I'm using FastAPI and in my schemas (that is, serializers) I have something like this: from pydantic import StrictStr, BaseModel class Str255(StrictStr): max_length = 255 # my schemas: class CatSchema(BaseModel): name: Str255 owner: Str255 age: int The reason I use Str255 is to a...

What are the best books, writings and great works by traditional scholars and Rabbis in Judaism dealing with the topic of humility? I want very traditional and age old works the likes of which you would see on Sefaria.com . For example the Sefer Hasidim (Book of the Pious) deals with being pious ...

Let $X$ be a normal projective irreducible surface over an algebraically closed field $k$. Let $\pi\colon Y\to X$ be a birational morphism, such that $Y$ is a smooth projective surface, and assume that no $(-1)$-curve of $Y$ is contracted by $\pi$. How do we prove that there is an isomorphism $\p...

This question's pretty simple really. A concept of the number 0 is a major landmark that's used when discussing advanced civilizations in pre-modern history. It was something that civilizations came to use after thousands of years and was a "major advancement". But why? 3 - 1 = 2, 2 - 1 = 1, a...

I came across an old image of one of my wife's ancestors from the late 16th century, and below it is written Jacobus Pamelius, Episcopus Audomaropolitanus designatus which in English is Jacobus Pamelius, appointed Bishop of Audomaropolitanus Does anyone know the modern name for Audomaropolita...

What do we consider a 'dwelling-place' for this purpose? A house? A city/within an eruv? By this logic, if I were outside a defined 'dwelling-place' on Shabbat (say, out in the wilderness and not on any land owned by a Jew), could I kindle a fire? Or since I am a Jew, does where-ever I am at the ...

Aliasing is bad, and we want good filters when downsampling. While what qualifies as aliasing is well-defined mathematically, and we can manually design filters with various tradeoffs, how do we actually measure the "amount of aliasing" that a filter admits or rejects? What about measuring aliasi...

Plot Summary I have only the vaguest recollection of this one. Apologies in advance for the scanty description and any potential inaccuracies in the details. As best as I can recall, the story centers around a doctor or a scientist of some sort who is in great danger. He reaches out to a woman ...

I'm installing a yoke on a canoe that didn't have one from the factory. It only had a cross brace (the center thwart). What way should I install the yoke? A. Yoke neck hole towards the front of the canoe? B. Yoke neck hole towards the back of the canoe?

The part that effects lands on Celestial Dawn says Lands you control are Plains In my head, this takes away any other type and abilities those lands have but the only thing I can find in the rulings for Celestial Dawn is the 29-Sep-2017 ruling that says if the land has an ability that would cau...

Bought a 2006 Honda Civic EX (not hybrid) from a mechanic last January. I drove it home for about 20 minutes at about 75 mph. I think he masked that it had a blown head gasket. I have brain damage and missed the red flags. I haven't had or done any work on it. Heater only works on the left side v...

Given the following: Dog rover = new Puppy("rover"); // Where Puppy extends Dog A student asked why would you ever want or need a Dog object to point to a Puppy object? The only answer I could come up with is the following: Suppose we have a game program with Dogs and Puppies. A Puppy may hav...

Reading about ultraproducts in model theory and in Banach spaces leads to two distinct definitions. E.g., for an ultrapower given by an ultrafilter $\mu$ on $\mathbb{N}$, both notions of ultrapower are quotients of the space of sequences $\sigma: \mathbb{N} \to \mathbb{R}$. In Model Theory Two se...

I have a domain that is about to expire. It was used for hosting my freeware which I do not maintain anymore but can still be found on shareware directories. The application points to my domain (hardcoded) for further info. What I am afraid of is that if someone buys the domain after it has expir...

According to Civi Documentation, "CiviCampaign has a feature that enables offline surveys...", which implies that there is no way to "send" a survey to a group/set of contacts (like online event registrations). Is this correct, or is there a way to create a survey, and send it to a group/list, et...

It seems to me like whenever we have a measure space $(X, \mathcal{A}, \mu)$, it's pretty much always more convenient to work with $(X, \mathcal{X}, \mu)$, where $\mathcal{X}$ is the completion, i.e. $$\mathcal{X} = \left\{ A \cup E : A \in \mathcal{A} \land \exists N \in \mathcal{A} \; \left( E ...

I have a question about the GDPR law. I am creating a mobile application where I will need to store some personal data in order for the app to work. I would also like to include personalized ads in the app. Now if GDPR applies, I would need to get explicit consent from the user before showing per...

