qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
values |
|---|---|---|---|---|---|
541,986 | [
"https://physics.stackexchange.com/questions/541986",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/191644/"
] | There exists a classical definition of the orbital angular momentum,
<span class="math-container">$$\mathbf{L}=\mathbf{r}\times\mathbf{p}$$</span>
Due to this definition, the following quantity is identically zero,
<span class="math-container">$$\boldsymbol{\nabla}\cdot\mathbf{L}=0$$</span>
because the divergence of a ... | In terms of quantum mechanical operators, the gradient is essentially the momentum operator,
<span class="math-container">$$\mathbf{p} = - i \nabla.$$</span>
So your first statement is equivalent to the assertion that <span class="math-container">$\mathbf{p} \cdot \mathbf{L} = 0$</span>. This is true, but it's not as s... | When considering the mechanics of a point particle, the quantity <span class="math-container">$\nabla \cdot (\mathbf r \times \mathbf p)$</span> is not well-defined.
The familiar gradient, curl, and divergence operators are objects which act on <em>fields</em> (vector fields in the case of curl and divergence, and s... | https://physics.stackexchange.com |
33,839 | [
"https://cs.stackexchange.com/questions/33839",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/332/"
] | I was programming a little Secret Santa tool for my extended family's gift exchange. We had a few constraints:
<ul>
<li>No recipients within the immediate family</li>
<li>Nobody should get who they got last year</li>
<li>The whole thing should be a cycle (Sandy gives to George, George to Tom, Tom to Susan, Susan back... | You can do slightly better on space by using reservoir sampling. The overall approach we take is the same as suggested by @jnalanko, and it only works well for small enough $n$. We generate each permutation of $\{1,\ldots,n\}$, but only keep one solution $X$ stored. At the end, $X$ will satisfy the property of being sa... | I'm not sure what you mean by an efficient algorithm, but the problem of finding any Hamiltonian path is NP-complete, which means that it is very unlikely that a polynomial time algorithm exists for your problem.
If the number of people $n$ is small, say less than 10, then it is feasible to solve the problem by brute ... | https://cs.stackexchange.com |
417,256 | [
"https://mathoverflow.net/questions/417256",
"https://mathoverflow.net",
"https://mathoverflow.net/users/148161/"
] | Motivation: for any ring <span class="math-container">$R$</span> there is the natural monomorphism <span class="math-container">$\mathrm{in} \colon R \to \mathrm{End}(R_{add}): r \mapsto (x \mapsto rx)$</span>, where <span class="math-container">$R_{add}$</span> is an additive abelian group ( rings are assumed to be as... | The rings, you call ``complete'' are known as <span class="math-container">$E$</span>-rings (as Ulrich Pennig mentioned in the comments).
Some comments on your questions
<ol>
<li>There are too many results on the <span class="math-container">$E$</span>-rings to list them here and I'd rather direct you to the book by Gö... | In the finitely generated case, it's relatively easy to see from the structure theorem that the only finitely generated abelian groups <span class="math-container">$A$</span> with an isomorphism <span class="math-container">$A \cong \text{End}(A)$</span> are the cyclic ones.
Here is a sketch of the proof of this claim ... | https://mathoverflow.net |
331,676 | [
"https://stats.stackexchange.com/questions/331676",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/76873/"
] | If all you are doing is re-sampling from the empirical distribution, why not just study the empirical distribution? For example instead of studying the variability by repeated sampling, why not just quantify the variability from the empirical distribution?
| Bootstrapping (or other resampling) is an experimental method to estimate the distribution of a statistic.
It is a very straightforward and easy method (it just means you compute with many random variants of the sample data in order to obtain, an estimate of, the desired distribution of the statistic).
You most likely ... | The key thing is that the bootstrap isn't really about figuring out features of the distribution of the <em>data</em>, but rather figuring out features of an <em>estimator</em> applied to the data.
Something like empirical distribution function will tell you a fairly good estimate of the CDF from which the data came ... | https://stats.stackexchange.com |
119,778 | [
"https://physics.stackexchange.com/questions/119778",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/50694/"
] | I was re-studying university physics last week, I'm now in the chapter about kinematics in 2 dimensions and specifically the one treating projectile motion. In page 86 of his book (Serway - Physics for scientists and engineers) he derives the equation of the range of the projectile motion to be: $$R=\frac{{v_i}^2\sin2\... | I don't understand question 1: where does he equate a speed to a position?
As far as question 2 is concerned, it is basically what DavePhD said, but maybe I can extend it a bit more saying something about the conservation of linear momentum:
Along the x-direction, there is no external force (because gravity points do... | The force of gravity is in the y direction only.
There is no force on the particle in the x direction.
Therefore, the x-component of velocity is constant.
| https://physics.stackexchange.com |
30,430 | [
"https://electronics.stackexchange.com/questions/30430",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1240/"
] | I'm using PIC18F4680 and am having problems running it form a 40 MHz external clock source or 10 MHz crystal in HSPLL mode. Using 10 MHz crystal in HS mode seems to be fine and 5 MHz crystal in HSPLL mode also works fine.
What happens is that the PIC starts, works for a few seconds and then shuts down for a while and ... | This is some pretty old advice, and I don't know if it will be relevant for your micro, but about 4 years ago I did a project with a PIC18F which encountered strange spurious resets. After reading the report and re-jogging my memory here is what seems to have solved it:
Do you have the <code>Low Voltage Programming E... | With a setup like this it is going to be almost impossible for us to say exactly what is going wrong. What we can say, however, is what is wrong. There are a lot of things wrong, or at least not as right as it cold be. Any one of these things could be the real source of your problem, but it also could require the co... | https://electronics.stackexchange.com |
632,555 | [
"https://physics.stackexchange.com/questions/632555",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/297608/"
] | Say you've tied a string to a bucket handle and you're swinging the bucket around.
It has translational kinetic energy, of course, but it is also rotating (at the same angular velocity as the rotation of the string about its pivot).
Is this rotation considered when doing energy calculations?
Is it ignored because there... | You must consider both motions translating and rotation about the center of mass <br/>
for translatory motion use <span class="math-container">$\frac{mv^2}{2}$</span> <br/>
for rotation about center of mass use <span class="math-container">$\frac{I{\omega}^2}{2}$</span> <br/>
the sum of both energies gives the total ki... | If you swing an object such as a bucket on a string, it undergoes both circular and rotational motion, and you should take both into account when performing energy calculations.
By circular motion, I mean motion about the centre of the circle. By rotational motion, I mean motion around the bucket's centre of mass.
If t... | https://physics.stackexchange.com |
299,992 | [
"https://stats.stackexchange.com/questions/299992",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/160011/"
] | I have read other posts here.
But i am still confused. As far as i understood there are two procedures:
1) Split data into train, validation and test set .
In this case my concern is that once we have chosen the model, do we combine the Validation and Train set to train the selected model and then report the error on ... | 1) Generally, yes, you can add the train and validation sets for final training because you'd be throwing out the validation set otherwise (actually not entirely since you'd used information from it to select a model, but pretty much).
2) From the model trained on the entire dataset, expect performance equal to the av... | To report on the quality of your model in machine learning, you always split the data into two parts, the training dataset (typically 2/3 of the data) and the test dataset (typically 1/3 of the data). With the training dataset you fit the model and with the test dataset you evaluate your model. You report the predictio... | https://stats.stackexchange.com |
638,726 | [
"https://physics.stackexchange.com/questions/638726",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/295378/"
] | Hi Sorry if this is a simple question I just can't seen to get my head at what law is being violated due to a neutral pion decaying into a photon (I have an inclining its to do with 4-vector momentum however that further makes the neutral pion decaying into 2 photons less sense to me.) If anyone could help that would b... | The pion has a rest frame where it has 0 momentum. Photons do not have rest frames, so if the pion decays into one photon, that photon will have momentum in every frame. So momentum cannot be conserved. With two photons, the net momentum between them can be zero, and so momentum conservation in the pion's rest frame... | <blockquote>
Why can a neutral pion decay into 2 photons but not one?
</blockquote>
It is due to the law of conservation of energy and momentum. A particle with a given mass cannot "decay" to only one smaller mass particle because the decay to one particle at the center of mass would not conserve energy, ... | https://physics.stackexchange.com |
2,988,539 | [
"https://math.stackexchange.com/questions/2988539",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/39106/"
] | Consider the following double sum identities
<span class="math-container">$$\sum_{n=0}^\infty\sum_{m=0}^n a(m,n-m) = \sum_{p=0}^\infty\sum_{q=0}^\infty a(p,q) = \sum_{r=0}^\infty\sum_{s=0}^{\lfloor{r/2}\rfloor} a(s,r-2s)$$</span>
The first identity I understand. The relation between <span class="math-container">$(n,m... | Write <span class="math-container">$K = \{(r, s) \colon r, s \in \mathbb{N}, \ r \geqslant 2s\}$</span>. The functions:
<span class="math-container">\begin{align*}
& f \colon \mathbb{N}^2 \to K, \ (p, q) \mapsto (2p + q, p), \\
& g \colon K \to \mathbb{N}^2, \ (r, s) \mapsto (s, r - 2s)
\end{align*}</span>
are ... | <blockquote>
Considering formal series we obtain
<span class="math-container">\begin{align*}
\color{blue}{\sum_{r=0}^\infty\sum_{s=r}^{\left\lfloor r/2\right\rfloor} a(s,r-2s)}
&=\sum_{r=0}^\infty\sum_{s=0}^r a(s,2r-2s)+\sum_{r=0}^\infty\sum_{s=0}^r a(s,2r+1-2s)\tag{1}\\
&=\sum_{0\leq s\leq r\leq \infty}\l... | https://math.stackexchange.com |
471,521 | [
"https://electronics.stackexchange.com/questions/471521",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/92462/"
] | In Intel's Pentium Processor Family Developer Manual, regarding the CPU clock, it says that "it is recommended that CLK begin toggling within 150 ms after VCC reaches its proper operating level. This recommendation is to ensure long-term reliability of the device."
From a circuit implementation perspective, how might ... | The clock undoubtedly operates charge pumps within the chip that provide bias voltages for various functional areas. Without proper bias, leakage currents are probably higher than the transistors are really designed to handle long-term.
| If tristate bus contention can occur, the shoot thru energy temperature rise would be of the same amount of time. It seems the power on reset is not enough.
| https://electronics.stackexchange.com |
688,000 | [
"https://physics.stackexchange.com/questions/688000",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/217903/"
] | If the following is a solution to the Dirac equation
<span class="math-container">$$(i\gamma^\mu\partial_\mu - m)(\psi_1+\psi_2)=0$$</span>
Therefore after distributing
<span class="math-container">$$(i\gamma^\mu\partial_\mu - m)\psi_1+(i\gamma^\mu\partial_\mu - m)\psi_2=0$$</span>
Can we assume that <span class="math-... | I think that the answers you quoted are all accurate enough.
There was never a time when all particle types propagated unimpeded at <span class="math-container">$c$</span>. In the early universe, the particle density was high, and mean free paths were short. As the energy density dropped and matter clumped, most partic... | You can see the difference between particles with and without invariant mass looking at the Energy-momentum relation <span class="math-container">${E^2}=(pc){^2}+(m_0c^2)^2$</span>.
The total energy <span class="math-container">$E$</span> of a particle with zero invariant mass <span class="math-container">$m_0$</span> ... | https://physics.stackexchange.com |
211,343 | [
"https://mathoverflow.net/questions/211343",
"https://mathoverflow.net",
"https://mathoverflow.net/users/31310/"
] | Let $H,H'\subset\mathbb{R}^m$ be two hyperplanes with unit normal-vector,
and let $P\subset\mathbb{R^m}$ be a convex polytope (defined via its corners $v_0, ... , v_n$, where $n\ge m$).
