I found this exercise in a book by Narkiewicz: Assume that the series $f(s)=\sum_{n=1}^{\infty} a_n n^{-s}$ with real monotonic coefficients is convergent in a half-plane and satisfies there the Euler product formula $$ f(s)=\prod_p\left(1+\sum_{k=1}^{\infty} \frac{a_{p^k}}{p^{k s}}\right). $$ P...

Currently I'm trying to find a Geometry Nodes solution on how to get the name of the object that is assigned in an Object Info node, as a string value, to be able to use it in a string type Compare node. I'm trying to figure this out because I need to be able to rotate geometry but only when a sp...

I thought that if a PDF is password encrypted, it is at least provides some kind of safety. However I received today an encrypted PDF, and was told the password. When I opened the document with my local PDF reader, I was expected to enter the password. However then I tried the following: There is...

A Girard semilattice is an algebra $\langle A, \wedge, \to, 1\rangle$ of type $\langle2,2,0\rangle$ such that $\langle A, \wedge, 1\rangle$ is a bounded semilattice and the following six conditions hold for all $a, b, c\in A$: $1\to a = a$, $a\to a \geq 1$, $(a \to b)\wedge (a\to c) = a\to (b\we...

I have just recently received my British Certificate of Naturalisation and I have three back to back trips for work in the next six weeks. I have a valid Canadian passport that I use. Can I come back into the UK using my citizenship certificate and a valid Canadian passport? And can I use electro...

I placed birds (as instances) on wires, but they are all facing the same direction. How can I make some of them randomly face different directions (some facing the right, others the left)? I do know how to apply random rotation, but what I need is a bit different. I want some pigeons to face rig...

Consider the following ODE: $$ \frac{dx}{dt}(t) = f(t,x(t)) \tag{1} $$ where we are solving for the function $x : [0,\infty) \to \mathbb R$ with its first derivative described by the function $f : [0,\infty) \times \mathbb R \to \mathbb R$. My understanding is that all ODE solvers are essentially...

I could use some advice on getting our more publications, fast and cheap! I'm an engineer focused on support for scientific field research in the first year of my Postdoc at a University. My biggest weakness is that my publication record is not very strong. I have done a lot of good work, but my ...

Hebrews 1:6 NIV And again, when God brings His firstborn into the world, He says: “Let all God’s angels worship Him.” If God brought his firstborn into the world from heaven instead of having his firstborn begin from earth, does this imply that the Son of God was firstborn in heaven among his b...

Here is an excerpt from Bach's first movement of Matthäuspassion. Note how the choral bass almost doubles the continuo, except for some small ornaments which are very much thematic; then it goes to diverge for a bar, then goes to 8ves and unisons. It's almost as if the continuo is the Schenkerian...

I am trying to implement small codes for quantum kernel estimation with Qiskit. In this challenge, I face the difficulty of implementing modular multiplication under a given prime number $p$. I have found some articles and a function in Qiskit to take modular multiplication under $N$, where $N = ...

Im starting out as a bug bounty hunter and found a website that might have a problem yet im unsure if its exploitable or not when sending any payload that contains % i get an error and this is the response i get on burp suite: [![enter image description here][2]][2] HTTP/2 400 Bad Request Cont...

I need to know what is the proper order of resolving effects, when character is under effect of those: Mirror Image, Blur/Displacement, Entropic Shield. My GM argues that Mirror Image goes first and other effects only apply to the "real" one (so are only resolved if the "real" one is hit after ...

The story, as best I remember, is that an alien species (robotic) visits Earth. They discover a box in orbit around Earth with a human and revive him into a robot. He wants to visit Earth, which they oblige him but finding nothing alive they fly off and he goes with them. It was supposed to be a ...

During the 1964 cyclone, I heard that an entire train carrying more than 100 passengers was washed away by the tidal wave. Some sourcescitation needed mention that it was on the Pamban railway bridge. I want to know that the train was on the Pamban railway bridge when it was washed away or betwee...

