Eugen Jahnke (1863 - 1921) studied mathematics and physics at the Humboldt University of Berlin, where he became a professor at the Mining Academy in 1905. His "Tables of Functions with Formulae and Curves" first appeared in 1909 and was printed into the 1960s (significantly expanded by Fritz Em...

The title says it all, but to be more specific, I am wondering if it is possible to record the screen of a Mac or take screenshots of it during its initial setup phase. I believe it is not possible, but maybe I'm wrong. Thank you

The link for the paper is available here. This is the case of the headmistress who says that next week, there will be a surprise exam one of the afternoons. The girl students argue that it is impossible for come Friday noon with no prior exam, the exam is no longer surprise later that afternoon. ...

I'd like to place some text along a path in TikZ. Said text is a quote, and for quotes I invariably reach for the csquotes package. However, \enquote does not appear to work when used with text along paths. Consider the following FMWE (fairly minimal working example): \documentclass{article} \use...

I’m trying to find a movie that I saw as a kid in 1964 or 1965, at the cinema. I had always assumed it was She, the 1965 film adaptation of Rider Haggard’s 1887 novel, She: A History of Adventure, but now realise that it wasn’t. It’s about a group of modern day explorers who find a lost undergrou...

Is it even possible? Like, for example, list all php files that contain the word “filter”?

I am using fontspec, Polyglossia and XeLaTeX to typeset a document in mostly English, but with a few Urdu phrases using the NotoNastaliq font. The problem is that the Urdu phrases get rendered correctly, but left-to-right, instead of right-to-left. I would like to use a specific font, which I hav...

Call an abelian group $G = (G,+)$ $m$-torsion for some natural number $m$ if one has $m \cdot x = 0$ for all $x \in G$. A subgroup $H$ of $G$ is said to be complemented if one can write $G = H \oplus K$ for some other subgroup $K$ of $G$. I was able to establish the following fact: Proposition...

I have been learning electrostatics and came across capacitors. I don't really get why do we say energy is stored in electric field rather than in the charges upon which we or the battery does work. I hope you could provide me the intuition. I don't understand the other answers on the same questi...

In axomiatic set theory one can define functions $f : C \to D$ between any two classes $C, D$ (even if one or both of them are proper classes). Let $C$ be a proper class and $D$ be a set. Consider all constant functions $f : C \to D$. Is it legit to say that these functions form a set? There is a...

When looking through datasheets I can't find a single one that shows the inner circuit of a triac driver optocoupler, all I get is this common diagram: What that zero crossing circuit looks like? how is it connected to the "triac"? I'm specifically looking for details of this part MOC3063M, but ...

I'm trying to solve the cartpole-v1 gym environment with only the linear and angular position, but the mean reward of the last 100 episodes isn't greater than 20 rewards. The longest train i made was a train with 90 000 episodes and the agent didn't get more than 20 reward. The algorithm that i'm...

In physics/chemistry/the life sciences there's a common experimental method of determining the concentration of a sample using spectrophotometers. We can measure the absorbance of the sample at a particular wavelength, and use Beer-Lambert's law to determine the concentration. Normally, the wavel...

Rob forcibly grabs an item from Bob's hands, genuinely believing that it is his (Rob's) item and that Bob is possessing it unlawfully. Rob does so while knowing that Bob contends that the item is his (Bob's); however, Rob is sure that Bob is wrong (either mistakenly or consciously). Does Rob comm...

Halachically speaking, one is obligated to honor parents. My question is, if a parent happens to have a serious mental health defect (such as say Alzheimer’s syndrome), is it permissible to put them in an institution like a nursing home? I don’t know if this constitutes a violation of the positiv...

It is useful to be able to provide default values in pattern-matching, for example, if an element has a key but no corresponding value, you can take the value to be zero: Cases[ { {a, b, {key, value1}, c}, {e, {key, value2}, e}, {o, p, {key}, t}, {e, f, g} }, {key, value_ : 0} :> valu...

I'd would like to confirm if the following proposition is indeed true in the case of an arbitrary measure space. Theorem: Let $(X,\Sigma,\mu)$ be a measure space and $\{f_n\}_{n\in\mathbb{N}}\subseteq \mathcal{L}^1_\mathbb{R}(\mu )$. If the limit $\lim_{n\to\infty}\int _Ef_nd\mu\in \mathbb{R} $ ...

This is my very first time writing choral music. I'm planning on having a choir making a re-exposition of an electric guitar theme. This way, I wrote a choir (bass, tenor, alto, soprano) fragment of 20 seconds, so legato, that it has no room for breathing. Now, I wonder: If the choir has enough m...