Let's further assume that
<ul>
<li>$dist(v_i,H) = 0,\ i\in [0,k]\ \wedge\ dist(v_i,H) \gt 0,\ i\in[k+1,n]$</li>
<li>$dist(v_j,H... | No. Take a triangle $v_0v_1v_2$ on the plane, $H'$ is its side $v_0v_1$, $H$ is almost another side $v_0v_2$. Then $\sum_{i=0}^2 {\rm dist}\, (v_i,H')$ is just a length of altitude from $v_2$, $\sum_{i=0}^2 {\rm dist}\, (v_i,H)$ is almost the length of altitude from $v_1$, which may be less than that from $v_2$.
As f... | It just occured to me that the question can be answered in the affirmative way for the following reasons:
<ul>
<li>the order relation doesn't change if the distance sum is divided by some positive constant value $c$. </li>
<li>if we divide the distance sums by $n+1$, then that value equals the distance of the vertic... | https://mathoverflow.net |
75,411 | [
"https://math.stackexchange.com/questions/75411",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/11921/"
] | Let $H$ be a simple group of order $60$. I am trying to see why it is embedded in $A_6$.
$H$ must have $6$ Sylow-$5$ subgroups and $H$ acting by conjugation on these subgroups gives an embedding of $H$ into $S_6$. But this is as far as i have
gone.
Please give me only a hint.
| Identify $H$ with its embedded copy in $S_6$ and consider $H \cap A_6$.
| Hint: there exists a canonical embedding of $S_5$ in $S_6$. That is, $S_5\leq S_6$. Why does this embedding imply that $A_5\leq A_6$?
| https://math.stackexchange.com |
470,163 | [
"https://electronics.stackexchange.com/questions/470163",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/80821/"
] | Consider the following 2 use cases:
<ol>
<li>Fully electric vehicle with 2 different insulated voltage systems: 1 high voltage @1000V DC insulated from chassis and 24VDC system with minus pole (-) at chassis. Would PE cable (connected to chassis) need to be shielded? If yes, then why?</li>
<li>Single phase house suppl... | I see no reason to shield the grounding (return) that is connected to chassis.
As standard design practice, we twist the supply (hot) line with its return.
If there is a need for an overall shield around that twisted pair bundle, then the shield is connected to chassis at both ends. The only reason for the shield ... | The problem with shielding any sort of safety grounding is <strong>what do you shield it <em>with?</em></strong>
I mean, you're out of groundy things. You have vehicle chassis or your local earthing rods, where do you get a better ground than that? You don't.
If your PE shield needs shielding, then what you rea... | https://electronics.stackexchange.com |
38,201 | [
"https://stats.stackexchange.com/questions/38201",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/14125/"
] | This might be a question for the programmers, but I thought I would ask here first. Im comparing browsing pressure on plants between sites. Ive a value to indicate Browsing Pressure and count data of trees that have been damaged between locations. Ive been using Crawleys R example (page 574) regarding sex ratios and... | Here is a solution.
First, I replaced <code>MS1</code> with <code>M2</code> since there is no varibale with the name <code>MS1</code> in your example data.
<pre><code>attach(data)
p1<-M2/(M2+M1)
y<-cbind(M2,M1)
</code></pre>
The model:
<pre><code>GM1<-glm(y~BPT,family=binomial (logit),data=data)
</code></p... | It looks like your data object <code>y</code> and the vector of predicted values you created (<code>xv</code>) are different length. If you do <code>dim(y)</code> it will show that you have 60 rows, but if you do <code>length(xv)</code> the vector is 71 elements long. If you just run <code>predict(GM1,list(density=ex... | https://stats.stackexchange.com |
694,503 | [
"https://physics.stackexchange.com/questions/694503",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/328110/"
] | <h2>Rocks that float and the madness that ensues</h2>
Hello, this is a question in two parts:
1- If an object could have its weight reduced to zero, how high would it float up? Let's say a 20kg rock having an anti-gravity handwavium of 20kg upwards. The maximum height would be determined by its volume?
2- If I jumped f... | The "stone" is pushed upwards by (following Archimedes' principle) a force <span class="math-container">$F=\rho V_{stone}g$</span>, where <span class="math-container">$\rho$</span> denotes the density of the air surrounding the stone (depends on the height of the stone) and <span class="math-container">$g$</s... | <ol>
<li>Up Up an away into space.</li>
<li>0+80Kg=80 Kg</li>
</ol>
| https://physics.stackexchange.com |
161,456 | [
"https://physics.stackexchange.com/questions/161456",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | <blockquote>
Given the wave function $$\psi(x)=A\exp\left[-a
\left(\frac{mx^{2}}{\hbar}+it\right)\right]$$ I would like to calculate $\sigma_{p}$.
</blockquote>
\begin{align}\langle p\rangle &=\int \psi^{\star}\left(\frac{\hbar}{i}\frac{\partial}{\partial x}\right)\psi dx\\
&=2imaA^{2}\int xe^{-kx^{2}}dx\\
&... | There is an error in my calculation.
In fact: $\int ^{\infty}_{-\infty} e^{-kx^{2}}dx = \sqrt{\dfrac{\pi}{k}}$
So $$\langle \widehat p^{2} \rangle=-2A^{2}ma\hbar [\frac{-1}{2}\sqrt{\frac{\pi}{k}}]=ma\hbar$$ given that $A^{2}=\sqrt{\frac{2am}{\pi\hbar}}$ as calculated using the normalization condition.
This, can be ... | You have made an error in your calculation of ⟨p2⟩. You've evaluated two integrals, the second of which is off by a factor of two.
| https://physics.stackexchange.com |
2,494,767 | [
"https://math.stackexchange.com/questions/2494767",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/399345/"
] | I don't understand the following limit
$$\lim_{ x \rightarrow 0 } \frac{ \frac{1}{1+x} - \cos x }{ x }$$
Can someone please help me ?
| $$\frac{\frac{1}{1+x}-\cos x}{x}=\frac{\frac{1-\cos x-x\cos x}{1+x}}x=\frac{2\sin ^2\frac x2-x\cos x}{x(1+x)}=\frac{\sin \frac x2}{1+x}\cdot\frac{\sin \frac x2}{\frac x2}-\frac{\cos x}{1+x}$$
Now $$\lim_{x\to 0} \frac{\sin \frac x2}{1+x}\cdot \frac{\sin \frac x2}{\frac x2}=0\cdot 1=0$$
And $$\lim_{x\to 0}-\frac{\cos x}... | <strong>HINT:</strong>
Multiply above and below by $1+x$ to get
$$\frac{1 - \cos x - x \cos x}{(1+x)x},$$
this can be equivalently expressed as the product of two limit given by
$$ \lim_{x \rightarrow 0} \frac{1}{1+x} \; \lim_{x \rightarrow 0} \frac{1 - \cos x - x \cos x}{x}. $$
The first limit is obvious. The ... | https://math.stackexchange.com |
66,634 | [
"https://mathoverflow.net/questions/66634",
"https://mathoverflow.net",
"https://mathoverflow.net/users/7139/"
] | Here is a quote from <em>Lectures on Ergodic Theory</em> by Halmos:
<blockquote>
I cannot resist the temptation of
concluding these comments with an
alternative "proof" of the ergodic
theorem. If $f$ is a complex valued
function on the nonnegative integers,
write $\int f(n)dn=\lim
> \frac{1}{n}\sum_{j=1... | I feel the answer is "no", at least while staying true to the spirit of Halmos's text. Halmos's "proof", if valid, would imply something far stronger (and false), namely that $\lim_{N \to \infty} \frac{1}{N} \sum_{n=1}^N f(T_n x)$ converged for almost every x, where $T_1, T_2, \ldots$ are an arbitrary sequence of meas... | There is a short proof in Katok's book. Introduction to the modern theory of dynamical systems [Book]
| https://mathoverflow.net |
265,522 | [
"https://physics.stackexchange.com/questions/265522",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/-1/"
] | [Sorry about the misleading title, as the query isn't entirely about half-life, but I couldn't find any better way to condense my question to make a brief enough title anyways..... and]
Radioactive decay is [as far as I know] an example of a First Order reaction. If I'm not mistaken, half-life [represented by t1⁄2] is... | The number of atoms in your radioactive sample falls exponentially with time, so we get something like:
$$ N = N_0 e^{-t/\tau} $$
where $\tau$ is a characteristic constant decay time called the mean lifetime. The half life is then defined by:
$$ \frac{1}{2} = e^{-t_{1/2}/\tau} $$
or:
$$ t_{1/2} = \tau\ln 2 $$
By ... | Half life is a common physics misconception. Half life does not actually mean the cencentration of a substance being reduced to half by radio active disintegration. But it actially means the activity of the substance being reduced to half. For example if a sample of wood is found have uranium content with 5000 disinte... | https://physics.stackexchange.com |
459,699 | [
"https://stats.stackexchange.com/questions/459699",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/280671/"
] | As far as I understand the <code>sum(variances)</code> should always be equal to the <code>sum(explained_variance_)</code>, however when I run:
<pre><code>data = [[1, 4], [5, 1], [1, 4], [6, 8], [7, 1], [2,3], [3, 4], [1, 5], [3, 9]]
model = PCA(2)
model.fit(data)
variances = np.var(data, axis=0)
print(sum(var... | <code>sklearn.decomposition.PCA</code> assumes that the model applied to a sample taken from a population, therefore when estimating the variances (actually the covariance matrice, but the variance sits in the diagonal) for unbiased estimation it uses <span class="math-container">$n - 1$</span> instead of <span class="... | For an unknown reason, you have to multiply the <code>sklearn</code> <code>explained_variance_</code> by <span class="math-container">$\frac{n - 1}{n}$</span> where <span class="math-container">$n$</span> is the number of observations to get the actual variance value. In your case, you have <span class="math-container"... | https://stats.stackexchange.com |
334,691 | [
"https://physics.stackexchange.com/questions/334691",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/75518/"
] | Suppose we have a classical statistical problem with canonical coordinates $\vec{q} = (q_1, q_2, \dots, q_n)$ and $\vec{p} = (p_1, p_2, \dots, p_n)$ such that they fulfill the usual Poisson brackets:
\begin{align}
\{ q_i, p_j \} & = \delta_{i,j} \\
\{ q_i, q_j \} & = 0 \\
\{ p_i, p_j \} & = 0 \\... | <strong>Why There is a Need for a Further Axiom</strong>
To derive Liouville's equation, you indeed need another axiom further to your assumptions. Something like: "there is no nett creation or destruction of any particle of any species throughout the particle system state evolution". The easiest way to understand th... | The probability for the system to be in the phase cell $d\Gamma(t)$ at time $t$ is $$ P(t)=\rho(q,p,t)d\Gamma(t). $$
The time evolution of the trajectories and the possible explicit time dependence of $\rho$ is also considered into this. Now infinitesimal $dt$ time later $$ P(t+dt)=\rho(q+dq,p+dp,t+dt)d\Gamma(t+dt), $... | https://physics.stackexchange.com |
388,611 | [
"https://stats.stackexchange.com/questions/388611",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/234958/"
] | I'm not even sure I'm phrasing the question properly, please let me know if there is any standard terms around this type of problem.
I'm trying to find an average number of attempts it would take to find a randomly placed pixel within a fixed size element. If a wrong pixel is chosen, it is removed from the choices.
S... | You're looking to calculate expected value of a variable <span class="math-container">$X$</span>, which we define as number of clicks until success.