This is a runoff discussion from another SE question which I decided to make its own thread. It seems like MATLAB and Python's NumPy/SciPy libraries work the same in the relevant regards, so I'll assume we're in either one of those languages (unless someone points out that they're different in so...

そもそもナンパもしたことない恋愛経験が人並みの人間に付き合ってほしいなんて言葉ハードル高いよ The character wants a partner, however he doesn't know how to break the ice and invite someone to date. In his mind he thinks this. How is this sentence exactly divided? Particularly I don't get how 人並みの人間に here works そもそもナンパもしたことない To begin with, I ...

I have a 3.3v circuit with a device that indicates Power Good with a single open-drain pin. When there is a fault, PG is actively pulled low; when normally operating, it is high-z floating. I'd like to use a single bi-color SMD LED, either independent or bi-directional. Something like Dialight's ...

All I remember about the story is that Earth is going to be destroyed in some about amount of time because human music is the best in the galaxy which owes Earth so much money that it is easier to destroy the planet than pay us off. I remember that the resolution involves putting something into ...

My hypothetical experiment is a controlled drug trial. Each person has a diagnosis and has been placed into 1 of 3 groups (control- continue their usual coping strategies, treatment - drug and placebo - will take a sugar pill). I have data on their age, gender, bmi, height, weight, blood pressure...

Has deep learning helped improve solving the Traveling Salesman Problem (TSP), such as by discovering better heuristics? It seems so, as reinforcement learning (RL) has helped discover more efficient matrix multiplication algorithms. related: "Can neural networks efficiently solve the traveling s...

I'm trying to make a world where bones or any other hard supporting tissue wouldn't develop only creatures without bones can exist. I was thinking maybe something to do with gravity or something to do with sound/shock waves that would shatter bone. I'm looking for why bones or exoskeletons never ...

I have the following 3D plot in Tikz which represents plane, segment that intersects the plane and the orthogonal projection of that segment onto that plane: \documentclass[tikz, margin=2mm]{standalone} \usetikzlibrary{angles, quotes} \usepackage{amssymb} \usetikzlibrary {arrows.meta, shapes.geom...

I'm trying to put together a query that finds all gaps within a road network where lines should be interesting but are not. I don't want the query to return dangles related to dead end streets. I have this but the query runs for ever with no output: WITH endpoint1 as( select id as sid1, st_end...

If I have a polynomial whose variables are encoded in the form $p_{i,j}$ Let our polynomial be as follows: $P=p_{1,2} p_{2,0}+p_{1,2} p_{2,1}+p_{1,0} p_{2,2}+p_{1,1} p_{2,2}+p_{1,2} p_{2,2}$ where $j=0,1,2$ Based on the following mathematical condition: $$\sum^m_{j=0}p_{i,j}=1$$ Using the simplif...

Chapter 3 of the Book of Daniel tells the story of three Jewish youths, during the Babylonian captivity, who refused to betray their faith, and got thrown into a "burning fiery furnace" as punishment but were miraculously saved from death. Putting aside the religious elements, I'm curious about t...

I'm self-learning Algebraic Topology and I have a question about induced maps on chain complexes. I came to this question while I'm studying exact sequences of homology. My question is: suppose $A$ and $B$ are topological spaces and that $i: A \to B$ is an injective continuous map. Consider chain...

Recent adventures in the symmetric group algebra have led me to the following nice theorem: Theorem 1. Let $A$ be a rng (= nonunital associative ring). Let $J$ be a (two-sided) ideal of $A$. Assume that both rngs $J$ and $A/J$ are unital. Then, the rng $A$ is also unital. Much as I enjoyed prov...

I am currently reading Petersen's Riemannian Geometry book. When presenting the Rauch comparison theorem, he explicitly states that "It is not important for the next result that M be complete as it is essentially local in nature". I was wondering whether other comparison theorem's (specifically t...