Inspired by How do you write dates in Latin? Challenge Given a month-and-day date, output that date in abbreviated Latin, as explained below. Input Input is flexible. You may choose to: Take a date in mm/dd or dd/mm format or two separate month,day arguments; Take a date in your language's date ...

Suppose I know the sequence is of the $a n^4 + b n^3 + c n^2 + d n$, with positive integers $a,b,c,d$, what is the easiest way to get them from the first few coefficients? Here are the sequences I'm looking at. Mathematica's FindSequenceFunction works for the first one, but not for the rest {15,...

In my modern fantasy novel, there is a species of people called the Hammerts. The Hammerts are small orange humanoids who have issues running and jumping after they reach adulthood. To compensate for their limited mobility, Hammerts all have a supernatural ability to access a hyperspace dimension...

The maximum compensation for lost luggage in Europe is 1,300 EUR. I think that's also similar to the Montreal convention covering other flights. I will need to travel with two laptops and I can't fit both in a small bag under my seat. They will travel in a carry-on trolley. The airline usually fo...

I have a parameter $q$ which is the probability of selecting a vertex (among $n$ vertices...) to be in a certain set. I am constructing the sets in an iterative way, having the vertex $v_i$ be in the set with probability $\leq \left(1 - q\right)^i$ (I'm not going into details about the order of t...

Suppose $C_n$ is a product of $n$ $d\times d$ matrices with IID entries coming from standard normal. The following appears to be true. Is there an elementary proof? $$E[\|C_n\|_F^2]=d^{n+1}$$ This follows from discussion on math.SE on the moment method, but unclear how to adapt it to this, since ...

I'm trying to show the following: Let $A$ be an $n \times n$ matrix over a field $F$ such that every sub vectorspace of $F^n$ is invariant with respect to $A$, then $A$ must be of the form $\lambda I_n$ with $\lambda \in F$. Intuitively, for any $v \in F^n$, since $\operatorname{span}(v)$ is inva...

What are the procedures in the United States for important people staying in the same place? Who can and who cannot fly together, etc. Where is this written down? I referring to government practices of not having too many people in the chain of succession to the presidency all in the same place a...

I bought a bag of LEGO in 2020, there is a frame which I think belongs to a vehicle. I have tried to search for the gray bricks with holes of 14x1 , but I could not identify the set. I might make a mistake with the color. Can anyone can identify the set from the photo? Any help is greatly appreci...

I am selecting a GaN FET for a buck-boost DC-DC converter application. The Vgs of the part I'm looking at combined with the gate charge and gate resistance lets me switch the FET on in about 5.3 ns. This would be 0.53% of the period with 1MHz switching frequency. Is this fast enough for 1MHz? Thi...

Okay so from my understanding and looking a the equation for the impedance a capacitor has, the high frequency signals would be relativley easy to be sunk to ground (if the capacitor was grounded) and hence the decoupling caps near IC,s. So (i think) from that perspective im okay. But its the big...

The thing I want to do The typical vector calculus course defines: A bunch of integrals of vector fields in $\mathbb R^2$ and $\mathbb R^3$: line integrals of a vector field along a curve, flux integrals of a vector field across a curve in $\mathbb R^2$, and flux integrals of a vector field acro...

In 3.5 there was a section in The Book of Vile Darkness (TBoVD) where if refers to fantasy use of drugs, such as "Devilweed" among others (pp. 41-44). It includes quite a lot information including effects and side-effects, costs, etc. I can't recall seeing mechanics for drugs come up in any other...

We have 180 people to photograph and 6 steps to stand on. There is enough room for all but who goes on the top row the tallest or shortest? How to best arrange everyone?

This year Christmas is on a Monday. My wife read in a neighboring parish's bulletin that we had to go to Mass on the Fourth Sunday of Advent (i.e. sometime Saturday night or Sunday Morning) and this greatly distressed my daughter who unfortunately wants maximum presents and minimum Mass for Chris...

In the key of C, where does Cmaj7 fit on the Circle Of Fifths? I'm writing a song for guitar and am using the chord progression C Cmj7, F Cmaj7, F G, F G C. I'm new to the Circle Of Fifths but have a rudimentary understanding of it and would like to know where/how to find suitable/compatible chor...

I have a large drive (4TB) that I've only written a few gigabytes to. I'm giving it to a friend, so I'd like to zero it out. I know I can zero out the whole drive with dd, but I'd like to know if: zeroing only the non-zero bits will be faster, and if so, how to go about doing that. EDIT: I trus...

When you complete the game in the new Honour mode, you can get the Foehammer achievement. In my game my party died. If you die, you can delete the save file, or play it in some "Dishonoured" mode. My questions are: When you continue your dishonoured game, can you still receive the Foehammer achi...

