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 |
|---|---|---|---|---|---|
71,490 | [
"https://mathoverflow.net/questions/71490",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16791/"
] | Let $S$ be an integral Dedekind scheme.
Let $f:X\longrightarrow \mathbf{P}^1_{S}$ be a finite flat surjective morphism, where $X$ is an integral normal scheme.
Let $\eta$ be the generic point of $S$. Note that $f_\eta:X_\eta\longrightarrow \mathbf{P}^1_{K(S)}$ is a finite morphism of curves over $K(S)$.
<strong>Que... | In your case the function field of $X_{\eta}$ is the same as the function field of $X$. Thus the following general remark answers your question affirmatively.
Assume $Y$ is an integral scheme and $L$ is an algebraic extension of the function field $K(Y)$ of $Y$. Let $\pi\colon X \to Y$ be an integral morphism of schem... | Yes. This follows from Zariski's Main Theorem (although there are probably more direct arguments in this case).
| https://mathoverflow.net |
2,972,412 | [
"https://math.stackexchange.com/questions/2972412",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/426335/"
] | So I've been learning a bit of logic for class and heard that if you begin with a false statement, you can then prove anything to be true, however I don't entirely understand what this means or how to do it.
For example, if <span class="math-container">$\sqrt{2}$</span> is rational, can you prove that <span class="mat... | just for fun! assume there exist <span class="math-container">$a,b$</span> relative prime integers such that <span class="math-container">$\frac{a}{b}=\sqrt{2}$</span>, we can assume <span class="math-container">$a$</span> odd (otherwise we can argue in a similar way with <span class="math-container">$b$</span>) hence... | I believe what you are referring to is vacuous truth, and it's for implications.
The statement:
"If <span class="math-container">$\sqrt{2}$</span> is rational, then <span class="math-container">$1=0$</span>" is true logically, because the hypothesis (if <span class="math-container">$\sqrt{2}$</span> is rational) is fa... | https://math.stackexchange.com |
531,072 | [
"https://electronics.stackexchange.com/questions/531072",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/173474/"
] | For example if you wanted to created a datasheet with an item specifying that the device requires AC power, what would that item be called. My first thought is current type but that does not seem right.
| Power = voltage x current
Calculate the power available:-
12 V x 1 A = 12 W
Calculate the power required:-
12 V x 1 A = 12 W
5 V x 3 A / 0.8 (estimated converter efficiency) = 18.75 W
Total power required:-
12 W + 18.75 W = 30.75 W
Clearly you not have enough power to run both devices, nor even enough to run the 5 V de... | You can certainly do this but you'll need a beefier 12V output converter.
The currents to the downstream devices of the 12V converter must add up to no more than it maximum output. One of your devices requires 12V at 1A which immediately uses up your current budget.
As a rule of thumb you can assume that the DC-DC conv... | https://electronics.stackexchange.com |
444,781 | [
"https://stats.stackexchange.com/questions/444781",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/270912/"
] | Can the likelihood be defined as the probability of the rate parameter given a range of data. Or as the probability of the data, given a range of rate parameters?
| The answer to the question in the title is obviously "yes", because you can discretize every continuous distribution by splitting the real axis into cells <span class="math-container">$I_k=[x_{min}+(k-1)\Delta x,x+k\cdot\Delta x)$</span> and then define
<span class="math-container">\begin{equation}P(k) := P(X\in I_k) =... | Your assumption is flawed. While you might be able to set up a situation in which a normal distribution is fit to binomial data, the choice is not yours to make, but rather dictated by the form of the data and the phenomenon generating it. Binomial data is discrete, and if generated by the binomial distribution, it s... | https://stats.stackexchange.com |
41,941 | [
"https://softwareengineering.stackexchange.com/questions/41941",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/15177/"
] | So you've heard it many times from those who do not truly understand the values of testing. Just to start things out, I'm a follower of Agile and Testing...
I recently had a discussion about performing TDD on a product re-write where the current team does not practice unit testing on any level, and probably have never... | <blockquote>
attempting it in the fashion of TDD, will merely make it a maintenance nightmare and impossible for the team maintain.
</blockquote>
You can't win that argument. They're making this up. Sadly, you have no real facts, either. Any example you provide can be disputed.
The only way to make this point ... | You can only convince such people (if at all) from the practical point of view, demonstrating the value of TDD in real life. E.g. taking some recent bug as an example, and showing how to construct a unit test which makes sure 100% that this bug may never appear again. And then of course write a dozen more unit tests to... | https://softwareengineering.stackexchange.com |
63,427 | [
"https://mechanics.stackexchange.com/questions/63427",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/45515/"
] | My fiance's 2005 honda civic has had the interior electronics shut off while she was driving on a couple of occasions (weeks/months apart). I have not been able to reproduce this or been around to witness it happening.
Symptoms on occurance:
-guage cluster shuts off, no lights, gauges read zero
-radio shuts off
-cl... | Edit:
Thanks to Alephzero's comment, now removed, I had to correct my answer :
If the stud is to be fitted into the hub, then the hub need to be "locked" or wedged to prevent rotation, with a bar wedged against a strong suspension point for example and the stud torqued into place using two nuts locked together on the... | I have only needed to do this on one wheel ( 6 studs) , but I simply tightened them to about 5 ftXlb. That held them in place , then when I put on the rim/tire and torqued it to about 80 ftXlb while on the ground , it pulled the studs into the wheel.
| https://mechanics.stackexchange.com |
93,431 | [
"https://stats.stackexchange.com/questions/93431",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/14803/"
] | I have a very simple data set: a parameter (concentration of a chemical) was measured at day 0, day 1 and day 2 in three subjects (there is a control group as well, but here all the values are always 0). The results are as follows:
<pre><code> S1 S2 S3
day 0 0 0 0
day 1 0 5 45
day 2 ... | You write:
<blockquote>
As a biologist, I would say that no statistics is even necessary, the
data are obvious: not a single observation of a non-zero concentration
in the control group, and an observable increase in all of the treated
subjects.
</blockquote>
As a statistician, I agree with you. Also because ... | Since this appears to be count data (Poisson) and repeated measures I would use glmer in the lme4 package:
<pre><code>d <- read.table( text=
"day c S
0 0 S1
1 0 S1
2 70 S1
0 0 S2
1 5 S2
2 250 S2
0 0 S3
1 45 S3
2 60 S3", header= TRUE )
library(lme4)
mymodel<-(glmer(c ~ day + (1|... | https://stats.stackexchange.com |
356,338 | [
"https://electronics.stackexchange.com/questions/356338",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/178217/"
] | I am trying to write a program where the user uses a dial to adjust the intesity of one LED at the frequency of Red light and another LED in the same circuit that is at the frequency of Far Red light is auto adjusted to keep the the overall photon flux at 20 mircomoles per meters squared per second. How do I relate thi... | If something uses N kWh in a 30-day month, has an average consumption of
$$N \frac{1000\text{ W/kW}}{720\text{ h/month}}\text{ watts}$$
In other words, to convert "energy" to "power", divide by "time".
<hr>
Just as an example, suppose you use a 1500 W toaster for 3 minutes to make toast for breakfast. That would be... | If <strong>energy</strong> consumption in one month is 305kWh the mean (i.e. average) <strong>power</strong> consumption during that month is \$\frac{305kWh}{30 \times 24h}=\frac{305000}{720}W\approx 423W\$ (assuming a 30 day month).
| https://electronics.stackexchange.com |
109,802 | [
"https://mathoverflow.net/questions/109802",
"https://mathoverflow.net",
"https://mathoverflow.net/users/27293/"
] | I have read in some lecture notes in the internet (without reference) the following result:
<blockquote>
Let $E$ be a differentiable sphere bundle whose base $B$ has dimension $n\geq 2$ and whose fibers $F$ have dimension $n-1$. If $B$ is non-compact, then it admits a global smooth cross-section.
</blockquote>
The ... | I am guessing that you misunderstand the claim.
Here are some facts that seem to be in the right ballpark: a bundle whose fibers are spheres of dimension $n$ over a base whose dimension is $n$ or less will certainly have a section. And if the base $B$ has dimension $n+1$ then it will have a section if and only if the ... | This is NOT an answer but since the OP's origional statement is not clear, here is the theorem in the book of Greub, W., Halperin, S. and Vanstone that OP mentioned in his own answer:
<blockquote>
Theorem III: Every sphere bundle with fibre dimension $n - 1$ over a connected base manifold of dimension $n\ge 2$ admit... | https://mathoverflow.net |
47,327 | [
"https://mechanics.stackexchange.com/questions/47327",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/31841/"
] | Good day. So we bought a used 98' Nissan Presage (2.5L Turbodiesel/YD25) and we noticed that the tires on the front are 205/65 R16 and the rear left is 215/65 R16 while the rear right is 215/70 R16. We bought the car for cheap and everything seems fine after we've checked it to a mechanic except the tires.
