qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
values |
|---|---|---|---|---|---|
3,548,486 | [
"https://math.stackexchange.com/questions/3548486",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/555017/"
] | I have a trigonometry problem which I am trying to solve for a lot of time, but nothing seems to work, here it is:
<blockquote>
<span class="math-container">$$\cos^7x + \cos^7(x+2\pi/3) + \cos^7(x + 4\pi/3) = 0$$</span>
We have to find the number of solutions of <span class="math-container">$x$</span> in the inter... | Let set <span class="math-container">$\begin{cases}c=\cos(x) & C=\frac c2\\ s=\sin(x) &S=\frac{s\sqrt{3}}2\end{cases}\quad$</span> then we can write <span class="math-container">$\begin{cases}\cos(x+\frac{2\pi}3)=-C-S\\ \cos(x+\frac{4\pi}3)=-C+S\end{cases}$</span>
Thus we need to expand:
<span class="math-co... | Let <span class="math-container">$a+b+c=3u$</span>, <span class="math-container">$ab+ac+bc=3v^2$</span> and <span class="math-container">$abc=w^3$</span>
Thus, <span class="math-container">$$a^7+b^7+c^7=$$</span>
<span class="math-container">$$=2187u^7-5103u^5v^2+3402u^3v^4-567uv^6+567u^4w^3-567u^2v^2w^3+63v^4w^3+21uw... | https://math.stackexchange.com |
650 | [
"https://physics.stackexchange.com/questions/650",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/337/"
] | If the physical world we know is made of matter stretched in time and space and some forces affecting it, what would be an Idea, pure Information or something similar.
Does those things don't exist in a physical model or did I just miss something.
If yes where to arrange it into the physical model? Is an idea just ma... | An "idea" is something that happens in the confines of your <em>mind</em>: two particles colliding don't have ideas, they simply behave following the so-called "Laws of Physics", and so on.
In this sense, an idea, or, more generally, <em>creativity</em> itself, is something that only "exists" (if that's an appropriate... | Information must always be represented by the state of some physical system. The idea in your head exists somewhere within the biological structures and electrochemical state of your brain, just as information in the computer is represented by the presence or absence of electric charge in the billions of bits of RAM.
| https://physics.stackexchange.com |
324,280 | [
"https://softwareengineering.stackexchange.com/questions/324280",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/236316/"
] | I am writing a telephone directory program and need to store the entries in a CSV formatted file. However, I am having difficulty keeping the entries in order when adding. I was considering reading in the entire file to an array of entries and then write it back out when the program exists, but this seems inefficient. ... | Your first instinct is correct: sort the entire thing in memory, then write it out. Performing line-oriented I/O to read and write the file will be far more inefficient than doing a bulk read and write of the entire file.
| <strong>My two cents:</strong>
<ul>
<li>Don't save to a file.</li>
<li>Save to a SQLite database table</li>
<li>Create an index for that table</li>
<li>The SQLite library maintains the index sorted and reports are sorted even when the data is not.</li>
<li>You can programativally export to CSV whenever you want.</li>
... | https://softwareengineering.stackexchange.com |
2,325,074 | [
"https://math.stackexchange.com/questions/2325074",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/283812/"
] | Let <span class="math-container">$C_{1}$</span> and <span class="math-container">$C_{2}$</span> be two circles, respectively with radius <span class="math-container">$1$</span> and <span class="math-container">$2$</span> endowed with the riemannian metric induced by the euclidean metric. I need to show that they are no... | The point is that the lenght of a curve does not depends on the parametrization. So $i \circ \gamma_1$ should be a reparametrization of $\gamma_2$, in particular they have the same lenght. So if $C_1, C_2$ are isometric this would implies as @Henning Makholm said that $2\pi = 4\pi$ which is absurd.
| My approach would be to prove that the metric induces a <em>measure</em> on the manifold which is preserved by isometries.
Then the two circles have total measure $2\pi$ and $4\pi$, respectively, and therefore cannot be isometric.
| https://math.stackexchange.com |
103,492 | [
"https://mathoverflow.net/questions/103492",
"https://mathoverflow.net",
"https://mathoverflow.net/users/25415/"
] | The wikipedia article(s) as well as the nlab article(s) about Grothendieck topologies and Grothendieck pretopologies are careful to differentiate the two very emphatically and to point out that distinct pretopologies can give rise to the same topology on a category. My (almost certainly trivial) questions are the follo... | A) Let $\tau$ be a Grothendieck pretopology on any category with fiber products. Define a new Grothendieck pretopology $\tau'$ where a cover $\{U_i \to X\}$ is a $\tau'$ cover if and only if there exists a refinement $\{V_{ij} \to X\}$ (i.e. there exists for each $ij$ an $X$-morphism $V_{ij} \to U_i$) such that $\{V_{i... | I think of pretopologies (and coverages and other variations of this idea) as convenient ways of <em>presenting</em> a topology, just as groups (and other algebraic structures) can be conveniently presented by generators and relations, or (since I'm a set theorist) a complete Boolean algebra can be conveniently present... | https://mathoverflow.net |
4,158,877 | [
"https://math.stackexchange.com/questions/4158877",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/800548/"
] | Alice is given two bags. The values of the contents of the bags are each uniformly (and independently) distributed over <span class="math-container">$[0, 1]$</span>. She looks in both bags and finds out their value. She then reveals the value of one of the bags to Bob. Bob then picks either the revealed bag or the hidd... | Here, I will expand the argument given by @QuesterZen in his last paragraph, and argue that Alice has no strategy that helps her in any way against Bob's strategy of "take anything <span class="math-container">$\geq 0.5$</span> and switch otherwise", and show that <span class="math-container">$7/12$</span> is... | Perhaps we can build up to the continuous case with smaller finite cases?
With only {0,1}, Bob always wins by accepting 1 and rejecting 0. His expected return is <span class="math-container">$\frac{3}{4}$</span>.
With only {0,0.5,1}, the only interesting case is if Alice has either (0.5,0) or (0.5,1), when she has to s... | https://math.stackexchange.com |
238,162 | [
"https://softwareengineering.stackexchange.com/questions/238162",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/129364/"
] | I know I have quite frequently heard that C typically has a performance advantage over C++. I didn't really think anything else of it until I realized that MSVC doesn't even seem to support the newest standard of C, but the newest it supports it C99 (as far as I know).
I was planning on writing a library with some cod... | I guess people often claim that C is faster than C++ because it's easier to <strong>reason</strong> about performance in C. C++ is not inherently slower or faster, but certain C++ code might obscure hidden performance penalties. For example, there can be copies and implicit conversions which are not immediately visible... | Code written in C++ can be faster than in C, for certain types of tasks.
If you prefer C++, use C++. Any performance issues are going to be insignificant compared to algorithmic decisions of your software.
| https://softwareengineering.stackexchange.com |
350,442 | [
"https://softwareengineering.stackexchange.com/questions/350442",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/265938/"
] | I understand test-driven development so far that you are only allowed to write productive code when you have a failing (red) unit test.
Based on this I have the question if the test-driven approach can also be applied to other forms of tests.
| All TDD requires of you is that you write a failing test, then modify your code to make it pass.
Typically "unit tests" are small and fast and test some part of your code in isolation. Because they are fast, it makes the red/green/refactor loop fast too. However, they suffer from only testing parts in isolation. So y... | The red green refactor cycle is built on one very sound principle:
<strong>Only trust tests that you have seen both pass and fail.</strong>
Yes that works with automated integration tests as well. Also manual tests. Heck, it works on car battery testers. This is how you test the test.
Some think of unit tests as cov... | https://softwareengineering.stackexchange.com |
13,353 | [
"https://dba.stackexchange.com/questions/13353",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/6792/"
] | I am setting up a web interface for data management. Users upload CSV or similarly structured files, and I want to store these in the database so they can do manipulations on them -- filtering, sorting, graphing, etc.
I do not know how to model this properly in a database. I have several ideas, but none seem to be t... | The question is so wide open that it is hard to say much.
And why are you using a database at all? Excel does everything you've described so far.
Seriously though, avoid making an inner system in your database that can store any kind of data. You have one already, called a DATABASE. Make code that creates the tables ... | MySQL has a CSV engine that may help you.. I never successfully tested it however.
<blockquote>
The CSV engine can treat comma-separated values (CSV) files as table,
but it does not support indexes on them. This engine lets you copy
files in and out of the database while the server is running. If you
export a ... | https://dba.stackexchange.com |
471,178 | [
"https://electronics.stackexchange.com/questions/471178",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/237979/"
] | I'm working on a project about a self-stirring robot with sensors to avoid walls.
This project is composed by one Raspberry responsible for all the algorithms, one Arduino to deal with the sensor and the motors, one sensor to measure the distance in front of the car and two motors to make the car walk though the envi... | We did something similar back in college for the IEEE micro-mouse competition.
Chris Stratton is correct in that I wouldn't mess with Lithium batteries just yet. Use a bunch of NiMH batteries, as they are robust against shorting (though the wires may not be!) and easy to charge.
I think for my project I used about 8 ... | You should choose a minimum battery voltage that can supply 5V-10% or so plus LDO dropout for a FET type LDO. e.g. 6V min to ? max
The <em>28BYJ-48–5V</em> Motor resistance is 50 Ohms and rated for 5V so the current 5V/50ohm= 100 mAmp. 12V supply voltage is less efficient with PWM but can be used to control heat,tor... | https://electronics.stackexchange.com |
35,226 | [
"https://quant.stackexchange.com/questions/35226",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/23856/"
] | In the book McMillian on Options the author states that in some cases an option market maker hedges himself by purchasing longer dated options. Unfortunately, the author does not go into detail why the market maker does that. I was unable to find on the internet literature that this is actually true. I was wondering if... | McMillian's example does not make sense to me. Typically short-dated contracts are liquid and longer expirations are less so, and it would make sense to hedge long-expirations contracts with more liquid (also typically tighter, and more leveraged) short-term ones, but not the other way around.
The only explanation for... | Toughest challenge you face as a market maker is <strong>inventory risk</strong>. To sell something, you should own it. Time between buy and sell is never zero and you have same exposure against market as any other participant.
Taking advantage of calendar spread makes you <strong>market neutral</strong>, but you stil... | https://quant.stackexchange.com |
305,962 | [
"https://physics.stackexchange.com/questions/305962",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/142487/"
] | Guys I want to know the difference between a system and an object ?
A system is collection of two or more objects but how ca we define an object suppose if we talk about a tennis ball its an object but at atomic level we can say it is a system because it is made of millions of atoms and each atom can be considered as ... | An object will be whatever you want to treat as an object.
If you were concerned about where the tennis ball would go, treating it as two half tennis balls would be a waste of effort. The system that the two half objects form will be essentially the same as considering the ball as a single object.