I started with the original recipe on the back of the All Bran box: 2/3 cup all-purpose flour 1/4 teaspoon salt 1/2 cup cocoa powder 2 eggs 1 cup sugar 1/2 cup Kellogg's® All-Bran® Buds cereal 1 teaspoon vanilla 1/2 cup margarine or butter, melted, cooled. "Stir together flour, salt and cocoa po...

Are there any halachic implications of relocating an established minyan? Here is a specific example that might help clarify my question: Suppose there is a small community that normally has Shabbat mincha and maariv at their synagogue every week. One week a member decides to invite the community...

Consider a standard game of chess. We make the following modification: on a turn, if a player makes a move which neither captures a piece nor puts their opponent’s king in check, then they may make a second move on the same turn with the same properties. (This does not stack, so at most two moves...

Given a presentation of some group, what are nice criteria to conclude that the presentation describes a free group? Even stronger is there a subclass of presentations (where one easily checks whether the presentation is in that class), for which it is algorithmically decidable whether a presenta...

In Star Trek III: The Search for Spock, Kirk asks Sulu the crew complement of a Klingon Bird-of-Prey, and Sulu answers immediately from memory. KIRK: Mister Sulu, what is the crew complement of a Bird-of-Prey? SULU: About a dozen officers and men. Why would Sulu know the answer moreso than Kirk...

In relation to a recent question, if somebody were to attack The Bahamas (or one of their ships etc.) can The Bahamas formally invoke any explicit defense treaty with some country with more military muscle, like the US or the UK? Or does The Bahamas have none of those and they'd have to rely on t...

I noticed a peculiar behavior of tabularx when using \verb. The following minimal working example illustrates the problem. Note the wicked extra space introduced between test and {123}. \documentclass{article} \usepackage{tabularx} \begin{document} \verb|tabular| \begin{tabular}{|l|} \hline \v...

Where does the name שכם come from? What exactly does it mean? I believe that names in the tanach are symbolic of qualities of whoever is that name, so what does שכם mean in relation to the person? Being “Ben chamor” is obviously a diss as him acting out like an animal, but what’s the first part o...

In the near-future, in a war between aliens and humans, the aliens hatch a plan to seemingly assassinate a human leader (on Earth), but make it look like it was done by other humans. They have it planned for a few months from now, to attack the human when they are traveling (predicted to be by he...

Consider a normal game of chess with one change. As soon as you put the opposing king in check you have won. If both players play optimally, how long is the game?

I'm utilizing Grover's algorithm to solve a straightforward problem. It presents eight options, but only four are correct (the 1's in the S column) $$\begin{array}{c|c|c|c} q_0& q_1\ & q_2\ &S \\ \hline 0 & 0 & 0 &1 \\ \hline 0 & 0 & 1 &1 \\ \hline 0 & 1 & 0 &1 \\ \hline 0 & 1 & 1 &0 \\ \hline 1 &

I've just watched this video from 3Blue1Brown which explains how prisms works, but when he talks about the "phase kickback" that light undergoes when passing through a layer of a medium he says that it lags behind exactly one quarter of a cycle behind. Why is that? I've tried reading chapter 30 o...

Is there a way to rewrite this expression as a single sum? $$\sum _{n=1}^k \frac{3^{-2 n}}{n}-\sum _{n=1}^{2 k} \frac{2\ 3^{-n}}{n}$$ It can be rewritten as $$\sum _{n=1}^k \frac{3^{-2 n}-2\ 3^{-n}}{n}-\sum _{n=k+1}^{2 k} \frac{2\ 3^{-n}}{n}$$ but that did not help me to simplify it any furthe...

I trying to sample using Gibbs from a proportional distribucion $f_{Z}(z)$: \begin{align*} f_{Z}(z) \propto e^{-z}\left(1-e^{-z}\right)^4, \quad z >0 \end{align*} using the joint $f_{Z,\textbf{U}}(z,\textbf{u})$ $$ f_{Z,\textbf{U}}(z,\textbf{u}) \propto e^{- z} \prod_{i=1}^4 I_{\left(e^{-z}, ...

I'm in the middle of a project where we removed a rotting deck (termites) and are in the process of installing a raised patio with pavers. The fill the contractor is using for the paver foundation is a combination of leftover concrete pieces and dirt. I am aware that wood siding should never be b...

The following question and translations are courtesy of Studies in Bereshit by Nechama Leibowitz. In Parshat Vayeshev, some pesukim suggest that Yoseph was sold by his brothers to Midianites, and others to Ishmaelites. The Ishmaelites are mentioned first ("Behold, a caravan of Ishmaelites...") fo...

I remember reading a novel from maybe the 80s about a village on Earth in the far future, after the Sun has gone red giant. The protagonist discovers that an 'alien' visitor is a descendant of humans who left Earth millennia ago. The visitor brings 'magic' technology that causes an existential cr...