I used to spend hours trying to get all of my drivers loaded in such a way that DOS games would still run. I actually managed to get a game that claimed it could not be run with DoubleSpace because of the amount of conventional memory it caused to run anyway. I knew people who made a different bo...

My mailbox was recently broken into with a pry bar. The door is steel but the hinge is aluminum (or other soft, non-magnetic metal). One of these: https://www.homedepot.com/p/Architectural-Mailboxes-Oasis-Classic-Black-Extra-Large-Steel-Locking-Post-Mount-Parcel-Mailbox-with-High-Security-Reinfor...

I would very much appreciate tips on Kavana (the ability to connect one's heart to one's mind i.e. pay attention to, and feel the meaning of the words one says during prayer and the actions one does during Mitzva observance, i.e. one's service, one's Avodah). I have seen a lot of different tips i...

The Catholic Church always has taught that Our Lord Alone redeemed mankind; and so, only through Him are salvation and Grace obtained. The term mediator means a "go-between." Thus, and in a sense, we are mediators when we pray to God on behalf of another person. Ven. Pope Pius XII (d. 1958) (as w...

When trying to compile the following MWE: test-package-small.sty \ProvidesPackage{test-package-small}[2025/02/11 v0.1 Package Template] \RequirePackage{kvoptions} \SetupKeyvalOptions{ family=tps, prefix=tps@, setkeys=true } \DeclareStringOption[blue]{maincolor} \ProcessKeyvalOptions\relax %...

I'm attending a German course, B2 level, and we were repeating the Te-Ka-Mo-Lo rule -- the order of adverbials in the sentence. Pretty simple from the first look, yet I struggle to understand the correct order of the words in a sentence, when the sentence has not only a subject and adverbials, bu...

Let's suppose Person A gets injured by Person B and says, "He attacked me for no reason and injured me." Person B says, "Yes, I injured Person A, but I was attacked by him for no reason and just defended myself." There are no witnesses, so all you have is the fact that Person A was injured by Per...

About a month ago, I submitted a manuscript to arXiv and then sent it to a journal that wasn’t a good match for its subject matter, resulting in a rejection. I’m now preparing to submit it elsewhere. After the first round of revisions, I noticed several typos and poorly written paragraphs (I am e...

Given the following code: out="$(mktemp)" rm -f "$out" clear printf '%s\n' 0 >"$out" { printf '%s\n' '1' >/dev/stdout printf '%s\n' '2' >/dev/stdout } >"$out" cat -e -- "$out" rm -f "$out" On Ubuntu this outputs: 2$ On MacOS this outputs: 1$ 2$ When explicitly appending, they behave c...

The Ming civilization has the following trait: -15 Science per turn for each Social policy, but not tradition, slotted. I played a game as Ming, and I never noticed a -15 Science Penalty for slotting what I thought were Social Policies. So either I didn't notice (possible!), or I don't actuall...

For "I travel vicariously through the videos of YouTubers," Google Translate returns "私はYouTuberの動画を通して間接的に旅行をします。For me, 間接的 doesn't seem sufficiently precise, although of course I understand the general meaning. Dictionaries give vicarious in various combinations such as 追体験 for vicarious exper...

Job 9:7 “Which commandeth the sun, and it riseth not; and sealeth up the stars.” What does that mean? I have read something similar in the Book of the prophet Isaiah but I'm just a layperson, with no experience really, and this is a difficult verse.

About a hundred years ago, the first Iranian journal in mathematics, titled حل المسایل ریاضیات (Problems and Solutions in Mathematics), was published. The third issue is dated February 5, 1928. In this issue, the 20-year-old Mohsen Hashtroodi, a recent graduate of the school of Dar ol-Fonoon (a s...

In Kato's book Perturbation Theory for Linear Operators, Chapter 2, Section 6.2, it is claimed that, for a Hamiltonian which is a holomorphic function of a real parameter $x$ (i.e. a time-dependent Hamiltonian), the orthonormal eigenvectors at each point $x$ can be chosen such that they are holom...

