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
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|---|---|---|---|---|---|
46,978 | [
"https://astronomy.stackexchange.com/questions/46978",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/44011/"
] | I would like to know that, since stars emit a lot of photons where some of them could be producing electrons-positrons pairs, if its mass affects the calculations, and if because of this is different from calculating the mass of a planet (which don't produce high energy photons)...
Are shinning objects more massive tha... | No, when we talk of the mass of a star, we mean its Mass-Energy. That includes the rest mass of particles it is composed of plus the kinetic/heat energy of those particles in our frame of reference, plus the energy in any photons that are part of the sun minus the gravitational potential energy that binds the sun. Th... | The mass of a star is determined by its gravitational effects, not by summing up the components that give rise to that gravity.
If we were to do the latter, then we would have to include all the mass <em>and energy</em> in the star. This would comprise of the rest mass of all particles, the kinetic energy of the partic... | https://astronomy.stackexchange.com |
39,708 | [
"https://mathoverflow.net/questions/39708",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4707/"
] | <blockquote>
Let $\mathcal{X} \to B$ be a flat family with some fibre $X_b \to b$. Suppose I have a coherent sheaf $F_b$ on $X_b$. When does it spread out to a sheaf $\mathcal{F}$ on $\mathcal{X}$ flat over $B$?
</blockquote>
What about a subscheme $z \subset X_b$? Arbitrary diagrams of sheaves?
(I am only c... | Suppose that $B_n$ it the $n^{\rm th}$ infinitesimal neighborhood of $b$ in $B$; that is, if $\frak m$ is the maximal ideal of $b$ in $B$, we set $B_n := \mathop{\rm Spec} \mathcal O_B/{\frak m}^{n+1}$. If $\mathcal F_n$ is as extension of $\mathcal F_b$ to $B_n$, there is a canonically defined element of $({\frak m}^{... | If $\mathcal{F}_b$ is an <em>invertible</em> sheaf and $B=\textrm{Spec} \mathbb{C}[\epsilon]/(\epsilon^2)$ (first-order deformations) then the obstruction theory for deforming $\mathcal{F}_b$ described in Angelo's answer becomes very explicit. Indeed, there is the following result, whose proof can be found in Sernesi's... | https://mathoverflow.net |
600,184 | [
"https://physics.stackexchange.com/questions/600184",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/278607/"
] | So my doubt is: my teacher told us that when a ball hits the ground, the velocity isn't 0, but I've encountered a problem that involves a ball falling (free fall) to the sand, and when hitting the sand the ball receives a negative acceleration of a=-605m/s, and then stops fully. At this last problem, the teacher used t... | Both cases are in fact more similar than you may think. Just before hitting the surface, the velocity of the ball is of course not zero. Then, the ball hits the surface, but it does not stop instantly. The precise description of what happens may be complicated depending on how precisely you want to model it. The most s... | Any real ball has some degree of elasticity, that is it is not 100% rigid. So, the moment that it hit the ground corresponds to the maximum falling velocity. From that moment, the ball starts to deform and decelerate, until stops and starts bouncing back. Here we consider that the ground is much more rigid than the bal... | https://physics.stackexchange.com |
156,583 | [
"https://electronics.stackexchange.com/questions/156583",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/51609/"
] | I have lame question. How does digital pullups work? I'm asking because I don't understand DHT11 driver code.
Sample code:
<code>bcm2835_gpio_write(pin, HIGH);
usleep(500000); // 500 ms
bcm2835_gpio_write(pin, LOW);
usleep(20000);
</code>
It will send start signal to DHT11, but it needs to be LOW for 500ms an... | The DHT11 is a humidity and temperature sensor using a single-wire communication between the microcontroller and the sensor.
<img src="https://i.stack.imgur.com/HF3wx.jpg" alt="enter image description here">
In the diagram above, the 5K resistor is the pullup resistor, which is tied to Vdd (power supply).. It keeps ... | A pull-up is used to drive a signal to a high state, for example Vdd, when no driver capable of driving the signal high is available in the circuit/net/device that output the signal. An example of such output would be an open drain output.
The idea is to use a resistor between the signal and Vdd where the value of the... | https://electronics.stackexchange.com |
660,262 | [
"https://physics.stackexchange.com/questions/660262",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/44690/"
] | In black hole thermodynamics, there is a nontrivial dependence of thermodynamical entropy on the area of the event horizon which is a geometric object. I want to know how this may be intuitively explained (or maybe by some back-of-the-envelope calculation)? And perhaps ask, why entropy should depend on geometry and not... | The Copenhagen Interpretation as formalised by John von Neumann is that when you make a measurement of an observable associated with a particle whose wave function is not an eigenfunction of that observable, the wave function of the particle changes as a consequence of the measurement to become an eigenfunction of the ... | It is a postulate that subsequent measurement of the same physical quantity will give same result regardless of the measuring device. If this is not so, we have to identitfy both the measured quantity and the measuring device for a theoretical description. However, if two devices give different result after subsequent ... | https://physics.stackexchange.com |
20,891 | [
"https://mathoverflow.net/questions/20891",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4621/"
] | Let <span class="math-container">$M$</span> be a differentiable manifold, <span class="math-container">$\Delta$</span> the closed simplex <span class="math-container">$[p_0, p_1,...,p_k]$</span>. A differential singular <span class="math-container">$k$</span>-simplex <span class="math-container">$\sigma$</span> of <spa... | This depends on what exactly is a smooth mapping from a simplex to the manifold. The standard definition is that the mapping of a non-open subset $X$ of $\mathbf{R}^n$ to a manifold is smooth iff it can be extended to a smooth mapping of an open neighborhood of $X$. With this definition the comparison theorem is true a... | You are asking: can one compute the singular homology using chains which are <em>smooth</em> mappings rather than just continuous ones.
The answer is that one can. The reason is that there is a chain homotopy between the complex of smooth chains and the complex of continuous chains. In fact, I think a standard smoothin... | https://mathoverflow.net |
112,955 | [
"https://stats.stackexchange.com/questions/112955",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/35513/"
] | I simulated a MA(1) process $y_t = \mu + \epsilon_t + \theta \epsilon_{t-1}$ in R and tried to recover the error terms $\epsilon_t$ just by computing them successively (supposing I know the parameters $\mu$ and $\theta$).
<pre>
# Variables
n = 30
mu = 10
theta = 5
sigma = 3
# Simulation of the MA(1) process
y = rep(1... | Let $\mathbf \varepsilon = (\varepsilon_1, \varepsilon_2, \ldots, \varepsilon_n)$, $\mathbf y = (y_1,y_2,\ldots, y_n)$, and $\mathbf{\mu} = (\mu, \mu, \ldots, \mu)$. The relationship among these vectors given in the question is
$$\mathbf y - \mathbf\mu = \mathbf{X}\mathbf \varepsilon$$
The matrix $\mathbf{X} = \mat... | Your linear recurrence relation for $\epsilon_t$ is unstable. If you know $\epsilon_1$ with some absolute error $\delta$, then the subsequent values for $\epsilon_t$ will have absolute error on the order of $\theta^t \delta$.
Note that the error doesn't have to come from the estimation error for the parameters, it cou... | https://stats.stackexchange.com |
590,525 | [
"https://stats.stackexchange.com/questions/590525",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/110222/"
] | My hypothesis is that the wording of a particular yes-no question affects whether people will answer "Yes" or "No", such that Wording 1 is more likely to be answered "Yes" than "No", and Wording 2 is more likely to be answered "No" than "Yes".
Here are the res... | A viable answer is contained in the comments and the answer by C8H10N4O2.
For hypothesis 1, a chi-square test of association (or independence) can be applied to the contingency table.
For a 2 x 2 table, a significant result can also be interpreted as suggesting that the two rows are significantly different.
In R,
<pre>... | It's best to show the outcome of testing Wording and Answer for independence. A Chi-squared test would probably work well for that. The 70/30/20/80 contingency table shown in the question will end up with a tiny p-value, so it will be safe to say the variables are not independent.
Follow that up with something like an ... | https://stats.stackexchange.com |
371,553 | [
"https://softwareengineering.stackexchange.com/questions/371553",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/140178/"
] | What is preferred and why?
<pre><code>void PrepMyInstantiatedObject(SomeComplexDTO someComplexDto){
someComplexDto.Name = SomeOtherClassHelper.DerivedName(someComplexDto.Name);
someComplexDto.Ids = SomeOtherClassHelper.Resolve(someComplexDto.RelatedIds);
someComplexDto.SingleId = SomeOtherClassHelpe... | Neither. But the reasons are complex
Firstly, if you are coming from an OOP perspective, the Method should be on the object
<pre><code>SomeComplexDTO.Prep();
</code></pre>
Secondly functions with side effects are also disapproved of. so from this angle you should have
<pre><code>SomeComplexDTO PrepMyInstantiatedOb... | If you are in doubt, always use the simplest solution. The simplest here is the first example, which does not return a superfluous value. For the second option users looking at the call site would wonder if the returned object is the same as the input object or what the difference is.
Just keep it simple.
| https://softwareengineering.stackexchange.com |
1,870,988 | [
"https://math.stackexchange.com/questions/1870988",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/321111/"
] | We can see manually that $2^p-1$ is not prime. As $2047$ is not a prime. $2^{11} = 2048$.
But I'm unable to figure out a formal way of disproving the statement.
| You've demonstrated a counterexample, so it is a formal proof.
All you need to write is something like "The statement is false: p=11 is a prime, but $2^{11} - 1= 23 \times 89$ is not prime."
Trying lots of cases is a valid technique to disprove something (but not necessarily to prove something unless you can do a com... | To disprove an assertion that is false, a single counterexample suffices, and in this particular case, you've already provided it: $$2^{11} - 1 = 2047 = 23 \times 89.$$
This is formal enough. For professional mathematicians, the simplest, minimal way to accomplish the goal is the best way, as evidenced in the old joke... | https://math.stackexchange.com |
67,947 | [
"https://dsp.stackexchange.com/questions/67947",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/50734/"
] | In book , 'fundamental of signal and system'by M.J ROBERT it is written that
<blockquote>
Since no practical system can ever produce an unbounded response, strictly speaking, all practical systems are stable. The ordinary operational meaning of BIBO instability is a system described
approximately by linear equati... | <ul>
<li>Make your block diagram</li>
<li>At each point where significant quantization can happen, add noise</li>
<li>Analyze your system's behavior with that added noise</li>
</ul>
If you <em>know</em> that the quantization effects will be essentially random, and if the following stages tend to low-pass or band-pass ... | Probably the simplest thing you can do is apply a specific example of noise shaping called "<strong>fraction saving</strong>".
Whenever a quantization, a word width reduction, is needed, just round down (that is drop the bits to the right of the quantization point), but remember those dropped bits in a state. In the ... | https://dsp.stackexchange.com |
146,442 | [
"https://electronics.stackexchange.com/questions/146442",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/62056/"
] | <img src="https://i.stack.imgur.com/tC8u3.png" alt="enter image description here">
I couldn't understand the purpose of the varying Vee.
| I do not think this is intended to vary Vee. I think this is simply a way to zero out the OPAMP offset voltage.
Can you give us the source of the picture?
| The label in the diagram refers to the wiper of the potentiometer, which is connected to Vee. The two outer terminals are connected to the offset-null of the Op Amp. The offset null terminals allow you to calibrate an op-amp to ensure the output is exactly zero at exactly equal inputs, despite manufacturing tolerances,... | https://electronics.stackexchange.com |
105,515 | [
"https://mathoverflow.net/questions/105515",
"https://mathoverflow.net",
"https://mathoverflow.net/users/15540/"
] | I have seen in many textbooks on analysis that the Archimedean property of reals is a consequence of the completeness axiom. However I am not convinced that we need to use such a powerful axiom (as the completeness axiom) to prove a very basic property like Archimedean Property. To me it looks simple enough as follows:... | One cannot prove the Archimedean property for the reals by appealing only to first-order algebraic truths of the ordered real field and the subring of the integers sitting inside it. The reason is that those statements are all first-order expressible in the structure $\langle\mathbb{R},{+},{\cdot},0,1,\lt,\mathbb{Z}\ra... | As Ramiro says, if you know that reals are well approximable by rationals, or even if you know that every real is within $1$ of an integer, then you can prove the Archimedean property immediately. From most definitions of reals, this is easy to check. The issue comes up when you try to axiomatize the reals.