I got one object that has “screw” modifier and when I join it to other object it gives it screw modifier too, I even tried with Boolean modifier but it doesn’t let me move both objects at the same time

In my story, I have a character who travels back in time to Africa just after the Youngest Toba supereruption, about 74,000 years ago in order to collect genetic samples from the human survivors at the time of the most pronounced human population bottleneck. During her time in the past, she drops...

I'm having trouble improving the upper bound on Markov/Chebyshev's inequality in this particular example: We have IID random variables where each $\mathbb{E}[|X_i|^2]<\infty$. Show that $$\lim_{n\to\infty} n\mathbb{P}(|X_1|\geq \epsilon\sqrt{n})=0$$ Clearly, Markov's inequality yields the upper b...

There was a prior question about golfing an HQ9+ compiler that translates HQ9+ code into the language it is written in, but that was closed as a duplicate of the interpreter challenge because converting an interpreter to a compiler is seen as trivial. This question is based on the closed one, but...

I don't quite understand the process of solving differential equations by MATLAB. It seems that it doesn't need the explicit function to specify the required solution, but only needs to input the vector formed by its derivative into ode45 to solve it. I want to implement the same code in Mathemat...

Im a not an electronic engineer nor do I understand optical science so forgive my basic pleas for help. I want to detect a light on my heating boiler. I think the led is on a PCB and there is a tube that directs the light to a diffuser on the front panel. The light is Green but not sure if that i...

"Let $G$ be a connected graph in which every vertex has degree three. Show that if $G$ has no cut-edge then every two edges of $G$ lie on a common cycle." I have an idea for this proof but I'm not certain that I'm using Menger's theorem correctly. Menger's theorem states that the size of a minimu...

Consider this toy example: f[t_?NumericQ, a_?NumericQ] := t + a tst = ParametricNDSolveValue[{x'[t] == f[t, a], x[0] == 0}, x, {t, 0, 1}, {a}] ParametricNDSolveValue::pdvar: Dependent variables {x, f[t, a]} cannot depend on parameters {a}. As we can see, f is just a black-box function involvi...

I want to write a passage of text that makes the reader feel like the person writing it is deranged or otherwise not in the right state of mind. It seems relatively easy to write incoherent, nonsensical text, but I still want the reader to be able to follow it. Any tips for how to do that?

The senior undergraduates at my (mathematics) department have this impression that postgraduate programmes don't want to admit multiple applicants from the same university in the same application cycle. So they are coordinating so that no two people apply to the same programme (i.e. if one studen...

simulate this circuit – Schematic created using CircuitLab simulate this circuit I'm primarily a VHDL and DSP guy, so I apologize in advance if this question is dumb. I have wire wrapped around a magnetic core. The coil is connected to an AC source. I want to calculate the extent to which e...

I had Moodle 3.11 i upgraded to 4.2 following the procedure from the docs. But after the upgrade, (i also moved it to a new VM) i notice that when ever I go to the platform, on the top right corner it shows that i'm connected anonnymously, next to the login button. I searched through the internet...

If someone makes a bet on something like chess or a board game, (we’ll include some types of card games as well), does that count as gambling in Halacha? Gambling (between Jews) is prohibited de-rabbanan, but does that only apply to chance-based gambling? Or are competition games included? Source...

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I'm just learning (multivariable) calculus and tried solve the following double integral: $$\int_0^2 \int_0^1 x y e^{x y^2} d y d x$$ I approached it initially using traditional u-substitution similar to one-dimensional integrals. Surprisingly, it yielded the correct result, but as I delved deepe...

My son KJ7NLL is working to contact the ISS using an antenna we built together, and we were wondering the approximate minimum transmission power to reach the ISS. If I understand correctly (and correct me if I'm wrong), roughly speaking, we need to solve for tx_power from the following equation ...

I accidentally removed about 1 hour of my work, how to restore? Last week I worked with file.md on my current computer and didn't save it into disk but just put my OS into a sleep mode. Yesterday I edited file.md on another machine. Today I made my first machine woken up and synchronized the file...

Continued from question, do I have to go from meter/main combo to the 2 ground rods ,then back inside connect to outside part of my copper water line,then back to the existing 100amp main breaker box, that will become a sub panel in one continuous, unbroken run to achieve proper grounding. The re...

Mythical Creatures on a farm (unicorns, basilisks, etc.). Relative having two children come to stay for summer. Children's book. Pre-2010.

What’s the conditions that need to be met so that spare the dying can work as a ranged spell. Basically what I’m asking is, do you need to see the target? The spell doesn’t account for that and the grave clerics ability doesn’t specify. Can I use spare the dying on a party member that’s around a ...