<span class="math-container">$$E[X] = \sum_{i=1}^{10,000} i \cdot Pr(X = i)$$</span>
Note that for each possible <span class="math-container">$i \in \{1,2,...,10000\}$<... | Well, simply write the expected value formula, i.e. <span class="math-container">$\sum{xp(x)}$</span>:
<span class="math-container">$$E[X]=1\times\frac{1}{10000}+2\times\frac{9999}{10000}\times\frac{1}{9999}+...=\frac{10000\times10001}{2}\times\frac{1}{10000}=\frac{10001}{2}$$</span>
where <span class="math-containe... | https://stats.stackexchange.com |
65,425 | [
"https://softwareengineering.stackexchange.com/questions/65425",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/4112/"
] | As part of a review of all job descriptions, my company has decided to include the following as a key output:
<blockquote>
website development completed on
time, within specification and <strong>error
free</strong>
</blockquote>
Given that specifications regularly change, there is no formal change control proce... | "Error Free" is <strong>far too subjective</strong>. One man's "Unfufilled feature request" is another man's "Error". Something like "Should substantially meet design specs" would be more appropriate. I've never actually seen what you describe in a job description. I've seen it for <em>contract work</em>, but not f... | I'll take an opposing position to most answers and say it's absolutely reasonable and realistic.
Will all development be completed on time? Of course it won't, not always.
Will all development be completed within specification? You'd like to hope so, but sometimes that will simply not be possible and you'll have to f... | https://softwareengineering.stackexchange.com |
409,755 | [
"https://stats.stackexchange.com/questions/409755",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/218474/"
] | I would like to ask for your help concerning the following issue.
In a nutshell, I would like to know, how demeaning works in a panel regression with two (separate) fixed effects.
Let us assume I have the textbook balanced panel with <span class="math-container">$N=100$</span> individuals <span class="math-container">... | If you use demean approach (which is theoretically right), then you have to do demean your data both cross sectionally and time series (irrespective of the order). See how it is works.
Assume following regression model:
<span class="math-container">$$y_{it} = u_i + \nu_t + \beta X_{it} + e_{it} \,\,\,\,\, i = 1, 2,... | Been trying to figure this out myself and saw the only other answer to this question is wrong here. You need to subtract time and group means but then add the overall mean back in. See Greene (2012) on Fixed Time and Group Effects (section 11.4.4). You can try it out yourself and see that just subtracting the time and ... | https://stats.stackexchange.com |
3,233,495 | [
"https://math.stackexchange.com/questions/3233495",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/641030/"
] | Show that <span class="math-container">$f(x,y)=\frac{1}{y}$</span> is differentiable in its domain, i.e.
<span class="math-container">$\lim_{(x,y) \rightarrow (x_0,y_0)} \frac{|\frac{1}{y} - \frac{1}{y_0} + \frac{1}{y_0^2}(y - y_0)|}{||(x,y)-(x_0,y_0)||}=0$</span>
I tried this:
<span class="math-container">$|\frac{... | <span class="math-container">$$\frac{|y-y_0|\left|\frac{1}{y_0^2}-\frac{1}{y_0y}\right|}{\sqrt{(x-x_0)^2+(y-y_0)^2}}\leq \frac{|y-y_0|\left|\frac{1}{y_0^2}-\frac{1}{y_0y}\right|}{|y-y_0|}=\left|\frac{1}{y_0^2}-\frac{1}{y_0y}\right|\rightarrow 0$$</span> as <span class="math-container">$(x,y)\rightarrow (x,y_0),$</span>... | If <span class="math-container">$f\colon U\to \mathbb R$</span> is a differentiable function on some subset <span class="math-container">$U\subset\mathbb R$</span>, then <span class="math-container">$g\colon \mathbb R\times U \to \mathbb R$</span> given by <span class="math-container">$(x,y)\mapsto f(y)$</span> is as w... | https://math.stackexchange.com |
1,026 | [
"https://physics.stackexchange.com/questions/1026",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/526/"
] | The weighing scales in my kitchen are currently showing 0 Kg. However, there is a column of air between the scales and the ceiling that is presumably exerting pressure on them. If I were to place those scales in a vacuum, would those scales show a negative weight?
| They would show only a very tiny <del>negative</del> positive weight. A typical kitchen scale has air above and below the weighing pan, and the pressure is very nearly the same because the thickness of the weighing pan is millimeters and the height of the atmosphere is a million times that. The net force of the press... | It would vary from weighing scale to weighing scale. In my experience, most of the scales subtract the weight of the "tare", which is the thing that you put your "thing to be weighed on". The scales which use this system will show a noticeable amount of negative weight.
However the types which do not subtract the amou... | https://physics.stackexchange.com |
552,342 | [
"https://physics.stackexchange.com/questions/552342",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/264558/"
] | Can we just say that if between 2 points in some given circuit, there's no load, then the potential at those 2 points are same?
| It depends on what you mean by “no load”.
Normally when we say “no load”, we’re saying there is nothing in the circuit drawing current. For example if nothing is connected across the terminals of a battery we say there is “no load” connected to the battery. Obviously in this case there’s a potential difference (volt... | It is better to think of this in terms of the p.d across those two points. I'll assume you are talking about ideal wires. Potential difference(voltage) is the work done moving a charge between two points. If the wires are ideal, they have no resistance, so no work is done when charges move between places on a wire. How... | https://physics.stackexchange.com |
666,388 | [
"https://physics.stackexchange.com/questions/666388",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/119231/"
] | So the earth is constantly rotating but it doesn't need a force to rotate. It'll rotate indefinitely.(?) But we and other masses on earth need a force on us to continue rotating along with earth? And if earth rotated a lot faster then we would notice it because we would not be planted to same place on earth?
| Assuming the earth has no external torque applied to it then the earth would rotate indefinitely. This is the conservation of angular momentum at play.
We stay on the earth's surface because we also have angular momentum, angular momentum such that our angular velocity matches that of the earth. If we didn't we would f... | The Earth doesn't need a force to make it continue to rotate- quite the opposite: it will continue to rotate unless a force is applied to stop it.
In fact the Earth's rotation about its axis will eventually slow to a halt as a consequence of its interaction with the Moon, but that will take billions of years.
The force... | https://physics.stackexchange.com |
537,980 | [
"https://electronics.stackexchange.com/questions/537980",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/271521/"
] | According to my research, mostly N-Channel is used for low side switching and P-Channel is used for high side switching. But if I want to use N-Channel for high side switching, what are the ways and what are the drawbacks of using N-channel for high side switching.
What I understand is the use of some kind of charge pu... | You will need a voltage that is well above the power rail to supply enough gate voltage to turn the N mosfet full on.
In PWM H-bridges this is often done with a charge pump which is pumped by the PWM cycle.
If you want the N mosfet to be on in a stationary situation you will have to provide that higher voltage by some ... | You can drive a high-side NMOS switch with special gate driver. It takes care of generating the high voltage necessary to fully turn on the high side NMOS. The search term is "high side gate driver."
PMOS is OK sometimes but because of the way the physics and chemistry of semiconductors works NMOS will always... | https://electronics.stackexchange.com |
705,805 | [
"https://physics.stackexchange.com/questions/705805",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/334074/"
] | A superconducting magnet works by energizing a superconducting magnetic coil, then short circuiting it to make a closed loop. Would it be possible to transfer the current back and forth between two superconducting magnets? This would allow perpetual motion, since you can move a magnet or a piece of metal back and forth... | A perpetual motion machine that merely 100% conserves energy and thus operates forever like a perfect flywheel is of little interest and is not the same as as a perpetual motion where you can continually extract said energy from it ad infinitum for use.
In reality, however, there are always losses and in your example i... | When current changes in time, the medium is no longer exactly superconducting. There are energy losses, if not due to internal dissipation mechanisms, then due to EM radiation of the changing current.
| https://physics.stackexchange.com |
7,912 | [
"https://chemistry.stackexchange.com/questions/7912",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/4223/"
] | I usually make tea by adding two spoons of tea powder to water at room temp. and start to heat it. My friend said it will be better to add the powder once the water starts boiling. She said that it will dissolve tea more easily because of the sudden temperature difference experienced by tea powder.
Does it make a diff... | <strong>I would say that your method is actually quicker (if that's what you mean by 'better').</strong> My reasoning is as follows: the solubility of the powder in water increases with increasing temperature, as does the dissolution rate but the dissolution rate remains finite all the time.
1) If you add the powder ... | Your friend is right. As the temprature increases, the solubility of tea increases. Hence your tea will dissolve more easily when the water is heated before adding the tea powder, rather than your method.
| https://chemistry.stackexchange.com |
168,566 | [
"https://physics.stackexchange.com/questions/168566",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/74630/"
] | In linear elasticity theory the stress tensor $\sigma$ is related to the strain tensor $\epsilon$ via the elastic tensor $C$. Specifically
$$
\sigma_{ij} = C_{ijkl} \epsilon_{kl}
$$
Because $\sigma$ and $\epsilon$ are both symmetric second rank tensors,
$\sigma_{ij} = \sigma_{ji}$ and $\epsilon_{kl} = \epsilon_{lk}$... | You should start with the strain energy density $\psi$, then define:
$$
C_{ijkl} = \frac{\partial^2 \psi}{\partial \epsilon_{ij}\partial \epsilon_{kl}}, $$
and then define $$
\sigma_{ij} = C_{ijkl} \epsilon_{kl}
$$
The remainder of my answer will be about explaining why you have to do it that way. Firstly it is phys... | Since <span class="math-container">$\epsilon$</span> is a symmetric tensor, it has 6 independent components that determine it. Hence use a multi-index <span class="math-container">$I\in\{(i,j)|1\leq i\leq j\leq 3\}$</span> to denote them. The strain energy density then becomes (perhaps one has to be careful with "... | https://physics.stackexchange.com |
321,114 | [
"https://electronics.stackexchange.com/questions/321114",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/120722/"
] | I have a component that has a very large array signal in it (a couple kilobits) and I currently write and read to it in only one component. I have checked in Vivado if this uses too much resources, and it doesn't. My question is I want to have a sub-component that can access this array (only read from it). If I merely ... | When you look at the design as a schematic, you might get a false sense that borders exist between your individual modules (or entities). But, by default Vivado flattens your design - which means your design is essentially treated as one big layout. All sub-component boundaries are ignored. So, just think of it as if y... | When you have a large array in HDL design (whether VHDL or Verilog) the synthesizer will often recognise it as a "ram" and implement it using block ram rather than a huge pile of registers.
However it can only do this in a limited subset of cases, if it can't map it to a ram you will end up with a huge pile of registe... | https://electronics.stackexchange.com |
142,262 | [
"https://chemistry.stackexchange.com/questions/142262",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/89178/"
] | <blockquote>
<strong>A</strong> is beaker with <span class="math-container">$\pu{0.1 M}$</span> <span class="math-container">$\pu{25 cm^3}$</span> solution of <span class="math-container">$\ce{NH3}.$</span> <strong>B</strong> is beaker with <span class="math-container">$\pu{0.1 M}$</span> <span class="math-container">$... | As the amounts of substance in the final solution are known to be <span class="math-container">$n(\ce{NH3}) = \pu{2 mmol},$</span> and <span class="math-container">$n(\ce{NH4^+}) = \pu{0.5 mmol},$</span> you may simply use the definition of the constant <span class="math-container">$K_\mathrm{b}:$</span>
<span class="m... | There is an accepted answer for this question. I think there is an another way to solve the problem using basic principles.
Beaker <strong>A</strong> contains <span class="math-container">$\pu{25 cm^3}$</span> of <span class="math-container">$\pu{0.1 M}$</span> <span class="math-container">$\ce{NH3}$</span> solution wh... | https://chemistry.stackexchange.com |
7,949 | [
"https://quant.stackexchange.com/questions/7949",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/3058/"
] | I'm trying to price a fixed rate bond one year from now on.
The bond is the PEUGOT 7 ⅜ 03/06/18, whose ISIN code is FR0011439975. I'm using such a specific example because in this way everyone can try to reproduce results.