Ideally your objec... | The concept of an "object" is a product of human intelligence. It's our ability to discern parts of reality from one another given our macroscopic view. Reality at a more basic level is excitations/propagations of continuous fields, not concrete cut and dry boundaries as our macroscopic view would imply. At a lower lev... | https://physics.stackexchange.com |
222,705 | [
"https://mathoverflow.net/questions/222705",
"https://mathoverflow.net",
"https://mathoverflow.net/users/23661/"
] | Let
$$X_t = m \cdot t + W_t$$
where $W_t$ is a Brownian motion. Let
$$Z = \sup \{ t\in [0,1] : X_t = 0\}.$$
It is known that if $m = 0$ then the distribution of $z$ is given by
$$\mathbb{P}[Z \leq y ] = \frac{2}{\pi} \arcsin \left( \sqrt{ y } \right).$$
What is the distribution of $z$ for general values of $m$?
| Here is a simple description:
$$Z\stackrel{d}{=}A\cdot Y_m$$ i.e. $Z$ is distributed as the product of two random variables, where the the factors are independent, $A$ is $\arcsin$-distributed, and $Y_m$ is distributed as $\min\{1,\exp(m^2/2)\}$.<br>
($\exp(\lambda)$ denotes an exponentially distributed rv. with exp. ... | I don't know if there is a nice closed-form expression for this, but you can try to work it out writing
$$
P[Z\leq y] = P[X_t\neq 0 \text{ for }x\in (y,1]] = \int_{-\infty}^{+\infty} f_{y}(v) P_v[X_t\neq 0 \text{ for }x\in (0,1-v]] \, dv,
$$
where $f_y(\cdot)$ is the transition density of the drifted BM at time $y$ (se... | https://mathoverflow.net |
280,904 | [
"https://physics.stackexchange.com/questions/280904",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/99516/"
] | I am given the following lagrangian:
$L=-\frac{1}{2}\phi\Box\phi\color{red}{ +} \frac{1}{2}m^2\phi^2-\frac{\lambda}{4!}\phi^4$
and the questions asks:
<ul>
<li>How many constants c can you find for which $\phi(x)=c$ is a solution to the equations of motion? Which solution has the lowest energy (ground state)?</li>
<li... | Looks good so far. To find the Hamiltonian you just use that if $L = T - U$ then $H = T + U$ (technically there are some extra assumptions there, but if your case it works out fine). Since $T = 0$ if $\phi$ is constant, you just need to find out which of those values $c$ minimize(s) the potential energy $-1/2 m^2 \ph... | You have a minor error from a missing minus sign here:$$\frac{1}{2}\Box\phi+m^2\phi-\frac{\lambda}{6}\phi^3-\frac{1}{2}\Box\phi.$$ It should be (after combining terms):
$$-\Box\phi+m^2\phi-\frac{\lambda}{6}\phi^3.$$
Now, for finding the Hamiltonian you might find it easier to integrate the term $\phi \Box \phi / 2$ by... | https://physics.stackexchange.com |
179,900 | [
"https://electronics.stackexchange.com/questions/179900",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/-1/"
] | Can we look at NVIC peripheral on ARM CPUs like some sort of thread? Main application is executing, and at the same time NVIC peripheral doing her own work? Or all of that is single thread application. Can someone explain if I am wrong, where and why?
| R1 and R2 are <strong>NOT</strong> in series.
Here is how you can do it:<br>
R1, R2 and R3 are in parallel. Calculate the parallel resistance of those three resistors so you can see them as one and call it R123.
Now R123 and R4 are in series. They form a voltage divider.
Now you should be able to calculate the volat... | This is an easy question if you have a solid knowledge in basics of circuits
So These are steps that I will use to solve your problem,
<ul>
<li>First find the equivalent resistance between L and M.And before that you want to ground a particular point of a circuit(this is a must because we want to find the voltage,... | https://electronics.stackexchange.com |
8,008 | [
"https://earthscience.stackexchange.com/questions/8008",
"https://earthscience.stackexchange.com",
"https://earthscience.stackexchange.com/users/5983/"
] | One day I was sitting in an Atlanta traffic jam wondering about all the engine exhaust heat warming the localised environment. Later that night, things will have cooled down. Where did the heat go? On a global scale, I understand our sun heats the earth via radiation, not conduction as the intervening vacuum of space... | The hotter the Earth gets the more it re-radiates energy back into space.You can see a tiny fraction of this energy by looking at the new moon. The feint glow is just a small part of the re-radiated spectrum.
The long term differential between incoming and outgoing energy is what is causing global warming. It isn't 'a... | A body has to emit as much thermal energy as it absobs to remain in thermal equilibrium. The Earth has been doing the same since its formation, i.e, it absorbs solar shorwave radiation by its atmosphere, solid earth and water body, and releases it in the form of longwave radiation. The amount that is released has to ... | https://earthscience.stackexchange.com |
39,645 | [
"https://chemistry.stackexchange.com/questions/39645",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/17885/"
] | I have learnt that internal energy, $U$, is a state function and it only depends on temperature... So if $\Delta T = 0$ then $\Delta U = 0$.
However when I was studying exothermic and endothermic reactions it was written in my textbook that at a constant temperature and pressure, $\Delta U$ is negative for exothermic ... | <blockquote>
TL;DR: Do <strong>not</strong> just memorise thermodynamics equations! And if you have an issue with the equations <span class="math-container">$\Delta U = 0$</span> or <span class="math-container">$\Delta H = 0$</span> for an isothermal process, read on...
</blockquote>
<hr />
<h3>The first problem</h3>
Y... | For exothermic reactions and endothermic reactions...as the reaction occurs, heat is evolved and absorbed by the reaction system respectively. Which means that there is a total change in the heat energy of the system and the change is suffered by the internal energy of the system. Let us consider the example: C+O2--->... | https://chemistry.stackexchange.com |
170,272 | [
"https://electronics.stackexchange.com/questions/170272",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/73667/"
] | I have a hand-wound coil I'm using in an LC Tank circuit. Using my multi-meter, I found out that the coil is drawing .6mA at 9v. Using Ohm's Law...
$$R = V/I$$<br>
$$R = 9/.0006$$<br>
$$R = 15kΩ$$
Is there a way to calculate the inductance of my coil from the DC resistance?
| An ideal coil has an inductance \$L = mew \times turn\text_density^2 \times Area \$.
The resistance of your coil is \$R = \rho \times \frac{length\text_wire}{cross\text_section\text_area\text_of\text_wire}\$. This can be simplified to \$R = constant\times length\text_wire\$
Naturally the if the coil has a greater tur... | No. If you have an LC tank circuit, I would recommend using an oscilloscope to measure the voltage across it and then use a function generator to inject a sinewave. Find the resonance in the form of a minimum or maximum in the response and calculate what the L should be, given the C that you are using.
It may also... | https://electronics.stackexchange.com |
54,534 | [
"https://physics.stackexchange.com/questions/54534",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/16281/"
] | Consider <em>any</em> wave packet describing a free particle (so no potential or other forces acting on it). Then it can be shown that $\Delta p$ does not change in time. However, my question is what happens with $\Delta x$ as we go forward in time? Does it have to increase at all times? Or is there a counter-example w... | If $\Psi(x,t)$ solves the Schrodinger equation, so does $\Psi^*(x,-t)$ , so no, there is nothing at all that must increase.
| I don't know the answer to this yet, but here is a calculation that others might find useful in determining the answer. Let's compute the time derivative of $\sigma_X$. First note that
$$
\frac{d}{dt}\sigma_X^2 = 2\sigma_X\dot\sigma_X, \qquad \sigma_X = \langle X^2\rangle - \langle X\rangle^2
$$
so
\begin{align}
... | https://physics.stackexchange.com |
521,041 | [
"https://physics.stackexchange.com/questions/521041",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/250148/"
] | The other day when I was cycling back from work in the rain I noticed an effect from the light on my bike. A single raindrop, as it passed the light, appeared as multiple dots or dashed that followed the expected trajectory of the raindrop. I haven’t thought about it before but I would have thought it would appear as a... | Yes.
LED lights are often fed from a circuit that causes them to flash so quickly they look continuous.
What you are seeing is the stroboscopic effect.
Cheaper lights use a resistor to control the current through the diode, but this wastes energy. The pulsing circuit increases battery life.
| Brightness of LED sources is controlled with PWM (Pulse Width Modulation) -- the LED flashes (time_on/time_of - duty cycle). Due this 'effect' you see rain drop multiple times with gaps. Human eye is capable distinguish movie 'frames' with frequency below 24Hz (nowadays a good TV provides 120Hz refresh rate).
| https://physics.stackexchange.com |
73,740 | [
"https://stats.stackexchange.com/questions/73740",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/31231/"
] | I have a model which includes the following priors:
$\lambda_C \rightarrow \dfrac{1}{\sigma_C^2}$
and
$\sigma \sim \text{uniform}(0,500)$
Where $\sigma$ is the standard deviation and $\lambda_C$ is the precision of a normal distribution.
Being a beginner, I have problems conceptualizing the prior of $\lambda_C$. H... | You can think of the relationship between $\lambda$ and $\sigma$ as just
a change of variables, a.k.a. a reparameterization, of the probability distribution that was initially specified in terms of $\sigma$.
We have the random variable $\sigma$ distributed as $p(\sigma)=1/500$ for $0<\sigma<500$. We want the di... | I am not sure if I really get what is troubling you, but perhaps a couple of hints will help you:
<ul>
<li>How can I conceptualize the prior of a deterministic variable in Bayesian data analysis? </li>
</ul>
Formally, deterministic variables don't have a probability distribution (yes you guessed it, since they are no... | https://stats.stackexchange.com |
416,119 | [
"https://softwareengineering.stackexchange.com/questions/416119",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/17309/"
] | DDD was chosen as an architectural pattern to tame a wild database model, as well as ubiquitous language. However, there is a sticky part of our model -- many of the rules are dynamic, and I don't know how to reconcile them with what I understand of DDD.
<pre><code>class Account {
private Mailing[] mailings;
... | <blockquote>
Where should these runtime checks happen?
</blockquote>
If it is <em>domain</em> logic, then the checks should happen inside the domain model. If it is <em>application</em> logic, then the checks should happen in the application code.
<hr />
If it is <em>domain</em> logic, and the configured information i... | How did you end up solving it, @bryan-boettcher?
I'm facing the same problem (including "multi-tenant with different roles and rulesets").
Here's what I'm considering (applying to your specific use case)
Application layer:
<pre><code>class SubscribeToMailingCommandHandler: ICommandHandler<SubscribeToMailin... | https://softwareengineering.stackexchange.com |
955 | [
"https://cstheory.stackexchange.com/questions/955",
"https://cstheory.stackexchange.com",
"https://cstheory.stackexchange.com/users/864/"
] | Parametrized maximum independent clauses problem:<br>
Input : A r-CNFSAT formula F having <strong>n</strong> variables and <strong>m</strong> clauses, <strong>k</strong><br>
Ques : Does there exists at least <strong>k</strong> clauses such that they are mutually independent i.e. no variable occurs more than once in al... | I'll assume that the k in k-CNF is different from the number of clauses k, and also that the latter is the parameter. I will replace k-CNF with k'-CNF in the following.
This problem is in FPT for every k'. Notice that no "logic" is being used in the problem definition, so you can just assume that you have a collection... | The problem is known as <strong>r-Set Packing</strong>:<br>
Instance: A collection $\mathcal{C}$ of subsets of size at most $r$ of a finite set $S$ and an integer $k$.<br>
Parameter: $k$<br>
Question: Is there a subcollection $\mathcal{C'} \subseteq \mathcal{C}$ which consists of at least $k$ mutually disjoint subsets?... | https://cstheory.stackexchange.com |
94,956 | [
"https://dba.stackexchange.com/questions/94956",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/56050/"
] | I will short my question. (SQL-Server 2008)
Is it a good idea , when crating a new table, to create an index for each column?
Why i'm saying this?
Today I was creating a database, and my boss was behind me, and he said:
<strong><em>"Oh, it's good to create an index, for every column"</em></strong> (and then he sho... | Would you find it useful to have the phone book, only having it as a list of Surnames with phone numbers, plus a list of Firstnames with phone numbers, and a list of towns with phone numbers? Because essentially, that's what you're getting if you index each column individually.
| Absolutely NO!