Is there a way that a sort of immortality could be achieved through genetic engineering or some other type of biological/medical technique? Not necessarily permanent immortality until the heat death of the universe, nor general invulnerability (just looking at anti-aging here, not necessarily bei...

Is there a known example of a set $S$ of Diophantine equations such that $S$ is computable; it is a theorem that every equation in $S$ has (at most) finitely many solutions; the function that maps an element of $S$ to its set of solutions is uncomputable? There are some famous finiteness theore...

I've just started studying Wheelock. In the Vocabula section, the entry for amo is amo, amare, amavi, amatum. Yet most dictionaries give the past participle as amatus. Which is correct?

I am mechanical engineer and have started learning python from a book called 'Introduction to computation and programming using python by John V. Guttag'. This is one of the examples. I know that there are several similar questions posted here, but I thought my program is too simplistic. Here is ...

I am stumbling upon a very strange situation unless I did something totally wrong in my measurement setup. Speaking of it, I've installed an acoustic measurement tool (REW) and measured for testing purposes an RC lowpass filter by using two mono audio jack cables attached to my external audio int...

I know not all groups can be realized as the automorphism group of a group. For example, it is well-known that no group can have $\mathbb Z/n\mathbb Z$, with $n > 1$ odd, as automorphism group. Now I'm wondering the same question about automorphism groups of rings, is there any result about this?...

Let $\mathcal{L}(X)$ indicates the law of a random variable from a probability space $\Omega$ into a Polish space $E$ (so $E=\mathbb{R}$ for a real random variable $X$, and $E=\mathbb{D}(\mathbb{R})$ is the space of all cadlag functions form $\mathbb{R}_{+}$ to $\mathbb{R}$ for a stochastic proce...

I am using a document that I compile with the LaTeX class www.sigmetrics.org/sig-alternate-per.cls. This class used to work fine with TexLive 2019 but now that I am working with a machine that has a TexLive 2022, there seems to be problem with spacing: For instance, let me consider the following ...

I want to find out if it is possible detect and identify individual rolling stock of an H0 scale model railway using a bar code scanner. The biggest problem is the short distances there is only 5mm or perhaps even less to the scanner and the actual bar code. Instead of using a commercial scanner ...

I am trying to replace the burnt out fluorescent bulbs in my basement with compatible LED lights, but I'm having trouble finding a type that works. These are the bulbs I'm replacing: This is the ballast: I'd really rather not have to rewire or replace all the fixtures in my basement, but I've h...

So I want to install an irrigation system in my garden. I am starting with one controller but there may be more. I was told, rather than install an in-use outlet, where bugs and spiders etc will hang out, the better plan is to cut the plug off of the power cord and run the cord into the non-metal...

In the context of measuring a sinusoidal source with an ADC, coherent sampling (i.e. capturing an integer number of periods) allows the use of a rectangular window without spectral leakage. How does one actually do this in practice? I am testing a 16 bit ADC that is sampling at 5 MSPS. I set my s...

My shop is wired with a whole bunch of 6-50r plugs around the walls running 220v AC. I just picked up a dust collector with a 6-20p plug on the end. I believe it is rated to pull 13 amps at 220v Single Phase AC. In a perfect world I would be able to use all of the 6-50r receptacles for both the w...

I want to apply a function to a list. The Code for that is: Function[x,x^2]/@list >1,4,9 But when I want to made a function of that function, passing the argument for x^2 doesnt work: xsquared[formula_,list_List] := Function[x,formula]/@list xsquared[x^2,{1,2,3}] >{x^2,x^2,x^2} Whats the p...

What is the meaning of, “…a man who had no truck with looking back..”? I understand the meaning of a man in a truck looking back, but “who had no truck with looking back” eludes me. Alternative meanings for “truck” in MW include “barter” and “swap.” The sentence appeared in NYT 05/02/2023: But...

I have a line of thought that strict naturalism (in the most extreme case, the belief that only particle physics is an accurate description of reality) is self-defeating. I say this because notions like intentionality, reference and semantic truth cannot be expressed in the language of particle p...

As a young researcher in economics, I have already published 3 papers in decent journals. Is it sometimes normal to write a paper in which the research question is not clear at all, the motivation is lacking and also you do not understand where the problem in the paper is? I have heard 2-3 times ...