We're gonn... | Generally speaking, SUVs get worse fuel mileage than a sedan with everything else being the same (yah, like that would ever happen). I agree with the other statements about the frontal area of the vehicle causing wind resistance at higher speeds, but there's another factor which hasn't been mentioned yet and that being... | Aerodynamics play a significant part in fuel consumption especially as speed increases. So, the frontal area as it increases cause a higher (worse) fuel consumption. But also driving style, habits and location have effects.
| https://mechanics.stackexchange.com |
8,095 | [
"https://physics.stackexchange.com/questions/8095",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/171/"
] | Every orbiting of a satellite around a mass is nothing else but a constant fall - and therefore acceleration - towards this mass. In a way it is a "falling around" that mass.
<strong>My question</strong><br> Is it possible to measure this acceleration on earth due to its "falling around" the sun?
| The answer depends in part on what you mean by "measure". You can certainly <em>calculate</em> the acceleration using the laws of kinematics and dynamics, as Lawrence B. Crowell points out in his answer. Does that, in your mind, count as "measuring the acceleration"?
Here's a much more direct recipe that I think would... | The acceleration can be found by a number of means. $F~=~ma$ with the Newtonian law of gravity and the centripetal acceleration $a~=~v^2/r$,
$$
m\frac{v^2}{r}~=~-\frac{GMm}{r^2}.
$$
This gives $v~=~\sqrt{GM/r}$, which is $v~=~29.5km/s$ or $v~=~2.95\times 10^4m/s$, for the mass of the sun and $r~=~1.5\times 10^11m$. T... | https://physics.stackexchange.com |
226,455 | [
"https://mathoverflow.net/questions/226455",
"https://mathoverflow.net",
"https://mathoverflow.net/users/83838/"
] | Let $M$ be a complete and noncompact Riemannian manifold. Fix a point $p$ in $M$. Let $\gamma$: $[0, L]\rightarrow M$
(parametrized by its arc length) be a geodesic starting from $p$. Denote by $d(\cdot, \cdot)$ the distance function on $M$ induced by
the Riemannian metric. $\gamma$ is minimal if $d(\gamma(s_1), \gamm... | The answer is yes. Consider a hyperbolic pair of pants where all three boundary circles are of the same size. Glue countably many of them together such each new one is glued to the existing manifold along exactly one boundary circle. Then the manifold looks like the boundary of a fattened tree.
Fix $p$ in one of the p... | Let me rephrase S. Goette's example in a slightly different way. Consider the complement of the triadic Cantor set in the complex plane. This is a Riemann surface that can be uniformized: there is a complete Riemannian metric of constant minus one curvature. The ends of this surface are in one-to-one correspondence wit... | https://mathoverflow.net |
111,126 | [
"https://electronics.stackexchange.com/questions/111126",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/43132/"
] | I was trying to find an answer everywhere, but all I can find is absorbtion and scattering, which doesn't limit the speed itself, just the quality of the signal.
| The speed at which you turn on and off the light source (laser) and the speed at which you can reliably read it, are typically the major limiters. Fiber optics may allow you to use light as your data medium, and of course at the speed of light, it would seem like an almost limitless way to transmit data. But in reality... | I've got a <em>really</em> informative book on this, unfortunately it is not where I am right now. So, with probably a lot of omissions and incorrect terms (you've got the internet, you look it up!), off the top of my head:
Over a short distance in ideal conditions, the limit is the laser & receiver;
- Modulation ... | https://electronics.stackexchange.com |
62,809 | [
"https://mechanics.stackexchange.com/questions/62809",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/25547/"
] | I know that accessory drive belts need to be changed every now and again as the rubber can dry out and crack.
I'm planning to replace the accessory drive belts on my 2008 Subaru Outback as preventative maintenance because they have never been changed in the car's life.
Should I, or would it be beneficial, to also rep... | Replacing the tensioner assembly would be a good idea as it usually has a bearing in it, given the age and probable mileage...
I don't see any need to replace any of the other pulleys unless they have been damaged.
| Changing out the tensioner pulley would not be a bad idea, especially while you're in there changing out the belt. However, it's not mandatory. Any of the pulleys up front are good until they aren't, but you can check it to see how it is fairing.
With the belt off, turn the tensioner pulley by hand.
<ul>
<li>How do... | https://mechanics.stackexchange.com |
493,100 | [
"https://stats.stackexchange.com/questions/493100",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/300645/"
] | I have two datasets with 35 points each. I know that both are pulled from normal distributions with equal variances. A two-sample t-test indicates they have the same mean, but the p-value is close to my alpha.
<ol>
<li>Knowing they are normal with equal variances, would it make sense to just create normal distributions... | No, you will assure yourself of eventually rejecting the null hypothesis of equality for a large enough sample size (1000 ought to do the trick unless the difference between sample means is tiny tiny tiny). All this would be doing is confirming your observation that the sample means are different, which you already kno... | But...why? Your data is as ideal as could be. It satisfies nearly every assumption of sophomore stats. People only write about this kind of problem.
Resampling opens you up to simulation noise in which you could falsely reject/fail to reject simply because of simulation error. The statistical significance would not... | https://stats.stackexchange.com |
155,063 | [
"https://dba.stackexchange.com/questions/155063",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/110384/"
] | I've got a question about a query.
I've got two tables. The first table has to columns, a start-date and an end-date.<br>
For example <em>start:</em> <strong>00:00:00</strong> and <em>end:</em> <strong>00:15:00</strong>
The first table <strong>period</strong>:
<pre><code>|---start---|----end----|
| 00:00:00 | 00:15... | Another way, that doesn't use dynamic SQL would be to first <code>CROSS JOIN</code> the <code>period</code> with a (derived) table that holds <code>DISTINCT name</code> values from <code>tt</code> and then <code>LEFT JOIN tt</code>:
<pre><code>SELECT
period.end,
n.name,
IFNULL(SUM(tt.punkte), 0) AS punkte... | idea next - for each distinct name we can calculate proper result:
<pre><code>SELECT
`end` ,
'AAAA' AS `name` ,
IFNULL((SELECT
SUM(points) FROM tt WHERE
tt.`name` = 'AAAA' AND (tt.zeit < period.END AND tt.zeit >= period.START)) , 0) AS punkte
FROM
period
</code></p... | https://dba.stackexchange.com |
16,172 | [
"https://ai.stackexchange.com/questions/16172",
"https://ai.stackexchange.com",
"https://ai.stackexchange.com/users/14504/"
] | I have an image classification task to solve, but based on quite simple/good terms:
<ul>
<li>There are only two classes (either good or not good)</li>
<li>The images always show the same kind of piece (either with or w/o fault)</li>
<li>That piece is always filmed from the same angle & distance</li>
<li>I have at ... | VGG is a more basic architecture which uses no residual blocks. Reset usually perform better then VGG due to it's more layers and residual approach. Given that resnet-50 can get 99% accuracy on MNIST and 98.7% accuracy on CIFAR-10, it probably should achieve better than VGG network. Also, the validation accuracy should... | Below is a listing of Keras application models that can be used easily in transfer learning. Note VGG has on the order of 140 million parameters which is why it is slow.
<pre><code>
Model Size Top-1 Accuracy Top-5 Accuracy Parameters 1Depth
Xception 88 MB 0.790 0.945 ... | https://ai.stackexchange.com |
365,427 | [
"https://softwareengineering.stackexchange.com/questions/365427",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/293148/"
] | I can see several post where importance of handling exception at central location or at process boundary been emphasized as a good practice rather than littering every code block around try/catch. I strongly believe that most of us understand the importance of it however i see people still ending up with catch-log-reth... | The problem isn't the local catch block, the problem is the <em>log and rethrow</em>. Either handle the exception or wrap it with a new exception that adds additional context and throw that. Otherwise you will run into several duplicate log entries for the same exception.
The idea here is to <strong>enhance</strong>... | This depends a lot on the language. E.g. C++ doesn't offer stack traces in exception error messages, so tracing the exception through frequent catch–log–rethrow can be helpful. In contrast, Java and similar languages offer very good stack traces, though the format of these stack traces may not be very configurable. Cat... | https://softwareengineering.stackexchange.com |
522,458 | [
"https://electronics.stackexchange.com/questions/522458",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/263411/"
] | Fuses and circuit breakers are often specified at a certain current they will 'blow'.