If all yo... | https://mathoverflow.net |
96,800 | [
"https://softwareengineering.stackexchange.com/questions/96800",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/11107/"
] | I have a boss that is not very technical. He can write some basic SQL, speak some dev lingo, but all in all not a pro dev. I get into trouble often, by giving him a lot of detail and asking him to make a decision as to which direction he wants to go.
For example, recently he asked for a bunch of changes to go int... | Not telling your boss about changes you have pushed, that they specifically asked to be removed doesn't seem like a solution at all. It seems insubordinate at best. So you have to be careful in how you explain to your manager why that decision was made, and how it does introduce undo risk into the product.
The trick ... | In order to make good decisions, managers primarily need to know two things from you: <strong>schedule</strong> and <strong>risk</strong>. For example, if he wants to remove 80% of a feature set at the last minute, tell him how much extra time it will take to remove, and your estimate of how likely that is to break o... | https://softwareengineering.stackexchange.com |
68,621 | [
"https://softwareengineering.stackexchange.com/questions/68621",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/6001/"
] | For both PHP and ASP.NET, which reporting tool you prefer to create, preview and print reports? Not just printing the web-page directly, any professional third-party or an open-source tool.
| HTML + CSS + (php or asp.net) is all you need, for multipage report, you should paginate the reports. i.e you can select 25 record per page.
search the web for php asp.net pagination
| We use ASP.Net here and for our reports we use Crystal Reports. The pro for that one is that you can do pretty much anything with it. The cons are many and trying to figure out how to do what you want can be a bit of a chore. The major issue being googling is annoying, as everything is behind a pay wall. Everyone wants... | https://softwareengineering.stackexchange.com |
312,216 | [
"https://softwareengineering.stackexchange.com/questions/312216",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/138918/"
] | We're doing a lot of unit testing and refactoring of our business objects, and I seem to have <strong><em>very</em></strong> different opinions on class design than other peers.
An example class that I am not a fan of:
<pre><code>public class Foo
{
private string field1;
private string field2;
private str... | Completely public classes have a justification for certain situations, as well as the other extreme, classes with only one public method (and probably lots of private methods). And classes with some public, some private methods as well.
It all depends on the kind of abstraction you are going to model with them, which... | <ol>
<li>By saying that "Private backing fields with no logic in the properties, seems unnecessary and bloats the class" you already have a decent argument.</li>
<li>It doesn't seem like multiple constructors are the issue here.</li>
<li>As for having all properties as public... Maybe think of it this way, if you ever ... | https://softwareengineering.stackexchange.com |
357,675 | [
"https://stats.stackexchange.com/questions/357675",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/-1/"
] | This might go better on academia stack exchange, but it seems probably the people who know the answer are on cross validated..
This is a pattern across the US. My classmates in, e.g., basic science PhD programs take only a few courses. The structure of the PhD is far more like an apprenticeship. Conversely, my classm... | I don't think the coursework is intended to be there as busywork in case you prove the Riemann hypothesis on your first day. More likely, the faculty has made the decision that it wants to get all of its graduate students up to some minimal level of mathematical/statistical competence prior to research training, and a... | That's a very country specific thing and I suspect that it did just grow historically. Many other countries are much more focussed on doing research leading to publications and/or a monograph. This mirrors differences that you can also see in undergraduate education (application first vs. "thou shalt not touch a real d... | https://stats.stackexchange.com |
36,397 | [
"https://mechanics.stackexchange.com/questions/36397",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/22368/"
] | 1989 Ford F350 5.8 EFI. Manual.
Clutch pedal was <strong>very</strong> stiff and was only able to disengage the clutch at the bottom of its travel. Bled the system, and now the pedal falls to the floor; clutch remains engaged. Relevant info:
<ul>
<li>The reservoir is full.</li>
<li>Master cylinder has no leaks on ... | After replacing the hydraulic lines as well as the master and slave cylinders, everything is working great. I confirmed the master cylinder was at least one of the problems. Testing it outside of the vehicle, the entire stroke of the cylinder couldn't move fluid at all. So yes, a hydraulic cylinder can go bad withou... | <blockquote>
"While some air almost certainly got in, I don't suspect it was enough
to make the pedal fall straight to the floor"
</blockquote>
You should have <em>no air at all</em> in the system. This symptom is typical of air in the system. A lot of care needs to be taken when bleeding, "close enough" will not ... | https://mechanics.stackexchange.com |
69,330 | [
"https://quant.stackexchange.com/questions/69330",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/60559/"
] | When calculating the correlation between two stocks I get an 85% correlation.
Does this indicate anything about the amount the stocks are going up (so if one goes up 10% so does the other) or just that when one goes up, so does the other, but at a totally different (positive) rate?
| Notice that linear correlation is just a standartized measure of variability for two variables <strong>around their mean values</strong>, loosely speaking.
In your concrete case of a linear correlation between stock returns, it won<span class="math-container">`</span>t say anything about magnitude because the mean of e... | Should have been a comment as there are already brilliant answers, but posting as an answer only because it is a bit lengthy! Ignoring the sample/population nuances, here is a simple illustration that correlation is an indicator of the strength (and direction) of the linear relationship but not the 'magnitude' :
<span ... | https://quant.stackexchange.com |
112,336 | [
"https://electronics.stackexchange.com/questions/112336",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/43680/"
] | I'm working on a small hobby project - a small (230V wall plugged) coreless induction furnace. I generally know what I'm doing, chosen a topology, calculated inverter and coil parameters, desired resonance frequency etc. Now my problem is - how do you, in reality, measure the very small inductance that the coil would h... | Arguably, the easiest way is to just measure it:
<pre><code> +--------+
| |
| [50R]
| |
| [C]
[GEN] |
| +------+
| | |
| [L] [SCOPE]
| | |
+--------+------+
</code></pre>
With... | You will be resonating the coil so I would use capacitors you are happy with i.e. C0G/NP0 that have a reasonable tolerance (maybe 5%) and use the circuit resonant frequency to tell you the inductance by using a re-arrangement of the standard formula: -
\$
f_0 = \dfrac{1}{2\pi\sqrt{LC}}
\$
I'm presuming you have a fre... | https://electronics.stackexchange.com |
447,030 | [
"https://physics.stackexchange.com/questions/447030",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/175404/"
] | In my latest assignment I'm tasked with finding a magnetic moment <span class="math-container">$\mu$</span> of a hydrogen atom, whose current distribution <span class="math-container">$\mathbf{j}(\mathbf{r})$</span> looks like
<span class="math-container">$$\mathbf{j}(\mathbf{r})=\frac{e\hbar}{3^8 \pi ma^4} \frac{r^3}{... | So the question may have been a bit vague ("have I done everything correctly?"), so I feel obliged to put up a proper answer now. I was wrong in a whole bunch of places
Firstly, as Cryo has pointed out in the comments, the <span class="math-container">$\hat{\theta}$</span> vector is position dependent and not uniquely... | Your basis vector <span class="math-container">$\mathbf{e}_\theta$</span> is angle-dependent. You have to take this into account when integrating. There are different ways of doing this. The easiest one is probably to re-express it in terms of Cartesian basis vectors. I am guessing <span class="math-container">$\mathbf... | https://physics.stackexchange.com |
21,456 | [
"https://softwareengineering.stackexchange.com/questions/21456",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/3305/"
] | In an attempt to reach at least beginner status with such a legendary editor, I have been coding in Emacs for the last two months. I try to keep an open heart, but I find myself continally disagreeing with one core design choice: that Emacs allow its users to never have to leave. In a 2010 world, I just think that ev... | I've been using emacs for the last 10 years (from and to), and I can only say that <strong>you are absolutely right</strong>. Back in the days, I used gnus and the w3 browser, but clearly they are no longer up to it when compared to dedicated programs. But, obviously, you cannot run Chrome in text mode so this is where... | Choose the right tool for the job.
Try running Chrome or Path Finder through an ssh connection - here you will need alternative toolings and Emacs was <em>designed</em> to run in a terminal.
| https://softwareengineering.stackexchange.com |
19,327 | [
"https://dsp.stackexchange.com/questions/19327",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/11753/"
] | I have used an MMSE STSA estimator to obtain the magnitude of an audio signal. The original signal is combined with white noise and I used an algorithm given in an old research paper by Ephraim and Malah to estimate the amplitude of the clean signal. Now I just have the magnitude information and I don't have the phase.... | What you have to do is use the phase of the original noisy speech signal, i.e. only the magnitudes are improved by gain factors computed according to some optimality criterion (MMSE in this case). So the speech signal is reconstructed from the (hopefully) improved magnitude and the original phase. Why this works has al... | Here is a MATLAB experiment for phase:
<pre>
[x Fs Nbit]= wavread('test.wav',1024*100); % Get a piece of song ;)
x = x(:,1); % Get a single channel
Y = abs(fft(x)); % Take FFT of the entire piece at once!
y = real(ifft(Y)); % Throw away all-phase information and reconstruct y
y2 = zeros(1,length(x)); % NOW: we will p... | https://dsp.stackexchange.com |
101,730 | [
"https://cs.stackexchange.com/questions/101730",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/97869/"
] | I'm learning graphs these days and need to clear few doubts-
<ol>
<li>Can I determine weather 5 points in two dimensions whose X and Y coordinates are given lie on the same straight line in O(1).</li>
<li>What is the efficient way to find out the degree of the specified vertex in an undirected graph (V,E)? I'm thinkin... | <ol>
<li>Yes, anything that has constant input could be done in <span class="math-container">$O(1)$</span>. Howether if the coordinates have size more than <span class="math-container">$O(1)$</span> than you will not be able to even read them in time.</li>
<li>That depends on your representation of the graph and what o... | Just adding to what @Artur said: You only need 2 points to find the slope of a straight line, even if you're given more, so that's <code>O(1)</code> for me...
| https://cs.stackexchange.com |
343,606 | [
"https://stats.stackexchange.com/questions/343606",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/14101/"
] | I am dealing with being Bayesian and looking for a closed form for a posterior for the scale parameter $\tau$ of a Laplace distribution, such that I can derive a full conditional in my Gibbs sampler.
I do not think I could exploit conjugacy for the Laplace, but any closed-form computation for the posterior would be us... | The likelihood for $n$ iid observations looks like:
$ f(x_1,...x_n|\lambda,\mu) \propto \frac{1}{\lambda^n} exp(-\frac{1}{\lambda}\sum_{i=1}^n|x_i-\mu|)$
Hence a conjugate prior for $\lambda$ with $\mu, x$ known must (thinking only about the algebra) look like:
$ f(\lambda) \propto \frac{1}{\lambda^a} exp(-\frac{b}{... | Conditioning on $\lambda$, the posterior on $\mu$ can be expressed in a reasonably closed form:
\begin{align}
\pi(\mu|x_1,\ldots,x_n) &\propto \pi(\mu) \exp\left(-\frac{1}{\lambda}\sum_{i=1}^n|x_i-\mu|\right)\\
&= \pi(\mu) \exp\left(-\frac{1}{\lambda}\sum_{i=1}^n|x_{(i)}-\mu|\right)\\
&= \pi(\mu) \sum_{j=0}... | https://stats.stackexchange.com |
2,998,137 | [
"https://math.stackexchange.com/questions/2998137",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/547191/"
] | <blockquote>
Let S = <span class="math-container">$\sum_{n=1}^{\infty}{\frac{n^k}{((n^3+n)^{\frac{1}{3}}-n)}},\forall\space\space\space\space k\in\mathbb{Z}.$</span> Say if this series converge of diverge.