Creating index on tables decreases insertion performance and you must create an index only if you really need that (if you include the column in select queries many times).
| https://dba.stackexchange.com |
66,394 | [
"https://physics.stackexchange.com/questions/66394",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/4075/"
] | I'm confused about the Kronecker delta. In the context of four-dimensional spacetime, multiplying the metric tensor by its inverse, I've seen (where the upstairs and downstairs indices are the same):
$$g^{\mu\nu}g_{\mu\nu}=\delta_{\nu}^{\nu}=\delta_{0}^{0}+\delta_{1}^{1}+\delta_{2}^{2}+\delta_{3}^{3}=1+1+1+1=4.$$
But... | In terms of your ordinary matrix multiplication, you have, for the case of a 4x4 matrix $M = g_{ab}$:
$M\cdot M^{-1} = I$, which is the same thing as $g_{ab} g^{bc} = \delta_{a}{}^{c}$
and
$Tr\left(M\cdot M^{-1}\right) = 4$, which is the same thing as $g_{ab}g^{ab} = \delta_{a}{}^{a} = 4$
| It's useful to know how matrix multiplication is defined:
For $n \times n$ matrices, $A$ and $B$, denote the entry in the $i$th row and $j$th column by $A^i_j$ and $B^i_j$ respectively. Then for $C = AB$, the entries are given by $$C^i_j = A^i_kB^k_j$$ (summation convention of course), which you can check by working... | https://physics.stackexchange.com |
199,671 | [
"https://mathoverflow.net/questions/199671",
"https://mathoverflow.net",
"https://mathoverflow.net/users/62367/"
] | Although the classification of simple Lie Algebras and their representations is fully understood, I wonder whether there is <strong>some book with exhaustive tables describing explicit irreducible representations in low dimensions</strong>. For instance, it would be very helpful for me to know which are the first irred... | I think "Group Theory for Unified Model Building" by R. Slansky qualifies. As the title suggests it is written with an application in physics (beyond my understanding) in mind, but the tables are very useful for purely mathematical purposes as well. (Disclaimer: it is quite some years ago that I last read it.)
| If all you really want to know are the irreducible representations of ${\frak{so}}(7)$ and ${\frak{so}}(8)$ up to dimension $30$, I can save you the trouble of looking up these tables:
For ${\frak{so}}(7)$, there are the following irreducible representations with dimensions below $30$:
<ol>
<li>$\mathbb{R}^1$ (the tr... | https://mathoverflow.net |
56,430 | [
"https://mathoverflow.net/questions/56430",
"https://mathoverflow.net",
"https://mathoverflow.net/users/13196/"
] | Let $\bf N$ be the set of positive integers and let $\bf Q$ be the set of all rational numbers. Consider all functions $f:{\bf Z}\to{\bf Q}$. We say $f$ is a sum of $q_1,q_2,\dots,q_s$ if for all positive integer $n$ the equality $f(n)=q_1(n)+q_2(n)+\dots+q_s(n)$ holds. How can one prove that for each $f:{\bf Z}\to{\bf... | One key observation is that with $3$ functions, we are free to have <em>one</em> of them assume any rational value at any Natural number. This is not possible when we only have $2$ functions where after we select the value for $q_1(n)$, we have $q_2(n)$ completely determined by $f(n) - q_1(n)$ and visa versa. The oth... | A simple example of a function which can't be written as a sum of two bijections is given by $f(0)=1$, $f(n)=0$ for $n\ne0$. If there were such bijections $q_1$ and $q_2$, then restricted to $n\ge1$ each would have range missing exactly one rational, and if (the restricted) $q_1$ is missing $r$ then $-r$ can't be in th... | https://mathoverflow.net |
583,653 | [
"https://physics.stackexchange.com/questions/583653",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/275200/"
] | In a LED the electrons in the n-type move to the p-type where they are then 'combined' with the holes in the valence shell of the p-type which produces photons. My question is that when this happens are the electrons gone or have disappeared?
Also do the electrons 'run out' in this process because they are being used u... | By 'combined' with the holes in the valence band (not shell), you mean the recombination process. To answer your question, you must understand the concept of 'hole'. You probably already know 'hole' is not a separate particle rather it is a lack of electron. In overly simplified words, you can think a positively charge... | Electrons absorb and emit photons IN response to local energy levels. They do not covert.
They do not disappear. It's in every introduction to the atom, on a basic level.
They do not die in the process of absorption or emission of photons.
| https://physics.stackexchange.com |
284,254 | [
"https://dba.stackexchange.com/questions/284254",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/70834/"
] | I just had a showerthought that the default Identity Seed is 1. I have some tables that I know will grow to the billions at a certain point. Wouldn't it make more sense to start on <code>int.Min</code> ( -2,147,483,648) for these tables?
This could just make the difference of migrating your key to <code>bigint</code> i... | There is nothing at all wrong with starting at -2,147,483,648 as far as SQL Server is concerned. Starting at 2,147,483,647 and counting backwards with <code>IDENTITY(2147483647,-1)</code> is perfectly valid too.
Things that would make me be wary of doing so:
<ol>
<li>It might confuse people who don't expect to see nega... | No, you're not missing anything. Identities are meant to be meaningless internal-only surrogates which are for the computer to allocate and deal with, and the computer doesn't care whether you use positive or negative numbers.
However.. it's never quite that simple. There will always be a human somewhere trying to read... | https://dba.stackexchange.com |
22,419 | [
"https://chemistry.stackexchange.com/questions/22419",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/6925/"
] | My lecture handout says:
$$C_V = \frac{\mathrm{d}q_V}{\mathrm{d}T} = \left(\frac{\partial U}{\partial T}\right)_{\!V}$$
I understand that $C_V = \mathrm{d}q_V/\mathrm{d}T$ and that $\mathrm{d}U = \mathrm{d}q_V$, but what's the need for the partial derivative? Why can't you just substitute and get:
$$C_V = \frac{\mat... | The turnover frequency is a rate. (It's actually the kinetic rate of the reaction in saturating substrate concentration, normalized to the amount of enzyme.)
It might be helpful to think about something like a factory that makes a certain number of widgets in a certain number of time. How would you naturally describe ... | As you say this represents "conversions per unit of time".
The mathematical expression for "per time unit" is 1/(time unit), and seconds is a particular time unit.
| https://chemistry.stackexchange.com |
642,015 | [
"https://electronics.stackexchange.com/questions/642015",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/322613/"
] | I have been struggling to find a method to actually run any assembly code on my 8086 chip. I have an 8086 chip and I am trying to implement it on hardware to power up a LED or anything simple.
On Proteus's simulation, this is easy to do because Proteus offers you to write code on run directly inside the simulation.
How... | The 8086 in itself doesn't have any memory, so you can't upload anything to it. You need to build a whole x86 computer with that chip in its core and then put a program in memory at the position the CPU fetches the first instruction, and then let the CPU run.
If you go to the Wikipedia page for the 8086 you'll see that... | You need to attach something to the CPU memory bus at specific starting location from where the CPU can fetch program code to execute.
For the 8086, it starts executing code from memory address 0xFFFF0 after reset, that is 16 bytes below the end of the 1 megabyte address space.
As the 8086 has a 16-bit data bus, you ne... | https://electronics.stackexchange.com |
149,433 | [
"https://electronics.stackexchange.com/questions/149433",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/64443/"
] | I understand about input impedance and capacitance... My question relates to the cable: What is the characteristic impedance of the cable connecting the probe to the scope? It must be terminated in a matched impedance to avoid reflections but the input impedance is typically 1 M ohm in parallel with a few pF - that can... | Probe cable is lossy coax.
Achieving a matched condition with an oscilloscope probe is virtually impossible because the source impedance of the circuit under test is unknown and generally different from the scope's 1MΩ or 50Ω input impedance.
On top of that the input impedance of the oscilloscope has a reactive com... | It's probably 50 ohms. It's basically just coax cable.
One reason for choosing 50 ohms over any other impedance is that some testgear has switchable 50 ohm terminations on its inputs, to improve accuracy for HF measurements, and in that case a 1x probe could be terminated correctly.
| https://electronics.stackexchange.com |
69,765 | [
"https://mathoverflow.net/questions/69765",
"https://mathoverflow.net",
"https://mathoverflow.net/users/14576/"
] | What is the holonomy group of the 1-dimensional octonionic projective space ?
| Following David Roberts' comment, and using the fact that the holonomy of the round sphere $S^n$ is $SO(n)$, you get $SO(8)$ as the answer to your question.
| Of course, it depends on the Riemannian metric you put on $\mathbb O \mathbb P^1 \cong S^8$. For the round metric you do indeed get $\mathrm{SO}(8)$ holonomy. A priori, one could imagine other "natural" metrics with reduced holonomy. However, we know by the Berger classification that if the metric was not locally symme... | https://mathoverflow.net |
196,502 | [
"https://softwareengineering.stackexchange.com/questions/196502",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/70273/"
] | Now, when I make a programming mistake with pointers in C, I get a nice segmentation fault, my program crashes and the debugger can even tell me where it went wrong.
How did they do that in the time when memory protection wasn't available? I can see a DOS programmer fiddling away and crashing the entire OS when he mad... | <blockquote>
I can see a DOS programmer fiddling away and crashing the entire OS when he made a mistake.
</blockquote>
Yeah, that's pretty much what happened. On most systems that had memory maps, location 0 was marked invalid, so that null pointers could be easily detected, because that was the most common case. ... | Back in my day, we didn't have memory protection and all that snazzy business! We used printf to determine where we were in the program, <em>and we liked it</em>!
Though in all seriousness, it usually meant we were just more careful. Where malloc is called, there had to be a free somewhere else in the program, and s... | https://softwareengineering.stackexchange.com |
3,969,906 | [
"https://math.stackexchange.com/questions/3969906",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/864508/"
] | The piecewise function is <span class="math-container">$f(x)$</span>=<span class="math-container">\begin{cases}
x, x \in \mathbb{Q} &\\
-x, x\in \mathbb{I}
\end{cases}</span>
I have to prove that this function is not monotonic in any interval and that it's invertible.
I watched a lot of videos on youtube to underst... | <strong>Hint</strong>: As <span class="math-container">$$a=\frac{(\sqrt[3]{4}+\sqrt[3]{2}+1)(\sqrt[3]{2}-1)}{\sqrt[3]{2}-1}=\frac{1}{\sqrt[3]{2}-1} $$</span> <span class="math-container">$${\left(\frac{1}{a}+1\right)}^3=2$$</span> can you proceed ....
| Note that
<span class="math-container">\begin{eqnarray*}
\frac{3}{a} + \frac{3}{a^2} + \frac{1}{a^3}= \frac{(a+1)^3-a^3}{a^3}.
\end{eqnarray*}</span>
Note also that <span class="math-container">$a+1=\sqrt[3]{2}a$</span> so ...
<span class="math-container">\begin{eqnarray*}
\frac{3}{a} + \frac{3}{a^2} + \frac{1}{a^3}= \... | https://math.stackexchange.com |
125,272 | [
"https://dba.stackexchange.com/questions/125272",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/83894/"
] | We recently deployed a new environment with a newer version of Oracle (12c) instead of 11r2.
Only recently I noticed my data returned is sorted differently.
Instead of having small letters, capital letters and numbers... (on Oracle 11r2)
I get my data sorted the opposite way:
numbers, capital letters, small letters (... | NLS_LANGUAGE determines the sort order. If you've went from, for example, FRENCH to the defaut, AMERICAN, you would get the difference in sort order you describe. To set the default NLS_LANGUAGE execute
<pre><code>alter system set nls_language ='FRENCH' scope=spfile;
</code></pre>
and bounce the instance. You can a... | Unless your queries are ordered (with an explicit ORDER BY ) the data returned from queries is not guaranteed to be in any order. They just happen to come out in a certain order and that order is typically static unless something massively changes in the tables or in the RDBMS kernel. This is not unique to ORACLE.
If ... | https://dba.stackexchange.com |
342,824 | [
"https://softwareengineering.stackexchange.com/questions/342824",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | I recently completed a black-box refactoring. I am unable to check it in, because I can't work out how to test it.