Increasing the current will also increase the power.
So if a fuse is rated for 12V DC and 20 A, this would be equal to 240 watts. If a different voltage is supplied, will this change the current at which the fuse will break? Does the ... | It's the watts dissipated in the fuse itself not the watts in the system. Therefore since the fuse has resistance (R) it's the current, which provides that power I^2*R.
The voltage has nothing to do with it : at 6V, 12V or 240V, the fuse still blows at 20A. However you cannot use a low voltage fuse in high voltage appl... | <blockquote>
<em>So if a fuse is rated for 12V DC and 20 Amps, this would be equal to
240 Watts. If a different voltage is supplied, will this change the
Amps at which the fuse will break? Does the fuse technically 'blow' at
240 Watts?</em>
</blockquote>
All the fuse knows (before it blows) is the current passing throu... | https://electronics.stackexchange.com |
282,617 | [
"https://electronics.stackexchange.com/questions/282617",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/137101/"
] | One of four (4) 750 ohm 5w ceramic resistors in a subwoofer's power amp section seems to be open. I want to replace it with a compatible ceramic resistor.
Questions:
<ol>
<li>Will the 10W one generate more heat?</li>
<li>Is it OK to mix one 10W resistor with three (existing) 5W resistors? (All 750 ohms and 5% toleran... | <ol>
<li>No more or less heat as total energy, but the 5W unit very likely runs hotter because its cooling is designed to be less effective due the smaller rating</li>
<li>No problems in circuit's function because Ohm's law is the same. Mechanical problems can occur. I've seen, how heavier parts make mechanical resonan... | <blockquote>Is it OK to replace a 750 ohm 5W ceramic resistor with a 750 ohm 10W ceramic resistor?</blockquote>
Yes.
<blockquote>Will the 10W one generate more heat?</blockquote>
No.
<blockquote>Is it OK to mix one 10W resistor with three (existing) 5W resistors? (All 750 ohms and 5% tolerance.)</blockquote>
Yes.
| https://electronics.stackexchange.com |
387,874 | [
"https://electronics.stackexchange.com/questions/387874",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/-1/"
] | I have a question!.
As I understand,the 3 diodes are "more or less" the same but with really important differences:
<ul>
<li>Zener diode: Clamps voltage at a breakout lvl.</li>
<li>Schottky diode: Like Zener but it lose less voltage in forward mode and it switches way faster.</li>
<li>TVS-Diode: The transient voltage... | Manuel,
Zener and TVS diodes are similar in that they are normally operated with reverse bias voltage. Zeners are mostly operated at breakdown to act as a voltage regulator or clamp. TVS diodes are used for protection against spikes from ESD and other transient events. They normally operate below breakdown where they ... | No, your understanding is not correct. Zener diodes are designed to have a specified reverse bias breakdown, and these diodes are typically used in reverse bias. A Schottky diode is specified to have a <strong>minimum</strong> reverse bias breakdown voltage but the actual breakdown may occur at a much higher voltage. T... | https://electronics.stackexchange.com |
3,296,144 | [
"https://math.stackexchange.com/questions/3296144",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/578160/"
] | I would like to sharpen my understanding re the following:
I am new to Differential Equations, and was recently taught how to find factors of integration by which to multiply existing formulas, in order to make them exact. I was taught that no set algorithm exists, but if I apply the formula <span class="math-containe... | Try <span class="math-container">$e^{-2x} $</span> as the integrating factor and it works fine.
Note that <span class="math-container">$$\frac {d}{dy} e^{-2x }(x+y^2)=2e^{-2x}y=\frac {d}{dx}(-e^{-2x}y)$$</span>
Thus the resulting equation is exact.
| It is easily checked that <span class="math-container">$\dfrac{1}{y^2}$</span> is not an integrating factor for
<span class="math-container">$$ (x+y^2)dx-ydy=0 $$</span>
Given
<span class="math-container">$$ \left(\frac{x}{y^2}+1\right)\,dx-\frac{1}{y}\,dy$$</span>
we get
<span class="math-container">$$\frac{\part... | https://math.stackexchange.com |
13,923 | [
"https://datascience.stackexchange.com/questions/13923",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/15412/"
] | I am trying to do sentiment analysis. In order to convert the words to word vectors, I am using Word2Vec model. Suppose I have all the sentences in a list named 'sentences' and I am passing these sentences to word2vec as follows:
<pre><code>model = word2vec.Word2Vec(sentences, workers=4 , min_count=40, size=300, wind... | 1- The number of features: In terms of neural network model it represents the number of neurons in the projection(hidden) layer. As the projection layer is built upon distributional hypothesis, numerical vector for each word signifies it's relation with its context words.
These features are learnt by the neural networ... | <ol>
<li>According to distributional hypothesis, individual dimension in the vector of the word does not signify much about the word in real world. You need to worry about the individual dimensions. If your question is so how should I select the number of dimensions, it is purely based on experiment for your data and i... | https://datascience.stackexchange.com |
2,118 | [
"https://mathoverflow.net/questions/2118",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1049/"
] | The rationals are clearly dense in the real number system, i.e. for every pair a < b of real numbers there exists a rational number p/q s.t. a < p/q < b. I conjecture the same to be true with p and q both primes. Any idea of how one could prove it? It should depend on some strong result on the distribution of ... | Yes. Take q sufficiently big and fixed (in terms of a and b). Then the question is, is there some prime p between qa and qb? Use the prime number theorem to estimate pi(qb) - pi(qa) > 0, where q is chosen to be big enough so that the main term is bigger than the error terms. QED.
| You don't need the prime number theorem. Suppose the result is false, i.e. for fixed a and b there are only finitely many q such that there is a prime between qa and qb. Then the nth prime p<sub>n</sub> grows at least as fast as (b/a)^n; in particular, sum 1/p<sub>n</sub> converges, which we know to be false (and whi... | https://mathoverflow.net |
549,261 | [
"https://math.stackexchange.com/questions/549261",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/99554/"
] | i try to find the biggest m that
$$f(h) = \frac{e^h-e^{-h}}{2h}-1$$
is $\in O(h^m)$ ($h \to 0, h > 0$)
I thought i have to use the definition.
So i wrote this:
$$ limsup_{h \to 0} \left | \frac{\frac{e^h-e^-h}{2h}-1}{h^m} \right | = limsup_{h \to 0} \left | \frac{e^h-e^{-h}-2h}{h^m \cdot 2h} \right |$$
bu... | I believe the fundamental problem (or confusion) here is that OP finds it difficult to believe that a rational number, which is a ratio of two finite integers, can have a representation which is infinite. This confusion is primarily due to the fact that most people try to think of a number and its representation as one... | $$\begin{align}
0.3333333333333\ldots &= 0.3 +0.03 +0.003 +0.0003+ \ldots\\
&=\frac{3}{10} + \frac{3}{100} + \frac{3}{1000}+ \frac{3}{10000} +\ldots
\end{align}$$
If you know the sum of a geometric sequence, that is:
$$a+aq+aq^2+aq^3+\ldots = \frac{a}{1-q} \quad\text{ if $|q| < 1$}$$
you can use it to conc... | https://math.stackexchange.com |
185,640 | [
"https://softwareengineering.stackexchange.com/questions/185640",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/55003/"
] | I guess this is more of a "comfort seeking" question than legality one.
You see, for the past couple of months I have been brainstorming and developing a product, all by myself. I was planning to release it under some kind of free license. While I know no idea is ever a unique one, I was quite happy to note that the w... | I would say, stop coding, stop testing and take a couple of days or weeks of and try to find a way to enhance and expand your product feature-wise and do it in such a way that it sets it apart from the other product. You may be able to think up some radical changes you hadn't thought of before.
| Is the other project "open source"? If so, you can join that community and improve it. If not, you can make yours open source and try to attract similar minded people.
As you can tell I am not from the business world either.
| https://softwareengineering.stackexchange.com |
219,257 | [
"https://softwareengineering.stackexchange.com/questions/219257",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/109547/"
] | I have read this statement:
"A parameter is used as a sort of temporary messenger, carrying data originating from outside the constructor or method and making it available inside it."
So, does that mean that values of parameters are stored at first in the constructors and then passed to fields?