</blockquote>
My attempt:
<span class="math-container">$$S=\sum_{n=1}^{\infty}\frac{(n^3+n)^{\frac{2}{3}}+n(n... | Note that<span class="math-container">\begin{align}\frac1{\sqrt[3]{n^3+n}-n}&=\frac1{\sqrt[3]{n^3+n}-\sqrt[3]{n^3}}\\&=\frac{\sqrt[3]{(n^3+n)^2}+\sqrt[3]{(n^3+n)n^3}+\sqrt[3]{(n^3)^2}}{n^3+n-n^3}\\&=\frac{\sqrt[3]{(n^3+n)^2}+\sqrt[3]{(n^3+n)n^3}+\sqrt[3]{(n^3)^2}}n\\&\in\left[3n,\frac{3\sqrt[3]{(n^3+n)^... | May be, you could start considering that, for large values of <span class="math-container">$n$</span>,
<span class="math-container">$$(n^3+n)^{\frac{2}{3}}+n(n^3+n)^{\frac{1}{3}}+n^2=3 n^2+1-\frac{2}{9 n^2}+O\left(\frac{1}{n^4}\right)$$</span>
| https://math.stackexchange.com |
2,875 | [
"https://electronics.stackexchange.com/questions/2875",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2387/"
] | My school uses HY 3005D-3 but I want to do it myself to save on $. Before opening it, I ask for tips about: not-to-break-it, cheap DC supply and DIY-materials (not that I know them soon). So how to build, to get cheap DC Power supply with such adjusting knobs?
| Before I got a real powersupply I used different kind of AC/DC or AC/AC power adapters, the kind that ship with toys, mobile phones, routers etc etc...
Then I just cut the cord and measured the voltage with a multimeter, and if needed added a simple linear regulator like the 7805 (if I wanted a clean 5V).
| Are you wanting a DC power supply for one specific purpose, or want a generic power supply that will do everything that the one you mention does?
You can fairly cheaply buy an AC/DC transformer that will give you something like 12v dc and then you can use a voltage regulator with an adjustable voltage.
If you want it... | https://electronics.stackexchange.com |
82,568 | [
"https://security.stackexchange.com/questions/82568",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/66660/"
] | What is the difference/relationship between data leakage analysis and vulnerability analysis? How much and what kind of vulnerability testing is required for data leakage analysis?
I have to give data leakage analysis report for some mobile applications. According to what I know, data leakage is happening when an app ... | "Data Leakage" is typically defined as unauthorized data that becomes available due to the actions of the normal operation of the program/user. As for your example of data transmitted unencrypted, I would see that as not a a vulnerability analysis but a normal part of a data analysis (any place the data touches require... | Vulnerabilities can range from "go home, you're pwned" to "pest". Of course, if you completely take over a system, all its data is there for you to harvest. Data leakage can be intrinsic to the design of an application (transmitting data on the wire in plaintext), a mistake in programming (hey, that session ID is off b... | https://security.stackexchange.com |
513,967 | [
"https://stats.stackexchange.com/questions/513967",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/302989/"
] | the following regression models were developed based on the same dataset:
model 1: y=a1<em>x1 + b1</em>x2 + c1
model 2: y=a2<em>x1 + b2</em>x3 + c2
model 3: y=a3<em>x1 + b3</em>x4 + c3
where a, b, and c are the regression coefficients; x1, x2, x3, and x4 are the independent variables. All models include x1 on the first... | In this very specific situation where your models all add one (different) variable to some baseline model with just the <span class="math-container">$x_1$</span> predictor, the highest F-statistic, so the lowest p-value from the F-test, will correspond to the highest <span class="math-container">$R^2$</span> and <span ... | In general there is no way to choose the “best” model for a given problem without knowing something about the particular things you are investigating and the particular hypothesis you have.
In this case because you include X1 in all 3 models I assume that your “main” hypothesis is that X1 is related to Y. If that’s the... | https://stats.stackexchange.com |
753 | [
"https://quant.stackexchange.com/questions/753",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/155/"
] | Suppose I have trend following strategy(on close to close data) that is not getting acceptable returns for some time. When should I start thinking about shutting it down?
| There are really a few issues here:
1) When do I turn off a model because I believe the model is <strong>invalid</strong>?
This is a subjective call and depends on many things such as how strong the economic reasoning behind the model is, how crowded the space is, and how poorly the model is performing relative to b... | You can use a equity based model. Stop trading when your equity drops below your "X-day" equity moving average, and resume trading when your equity crosses above the "X day" equity moving average. You could also do this by measuring the slope of the curve, and not trading when the slope is statistically below 0. I like... | https://quant.stackexchange.com |
19,973 | [
"https://physics.stackexchange.com/questions/19973",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/7277/"
] | Are virtual particles only popping in and out of existence where the local energy density is below a certain point? What I wonder is, does any kind of matter prevent the pairs from appearing? Is there a shell surrounding an atom or maybe I should call it a boundary beyond which particle pair production occurs, and wi... | Virtual particles influence physics at every point of space, whether or not there is a nearby atomic nucleus or orbital. All electrons in an atom receive energy shifts analogous to the Lamb shift (from virtual photons), aside from other quantum corrections. In fact, the influence of the virtual particles only becomes t... | Virtual particles are mostly the name given to a <em>category of mathematical expressions</em> (contained in Feynman diagrams): while virtual particles are mathematically associated to real, physical particles (virtual electron, etc.), they have no reason to exist physically. Essentially, the name is somewhat of a mis... | https://physics.stackexchange.com |
23,019 | [
"https://softwareengineering.stackexchange.com/questions/23019",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/526/"
] | I wonder how do you decide on the version number of your apps, do you really record down all changes made (for a change log)? Then how will you decide how to increment the version number. eg. +0.0.1 for each bug fix or something, +0.1 for each new feature release? or maybe you bundle many changes into +0.1 of your vers... | Major.Minor.Revision
<ul>
<li>Major. Big change, new features, breaks compatibility, stuff you want to charge extra for.</li>
<li>Minor. New features that you can give away. Doesn't break stuff.</li>
<li>Revision. Bug fixes.</li>
</ul>
| Major.Minor.Revision.Build
| https://softwareengineering.stackexchange.com |
57,625 | [
"https://electronics.stackexchange.com/questions/57625",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2028/"
] | I have a few old 24V solenoids which I've used for years for random (often Halloween-related) projects. I can't recall where I got them. I'd like to get some more, but new ones can be rather high priced.
I sometimes buy junk printers to salvage stepper motors, or dismantle speaker cabinets to acquire a driver.
What o... | Cash Registers use solenoids to latch the drawer in place. Sprinklers use solenoids. As do cars for multiple parts, from door locks to fluid systems. You are most likely to find solenoids at a Junk yard than you are at a electronics recycling plant or a thrift store. Consumer electronics just don't need short range sol... | If you can find an old dot matrix printer, they have a solenoid per pin. Before high-quality printers became available, 9-pin printers were very common. That's 9 solenoids from 1 cheap device.
| https://electronics.stackexchange.com |
190,485 | [
"https://physics.stackexchange.com/questions/190485",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/42743/"
] | When you are accelerating upwards in an elevator, you feel an increase in apparent weight.
A scale measures the total amount of force pushing down on it, and if you were to step on a scale in an elevator, you would see an increase in its reading.
However, when accelerating upwards only the normal force increases -- ... | As you said correctly: as you accelerate upwards, the normal force acting on <strong>you</strong> will increase. Now look at the situation from the <strong>scale's</strong> "perspective" -- consider the forces acting on the scale:
Since the ground (i.e. the scale on which you stand) applies a normal force $F_N$ (upwa... | The normal force will be equal to the weight (which is a force) if the object is "resting" on the surface which is producing the normal force. Essentially weight is always apparent because the weight of a 10kg mass on earth is different than its weight on mars which is also different than its weight in an elevator on e... | https://physics.stackexchange.com |
367,448 | [
"https://softwareengineering.stackexchange.com/questions/367448",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/54726/"
] | For example, given node types <code>User</code> and <code>Post</code>, and expressing that a user posted something on Twitter, what factors would I need to consider in deciding between:
<code>(u:User)-[posted]->(p:Post {platform: 'twitter'})</code>,
<code>(u:User)-[posted {platform: 'Twitter'}]->(p:Post)</code>... | Some things to think of are what your use case is and what the most likely queries will be. Depending on your graph, and I don't know specifically about neo4j, attributes on nodes and edges may create a lot of data duplication if each node or edge stores a copy of the same attribute.
If you link to a node like the the... | I think it is important to construct a model of the data that captures the business domain's understanding. The nodes and edges will flow naturally from that. This touches on ontology, too.
If I construct a sequence of words, and send it to Twitter, and then send the same words to Facebook, have I made two distinct PO... | https://softwareengineering.stackexchange.com |
37,330 | [
"https://engineering.stackexchange.com/questions/37330",
"https://engineering.stackexchange.com",
"https://engineering.stackexchange.com/users/5591/"
] | Let's say I design a simple piece of carbon fiber to be manufactured, in the shape of a simple cylinder with a diameter of 2cm and a height of 3cm (pretty small).
Is it possible and/or practical to try to mold this piece of carbon fiber in such a way that it could be hollow on the inside?
And if so, is it possible to m... | Another perspective : A friend retired as a manager with a large lumber company ( Louisiana Pacific ). He had spent much of his career overseeing cutting crews. They did not try to figure out when or how a chain might break , he just wore a heavy leather apron whenever he used a chainsaw . I understand his crews also ... | Best solution is:
<ol>
<li>have and use the proper safety gear including the trousers (these are designed to catch the chain before they get to your skin and they work), helmet with face shield and safety boots.
</li>
<li>maintain bar, chain and sprockets correctly. I have used chainsaws for the last 40 years and at on... | https://engineering.stackexchange.com |
251,990 | [
"https://mathoverflow.net/questions/251990",
"https://mathoverflow.net",
"https://mathoverflow.net/users/74274/"
] | I have the functional equation
$$ f(x+g(x)y)=f(x)+f(g(0)y)-f(0) $$
where
<ul>
<li>$f$ is positive, monotone increasing and continuous</li>
<li>$g$ is continuous and positive</li>
<li>The domain of both functions is a closed interval that includes 0.</li>
</ul>
The obvious solutions are:
<ul>
<li>$g$ constant and $... | A very nice question!
The answer is no, there cannot be a perfect set in $V[c]$
consisting entirely of ground-model reals.
Suppose towards contradiction that there is a such a set. So this
set consists of the paths through a certain perfect tree $T\subset
2^{<\omega}$ in $V[c]$.
Note, as an easy first case, that ... | There is a more general result proved by Groszek and Slaman which says that if there is a nonconstructible real, then every perfect set has a nonconstructible element. The constructibility can be replaced with any inner models.
| https://mathoverflow.net |
182,690 | [
"https://dba.stackexchange.com/questions/182690",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/117527/"
] | As per my understanding when all the secondary read only replicas are shut down, the primary replica is the one that will take all the read write requests and <strong>read-only requests</strong> as well.
But when I was validating this scenario yesterday, my primary instance didn't take read-only requests from my appli... | Make sure you include the primary in the read_only_routing_list
<pre><code>ALTER AVAILABILITY GROUP aggroup
MODIFY REPLICA ON 'node1'
WITH
(
PRIMARY_ROLE
(
READ_ONLY_ROUTING_LIST= ('node2','node3','node1')
)
);
</code></pre>
Do the same for the other 2 nodes. and you can test using this query
<pre><code>SELECT ... | <blockquote>
As per my understanding when all the secondary read only replicas are shut down primary replica is the one which will take all the read write requests and READ ONLY REQUESTS as well.