In Glass Onion: A Knives Out Mystery, there is a scene where a character named Peg is pleading with Miles not to make Birdie Jay go through with making a statement to the press about Bangladesh. Peg is worried that if Birdie Jay makes the statement, her name will be destroyed. Peg: Bird showed m...

Roughly 120 years after a nuclear apocalypse, an external group that didn't experience the apocalypse (the why of it isn't going to be explained here) came to the land that did, to pull apart their cities for scrap metal. How much steel could be recovered from those cities? The area in question t...

I want to type the date in yyyymmdd format, but the formatted content should show yyyy-mm-dd. I don't want to enter the dashes (or slashes), but I want Google Spreadsheet to add them automatically between year, month and day. The problem is that I type quickly and entering the dashes slowes the p...

This is about the Fourier uncertainty principle, which is closely related to, but not the same as the Heisenberg uncertainty principle in physics. So no $\hbar$. This may be expressed with scaling and definitions more preferred by electrical engineers than might be the habit of mathematicians. T...

I have a neon pothos plant. First pic is its original state (IMG_1258), second pic is post-being bitten by a Beagle (IMG_6078) Before After I took it to a horticulturalist after it developed brown spots (I had left it in the sun) and the horticulturalist cut the leaf off. I contacted a plant do...

Ok, So I was reading my book and there I found this statement:- We can conclude that the work done by static friction can be positive, negative or zero. When we consider the net work done by static friction at the contacting surfaces, since there is no relative displacement between the surfaces,...

In Glass Onion A Knives Out Mystery (2022), Duke was holding his phone, smiling, as billionaire Miles and Birdie danced: Miles: Hey. Duke's smiling. There it is, there's my guy. What's going on? You look like you got good news. Miles approaches Duke and Duke shows him his phone.: Duke: I was w...

Nothing I see in the definition of a catenary says this must be the case, but every illustration I've seen draws it that way. I'm assuming that a cable hanging from two points at different heights off the ground is still a catenary but how does that change the equation and properties?

I'm using Microsoft Excel 2021 I wish to be able to drag the cells in a column down in increments of 22 for example I typed in this in a column L25 L47 and ideally, when I drag this it turns into L25 L47 L69 L91 However, what I get after highlighting the two cells and dragging is this L25 L47 L2...

Anyone have idea how to turn this: FX_AM140_EML AM140 Backend/aa.java Backend/bb.java Backend/cc.java Backend/dd.java Backend/ee.java FX_AM172_EML AM172 Backend/aa.java Backend/bb.java Into this? FX_AM140_EML AM140 Backend/aa.java FX_AM140_EML AM140 Backend/bb.java FX_AM140_EML AM140 Backend/cc...

Sometimes, DSolve would return Inverse functions are being used by Solve, so some solutions may not be found but it seems it has returned all results. For example, DSolve[{y'[x]*Sin[x] == y[x]*Log[y[x]], y[Pi/2] == E}, y[x], x] produces {{y[x] -> E^Tan[x/2]}} I calculated by myself, it seems ...

Given some function I want to find a root around some value $x=x_0$ so I use FindRoot, for example: root = FindRoot[Exp[x]+Sin[x],{x,0}] But I want the root to be a number such that: root = -0.588533 but instead I recieve strange object given by: {x -> -0.588533} how to transform it to a number?

I am not a mathematician, I'm a chemist who happened to also be a math enthusiast. I was playing with error function the other day, and just out of curiosity compute these integrals using Desmos. $$ \int _{-\infty}^{\infty} e^{-(x^2+x+1)} dx \approx 0.837247915445$$ Then, I just add more terms...

As far as I know Bitcoin Core knows two types of RBF. These are Full RBF and Opt-in Full RBF. In both cases, the transaction will be replaced if a new one arrives that consumes at least one of the same inputs, is valid and has a higher fee. The only difference is that with Full RBF this applies t...

Which Sudoku technique can be used to solve this?

This question was initially posted on math.stackexchange.com but did not receive any answers for half a week. While analyzing the properties of an algorithm I am working on (I'm a computer scientist), I came up with the following inequality. I am counting the occurrences of two different events u...

I am an academic from China and I am currently studying the accreditation and quality assurance of German master's and doctoral degrees. However, the existing English literature does not clearly explain how German doctoral degrees are authorized. My questions are as follow: Do all comprehensive u...

I want to install a few banking apps for my bank accounts. But I also have mod or cracked games/applications installed on my phone. But my ohone is not rooted. Will adding a banking app increase the risk of it getting hacked?

Can you modulate sound waves? Like can you have a sound wave of a relatively low frequency and modulate it with a sound wave of a much higher frequency which people cannot hear and send it through the air to then be demodulated at its destination?