As shown in the picture below, why does the Copy Rotation constraint behave this way? Initially, the two bones are aligned in both direction and position. The Before Original option is enabled, and World Space to World Space is set. When a Copy Rotation constraint is added, an offset appears. How...

Movie opens with unconscious naked humans in bubbles underwater then bubbles break/surface on body of water near shoreline... children and adults struggle to shoreline naked to gather clothes thrown-about the sand. Children and adults don't know how they got to their current location, so they jo...

Comment experime-t-on l’état de se trouver orienté directement vers le soleil tel que la lumière intense empêche la vision et entraîne une gêne ? En anglais on dit « have the sun in one’s eyes » ou que le soleil « is in one’s eyes ». Google Translate gives what looks like a word-for-word (and thu...

I'm building a world with the "perfect" conditions for very biodiverse and competitive ecosystems, with vast and old rainforests dominating the global picture (though not ubiquitous). This is also a fantasy world (beyond other things, inspired by my appreciation for ecology and biology in general...

According to the official Keccak data, the second preimage resistance of SHAKE256 is given as min(d, 256), where d is the output length. Based on the definition of second preimage resistance, consider the following cases: Given an input m₁ that produces a 255-bit output out₁, finding another inp...

I want to typeset a multiletter variable with a subscripted label. Googling I found this answer by egreg. Based on it, I created the following MWE \documentclass{article} \usepackage{unicode-math} \setmainfont{Latin Modern Roman} \begin{document} \(\mathit{diff}_{\textnormal{eff}}\) \end{docu...

Contingency: The spell to be brought into effect by the contingency must be one that affects your person and be of a spell level no higher than one-third your caster level (rounded down, maximum 6th level). Haste, targeting me and my friends, affects me; it also affects my friends. Is this a v...

The following minimal example typesets exactly the way I want (it requires two compilations), but I don't know how to solve the compilation errors. I looked at a few other questions regarding having equation environments in a caption, but they did not solve the errors. The errors tell me a number...

Let $S$ be a normal projective surface (over $\mathbb{C}$) whose singularities are locally analytically isomorphic to quotient singularities $\mathbb{C}^2/G$ where $G \subset \text{GL}(2,\Bbb C)$ is a finite group whose action is fixed point free outside the origin. Locally at each of the singula...

In this example \includegraphics[width=0.6\textwidth]{example-image-a} How to divide 0.6 by say 5, and have the result be used instead of 0.6? I tried to use the fp package to do the division, but keep getting error from \includegraphics command. Here is MWE. I made newcommand called \scaleIt ...

I am reading Aquinas' list of order approaching Aristotle's texts, and two titles popped out: 1. Ethica, 2. Tabula Ethicorum. Here: What is the best order to read Aristotle in? I've searched on the Internet but there aren't any results for "Tabula Ethicorum". I wonder what are their English names...

I have been asked to produce a list of all of our shires public toilets, with the distance of the closest toilet along with the location details of both the source and target location. I have used the distance matrix tool to show all distances between all public toilets, of which I only want to s...

I ran some numbers using the relativistic longitudinal Doppler effect formula $$\lambda_r = \sqrt{\frac{1+\beta}{1-\beta}}\cdot\lambda_s$$ where $\lambda_s$ and $\lambda_r$ are source and received wavelengths respectively, and $\beta = v/c$. Then I plugged in the wavelength of a red laser (630 nm...

Has ECL logic been used in home and personal computers? I am interested in the period up to the late 1980s. Even a single discrete chip can be considered a yes.

I recently installed Zorin OS by partitioning part of my G drive for Zorin. There was and still is a partition specifically for EFI and another for the rest of Linux. However, when I unplug this drive, Grub still boots in, but I normally use "exit" to boot into Windows. Now, I'd like to delete Zo...