At a high level, I have a class whose initialization involves grabbing values from some class B. If class B is "empty", it generates some sensible defaults. I extracted this part to a method that initial... | <strong>You are doing fine!</strong>
Creating automated regression tests is often the best thing you can do for making a component refactorable. It may be surprising, but such tests can often be written without the full understanding of what the component does internally, as long as you understand the input and output... | An important reasons for writing unit tests is that they document the component API somehow. Not understanding the purpose of the code under testing is really a problem here. The code coverage is another important goal, difficult to achieve without knowing which execution branches exist and how are they triggered.
How... | https://softwareengineering.stackexchange.com |
18,304 | [
"https://softwareengineering.stackexchange.com/questions/18304",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/7083/"
] | I would like to know what kind of <strong>jobs/roles</strong> one could expect on their career path if they start as a developer.
I also want to know <strong>how many years</strong> you'll be expected to stay in the same role until you progress to the next level.
The career path is of course, based on how good you d... | Broadly speaking I've seen people take the following routes:
1) <strong>Stay as a developer</strong>. There's no reason to actually move on at all, developing is just fine and there are a lot of people I know into their 30s and 40s who have no intention of moving from something they enjoy into something they won't ju... | What do you expect? Money? Underlings? Self-fulfillment? Freedom? Power? Whenever I hear someone wants to make a <em>career</em>, I get a feeling that this someone has no clear <em>goals</em>.
| https://softwareengineering.stackexchange.com |
42,776 | [
"https://dba.stackexchange.com/questions/42776",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/3400/"
] | I have to design a table where user has 10 fields and 6 are dropdown. Some are single selections and some multiple. Dropdown data is supposed to change very rarely.
For e.g., the user is presented with days of the week and can select any number of days. It is going to be a one to many table <code>UserDayPref(user_id,... | You can use the <code>dbstart</code>/<code>dbshut</code> scripts which come with an Oracle install. They are available under <code>$ORACLE_HOME/bin</code>.
After a fresh install you have to edit the <code>/etc/oratab</code> file:
<pre><code># cat /etc/oratab
# format: $ORACLE_SID:$ORACLE_HOME:N|Y
my_sid:/home/juser/a... | Why do you need it at all? What is the reason? For shutdown you have 3 options:
<ul>
<li>plain <code>shutdown</code> - waits for sessions end</li>
<li><code>shutdown immediate</code> - rollbacks and ends sessions (waits for rollback finish)</li>
<li><code>shutdown abort</code> - kills everything - usually database has... | https://dba.stackexchange.com |
15,198 | [
"https://quant.stackexchange.com/questions/15198",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/7451/"
] | I have a code that finds the implied volatility using the Newton-Raphson method.
I set the number of trial to 1000 but sometimes it fails to converge and doesn't find the result.
Is there a better method to find the result? Are there any technical conditions in which this numerical method is expected to fail to conv... | Peter Jaeckel wrote a paper just on how to solve this problem:
By Implication (July 2006; Wilmott, pages 60-66, November 2006). Probably the most complicated trivial issue in financial mathematics: how to compute Black's implied volatility robustly, simply, efficiently, and fast
downloadable from jaeckel.org
In my e... | Bracketing methods such as Bisection and Regula Falsi are always known to converge but they are very slow.
Newton Raphson and secant methods are fast (quadratic convergence) but has convergence problems. Google for Newton Raphson convergence pitfalls. Classical ones such as"Trapped in local minima", "Diverge instead o... | https://quant.stackexchange.com |
270,089 | [
"https://softwareengineering.stackexchange.com/questions/270089",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/13181/"
] | I've consulted for a number of Fortune 500 and 100 companies all of whom have made some kind of effort at creating a "Master" data model even to the point that they'd attempt to have all applications work with a shared database (Imagine the change management issues in that world).
I've seen companies throw millions of... | One hundred database tables is not a whole lot, once you consider ordinary data tables, lookup tables, many-to-many linking tables, OLAP, and so forth.
<blockquote>
Is an enterprise-wide data model truly feasible?
</blockquote>
It better be. How else are you going to maintain and extend it?
Rather than think of a... | <blockquote>
My instinct leans more toward a message driven/SOA model where individual components were responsible for a subset of data and any component that needs access to that data would go through the appropriate channel.
</blockquote>
We actually have something just like this where I work. Our company offers f... | https://softwareengineering.stackexchange.com |
340,285 | [
"https://physics.stackexchange.com/questions/340285",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75621/"
] | I've been told that electrons can have $+{1\over 2}$ or $-{1\over 2}$ spin. And that because of the Pauli exclusion principle this is how they can occupy the same shell. But when I look online I only ever see that particles with mass have only positive spin of ${1\over 2}$ (especially when I look at the table of elemen... | In quantum mechanics, spin is a kind of angular momentum that is intrinsic to a particle. Like normal angular momentum, when we go to the quantum world there are two numbers that describe the spin of a body, which we label $s$ and $m_s$. $s$ can be integers or half integers, depending on what you're trying to describe,... | This is a case where our use of the word "spin" is a little sloppy. We use it to describe both the spin quantum number which is 1/2 for electrons, and also to describe the component of the spin vector along the z-axis which for electrons can be either +1/2 or -1/2. It is usually obvious by the context which of these ... | https://physics.stackexchange.com |
140,225 | [
"https://electronics.stackexchange.com/questions/140225",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/59071/"
] | Like most computer hobbyists and programmers, I've amassed boxes of USB cables to connect USB, Micro-USB, and Mini-USB to chargers, computers, and gadgets. These cables are a mix of phone charger cables, and cables that came with external hard drives, bike lights, GPS units, and other miscellaneous gadgets. The problem... | The kind of cable you mean is missing the D+ and D- data lines. It simply doesn't have those wires inside the cable.
You can test for continuity or resistance using a multimeter. Probe between the corresponding data pins: D+ on one side to D+ on the other, or D- to D-. The D+/D- lines are the middle two pins of a USB ... | If the cable has any markings on it, look for the wire size and amount on it. They will typically say AWG 22-2 or similar for a 2 conductor of AWG size 22 cable. A 4 conductor cable would be different.
Of course, <strong><em>you could</em></strong> find a cable that has four conductors inside but not all four wires co... | https://electronics.stackexchange.com |
482,174 | [
"https://physics.stackexchange.com/questions/482174",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | I need to find the ratio between horizontal and vertical accelerations exerted on a train by the rails it is running on , given that the train is traveling East at a speed of <span class="math-container">$v_r=250$</span> km/h, along the 30 degree North parallel (<span class="math-container">$\gamma = 30^o = \pi / 6 \hs... | A black hole evaporates by radiating away energy in the form of photons, gravitons, neutrinos, and other elementary particles in a process that involves quantum field theory in curved spacetime. This causes it to lose mass, and so its radius shrinks. It remains a black hole as it shrinks. The increased spacetime curvat... | No black hole has ever yet evaporated;the energy they absorb from their surroundings far exceeds what they lose by Hawking radiation. It may well be the case that the universe will collapse & be recycled in a Big Crunch before the first black hole has had time to evaporate. To those who say the universe is expandin... | https://physics.stackexchange.com |
10,070 | [
"https://quantumcomputing.stackexchange.com/questions/10070",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/9918/"
] | I am following Nielsen and Chuang, section 2.2.5:
<blockquote>
A projective measurement is described by an <em>observable</em>, <span class="math-container">$M$</span>, a Hermitian
operator on the state space of the system being observed. The
observable has a spectral decomposition, <span class="math-container">... | <span class="math-container">$Z\otimes Z$</span> is an observable which specifies <em>a</em> measurement but, as you have realised, it's not specific enough to fix it as being the measurement you want. There's no unique way of doing this, but you could use something like
<span class="math-container">$$
2Z\otimes I+I\ot... | An observable having degenerate eigenvalues means that it doesn't completely collapse the system. For example, <span class="math-container">$Z\otimes Z$</span> would describe a type of measurement in which you are only asking whether the state is in the span of <span class="math-container">$\{|00\rangle,|11\rangle\}$</... | https://quantumcomputing.stackexchange.com |
416,309 | [
"https://softwareengineering.stackexchange.com/questions/416309",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/375564/"
] | I'm a beginner at collaborative development, I started learning about merge conflicts.
And I have this question.
Is it possible for a developer to deliberately postpone merging because he doesn't want to be the one resolving a potential conflict?
If this isn’t the solution, what are the strategies that work?
| Oh god yes.
I broke the build my first time. Made me so gun shy I was hiding versions in folders. Of course delaying my check-ins just made things worse. I was in hell until I figured out what I needed.
I needed a safe place to play.
I created my own toy project so that I could deliberately cause merge conflicts. Lear... | In general, individual developers will be responsible for merging their own work. Delaying things only means it's more likely for others to get code into your merge target, making the merge worse.
| https://softwareengineering.stackexchange.com |
199,810 | [
"https://softwareengineering.stackexchange.com/questions/199810",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/92463/"
] | Suppose I own a copy of a physics book containing <em>original</em> research. Suppose that this book is licensed under a non-free license.
If I use the formulas and concepts explained in that book in my program, am I infringing the book's copyright?
In my opinion the answer is no because I'm copying ideas, not text, ... | Mathematical formulas usually are not covered by copyright, since there is a limited number of ways to express them. And unless you're copying mathematica source code, you have to "re-write" the formula anyway.
That said, it's possible that you may be encumbered by a separate license relating to How you acquired the ... | Copyright isn't your only concern. You also need to potentially worry about associated patents. However, most academics publish their work because they <em>want</em> others to use them, and in my experience, most would welcome a practical implementation, <em>especially</em> if that implementation is freely licensed.
... | https://softwareengineering.stackexchange.com |
345,157 | [
"https://softwareengineering.stackexchange.com/questions/345157",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/102787/"
] | I've started to develop an application that allows the user to play notes on instruments. In particular, traditional Balinese instruments. As with many instruments, they have a certain amount of notes within an octave. Now I am completely out of my depth here on how to get started about the musical theory. My initial p... | I don't see what is fishy about the process you describe. If you have iterative development with short release cycles (even if it is just internal releases) and continuous product-owner feedback and reevaluation of plans based on the knowledge gained by each release, I would say you are agile.
The benefit of iterativ... | The biggest fear for some may be due to calling yourself agile when you're really not. Are we doing Scrum if we only follow half of the principles? What will my developer friends think about this hypocrisy?
The Agile Manifesto isn't very specific. That was done intentionally. They just prefer doing some things than ot... | https://softwareengineering.stackexchange.com |
749,290 | [
"https://physics.stackexchange.com/questions/749290",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/62211/"
] | So assuming we know all the laws of physics in differential equation form, and I have an estimate for the current large scale state of the universe (whatever standard assumptions/data cosmologists use about the current large scale state of the universe in order to extrapolate the state of the universe on the large scal... | Let's not even talk about big bangs yet. Consider a simple non-linear ODE <span class="math-container">$\frac{dx}{dt}=-x^2$</span> with the condition <span class="math-container">$x(1)=1$</span>. There is a <strong>unique maximal solution defined on a connected interval</strong>, which in this case is easily seen to be... | Your accepted answer explains why we cannot do it today - mostly because we simply are not capable to solve the equations we came up with, and even for incredibly simple examples like <span class="math-container">${dx}/{dt}=-x^2$</span> the resulting formulas are already nixing any chance of success. In a sense this is... | https://physics.stackexchange.com |
1,405,109 | [
"https://math.stackexchange.com/questions/1405109",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/263548/"
] | Someone I know said that Christmas is on the horizon. If that is the case we should be able to calculate its height given that we are on a curved sphere of known circumference and know the pace at which Christmas is approaching.
Given the earth's circumference at the equator at 24901 miles and Christmas arriving ever... | The ray from Christmas to us (I'm going to assume that Xmas travels in a circle above the equator, and we are on the equator) is tangent to the equator at some point $P$ that's on our horizon. The angle from us to $P$ is
$$
\arccos((24901/(2\pi)) / ((24901/(2\pi)) + 5.75/5280) ) \approx 0.000741333199
$$
(where that'... | This is really a kooky question.