I still didn't unders... | So when you see a constructor:
<code>Foo(int x){ this._x = x; }</code>
The parameter <code>x</code> is a temporary, local variable that contains the value passed into the constructor (or any other function). You then assign it to <strong>another</strong> variable <code>this._x</code> <em>but you don't <strong>have</s... | <pre><code>public class Whatever {
public static int foo(int a){
return a+2;
}
public static void main(String[] args){
int x = 1;
System.out.println(Whatever.foo(x));
}
}
</code></pre>
"Parameter" is "a". It is a name that exists only in local scope (scope is part of code where... | https://softwareengineering.stackexchange.com |
82,285 | [
"https://security.stackexchange.com/questions/82285",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/34347/"
] | My Girlfriend has a years-old laptop from lenovo. I checked it over and wasn't surprised that the Superfish / Komodia Root CA certificate was not present. However I found some others that appear to be similar in function if not purpose.
There's keys which appear to have been installed by Avast anti-virus and Skype, ... | My understanding is that Superfish installs the exact same certificate and private key into every computer, so once you obtain the hard-coded private key you can use it to man-in-the-middle anyone who has superfish installed. Avast does not do this; it dynamically generates a unique certificate and private key for ever... | IF you are unsure about Avast's behaviour, check the Avast Certificate validity date.
Avast reports, as for now, the Certificate to be valid between 2013- 10- 22 and 2016- 07- 06 as expiry date for this page in HTTPS://, Issued to *.stackexchange.com, and issued by
"avast! Web/Mail Shield Root".
Disabling Avast pro... | https://security.stackexchange.com |
3,306 | [
"https://security.stackexchange.com/questions/3306",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/-1/"
] | Is there a reason for sites to ask for another CAPTCHA verification when some other part of the registration form, e.g. the username, was invalid?
| If the site has a means of knowing it's the same user in the same session, then no. So for example given a cookie or an ssl session then it seems OK to assume it's still a human user (within the limits of captcha).
If it's just a cookie that establishes the session (i.e. this is over http without SSL) then make sure ... | No. But then, was there a reason to ask for a CAPTCHA in the first place?
Let's take a random example of a platform that implements CAPTCHA; say, Stack Exchange. What Stack Exchange sites want is a collection of high-quality questions and answers on a particular topic. There's nothing there that intrinsically requires... | https://security.stackexchange.com |
2,733 | [
"https://mechanics.stackexchange.com/questions/2733",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/294/"
] | My 2002 ford focus (built after may 23) died and the AAA and tow guy both said that it needs a new fuel pump.
Anyway I went to the mechanic and he said it'll be 350 for the pump and 200 for labor. I called Autozone and found it for 170 so I bought the part and brought it to the mechanic and only paid for labor.
Anyw... | <ol>
<li>There is often a huge gap in the price of parts. There are some components for my car that when bought through the dealer are over £2000 but when sourced on the internet may be under £500. Some of the price differential is down to warranty, dealer specifics, supply and demand.</li>
<li>Generally for cars that ... | Your mechanic probably quoted you pricing for either OEM, or high-end replacement market (like NAPA). They usually use those parts as they're trying to minimize the liklihood of you having to comeback for the same problem soon. The lower cost parts available on the Internet and from discount stores tend to have a hig... | https://mechanics.stackexchange.com |
13,574 | [
"https://electronics.stackexchange.com/questions/13574",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1944/"
] | I saw quite a few custom computer units and laptops that are powered by adapters/batteries totalling 18 to 24 V. What's the significance of this design choice?
| There are a few things that come into consideration with this voltage.
One item is the voltage required by LCD backlights. A higher voltage makes it much easier to power them instead of having to go into some variable voltage boosting.
Another item is the chemical make up of batteries and the number of battery cells ... | Absolutely nothing inside the system works directly on the main DC voltage, there is always a DC/DC converter in between, so designers tend to choose the voltage high enough to get the current down to something the connectors and wires will take as long as it's not chosen so high that it becomes a risk and components g... | https://electronics.stackexchange.com |
361,963 | [
"https://softwareengineering.stackexchange.com/questions/361963",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/198751/"
] | I apologize in advance for the length of this question; it requires some explanation. I'll try to make it as clear as possible.
I am developing and maintaining a mobile app (Xamarin, F#) that communicates with a web API (ASP.NET Core, F#). The server-side API exists only to communicate with the app and do database ope... | Binary serialization can be very brittle. I would only use binary serialization in very special cases where you need the economy that such serialization would provide (e.g. file transfers), you don't have to pass through firewalls, you have complete control over both ends of the communication, and the data format will... | I'm a bit confused by your setup, let me lay my usual approach out:
<ul>
<li>Shared Anaemic Models</li>
<li>Client logic services - perform client side logic</li>
<li>Versioned Client - serialised/deserialises to JSON (or alternative) and sends to server</li>
<li>Versioned Server - deserialises to Model and calls serv... | https://softwareengineering.stackexchange.com |
240,961 | [
"https://softwareengineering.stackexchange.com/questions/240961",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/66482/"
] | It seems to be a very common thing to have to tell whether some list or set contains at least one object matching a given condition, yet my prior searching and reading have never found a satisfactory best practice or design pattern to speak of. In the situations I am thinking of, merely using "contains" is not suffici... | Algorithmically, the for-each and the while-with-indexing version implement <em>linear search</em>. This is okay for small collections or when you only do such a check very occasionally, but if it's an important building block of your program, you'd want a dedicated mapping structure which speeds up these queries by do... | Both your suggestions are unnecessarily verbose, and the input type is too specific. Prior to Java 8 I would write:
<pre><code>private boolean doFoosHaveGoodQuality(Iterable<Foo> candidates) {
for (Foo item: candidates) {
if (<< item passes some test >>) return true;
}
return fal... | https://softwareengineering.stackexchange.com |
262,215 | [
"https://softwareengineering.stackexchange.com/questions/262215",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/129348/"
] | The following code looks rather harmless on first sight. A user uses the function <code>bar()</code> to interact with some library functionality. (This may have even worked for a long time since <code>bar()</code> returned a reference to a non-temporary value or similar.) Now however it is simply returning a new instan... | Let's think about this very carefully. libA.so is statically linked with the STL. However, the STL does not exist in isolation, it requires the C runtime (CRT). They both reside in the libstdc++.a static library. This means that libA.so and libB.so have separate CRT data structures. In particular, the heap used by libA... | The STL is so-called "state-full" (as opposite to being "state-less") meaning that it has some static stuff inside. When you link STL statically to both libA.so and libB.so you get two instances of STL library in memory at run-time (with two copies of static stuff).
Each of those two copies manages allocated resources ... | https://softwareengineering.stackexchange.com |
417,800 | [
"https://mathoverflow.net/questions/417800",
"https://mathoverflow.net",
"https://mathoverflow.net/users/477847/"
] | I am working on a paper which will extend a result in my thesis and have boiled one problem down to the following: show that the symmetric matrix <span class="math-container">$M_p$</span>, whose definition follows, is invertible for all odd primes <span class="math-container">$p$</span>. Letting <span class="math-conta... | Experimentally, we have the following formula for <span class="math-container">$p$</span> prime:
<span class="math-container">$$\det(M_p)=(-1)^{(p^2-1)/8}(2p)^{(p-3)/2}h_p^-\;,$$</span>
where <span class="math-container">$h_p^-$</span> is the minus part of the class number of the <span class="math-container">$p$</span>... | Here are some elements to solve the question.
<strong>1st step</strong>. Extend <span class="math-container">$M_p$</span> as a <span class="math-container">$(2\ell)\times(2\ell)$</span>-matrix <span class="math-container">$N_p$</span>, with the same definition of entries. By the way the entries may be writen as <span c... | https://mathoverflow.net |
103,166 | [
"https://datascience.stackexchange.com/questions/103166",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/126520/"
] | I am working currently on churn <strong>prediction problem</strong>.
As an input I use data from date warehouse for a period <strong>082016 - 032021</strong>(one row per month for each customer).
Based on this data I have created a time window of 18 months, where I track customer behaviour(feature engineering).
Based o... | 2020 has thrown a lot of models off. I'ld suggest training your model on 2016-2018 and evaluating it on 2019 data. If that looks good, you'll know that your pipeline is fine
| You are unlikely to get a useful answer without a lot more details as there are lots of things that could cause this.
How many features and how many observations do you have?
It is possible that you have massively overfit your training set:
<ul>
<li>Did you do a lot of hyper parameter tuning on your model?</li>
<li>whe... | https://datascience.stackexchange.com |
157,620 | [
"https://electronics.stackexchange.com/questions/157620",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/39947/"
] | If my schematic calls for a 1% resistor, can I use a 10% resistor that measures to the correct resistance within 1% or is there some quality to tolerance beyond what it measures Ohm-wise?