I am using these instruments:
<ul>
<li>Bloomberg <code>YAS</code> function</li>
<li><code>RQua... | in RQuantLib you need to set the evaluation date using setEvaluationDate()
This is the date used by all QuantLib valuation functions in your case 10 May 2014.
| Let's approximate the time to maturity to be 3 years and 10 months. Assume that coupon is paid on March 6 each year. Let face value $F=100$ and coupon $c=0.07375F$. Let the discount factor be $d(0,T)=e^{−r T}$ where $r=0.06535$. The price of the bond is
$$ce^{−10/12 \bullet r}+ce^{−22/12 \bullet r}+ce^{−34/12 \bullet r... | https://quant.stackexchange.com |
3,104 | [
"https://mathoverflow.net/questions/3104",
"https://mathoverflow.net",
"https://mathoverflow.net/users/412/"
] | Caveat: I don't really know anything about PDEs, so this question might not make sense.
In complex analysis class we've been learning about the solution to Dirichlet's problem for the Laplace equation on bounded domains with nice (smooth) boundary. My sketchy understanding of the history of this problem (gleaned from ... | Well, I don't understand the electrostatics, but here is another physical heuristic:
Impose a temperature distribution at the exterior, and measure (after some time has passed) the temperature in the interior. This gives a harmonic function extending the exterior temperature. [What's the electrostatic analogue? Former... | Physical intuition tells us that the potential determined by a distribution of charge on the boundary will minimize the energy. If D is a bounded domain in R^d (d=3 in real applications), then the energy of a potential u on D is given by Dirichlet's integral:
DI(u) = \int_D |grad(u)|^2 dx
Thus, if we minimize DI(u) ... | https://mathoverflow.net |
59,322 | [
"https://softwareengineering.stackexchange.com/questions/59322",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/587/"
] | Our company ships a range of desktop products for Windows and lots of Linux users complain on forums that we should have been written versions of our products for Linux years ago and the reason why we don't do that is
<ul>
<li>we're a greedy corporation</li>
<li>all our technical specialists are underqualified idiots<... | Keep in mind the majority of people are employees, and thus don't live in a world where they need to care about making a profit. They show up at work, do their thing, and go home, never really giving a thought to how the whole process works. And while very smart, a lot of techies are positively ignorant about busines... | There are two things to consider here I think:
The first is that, in a way, they are right. Writing cross platform C++ isn't that hard <strong>if you planned for it from the beginning</strong>. This is almost certainly the problem you're seeing. Most open source applications (most of the applications a Linux user touc... | https://softwareengineering.stackexchange.com |
126,103 | [
"https://electronics.stackexchange.com/questions/126103",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/32770/"
] | If I have, for example, 4-8 (or more) inputs that I need to AND together (or even NAND or OR) should I look for larger input devices like the 7430 NAND or is common practice to daisy chain multiple quad 2-inputs together?
I'm reading the ZX Spectrum ULA book and a lot of the circuits seem to have up to 8 inputs going ... | Try searching yourself at a distributor such as Digikey to get some idea of availability.
I'll take you through a step-by-step if I was looking for, say, a NOR gate with at least 4 inputs. I'll be primarily interested in 4000 series CMOS or 74HC CMOS families (usually it would not be for the same application).
Firs... | There were quite a few 3-input gates made, with three circuits per package. This meant that 12 pins would be needed (3 inputs, 1 output) x 3 and adding VCC and GND uses up all 14 pins in a 14-pin package which was very popular at the time these parts were designed 40 some years ago. Here are the 3-input logic ICs I a... | https://electronics.stackexchange.com |
495,489 | [
"https://physics.stackexchange.com/questions/495489",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/233058/"
] | The Universal Law of Gravitation states that the module of the force, <span class="math-container">$F$</span> is
<span class="math-container">$$F = \frac{GmM}{r^2},$$</span>
where <span class="math-container">$m$</span> and <span class="math-container">$M$</span> are the mass of the two objects and <span class="math-c... | At <span class="math-container">$r=0$</span>, the force is <span class="math-container">$+\infty$</span>, and the potential energy is <span class="math-container">$-\infty$</span>. This arises if you consider point masses, which we model mathematically using Dirac-delta distributions. Physically, we cannot have two poi... | The thing is, that, as every equation, these are based on model views. The model in this case includes the representation of the mass object as a point mass. Hence we are able to attribute to it some coordinate and measure distances between objects, which, in fact, consist of several gravitating "sub"objects. One of th... | https://physics.stackexchange.com |
73,568 | [
"https://mathoverflow.net/questions/73568",
"https://mathoverflow.net",
"https://mathoverflow.net/users/13070/"
] | Dear All!
At the time when Lyndon and Schupp wrote their book there was an open question:
Question: Does every finitely presented group with soluble word problem embed in a finitely presented simple group?
Is it still open? Could you hint at some useful references about this? Thanks!
| I believe it is still open. By the Boone-Higman Theorem (W. W. Boone and G. Higman, "An algebraic characterization of the solvability of the word problem", J. Austral. Math. Soc. 18, 41-53 (1974)), a finitely presented group has solvable word problem if and only if it can be embedded in a simple group that can be embed... | There is a strengthening of the Boone-Higman result, due to Thompson. He showed that we can take the simple group to be finitely generated. In full, this reads:
"A finitely presented group has solvable word problem if and only if it can be embedded in a finitely generated simple group that can be embedded in a finitel... | https://mathoverflow.net |
673,824 | [
"https://math.stackexchange.com/questions/673824",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/80219/"
] | I have this question posted by professor in graduate Number Theory class. First he asked for proof that the sum of cube of 3 consecutive integers is divisible by 3, which is very easy to prove, but then he continued by asking to prove its generalization, ie., n | 1^n + 2^n + 3^n + ... + n^n.
Here you can easily find a... | Since this is a graduate level number theory class, I think it's safe to assume that you are familiar with modulo arithmetic?
Given any list of $n$ consecutive integers, $a, a+1, a+2, \dots, a+n-1$, modulo $n$ this list is equivalent to $0,1,2,3,\dots,n-1$ modulo $n$. (Note that I am not saying $a \equiv 0 \pmod{n}$)... | The remainders modulo $2k+1$ can be (re)written as $0,\pm1,\pm2,\ldots,\pm k$. By rising them each to any positive odd power of our choosing, they will maintain their sign, while their absolute values will be pair-wise equal, so ultimately their sum will be divisible through $n=2k+1$.
| https://math.stackexchange.com |
39,549 | [
"https://chemistry.stackexchange.com/questions/39549",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/21183/"
] | I was introduced to the concept of balancing chemical equations in school and I did some practice examples, which were easy and took me about 2 minutes per question. I used the systematic trial and error method and I don't really like it.
I'm worried that my teacher will give us a more difficult question, so I'm looki... | When using matrices, you are really just solving a system of equations. You can use any technique you know to solve the system of equations that a chemical equation represents. Using matrices is only one technique that may be useful for complicated equations or if you have a calculator/MATLAB on hand. In the given exam... | Always start balancing by <strong>equating the number of atoms of elements which appear only once.</strong> For example, in the equation you have mentioned, oxygen appears in both the compounds, whereas, hydrogen and carbon appear only once. So, balance <span class="math-container">$\ce{H}\;(=8)$</span> and <span class... | https://chemistry.stackexchange.com |
333,607 | [
"https://softwareengineering.stackexchange.com/questions/333607",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/185297/"
] | I have been asked to document coding standards for javascript at my organization level. Does maintaining coding standards at my organization level sound worth enough? kind of old timers? with the way, how javascript evolving with frameworks like AngularJS, should we just refer the industry standard instead of keeping t... | Coding standards generally have two aims
<ol>
<li>They try to set a common style guide for the code.<br>
Having a common style makes it easier for people to understand the codebase as a whole, because they don't get distracted by trivialities like changes in indentation or brace placement.
It is paramount that a comm... | Some observations and my conclusions:
<strong>Different styles of JS approach</strong>
While one team might work on pretty new Angular Typescript Stuff, another team might have older software to maintain. And there is team culture as well. There will be just not one standard for all. People even will look in other l... | https://softwareengineering.stackexchange.com |
334,627 | [
"https://physics.stackexchange.com/questions/334627",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/156839/"
] | I've gotten pretty good with the math when it comes to rays/optics, but I'm still missing some of the vocabulary. When a question says "A light ray is incident on glass at $30^{\circ}$" does this mean this is the angle from the normal? Here's the context of the question I'm asking this about:
<blockquote>
A sheet o... | It just means that the path of the light intersects the plane of the glass. The angle between this ray and the perpendicular or normal to the surface is the angle of incidence. The reflected ray corresponding to a given incident ray, is the ray that represents the light reflected by the surface.
| Yes it does mean the angle with the normal.. in this case an incident angle of 30 degrees would mean the incident ray (the light ray flaling on the reflecting surface) makes as angle of 30 degrees with the normal
| https://physics.stackexchange.com |
128,570 | [
"https://electronics.stackexchange.com/questions/128570",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/45569/"
] | So I was thinking about making a basic Highpass filter. I was wondering if there was any reason to use an RL configuration as opposed to a CR configuration.
| I'd use both a transistor between the FPGA and the relays to reduce the currents through the FPGA, and add a flyback diode across the relays to protect the transistor.
| Since the FPGA gpio pins only will be used as outputs an easy solution would be to use N-MOS transistors as a simple low side switches to control the relays.
| https://electronics.stackexchange.com |
14,358 | [
"https://mathoverflow.net/questions/14358",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | If one views a group as a one object category with the elements of the group as morphisms then a natural transformation between functors of such categories is an inner automorphism, i.e. if we have two group homomorphisms $f,g: A\to B$ then a natural transformation $\eta :f\to g$ is just an element $b\in B$ such that $... | The comments thread is getting a bit long, so here's an answer. The category $C(G)$ that David associates to a group $G$ (by his second recipe) has the elements of $G$ as its objects, and exactly one morphism between any given pair of objects. It's what category theorists call an indiscrete or codiscrete category, an... | I like the notation $\mathcal{B}G$ and $\mathcal{E}G$ for the two constructions of a category out of a group $G$ in David's question. $\mathcal{E}G$ is what Tom calls the <em>codiscrete category</em> $C(G)$.
Of course there is a third construction: it has $G$ as the objects, and only identity morphisms. Let's denote ... | https://mathoverflow.net |
399,336 | [
"https://electronics.stackexchange.com/questions/399336",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/69769/"
] | I have been writing a software for an embedded controller in C++. I have noticed
that I have some problems with ram memory (I have probably run out of the
available memory). I have decided to inspect a map file but I have found that
I am not able to find several queues in the map file. These queues are defined
as priv... | Note that "automatic variables" in C don't persist outside of individual invocations of a subroutine, and are usually dynamically allocated on the stack. Those therefore don't show up in a map file since they don't exist at that level.
They do, however, consume stack space. You have to make sure the amount of memory... | Compositions show up in different places than you might expect. The visibility defined in the code has no effect on that. Private data shows up in the link file just like any other data.
We have a static system build (no dynamic memory management) so in the map file, all RAM is allocated by the "mother" object which h... | https://electronics.stackexchange.com |
89,676 | [
"https://stats.stackexchange.com/questions/89676",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/40128/"
] | If you are running K-medians, and your distance metric is the L1 norm, how do you derive that the center of each centroid is the median of the data points assigned to it?
Second, how do you compute the geometric median?
Third, are there any implementations of k-medians algorithm?
| The definition of the geometric median <em>is</em> that of the $L_1$ optimum.
There seem to be two common approximations in use:
<ul>
<li>component-wise medians, optimizing each dimension independently</li>
<li>medoids, taking only the data samples into account</li>
</ul>
It's not clear to me why the component-wise ... | How do you compute the geometric median? By solving an optimization problem, it would be very optimistic to expect some closed formula.