I do not really understand how the soft start circuitry of the UC3845 is really working. Here is what is explaining: Here is the architecture of the chip: I understand that we need a transistor as it is said for separating the "normal mode" from the "other modes" (like soft start mode"). Nevert...

Are both terms equivalent? They seem very similar to me. Or does one imply the other?

Is the location of the star that would have created our sun known? Meaning our sun's parent star which would have provided the material when it died? If not, has there been any theories on what kind of star it would have been, it’s age, mass etc? And would our sun parent star created other near b...

I'm trying to cut and delete some lines in a shapefile with QGIS. The output of this edit is the input to the Basemap.readshapefile function in matplotlib. My edited shapefile does not work well. It complains about this: ValueError: readshapefile can only handle a single shape type per file After...

I came across this integral in my maths textbook. $\int\dfrac{\left(x^2-2\right)\mathrm{e}^x}{\left(x-1\right)\sqrt{1-x^2}}$ after close to 30 minutes of trying u-sub, trig sub, integration by parts I gave up and plugged it into wolfram-alpha and the following integral calculator - https://www.in...

I'm going to allow a server administrator freelancer to access my server to do some tasks for me, so I want to save all the SSH commands that will be used in a file so I can access this file later and make sure that he didn't execute any malicious commands on my server. I don't want the commands ...

During the electrical upgrade, several PEHD tubes were laid through a hole in the wall (60cm thick). I am not sure how to fill the hole - want to keep the water and the dirt outside. Insulation is not a requirement, since it is in the basement (c.a. 70-80cm under ground level). I currently do not...

I am looking for a simple and short proof showing that $X \to \|X X^\top\|_F^2$ is a convex function where $\|\cdot\|_F$ is the Frobenius norm. I have one proof by showing that the derivative is monotone but it is quite heavy. I expect that there are simple arguments showing this.

I would be very happy if anyone can help me find answer regarding to questions below: The lead compensator is added to the system to increase the phase margin. 1'st picture is related to the uncompensated loop gain-phase graph. 2'nd picture is the summary of the lead compensator. Poles and zeros ...

What are the solutions of this system of equations, where $x,y,z\in \mathbb{R}$? $\begin{cases} \frac{1}{x} + \frac{1}{2y} = (x^2+3y^2)(3x^2+y^2)\\ \frac{1}{x} - \frac{1}{2y} = 2(y^4-x^4) \end{cases}$ First I rewrote the equations as $\begin{cases} \frac{1}{x} + \frac{1}{2y} = 3x^4+3y^4+10x^2y...

I know there are many questions on the site about finding a proof that π is irrational, but I'm posting the question separately to discuss a particular proof further We know that the Wallis Product is : $$\frac{π}{2}=(\frac{2}{1}\cdot\frac{2}{3})(\frac{4}{3}\cdot\frac{4}{5})(\frac{6}{5}\cdot\frac...

I have problems compiling a beamer presentation that I wrote and used two years ago. As the code hasn't changed, I guess some update must be the culprit. (I'm using MiKTeX on Windows with all updates installed as of today.) I was able to boil down the problem to the following minimal example: ...

In QGIS attributes I have text strings that sometimes include a measurement as part of descriptions, "such as cut at 10 m". In order to make these look nice when presented in multiline fixed width tables in a layout I would like to replace the spaces with non breaking spaces. I think regexp_repl...

I'm estimating the simple model communication_share ~ grid_size * n_procs. From the theoretical background I would expect a negative effect of grid size and a positive effect of number of processors. Estimating my model gives me the following coefficients. Predictor B SE t p Intercept -5....

I've got a Bosch cooktop (part number PKF645E01A) and the inner-ring of the double-burner element has stopped working (the outer ring works fine). I've opened up the cooktop and notice that the double-burner element has 3 wires. I've checked the resistance between the wires and have found the fol...

I have problem with fit sinus to my date, because this sin is very tiny. This is my code: DANE = ReadList[ "C:\\Users\\student\\Desktop\\jd100\\projekt\\wynik.txt", Real]; k = Length[DANE]/2; xx = DANE[[1 ;; k]]; yy = DANE[[k + 1 ;; 2 k]]; dane2 = Transpose[{xx, yy}]; fit2 = FindFit[dane2, ...

I have two screens. Since Screen 1 is faulty, the signal comes to this screen after approximately 10 minutes. I want to use only Screen 2 using the "Second screen only" option until the signal comes to Screen 1. But when I use the Win+P shortcut, Windows 10 shows the "Project" menu only on Screen...

I am a Phd student who has recently tried to initiate a collaboration on a paper with a professor to a university unrelated to mine. I have already collaborated successfully with this professor a few years before but the collaboration was textual via email. The professor now wants to see me via ...