For example, my schematic calls for a 1% 1000-Ohm resistor. I have a 1000-Ohm resistor with a silver band (10%). I measure the resi... | Resistors based on carbon tend to have quite more noise (there are a number of noise types apart from basic thermal noise). So you usually don't want them in an audio circuit even if the accuracy itself may not be much of an issue.
| You don't provide much info regarding the environment that the circuit will be used in or the specific resistor types.
If you expect temperature variations (or even temperature change caused by self heating) then temperature coefficient becomes important and the initial measured resistance value may be soon way off.
B... | https://electronics.stackexchange.com |
173,639 | [
"https://physics.stackexchange.com/questions/173639",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/42117/"
] | As we all learn in Basic Quantum Mechanics (the first quantization), we promote the classical variables to operators. Say, the classical hamiltonian $\frac{p^2}{2m}+V(x)$ to $-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}+V(x)$, where we have replaced $p$ by $-i\hbar \frac{\partial}{\partial x}$ in coordinate representation.
But ... | This problem is rooted in the way we derive quantum mechanics from the classical theory. Basically a quantum theory is a more complex object than a classical theory, so you will need to specify more information about it in order to it to be well defined. Thus after you have defined the hilbert space and it's operators ... | When you have a product of operators in the classical Hamiltonian, the ordering of the operators in the quantum prescription is ambiguous. In the general case, suppose we have some classical operator $o=px$. As you noted, simply writing $O=PX$ is not Hermitian. The standard procedure is to symmetrize the sum, so that
$... | https://physics.stackexchange.com |
1,876,483 | [
"https://math.stackexchange.com/questions/1876483",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/140396/"
] | I have the following matrix:
$$
\left( \begin{array}{ccc}
13 & 9.1 & 8.19 & 8.281 & 8.9271\\
9.1 & 8.19 & 8.281 & 8.9271 & 10.02001\\
8.19 & 8.281 & 8.9271 & 10.02001 & 11.562759\\
8.281 & 8.9271 & 10.02001 & 11.562759 & 13.6147921\\
8.9271 & 10.02001... | The inverse is:
$$\begin{pmatrix} \dfrac{809}{143} & -\dfrac{6950}{143} & \dfrac{53375}{429} & -\dfrac{17500}{143} & \dfrac{17500}{429} \\
-\dfrac{6950}{143} & \dfrac{95565775}{204204} & -\dfrac{110879125}{87516} & \dfrac{9395000}{7293} & -\dfrac{9603125}{21879} \\
\dfrac{53375}{429} ... | Glance at the derivations of the normal equations for least squares regression and can see a relatively numerically stable way to get the fitted values for the given X axis data points if don't care about accurate values for the coefficients. This works even if are 'overfitting'.
Under mild assumptions, the normal equ... | https://math.stackexchange.com |
65,911 | [
"https://electronics.stackexchange.com/questions/65911",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/18772/"
] | I have a fairly simple circuit that works perfectly on the breadboard, but I am having a lot of trouble transferring it to a PCB. I am seeing very strange behavior which lies outside of my current experience, so I hope to get some advice.
The circuit implements a wifi motion sensor, although the problem I am having h... | EDIT - because of my misinterpretation of the circuit I'm editing the answer to focus on the output of the sensor - are you using the analogue output to feed into the inverter - if you are maybe you should try a Schmitt trigger like a 74HC14
| Without studying your circuit in great detail, the obvious thing is you have no decoupling capacitors.
Solder one across the power pins of each chip.
Also, your 'scrubbing makes it work' comment suggests you have a dry joint or intermittent connection somewhere. Inspect all your soldering carefully.
Regarding a DIL ... | https://electronics.stackexchange.com |
310,695 | [
"https://softwareengineering.stackexchange.com/questions/310695",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/217217/"
] | In colleges and in algorithm textbooks, it is quite common for the teacher and author to explain control flow in pseudo-code. With the advent of more expressive languages like Python and Haskell among others, is it reasonable that colleges switch to explain algorithms via one of these languages?
The only advantage of ... | No. The point of pseudo-code is that it doesn't have to compile. I can quickly gloss over irrelevant details. In contrast, even languages that look like pseudocode at the first glance can have very non-intuitive details that would just detract from the algorithm. Let's take for example Quicksort in Haskell:
<pre class... | No.
The entire purpose of pseudo-code is to abstract away the details and complexities of individual languages so that you focus on what the program's supposed to do, rather than how it does it. With pseudo-code you can make up arbitrary rules that do not need to conform to actual implementation requirements the way t... | https://softwareengineering.stackexchange.com |
140,621 | [
"https://softwareengineering.stackexchange.com/questions/140621",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/49184/"
] | I was sent out to discuss a system that a certain company is currently using and what should be done with it.
The company manufactures various carton displays. This system was developed to keep track of clients, orders and prices. Lots have happened since the system was created and the system is now, as the manager de... | Something with only 6 forms and such <em>should</em> be easy to rebuild on a more modern framework. I've worked with migrating VB6 projects that had around 200 forms along with dozens of classes and database tables. It doesn't sound like you're looking at anything that messy but looks can be deceiving.
I'd have to an... | I have slightly different advice the most of the responses so far.
<blockquote>
Attempt to patch the current system
</blockquote>
I would at least learn the current system well enough to explain to the client how to use it. I would take this time to explain the flaws in their current system, avoid negative words, ... | https://softwareengineering.stackexchange.com |
183,597 | [
"https://dba.stackexchange.com/questions/183597",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/132736/"
] | In MySQL, the foreign keys of a table standing for a many to many relationship do not work even though I did set them to the "child" table named <code>course_inscription</code>.
When I execute a statement to insert a new row into <code>course_inscription</code>, MySQL must launch the error due to the checking of the ... | Worth checking that you are using a Storage Engine that supports Foreign Key Constraint checking.
<pre><code>SELECT TABLE_NAME,
ENGINE
FROM information_schema.TABLES
WHERE TABLE_SCHEMA = 'dbname';
</code></pre>
The MyISAM Storage engine for instance does not support checking of Foreign Key Constraints.
If... | This is not the expected behaviour of MySQL. I try to reproduce the error, but MySQL prompting foreign key constraint error. For reference:
<pre><code>mysql> create database studentmgmt;
Query OK, 1 row affected (0.00 sec)
mysql> use studentmgmt;
Database changed
mysql> CREATE TABLE student(
-> i... | https://dba.stackexchange.com |
213,567 | [
"https://stats.stackexchange.com/questions/213567",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/23946/"
] | I am running a regression of the form
$$\log\left(Y\right)=x_0 + x_1\beta_1+\log (x_2)\beta_2 +x_3\beta_3+ \epsilon$$
where all the covariates $x_1$,$x_2$,$x_3$ are endogenous. I have an instrument for only one of them ($x_1$) and have no instrument for $x_2,x_3$.
I am estimating the above regression with 2 stage le... | Ignoring any issues of model construction and fitting, let's answer the question: how does the predicted value of $Y$ change when $x_1$ is changed by a small amount? To find this, <strong>treat only $x_1$ and $Y$ as variables, ignore the random components in the model, and differentiate:</strong>
$$\eqalign{\frac{dY}... | To use $Y$ in feature construction is a delicate thing as it almost always introduces endogeneity issues. Maybe you remember that in "classic" inference on the linear model, all regressors are considered to be fixed design points. This assumption will be invalid in your case quite certainly.
The interpretation of a be... | https://stats.stackexchange.com |
439,875 | [
"https://math.stackexchange.com/questions/439875",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/28743/"
] | Are there general expressions for $\sin(2^n x)$ and $\cos(2^n x)$ that only involve $\sin x$ and $\cos x$, and that moreover involve only <strong>polynomial</strong> (in $n$) number of terms?
<strong>Edit</strong>:
$2^n$ is not polynomial in $n$. A proof that no such expression exits (perhaps using the uniquness of ... | If I understand the spirit of the question, no such expressions exist. First, $\cos(2^n \theta)$ is even, so a polynomial in $\sin \theta$ and $\cos \theta$ that is equal to $\cos(2^n \theta)$ contains only even powers of $\sin\theta$, and therefore may be written as a polynomial in $\cos\theta$, as marty cohen notes.