</blockquote>
Correct.
<blockquote>
But when I am validating this scenario yesterday my primary instance didn't take r... | https://dba.stackexchange.com |
382,059 | [
"https://math.stackexchange.com/questions/382059",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/2230/"
] | <img src="https://i.stack.imgur.com/jQfku.jpg" alt="enter image description here">
My thought is that the two functions must have the same set of solutions?
Because this is true:
<img src="https://i.stack.imgur.com/qsDv6.png" alt="enter image description here">
That didn't really get me anywhere, where should I sta... | In particular, you must choose $a,b$ such that $$g'(1):=\lim_{x\to 1}\frac{g(x)-g(1)}{x-1}$$ exists, meaning we need for $$\lim_{x\to 1^-}\frac{g(x)-g(1)}{x-1}=\lim_{x\to 1^+}\frac{g(x)-g(1)}{x-1},$$ so we need $$\lim_{x\to 1^-}\frac{(x^2-bx)-(1-b)}{x-1}=\lim_{x\to 1^+}\frac{(ax^2+1)-(1-b)}{x-1},$$ or rather, since $(x... | Hint: $g(1+0)=g(1-0)$ and $g'(1+0)=g'(1-0)$.
| https://math.stackexchange.com |
3,229,153 | [
"https://math.stackexchange.com/questions/3229153",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/665841/"
] | I am trying to learn how to solve Igusa type local zeta function.
Ex. <span class="math-container">$$\int_{\mathbb{Z}_{p}}||x^3,x^2y,y^2||d\mu(x,y)$$</span>
A nice method I was recently introduced to was to substitute <span class="math-container">$x=a+px'$</span> and <span class="math-container">$y=b+py'$</span>, wher... | Rewriting the equation as
<span class="math-container">$$\int_{x-y}^{x+y}f(t)dt=2yf(x)$$</span>
and differentiating the above equation twice with respect to y one obtains that:
<span class="math-container">$$f'(x+y)=f'(x-y)$$</span> from which one can conclude that, after setting respectively <span class="math-conta... | Since <span class="math-container">$\int_{x-y}^{x+y} {f(t)dt}= 2yf(x)$</span>, <span class="math-container">$f(x+y)+f(x-y)=2f(x)$</span>by differentiating by <span class="math-container">$y$</span>.
This means that <span class="math-container">$f(x)$</span>is symmetric by (x, f(x))for all <span class="math-container">$... | https://math.stackexchange.com |
1,845,260 | [
"https://math.stackexchange.com/questions/1845260",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/122351/"
] | Let $X$ be a topological space, and $A,B, \subset X$, then since the closure of a set may be characterized as as the smallest closed set containing the set, certainly we have $A \subset \overline{A}$ and $B \subset \overline{B}$, and hence $A \cap B \subset \overline{A} \cap \overline{B}$. Also, since $\overline{A}$ an... | You incorrectly go from "$\overline{A}\cup \overline{B}$ is a closed set containing $A\cup B$" to "by definition $\overline{A}\cup \overline{B} \subset \overline{A\cup B}$". The reason is that, as you started with, $\overline{A\cup B}$ is the <em>smallest</em> closed set containing $A\cup B$, so if $C$ is a closed set... | It's right that, from $A\cap B\subset \overline{A}\cap\overline{B}$, you can conclude that
$$
\overline{A\cap B}\subset \overline{A}\cap\overline{B}
$$
because $\overline{A}\cap\overline{B}$ is closed.
On the other hand, you can have $A\cap B=\emptyset$, but $\overline{A}\cap\overline{B}\ne\emptyset$; the easy example... | https://math.stackexchange.com |
304 | [
"https://scicomp.stackexchange.com/questions/304",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/164/"
] | In my computational science PhD program, we are working almost exclusively in C++ and Fortran. It seems like some professors prefer one over the other. I am wondering which one is 'better' or if one is better than the other in a certain circumstance.
| As so often, the choice depends on (1) the problem you are trying to solve, (2) the skills you have, and (3) the people you work with (unless it's a solo project). I'll leave (3) aside for the moment because it depends on everyone's individual situation.
Problem dependence: Fortran excels at array processing. If your ... | I think that both C++ and Fortran are good enough and work well.
However I think that Fortran is better for <em>numeric</em> scientific computing, for algorithms that can be expressed using arrays and don't need other sophisticated data structures, so in fields like finite differences/elements, PDE solvers, electronic... | https://scicomp.stackexchange.com |
74,490 | [
"https://dba.stackexchange.com/questions/74490",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/39298/"
] | Postgres 9.3
Debian 7
I want to create a monitor user called monitor that the only permission is to run queries to monitor all the database activity.
I created the user and it can select from pg_stat_activity, the problem is that it only sees it's own activity and I want this user to see all users activity.
Is there ... | At this time, only superusers can see others' activity details in pg_stat_activity.
PostgreSQL could use a finer-grained rights model, where you can <code>GRANT</code> the <code>MONITOR_QUERIES</code> right to a user, for example. But right now it doesn't have one, and quite a few things are superuser-only. This is on... | We can create a normal user and provide the default <code>pg_monitor</code> role to get all monitoring metrics. Simple two steps:
Create a user:
<pre><code>CREATE USER db_monitor WITH PASSWORD 'password';
</code></pre>
Grant the role to monitor:
<pre><code>GRANT pg_monitor TO db_monitor;
</code></pre>
<code>pg_monitor<... | https://dba.stackexchange.com |
17,149 | [
"https://stats.stackexchange.com/questions/17149",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/-1/"
] | What are some practical objections to the use of Bayesian statistical methods in any context? No, I don't mean the usual carping about choice of prior. I'll be delighted if this gets no answers.
| I'm going to give you an answer. Four drawbacks actually. Note that none of these are actually objections that should drive one all the way to frequentist analysis, but there are cons to going with a Bayesian framework:
<ol>
<li>Choice of prior. This is the usual carping for a reason, though in my case it's not the us... | From a purely practical point of view, I am not a fan of methods which require lots of computation (I am thinking of Gibbs sampler and MCMC, often used in the Bayesian framework, but this also applies to <em>e.g.</em> bootstrap techniques in frequentist analysis). The reason being that any kind of debugging (testing th... | https://stats.stackexchange.com |
234,185 | [
"https://physics.stackexchange.com/questions/234185",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/95956/"
] | Within a conducting sphere, the electric field is 0, but is the electric field still 0 exactly on the surface?
| The answer is "it depends what you mean by <em>exactly on the surface</em>".
The electric field depends on the amount of charge enclosed. From Poisson's equation:
$$\nabla\cdot E = \frac{\rho}{\epsilon_0}$$
If the charge on the surface is an infinitely thin sheet of charge, then the electric field will be zero on on... | The point about the E-field being zero inside is a conductor is that you must be writing about electrostatics, the study of charges when they are not moving.<br>
In the ideal world every bit of metal inside your surface (an infinitely thin shell) has no E-field within it.<br>
In the real world when the surface is parti... | https://physics.stackexchange.com |
632,543 | [
"https://electronics.stackexchange.com/questions/632543",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/210249/"
] | I am trying to understand the power lost via heat (friction) from a resistor as opposed to what flows through and is available for the next component in series, and how I estimate this.
I have read a lot of articles on this and they all seem to calculate heat dissipation total consumption -- i.e. use Ohm's law to work ... | When you "multiply by the voltage", that is the voltage across the resistor. If your circuit was supplied with 12v and you saw 3v across the resistor, that would leave 9v available for doing other work around the circuit.
The thing you multiply the voltage by is the current, and the current is the same every... | When you have one or more components in series driven by a voltage source, the same current flows through the entire circuit. The current will be determined by the voltage and the total resistance of all elements added together. The voltage across each element is determined by its resistance, and each element will diss... | https://electronics.stackexchange.com |
3,248,144 | [
"https://math.stackexchange.com/questions/3248144",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/617563/"
] | I'm just getting familiar with analytical geometry and basically I have two probably very simple questions.
<strong>Question 1:</strong>
Let's assume I have some plane, i.e: <span class="math-container">$\pi: x - 2y + 4z - 8 = 0$</span>
What should I do to find points on that plane?
My take on this: to find any poi... | Your first idea is precisely what I would do (and have done before): on a plane, one has <span class="math-container">$2$</span> degrees of freedom of movement, corresponding to the fact that one has freedom in choosing values for any two of the variables<span class="math-container">$^\dagger$</span>, and this will det... | I am not sure if this can be considered a complete answer, or if this is what you want, but I hope this is at least helpful:
<strong>Question 1:</strong> So, a point in that plane is a point satisfying the equation, and the way you found it is the right idea. For instance, say you fix <span class="math-container">$x,y... | https://math.stackexchange.com |
18,595 | [
"https://quant.stackexchange.com/questions/18595",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/-1/"
] | Let $(\Omega,\mathcal{F},P)$ be a probability space and $\{W_t ∶ t ≥ 0\}$ be a standard
Wiener process. By setting $\tau$ as a stopping time and defining
\begin{align}
W^*(t)=\Big\{\matrix{W_t\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,t\leq\tau\cr2 W_{\tau}-W_t\,\,,\,t>\tau}
\end{align}
Why $W^*(t)$ is standard Wiener pr... | If $\tau$ is finite then from the strong Markov property both the paths $X_t = \{W_{t+\tau} −W_\tau ∶ t\geq 0\}$ and $−X_t = \{−(W_{t+\tau} − W_\tau) ∶ t \geq 0\}$ are standard Wiener processes and independent of $Y_t = \{W_t ∶ 0 \leq t \leq \tau\}$, and hence both $(X_t, Y_t)$ and $(X_t ,−Y_t)$ have the same distribut... | First note that paths are a.s continuous.
Then by strong Markov property and reflection principle, $(W_\tau - W_t)$ is a Brownian motion independant of the before tau part.
Then you can verify that increments are independent and gaussian by decomposing them in before and after tau part.
Or you can décompose the quad... | https://quant.stackexchange.com |
76,066 | [
"https://security.stackexchange.com/questions/76066",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/3339/"
] | What is the difference between ISO 27001 and ISO 27002? Are they related to each other or not?
| The ISO 27000 series of standards are a compilation of international standards all related to information security. The difference is that the ISO 27001 standard has an organizational focus and details requirements against which an organization’s Information Security Management System (ISMS) can be audited. ISO 27002 o... | ISO 27001 establishes requirements. If an organization wants to certify its Information Security Management System (ISMS) it needs to comply with all requirements in ISO 27001.
On the other hand, ISO 27002 are best practices that are not mandatory. That means that an organization does not need to comply with ISO 27002... | https://security.stackexchange.com |
132,105 | [
"https://chemistry.stackexchange.com/questions/132105",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/90003/"
] | I’m looking into purchasing a cheap uv-vis spectrophotometer but am not affiliated with an institution at the moment given the whole COVID 19 situation. Are there any good recommendations for cheap visible light spectrophotometers that can analyze wavelengths of light on the order of 370nm and are purchasable directly ... | Not much. Given all other variables which influence the viscosity of honey (sugar composition, including polysaccharide content, humidity, degree of crystallization), pH would not be regarded as a key determinant.
Honey has a pH of 3.4-6.1 (average around pH 3.9) according the National Honey Board of America. This tr... | OK, speculation here: time. What?
Well, consider asphalt, as in asphalt concrete. The mass of asphalt (petroleum residue) plus stone is heated in a large mixer, quite hot, then loaded into a truck for delivery to some location for deposit onto a street. It is dropped and rolled to about 2 inch thickness, then rolled a... | https://chemistry.stackexchange.com |
613,321 | [
"https://physics.stackexchange.com/questions/613321",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/8144/"
] | Sorry for brevity, but what is the exact physics explanation of why smaller quantities placed inside a microwave oven heat up faster than when you place a larger quantity of a similar material inside?
| The magnetron injects microwave radiation at a certain rate. Ignoring losses, that radiation bounces around the walls until it’s absorbed by the food. If you put two burritos in there instead of one, on average there will be fewer bounces before absorption. That means that with two burritos, the average intensity of th... | Let <span class="math-container">$P$</span> be the power (in <span class="math-container">$\mathrm{Watt}$</span>) the microwave delivers then a simple heating model can be stated as follows.