Whenever the bandwidth of a medium linking two devices is greater than the bandwidth needs of the devices, the link can be shared. Multiplexing is the set of techniques ... Forouzan, Data Communications, p. 156 I always knew that bandwidth is always of a signal. Composite signals (made of many ...

I'm an Arcanist. This time I want to go heavily for save-or-die and save-or-suck spells, kind of a dark wizard fantasy. To do this I need to maximize my chances of actually affecting enemies with my spells. I already know I need to use Persistent Spell and maximize my main stat for spell DC. Nest...

Common in sci-fi tropes but absolutely climactic nonetheless, a spaceship faces impending doom after encountering a gravity well such as a stellar black hole. The spaceship's captain gives the order to discard all reactor cores onboard and detonate them to produce a powerful shock wave, the space...

In English, for example, if you say "How can it possibly take this long [to release a game]?!" you are expressing anger and impatience. In Japanese, can you express that same anger and impatience by saying どうやって[ゲームをリリースする]ようにこんなんに長い時間がかかる可能性がありえるのか？！ Or is there a different way to say expres...

how physically put a new(custom) SXA component for XM Cloud at different code folder structure and not to have all components under components folder ? at Sitecore it is possible to use SXA modules, and helix structure but at the component lave is it not clear. How to re-create the same structure...

Thinking about the four square theorem and related questions, I found myself wondering: What is the minimal density of a set $A \subset \{0, 1, 2, ... \}$ such that $A + A = \mathbb{N}$? What I know: If A has less than quadratic density, then $A + A$ is not $\mathbb{N}$ by a simple counting argu...

(Note: I'm a beginner in antenna theory) When browsing for low cost antennas online, there seems to be class of monopole antennas that have a built in coil or two into the monopole, and are advertised to be suitable for operation in the GHz range despite being 200~300mm in length. For example: Q...

I have data from 4 populations : A (n=16), B (n=16), C (n=14) and D (n=16). Data from A and B are not normally distributed. Data from C and D are normally distributed. All data passed the Levene's test for equality of variance. Kruskal-Wallis test does not show any differences between group. The ...

Cloak of Displacement: While you wear this cloak, it projects an illusion that makes you appear to be standing in a place near your actual location, causing any creature to have disadvantage on attack rolls against you. If you take damage, the property ceases to function until the start of your ...

Sometimes I see a claim like "80% of respondents agreed" and I think "what was your sample size? 5?" because, of course, with a sample size of 5 it's possible to get 80% to agree on something. If the claim is "47% of respondents agreed" then I know it must be a larger sample size.[1] challenge Gi...

Another very specific question: How would you approach modelling this shape? I have 0 experience with animal/organic shapes like this so it's a bit outside my wheelhouse. If anyone with experience would be able to suggest a simple approach for making carved styles like this, I'd really appreciate...

Ubuntu 24.04 does not have any software that will burn a audio CD. There is no software centre to install from. Many of the apps that come with Ububtu 24.04 have lost the three button top left, close, min, full screen. The only way to close some apps is right click the taskbar icon and click QUIT

I want to open a channel from my CoreLightning node to my LND node, and I want that channel to use anchor outputs to be used for the channel closing later on. How can I enforce my CoreLightning node to create Anchor Outputs? Right now it just opens a "legacy" channel. Context: I'm using nigiri on...

I have a cabin on stilts in Maine where the frost line is 4ft deep. I’m looking to make a system to supply water to the house that I could use in the winter. Seeing as the cabin will not stay above freezing when I’m not around (and possibly even at night when I am around from time to time if it’s...

This puzzle is part of the Puzzling Stack Exchange Advent Calendar 2023. The accepted answer to this question will be awarded a bounty worth 50 reputation.< Previous Door Next Door > A Connect Wall is a set of sixteen words/proper nouns/phrases which can be broken into four groups of four related...

I want to create an inverter LED light source. I would be using 2 COB LED lights rated at 4 volt DC, 8 watt. My idea is that when the phase is connected, I want the light to glow and at the same time charge the battery. When the phase is not available I want the bulb to use battery back up and gl...

I read on https://www.ica.gov.sg: Short-Term travellers should have sufficient cash and proof of onward travel (tickets, visas), and ensure that you do not stay beyond your visit pass validity. How much cash do I need to enter Singapore? I'll enter via Singapore Changi Airport (SIN) as a French...

I have a raster like this one: https://drive.google.com/drive/u/0/folders/1AEKu4TKpzJg95oXv8dxep24xpXaesr0F I want to find the locations (can be the centroid or the bounding box of these cells) for the extreme values (minimum and maximum). Here is a great answer on how to do it using stars Howeve...

I recently purchased a house with a high pony wall that divides the dining and living rooms. The pony wall has a column at one end that I'm concerned may be load bearing. To make matters worse, the pony wall is off-center of the vaulted ceiling. A structural engineer wants more than $800 to asses...