In an ordinary, non-leap-year like $2015$, Christmas is the $359$th day of the year. Today, August $21$, is the $233$rd day of the year. Christmas is therefore $359-233 = 126$ days away. That equates to about $126/365\cdot360 = 124$ degrees. Unfortunately, that is more than $90$ de... | https://math.stackexchange.com |
155,994 | [
"https://electronics.stackexchange.com/questions/155994",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/65238/"
] | How can i implement the full adder of two 1-bit numbers using only multiplexers 4/1? I created a truth table for a one-bit full adder, which looks like this:
<img src="https://i.stack.imgur.com/YAzBF.png" alt="enter image description here">
A = first bit<br/>
B = second bit<br/>
Pu = bit from lower position (used t... | Yes, it's correct.
This is the sort of optimization that used to happen manually in the old days of FPGAs and before that with PALs. You had to rejigger your result based on selection and minimal logic gates.
I've not run across this solution, but then I've never been stuck with just multiplexors.
Oh incidentally,... | Yes, your P MUX is very correct:
0+0 inhibits carry (switch carry for 0)
0+1 propagates carry (switch carry through)
1+0 propagates carry (switch carry through)
1+1 generates carry (switch carry for 1)
Especially advantageous now to use a switched MUX, never a combinatorial.
Why? All multiplexers can switch simultaneou... | https://electronics.stackexchange.com |
104,803 | [
"https://physics.stackexchange.com/questions/104803",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/41316/"
] | I wanted to ask about the following problem:
An ideal monatomic gas is separated into two volumes $V_{1}$ and $V_{2}$ through a diathermic piston, such that each volume containing $N$ atoms and the two sides are at the same temperature $T_{0}$. The entire system is isolated from the outside by means of insulating wall... | We know that for reversible processes in isolated systems the entropy remains constant. You have mentioned that the system is isolated and that the plunger is reversibly manipulated. So considering the 2 gases as one isolated system we get that the entropy of the system is a constant. So $\Delta$$S$ = $0$
Now since the... | There can be heat interactions between the two volumes themselves if you treat them as two seperate systems. So even though the entire system is isolated heat interactions are possible between the two volumes.
| https://physics.stackexchange.com |
403,181 | [
"https://stats.stackexchange.com/questions/403181",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/160798/"
] | Is it possible to have a right-skewed distribution with mean equal to mode? If so, could you give me some example?
| Easy examples come from binomial distributions -- which can hardly be dismissed as pathological or as bizarre counter-examples constructed <em>ad hoc</em>. Here is one for 10 trials and probability of success 0.1. Then the mean is 10 <span class="math-container">$\times$</span> 0.1 = 1, and 1 also is the mode (and for ... | If the distribution is discrete, sure. It's easy. For example, a distribution with probability mass function
<ul>
<li><span class="math-container">$P(X=0) = 0.36$</span> </li>
<li><span class="math-container">$P(X=1) = 0.40$</span> </li>
<li><span class="math-container">$P(X=2) = 0.13$</span> </li>
<li><span class="ma... | https://stats.stackexchange.com |
25,455 | [
"https://electronics.stackexchange.com/questions/25455",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/7665/"
] | I'm curious to know how does an electrical device can consume any amount of power it is required? Suppose the voltage here is 220V. How can you get any amount of electrical power say. 1000 watts out of it? Please tell me what I'm misunderstanding.
| The power line may be supplying a fixed voltage, like 220V, but how much <i>current</i> the device draws is up to the device. Power is voltage times current, so you can see how the device determines the power by determining the current.
For exmaple, in order to take 1 kW from a 220V line, a device would have to draw ... | It's a quite general question, that can have many answers, and also can be intended in many ways.
The power is the amount of energy consumed/supplied (in fact it's an abstraction because the energy is conserved for the physical principle - but focus on the electric side) over a time unit (second). In electricity, this... | https://electronics.stackexchange.com |
39,481 | [
"https://electronics.stackexchange.com/questions/39481",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1305/"
] | Since radio-waves are additive, I would expect that overlapping stations <em>(eg. two different signals broadcasting on 95.7 within range)</em> to both play over my radio at the same time.
But that's not what happens. Instead, I hear only one station at a time, with the radio switching back and forth between the two ... | Your mention of the frequency (97.5 MHz) tells us this is an FM receiver. (AM will behave differently, as will other modulation schemes).
Because FM is encoded by modulating the signal frequency, anything to do with AM is undesirable. To deal with this, most receivers over-amplify the signal until it becomes larger ... | Here's my take on it:
While the carrier signals may have the same <em>frequency</em>, they have different <em>phases</em>. As the PLL in the FM decoder drifts, it locks first onto one phase and then onto the other, leading to alternating broadcasts being decoded as time goes on.
| https://electronics.stackexchange.com |
40,125 | [
"https://mathoverflow.net/questions/40125",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2841/"
] | Is there an ordinal $\alpha$ such that $ZF$ believes that $V_{\alpha}$ is a model of $ZF$? (If it is problematic to state this since we have to check infinitely many axioms at once, formalize logic in $ZF$. ) If $\alpha > \omega$ is a limit ordinal, then $V_{\alpha}$ is a model of $ZF - R$, where $R$ stands for the ... | You cannot prove that there is such an ordinal, but (under a suitable large cardinal assumption) it is consistent that there is such an ordinal.
If you could prove that there was such an ordinal, then you will have proved Con(ZF) in ZF, contrary to the incompleteness theorem.
Another way to see it is: if there were... | Joel has thoroughly answered the question, but let me point out a related result that I think deserves to be better known. It's due to Montague and Vaught ["Natural models of set theories" Fund. Math. 47 (1959) 219-242]. Suppose there is an inaccessible cardinal, and let $\delta$ be the first one. Define $\alpha$ to ... | https://mathoverflow.net |
4,344,919 | [
"https://math.stackexchange.com/questions/4344919",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/838062/"
] | The question goes as follows
<blockquote>
Let X and Y be topological spaces, and let f:X <span class="math-container">$\rightarrow$</span>Y Define Z = {f(x)|X <span class="math-container">$\in$</span> X} <span class="math-container">$\subseteq$</span> Y to be the image of the function f, and equip Z with a topology as ... | For functions between two topological spaces, <span class="math-container">$f$</span> being continuous means that the preimage of any open set in <span class="math-container">$Y$</span> is open in <span class="math-container">$X$</span>, not the other way around as suggested in your post. So if <span class="math-contai... | Note that <span class="math-container">$f=\bar{f}$</span> as the two functions are comprised of precisely the same ordered pairs. Moreover, given open <span class="math-container">$U\subseteq Y$</span> then <span class="math-container">$f^{-1}[U]=f^{-1}[U\cap Z]$</span> and therefore <span class="math-container">$f$</s... | https://math.stackexchange.com |
44,005 | [
"https://mathoverflow.net/questions/44005",
"https://mathoverflow.net",
"https://mathoverflow.net/users/10408/"
] | I asked this on mathematics stack exchange and did not receive answer . I hope it is good manners to ask here. Thank you very much.
Let $X$ be integral scheme and $\mathcal K$ sheaf of rationnal functions on $X$. For any
point $y\in X$ different of generic point we know that fiber of $\mathcal K$ (defined as usual as... | The non-classical aspect of this setup is that you're using a quasi-coherent sheaf that is not coherent, and beyond the coherent case one cannot expect information about a fiber (e.g., vanishing, 6 generators, etc.) to "propogate" to information in a neighborhoood (which would be the spirit behind the choice of word "c... | Your intuition is confusing the 'fiber over a point' with `restriction to a closed subscheme'. In general these can be very different, even if they come from the same place conceptually. Rational functions give a good example of when the fiber is zero but the restriction isn't.
For an example the other way, consid... | https://mathoverflow.net |
752,123 | [
"https://math.stackexchange.com/questions/752123",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/108294/"
] | I'm asked to compute the following Lie Bracket:
$\left [ -y \dfrac{\partial}{\partial x} + x\dfrac{\partial}{\partial y} , \dfrac{\partial}{\partial x} \right] $ on $\mathbb{R}^2$.
Just writing it out, I get
$\left( -y \dfrac{\partial}{\partial x} + x\dfrac{\partial}{\partial y} \right) \dfrac{\partial}{\partial ... | Your vector fields really are derivation, so think that they will be applied to functions!
Take a test function $f:\mathbb{R}^2\longrightarrow\mathbb{R}$ of class $C^\infty$. Then apply your vector field to this function (and you'll have to use the product rule and Schwarz' theorem at some point):
$$\begin{align*}
&am... | The idea is to operate on a (sufficiently nice) function. In your case, "sufficiently nice" means at least twice continuously differentiable (since you will have mixed partials). Here's an example that can guide you through the computation. Suppose we want to evaluate $\left[x,\frac{d}{dx}\right]$. Derivatives don't ma... | https://math.stackexchange.com |
101,249 | [
"https://dba.stackexchange.com/questions/101249",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/40786/"
] | I have a table <code>tabName</code> with the following rows:
<pre><code>id(PK) .. Created(datetime) Resolved(datetime) Status(new/resolved/open)
1 2015-05-10 00:00:00 1970-01-01 .. open
2 2015-05-10 .. 1970-01-01 .. new
3 2015-05-10 2015-05-12 re... | You can use conditional sum for this calculation something as
<pre><code>select
date_format(created,'%d-%m') as created_date ,
sum( case when status='open' then 1 else 0 end )+
sum( case when status='new' then 1 else 0 end )+
sum( case when status='resolved' and date(resolved) > date(created) then 1 else 0 end ) ... | I see a problem when you don't have a ticket created on specific date but you get ticket closed.
Example, I created like this:
<pre><code>+----+---------------------+---------------------+----------+
| id | created | resolved | status |
+----+---------------------+---------------------+--------... | https://dba.stackexchange.com |
21,252 | [
"https://astronomy.stackexchange.com/questions/21252",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/10813/"
] | As far as I understand, in the events detected by LIGO, about 4% of the total mass of merging binary black holes was converted to gravitational waves.
Where does this energy come from, i.e. what exactly gets converted into gravitational waves?
Is it simply the kinetic energy of the merging objects (velocities of th... | Radiating gravitational waves makes an inspralling binary orbit closer and faster. (Rob Jefferies)
The source of the energy for both increased kinetic energy, and the gravitational radiation is the same: gravitational potential energy. (PM 2Ring)
Two black holes at a distance of 1 light year have a huge amount of pot... | As Rob correctly pointed out, the emission of gravitational waves reduces the orbital energy and result in an inspiral. This reduction in total energy also reduces the mass of the final BH, since $E=mc^2$. The bulk of the gravitational wave energy is emitted (and energy=mass lost) in the final chirp, when the separatio... | https://astronomy.stackexchange.com |
368,402 | [
"https://physics.stackexchange.com/questions/368402",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/175179/"
] | Does a free particle e.p. an electron with a measured Spin up |1/2, 1/2> at t= 0 stay in the "Spin-up" state for all t>0?
Or in other words, is there a time-evolution which effects the Spin of a free particle (no magnetic field)?
| Yes it maintains its spin orientation.
Presumably there was at some earlier point an initial region with magnetic field so one could establish an “up” direction, but once it exits this region and propagates freely, it will maintain its original orientation in the sense that, when entering at some later point a second... | We have to be careful with what means spin up and down. First at all
<ul>
<li>the spin of the electron is an intrinsic property and</li>
<li>one by one correlated with its magnetic dipole moment.</li>
</ul>
The positron has a spin of the same value but opposite sign and pointing in the opposite direction in relation ... | https://physics.stackexchange.com |
406,608 | [
"https://softwareengineering.stackexchange.com/questions/406608",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/328802/"
] | Let's assume that I have an attribute called <em>Ticket_Case</em> that has a predefined value (for the sake of arguments, say 1 to 20) that model different real-life use cases. They are an attribute to an ticket itself.