Let $A,B\subsetneq\Sigma^*$ be PSPACE-complete problems for some fixed $\Sigma$ such that $A\cup B\neq\Sigma^*$ and $A\cup B\in\mathrm{PSPACE}$. Does it follow that $A\cup B$ is PSPACE-complete? In general, is there a sufficient condition for the union of PSPACE-hard (or complete) problems to be...

Context In my world, magic has been granted to mortals by their gods. As a result, the Church heavily regulates it, and the only legal spellcasters are clerics and clergymen. Magic use is heavily regulated by a continent-wide neutral organisation of high clerics, bishops and cardinals (think of i...

I want to be the DM of a published adventure: The Dragon of Icespire Peak, but am unsure of how to run it beyond 6th level. It offers suggestions to run beyond 6th level that I just don't understand. What should I do to run it beyond 6th level?

At their closest flyby, Earth is ‘new’ and dim from Mars, and Mars is ‘full’ from Earth and brightest as seen from Earth. When Earth is 39 degrees from the Sun then Earth is brightest as seen from Mars, then at a ‘crescent’, and Mars ‘gibbous’ to Earth. https://astronomy.com/magazine/ask-astro/2...

In literature, movies, and TV, it's very common for speakers to switch betwen vouvoiement and tutoiement in order to show (or hide) changing relationships. For example, disrespect during an argument in Le Cid, or how two people might continue using vous in public to hide the fact that they're in ...

I'm not a Swift programmer, so I have no clue about the language. I'm just asking out of curiosity. I came across a language construct where self inside a mutating function gets assigned a new value like in the function moveByAssigmentToSelf in the example below. struct Point { var x = 0.0 ...

I have a for loop and case statements. The for loop has quite a bit element list and the case statement will assign an 1D array or a vector. These values will be used in for loop after. I have the following code. What happens is that the for loop does the job only for the first value in the vect...

When the photon is incident on free electron, we say that compton happens. Though, we require that photon is x-ray or gamma ray. I wonder why at least x-ray is required. I have my own observation and correct me if I'm wrong. I just want to make sure. Due to the formula of $$ λ_f - λ_i = \frac{h*(...

I have been reading this article about the quantum vacuum state, and in the section that I linked to, there is a video showing an experiment that shows visibly that quantum fluctuations are actually happening (see the video in the link). The quantum fluctuations are visible because they amplified...

I am quite familiar with preimages, however, I have recently been taking a course on Set Theory and came across questions that involve preimages of functions with empty domains (and sometimes empty codomains too). I was wondering how we treat these particular cases and whether or not there is a p...

What I'm talking about is like in C, you get to use namespaces with the statement using namespace blah blah blah, can you do the same thing but in bash?

How can I fill the part of a shape between two positions with a color? Is there an easy way with 'path picture' etc.? PS: · I know there are examples for that task, but these mostly for paths, not for shapes. · Yes, there should be a brute force solution (by drawing an arc) in that case as well....

I'm genderfluid, and I use xe/xem as my default pronouns. Other pronouns, such as he/him or she/her, are not always wrong for me but my preference varies, so I prefer not to put them anywhere semi-permanent. I don't like using they/them because it often feels impersonal: they're just using it as ...

We have had the phases balanced, and the problem is still occurring. We initially added a 60 kVA generator taking out our amenities block, and this helped during peak power times of day. It is no longer solving the problem, and the B phase is again rising and blowing circuit breakers. We have now...

I sometimes visit a small restaurant owned by a couple. The husband is the chef and the wife serves as the waitress. They do not have any employees. As I understand, most tipping occurs socially in lower-paying jobs that require little skill or education. Tips are to supplement the low income of ...

I had a dispute regarding a tip charge on my credit card when I dined in a restaurant. The tip amount which I signed to pay is $8.98 but the restaurant charged me $15.00. A few days later when I realized this, I filed a dispute with my credit card company and uploaded a picture of the receipt sho...

I was wondering if anyone could help me with my current predicament. I have been offered a postdoc position in Germany at TV-L 13. I completed my PhD in Australia last year but have not done a master’s (in my country a special year is added after a bachelor’s). After receiving my offer, I’ve been...

We recently had a new member join our team. We are all fully remote. I have become 99% convinced that my new coworker is just ChatGPT. Here's the background: We rarely have team calls, and generally communicate through IM. When he joins calls, he's super quiet and just says "message me on IM f...

What does "I plead the blood of Jesus Christ" mean? Is this something Christians say? Supposedly "I plead the blood" is a legal term.

@5:08 The video mentions: "The insertion point should have a low output impedance and high input impedance" What is the background for this condition?