The heat energy <span class="math-container">$q$</span> needed to heat an object is:
<span class="math-container">$$q=\varepsilon... | https://physics.stackexchange.com |
186,366 | [
"https://physics.stackexchange.com/questions/186366",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/81992/"
] | Here is a problem I am having some trouble with:
<img src="https://i.stack.imgur.com/1Cs61.jpg" alt="enter image description here">
The solution is below, my question is, why is conservation of energy valid in this situation.
From my understanding, just before the box hits the springs, energy is conserved since its... | <strong>Short Answer:</strong> The contact force (normal force if you like) between the pan and the box is 0 because the pan has negligible mass.
<strong>Long Answer:</strong> The key point in this problem is that the pan has <em>neglible mass</em>. Suppose for a second that the pan had some mass $m_p$. After falling ... | Newton's second law reads:
$$F = ma$$
In the case of zero mass, the total force is always zero (although the acceleration may be nonzero, which might be slightly counterintuitive).
Since the sum of the forces on the pan is zero, the contact force must be equal in modulus to the (sum of) forces of the springs on the ... | https://physics.stackexchange.com |
54,181 | [
"https://cs.stackexchange.com/questions/54181",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/47611/"
] | I have a CFG:
<pre><code>S --> 0S1S | 1S0S | ε
</code></pre>
I'm trying to prove that it is ambiguous, but the steps to proving so are confusing me.
So if I pick a string, let's say 010110, I just have to show that there are two different parse trees for the string?
| Proving inherent ambiguity of a language is difficult, but proving ambiguity of a grammar is relatively quite easy.
The definition of ambiguity of a grammar does not say that every string has to have different parse trees. It says there need to exist only one string which has different parse tree to make a grammar amb... | You have to find a string which has two different parse trees. That string might be 010110 or it might be something totally different. In this kind of situation my recommendation is to refer back to the definition in your textbook and work out what the definition is saying.
| https://cs.stackexchange.com |
356,217 | [
"https://physics.stackexchange.com/questions/356217",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/168273/"
] | <blockquote>
Consider a block of mass $m_1$ attached to a spring. It's advancing
with a slower velocity $v_1$ as compared to that of an approaching
block of mass $m_2$'s velocity $v_2$ on the friction-less surface. Obviously, the two blocks
will collide.
</blockquote>
Now, I have read at several places that th... | Let $m_1,m_2$ have velocities $v_1,v_2$, where $v_1<v_2$ and $m_1$ is initially ahead of $m_2$.
$m_2$ has a spring attached to its front (in direction of motion).
Once $m_2$ catches up with $m_1$, the spring will be compressed between the two masses, and will (in an effort to return to its initial state) exert a f... | Although it should be obvious, and physical explanations as given in other answers are always much better, you can verify it by doing simple calculations. Let:
<ul>
<li>displacement of $m_1$ be $\vec{x_1}$ </li>
<li>displacement of $m_2$ be $\vec{x_2}$</li>
</ul>
Now, the compression/elongation in spring will be $X... | https://physics.stackexchange.com |
117,433 | [
"https://stats.stackexchange.com/questions/117433",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/56211/"
] | I am finding that there is no significant difference between a number list and another list which has 100*same numbers. The P value is 0.4487. The means are obviously very different (100 times). Why is it so?
Following is code and data in R:
<pre><code>> t.test(vnum, 100*vnum)
Welch Two Sample t-test
da... | The answer to your question lies in the variance. The sample mean differ by a factor of 100, yes, but what happens with the variance if you multiply a stochastic variable by a constant?
Lets look at this in more detail:
$$
Y = 100\cdot X
$$
The sample mean is then
$$
\hat\mu_Y = \frac{1}{n}\sum_{i=1}^nY_i = \fra... | We can see pretty much everything we need from the empirical cdf of the two samples:
$\quad\quad$<img src="https://i.stack.imgur.com/kaoBr.png" alt="enter image description here">
Relatively speaking, there's essentially no variation in <code>vnum</code>, so it's almost the same as doing a one sample test of 100vum w... | https://stats.stackexchange.com |
847,413 | [
"https://math.stackexchange.com/questions/847413",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/150347/"
] | Let $f:\mathbb{R}\rightarrow\mathbb{R}$ of class $C^\infty$
$\forall n\in\mathbb{N}^*,f\left(\frac{1}n\right)=\frac{n^2}{n^2+1}$
Let $p\in\mathbb{N}^*$
What is the value of $f^{(p)}(0)$ ? (by $f^{(p)}$ i mean the $p$th derivative of $f$)
<hr>
I have no clue how to do that. Any help is appreciated.
<strong>Thank y... | First note that if $g(x)$ is differentiable at zero and $g(1/n) = 0$ for all $n$ then $g^{(p)}(0) = 0$ for all $p$.
Now if we write $g(x) = f(x) - \frac{1}{1+x^2}$ we see that $g(1/n) =0$ for all $n$ and it follows that $$f^{(p)}(0) = \frac{d^p}{dx^p} \left. \frac{1}{1+x^2} \right|_{x=0}$$
We can determine the deriva... | If $p=1$ you can calculate $f'(0)$ as
$$
lim_{n\rightarrow\infty}\frac{f(1/(n+1))-f(1/n)}{1/(n+1)-1/n}=0.
$$
For general $p$ you can use the $k$-th Taylor polynomial
$$
f(1/n)=1 + \frac{1}{2\cdot n^2}f^{(2)}(0)+\frac{1}{3!\cdot n^3}f^{(3)}(0)+\ldots+\frac{1}{k!\cdot n^k}f^{(k)}(0)+O(\frac{1}{n^{k+1}}).
$$
Substracting ... | https://math.stackexchange.com |
84,811 | [
"https://electronics.stackexchange.com/questions/84811",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/8401/"
] | I am adding two hex numbers and determining what bits in the condition code register.
The numbers I am adding are <code>4D</code> (base 16) and <code>66</code> (base 16). I converted both to their binary equivalents.
<pre><code>4D (base 16) = 0 1 0 0 1 1 0 1
66 (base 16) = 0 1 1 0 0 1 1 0
</code></pre>
Once I added ... | A 2's complement overflow is indicated when the source values have the same sign but the resultant sign differs. In the case of your example, both source values have 0 as the MSB but the result has 1, therefore an overflow has occurred.
The sum is 0xB3, since the result itself is not modified by the status registers, ... | For your processor, the 8 bits in a value can be interpreted in two ways:
<ol>
<li>as an unsigned number, range <code>0 .. 255</code></li>
<li>as a 2s-complement number, range <code>-128 .. +127</code></li>
</ol>
(There are other ways an 8-bit value can be interpreted, for instance as an ASCII character, as a sign-ma... | https://electronics.stackexchange.com |
212,087 | [
"https://dba.stackexchange.com/questions/212087",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/120227/"
] | I want to try out Cassandra Cluster. My main question is about scalability.
Every node in a Cassandra cluster has the same copy of data. So when I have in total 1 TB and have 5 nodes -> 5TB.
This at some point will get huge. How do I scale Cassandra so that the storage can be distributed? Do I need to shard manually ... | The data is automatically distributed in the cluster based on the value of the partition key of your tables. So you need to take care about creating correct data model - don't have the partitions that have hundred thousands of rows, etc.
If the data model is correct, then you can scale Cassandra by just adding the new... | Cassandra does store its data in distributed fashion among the cluster nodes, using the murmur3partitioner(your 1 tb will be distributed 0.2 tb on each node). If you don't want your 1 tb data to become 5 tb change the replication factor from 5 to a desired lower value and run nodetool cleanup on all nodes.
| https://dba.stackexchange.com |
8,178 | [
"https://mathoverflow.net/questions/8178",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1887/"
] | I am trying to understand divisors reading through Griffith and Harris but it is difficult to come up with any particular interesting example. I have browsed through Hartshone's book but everything is expressed in terms of schemes, and I believe it is still possible to find some toy example to carry with me without hav... | Hartshorne is the reference where you can find the following example which might be useful.
I what follow everything is with <strong>multiplicity</strong>. Now Alberto pointed out above the case of the divisor over $\mathbb{P}^1$ associated to its "tangent bundle": Two points over the sphere counted with multiplicity (... | You want concrete? Then you want curves and surfaces! Check out Chapter V of Miranda's "Algebraic Curves and Riemann Surfaces" to see lots of stuff about divisors, how they're made up of functions, how they can give maps to projective space, etc. As for how to choose a pencil, that's just choosing two divisors that ar... | https://mathoverflow.net |
261,916 | [
"https://electronics.stackexchange.com/questions/261916",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/109173/"
] | This is a question I found in one of the textbooks I have. The textbook didnt explain thoroughly about the concept or theory of the op-amp, and that left me confused. So please correct me if I'm wrong. I was just wondering if the voltage of the noninverting pin of the op-amp is zero, as shown in the picture. Does that ... | There are <strong>Three</strong> gains involved in your diagram (I'm assuming you mean the DC gain).
The gain of the circuit with respect to the V1 input, the gain of the circuit with respect to the V2 input, and the gain of the op-amp itself.
From that diagram, if we assume the gain of the op-amp to be infinite, the... | An ideal op amp is assumed to have infinite gain. Basically, it will drive the output voltage to whatever is necessary to make its inputs equal.
The way to solve op amp circuits like this one is to assume the op amp inputs are at the same voltage and the current flowing in to them is zero, then figure out what the op ... | https://electronics.stackexchange.com |
313,915 | [
"https://electronics.stackexchange.com/questions/313915",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/52785/"
] | <strong>I little background first..</strong><br>
I have 4 separate wheels in my robot and an encoder on each wheel. I am using an arduino mega 2560 which only has 6 interrupt pins, every code that I've seen either uses 2 interrupt lines per encoder or 1 but then its not that precise.
<strong>My idea:</strong><br>
My i... | Why not use Boolean operators?
<pre><code>assign Z = (a != b) != c;
assign cout = (a && b) || ((a != b) && cin);
</code></pre>
All three options are functionally equivalent ways of implementing a standard full adder.
The simple answer to your question (and to my rhetorical one) is probably simply th... | No one in industry uses bit-wise models. Less typing, equivalent functionality. Perhaps more optimized in the simulator.
| https://electronics.stackexchange.com |
1,576,007 | [
"https://math.stackexchange.com/questions/1576007",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/298751/"
] | I just completed an exam and was curious as to the following question:
<blockquote>
How many surjections are there from $\{1, 2, 3, ..., n\}$ to $\{1, 2\}$ if $n \geq 3$?
</blockquote>
My assumption was the following:
The first element of the domain has the possibility to map to either 1 or 2.
The second element ... | Basically you can think of it as a binary string, $0$ means the element in the domain maps to the first element in the codomain, $1$ means the element maps to the second element in the codomain. There are $2^n$ ways to make a binary string of length $n$, but with the rules of surjectivity we need to take away the case ... | You had some of the right ideas, but you are not quite right. Let's start with finding the number of functions from ${1,2,...,n}$ to ${1,2}$ without any restrictions on the function. Then each of the numbers $1,2,...,n$ can be mapped to either $1$ or $2$, and there are hence $2^n$ such functions. How many of these are ... | https://math.stackexchange.com |
113,839 | [
"https://softwareengineering.stackexchange.com/questions/113839",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/38479/"
] | My non-technical manager just paid for a license to use a tool which designed to pick mentions of your brand name at blogs, "social media", comments, etc. and gauge the sentiment (positive, neutral, negative) of the post. What he wants me to do is use it to do a task which can only be achieved with a certain level of n... | Simply send an e-mail to the tech support of the product: "How should I do task Y using your tool?"