In a different context of the system, I need to generate different messages based on the ticket cas... | One could introduce the concept of a two-dimensional message table, where the dimensions are the use case number and something like a context number. This "table" is just a helper class with one object, and the object could be initialized once at startup time (or you could implement it with a huge switch-case internall... | Similar to Docs answer, but instead of a table use a dictionary
<pre><code>TicketCaseMessager : IMessageGenerator
{
private Dictionary<string,string> messageMap;
public string GetMessage(Ticket t)
{
return messageMap[t.Case] ?? "Unknown Case";
}
}
</code></pre>
This allows you to s... | https://softwareengineering.stackexchange.com |
307,565 | [
"https://softwareengineering.stackexchange.com/questions/307565",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/106675/"
] | Not sure if it's an appropriate question, but here it goes.
I know Haskell's do notation pretty well. And I realized that Scala's "for comprehension" really is just mostly the same as do notation in Haskell. Something I don't quite understand is why did the designers choose this name though? The words "for" and "yield... | I think you are creating a bit of a false dichotomy here.
Haskell has monad comprehensions built into the language. One reason for that is the use of monads for imperative-style I/O. Therefore, the designers of Haskell decided to make it look mostly like a code block in a generic C-style language, complete with curly ... | I don't have much background on why Scala designers made that particular wording choice, but in F#, local "do notation" equivalent is called a "computation expression". The reasoning behind that word choice is one of PR and marketing rather than any concrete technical reason.
Haskell has a hard-earned reputation of be... | https://softwareengineering.stackexchange.com |
45,478 | [
"https://dba.stackexchange.com/questions/45478",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/25507/"
] | I have a back up-of a MySQL database which is contained in a <strong>.tar.gz</strong> file - I need to restore it.
I've never had to do this before. The only way I can access the database is through phpmyadmin. There is an 'import' feature in <strong>phpmyadmin</strong>, but this doesn't accept files in the tar.gz for... | These are your binary logs.
For some reason, your config file lists:
<pre><code>log-bin = 0
</code></pre>
Did you mean by that to <em>disable</em> binary logs? Well, instead, you've simply named them as "0". Which is why you get all these files: <code>0.000001</code>, <code>0.00002</code> etc.
If you want binary log... | Consider setting <code>expire_logs_days = 14</code>. This will toss the files after two weeks. However, if you have no use (eg, replication or backups) for binlogs, then turn it off. (See Shlomi's answer.)
| https://dba.stackexchange.com |
572,853 | [
"https://physics.stackexchange.com/questions/572853",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/270761/"
] | Q. A thin biconvex lens is kept on a plane mirror. When an object is kept at <span class="math-container">$20 cm$</span> in front of the lens, its image is formed at the same point. The focal length of the convex lens is
The solution given is
<span class="math-container">$\frac{2}{20}=\frac{1}{v}-\frac{1}{u}$</span>
an... | It's the zeroth component
<span class="math-container">$$
\bar \psi \gamma^0 \psi = \psi^\dagger\gamma^0\gamma^0\psi = \psi^\dagger \psi
$$</span>
of Lorentz vector
<span class="math-container">$$
\bar \psi \gamma^\mu \psi.
$$</span>
Nothing more, nothing less.
<span class="math-container">$\psi^\dagger \psi$</span> is... | To be explicit, <span class="math-container">$\psi^\dagger = (\psi^*)^T$</span>. We have that <span class="math-container">$S[\Lambda] = \exp(\frac12 \Omega_{\mu\nu}S^{\mu\nu})$</span> and you can check that,
<span class="math-container">$$S^\dagger = -\frac14 [{\gamma^{\mu\dagger}}, \gamma^{\nu\dagger}]$$</span>
is no... | https://physics.stackexchange.com |
472,122 | [
"https://electronics.stackexchange.com/questions/472122",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/187740/"
] | As a electrical and electronics engineering student I still do not understand what we actually mean by designing a circuit. Are we just trying to shape signals using components or make sure specified amount of current goes through a particular element or there is somehing much more deep in this? We learn about solving ... | This is a very thoughtful statement and reflects my own experience going through a EE degree.
Circuit analysis ("solving circuit problems") is the foundation on which circuit design/synthesis is built upon. You can't really build something if you can't analyze it. (eg. you can't build a car if you can't diagnose simp... | I teach students electronics, and my goal has always been to allow you guys to design your own circuits. To me, <em>designing</em> fundamentally means being able to <em>use</em> anything <em>at your disposal</em> to come up with a solution to a problem. The problems are often obvious, but the solutions can almost invar... | https://electronics.stackexchange.com |
339,286 | [
"https://stats.stackexchange.com/questions/339286",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/46697/"
] | It is well-known that a 1-1 function of a sufficient statistic is also sufficient for a parameter $p$.
I am however confused by the consequence that if $T$ is sufficient for a parameter $p$, then a one-to-one function $f(T)$ is sufficient for $p$ or is it for $f(p)$?
| Sufficiency is not linked to the parameterisation of the model or of the observations, so
<ol>
<li>conditioning on a random variable $Z$ is identical to conditioning on any bijective and measurable transform $\Psi$ of $Z$, $Y=\Psi(Z)$;</li>
<li>the distribution of $X$ given $Z=S(X)$ being constant in the parameter $p... | I would say both since $F_p(x)=F_{f^{-1}(f(p))}(x)$, so that if $P(X\in A |f(T),p)=P(X\in A|T,p)=P(\in A|T)=P(X\in A|f(T))$, since $f(T)=c\Leftrightarrow T=f^{-1}(c)$.
| https://stats.stackexchange.com |
2,664,203 | [
"https://math.stackexchange.com/questions/2664203",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/323580/"
] | <blockquote>
Let $S = \{1, 2, 3, 4, 5, 6, 7\}$. You choose a uniformly random 3-element subset $X$ of $S$. Thus,
each 3-element subset of $S$ has a probability of $1{}/{{7}\choose{3}}$ of being $X$.
Define the event<br>
$A =$ “$4$ is an element of $X$”
What is $Pr(A)$?
</blockquote>
The answer is $\fra... | Maybe it would make more sense if you write out the probability as
$$\frac{{1 \choose 1}{6 \choose 2}}{7 \choose 3}$$
We choose the $4$ to be selected giving the ${1 \choose 1}$
We choose $2$ of the other $6$ numbers to be selected giving the $6 \choose 2$
| View it as $$\frac{\binom62 \binom11}{\binom73}= \frac{\binom62 }{\binom73}=\frac37$$
| https://math.stackexchange.com |
332,430 | [
"https://electronics.stackexchange.com/questions/332430",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/143764/"
] | Telephones are older than vacuum tubes and of course transistors. How was signal amplification done?
I mean the technology, not the details.
<strong>EDIT</strong>
Some additional informations that I should have given at the beginning :
<ul>
<li>The question is restricted to telephony </li>
<li>I'm not interes... | It wasn't.
In the early days (ca 1890) long-distance telephony was done from sound-proofed booths and often using non-standard (4-wire) telephones. New York to Chicago was the limit on range. By 1911, the use of loading coils allowed communication from New York to Denver. Notice, though, that this was pretty frustrati... | Amplification, before tube amplifiers were available, could be achieved in several ways. Some of them are:
<ul>
<li>Using a electrodynamic speaker coupled to a carbon microphone, to form a repeater.</li>
<li>Using the negative resistance of a mercury lamp (even if it the physical nature of the negative resistance was ... | https://electronics.stackexchange.com |
25,332 | [
"https://mathoverflow.net/questions/25332",
"https://mathoverflow.net",
"https://mathoverflow.net/users/5627/"
] | I am certainly sure that any one who has read Gil Kalai's witty community wiki has benefited a lot.
Here I follow a similar track in asking this question.
So let's compose a list of fundamental theorems in mathematics which may not even have the tag "fundamental" but have serious wight in the respective branch of math... | In his book <em>Topics in Geometric Group Theory</em>, Pierre de la Harpe calls the following result the <strong>Fundamental Observation of Geometric Group Theory</strong> (though he also calls it a theorem!). It is also often called the Svarc--Milnor Lemma. Roughly speaking, it asserts that the coarse geometry of a g... | I used to joke that The Fundamental Theorem of Combinatorics is interchange of summation.
| https://mathoverflow.net |
288,640 | [
"https://physics.stackexchange.com/questions/288640",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/121700/"
] | I've been studying Capacitance and Dielectrics and I can't understand why the capacitor will only discharge if there is a wire connecting them. I understand that when the capacitor is charged up, there is an electric potential difference between the plates that makes the electrons "want to move" from the higher to the ... | Think about it using Ohms Law. You got a layer of air (or any dielectric) between the plates. It happens that the difference of potential is not big enough to make the electrons move in the air (the air is not a very good conductor). Some capacitors have dielectrics because their operation happens in bigger potential d... | The Coulomb force is a force trying to move electrons from one plate to the other. That is correct. But remember that there are more forces working here.
There is a huge resistance against charge motion in an insulator. The resistance pushes back and prevents electrons from just moving into thin air.
In other and m... | https://physics.stackexchange.com |
278,595 | [
"https://dba.stackexchange.com/questions/278595",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/217624/"
] | I am trying to create a stored procedure in MySQL 5.5.8. using connector 8.0.13. Once this procedure is debugged, it will have to be embedded into a c#.net application, to be created on the fly every time the program is set up. For now, I am doing it manually.
For someone like me, with MS SQL, Oracle, and DB2 backgroun... | Table a should reference (foreign key) b and vice versa. On the foreign keys you create a unique index, so you have a 1 on 1 relationship.
The following data respects these constraints, but is probably not what you'd like.
<pre><code>Tab a Tab b
PK FK PK FK
1 a a 2
2 b b 1
</code></pre>
So you may need ... | You have several possibilities, each of them with advantages and disadvantages.
<h3>Solution 1</h3>
Define a single table:
<pre><code>AB(a b c d e f)
</code></pre>
with two candidate keys, <code>b</code> and <code>e</code>. You chose one of them as primary key, and declare the other as unique.
<em>Advantages</em>: All ... | https://dba.stackexchange.com |
538,595 | [
"https://stats.stackexchange.com/questions/538595",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/94790/"
] | Many libraries that scale linear and logistic regression assume a tall-skinny design matrix (many samples, few features), but I don't understand why you would need billions of samples if your data has 250 features.
In what scenarios would more data help? It seems like, instead of using more computational resources, you... | Facebook's revenue in 2020 was 86 billion dollars, mostly by selling ads. So if your large scale logistic regression model can improve the click-through rate by 0.01%, you would make facebook 8.6 million dollars per year (86000000000*0.0001), which is enough money to justify spending a couple of millions on some grad s... | Your general premise is correct: you don’t need more data than you need. But also, as noticed in the other answer and comments, it may be more tricky than you’re assuming. First of all you need large enough, high-quality sample of data. Using more data than is needed for the desired precision would be wasteful. On anot... | https://stats.stackexchange.com |
22,883 | [
"https://mathoverflow.net/questions/22883",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4333/"
] | Let <span class="math-container">$U$</span> be an open subscheme of <span class="math-container">$\textrm{Spec} \ \mathbf{Z}$</span>. The complement of <span class="math-container">$U$</span> is a divisor <span class="math-container">$D$</span> of <span class="math-container">$\textrm{Spec} \ \mathbf{Z}$</span>.