In the above graph, I would like to display plots with slope-dependent plot styles (solid, dashed and dotted). Specifically, the regions a---b1, a---b2 and a---b3 with solid lines(Thick), then b1---c1, b2---c2 and b3---c3 with Dashed lines and beyond c1, c2 and c3 with DotDashed lines. Is there...

I'm attempting to find the volume of a solid in Mathematica when it is revolved around a line that isn't the axis. I'm revolving what I get within the x > 0 region of these two curves, f(x) and g(x). I believe I got this working with the y-axis: f[x_] := 3x^3 - 0.75x^5 g[x_] := x^2 - 6x + 2 {x1, ...

Can you guess the above phenomenon?

I am currently building a functional Lego minifigure-scaled escalator that can transition from flat platforms to stairwell. My first iteration for its guiding rail includes a slope of ~39.5 degree inclination as thus: And here is the first staircase which the guiding rail is designed around: B...

I am in the midst of reworking my latest manuscript into a shape that someone might be inclined to publish. To help me along I hired a professional editor and writer, whose comments and suggestions, for the most part, have been very helpful. However, I am struggling with her insistence that I avo...

Tor Browser conceals the user's operating system by spoofing user agents. Currently it is Mozilla/5.0 (Windows NT 10.0; rv:102.0) Gecko/20100101 Firefox/102.0. I decided to test whether the function actually does its job by visiting multiple detection websites on Tor Browser in both Windows and L...

So I have an image I am trying to georeference using QGIS. The coordinates I want the image to be placed at are: top left = 50N, 140E top right = 50N, 160W bottom left = 15N, 140E bottom right = 15N, 160W But when I attempt to load those into QGIS - Georeference tool, it only appears to want: X ...

If $B$ and $C$ are $n * n$ complex matrices such that $BC=qCB$ for some $q$ in $ℂ$, then we can apply the following argument to show that $q^m = 1$ for some $m ≥ 1$. Let's assume that $q$ is an eigenvalue of $BC$ with corresponding eigenvector $v$. Then we have: $BCv = qCBv = qC(Bv)$ Since v is n...

After seeing this question, I was curious on how we define the Apogee of Earth. On a quick search it said that the Apogee is the point when Earth is the furthest way from the sun. However, all the objects in the solar system effect the shape and position of the sun up to some degree. If the loca...

I have a layer with point geometry with a field STREETCODE that represents the entry number of each house. On the other hand, I have, a layer with line geometry with the field STREETCODE, representing the centerline axis of each street. My objective is to use an expression to obtain a graphical r...

I store the ciphertext and the nonce in a SQL database. If I decrypt the ciphertext change it and encrypt it again I generate a new nonce, so that I do not encrypt two different plaintexts with the same nonce. After encrypting the updated plaintext I store the ciphertext and the new nonce back to...

I want to draw a horizontal line on a word in LaTeX. I've tried \cancel but it draws a diagonal line. I checked the \cancel documentation and couldn't find anything about drawing a horizontal line.

A = Table[{x, 2 + Sinc[x], 2 + Sinc[0.9 x], 2 + Sinc[0.8 x]}, {x, 0, 10.0, 0.1}] // N; ListLinePlot[A[[All, {1, #}]] & /@ {2, 3, 4}, PlotStyle -> {Red, Blue, Black}, PlotRange -> {1.6, 3.2}] In the above graph, I want to show the curves with slope-dependent PlotStyles (solid, dashed and d...

We see this trope in comics and manga, and also in cyberpunk fiction, where characters have weapons integrated onto prosthetics, like arm cannons. It can sometimes even be a bit absurd, where guns are integrated onto people's heads, legs, chest, etc. What were the earliest examples of this in fic...

I want to create a model of an octagonal tower which is part of the roof of a building which has exterior framing timber on the edges and can think of only one way which would be to create another octagonal cylinder slightly larger and then use the boolean modifier to remove all the bits not requ...

In the depicted geometry nodes setup, capture attribute is used with the "position" field added as input, in two nodes. I expect that this gives no new information to the geometry that is passed through capture attribute, since it's simply declaring properties inherent to the geometry. Yet, when...

The Extradition Act deals with extradition in India. But in its Sections it doesn't have any such provisions or details. and can State High court of India enquire into such extraditions?

I want to know the dominant orientation of the green lines in the purple box because I want to place a grid perpendicular to these lines.