Maybe you'll be surprised, maybe your manager...
| First of all, be cautious when explaining him that the tool he choose isn't apt. Your intentions, however good they may be, they may be perceived as a way for you to evade doing the task or even worse - you can make him feel stupid (and you don't want that).
As you explained here - the tool isn't capable of doing suc... | https://softwareengineering.stackexchange.com |
291,970 | [
"https://softwareengineering.stackexchange.com/questions/291970",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/189943/"
] | I've seen this example in a text book and am a little confused how to interpret the operator precedence rules. Given this struct:
<pre><code> typedef struct {
char *data;
size_t start, end;
} str_wends;
</code></pre>
Let <code>B</code> be declared as a pointer to this struct,that is.
<pre><code> str_we... | Concerning this:
<pre><code>&B->data[B->start]
</code></pre>
you assert in comments that:
<blockquote>
If I read the tokens from left to right, the operators are ->, [], ->
</blockquote>
But those are <em>not</em> the operators reading left to right: you're including the closing <code>]</code> with the ... | Actually, it doesn't matter whether B->start or B->data is "evaluated" first. The result of interest is address of the referenced element, which is the sum of the base address and the product of the index and the size of the element. The two addends are independent, meaning that the order of their evaluation is irrel... | https://softwareengineering.stackexchange.com |
129,736 | [
"https://electronics.stackexchange.com/questions/129736",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/29737/"
] | In Atmel Microcontrollers, there are simple delay functions such as <code>__delay_ms()</code> and <code>__delay_us()</code> found in <code>utils\delay.h</code>.
I am using a Tiva™ C Series TM4C1294 development board, with a TM4C1294NCPDT microcontroller. However, I can't find any libraries to do similar delay function... | Try this:
/* Delay cycles for 1 second */
SysCtlDelay(16000000u / 3u);
| I test 1 second with this:
<pre><code>SysCtlDelay(SysCtlClockGet() / 3); // delay 1 second
</code></pre>
The SysCtlDelay is implemented by assembly code
<pre><code> SysCtlDelay():
000008f0: 1E40 subs r0, r0, #1
000008f2: D1FD bne SysCtlDelay
000008f4: 4770 ... | https://electronics.stackexchange.com |
57,734 | [
"https://chemistry.stackexchange.com/questions/57734",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/33709/"
] | I understand that the term <em>valency</em> refers to the number of bonds an element would be able to form with either chlorine or hydrogen. If this is directly related to the number of valence electrons an atom has, why do transition metals have variable valencies?
| When working with nucleophiles and electrophiles, it is easier to think of them as "positive-ophiles" and "negative-ophiles" respectively.
With that said, NH<sub>3</sub> (ammonia) has a lone pair of electrons that is attracted to positive charges. The carbon atom with three bonds is electron deficient and positively ... | It's all about thermodynamics. The decrease in energy brought about by filling the carbon octet is larger in magnitude than the increase in energy caused by having a positive charge on the nitrogen atom (it is positive since the total charge of the system must stay the same). This means the sum of the energies of the p... | https://chemistry.stackexchange.com |
300,080 | [
"https://softwareengineering.stackexchange.com/questions/300080",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/200567/"
] | <strong>Dilemma</strong>
I've been reading a lot of best practice books about object oriented practices, and almost every book I've read had a part where they say that enums are a code smell. I think they've missed the part where they explain when enums are valid.
As such, I am looking for <em>guidelines and/or use-... | Enums are intended for use cases when you have literally enumerated every possible value a variable could take. Ever. Think use cases like days of the week or months of the year or config values of a hardware register. Things that are both highly stable and representable by a simple value.
Keep in mind, if you're m... | Firstly, a code-smell doesn't mean that something is wrong. It means that something might be wrong. <code>enum</code> smells because its frequently abused, but that doesn't mean that you have to avoid them. Just you find yourself typing <code>enum</code>, stop and check for better solutions.
The particular case that h... | https://softwareengineering.stackexchange.com |
619,040 | [
"https://electronics.stackexchange.com/questions/619040",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/313106/"
] | Assuming one had access to old CPUs, ram, hard drives, and mainboards with I/O connections and BIOS chips and other chips in them.
I know the basics of the gates to make CPUs and RAM, and I know it's all very simple for the basic concepts. So assuming all of the advanced parts, like the chips were already available, ho... | It used to be common for electronics hobbyists to make their own circuit boards. The equipment needed is essentially:-
<ul>
<li>Copper-clad boards. These are PCBs with a continuous layer of copper across the surface.</li>
<li>Etch-resist pens or sticky tapes.</li>
<li>Etching chemicals, bought as a concentrated liqui... | Tape and etch resist pens for very simple stuff; iron-on for more complex designs. We have a Voltera for small-scale prototyping and production. The biggest thing you are going to run into is multiple layers; the most you can get realistically is 2-layer and most motherboards are pushing double-digits, probably more ... | https://electronics.stackexchange.com |
2,818 | [
"https://scicomp.stackexchange.com/questions/2818",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/1611/"
] | I have been reading a book by Thomee and he considers the case of $u_t=(au_x)_x$, for the case of $a$ possibly being discontinuous. Then he says that the problems with convergence might occur, and thus to fix that one can smooth the coefficient $a$ and restore convergence rate.
Please correct me if I am wrong but dis... | I don't know what exactly Thomee had in mind, but if you can't get solution at all for a discontinuous coefficient and a particular discretization scheme, you can smooth the coefficient <em>on a lengthscale proportional to the mesh size $h$</em> and obtain a problem that's solvable. Then you make the smoothing distance... | Strong form discretizations are extremely cumbersome for the case of discontinuous coefficients. It is better to use weak form methods that do not require differentiating the solution. Furthermore while the product $a u_x$ is continuous even for discontinuous coefficients, $u_x$ alone is not. Therefore even evaluating ... | https://scicomp.stackexchange.com |
8,774 | [
"https://dsp.stackexchange.com/questions/8774",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/3262/"
] | I am computing the fourier series of the following function between $[-0.5, 0.5]$
$$\displaystyle f(t) = \frac{1}{2} - |t|$$
According to the definition of Fourier Series the coefficients are given by
$$\displaystyle \hat f_n = \frac{-(-1)^n}{2\pi ^2 n^2} + \frac{1}{2\pi ^2 n^2}$$
That's easy to calculate. So far so go... | The coefficients of the Fourier series that you have computed are, in effect, the spectrum of the <em>periodic</em> signal consisting of the sum of signals $f(t)$ delayed in time or advanced in time by integer multiples of $1$ second. Mathematically, the Fourier <em>transform</em> of a periodic function has <em>impuls... | As correctly pointed out by Dilip Sarwate, the Fourier coefficients apply to the periodic continuation of your triangular function. However, they are also samples of the continuous Fourier transform of the original (non-periodic) triangular function. So the Fourier coefficients can also be used as a discrete approximat... | https://dsp.stackexchange.com |
10,022 | [
"https://chemistry.stackexchange.com/questions/10022",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/2368/"
] | <img src="https://i.stack.imgur.com/xGCJJ.jpg" alt="enter image description here">
<blockquote>
A solution having composition $p$ (left side of graph) is cooled to just above the eutectic temperature (point $s$ is at $0.18$ $x_{\ce{Si}}$ and the corresponding tie line intersects the liquidus curve at $0.31$ $x_{\ce{... | You are correct. Another way to calculate it is: $$X_{\mathrm{L}} = \frac{s-b}{e-b} = \frac{0.18-0}{0.31-0}=0.58$$
You can also inspect the diagram visually and see that the $bs$ line is longer than the $se$ line. The lever rule dictates that the line length is proportional to the percentage of the phase opposite from ... | Using the lever rule, the amount of liquid in the 2 phase region is given by
<span class="math-container">$$\frac{18-0}{31-0}=0.58$$</span>
Hence for the amount of solid in the same region we get
<span class="math-container">$$1-0.58=0.42$$</span>
since the overall sum of the liquid and solid in the two phase reg... | https://chemistry.stackexchange.com |
154,566 | [
"https://electronics.stackexchange.com/questions/154566",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/64910/"
] | I'm self studying with Chu's FPGA prototyping book. Exercise 4.7.1 asks for a programmable square wave generator:
<blockquote>
A programmable square-wave generator is a circuit that can generate a square wave with
variable on (i.e., logic 1) and off (i.e., logic 0) intervals. The durations of the intervals are
s... | If you want to implement something that requires a number of count N (4 for example), you can either count 0, 1, ..., N-1 (example, 0, 1, 2, 3, 0, 1...). Or you can count 1, 2, ..., N (example, 1, 2, 3, 4, 1, 2...). So if you want to end the count at the number N, start the count at 1.
Often, coding styles are just pe... | Well for starters you are using two always blocks where one would be fine. Merging everything into one block gets rid of all those ugly "next" signals.
We can also make the output a reg getting rid of the wave_reg signal.
<pre><code>module sqwaveGen
#(
parameter interval_quant_ns = 5
)
(
input wire clk,
input wire r... | https://electronics.stackexchange.com |
11,688 | [
"https://mathoverflow.net/questions/11688",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | How does one prove that the splitting of primes in a non-abelian extension of number fields is not determined by congruence conditions?
| Here's an answer for the special case when the base field is $\mathbb{Q}$. It involves a large bit of class field theory over $\mathbb{Q}$, so I'll be terse.
We start with the lemma which Buzzard mentioned.
<strong>Lemma</strong> - Let $K$, $L$ be finite Galois extensions of $\mathbb{Q}$. Then $K$ is contained in $L$... | OK how's about this to finish (I don't think either argument posted so far deals with this case). Say $K/\mathbf{Q}$ is finite and (away from a finite set of exceptions) $p$ splits completely in $K$ iff $p$ mod $N$ is contained in a subset $S$ of $(\mathbf{Z}/N\mathbf{Z})^\times$. I <em>think</em> the other two answers... | https://mathoverflow.net |
76,327 | [
"https://chemistry.stackexchange.com/questions/76327",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/46560/"
] | I'm pretty new to chemistry and I've been stuck on it for hours.
Question: $\pu{10g}$ of the hydroxide of a metal on ignition gave $\pu{8g}$ of oxide. The equivalent weight of the metal is:<br>
a) $\pu{136g}$<br>
b) $\pu{40g}$<br>
c) $\pu{56g}$<br>
d) $\pu{28g}$
I used the law of equivalence but the answer I got wa... | I found your numbers confusing, but I think the first equation you wrote is not correct. This is how I'd solve it:
Let's say we have $\mathrm{n}$ equivalents of metal in the sample, and let's call the equivalent weight of the metal $\mathrm{e}$. For the hydroxide sample, we have:
$n(e+17)=10$
where $\mathrm{e+17}$ i... | Nothing wrong with Vic's answer. I'd solve it differently, but hopefully you are familiar enough with algebra to understand that there are various ways to correctly come up with the correct answer...<br>
Here's how I did it: There is a loss of 2 grams of what we assume is water.