... | I might be missing something here... but the identity $\cos(2x)=2\cos^2(x)-1$ can be trivially applied $n$ times to obtain an <em>expression</em> with polynomial length:
$$\begin{eqnarray}
\cos(2^nx) & = & 2\left(\cos(2^{n-1}x)\right)^2-1 \\
& = & 2\left(2\left(\cos(2^{n-2}x)\right)^2-1\right)^2-1 \\
&a... | https://math.stackexchange.com |
121,225 | [
"https://softwareengineering.stackexchange.com/questions/121225",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/65563/"
] | I have two classes (named <code>MyFoo1</code> and <code>MyFoo2</code>) that share some common functionality. So far, it does not seem like I need any polymorphic inheritance but, at this point, I am considering the following options:
<ol>
<li>Have the common functionality in a utility class. Both of these classes call... | Are <code>Foo1</code> and <code>Foo2</code> actually related (conceptually, that is) or do they simply share some functionality?
If they're conceptually related, I would go with an abstract class.
If they simply share the functionality, I would break out that functionality and make a separate class. You can then use ... | As always it depends.
If all instaces of <code>Foo1</code> and <code>Foo2</code> can logically be called <code>FooParent</code> then use inheritance.
For the utility class to make sense it should be something that be used across multiple projects, think about the Apache libraries on this one.
Typically in thes... | https://softwareengineering.stackexchange.com |
135,478 | [
"https://security.stackexchange.com/questions/135478",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/91253/"
] | I'm considering sending more than 100,000 emails as fast as possible to different users of my website. These is not spam but requested emails. I'm using my own mail server (Exchange 2010).
May I have into account any security concerns?
For example, I think that:
<ul>
<li>My IPs may be blacklisted by remote mail serv... | Mail receivers often track sender spam <strong>reputation per IP address</strong>. If you use a <strong>third-party</strong> provider to send the emails, then it is their IP which will take the reputation hit not yours. This is important to understand, as you <strong>don't</strong> want your all-important company Email... | If you do not implement proper rate limiting, your mail server's IP Address could get blacklisted and all mail rejected.
<strong>Good Practices:</strong>
<ul>
<li>Only send a few emails per second (do not send 1000s emails in 3 seconds).</li>
<li>Use proper SPF records.</li>
<li>DKIM sign all messages.</li>
<li>Inclu... | https://security.stackexchange.com |
83,488 | [
"https://electronics.stackexchange.com/questions/83488",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/29484/"
] | Having trouble with a circuit on my problem set and was wondering if anyone wanted to give me a push.
<img src="https://i.stack.imgur.com/ufWVS.png" alt="enter image description here">
<em>The ideal transformers winding relationship N1/N2 can be varied, as can the capacitance.</em>
<em>Decide the optimal ratio and th... | To maximize power into the resistors the inductive reactance needs to be cancelled by the capacitive reactance. This is because the circuit is series-tuned (despite the presence of the transformer).
You know the frequency (1kHz) and you know the inductance (1uH) and the natural resonant frequency for an LC circuit (se... | It's a bit of a trick question.
When you understand that the inductor and the (transformed) capacitor form a series-resonant tuned circuit, which cause their impedances to cancel, you're simply left with the source resistance R1 and the load resistance R2, and their ratio determines the required turns ratio of the tra... | https://electronics.stackexchange.com |
406,223 | [
"https://electronics.stackexchange.com/questions/406223",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/204029/"
] | Why is Common Collector amplifier is also known as Emitter Follower?
| The spec says that the input is guaranteed to be read as a Low below 0.25 Vdd, and as a High above 0.75 Vdd.
It does not specify where the actual switching threshold is - from the spec, we only know that the switching threshold is somewhere between 0.25 Vdd and 0.75 Vdd. The actual threshold may vary between parts ... | (0.825 V + 2.475 V)/2 = 1.65 V. Seems your observed value (1.67 V) is almost exactly in the middle between the theoretical values.
I want to use an ESP8266-S01 to indirectly measure a variable resistor using this method: charging a capacitor over a GPIO and measuring the time of discharge until the voltage threshold is... | https://electronics.stackexchange.com |
314,453 | [
"https://physics.stackexchange.com/questions/314453",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/142851/"
] | I have a homework question that asks me to calculate the change in the entropy during the isothermal expansion using the Sackur-Tetrode. Then, show that it is a reversible process.
I have finished the first part and got $\Delta S = Nk\ln(\frac{V_f}{V_i})$. According to the definition of the book, I am using, a process... | Reversibility is when $dS=\frac{\delta Q}T$ so entropy can change but equality sign should be satisfied.
So you have already got $\Delta S = Nk\ln(\frac{V_f}{V_i})$
Note for an isothermal process, $\delta Q=dW$. For ideal gas, $PV=NkT$ or $P=\frac{NkT}{V}$
So, the work done during the expansion is $dW=\int_{V_i}^{V... | A process is reversible if the change in entropy of the <strong>system and its surroundings</strong> total zero. The entropy of the system can change and the entropy of its surroundings can change in a reversible process as long as their sum doesn't change. In your case, if the gas was in contact with a constant temp... | https://physics.stackexchange.com |
280,883 | [
"https://physics.stackexchange.com/questions/280883",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/56799/"
] | Equaling relativistic version of 2nd Newton law to Lorentz force
$$
\frac{d}{dt} (\gamma_u m \mathbf{u}) = q(\mathbf{E} + \mathbf{u} \times \mathbf{B})
$$
we can see that a point particle (of mass $m$ and charge $q$) in a electromagnetic field ($\mathbf{E},\mathbf{B}$) has acceleration
$$
\mathbf{a} =
\frac{q}{\gamm... | Laminar flow occurs when the liquid layers move parallel. Otherwise stated, the motion of the particles of the fluid is very orderly with all particles moving in straight lines parallel to the pipe walls. The condition in which Bernoulli's principle has been derived is that the viscosity of the fluid should be negligib... | MrYouMath said it correctly.
Laminar flow doesn't imply $\Delta \times \vec{u} = 0$.
Best expample is laminar boundary layer. Assume in a flat-plate you have a boundary layer which is laminar with $u = (y/\delta)^2 $ (a parabolic velocity profile with boundary layer thickness $\delta$.)
$ \Delta \times \vec{u} =... | https://physics.stackexchange.com |
14,853 | [
"https://cs.stackexchange.com/questions/14853",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/7890/"
] | Let $f(x)=a_0+a_1x+a_2x^2+\dots+a_nx^n$, where $a_i\ge0$ and $a_i$ is integer.
Given $f(1)=p$ and $f(f(1))=q$, we have to find $a_0$, $a_1$, $a_2$, $a_3$, $\dots$, $a_n$, where such $f(x)$ exists. Or we have to confirm if such $f(x)$ exists or if the polynomial is ambiguous e.g. for $p=1$ and $q=2$, no such $f(x)$ exi... | The conditions $f(1) = p$ and $f(p) = q$ imply the following two equations:
$$
\begin{align}
&\sum_{i=0}^n a_i = p, \\
&\sum_{i=0}^n a_i p^i = q.
\end{align}
$$
When $p < 0$ or $p$ is not an integer, there are no solutions. When $p = 0$, the first equation implies that the polynomial must be $0$ and so $q = ... | If $p=1$, then the constraints are $f(1)=1=q$ which is easily solved depending on the value of $q$. Let's now assume $p \ge 2$. Suppose that $f(x) = \sum_k a_k x^k$ is a solution. Then $q = a_0 + a_1 p + a_2 p^2 + \ldots + a_n p^n$ where $n$ is the degree of $f$ ($a_n \ne 0$).
For any $k \le n$, $a_k \le \dfrac{q}{p^k... | https://cs.stackexchange.com |
588,617 | [
"https://physics.stackexchange.com/questions/588617",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/277761/"
] | If I have 3 LED lights of following colors and wavengths:
Red 650 nm
Blue 450 nm
Green 550 nm
All three are placed side by side and turned ON.. then what will be the wavelength of the combined light that my eye will see? Most probably the combined color will be 'whitish' because the mixing of RGB colors give white colo... | Yes, typical bathroom scales measure weight <span class="math-container">$mg$</span>, not mass <span class="math-container">$m$</span>. But for convenience they are calibrated to show a reading in mass units, eg kilograms (or pounds).
So if the scales indicate that your "weight" is 50 kg that really means tha... | Typical bath scales do measure weight and report the weight in units of mass. These scales will report a lower weight for the same mass at the equator compared to the poles and at a high altitude compared to a low altitude. Usually these errors are far below the precision of the reported weight.
However, there are simi... | https://physics.stackexchange.com |
79,467 | [
"https://electronics.stackexchange.com/questions/79467",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/19215/"
] | I want to define a parameter in Verilog in such a way that several modules will be able to use it.
