying such. Is there any scriptural proof??

I started using geo nodes recently and sometimes the "Group input - geometry" is so far away and there are so many overlapping connections... I don't know if doing that makes any noticeable difference in performance. Does anybody know if this is memory wise inefficient (like if Blender has to now...

Poe says to his team, who are attacking the fleet: Poe: Get to their altitude. They can't fire on us without hitting each other. Don't give up. Why would the fleet hit each other ?

I am confused - this article says that car body weight only 153kg. For a car's frame that is very little (as far as I know). Or do they mean body as all the outside parts - bonnet, doors, etc. - not frame itself? Can car's frame weight so little?

From scanf() to fgets(), we need to first specify the maximum length of the string input, due to which input gets a limitation, which isn't that good. As input can vary from [0, ∞), due to computer limitation input will never reach ∞, but it can be very large. I have seen in C++, there no limit f...

I have never seen any ground cover plants with houseplants. Why not? In my specific case, I have some young dragon trees and some leftover seeds for "Easter grass" (Timothy). Will I eventually regret it if I plant the seeds into one of my dragon tree's pot?

I have a very naive question about the density function of the MVN distribution. According to the wiki page, the density function formula sometimes has a constant k (dimension of the MVN variables) and sometimes not. For example, see the PDF on the right-hand side on the wike page, it has no k, w...

I'm currently working on a project on digital watermarking in a color image. The host image is a color image, and the watermark image that will be embedded is a gray. Is it necessary that the watermark will be a color image to ?

Can OS project published on Github be dual licensed for AGPL and EUPL 1.2? If so, what technically needs to be done for that?

I'm playing in a band (drums, bass, guitar, keys + 2 singers), and we are considering putting together an in ear system. The main problem is small venues, everyone is close to the drummer, and we can't really hear ourselves. Wedges are not always an option, the volume is also not great for our ea...

Why can't I add to the dynamic variable z below? z = 1; Dynamic[z] + 1 returns 1+1 and not 2 as expected? Questions: Using the Head, I could see that the expression Dynamic[z] is not Integer as I expected, but is Dynamic. I was hoping that Mathematica would automatically take care of this, cha...

I am reading chapter 1 of Michael Sipser's "Theory of Computation" and in the section "Formation defination of NFA" he says the following: 3rd point of the above image is the point of interest in the post According to a few stackoverflow post: 1)https://math.stackexchange.com/questions/1689850/i...

Let's say I have multiple lines of math symbols from which I want to create a kind of "waterfall aligning, i.e. At any given line, the proceeding line will start at the (horizontal) position of end of the current line. I have attempted to do it with the align environment (using & and &&) but it d...

We have submitter a paper reporting a statistically significant result. One reviewer asks us to report what is the power to detect a significant association. As there was a previous paper on this issue, we could use the effect size of that paper to do the calculation. However, we are surprised by...

When I go many levels down into the menus in the menu bar, is there a way to go back up just one level? To illustrate: Start Emacs Press F10 to open the menu bar Press Ctrlf to reach the "Edit" menu. Press Ctrln repeatedly until the "Search" menu item is highlighted: Then, press Enter to op...

In older versions of blender, there were more options for translating (using the default "G" hotkey) than there appears to be in the current version. How do I get these back? Particularly the axis constraint checkboxes. I use those very often to quickly check how subtle movements affect things...

19 Because in Him, it was well-pleased for all the fullness to dwell, 20 And through Him to reconcile completely all unto Himself, having made peace through the blood of His cross- through Him- whether the things upon the earth, whether the things in the heavens. Colossians 1:19 (Literal Emphasi...

This question Is it true that men are forced to pay child support for children they didn't consent to have? and some related popped up on my side bar and prompted a thought experiment. Suppose a prospective parent stole cells from an unwilling donor and used them to conceive a child. Typically th...

Why does während take genitive in the first example and dative in the second? Was hast du während der Ferien gemacht? Während dem Vortrag schlief er ein.

The first restriction on coroutines specified in cpp reference page is that coroutines cannot use variadic arguments. But when I try to use a coroutine that accepts varidaic arguments in its parameter list, for e.g.: template<typename ...Args> ReturnObject coro_with_variadic_argument1(Args ...ar...

I want to approximate the zeros of the following system of polynomial equations using the Newton-Raphson method: \begin{align} f(x,y) &= x + \frac13 y^9 + \frac19 x^{243} + \frac{1}{27} y^{2187} =0\\ g(x,y) &= y + \frac13 x^{27} + \frac19 y^{243} + \frac{1}{27} x^{6561} =0 \end{align} I have use...

We know that, for Bosons, the Equation of State is given by $pV=\frac{2}{3}U$; where $p$ is the Pressure, $V$ is the Volume and $U$ is the Internal Energy of the Boson Gas. (see Equation of State of Fermion & Boson gas) But, for Photon gas, the equation of state is given by $pV=\frac{1}{3}U$; whe...

I have a circuit with a Attiny85 micro controller that is powered by a solar cell and a capacitor (10F 3V8). When I want to change the code on the micro controller I have to attache a USB programmer that operates (and provides) 5V. Since the circuit will be soldered I wont be able to detach the c...

function: This is to calculate the values for the equation: $$\rho = \frac{m}{v} = \frac{mass}{volume}$$ what I need help with: I still can’t get my head around classes and want to know if I’m doing them right any suggestions are most welcome. code: from decimal import Decimal from dataclasses im...

Exercise 2 from Missing Semester asks the following: Run PATH= and try running the previous commands again, some work and some don’t, can you figure out why? Setting PATH= removes all the contents from the PATH variable. Then echo $PATH yields just an empty line. But when I restart the shell, a...

I've heard cessationist arguments quoting Paul's teaching in 2 Timothy 3:16-17, to the effect that we have everything we need in the Bible, and that nothing beyond the Bible is required, given that the canon is now complete: 16 All Scripture is breathed out by God and profitable for teaching, fo...

All the starting conflux spells for the various Magus hybrid studies let you make a strike. As far as I can tell, these are eligible for spellstrike if you have Expansive Spellstrike (without the feat, they're not applicable as they don't require a spell attack) Conflux spells are spells They re...

I read a collection of vampire short stories in the 90s. One stood out about a group of UN inspectors or delegation of some sort in Romania after the fall of Ceaușescu. One of the group is a vampire and is secretly investigating the effects of AIDS on the vampire population. One scene shows a vi...

2018 Silverado here. Over the winter I noticed a prominent rattling coming from somewhere underneath the vehicle that was made worse whenever I am stopped but in drive. For example, its the absolute loudest/worst when I'm going through a drive-thru and having to move forward and stop, move forwar...

I am a non-native English speaker. Grammarly is an online writing assistant. This is a line in my draft I liked the office, and I liked the environment-- the minimalist furniture, the Macs and Xerox machines, the coffee room, and the lounge. I have written it like that, with the phrase, 'I like...

I'm building an exercise database. The exercises are stored in the form \begin{Exer} Text of the exercice \item first answer \item* second answer \end{Exer} where the * denotes the correct answer And from this I need to define macros \text, \firstanswer, \secondanswer, \correctanswer. For ...

Is the following anyhow related to 'Papañca' in the apparent 'proliferation' as you understand it? And which are the 18 craving-verbalizations dependent on what is internal? There being 'I am,' there comes to be 'I am here,' there comes to be 'I am like this' ... 'I am otherwise' ... 'I am bad' ...

A = {1, 2, 3, 4, 5} and, Dd[P_] := P + 1 How can I map "Dd" into "A" such that the outcome is: {1, 3, 3, 5, 5}? (Dd is only applied to the elements that its indexes are even)