Now since we know we started from M<sub>... | https://chemistry.stackexchange.com |
23,630 | [
"https://dba.stackexchange.com/questions/23630",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/11335/"
] | I'm building a website that will host a variety of questionnaires. Each questionnaire has a different number of questions and each question has a different number of answers. I have attempted to design a database to hold the questions and possible answers for each questionnaire, but I end up having separate tables for ... | We have an application at our workplace that does a similar thing. It works by having a table that contains a list of all possible questions like such:
<pre><code>CREATE TABLE QUESTIONS
(
ID INT NOT NULL PRIMARY KEY,
SUMMARY NVARCHAR(64) NOT NULL UNIQUE,
DESCRIPTION NVARCHAR(255) NULL
);
</code></pre>
Then y... | <h3>QUESTIONNAIRE</h3>
<pre><code>QUESTIONNAIRE_ID (PK),
QUESTIONARIE_TITLE
</code></pre>
<h3>QUESTIONNAIRE_QUESTIONS</h3>
<pre><code>QUESTIONARIE_QUESTIONS_ID (PK),
QUESTIONARIE_QUESTIONS,
QUESTIONNAIRE_ID (PK)
</code></pre>
<h3>ANSWERS</h3>
<pre><code>ANSWER_ID (PK),
QUESTIONARIE_QUESTIONS_ID (FK)
</code></pre>
| https://dba.stackexchange.com |
218,570 | [
"https://softwareengineering.stackexchange.com/questions/218570",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/12893/"
] | Today I lost a method that I was using since my co-worker redefined it to take its superclass instead. So after synchronizing with the repository I had trouble. Would it had been better in this case to use some annotation like <code>@Deprecated</code> instead of removing the method so that I would get an error message ... | <code>@Deprecated</code> annotation is the correct thing to do. Removing code creates breaking changes in the API that is being used - this can be bad.
The thing is that often people ignore the 'bad' thing and still use deprecated methods because it doesn't fail the build. Thus, the next correct thing to do is to ma... | For Java, I'm not sure the specifics of deprecation beyond the <code>@Deprecated</code> annotation. To answer your question, I am not aware of Git at least being able to adequately and clearly deprecate methods themselves (I may have not come into contact with them). In my experience, wholesale removing methods may be ... | https://softwareengineering.stackexchange.com |
151,529 | [
"https://dba.stackexchange.com/questions/151529",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/1799/"
] | My environment:
<pre><code># cat /etc/redhat-release
Red Hat Enterprise Linux Server release 6.8 (Santiago)
# uname -a
Linux A.B.C 2.6.32-642.4.2.el6.x86_64 #1 SMP Mon Aug 15 02:06:41 EDT 2016 x86_64 x86_64 x86_64 GNU/Linux
# rpm -q mysql-server percona-toolkit
mysql-server-5.1.73-7.el6.x86_64
percona-toolkit-2.2.19-... | It's actually surprisingly easy using <code>DAY()</code>, as 1-7 will be 1, 8-14 will be 2, 15-21 will be 3, 22-28 will be 4 and 29-31 will be 5. Doesn't matter what the name of the day is, that will always hold true.
<pre><code>select case when DAY(yourdate) <=7 then 1
when DAY(yourdate) <=14 then ... | Alternatively you could calculate the result using a formula:
<pre><code>SELECT
(DAY(YourDate) + 6) / 7 AS Iteration
FROM
dbo.YourTable
;
</code></pre>
In cases where both operands of a division operation are integers, the result is also an integer, and a rounded down one at that.
So, <code>DAY(YourDate)</code> ... | https://dba.stackexchange.com |
12,935 | [
"https://dba.stackexchange.com/questions/12935",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/-1/"
] | I have some fields for my tables that are strings and at the moment, most of the field size have pretty high character limits. For instance, 100 char for the street name. Is there a penalty for using large field size? If I change the limit to 30 char for this field for instance, will there be a performance gain or an e... | If you're talking about <code>varchar</code> and <code>nvarchar</code> then no, there is no penalty for allowing a higher field length.
<hr>
<em>Some caveats to bear in mind, though:</em>
<ul>
<li><strong>There is a 2 byte overhead per row for variable length fields</strong> (per field). If you have a very short fi... | If you mean, "Is there a penalty for declaring the field size bigger than any values that are actually stored in it?", then as long as it is declared varchar, the answer is no. Every SQL DB engine that I know of stores only the number of characters actually given in the data (plus a length value). So if you define the ... | https://dba.stackexchange.com |
515,813 | [
"https://physics.stackexchange.com/questions/515813",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/207871/"
] | In Photonic Devices by Jia-Ming-Liu, it is mentioned that magnetization at optical frequencies is zero. I know that electrons behave like an oscillator in EM fields and the amplitude of oscillation as :
<span class="math-container">$\frac{F_0}{m((\omega_0-\omega_d)^2+\gamma^2\omega_d^2)^{1/2}}$</span> and decreases as ... | As Pieter said, there are two main reasons for vanishing magnetization at optical frequencies. I will elaborate on this a little more.
<strong>Amplitude</strong>:
Without an EM field, the net magnetization of a magnetic material will be zero because magnetic domains will form. All these domains will have different ori... | For sizeable magnetization one needs ferromagnetism: domains of ordered moments. At optical frequencies, fields are smaller than coercive fields. And domain walls could not move that fast anyway.
But there are ferrites for radio frequencies.
| https://physics.stackexchange.com |
7,225 | [
"https://robotics.stackexchange.com/questions/7225",
"https://robotics.stackexchange.com",
"https://robotics.stackexchange.com/users/7185/"
] | I have a requirement for a motor that pulls a piece of rope until the rope is taught. However I'm at a loss as to how to achieve this, I'm sure it must've been done before but I'm not sure how to best describe this in a way that would get me more results. I wondered if there are any sensors or pre-established methods f... | There are two ways that I can think of measuring this:
<ul>
<li>Motor current, as the resistance to motion increases the current increases linearly, you could measure the desired torque and the current and simply pull until this is met</li>
<li>You could have a tensioner wheel with a potentiometer to measure when the ... | If you know how much force should be on the rope, you could simply mount the winch against a spring that takes that same amount of force to compress. Then, just use a limit switch to detect when the spring has been compressed.
| https://robotics.stackexchange.com |
63,712 | [
"https://stats.stackexchange.com/questions/63712",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/24230/"
] | I haven't been able to find a good answer for this (though I know that there are a few related questions):
How does Amazon determine how to price a product? How does it figure out when to downprice, and by how much? I'm sure that there's some machine learning involved here, but what does it involve?
Doesn't have to b... | "Hey guy, what is the ultra-secret recipe of coca-cola ?".
I don't think you will get a precise answer.
I think it is a very complex and well optimised process, I don't have any other clue. I can only imagine that it is very far from a supply and demand process (in the basic economical sense).
It will depends on s... | I have no idea but I can guess based on how I would do it. I would take a reinforcement learning approach. Essentially, have an agent that takes an action (to decrease or increase the price of an item) based on the observed state of the system (traffic, season, other factors idk...) and the agent would then get some ... | https://stats.stackexchange.com |
13,274 | [
"https://computergraphics.stackexchange.com/questions/13274",
"https://computergraphics.stackexchange.com",
"https://computergraphics.stackexchange.com/users/19542/"
] | If I understood correctly this is the process of rendering an object:
<ol>
<li>Array of 4d vector defining points 3d points(with the fourth component 1) representing object's vertices in object/local space:<br>
<code>{1, 1.21, 2.12}</code><br>
<code>{1, 1.21, 2.12}</code><br>
<code>{1, 1.21, 2.12}</code><br>
<code>{1, ... | Others have interpreted your question as being about “progressive JPEG”, but “line by line from top to bottom” is <em>not</em> how progressive JPEG appears. Progressive JPEG organizes the data in the file so that low-detail data (the average color of 8×8 blocks) is stored before the data required for higher detail. A s... | What you are referring to is called a "progressive JPEG" file. This is a property of the way the file was compressed file which allows its decompression to be done in stages, such that a less-detailed version of the image can be shown despite not having the entire file. This technology was originally invented... | https://computergraphics.stackexchange.com |
215,747 | [
"https://physics.stackexchange.com/questions/215747",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/96173/"
] | I am a student of class 9. When I was going through magnetism and read that an earth is a magnet I got some doubts. My question is: is earth really a magnet? Doesn anyone have any proof that earth is a magnet? Is there a magnetic core at the center of the earth? Has anyone reached the core of the earth?
| Earth has a magnetic field. You can verify this yourself; it is why a compass works. Just take any magnet and hang it carefully from a string. As long as there's nothing else magnetic around and it's well-balanced and free to rotate, it will line up with Earth's magnetic field.
We have measured the Earth's magnetic f... | Yes, Earth does have a magnetic field(check it out with a compass!).<br>
In geology, they explain this in this way:
The Earth's core is divided between the inner and outer cores. The inner core is solid because of the very high pressure. The outer core, although it also has high pressure, it is not as high as the inner... | https://physics.stackexchange.com |
257,989 | [
"https://softwareengineering.stackexchange.com/questions/257989",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/102390/"
] | I inherited a project that I've been maintaining for approximately a year now. The project primarily revolves around performing various financial calculations for the end user. It's roughly 100,000 lines of spaghetti code held together with duct tape and gumption. I've been slowly going through and refactoring the code... | How old is your app?
Almost two years ago I inherited a similar situation in a 5 years old app and we keep calm and carry on, small, small continuous improvements.
If I could, I would start from the <strong>client</strong> and the final <strong>user</strong>. I'd be gathering requirements in the <strong>same way as ... | I started programming in 1999 and I provide software outsourcing services since 2009 as my own business. During this time I participated to over 300 software engineering projects for over 100 customers in different countries.
The good news are that the only one company with good specifications I've seen is NASA. The o... | https://softwareengineering.stackexchange.com |
23,268 | [
"https://datascience.stackexchange.com/questions/23268",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/201/"
] | I used Data Science Studio (Dataiku) to create a Decision Tree model. Then I took the pickle file and loaded into Python to continue using it.
<pre><code>import pickle
f = open('clf.pkl', 'rb')
loaded_model = pickle.load(f, encoding='latin1')
</code></pre>
On model settings, I used <code>standard rescaling</code> wh... | Adding to jrouquie's answer, the formula would be:
For each column,
<pre><code>rescaled_feature = (input_feature - shift) * inv_scale
</code></pre>
| Note that the approach is brittle as DSS makes no guarantee about the data format in the pickle. But as long as you don't upgrade it, you should be fine.
Have you tried the "export to python notebook" feature in the model page? This one is meant to be readable and could help you.
| https://datascience.stackexchange.com |
1,811,381 | [
"https://math.stackexchange.com/questions/1811381",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/284594/"
] | One machine element is being produced in $3$ series, each series consisting of $20$ elements. In the first series, there are $15$ elements that work correctly, in the second series there're $18$ and in the third series there are $16$. A series is randomly picked, and a single element is also randomly picked from the ch... | Let us define some events in order to clean up notation a bit. Let $W_1,W_2$ be the events that the first element works and second element works respectively. Let $S_1,S_2,S_3$ be the events that we are pulling items from series $1,2$ and $3$ respectively.
The problem asks us "What is the probability that a second e... | Let $A_i$ be the event were our ith picking yields a working element. Also let $S$ be the chosen series, with values $a, b, c$, for the series with $15, 18, 16$ working elements, respectively. Then we can see that:
$$P(A_i|_{S=a}) = \frac{15}{20}, P(A_i|_{S=b}) = \frac{18}{20}, P(A_i|_{S=c}) = \frac{16}{20}$$
With th... | https://math.stackexchange.com |
622,417 | [
"https://physics.stackexchange.com/questions/622417",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/292242/"
] | I've done a derivation showing that the wave length of light in a waveguide is longer than that of free space light. But I don't really have an intuitive understanding of why this is. I think my prof gave an example but i'm not sure I get it. Basically, two waves are propagating down the wavelength. But their angle of ... | It's better to understand this in the wavenumber domain. The dispersion relation (relating frequency and wavenumber) in a wave-guide is:
<span class="math-container">$$ \omega_{WG} =\sqrt{(ck_{WG})^2 + \omega_0^2}$$</span>
where <span class="math-container">$\omega_0$</span> is the cutoff frequency.
In free space, <spa... | Here is a way of thinking of this a little more intuitively, which might help.
The waveguide has a characteristic impedance which is different from that of free space. Therefore we expect that the propagation velocity of an EM wave in a waveguide will be different from its free-space value. And indeed it is; it will al... | https://physics.stackexchange.com |
411,268 | [
"https://math.stackexchange.com/questions/411268",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/69780/"
] | Please, somebody can help me with this problem?