Each module is implemented in different file.
Can it be done or should I (re)define this parameter in each module ?
| If you want to share a parameter among a limited set of modules within your ovarall design, you can define the parameter in an enclosing module, and then pass it into the modules that need it using the following instantiation syntax:
<pre><code>parameter PARAM = value;
module_name #(.PARAM(PARAM)) instance_name ( ...... | How about putting the parameter into a separate file, and then `include this file into any files that want to have the parameter defined? That gives you single point of update in case you want to change the value later.
I'm assuming you don't just want it to be global, or else you can just use `define.
| https://electronics.stackexchange.com |
81,644 | [
"https://security.stackexchange.com/questions/81644",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/68331/"
] | Now I assume that everyone knows of aircrack-ng and John The Ripper with it's fantastic ability to pause and resume cracking.
With that aside, I want to add Crunch into the mix, however I can't seem to add crunch to it.
The plan as goes:
<strong>Crunch > John OR Aircrack</strong> [ If > John, then Crunch > John > Ai... | Crunch (this provides the output for AirCrack) and then John (this turns it into a session) and that AirCrack (which cracks it).
Like this:
<blockquote>
crunch 8 20 -f ~/crunch-3.6/charset.lst mixalpha-numeric-symbol14-space -i |./john --stdin (This accepts crunch's words) --session=stpcrunch --stdout (this then forwar... | <blockquote>
crunch 8 26 abcdefghijklmnopqrstuvwxyz0123456789 | aircrack-ng psk-01.cap
</blockquote>
is an example of what you could try.
| https://security.stackexchange.com |
30,737 | [
"https://electronics.stackexchange.com/questions/30737",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/5029/"
] | I'm little confused about this one and don't know where to start. The idea is to have micro-controller or FPGA output PWM signal (5V or 3.3V while PWM is 100%), and then use a transistor to power ventilator that needs 12V to run.
I know that I need to connect grounds of ventilator's power supply and FPGA's (or μC's) p... | A (two-level) PWM signal has two states: high and low. Regardless of whether the supply for your FPGA/MCU is 5 V or 3.3 V, you want the low state to turn into 0 V across your fan, and the high state to turn into 12 V across it (or vice versa). That way, by varying the duty cycle of the PWM signal, you will be able to d... | I see that Telaclavo has given you a good answer for a bipolar transistor. Here is what it would look like with the right kind of FET:
<img src="https://i.stack.imgur.com/ogjMh.gif" alt="">
For low voltages like 12 V, FETs are available that turn on well enough with only 5V or even 3.3V on the gate. These are somet... | https://electronics.stackexchange.com |
70,142 | [
"https://mathoverflow.net/questions/70142",
"https://mathoverflow.net",
"https://mathoverflow.net/users/2082/"
] | The de-Rham complex in one dimension describes phenomena that can be described in terms of ordinary differential equations. The de-Rham complex in three dimensions can be used to describe classical results in vector analysis.
Whereas the cochain morphism from the de Rham complex to complexes build out of scalar and ve... | After writing this, I noticed that Donu Arapura made essentially the same point in a comment. But perhaps my added detail will be of use.
There are two missing ingredients in what you wrote.
First, when you identify 1-forms with vector fields, you have implicitly chosen a bundle isomorphism $T\mathbb{R}^n \cong T^... | In $\mathbb R^3$ if you interpret $1$-forms as vector fields in a certain obvious way then the de Rham operator on $0$-forms becomes grad. If you now interpret $2$-forms as vector fields in a certain way then the de Rham operator on $1$-forms becomes curl and the de Rham operator on $2$-forms becomes div.
Generally, i... | https://mathoverflow.net |
577,320 | [
"https://electronics.stackexchange.com/questions/577320",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/285494/"
] | I am trying to implement a DIY MPPT into my solar tracker project and I wanted to know if it was possible to charge all of the three li-ion 3.7v batteries in series with just one feedback buck converter; BMS modules charge each cell individually so they can discharge every cell that has stored extra charges, which make... | Most BMS modules do actually charge all cells in series with a single converter. They just have extra circuitry to discharge single cells that are charged too much. This can be achieved by simply putting a resistor in parallel with each cell which can be activated using a FET to discharge the cell a bit. If you want a ... | When the equivalent capacitance of batteries are mismatched, the weaker cells charge and discharge faster. This quality factor is never given by suppliers and changes with stress by heat and extended under/over charge.
You know about tolerances in ecaps being 10% or more, the same is true with good quality Lithium cel... | https://electronics.stackexchange.com |
346,270 | [
"https://electronics.stackexchange.com/questions/346270",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/131243/"
] | It is said that voltage across capacitor/inductor is higher than the applied AC voltage. How?
| Consider a series LCR circuit with an a.c. voltage, \$V=2\:\small V\$ applied. Let the resistance be \$R=1\:\Omega\$, and let the reactances be \$X_L=X_C=10\:\Omega\$, which means that the complex reactances are \$j10\$, and \$-j10\$.
The series circuit has an impedance: $$Z=R+jX_L-jX_C=1+j10-j10=1+j0$$
That is, \$Z\... | The reason for this phenomenon is called resonance, in this case between the capacitor and the inductor. When you apply DC voltage to a capacitor or an inductor they will store energy by forming an electric field. When you take away the voltage, the stored energy will be flowing back into the circuit. As mentioned, bot... | https://electronics.stackexchange.com |
4,026,279 | [
"https://math.stackexchange.com/questions/4026279",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/519543/"
] | <span class="math-container">$\lim_{n\rightarrow\infty}\sum_{k=1}^{n}{2n\choose k}\frac{1}{4^{n}}=\lim_{n\rightarrow\infty}(1+\frac{1}{4^n})^{2n}$</span>
using <span class="math-container">$(1+x)^n=1+nx+\frac{n(n-1)x^2}{2!}....$</span>
<span class="math-container">$\lim_{n\rightarrow\infty}=1+\frac{2n}{4^n}+\frac{2n(2n... | If you want to find the limit of <span class="math-container">$ \sum\limits_{k=0}^{2n} \binom {2n} {k} \frac 1{4^{k}}$</span> then you can write the sum as <span class="math-container">$(1+\frac 1 {4})^{2n}=(\frac 5 4 )^{2n}$</span> and the limit is <span class="math-container">$\infty$</span>
However, if you want t... | For the first sum we have
<span class="math-container">$$\begin {align}
S_n&=\frac1{4^n}\sum_{k=1}^n \binom{2n}k\\
&=\frac1{4^n}\times\frac12\left[{2^{2n}+\binom{2n}n}-2\right]\\
&=\frac12\left[1+\binom{2n}n\frac1{4^n}-\frac2{4^n}\right],
\end {align}$$</span>
which implies:
<span class="math-container">$$
... | https://math.stackexchange.com |
27,764 | [
"https://chemistry.stackexchange.com/questions/27764",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/15151/"
] | <blockquote>
Write equations for the reactions of each of: (a) nitric acid (b) sulfuric acid *(c) hydroiodic acid, with each of: (i) sodium hydroxide (ii) zinc oxide (iii) ammonia.
</blockquote>
So, the reaction of nitric acid with sodium hydroxide and zinc oxide is simple because I know that acid + base = salt + wa... | <blockquote>
In the second part, for example, $\ce{Zn}$ is 2+ and $\ce{H}$ is -1. So using the criss-cross method, you get $\ce{Zn(NO3)2}$ and water. I understand this.
</blockquote>
I don't agree on the -1 for hydrogen, let's look again at that example:
$$\ce{2HNO3(aq) + ZnO(s) -> Zn(NO3)2(aq) + H2O}$$
<strong... | <blockquote>
How am I supposed to know this equation?
</blockquote>
You have to <em>memorise</em> it. In aqueous solution, $\ce{NH3}$ deprotonates a small fraction of the water to give ammonium and hydroxide
$$
\ce{NH3 + H2O <=> NH4+ + OH−} \, ,
$$
and while it is usually impossible to isolate $\ce{NH4OH... | https://chemistry.stackexchange.com |
100,810 | [
"https://cs.stackexchange.com/questions/100810",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/97115/"
] | The dominance law states that <strong>x + 1 = 1</strong>
If we go by that logic, does that mean that <strong>x' + 1 = 1?</strong>
Please just tell me if it's a yes(as I think that this is the answer but I just want to clear my doubts) and maybe provide a little explanation if it's a no.
Thanks!
| If <span class="math-container">$x+1=1$</span> then, substituting <span class="math-container">$x'$</span> for <span class="math-container">$x$</span>, we deduce that <span class="math-container">$x'+1=1$</span>.