This question is a more precise version of this question. Let's assume we have the matrix $$\left( \begin{array}{ccccc} 0 & a & 0 & 0 & 0 \\ f & 0 & b & 0 & 0 \\ 0 & e & 0 & c & 0 \\ 0 & 0 & d & 0 & r \\ 0 & 0 & 0 & g & 0 \\ \end{array} \right)$$ If we square it, we get the matrix $$\left( \...

Is the Lagrange multiplier: The marginal cost of the constraint? The marginal benefit of relaxing the constraint? Through duality, both interpretations imply the other? If anyone were so kind, I have another question on Lagrange Multipliers and Non-Negativity constraints here. Thanks!

I understand that iota can be complex(e.g. infinite), so this can not be done easily in general case, but in some cases it should be possible to do find/contains operation in O(1). For example int main() { auto vals = views::iota(10'000'000'000, 100'000'000'000); return ranges::find(vals,...

We have multiple SQL Servers with each holding dozens of databases - one per client (a client in this case means a customer organization). These databases are accessed via an application, but the application is currently using a single Windows login. Therefore, this creates a security risk, i.e.,...

So we're writing a big grant proposal with about 10 PIs. My supervisor is the lead PI. In our small group meeting going through the proposal, once we got to the diversity section my PI suggested that I should do it (as I'm female). He's also emailed the only two female PIs on the project for thei...

What are the differences between \visible<>{}, \uncover<>{} and \only<>{} in beamer/tikz? At the moment I am using them interchangeably and could not understand their particular use cases. I think one of them already assigns the space required for the object to be revealed and one of them reveals...

How did the adverbial use of "smack" come into use? For example: "smack in the middle" or "smack in front" of something etc.

I would like to simulate and plot many paths of a discrete random variable $\tau_{t}$ that follows the following process: with probability $\tau_{t-1}$, $\tau_{t}$ is either $0.6$ with probability $x$ or $0.4$ with probability $1-x$. Then, $\tau_{t+1}$ is drawn according to the process. with pro...

Matthew 13:19 "When anyone hears the word of the kingdom and does not understand it, the evil one comes and snatches away what has been sown in his heart. This is what was sown along the path." ESV. My emphasis. What has not been understood, so that the evil one is able to snatch away what was ...

Let $\Omega$ be an open subset of $\mathbb R^n$ for $n \geq 2$, and $p \in \Omega$. Let $k$ be a positive integer. Suppose that $f: \Omega \setminus \{p\} \to \mathbb R$ is in $C^k$, and $\lim_{x \to p} D^k f (x)$ exists. Question: Is it true that $f$ admits an extension to $\Omega$ that is in $C...

Recently I have synthesized the polymer that contains 1-aza-18-crown-6 in the repeating unit. I want to know if there is any UV/Vis absorption difference after the chelation of metal ion. Considered metal ions are Cs, Co, Sr. In the other papers that compare the UV/Vis absorption difference, they...

I know someone who went to purchase a new car from a dealer in the US. The customer came in with an internet ad and asked to test drive the car listed. After the test drive, she paid for it. But when she returned outside, and got in the new car, she found inside was different. Less features. Less...

It is a bit stupid question, but I am so confused. Please examine my explanation. What is the space that exponents the generator $g$ of a cyclic group $G$ of prime order $p$? I think it is $\mathbb{Z}_p$ since $|G|=p$, so that $G=\{g^0, g^1, \ldots, g^{p-1}\}$. Thus the space that the exponents l...

(Note: I am not yet sure about the population numbers involved here, but if it is a very crucial aspect of the answer, somewhere between 1 million to 100 million at the start is almost certainly correct. The tech-level when magic appears is late bronze/iron age, and technological progress is simi...

It is in the news that the UK government is making a significant investment in "a clampdown on the use of cold calls to sell financial products". This involves significant investment in specialist skills: The new fraud strategy, a response to the massive growth of web- and phone-based scams, wi...

I am moving from the USA to Japan and I really want to take my espresso machine with me. Japan runs on a lower voltage (Japan's voltage is 100 V and the frequency is 50-60 Hz). I have attached a screenshot of the electrical information for my espresso machine but there are two lines. I am not sur...

Every spring when I jet wash my driveway I collect about 80 litres of moss. I have a large garden with many plants that can benefit from any nutrients I throw on them, and I’m thinking whether the process of jet washing has effectively killed the moss and it can be safely used as a compost? Or ...

There is an integrated feature in Windows 10 which allows us to do a screen recording without resorting to a third-party software: How to Screen Record in Windows 10 or Windows 11 by doing WIN+ALT+R. How to make that "clicks" are recorded as circles (to show where the clicks happened)? There is a...