<hr>
Let $V$ and $W$ be two closed subspaces of a Hilbert $(H, \langle \cdot,\cdot\rangle)$, and let $P:H\rightarrow V$ and $Q:H\rightarrow W$ the orthogonal projectors respectively. Show that
$$\langle\ (Q-P)(x),\ x\ \rangle\ \geq\ 0,\ \forall\ x\in H\quad \mbox{ if and... | Note that
$$\binom{n}k\binom{k-1}2=\frac12\binom{n}k(k-1)(k-2)\;,$$
where the $(k-1)(k-2)$ looks like the coefficient of the second derivative of $x^{k-1}$. That suggests looking at something like
$$g(x)=\sum_{k=3}^n\binom{n}kx^{k-1}$$
and differentiating twice with respect to $x$ to get
$$g''(x)=\sum_{k=3}^n\bino... | Use the Binomial Theorem to write down the expansion of
$$\frac{(1+x)^n-1}{x}.$$
Then differentiate twice, and set $x=1$. You will get a very close relative of your sum.
| https://math.stackexchange.com |
318,445 | [
"https://electronics.stackexchange.com/questions/318445",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/2213/"
] | I want to modify an electric guitar to add an ADC and microcontroller to drive some LEDs for fancy effects that follow music.
Since typical output levels of pickups are about 100mV, I was thinking of adding an op-amp circuit in parallel to the output of the guitar, independent of the any other amps the user may connec... | The output impedance of a guitar is in the order of 10k ohms. If your op amp circuit has an input impedance of say 100k ohms, there will be no significant loading of the guitar output nor any affect on downstream amps or effects boxes.
In order to keep the input impedance of your added circuit as high as possible, pic... | You won't be able to drive your LED's without a separate power source, so I would recommend you use a microcontroller board with a battery. A small Arduino board would have an on-board ADC and provide the ability to directly drive a small number of LEDs. I don't use them myself, but I would recommend you use the Ardu... | https://electronics.stackexchange.com |
2,298,886 | [
"https://math.stackexchange.com/questions/2298886",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/375665/"
] | Suppose A and B are two sets with $(A \times B) \cup (B \times A) = A \times A$. Prove that $A ⊆ B$
How would i start the proof off?
I know that $A \times B = \{(a, b) | a ∈ A, b ∈ B\}$, would this help me?
Pick $x ∈ B$, what are the steps i take? Sorry i'm new to proofs.
| In general, to show a set $A$ is contained in another set $B$, we take an arbitrary element $a\in A$ and show that $a$ must be contained in $B$ as well. Let's try.
If $a\in A$, then we know $(a, a)$ is contained in $A\times A$ by definition of the set product. Now we use the hypothesis that $A\times A= (A\times B)\cu... | Hint:
For any element $$x\in{B}$$ and $$a\in{A}$$, $$(a,x)\in{A×B}$$ $$\Rightarrow (a,x)\in{A×A} \Rightarrow x\in{A}$$. Thus all elements of $B$ are in $A$.
| https://math.stackexchange.com |
176,033 | [
"https://softwareengineering.stackexchange.com/questions/176033",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/72770/"
] | I was referred here from stackoverflow as my question was apparently too broad.
I'm working on a template, and I know using CSS is preferred over HTML tables for positioning... But, is it acceptable to get the best of both worlds and use table-like styles on my divs? For example:
<pre><code>display: table;
</code></p... | Using tables for layout is discouraged because it is semantically wrong -- table markup is supposed to be for tables and specifically for tabular data. Your HTML says what something is (e.g. a table, a paragraph, or a generic text division) CSS is just instructions for displaying it.
If it's consistent across browsers... | IE7 doesn't support 'display: table', so you can only use it for IE8 and up. Other browsers handle it fine, mostly.
| https://softwareengineering.stackexchange.com |
271,952 | [
"https://electronics.stackexchange.com/questions/271952",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/127015/"
] | I am a student, and studying Electrical Engineering now. I was tasked with building a 24VDC to 12V dc linear power supply. One of the requirements was big precision of line/load regulation (up to the fourth decimal). From what I read, this is achievable by using a feedback loop, however, I cannot find any reliable sour... | Are you sure that the 100nF cap isn't short circuit? Try replacing it.
| I see you had the input capacitor shorted but you will likely hit another problem with this op-amp.
There is a significant problem in running your amplifier at a total power rail of only 5 volts and it is listed on page 5 of the data sheet. The table on page 5 states that the input common mode range is (V-) + 2.5 volt... | https://electronics.stackexchange.com |
550,076 | [
"https://math.stackexchange.com/questions/550076",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/98240/"
] | For homework I need to prove the folloving:
$$
A \cap (A \cup B) = A
$$
I did that in the following manner:
$$
A \cap (A \cup B)\\
x \in A \land (x \in A \lor x \in B)\\
(x \in A\ \land x \in A) \lor (x \in A \land x \in B)\\
x \in A \lor (x \in A \land x \in B)\\
\text{now I have concluded that x belongs to A,}\\
\te... | Yes, you are correct. The given equality can be expressed by the two implications: $x \in A\cap (A \cup B) \implies x \in A$, and the implication $x \in A \implies x \in A \cap(A\cup B)$. Since both implications are satisfied, so is the set equality.
Just be careful in your "equations" (i.e., your use of the "equal s... | Or you can just think that $A\subset A\cup B$ and thus from the definition of $\cap$ you have that $A\cap (A\cup B)=A$
| https://math.stackexchange.com |
84,683 | [
"https://cs.stackexchange.com/questions/84683",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/79971/"
] | What kind of algorithm can have $O(1/n)$ complexity, where $n$ is a natural number?
Or, is there any algorithm that the time it takes decreases when the data input increases?
| No algorithm really has an $O(1/n)$ running time, but that notation might be used informally for an algorithm who's running time is really $O(m/n)$ where $m$ is large and not expected to vary. Here's an example of such an algorithm:
Given an unordered set (e.g. a hash table) containing $n$ values from the integer rang... | Considering that even the algorithm
<pre><code>return 1
</code></pre>
has $\Omega(1)$ running-time cost, it seems obvious that running-time in $o(1)$ is impossible.
Other cost measures are often equated with running time, e.g. comparisons in sorting. That makes sort of sense since, usually, we pick dominant operatio... | https://cs.stackexchange.com |
12,897 | [
"https://astronomy.stackexchange.com/questions/12897",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/10164/"
] | I know that asteroids are huge chunks of rock, orbiting a solar system. Do asteroids have a gravitational field and do they gravitationally attract each other to form planets?
| By definition, gravity is a result of mass. Any body with a non-zero mass (even atoms) will have a gravitational field associated with it. The higher the mass the stronger will be the field. This is basic of classical mechanics. Until we reach quantum scale where the gravitational force is dominated by other 3 forces a... | Sure. <em>Any</em> mass has its gravitational field. However, its size is proportional to the mass, so as most asteroids have little mass, they have little gravitational field, and therefore pull only very slightly at each other, resulting in not enough effect to get them to lump together.
Typically, their difference ... | https://astronomy.stackexchange.com |
1,541,800 | [
"https://math.stackexchange.com/questions/1541800",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/136368/"
] | I happened to stumble upon the following matrix:
$$ A = \begin{bmatrix}
a & 1 \\
0 & a
\end{bmatrix}
$$
And after trying a bunch of different examples, I noticed the following remarkable pattern. If $P$ is a polynomial, then:
$$ P(A)=\begin{bmatrix}
P(a) & P'(a) \\
0 ... | If $$ A = \begin{bmatrix}
a & 1 \\
0 & a
\end{bmatrix}
$$
then by induction you can prove that
$$ A^n = \begin{bmatrix}
a^n & n a^{n-1} \\
0 & a^n
\end{bmatrix} \tag 1
$$
for $n \ge 1 $. If $f$ can be developed into a power series
$$
f(z) = \sum_{n=0}^\infty... | It's a general statement if <span class="math-container">$J_{k}$</span> is a Jordan block and <span class="math-container">$f$</span> a function matrix then
<span class="math-container">\begin{equation}
f(J)=\left(\begin{array}{ccccc}
f(\lambda_{0}) & \frac{f'(\lambda_{0})}{1!} & \frac{f''(\lambda_{0})}{2!} &am... | https://math.stackexchange.com |
197,724 | [
"https://security.stackexchange.com/questions/197724",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/182322/"
] | I've noticed that the following Stored XSS does not execute, whereas in the JS console it works:
<pre><code><img src=0 onerror=alert(document.domain+": "+Date.now())>
</code></pre>
This doesn't prompt an alert box. Whereas the following do:
<pre><code><img src=0 onerror=alert(Date.now())>
<img src=0 o... | You have to remove space in <code>": "</code> or add quotes for onerror attribute value:
<pre><code><img src=0 onerror='alert(document.domain+": "+Date.now())'>
</code></pre>
| <strike>You put a quote in the original one. This messes up the HTML parser because <code>"</code> has special meaning inside the attribute space of a tag.</strike>
I'm wrong. It's the space.
| https://security.stackexchange.com |
108,454 | [
"https://softwareengineering.stackexchange.com/questions/108454",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/36817/"
] | A problem that I am facing and would like some input into is; a Product Owner introduces ungroomed (unfamiliar, not estimated) User Story(s) into the Sprint Planning meeting.
The issue that this has caused is the team rushes to understand and estimate the User Story(s), which puts significant time pressure on the com... | Given they've just been given the story during planning (regardless of it being a new story or not having estimated it earlier) you have a few choices.
First, you can ask the product owner if the story can be left on the backlog so that it can be properly checked and estimated during this sprint, and take it next spri... | Estimation is not something that should be done off-the-cuff or quickly and without thought, regardless of your methodology. I wouldn't expect the team to be able to quickly come up with a reasonable estimate without having an opportunity to look at the user story and think about it for a while. At the same time, I do ... | https://softwareengineering.stackexchange.com |
742,337 | [
"https://physics.stackexchange.com/questions/742337",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/352683/"
] | In my physics textbook, I have the following worked out example:
<blockquote>
A table with a smooth horizontal surface turns at an angular speed <span class="math-container">$ω$</span> about its axis. A groove is made on the surface along a radius and a particle is gently placed inside the groove at a distance <span cl... | That the Fourier coefficients of the field are creation and annihilation operators is a consequence of the commutation (or anticommutation for fermion fields) relations imposed on the quantum field. For a free scalar field with Lagrange density
<span class="math-container">$$\mathcal{L}=\frac{1}{2}(\partial^{\mu}\phi)... | I would like to add to Buzz excellent answer that the development of a quantum field operator in annihilation and creation operators as mentioned in Buzz's answer is only valid for free quantum fields, i.e. fields that do not couple to another quantum field. If a quantum field couple to another field, so that the field... | https://physics.stackexchange.com |
971,191 | [
"https://math.stackexchange.com/questions/971191",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/134290/"
] | Would this be the same thing as saying "Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for <em>any</em> $s, t \in \mathbb{Z}$"? I can do the proof for any integers $s$ and $t$, but if <em>any</em> and <em>all</em> mean the same thing, then I can do this proof. If not, how can I do this?
| In response to your question about <em>any</em> and <em>all</em>, they generally mean the same thing. The symbol $\forall$ can be read "for all" or "for every" or "for any" or "for each". These all mean the same thing.
This is how you could write the proof, with meticulous rigor.
<hr>
Let $a,b,c \in \mathbb{Z}$ wit... | try writing both numbers as a combination of integers and remainders
b=qa+r
c=q'a+r
sb+tc=sqa+sr+tq'a+tr=a(sq+sq')+r(s+t)
since a divides b, c, and 0 <= r <=a , we conclude r must be 0.
from here, forall s,t in Z, a divides any linear combination of b and c
| https://math.stackexchange.com |
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