<stro... | As Kevin points out, $V$ is indeed $\mathcal{O}_K[\frac{1}{2}]$ in your example. Your link to the fundamental group is also correct. $\pi_1(U)$ is the Galois group of the maximal extension of $\mathbb{Q}$ unramified outside 2 (since you can restrict attention to the <em>connected</em> etale $\mathbb{Q}$-algebras)*. ... | As to your addendum regarding the fundamental group of Riemann surfaces, the situation is as follows: If $X$ is a smooth projective algebraic curve of genus $g$ over an algebraically closed field $K$ of characteristic $0$, and if $U\subset X$ is obtained by removing $r$ distinct closed points, then $\pi_1(U)$ is the pr... | https://mathoverflow.net |
202,226 | [
"https://electronics.stackexchange.com/questions/202226",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/52466/"
] | I have been monitoring the voltage in my own home (Mexico 120V 60Hz). I have been graphing the values every minute and I'm starting to notice that during the morning voltage gets up to 127, and during the day (4pm) it can go as low as 118V — why does this happen?
The effect is quite similar to when I turn on th... | <strong>TL,DR; What you are seeing is primarily the result of reactive load droop sharing, with secondary loading voltage drops in the transformers and lines.</strong>
When generators run in parallel like they do to supply national grids, there are two mechanisms at play that largely go unnoticed by the local populati... | Your power utility will generally try to generate at constant voltage. The power distribution network of power lines and transformers will have some resistance and this will cause voltage drop along the network. The voltage drop will be proportional to the current drawn and this varies through the day. From your voltag... | https://electronics.stackexchange.com |
73,433 | [
"https://security.stackexchange.com/questions/73433",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/-1/"
] | If a server installed all patches for known bugs and the attacker can't do a 0-day attack, then is the server absolutely safe?
| The question itself relies on some pretty critical, and invalid, assumptions:
<ol>
<li>We know who the attacker is.</li>
<li>We know what the attacker does and does not know.</li>
<li>We know that the attacker does not know about zero-day vulnerabilities in our system.</li>
<li>The attacker's level of knowledge and sk... | Nothing is "absolutely safe" there will always be a way to crack into any system given enough time and resources.
If you have patched all the latest software that's awesome! But that doesn't mean you still don't have to take precautions against weak passwords, spear phishing attacks, or weak code that doesn't prevent ... | https://security.stackexchange.com |
111,059 | [
"https://mathoverflow.net/questions/111059",
"https://mathoverflow.net",
"https://mathoverflow.net/users/18938/"
] | as far as I know, there are two main ways to have a relative version of De Rham Cohomology for a pair (M,N), where M and N are smooth manifolds and N is a closed (as a topological subspace) submanifold of M:
1) Godbillon, Elements de topologie algébrique: $\Omega^p(M,N)$ is the space of all forms on $M$ whose restrict... | A chain map $\Theta$ from the Godbillon theory to the Bott-Tu version is given by $\omega \mapsto (\omega,0)$ (note that is a chain map only on $\Omega^{p} (M;N)_{G}$).
I claim that this induces an isomorphism on cohomology. A couple of special cases is obvious: if $N=\emptyset$, then both theories agree with absolute ... | The fact that the DeRham cohomology of $M$ computes the singular cohomology is a reflection of the fact that the cohomology of a sheaf (in this case the constant sheaf $\newcommand{\bR}{\mathbb{R}}$ $\underline{\bR}$ over $M$) can be computed by using any (soft, flabby) resolution of this sheaf. The geometry appe... | https://mathoverflow.net |
233,927 | [
"https://softwareengineering.stackexchange.com/questions/233927",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/123106/"
] | I can see two ways to fill an empty file with data:
<pre><code>$ run_program arg1 > data_file
</code></pre>
or, specifically write code that manages a file and write to it? ie. a file stream?
<strong>Which is better to implement?</strong>
| If you already have access to a convenient way of redirecting data to a file, e.g. UNIX's <code>></code> operator, then it makes absolutely no sense to hard-code file-opening and writing logic into your program.
Even if you always want to create a specific file, you can just create a script, alias or function that... | In a strict sense, the Unix tradition would dictate to only deal with input and output streams and not duplicate the functionality of writing to files that is already present in the shell.
But of course, almost all real-world Unix utilities <em>do</em> have options for writing to and reading from files. And it's prett... | https://softwareengineering.stackexchange.com |
989,944 | [
"https://math.stackexchange.com/questions/989944",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/175809/"
] | <blockquote>
If $R{^m}$ is isomorphic to $R{^n}$ as $R$-modules and if $M$ is a maximal ideal of $R$ then how can I show that image of $M{^m}$ is $M{^n}$?
</blockquote>
Background: I was trying to prove that if $R{^m}$ is isomorphic to $R{^n}$ as $R$-modules then $m=n$. For this I need a step like $R{^m/M{^m}}$ iso... | You should look at a much more general statement: For any ideal $I\subset R$, and any homomorphism $f: N\to N'$ of $R$-modules, $f(IN) \subset IN'$. This statement is immediate from the definition of a module homomorphism.
If $f$ is an isomorphism, then we can apply the same claim to $f^{-1}$, and see that $f$ restri... | Let $f:R^n\rightarrow R^m$ be an isomorphism. Consider $\overline{f}:(R/M)^n\rightarrow (R/N)^m$ given by $\overline{f}([r])=f(r)$ (the map is clearly well-defined). Proceeding in an analogue way we can construct $\overline{f^{-1}}$. It is clear that $\overline{f^{-1}}$ is the inverse of $\overline{f}$.
| https://math.stackexchange.com |
379,006 | [
"https://physics.stackexchange.com/questions/379006",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/181107/"
] | Some theoretical questions that got me confused during physics lecture today.
<ol>
<li>Bringing a conducting balloon to a negatively charged rod close will allow the conducting balloon to have positive charges closer to the rod. When the rod touches the conducting balloon, why is it that the rod(dielectric) transfers i... | The speed is irrelevant. Astronauts do space walks around spaceships and space stations regularly. In the reference frame of the ship, the astronauts have very small velocities. The speed of the ship itself is only relative to some other reference frame.
| As others have pointed out, speed itself is irrelevant. Astronauts would not notice their speed in any way; there will be no drag on the rope.
However, there is another way in which speed is very relevant. As the astronauts are moving at $0.5c$ it means that all other matter they encounter will strike them with that s... | https://physics.stackexchange.com |
1,470 | [
"https://biology.stackexchange.com/questions/1470",
"https://biology.stackexchange.com",
"https://biology.stackexchange.com/users/338/"
] | Some insects, like the crickets pictured below, have such slender antennae it seems no blood could fit. How do they get blood through their antennae?
<img src="https://i.stack.imgur.com/DMeVR.jpg" alt="enter image description here"><img src="https://i.stack.imgur.com/r37ZV.jpg" alt="enter image description here">
| Insects do not posses closed circulatory system, but a space where organs float in a fluid called hemolymph. They don't have blood vessels (but some arthropodes have pumps that act a like heart). The hemolymph allows nutrients and excretion products to diffuse, but usually doesn't serve as a means to transmit oxygen to... | Insects primarily get oxygen through diffusion of air through their skin. I doubt the antennae need hemolymph circulation.
| https://biology.stackexchange.com |
62,988 | [
"https://mechanics.stackexchange.com/questions/62988",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/45111/"
] | Is it safe to put oil in a car that is leaking oil and then drive it to a auto shop down the street.
We try to get a tow but there no one avalible. The auto shop is down the street there is no oil in it. Been like that for few days
| I suppose the guys at the shop are more the right people to address this issue, especially since you need to make an appointment there and they should be near enough to make an assessment.
So just ask them how you are supposed to bring your car there with a massive oil leak (or broken oil pan?).
Perhaps they organiz... | <strong>IF</strong> as per your comments the oil pan or sump is made of steel, then one possible temporary repair is to screw a self-tapping screw or bolt into the hole with plenty of sealant.
This repair worked on an old truck once. Then we took the sump off and welded it, but it lasted a couple of weeks in our case... | https://mechanics.stackexchange.com |
560,201 | [
"https://physics.stackexchange.com/questions/560201",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/191417/"
] | Suppose there are 2 scientists who have decided to measure the location of an electron at a same fixed time. Is possible that while one observes the wavepacket localized at (position=<em>x</em>) while the other observes the wavepacket localized at (position=<em>y</em>). The condition however is position <em>x</em> is n... | In order to observe an electron one must interact with it in some way. For example one could shine light at it so that it scattered the light, or one could arrange for it to hit something like a multi-channel array (a charge detector with many small elements). The various observers will study some sort of large-scale s... | I will confess that this I am not certain on this, as this is a quite odd question. but I have formulated what seems like a very reasonable answer. Also the very first thing to mention is that one cannot physically observe the wave-function, we can only predict how it evolves, and then measure a property of a particle,... | https://physics.stackexchange.com |
93,801 | [
"https://softwareengineering.stackexchange.com/questions/93801",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/44250/"
] | OK, I was pondering this today, and I've come to ask for <em>completely subjective and bias</em> opinions on it. Paradoxically, despite this, I don't think it's flame-war fodder either. I think there is room for perfectly civilized conversation -- It's hardly Vim vs Emacs.
I've used a lot of concurrency abstractions, ... | Good observation, there is definitely a trend towards <strong>explicit</strong> sharing (whether through functional languages or convention). The comment about processes being slower i would adapt a little: they are more <strong>heavy-weight</strong>, meaning that they are not slower executing in raw performance but ev... | I think it's a less a matter of X emulating Y, than of trying to find a balance.
Completely separate processes keep life relatively simple. They make it fairly easy to build things like pipelines of processes that take at least some advantage of multiple processors. There are some pretty obvious downsides as well thou... | https://softwareengineering.stackexchange.com |
423,107 | [
"https://math.stackexchange.com/questions/423107",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/48318/"
] | I've been struggling with a concept concerning the Archimedean property proof. That is showing my contradiction that For all $x$ in the reals, there exists $n$ in the naturals such that $n>x$.
Okay so we assume that the naturals is bounded above and show a contradiction.
If the naturals is bounded above, then... | $u-1$ may not be an element of $\mathbb{N}$, but we can be certain that $u-1 < u$. Since $u$ is the <em>supremum</em> of $\mathbb{N}$ then $u-1$ cannot be an upper bound for $\mathbb{N}$. This means that there is an $n \in \mathbb{N}$ such that $u-1 < n$. But then $n+1 \in \mathbb{N}$ and $u = (u-1)+1 < n+1... | I dont think you need the fact that $u\in N$(the fact is even not true) .And for the second difficulty the fact follows from the supremum property.As $u-1$ is not an upper bound so there exists a natural number greater than it.
| https://math.stackexchange.com |
405,405 | [
"https://softwareengineering.stackexchange.com/questions/405405",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/293429/"
] | I have always written my if statements like this when I want the negative condition to enter me into the if block.
<strong>Example 1</strong>
<pre><code>if(condition == false){}
</code></pre>
However, we just hired a new senior on the team that insists we should refactor to
<strong>Example 2</strong>
<pre><code>... | This is not a question where you will get a direct answer, because both <em>work</em>. Most people will tell you it's a matter of taste. My personal opinion is: Don't lose sight of the end goal readability.
<h1>My Favourite in a Perfect World</h1>
I prefer to write code that's "small and easy"; simple statements that... | Personally, I prefer <code>if (condition)</code> or <code>if (!condition)</code> to <code>if (condition == true)</code> or <code>if (condition == false)</code> or worse, <code>if (condition != true)</code>, because the latter three look like someone did not fully understand how if- (and other) conditions work.
Beginn... | https://softwareengineering.stackexchange.com |
461,032 | [
"https://physics.stackexchange.com/questions/461032",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/222533/"
] | I have an horrible doubt, as I found that in my books the question is never directly addressed. How is collapse defined to work for measures of composite system?