In this video, EigenChris mentions that there is no spacetime distance in Galilean relativity. And in this video he replies to a comment as follows: @hariszachariades8299: If the "spacetime separation vector" has components $(\Delta x,\Delta t)$, there is no combination $a\Delta x^2 + b\Delta x...

I have read the maybe relative link here. But I still found it strange with \parbox as normal while \framebox changed the baseline? What is the difference between \parbox and \framebox? How to change the second case to vertical align it? \documentclass{article} \usepackage{tabularray} \usepacka...

If I understand it correctly, the ONLY way in the 5e 2024 rules to add your ability modifier to damage with the Light weapon property's extra attack while fighting with two weapons (or for that matter the extra attack from the Dual Wielder feat) is to have the Two-Weapon Fighting Fighting-Style f...

As far as I know, double barlines can be used to separate sections of a piece. Some examples I found on my books: between variations (if there is no repeat sign) between an introduction and the solo entrance to highlight the da capo al segno points when the piece is composed of different parts (...

A rechargeable battery is charged at particular max. charging voltage from a source. After the battery gets charged to its maximum rated voltage, the charger circuit cut-off the supply. How does the charger circuit know and automatically cut-off supply, when the battery reaches its max. voltage? ...

Let's say I have below given dc-dc converter The converter operates in the buck mode where the \$T_1\$ is switching and in the boost mode where the \$T_1\$ is on and the \$T_4\$ is switching. The current flows from the dc link to the battery. I would like to calculate power delivered by the dc l...

I'm aware of the Coptic script descending from Egyptian hieroglyphs, but that's it. Are there any other examples of a primarily logographic writing system becoming entirely non-logographic over time? For that matter, are there any writing systems going through this today? This is conjecture, but ...

This is part 80 of the puzzle series Around the World in Many Days. Each part is solvable on its own. Dear Puzzling, Each of the following triplets has two correct words and one incorrect word which belongs to some other triplet. The positions of words within the triplet do not change, so e.g. i...

I am working with a Monte-Carlo based simulation program for particle physics and I am trying to understand some of the randomness I observe. The principle of this program is that it injects a particle into some medium and then it uses a random number generator to decide what type of interactions...

The \else of \ifwindows binds wrong IMHO. Is this a bug - or a feature? \documentclass{article} \usepackage{iftex} \ifluatex \usepackage{ifplatform} \ifwindows lua-win \else lua-non-win \fi \else no-lua \fi \begin{document} Test \end{document} Output of pdflatex test.tex: This ...

I am working on a research project, where we need to measure a small amount friction during a high speed orbital motion (up to 400 Hz). The plan is to two load cells in X and Y direction, which output a signal in the mV range and then measure its amplitude. I know that for electronics 400 Hz is a...

Load regulation describes how good linear regulators are able to keep their output voltage when load impedance changes. Some datasheets (e.g. NCP114) simply state this value in Volts: See: https://www.onsemi.com/pdf/datasheet/ncp114-d.pdf Other datasheets (e.g. LP5907) give a percentage ("%/mA")...

When it comes to character descriptions, should the main characters' physical appearance be described in detail? Or should it be left to the reader to imagine what the character looks like? Should the description instead focus on personality traits, to better draw in the reader?

I am trying to prove the classic interpolation inequality in $L^p$ spaces in the case where one of the two spaces is $L^\infty$, namely: Let $u\in L^p(\mathbb{R}^n)\cap L^\infty(\mathbb{R}^n)$ with $1\leq p$. Then $u\in L^r(\mathbb{R}^n)$ for every $r\geq p$, moreover \begin{equation} \|u\|_r\le...

When I typed this code: $$\begin{Large}\textbf{Volume = } \; \bm{{\tfrac{1}{3}}\pi}\textbf{h}\bm{^2}\textbf{(3R} \bm{-} \textbf{h)}\;\; \textbf{or}\;\; \bm{{\tfrac{1}{6}}\pi\textbf{h}(3r^2 + \textbf{h}^2)}\end{Large}$$ it outputted this: which is exactly what I want. When I typed this code in th...