Below some R code, solving it by hand, using the <code>optim</code> function:
<pre class="lang-r prettyprint-override"><code>library(Matrix)
Norm <- function(X, x) {
X <... | https://stats.stackexchange.com |
39,491 | [
"https://mathoverflow.net/questions/39491",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1590/"
] | Consider a planar point process $X$ and call $N_A = \text{Card}\big( X \cap A\big)$ the number of points inside the subset $A \subset \mathbb{R}^2$. If one knows the law of $(N_{A_1}, \ldots, N_{A_r})$ for any sets $A_1, \ldots, A_r$, then the process is completely characterized. I recently learned that it in fact suf... | This is only true for <b>simple</b> point processes (no duplicate points).
By the inclusion-exclusion principle, $f$ determines the joint distribution of several (disjoint) sets being empty or occupied. If the process is simple this allows recovering the law of $(N_{A_1},\dots,N_{A_r})$ as a limit over finer partition... | To add to Omer's concise explanation, the general result is known as Choquet's capacity theorem. It says that the void probabilities characterise any random closed set. Simple point processes are an example of random closed sets.
| https://mathoverflow.net |
436,747 | [
"https://physics.stackexchange.com/questions/436747",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/118048/"
] | Whenever I measure a positive quantity (e.g. a volume) there is some uncertainty related to the measurement. The uncertainty will usually be quite low, e.g. lower than 10%, depending on the equipment. However, I have recently seen uncertainties (due to extrapolation) larger than the measurements, which seems counter-in... | Indeed, uncertainties that large don't really make sense.
In reality, we have some probability distribution for the parameter we're describing. Uncertainty is an attempt to describe this distribution by two numbers, usually the mean and standard deviation.
This is only useful if the uncertainties are small, because ... | Uncertainties larger than measured values are common. Especially in measurements where the value is expected to be (close to) zero. For example values for the neutrino mass.
The particle data group lists these as smaller than some value with a 90 % confidence limit. But I have seen papers where <span class="math-conta... | https://physics.stackexchange.com |
91,229 | [
"https://stats.stackexchange.com/questions/91229",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/6493/"
] | I need to run an inferential test on some large data where the individual data points have a heavily skewed distribution. I'm considering doing a paired t-test across a number of days comparing the results of the test group to the control group. But if I take daily means, I'm still subject to outliers influencing those... | As you point out, there are merits with all three approaches. There clearly isn't one option that is 'best'. Why not do all 3 and present the results as a sensitivity analysis?
A meta-analysis conducted with ample and appropriate sensitivity analyses just shows that the author is well aware of the limits of the data a... | Here are the steps that I would take (and that I teach to my students):
1) Contact the authors of the original research. Be polite and request exact effect estimates to use in your meta-analysis. Worst thing that can happen is that they don't reply or refuse to give you the information. Best case scenario is you get t... | https://stats.stackexchange.com |
53,058 | [
"https://datascience.stackexchange.com/questions/53058",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/64138/"
] | I have a dataset with 400+ columns. Almost 90% of these are categorical data with One-Hot-Encoding (OHE). I'm using the dataset for a classification problem.
My professors asked me to perform feature selection using sequential forward selection (mlxtend).
Is there really a point of doing this since it is also very t... | Sequential forward selection appears to be a greedy search algorithm if I am not mistaken? It appears you initially fit all possible one variable models, and then choose the one variable model that is highest performing. You then attempt to add a second variable to the highest performing one variable model from the pri... | This important point is missing:
SFS is suitable as it has no assumption for features to be categorical or numerical. However, one-hot encoding is redundant when you are planning to use SFS. You just make the process longer by one-hot encoding since by doing so SFS needs to check more number of features than what it ac... | https://datascience.stackexchange.com |
657,745 | [
"https://physics.stackexchange.com/questions/657745",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/310770/"
] | How can a reversible adiabatic process (theoretically) be brought about since the system is insulated? A <span class="math-container">$\mathrm dP$</span> change in pressure will lead to a <span class="math-container">$\mathrm dT$</span> change in temperature thus disturbing the thermodynamic equilibrium.
Because ther... | When they say adiabatic, they mean perfectly insulated.
You can have a temperature difference between the system and the environment, but you just pretend that zero heat flows. That’s just a given. You are told to assume it.
Maybe that is not always realistic, especially when there are big temperature differences. But ... | I tried to explain this in connection with your other answer. But here's another try.
A reversible process is one in which no entropy is generated. Causes of entropy product include, but are not necessarily limited to, the following:
<ol>
<li>Heat transfer occurs across a finite temperature difference.</li>
</ol>
This ... | https://physics.stackexchange.com |
2,660 | [
"https://physics.stackexchange.com/questions/2660",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/955/"
] | Initially Wheeler and Feynman postulated that, the electromagnetic field is just a set of bookkeeping variables required in a Hamiltonian description. This is very neat because makes the point of divergent vacuum energy a moot point (i.e: an example of asking the wrong question)
However, a few years later (1951), Fey... | the original strategy of Feynman and wheeler was really about the desire to get rid of all self-interactions. In the modern language, it would eliminate most loop diagrams.
In particular, consider an electron propagator, in the modern language. One may attach a photon propagator on it. That modifies the electron's sel... | In CED one can obtain an exact solution of equations and exclude the electromagnetic field from the "mechanical" equations. In QED it was impossible and the field remained in some approximation in the perturbative calculations. Perturbative modifications of this field were called "vacuum polarization" effects. They tho... | https://physics.stackexchange.com |
47,277 | [
"https://cs.stackexchange.com/questions/47277",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/16703/"
] | The following example was given in an online lecture I was watching.
A phone directory is 1000 pages long, and we have to find the name "Zurich Smith". The algorithm is as follows:
<ol>
<li>Split the phone directory into half. If the name is in the first
half, get rid of the second half; and if the name is in the se... | <blockquote>
but they, in the lecture, are saying that this algorithm involves 10
steps. Why?
</blockquote>
He says:"10 <strong>- give or take</strong>" in the lecture, which means that 10 is an estimate with a small uncertainty in either direction. He accepted it as estimate from the audience, which replies to hi... | To find the right page using binary search would take at most $\lceil log_2 1000\rceil = 10$ steps, which I guess the lecture refers to. But that is not exactly what you do: note that there are a number of steps where you are left with an odd number $n$ of pages, and say that for the next step, you have $\lfloor n/2\rf... | https://cs.stackexchange.com |
271,328 | [
"https://softwareengineering.stackexchange.com/questions/271328",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/45536/"
] | So, if I am designing a system as a set of different roles (client, app-server, backend services 1 to n). Each of these roles will have their own logging mechanism. I can aggregate all the logs at one location, but how can I sequence the logs from different sources, to show an interleaved log?
I can make my own strate... | Normally you view the logs independently. Too much log is a real problem. There is almost no reason to view an interleaved log. If you really need to log an "action" through all the services have them write to a central log
syslog is a great example
apache writes to one log mysql to another, and there's usually neve... | At my current company we have a similar setup: public facing websites, a few API's for partners, and a whole bunch of background tasks and services. One thing I pushed for when I joined the team several years back was to <em>log everything to one database table</em>. Skeptical?
<ul>
<li>Yes, the DBA was too. I convinc... | https://softwareengineering.stackexchange.com |
134,518 | [
"https://mathoverflow.net/questions/134518",
"https://mathoverflow.net",
"https://mathoverflow.net/users/35229/"
] | Let $F_n$ be the free group on $n\geq 2$ generators and let $H < F_n$ be a finite index normal subgroup. Let $P\subset F$ be the subset consisting of primitive elements (an element of $F_n$ is called primitive if it is a member of a free basis). Furthermore, we define $\tilde P\subset H$ to be the subset consisting ... | If $x_1 \in H$ then, since $H \unlhd F_n$, all conjugates of $x_1$ in $F_n$ are in $H$ and hence also in $\overline{H}$. So the normal closure $N$, say, of $x_1$ in $F_n$ lies in $\overline{H}$.
Now any element of $H$ can be written as $nh$ with $n \in N$ and $h \in \langle x_2,\ldots,x_n \rangle$. But $x_1 h$ is a ... | Here is a counterexample. Let $\phi$ be the natural homomorphism from $F_2$ to $A=\mathbb{Z}_n\times \mathbb{Z}_n$ where $n$ is a very large odd number (say, $\ge 665$), $H=Ker(\phi)$. Then the image of every primitive element of $F_2$ is a generator of $A$, so it has exponent $n$. Therefore $\tilde P$ is a subgroup of... | https://mathoverflow.net |
431,583 | [
"https://physics.stackexchange.com/questions/431583",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/21270/"
] | I am trying to compute the <span class="math-container">$2$</span>-point Green function <span class="math-container">$\tau_2(x,y)$</span> for free Dirac fields. The corresponding formula for <span class="math-container">$\tau_2(x,y)$</span> is given by
<span class="math-container">$$\tau_2(x,y) = -\frac{\delta^2}{\del... | First of all, the functional integral <span class="math-container">$Z_0$</span> is a real number, since it is defined as an vacuum expectation value:
<span class="math-container">$$Z_0[\zeta,\bar{\zeta}]:=\langle0|T\,e^{i\langle\bar{\zeta}_x\psi_x+\bar{\psi}_x\zeta_x\rangle}|0\rangle$$</span>
where <span class="math-co... | <blockquote>
I am trying to compute the 2-point Green function <span class="math-container">$\tau_2(x,y) = -\frac{\delta^2}{\delta\eta_x \delta \bar{\eta}_y} \, Z_0[\eta, \bar{\eta}]$</span>
</blockquote>
You have to take the <span class="math-container">$\eta=0$</span>/<span class="math-container">$\bar{\eta}=0 $</... | https://physics.stackexchange.com |
595,725 | [
"https://math.stackexchange.com/questions/595725",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/113262/"
] | <blockquote>
Suppose a plant has $X$ offspring in a year with $P(X = x) = \frac14$ for $X = 1, 2, 3, 4$ and, independently, each offspring has from one to four offspring in the next year with the same discrete uniform distribution. Let $Y$ denote the total number of offspring in the second generation. Find the values... | Let $X_{n}$ stand for the offspring of the $n$-th generation. Here
$X_{0}=1$ and $X_{1}$ has the distribution that you mention, so
$\mathbb{E}\left(X_{1}\right)=\frac{5}{2}$ .
Under condition $X_{n-1}=k$ we have an offspring of $\frac{5}{2}k$ in the next generation.
This tells us that $\mathbb{E}\left(X_{n}\mid X_{n-... | i take you to mean that each plant continues generating offspring indefinitely. let the probability that the total number of generators after $t$ epochs is $n$ be $p(n,t)$. then if this is the coefficient of $x^n$ in the function $G_t(x)$. we can see that
$$
G_{t+1}(x) = G_t(x)G_t(\frac14[x+x^2+x^3+x^4])
$$
in particu... | https://math.stackexchange.com |
212,781 | [
"https://mathoverflow.net/questions/212781",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1474/"
] | Fix a commutative ring $R$. There's a contravariant functor from finite sets to finite $R$-algebras sending $X$ to $R^X$. Viewed as a covariant functor $\text{set}^{op}\to R\text{-alg}$, this functor preserves finite limits and colimits; this is easy to verify directly by checking finite products ($R^{\coprod_i X_i} \... | Maybe this is more complicated than you are looking for, but you can get your right adjoint to exist without any Noetherian hypothesis by extending the domain to the category of all Boolean algebras. Specifically, let $\text{Bool}$ be the category of Boolean algebras and $R\text{-Alg}$ be the category of $R$-algebras ... | I don't know if this is short enough, but:
Once we know $R^{(-)}$ preserves coproducts we're left with reflexive coequalizers, and we can compute those after forgetting down to <em>Set</em>. But it's not so hard to see that for <em>any</em> set $Y$, the functor $\text{Hom}(-, Y): Sets^{op} \rightarrow Sets$ commutes w... | https://mathoverflow.net |
12,500 | [
"https://mathoverflow.net/questions/12500",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1238/"
] | I think it should be a standard procedure to construct such things, can anyone give a reference or give a hint? Can this be done over any base scheme?
| Hint: use quadratic twists.