I am trying to stabilize the current in coils in my experiment. For that I am using a circuit as in the picture: First section is a fast switch. It is also galvanically isolated from the TTL signal with opto-coupler (not in the picture) Second section is fast discharging of the coils. When we su...

In The Demolished Man by Alfred Bester, which was published over the course of 1952–1953, the existence of a professional caste of psychics is central to the plot. Much of what happens in the novel is about the steps that one of the protagonists, Ben Reich, takes to conceal the crime he plans an...

I met with a faculty member for a history MA program but have decided not to aaply there. Simply put there are better programs that I would be a better fit for and also it requires an expensive verification of my transcript which other universities don't require. However, I met with the graduate ...

The US maintains a lot of military facilities in countries like Germany, the Netherlands, Belgium, etc. This doesn't make economic sense. The US military expenditure is on trajectory to reach a Trillion dollars, and maintaining these bases is just a drain on the treasury. This also doesn't make ...

I bought my house in 2013 and have been renting it to present time. I never lived in it. I am thinking of starting to live in the house in 2025 and 2026 and then sell it in 2027. What do I have to do to claim the house as my principal residence? Do I have to pay any capital gains tax?

Cyberpunk Red starts with a little text from the author of original Cyberpunk, and it contains in a nutshell, why Cyberpunk Red is not just a continuation of Cyberpunk 2020 and that there are a lot of changes. In fact, Mike Pondsmith promises that quite some things from Cyberpunk 2020 have been r...

I'm a Software Engineer who sometimes need to review the code of my fellow team members. I often look at the source code and think; this looks fine. I'm having a hard time to think critical about it. I can be very critical when writing code myself since I'm active/highly involved with the code, b...

I have a directed graph: a = {{0, 1, 0, 0}, {0, 0, 1, 0}, {1, 0, 0, 1}, {1, 0, 0, 0}}; AdjacencyGraph[a] I want to determine the cycle lengths in the directed graph. In the example above I would want Mathematica to return {3,4} because there is a cycle of length 3 and a cycle of length 4 in th...

This is the problem:A piece of ice floats in a vessel with water above which a layer of a lighter oil is poured. How will the level of the interface change after the whole of ice melts? What will be the change in the total level of liquid in the vessel? I understood most of the answer to this sol...

The short story begins with the protagonist waking up from the aftermath of a cult orgy, and while in the bathroom washing his face, he remembers his past lives. The story goes through what he remembers, sometimes linked with sex and sometimes linked with death. I think in his first life he was a...

I'm running Ventura 13.4 on an M2 MacBook Air. I run the FT8 and FT4 digital modes for ham radio. FT8/4 requires fairly accurate time synchronization. It seems that macOS gets out of sync when waking up from sleep. (See Time.apple.com sync). The solution for better time synchronization is to run ...

Let $f(x)$ be differentiable twice and for which it's true that $f(0) = f'(0) = 1$ and $f''(x) > \frac{1}{x^2 + 1}$ for all values of $x$. Prove that $\forall x \ge 1: f(x) > 2$. I thought this might be solvable using Taylor's theorem. Around the point $0$, $f$ can be written as $f(x) = f(0) + f...

Consider the following command (which is part of a script I'm writing): ssh -oClearAllForwardings=yes -NL 5555:localhost:5555 foo I want ClearAllForwardings=yes because I might have LocalForward options in my ssh config and I don't want these to happen within this command (if they're already bei...

Some of the leaves have stared turning yellow and drooping. The soil is completely dry right now but I was afraid the yellowing was because of overwatering. Please help :)

I came a cross an exercise the other day considering the following quotient space: Let $T$ be a torus and let $A, B \hookrightarrow T$ be two parallel circles. Let $X$ be the quotient space collapsing all of $A$ to a point, and all of $B$ to a different point. What would be the geometric interpre...

A full professor teaching the history of mathematics at Masters level recently told a friend of mine that there was nothing of interest left to explore in the mathematics written in Latin over the last 1000 years. Given that a significant part of Euler's work has never been translated into a mode...

My latex code: \documentclass{article} \usepackage{tikz} \usetikzlibrary{graphs,graphdrawing} \usegdlibrary{trees} \begin{document} \begin{figure} \centering \begin{tikzpicture} % draw a tree \tikz [grow'=up, binary tree layout, nodes={circle,draw}] \node {9} child { ...

The following code fails: \documentclass{article} \usepackage{expex} \usepackage{unicode-math}% Works without this \begin{document} \pex<ex> \a<foo>\begingl \gla foo// \glb foo// \glft foo// \endgl \xe \end{document} After removing unicode-math it works perfectly though. Agreeably It is becau...