I'm noticing my model gets better values for most metrics on the training dataset but for precision in particular it's much better on the validation dataset, which has me confused. Also, please see the graphs here: The dataset is imbalanced with some classes having less than 10 entries in the tr...

I often see words like 概説, 概略, 大筋, 粗筋, 概論, 大体, 概要, and 要領 used when referring to summaries or overviews, but I’m not sure about the nuances between them. From what I understand: 概説 and 概論 seem to be used in academic contexts, but how do they differ? 概略, 大筋, and 粗筋 all seem to mean "outline" or "...

When Batman: Legends of the Dark Knight issue #4 got released some years ago, many fans noticed something odd with one of the buildings Batman is observing in one scene. This is not any random building. This is actually the entrance to Casinopolis, straight from Sonic Adventure. Even the monitor...

My kitchen is next to my laundry room. Whenever my kitchen faucet (double bowl style) doesn’t drain water, I run the disposal and I see water filling on the second bowl (the one without the disposal). As water goes down in both bowls, water and food particles start coming out of the water stand p...

Edit: this has gotten some great responses, thank you! I am going to do a bit of research. Thank you all so much! Im making a species of aliens that life on a semi-earthlike planet. I want to make them breath something other than oxygen to make them unique. I know their atmosphere does not have s...

What figure must replace the question mark in this sequence? (ignore the green color, not important) • • ❎ ❎ • ❎❎ ❎❎ ❎❎ • ❎❎ ❎❎❎❎ ❎❎❎ ❎❎❎ • ?

Problem Statement Given two sets of strictly positive real numbers $A = \{a_i\}_{i=1}^n$ and $B = \{b_i\}_{i=1}^n$. They have the same products (same geometric mean): \begin{equation} \Pi_{i=1}^n a_i = \Pi_{i=1}^n b_i \end{equation} Set $A$ has a larger summation than $B$ ($A$ has larger arithmet...

If I use single-supply, how do I connect VDD_1 and VDD_2 (2 pins -- 13, 14 -- both labeled as VDD) of ADG725 IC? I can not find any information in the datasheet. VSS in this case is connected to ground. Perhaps VDD_1 and VDD_2 should be connected together? Datasheet can be found here .

I ran a pipeline on 16S data (16S-SNAPP-py3 on github) which used fasttree to create a phylogenetic tree. Ostensibly it returns a tree in the Newick Format. I was trying to use phyloseq to load it in using the read_tree command which returned a null. I saw that the command is a wrapper for read.t...

I can use closed cell tubing to insulate PEX/copper but every 14.5" there's a 1.5" break as it travels through the stud/joist. I'm trying to make sure my recirculation line is insulated to the nth degree and am curious how I can properly insulate it as it travels through the studs/joists. Is simp...

Does earning a PhD in a specific discipline limit job opportunities to that field alone, even when research interests overlap with other disciplines? While this likely varies by department, university, and country, certain fields can comprise many disciplines, so it seems reasonable to assume tha...

I am using Qiskit latest version and I am trying to compare the noise of a QFT circuit. I already managed to do so with circuits like the one for the Bernstein-Vazirani Algorithm, where i get to qc.measure_all(). But with a QFT circuit, since I can't measure the qubits or I would lose the Quantum...

I have been reading the lattice ice40hx docs on supplying power (specifically, I downloaded the hardware checklist on page 47) I am new to this, and so am sure that there is something I have missed. My idea was to solder on a 5V battery to a PCB and then split the voltages and pass them through ...

How can I typeset coll'ottava (or col 8, coll' 8, etc.) markings in order to double music at the octave in LilyPond? A coll'ottava isn't the same as an 8va or 8vb. From Wikipedia: The abbreviations col 8, coll' 8, and c. 8va stand for coll'ottava, meaning "with the octave", i.e. to play the not...

The symbol := can be written as \coloneqq using the mathtools package. However, I am unsure how to represent the reversed symbol, =:.