I always assumed that when we measure on a subsystem <span class="math-container">$I$</span> of a quantum system <span class="math-container">$I\otimes J$</... | In air radiowaves will eventually dissipate. The waves that escaped into space however are still speeding away from us, for ever. Much like the sunlight from the day the the dinosaurs were wiped out by an asteroid.
| the radio waves that this particular radio was designed to receive are prevented from escaping into space by the ionosphere, and hence bounce around between the earth and the underside of the ionosphere. Each bounce dissipates some of the energy of the radio wave, to the extent that after the 3rd or 4th bounce, the rad... | https://physics.stackexchange.com |
5,997 | [
"https://engineering.stackexchange.com/questions/5997",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/3591/"
] | I have purchased a fuel cell, and the supply pressure must not exceed 0.55 bar. My question is how can I supply the hydrogen at this pressure given that it is below atmospheric pressure.
| "Micro" and "pure sine wave" are orthagonal, even if "micro" had a real definition. "Micro" is just a relatively content-free marketing term. It says that the inverter is intended for a small array or single panel, but of course without a spec it doesn't mean anything.
Anything connected back to the power line shoul... | Stop.
You can't just attach <em>any</em> inverter on a PV panel or array, even if it does have the right power rating.
Your inverter needs to be a PV inverter specificaly. It has to be designed to do max-power-point tracking. That's because the panel doesn't have any specific potential difference: that has to be impo... | https://engineering.stackexchange.com |
334,208 | [
"https://mathoverflow.net/questions/334208",
"https://mathoverflow.net",
"https://mathoverflow.net/users/95347/"
] | <em>Notation:</em> Let <span class="math-container">$\phi$</span> be any formula in <span class="math-container">$\mathsf{FOL}({=},{\in}, W)$</span>; let <span class="math-container">$\varphi$</span> be any formula in <span class="math-container">$\mathsf{FOL}({=},{\in})$</span> having <span class="math-container">$x$<... | In regards to your comments, if you have two infinite theories <span class="math-container">$T$</span> and <span class="math-container">$T'$</span>, if <span class="math-container">$T'$</span> consists of <span class="math-container">$T$</span> plus the schema <span class="math-container">$M\vDash T$</span> for some co... | I tried to check that, for each axiom of ZFC, your theory proves that the set <span class="math-container">$W$</span> with the relation <span class="math-container">$\in$</span> satisfies each axiom of ZFC. This implies the consistency strength of your theory is at least the consistency strength of ZFC.
I succeeded fo... | https://mathoverflow.net |
2,531 | [
"https://mechanics.stackexchange.com/questions/2531",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1322/"
] | I have <code>2006 BMW 330xi</code> whose car-keys (the automatic one) is dead. I think its batteries are dead. What are my options?
I tried driving around to charge it but that didn't work.
| You should be able to get the battery changed, either by an automotive locksmith or by your nearest BMW dealer. The batteries are usually standard coin cells, but I wouldn't try changing one without checking first as you might find it will need to be re-programmed afterwards.
Try a locksmith first as they will probabl... | Not sure on your 330, but on my E39 the the battery in the key is automatically recharged when it is in the ignition. There's a clever induction system that keeps the battery charged.
Your battery may not work that way and may have died.
You may also have somehow gotten the car security system to "forget" your keys, ... | https://mechanics.stackexchange.com |
55,743 | [
"https://mechanics.stackexchange.com/questions/55743",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/38830/"
] | After several hours of thorough research, I still haven't found a satisfying solution to my problem. My electrician bought a 90 amp alternator for my boat and I count on charging three batteries simultaneously and individually depending on the battery level of each. The most practical solution it seems, would be to con... | That white stuff is definitely filler and can cover or hide a serious amount of damage.
A friend removed over 6kg from a three-quarter panel... He cut it all out and hand-made a panel beaten to shape to replace it - he trained as an aircraft panel fitter...
You need to find out what the underside of that wing is like... | The white stuff is bondo. It's there for a reason (usually, to hide body damage). Once you strip the paint and bondo off that nosecone, you're probably going to find much more rust and damage than that. My guess is that you'll end up replacing most of the nosecone. But as you say, it's a project. It's just gotten to be... | https://mechanics.stackexchange.com |
371,034 | [
"https://softwareengineering.stackexchange.com/questions/371034",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/305926/"
] | I have a coupled web application (frontend and api backend served from the same application). It's worked well for our needs but I've been curious about the differences that would go into having a completely decoupled front and backend.
I'm specifically wondering about how handling authentication requests would work w... | You would handle it much the same as you do now. Decoupling the Api doesn't mean you have zero server side code on your website.
Specifically you want to be able to deny unauthenticated users access to your javascript, images, html and other content.
You can do this by keeping your current server side authentication ... | The way I did it, with an OAuth2 server was this:
<ol>
<li>Client reaches content server.</li>
<li>Client does not have an active session, is redirected to authentication server with a callback to content server.</li>
<li>Client authenticates and is redirected back to content server with an authentication token.</li>
... | https://softwareengineering.stackexchange.com |
637,059 | [
"https://electronics.stackexchange.com/questions/637059",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/310554/"
] | Say I have the following transfer function:
<span class="math-container">$$\mathcal{H}(s) = \frac{Bs^2}{a^2 + \frac{a}{Q}s +s^2}$$</span>
I want to prove it is a Low-Pass filter. In order to do it I'd like to change it to phasor form so I can calculate the gain <span class="math-container">\$|G|\$</span> when <span cla... | For all 2nd order of forms:
<span class="math-container">$$\frac{a_2s^2+a_1s+a_0}{b_2s^2+b_1s+b_0}$$</span>
Set <span class="math-container">\$\omega_{_0}=\sqrt{\frac{b_0}{b_2}}\$</span> and <span class="math-container">\$Q=\frac{\sqrt{b_2 \,b_0}}{b_1}\$</span> and find the following equivalent:
<span class="math-conta... | The correct way to do the transformation is to set <span class="math-container">\$s=j\omega \$</span>.
<span class="math-container">$$s=\sigma +j\omega$$</span>
So
<span class="math-container">$$H_{1}(s)=H_{1}(\sigma, j\omega)$$</span>
Signals that are represented where <span class="math-container">\$\sigma<0\$</spa... | https://electronics.stackexchange.com |
45,320 | [
"https://physics.stackexchange.com/questions/45320",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/14445/"
] | Today, in my high school physics class, we had an introductory class on electromagnetism. My teacher explained at some point that an object with a very high speed (he said it started to get somewhat clearly noticable when travelling at 10% of the speed of light) will gain mass, and that that's the reason why you can't ... | In fact you are more or less correct. I assume the increase in mass mentioned is that described in special relativity. The example given by your teacher is incorrect. As the speeds of 10m/s and 40m/s are hardly relativistic, so we can for now assume $E=mc^2$. Increasing the kinetic energy by $\frac{1}{2}mv^2$ thus incr... | If you look at an object at rest, and then you look at the object at some speed $\vec{v}\neq0$ and constant, the special theory of relativity tells you how things change.
There is an invariant (i.e. non changing) mass which we call rest mass $m_0$, and there is a "relativistic" mass $m$ which changes.
You have an st... | https://physics.stackexchange.com |
421,649 | [
"https://softwareengineering.stackexchange.com/questions/421649",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/62302/"
] | One of our customers had a pen test performed on our application this week and let's just say it didn't go well.
The main issue they have is that user authentication takes place on the client, rather than the server. The reason being that an attacker could decompile our (C#) application and build a modified version whi... | I'd have to agree that a stored token doesn't solve the local attack problem.
Consider encryption.
The security model you're looking for is one where the thing doesn't work when the password isn't present. So store locally but encrypt data so that without the password it's useless gobbledy gook.
Don't store the passwor... | <blockquote>
The main issue they have is that user authentication takes place on the client, rather than the server.
</blockquote>
So you do <em>have</em> a server?
<blockquote>
a requirement from our customer is that the application needs to work offline
</blockquote>
<em>All</em> the time?
Is there <em>no</em> opport... | https://softwareengineering.stackexchange.com |
373,307 | [
"https://softwareengineering.stackexchange.com/questions/373307",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/212690/"
] | Is it better to store state in a global variable or in a coroutine, specifically in Python? I don't understand the best practice here.
For example, consider a simple Flask script:
<pre><code>from flask import Flask
...
app = Flask(__name__)
### GLOBAL MEMORY ############ OPTION 1
exmple_variable = 'contents of som... | Your coroutine implements a read-only global variable but with extra steps. I don't see how it has any value compared to simply using a global variable directly (especially considering that the variable holding the coroutine is also a global variable). The coroutine approach is arguably worse because the coroutine stat... | I'd say the bigger issue with global variable is the mutable global state itself. If any dependency of a function reads or writes the global state it effectively becomes a hidden interface of the function, which should be considered when you use it. So it does not matter much how do you prettify and hide them. It can b... | https://softwareengineering.stackexchange.com |
3,797,100 | [
"https://math.stackexchange.com/questions/3797100",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/631035/"
] | I have two coupled ODEs for <span class="math-container">$T(x)$</span> and <span class="math-container">$t(x)$</span>:
<span class="math-container">$$\frac{d^2 T(x)}{d x^2}-\beta (T(x)-t(x))+K=0 \tag 1$$</span>
<span class="math-container">$$\frac{d t(x)}{dx}-\alpha(T(x)-t(x))=0 \tag 2$$</span>
<span class="math-contai... | <span class="math-container">$$\frac{d^2 T(x)}{d x^2}-\beta (T(x)-t(x))+K=0 \tag 1$$</span>
<span class="math-container">$$\frac{d t(x)}{dx}-\alpha(T(x)-t(x))=0 \tag 2$$</span>
HINT :
From <span class="math-container">$(2) \qquad T=\frac{1}{\alpha}\frac{d t}{dx}+t$</span>
<span class="math-container">$\frac{d^2T}{dx^2}... | Hint :
Substitute <span class="math-container">$T(x)=\frac{1}{\alpha}\frac{d t(x)}{dx}+t(x)$</span> in <span class="math-container">$(1)$</span> :
<span class="math-container">$$ \frac{1}{\alpha}\frac{d^3t(x)}{dx^3}+\frac{d^2t(x)}{dx^2}-\frac{\beta}{\alpha}\frac{d t(x)}{dx} +K = 0$$</span>
Then solve for <span class="... | https://math.stackexchange.com |
96,525 | [
"https://electronics.stackexchange.com/questions/96525",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/35595/"
] | I am using an alu SN74ls181 . I am unable to figure out how active high and active low are decided . Is it during the manufacturing or some circuit parameters decide if the circuit is active high or low.
| The chip does not care, it reacts to voltage levels, not to logic signals.
This chip has two tables that describe the logic function it implements. The first one shows the functions when YOU define low = 1, high = 0:
<img src="https://i.stack.imgur.com/OZ6ja.gif" alt="enter image description here">
The second table ... | It's because when using the active low convention, the 1's are treated the same as 0's are in active high convention.
For example, having A = 1111 and B = 1011 and HHHL as selection:
- In active high, F equals A | B. In this case, F = 1111.
- In active low, A would be seen as 0000, B as 0100 and F as 0000; which is ... | https://electronics.stackexchange.com |
110,740 | [
"https://datascience.stackexchange.com/questions/110740",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/135456/"
] | I'm doing sentiment analysis of tweets related to recent acquisition of Twitter by Elon Musk. I have a corpus of 10 000 tweets and I'd like to use machine learning methods using models like SVM and Linear Regression. My question is, when I want to train the models, do I have to manually tag big portion of those 10 000 ... | Maximum likelihood is a method for estimating parameters.
Gradient descent is a numerical technique to help us solve equations that we might not be able to solve by traditional means (e.g., we can't get a closed-form solution when we take the derivative and set it equal to zero).
<strong>The two can coexist.</strong>
I... | I think you are comparing apples and oranges here. Maximum likelihood is a the maximum value of your likelihood function, which somehow describes your data generation process. Specifically likelihood gives you the probability of observing your data, given the data-generation model you imagine. It is similar to a loss m... | https://datascience.stackexchange.com |
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