<b>Edit</b>: So as not to drag things out, I hope it's okay if I just give you a standard example. Let
$E_0: y^2 = x^3 + Ax + B$
be your favorite elliptic curve over $\mathbb{Q}$ (i.e., any will do). Consider the
elliptic curve
$E: t y^2 = x^3 + Ax + B$<br>
over the rational function f... | (<b>Edit:</b> added motivation for my "answer" even though it isn't exactly what was asked for. It shows the moduli space of genus 1 curves cannot be fine - see last paragraph.)
The Hopf surface is a (non-algebraic) example of a non-trivial family of isomorphic elliptic curves. Here I use "elliptic curve" to mean "sm... | https://mathoverflow.net |
2,487,377 | [
"https://math.stackexchange.com/questions/2487377",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/495125/"
] | Prove $\frac{a+b+c}{2} ≥ \frac{bc}{b+c} + \frac{ca}{c+a} + \frac{ab}{a+b}$
I feel like this problem would have a much simpler solution than just expaning out and simplifying. Any pointers are appreciated
| After also dividing each series by $n^2$, as suggested by $@Claude Leibovici$.<br>
$$
\begin{align}
\frac{t_{1}}{4*1} = 1\\
\frac{t_{2}}{4*2^2} = 2\\
\frac{t_{3}}{4*3^2} = 4\\
\frac{t_{4}}{4*4^2} = 8\\
\frac{t_{5}}{4*5^2} = 16\\
\frac{t_{6}}{4*6^2} = 32\\
\frac{t_{7}}{4*7^2} = 64
\end{align}
$$.<br>
I can clearly see t... | <strong>Hint</strong>
What you did is good. Try now dividing $\frac{t_n}4$ by $n^2$.
Your turn and ... let me know.
| https://math.stackexchange.com |
88,299 | [
"https://physics.stackexchange.com/questions/88299",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/8163/"
] | Suppose we have a system of bosons represented by their occupation numbers
$$\tag{1} | n_1, n_2, ..., n_\alpha, ... \rangle$$
Then we can define creation and annihilation operators
$$\tag{2} a_\alpha^\dagger| n_1, n_2, ..., n_\alpha, ... \rangle = \sqrt{n_\alpha+1} | n_1, n_2, ..., n_\alpha+1, ... \rangle$$
$$\tag{3} a... | Here are three properties that would make your definitions awkward.
You can think of $a^\dagger\,a$ as the LU (lower triangular, upper triangular or Cholesky) decomposition of the number observable. Actually, it's not the unique Cholesky factorisation but it is the one found by the outer product version of the algorit... | The problem is that the physical states have positive occupation numbers $n_1, n_2,...$.
With your operators, you have, for instance :
$ c_\alpha| n_1, n_2, ..., 0, ... \rangle = | n_1, n_2, ..., -1, ... \rangle$.
This gives you a totally unphysical state, so you would have to add by-hand constraints like $n_1 \ge... | https://physics.stackexchange.com |
11,568 | [
"https://stats.stackexchange.com/questions/11568",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/4883/"
] | I have one data sample of non-negative random variable $X$ with unknown distribution and predefined expected value $y$. Is there any test able to check null hypothesis $\mathbb{E}[X]\geq y$ or $\mathbb{E}[X]\leq y$?
Actual data samples are gathered in realtime. More specifically, it's an intervals between HTTP-request... | The problem with allowing <em>any</em> distribution is that it could have a tiny chance of yielding a huge value. That eliminates any possibility of testing the mean with satisfactory confidence.
Here are the details. Choose a unit of measurement in which $y$ is hugely greater than $1$. Let $\alpha$ be the desired... | Intervals between things like requests are often modeled well with exponential, gamma, and Weibull distributions. These can have pretty fat tails, so @whuber's concern is already accounted for, to some extent, when you calculate your confidence intervals.
| https://stats.stackexchange.com |
151,455 | [
"https://security.stackexchange.com/questions/151455",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/139533/"
] | In a brief, can be long connections threated as security vulnerability? By long connections i mean connections where for long period of time data is not being sent at all. For example client-server connection when client or server has to retrive recived data and it take long period of time? Right now i'm working with s... | From an infosec standpoint, expiring TCP sessions are needed to reduce the possibility of exhausting resources on firewalls, routers and other equipment.
Keepalives help when higher level protocols take a long time between transmissions, e.g., when processing information client side.
The downside to keepalives, espec... | The only problem that I can see arising out of this is: Multiple clients connect to your server, thus eating up its resources and effectively creating a Denial-of-service condition.
| https://security.stackexchange.com |
252,312 | [
"https://security.stackexchange.com/questions/252312",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/261215/"
] | I'm researching about SOCKS5 protocol. After understanding it, I know that SOCKS5 does not encrypt data from clients to proxy server. Therefore, can we use TLS/SSL to encrypt data? secure SOCKS5?
| Depends how confident you are in the "no subdomains" and "no browsers too old to understand <code>SameSite</code> cookie flag" conditions. Both of those have several ways to break them.
The "no subdomains" thing requires not only that <em>you</em> not have any subdomains, but that nobody e... | Yes, you still need it.
Yes, I can’t think of a way to break your site today, but that isn’t the security question, and this is a security site.
No, there are no other security benefits to using a csrf token. You could look at crypto systems that use nonces, or anti-replay stuff but that’s not what the csrf is doing.
T... | https://security.stackexchange.com |
129,414 | [
"https://cs.stackexchange.com/questions/129414",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/125636/"
] | I have the following two CFL: <span class="math-container">$A =\{a^m b^n c^n\}$</span> and <span class="math-container">$B = \{a^m b^m c^n\}$</span>.
I don't understand why the intersection of this languages is <span class="math-container">$\{a^n b^n c^n\}$</span>: can anyone explain to me why the power is to the <span... | The set <span class="math-container">$A$</span> cointains all the strings on the alphabet <span class="math-container">$\{a,b,c\}$</span> starting with <span class="math-container">$a$</span>, ending with <span class="math-container">$c$</span> and with the same number of <span class="math-container">$b$</span>s and <s... | You have that <span class="math-container">$A=\{a^mb^nc^n:\ m,n\in\mathbb{N}\}$</span> and <span class="math-container">$B=\{a^mb^mc^n:\ m,n\in\mathbb{N}\}$</span>. If <span class="math-container">$w\in A$</span>, then there are <span class="math-container">$r,s\in\mathbb{N}$</span> such that <span class="math-containe... | https://cs.stackexchange.com |
94,237 | [
"https://cs.stackexchange.com/questions/94237",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/84342/"
] | What are the practical and theoretical implications of the unit <em>type</em> and the unit <em>value</em> being the same or different entities?
For example, in Haskell the unit type and unit value are both spelled <code>()</code>. In ML, the unit type is spelled <code>unit</code> and it's value is <code>()</code>.
Ar... | You have been confused by Haskell's notation. The unit type and unit value are of course different, and it just happens that Haskell uses the same notation for both.
As for the consequences: there are none. Notation is irrelevant here. You can call the unit type <code>Dog</code> or <code>BauwnNuYwvb</code> (i.e., nons... | If you reason in terms of sets, what you call the "unit type" is really a one element set, and its single element is what you call the "unit value". So they are obviously not the same thing.
| https://cs.stackexchange.com |
600 | [
"https://mechanics.stackexchange.com/questions/600",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/109/"
] | My Probe's heater has stopped working and only ever blows cold air. In addition to this, I notice the temperature gauge on the dash display is creeping very high.
What part (or parts) is likely to be the culprit and how would I best go about fixing it?
| The heater in a water-cooled car relies on coolant from the engine. Lack of heat together with an overheating engine suggest a cooling system problem. I suggest the following:
<ol>
<li>Check the coolant level. If you're lucky, you're just low on coolant. The question then becomes: where did it go? Is there a leak? Are... | There are a few tests you need to do to help with the problem. First, is the presure cap on the overflow bottle {degass bottle} or on the radiator, this will tell you what system you are working with and I will need to know that first before we can go any further.
| https://mechanics.stackexchange.com |
563,960 | [
"https://stats.stackexchange.com/questions/563960",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/155235/"
] | CDF is the probability that a random variable takes on a value less than or equal to a fixed <span class="math-container">$x = a$</span>.
Assuming we have a a random variable <span class="math-container">$X$</span> that <em>has</em> a PDF, both CDF and PDF have the same information as the following PDF gives us the exa... | I think you are making a false distinction here.
<span class="math-container">$$
\int_{-\infty}^{a} f(x) \,dx
$$</span>
<strong>is</strong> the CDF. When you take the integral, you are calculating the CDF. Having closed-form CDF just means that someone already did this for you.
| There are situations where the CDF comes in handy. E.g. for computing quantiles or copulas or transforming distributions into each other. Some proofs work better/only with CDFs.
But you are right, in case there is an integrable PDF, you also have a CDF.
Of course, the interesting case is when you have a CDF for which t... | https://stats.stackexchange.com |
86,700 | [
"https://datascience.stackexchange.com/questions/86700",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/108857/"
] | my network has two outputs and single input. I am trying to write a custom loss function
<span class="math-container">$$
Loss = Loss_1(y^{true}_1, y^{pred}_1) + Loss_2(y^{true}_2, y^{pred}_2)
$$</span>
I was able to write a custom loss function for a single output. But for multiple output, I am struck. Below I wrote a ... | <pre><code>import tensorflow as tf
from tensorflow.keras.layers import Input, Dense
from tensorflow.keras import Model
from tensorflow.keras.optimizers import RMSprop
import tensorflow.keras.backend as K
import numpy as np
def model(input_shape=4, output_shape=3, lr=0.0001):
"""
single input and... | Multi input/ Multi output Model and learning in tensorflow
<pre><code>import tensorflow as tf
from tensorflow.keras.layers import Input, Dense, Concatenate, Add
from tensorflow.keras import Model
from tensorflow.keras.optimizers import RMSprop
import tensorflow.keras.backend as K
import numpy as np
def model(input_sha... | https://datascience.stackexchange.com |
327,275 | [
"https://electronics.stackexchange.com/questions/327275",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/161801/"
] | How do you know if a transfer function for a RC filter is correct?
For example how would you tell whether or not this is a correct transfer function:
\$\frac{\frac{R_1}{R_1R_2}}{1+j\omega R_1C}\$
Or generally how would you tell if a function is indeed a correct transfer function?
Edit: If I have understood this corr... | No way to be 100% sure of the correctness, but some validations can be done:
1) calculation of units/dimmension
You add 1 (adimensional) and \$j\omega R_1C\$ thus \$\omega R_1C\$ must be adimensional. It is, pass check 1.
The global function has unit \$ \Omega^{-1} \$, this is not valid for a transfer function of ty... | A <strong>simple</strong> RC filter might be high pass or low pass and it will have the transfer function form of: -
\$\dfrac{j\omega CR}{1+j\omega CR}\$ for a high pass
And
\$\dfrac{1}{1+j\omega CR}\$ for a low pass
If you know that <em>your</em> formula relates to a high pass or low pass <strong>simple</strong> R... | https://electronics.stackexchange.com |
109,813 | [
"https://mathoverflow.net/questions/109813",
"https://mathoverflow.net",
"https://mathoverflow.net/users/9833/"
] | Let $X$ be a Kahler manifold and $Z\subset X$
be a smooth hypersurface. How to compute the Hodge
diamond of the double covering $Y\to X$ ramified
over $Z$? (And what I have to know? Would the map
$H^*(X)\to H^*(Z)$ be enough?)