I am preparing a presentation for a mathematical modeling conference soon involving online discourse which contains racist and other slurs as one of the prominent features under study, and the specific slurs used as keywords are a not insignificant part of the experimental methods. I would like t...

I'm trying to draw a Samtaegeuk symbol, which is essentially a yin-yang symbol with three swirls, each one a different colour. I found the guide below for drawing the two-swirl Korean taegeuk, but I need something similar for the three-swirl one.

The Broyden (Broyden—Fletcher—Goldfarb—Shanno or BFGS) algorithm can be known in the matter modeling to optimize a crystal lattice geometry — to clarify positions of nodes of a crystal lattice in calculation process of eigenvalues and eigenfunctions with a Hartree-Fock (or DFT) method. How much w...

Yes, these questions/answers are related but do not answer my question. I work in a company that, to my understanding, handles very sensitive information on its network. The open space in which I am currently located accomodates roughly 20 people at most. Since I arrived at my desk, I see some c...

From Wikipedia, I'm copying two things: It is the low-energy limit of Compton scattering: the particle's kinetic energy and photon frequency do not change as a result of the scattering. In the low-energy limit, the electric field of the incident wave (photon) accelerates the charged particle, ca...

I have started running Keys from the Golden Vault with my group. We just finished the first heist, the Murkmire Stone, which we ran at level 1. This caused one of the players to take (relatively) massive damage, leaving them at 2/8 hp. They asked if they could take a short rest alone in that roo...

We live in very comfortable times (more or less). Nowadays communication between people from different parts of the world is very easy. In addition, many people are born into wealthy families, so they have the possibility to dedicate their lives to whatever they want. With this in mind, it seems ...

I have a device with too many external contacts exposed to ESD, I search for a way to reduce cost of ESD protection. According to datasheet BAT54 can stand 1 A non-repetitive peak forward current. So if I put a 10 kΩ resistor in front of it, it should stand ESD up to 10 kV. Will it work?

I want to change the orientation of the raster/polygons with a numeric value around the centroid of the total grid. I have tried rotate($geometry, 45) in the field calculator but nothing happened.

Someone used the words 'bomb peck' in conversation to me yesterday and I queried what they meant. I have found the expression being used colloquially online but with no explanation of what 'peck' means or what the origin of the saying is. I remember the bomb peck between Wilkinson Street and Mil...

Suppose $G$ is a word hyperbolic group i.e. every geodesic triangle in a cayley graph with respect to a finite generating set of $G$ is $\delta$-thin, for some $\delta>0$. There are various analytical properties these groups admits. Like some hyperbolic groups have Haagerup property, e.g. free g...

In an effort to recover some old dust, I've been working on a sweep script to be used on a bunch of old private keys with a little BTC locked inside multiple p2pk utxos. First I tried using python's bitcoinlib, but after creating and signing the hex, it was rejected on broadcast with {"code":-26,"...

I want to expand this trigonometric function Sin[π/4 + α - β] such that $\alpha - \beta$ is treated as "one" expression, resulting in Sqrt[2]/2 Cos[α - β] + Sqrt[2]/2 Sin[α - β]

My question is around applying undersampling methods to an imbalanced, and highly dimensional dataset, with mixed data. Lets say as an example, I have 150 features, also a highly imbalanced binary target variable. I want to apply a sophisticated undersampling method, not random undersampling. Let...

Two sentences: I will have the mechanic repair my car tomorrow. I will have the mechanic repairing my car tomorrow. Is there any difference between them?

I found in the TikZ-Handbook, page 1022 lines which have 3 parts in different colors and widths: one inner linewidth and two outer lines. But this has a pgfpicture-code... I asked myself: How can I use that at a shape? I would like to have an inner line (pink, 5mm) and two outer lines above and...

I'm struggling to answer this question : Show that this function admits partial derivatives in every direction without being continuous in $(0,0)$: $f(x,y)=\begin{cases} y^2\log \left|x\right|& \text{ if } x \neq 0 \\ 0 & \text{ if } x=0 \end{cases}$ I have no problem showing that f admits pa...

I have written a first draft of a paper, but I have found it is way too long for any journal, so I decided to divide it into two separate papers with titles along the line: My paper I - Theory My paper II - Applications How do I submit the two papers together to the same journal? I am afraid th...

House was built in 1964. Slab is about 3 feet across.