P.S. I tried the Gysin sequence, but it looks
like there are many loose ends.
| The answer goes back to Esnault and Viehweg:
$$H^q(Y,\Omega_Y^p)= H^q(X,\Omega_X^p)\oplus H^q(X,\Omega_X^p(\log Z)\otimes L^{-1})$$
where $L$ is the anti-invariant part of the direct image of $O_Y$ to $X$ under the
natural $\mathbb{Z}/2$ action.
| This is more like a comment that in order to get a positive answer you need to specify more data.
Let us consider the simplest situation when $Z$ is empty, so $H^{\ast}(X)\to H^{\ast}(Z)$ is
the zero map. It might happen in this situation, that there is more than one (unramified) double cover of $X$ and moreover doub... | https://mathoverflow.net |
344,025 | [
"https://electronics.stackexchange.com/questions/344025",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/147125/"
] | Suppose you are building a device that needs a small CPU, it's running on battery power so you want to minimize the energy consumption, and you only need a small amount of computation. What's the most energy-efficient CPU?
My first thought would be that an 8-bit CPU would use the least energy. But on thinking about it... | That old 6502 is far outclassed by modern low-power microcontrollers. Some considerations that affect power consumption of modern microcontrollers:
<ul>
<li>Supply voltage: modern chips operate at low DC voltages.</li>
<li>uA/MHz: supply <strong>current</strong> is proportional to speed... modern:100-200uA/MHz</li>
<l... | It is possible to benchmark an MCU for power consumption if you know what tasks you wish to perform. For example, an MSP430 might have a uA range current consumption, but it might require more instructions than an ARM M0 for the same task, and then, assuming their clocks are identical, you can estimate which one consum... | https://electronics.stackexchange.com |
39,833 | [
"https://dba.stackexchange.com/questions/39833",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/22465/"
] | Why are constraint applied in Database? Will it not be more flexible to put it in the code?
I'm reading a beginners book on implementing databases, so I'm asking this as a beginner. Let's say I have designed a database, including this entity model:
<pre><code> entity type | sub-types
----------------+-----------... | Some constraints are best enforced in the database, and some are best enforced in the application.
Constraints that are best enforced in the database are usually there because they are fundamental to the structure of the data model, such as a foreign key contraint to ensure that a product has a valid <code>category_id... | Because:
<ol>
<li>I want <em>all</em> the data in the database to be subject to the same constraints, not just the <em>new</em> data to be subject to the constraints in the version of the code that's running today.</li>
<li>I want declarative constraints, not programmatic constraints.</li>
<li>Data in the database oft... | https://dba.stackexchange.com |
86,558 | [
"https://mathoverflow.net/questions/86558",
"https://mathoverflow.net",
"https://mathoverflow.net/users/11765/"
] | Let $G$ be be a connected real algebraic reductive Lie group. Is it always possible to find finitely many maximal algebraic $\mathbf{R}$-tori $\{T_i\}_{i=1}^n$ such that the group generated by the $T_i$'s is $G$.
P.S. The assumption for $G$ to be reductive is essential since $\mathbb{G}_a$ does not contain any real to... | At least for affine algebraic groups this is true. Indeed, let $G$ be a connected affine real algebraic group. Assume $G$ contains at least one diagonalizable element. Then diagonalizable elements are dense in $G$. Let $U$ be a neighborhood of 0 in the Lie algebra $g$ of $G$ such that $exp|U$ is a diffeomorphism. Choos... | For a more algebraic version of algori's approach, I'd suggest a conceptually simple method based on the Borel-Tits structure theory. Of course, some tweaking would be needed to deal with real Lie groups which aren't algebraic, like the universal covering group of $SL_2(\mathbb{R})$. Without loss of generality, take... | https://mathoverflow.net |
241,418 | [
"https://electronics.stackexchange.com/questions/241418",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/11022/"
] | I notice that the higher the number of poles, the slower the induction motor spins. Likewise, the lower the number of poles, the faster it spins. How does the number of poles affect its speed? Also, does the number of poles have any effect on its output torque?
| During half of a cycle of the power frequency, the position of a rotor pole moves from one stator pole to the opposite pole of the same pair. If the motor has only two poles, that rotor pole moves back to the original position during the next half cycle. So there is one revolution per cycle of the power frequency. If t... | Not accounting for slippage, the rotor will move one pole-pair every cycle of the AC current. So the more poles you have, the more cycles it take to complete a full revolution.
In general, torque is a function of current. But it's more complex in an induction motor, as torque is also a function of the relative angle b... | https://electronics.stackexchange.com |
198,449 | [
"https://electronics.stackexchange.com/questions/198449",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/57453/"
] | Why do all the gameboy cartridge mods for nonvolatile save use a type of ram like fram? Why isn't a <em>sufficiently fast</em> eeprom or flash ic used?
EDIT: We all know this is about <em>parallel</em> interface ICs, right?
| Because it costs the generating companies 1:1 to supply you with watts, with real power.
While it is not free for them to supply you with VA, because that extra current needs bigger cables and transformers, and causes larger voltage drops, which cause increased losses in the distribution network, it does not cost the... | Watts can be used to power your kettle, run your TV, refrigerator and power your hi-fi. You get billed for watts. However, some appliances will take more than just watts - they'll take reactive power (VAr) and although this doesn't contribute to lighting a lightbulb or actually turning a fan, this reactive power is tak... | https://electronics.stackexchange.com |
48,183 | [
"https://chemistry.stackexchange.com/questions/48183",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/27279/"
] | Lecture tells me that double bond, with the sp^2 bonding will have more s-character, which will hold the electons closer to nucleus, which means a more deshielded proton which means downfield chem shift.
But it doesnt follow the same idea with triple bond, with sp bonded carbon, and this is where diamagnetic anisotropy... | Maybe it will help if you look at reactivity in terms of ability to attract electrons instead of bond enthalpies. Alkanes are $sp^3$ hybridized, and hence have $25$% $s$ orbital character and $75$% p character. $s$ orbitals are closer to the nucleus and thus have a 'contracting' effect on the hybrid orbital. Greater th... | The three bonds consist of two pi and one sigma bond.. Pi are very easy to break and sigma is difficult.. So alkynes can be easily broken as they have a more number of pi bonds while alkanes have only one sigma bind which is difficult to break.
| https://chemistry.stackexchange.com |
16,460 | [
"https://mathoverflow.net/questions/16460",
"https://mathoverflow.net",
"https://mathoverflow.net/users/348/"
] | Two things today motivated this question.
First, the professor said that in a lecture Thurston mentioned
<blockquote>
Any manifold can be seen as the configuration space of some physical system.
</blockquote>
Clearly we need to be careful here, so the first question is
<blockquote>
1) What is a precise formula... | Let's start by answering the first question.
Let $M$ be any manifold. Consider a physical system consisting of a point-particle moving on $M$. What are the configurations of this physical system? The points of $M$. Hence $M$ is the configuration space.
Typically one takes $M$ to be riemannian and we may add a pot... | This is just to add to what the previous posters have said so much better. It is a wonderful "fact" that whatever manifold you choose, there will always be some mechanical system that can be encoded as geodesic flow on this space (relative to some metric). Here are some examples:
<ol>
<li>$SO(3)$ : rigid body dynami... | https://mathoverflow.net |
147,101 | [
"https://stats.stackexchange.com/questions/147101",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/17590/"
] | I have a least square fitting like this:
<pre><code>fit = lsfit(log10(M), log10(RS), wt)
</code></pre>
This function lists statistics and p-values for the coefficient considering the null hypothesis is zero but I want to change the null hypothesis of the coefficient from 0 to 0.5. So when I look at the t-statistics o... | Your case is very simple - just subtract 0.5 from the coefficient of <code>log10(M)</code> and divide it by the standard error to get your t-statistic, and then calculate a p-value.
In other words:
<pre><code>fit = lsfit(log10(M), log10(RS), wt)
fsum = ls.print(fit)
# Grab SE and DF from ls.print, its output is a bit... | For any linear hypothesis (i.e. determining if a coefficient in a linear model is different from a particular value), one method is to subtract from each $y$ value your desired hypothesis multiplied by the $x$ value. So for your example
<pre><code>fit<-lsfit(log10(M),log10(RS)-.5*log10(M), wt)
</code></pre>
You st... | https://stats.stackexchange.com |
202,139 | [
"https://physics.stackexchange.com/questions/202139",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/89984/"
] | Ok I know there is a similar question already on here, but mine takes it just a step further. What I would really love to know is exactly how much energy is being transferred from a battery into a capacitor. I am under the assumption that it is 100% of the energy and can not for the life of me understand how it could p... | <blockquote>
I understand also that there would be a tiny minuscule resistive loss
through the wire, but really it's not enough to say anything about.
</blockquote>
On the contrary, it's <em>crucial</em>.
Assuming an ideal voltage source (can supply unlimited current) of voltage $V_S$, an ideal resistor of resist... | When you connect a battery to a capacitor, a "real" circuit has at least four components in series:
<ul>
<li>the voltage source (battery)</li>
<li>the capacitor</li>
<li>series resistance</li>
<li>series inductance</li>
</ul>
Any wire has inductance, since current flowing through it will induce a magnetic field. It i... | https://physics.stackexchange.com |
114,673 | [
"https://chemistry.stackexchange.com/questions/114673",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/72973/"
] | Consider the reaction
<span class="math-container">$$\ce{A(g) + H2O(l) <=> B(aq) + C(g)}$$</span>
If all gases and solutions were ideal, the standard state would be pure water, the solute B at a concentration of 1 M, the gases A and C each at a pressure of 1 bar, and the system at a pressure of 1 bar.
For non-... | The standard states are <em>limiting states</em>. In these limits you can write the chemical potential of the component as
<span class="math-container">$\mu = \mu^\circ+RT\log(x)$</span>
where <span class="math-container">$x$</span> is a measure of the concentration of solute (for Henry's law, where the standard sta... | You don't measure <span class="math-container">$\Delta G^\circ$</span>. You measure <span class="math-container">$K$</span> and then compute <span class="math-container">$\Delta G^\circ = -RT\ln(K)$</span>. Crudely put, the value of <span class="math-container">$K$</span> will depend on the units you use for concentrat... | https://chemistry.stackexchange.com |
572,549 | [
"https://physics.stackexchange.com/questions/572549",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/263675/"
] | In classical Mechanics it is possible to prove that the total Energy <span class="math-container">$E = T + V$</span> is conserved if the force is conservative. However, if you assume the mass is time-dependent this proof no longer holds:
<span class="math-container">\begin{align}
\frac{dE}{dt} = \frac{d}{dt}(\frac{1... | The correct statement of the law of conservation of energy is that the total energy of an <em>isolated</em> system is conserved. This is valid both for classical and for relativistic mechanics.
In your example, the energy is not conserved as a consequence of the fact that the total mass of the system is not constant. I... | I try to explain the idea that I got following the computational study of a variable mass system.
Let us consider an isolated system in a certain state of motion. It will have a certain mass and geometry, i.e. a moment of inertia, which quantify its ability to oppose changes in its dynamic state.
Imagine that its mass ... | https://physics.stackexchange.com |
26,825 | [
"https://astronomy.stackexchange.com/questions/26825",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/23217/"
] | Beside that, is that possible our sun became <strong>pulsar</strong>? And if not (and i know likely) but how much more mass does it need to become one ?
| There are at least two types of supernovae (SNe): thermonuclear supernovae (TSNe) and core-collapse supernovae (CCSNe).
TSNe come from the explosions of white dwarves (WDs) in binary systems. A star with mass at zero age about < 8 solar mass, it normally evolves and ends up being a WD. Our sun is in this category. ... | The smallest stars that could explode in supernova have a mass of at least about 8 times the mass of the sun. So it is impossible for the sun to become a pulsar at the end of its life. It will form a red giant which will then lose its outer layers and form a white dwarf.
| https://astronomy.stackexchange.com |
128,164 | [
"https://electronics.stackexchange.com/questions/128164",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/40761/"
] | I'm using atmega32 µc with the internal 10-bit ADC. I connected my potentiometer to the ADC 1 and I'm using 5 V Voltage Reference.
using the following code, I did the ADC-config
<pre><code>void ADC_init(void)
{
//Turn on the ADC
ADCSRA |= 1<<ADEN; // Turn On ADC (Enable ADC)
//ADMUX |= 1<<... | You have incorrect multiplexer setting. To select channel 1, it should be
<pre><code>ADMUX |= 1<<MUX0 ; // ADC-Channel 1
</code></pre>
<strong>Edit:</strong> Another thing is incorrect clock prescaler. To get \$f_{clk}/128\$:
<pre><code>ADCSRA |= 7<<ADPS0; // Assign ADC-prescaler 128
</code></pre>
| Try:
<pre><code>ADC_TenBit = (uint16_t)ADCH<<8 | theLow;
</code></pre>
And you did declare <code>ADC_TenBit</code> uint16_t, right?
| https://electronics.stackexchange.com |
265,617 | [
"https://dba.stackexchange.com/questions/265617",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/37509/"
] | Any field that I would expect a value (Like an orderNumber or customerNumber) I would set as not nullable.
If I'm expecting the value of the field to be not null, shouldn't I also always have a constraint that does not allow for zero length strings or space only strings?
| <ul>
<li>If the sequence is used in the <code>DEFAULT</code> clause of the table column, it is enough to rename the sequence.
That is because the <code>DEFAULT</code> clause is <em>not</em> stored as string, but as parsed expression tree (column <code>adbin</code> in catalog <code>pg_attrdef</code>). That expression t... | I don't think the mentioned method is going to solve your problem. In both cases, PostgreSQL is going to acquire a lock on the table, and the application has to wait for the ALTER command to be finished.
<pre><code>ALTER SEQUENCE <sequence name> RENAME TO <new sequence name>
</code></pre>
Above command sh... | https://dba.stackexchange.com |
479,055 | [
"https://physics.stackexchange.com/questions/479055",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/231589/"
] | I was taught that when the acceleration experienced by a body is constant, that body follows a parabolic curve. This seems logical because constant acceleration means velocity that is linear and position that is quadratic. This is what I learned from projectiles: Bodies are thrown with an initial velocity near the surf... | <blockquote>
Now that doesn't apply on the orbit of the Earth. The gravitational force can be thought of as constant since the distance fron Earth to Sun can be thought of as constant too
</blockquote>
You are correct that the strength or magnitude of the sun's gravitational field is very similar over the length of ... | <blockquote>
The gravitational force can be thought of as constant since the distance fron Earth to Sun can be thought of as constant too, which by Newton’s second Law means the acceleration of Earth is also constant. Wouldn't that mean that the Earth should just follow a parabolic path ?
</blockquote>
No, the grav... | https://physics.stackexchange.com |
933,003 | [
"https://math.stackexchange.com/questions/933003",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/175846/"
] | I have a strong feeling that the following limit is zero, can anybody help me prove it.
<ol>
<li>$ \lim\limits_{(x,y,z) \to (0,0,0)} \frac{{xyz}}{{x+y+z}}$</li>
</ol>
Thanks!
| Hint: what happens when, say, $y = x$ and $z = -2x$?
| Write $z=u-(x+y)$ so that
$${xyz\over x+y+z}={xy(u-(x+y))\over u}=xy-{xy(x+y)\over u}$$
Now let $x=au^{1/3}$ and $y=bu^{1/3}$, giving
$${xyz\over x+y+z}=abu^{2/3}-ab(a+b)$$
Note that $(x,y,z)\to0$ as $u\to0$ regardless of what $a$ and $b$ are, but this gives $${xyz\over x+y+z}\to -ab(a+b)$$ which can be anything. ... | https://math.stackexchange.com |
3,919,451 | [
"https://math.stackexchange.com/questions/3919451",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/850070/"
] | Could somebody explain why for any given linear maps S and T over a finite dimensional vector space V, ST is invertible if and only if TS is? Why is it so important that V is finite dimensional for this to hold true?
Edit: I am looking for an approach without using matrices or determinants.
| I thought there was already such a question here, but I did not find it.
As the comments say, there is no simple formula for <span class="math-container">$\int f g dx$</span> in terms of <span class="math-container">$\int f dx$</span> and <span class="math-container">$\int g dx$</span>. There are lots of ways to see t... | If we look for any arbitrary <span class="math-container">$f(x)$</span> and <span class="math-container">$g(x)$</span>, there are only 2 combined derivatives that include the product of these function (and their individual derivatives): The quotient rule and the product rule. As its clear we are not dividing by <span c... | https://math.stackexchange.com |
264,304 | [
"https://softwareengineering.stackexchange.com/questions/264304",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/157151/"
] | I am working on a multi client/single server app. Communication between the two happens via RESTful API. There are several resources that need to stay in sync across all clients, including images captured from camera, likes and comments on these images, user profiles and user followers/followings. My current approach i... | In REST, you should think of URIs as identifying an addressable resource. So as long as you think of a "sync" as a noun ;) you can define that resource in whatever manner suits your requirements.
At surface level, in REST we talk about collection resources (like the collection of users) and individual resources (like ... | Second approach is a bad/inferior idea.
<ul>
<li>You lose the ability to cache individual resources using standard caching methods (both on the server and client).</li>
<li>You lose the ability to sync individual resource state using HTTP headers and timestamps</li>
<li>You lose the ability to update resources as you ... | https://softwareengineering.stackexchange.com |
211,288 | [
"https://electronics.stackexchange.com/questions/211288",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/92877/"
] | I have two transceivers, one for CAN and one for RS485, and both are isolated. Both standards require 3 wires (two differential pairs and one common GND).
I am trying to use one termination connector and depending on which standard I am going to use (CAN or RS485) only one bus is going to be connected to termination c... | If I had to design a product that needed to be able to connect to either CAN or RS-485, I'd probably start by considering separate connectors or separate pins on the same connector for the two busses. The ground pin can be common if on the same connector.
Jumpers can be made to work, but users don't always set them r... | How hard are you "pushing" the bus? For a relatively short, lowish speed bus, you could probably connect them in parallel and use PHY chips with an output enable function and disable the device you are not using in software...
| https://electronics.stackexchange.com |
252,625 | [
"https://security.stackexchange.com/questions/252625",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/261727/"
] | Imagine that there is server required authentication for getting an access to some endpoint.
And developer added some logic to bypass the authentication: if server recieve HTTP header give_me_access=true, then server answers without requiring authenticaton.
Is there way for an attacker to know that the server accept th... | No, not really. There is no part of the HTTP protocol where the server is expected to list headers it is interested in. It's not common practice for servers to do either - I have never seen anything like that anywhere.
You could guess the name or try to brute force it. But unless the name is obvious, you are very unlik... | In my opinions, this is actually an XY problem.
Based on header name <code>give_me_access</code> I would suppose, that the real question the author wanted to ask is following:
<blockquote>
What are the risks if the security is based on the secrecy of the name of the custom HTTP header?
</blockquote>
The <em>formal</em>... | https://security.stackexchange.com |
233,648 | [
"https://softwareengineering.stackexchange.com/questions/233648",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/47215/"
] | I'm currently developing a responsive website with CSS media queries. It would be much easier if the server returned a different HTML/CSS for each viewport.<br>
I was wondering why couldn't the client include its viewport information when requesting an HTML file. This behavior is already common for returning websites i... | <strong>In short, that was not how the Wild Wild Web was designed to work.</strong>
The original design was simply that the HTML gave the browser hints about the document. Which bits to emphasise, where to go to get image files. Decisions about the font (as well as what size) was the job of the browser and local con... | I think you haven't totally got the idea of <em>Responsive Web Design</em>. Serving different HTML/CSS/JS based on the client's web-browser has been there for a while and I'm pretty sure there are still some websites still doing that -- a very clear example is the old-school way of serving a mobile-friendly theme for a... | https://softwareengineering.stackexchange.com |
3,422,272 | [
"https://math.stackexchange.com/questions/3422272",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/679568/"
] | There are N cards (numbered from 1 to N) in a box. N is a positive integer. We choose two cards randomly, and we divide the the smaller number on the cards with the other number (so the smaller one is in the numerator...). <span class="math-container">$Z$</span> denotes the ratio calculated as we discussed before. What... | In general,
<span class="math-container">$$P(\text{event happens}) = 1 - P(\text{event doesn't happen}).$$</span>
Here, the opposite (complement) of "at least one chip is defective" is "all four chips are not defective." This gives the first line of the solution.
To compute the probability of "all four chips are not ... | Whenever solving a probability puzzle involving the term "at least", you know you have to use <span class="math-container">$1-(x\text{ not happening})$</span>. That's how it is 90% of the times and will make the problem way easier. In your case, solving it without this method would have led to you having to write down ... | https://math.stackexchange.com |
73,634 | [
"https://mathoverflow.net/questions/73634",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16876/"
] | One knows that the support $S$ of a coherent sheaf on a noetherian scheme is closed.
E.g. on an affine scheme $X=Spec(A)$ and $F$ corresponding to a finitely generated $A$-module $M$, then the closed subset which corresponds to $S$ is just $V(Ann(M))$.
One often says that $S$ is endowed with the structure of a closed ... | No it isn't the reduced induced closed subscheme structure in general.
For example, let $A={\bf Z}$, $M={\bf Z}/4{\bf Z}$. Then ${\rm Ann}(M)=4{\bf Z}$ and the prime ideal defining $S$ (with its reduced structure) is $2{\bf Z}={\rm rad}({\rm Ann}(M))$. So if $S$ is endowed with the reduced structure, it is isomorphic ... | The answer to your second question is pleasantly general and simple.
Given a completely general scheme $X$ (no noetherian, separation, ...hypothesis) and an arbitrary closed subspace $F\subset |X|$ of its underlying topological space, there is a <em>unique</em> closed reduced subscheme $Y\subset X$ whose under... | https://mathoverflow.net |
26,173 | [
"https://mechanics.stackexchange.com/questions/26173",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/10884/"
] | Does the rear window defogger only work with both side terminals connected?
I observed that one of the terminal of my rear window is broken, so is it that now it wont even defog half of the screen? Or it works only if the other is connected as well?
| The rear defogger must have two connections. It works off of DC current and needs a positive connection and a negative connection in order for the electrons to flow and create heat. There are some kits out there which might help you to get this fixed, but I've never used them and don't know their voracity. They basical... | Rear window defrosters/defoggers can be configured in several different variations. The most common have a + positive wire going in one end of the grid and a - negative (ground wire) going to a metal part of the frame. This completes the circuit. The ground wire is usually on the opposite end of the (+) grid, but can ... | https://mechanics.stackexchange.com |
2,596 | [
"https://security.stackexchange.com/questions/2596",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/1768/"
] | I'm wondering if you can actually have 2 (or more) promiscuous (sniffing) ports on a single machine, to monitor multiple network segments? And can you monitor them all with snort?
| Absolutely. Specifically "promiscuous" mode is just a flag on the network stack that passes all packets seen on that interface up to the application layer. Using snort as an example, this is often how one will properly monitor multi-homed systems. One NIC monitoring each uplink.
Using snort as your IDS, please be care... | Yes you can.
I've had two wireless cards in promiscuous mode sniffing two different channels at the same time.
| https://security.stackexchange.com |
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