In other words, your claim follows from the fact that <span class="math-container">$x'$</span> has the sam... | That is correct.
In Boolean Algebra, '+' is synonymous to '∪' (<strong>union</strong>), and your problem can be illustrated as the '<strong>or</strong>' logic gate to better understand it:
<img src="https://i.imgur.com/IyhZwBQ.png" alt="OR Gate">
If we allow <em>B</em> to be 1, <em>Z</em> is always 1, regardless of ... | https://cs.stackexchange.com |
7,720 | [
"https://scicomp.stackexchange.com/questions/7720",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/4562/"
] | I want to use the PETSc library to do some numerical work on finite element and parallel computing, but I wonder what I should know first to use these libraries. Could you give me some guiding information? Any answer of comment will be appreciated. Thank you.
| PETSc is an outstanding linear algebra library. It also has modules for nonlinear solvers and, to some degree, for meshes and finite elements, but the latter aren't frequently used as there are much more comprehensive finite element packages out there. So, if you're interested in FEM calculations, my recommendation wou... | Start with src/ksp/ksp/examples/tutorials/ex2.c or ex2f.F and work your way upwards.
PETSc is very easy to use. You just have to worry about local element level calculations (matrices, rhs etc.) and PETSc takes care of everything else (e.g. parallel assembly and solving).
Developing a parallel high performance FE co... | https://scicomp.stackexchange.com |
128,690 | [
"https://electronics.stackexchange.com/questions/128690",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/16840/"
] | Say I have some low pass filter of the form:
$$G(s) = \frac{a}{s+b}$$
How do I find the bandwidth? I know for example that with bandpass filters it's the difference between +-3dB of the cutoff frequency but I'm not sure how that would work for this example.
| In your case $$G(s) = \frac{a}{s+b} = \left(\frac{a}{b}\right)\left( \frac {1}{1+\frac {s}{b}}\right)$$
The output will be -3dB compared to the passband when \$s = jb\$ (equivalent to \$\frac{b}{2\pi}\$ Hz) so the bandwidth is \$b\$ radians/second and the passband gain is (a/b).
| Bandwidth is just a matter of definition, of how we label what's around us.
A low pass filter is a box that let all the frequencies up to the cutoff pass <em>almost</em> untouched, so the width of the bunch of frequencies that can pass is from 0 to \$f_C\$, and we call this bandwidth.
A 100Hz cut off low pass filter ... | https://electronics.stackexchange.com |
43,571 | [
"https://physics.stackexchange.com/questions/43571",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/11142/"
] | Suppose a projectile is launched from the Earth's surface with initial velocity $v_0$ well below speed of light and initial angle $\theta_0$ with respect to the vertical line perpendicular to the Earth's surface. Omitting Earth's rotation, but knowing that Earth is not flat (as in the real world), what is the maximum h... | I do not have the book you mentioned, but I could find something in my notes from last year's Classical Mechanics lecture.
Firstly, if your projectile reaches escape velocity, then it will of course travel away from the Earth forever, which answers your question with $\infty$. When does this happen? The potential ener... | If you're taking into account the curvature of the Earth you presumably also have to account for the change in gravitational acceleration with distance from the Earth. In effect your object is in orbit and travelling in an ellipse. It just happens that the ellipse intersects the surface of the Earth. So your problem re... | https://physics.stackexchange.com |
88,084 | [
"https://mechanics.stackexchange.com/questions/88084",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/71314/"
] | I’m 200 miles from home for the weekend and an in-ground pipe in the parking garage tore off my front bumper (2016 Camry). We zip-tied the top of the bumper back on through the holes where the clips once were. As garages in Atlantic City are probably sketchy and closed on weekend, will zip ties hold this on for my 200 ... | If you are using the same mounting holes which once had clips in them, the zip ties should hold just fine. If the holes are torn or lost their integrity, I doubt it will. Zip ties have a pretty good shear strength, so should work just fine. If you don't think one will do it, then put two in place. Once down the road a ... | Some bumpers, exhaust pipes or protective covers are run for years with a zip-tie or wire mount.
Just use large enough ties. Or a large number of smaller ties.
| https://mechanics.stackexchange.com |
98,796 | [
"https://dba.stackexchange.com/questions/98796",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/64104/"
] | I want to look for all the records that occur on specific dates.
<pre><code>SELECT *
FROM table1
WHERE date(column) in ($date1, $date2, ...);
</code></pre>
However, as many of you, know this kind of comparison doesn't get along with indexes. So, I was wondering if there is a simple way to convert this query to somet... | <h1>SUGGESTION #1</h1>
<pre><code>SELECT A.* FROM table1 A INNER JOIN
(
SELECT '2015-03-01' dtcolumn
UNION SELECT '2015-03-15'
UNION SELECT '2015-04-01'
UNION SELECT '2015-04-15'
UNION SELECT '2015-05-01'
) B ON
A.dtcolumn >= B.dtcolumn
AND A.dtcolumn < B.dtcolumn + INTERVAL 1 DAY;
</code></p... | Try something like this:
(I did this on Oracle, it should mostly work elsewhere, the WITH clauses are mostly for just faking sample data .. so not entirely necessary)
<pre><code> with w_date_list as ( -- just some sample input dates - these are from your IN list (note that you want to re-org them as a "table" not an... | https://dba.stackexchange.com |
11,554 | [
"https://astronomy.stackexchange.com/questions/11554",
"https://astronomy.stackexchange.com",
"https://astronomy.stackexchange.com/users/7954/"
] | If an astronaut went into space with a sealed container of oxygen and opened it up in space and let all the oxygen go, what would happen to it? would it all just dissipate into some other particle or matter or would it just stay there until something consumed it
| Gases tries to occupy all the volume of the container in which they are encased in equilibrated pressure. This happens because the gas molecules are always colliding and kicking each other in a 3D high velocity brownian motion. The result is that the gas molecules occupies all the container's volume homogeneously.
So,... | It's sort of like a pool and water: a big empty pool is space, and water is air; if you pour one drop of water in the pool, that's not going to fill it up. Instead, the water tries to fill the pool evenly. Hope this helps/helped!
| https://astronomy.stackexchange.com |
63,634 | [
"https://security.stackexchange.com/questions/63634",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/52421/"
] | As a part of work, I've come across content sniffing, and i understand web apps can be vulnerable to xss because of it. There is another post, regarding content sniffing and xss, but didnt quite answer my question, or maybe i just misread it. content sniffing will read the file to try and determine what type of file it... | No, loading an HTML file from your computer is never an XSS vulnerability. You can run whatever code you want locally, but that doesn't affect the website.
Cross-site scripting is about getting your code executed on other user's browsers so you can interact with their session for that site. Whether that is stealing ... | No, not at all. <br><br>
What you did, is just a simple XSS test on your own browser. No other user can be affected by the XSS you coded to run on your own computer.<br><br>
You can deploy the same vulnerability on your own hosted website: that way, your website will be either XSS vulnerable. In which case, it can eit... | https://security.stackexchange.com |
254,494 | [
"https://softwareengineering.stackexchange.com/questions/254494",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/34069/"
] | I believe in the user experience of always having a confirm pop-up for deletions.
However (though we're very used to it), a separate small pop-up window is not ideal and for users on different browsing devices, using different input devices, they can be a nightmare.
So I was thinking of changing all my 'confirm delete... | I would think of the problem in the opposite way. Instead of "soft delete" think of it as an archive flag. You should never plan on restoring the record, since you will either have to circumvent your rules for new records, which may have changed since this record was created, or allow the record to slip past your "new ... | TBH I wouldn't move it to a separate database or table as that would just be an extra layer of complication.
In my last job, who developed and maintained enterprise solutions for large clients, we would leave the records in place, just using a bit field/boolean to hide it from the user. A user with higher privileges c... | https://softwareengineering.stackexchange.com |
30,468 | [
"https://physics.stackexchange.com/questions/30468",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/7896/"
] | In cryogenics, liquid nitrogen and liquid helium are often used as coolants. Other than their low boiling point of 77K and 4.2K respectively, what properties make them suitable as coolants? Are there any other possible candidates around the same temperature range?
| Liquid nitrogen is used because nitrogen is extremely abundant on earth. Nitrogen makes up approximately 78% of the atmosphere by volume. Hence, liquid nitrogen is rather easy to make (and consequently cheap). I've heard for instance that Fermilab buys liquid nitrogen for cheaper than what you pay for water.
Liquid he... | I feel it is worth to emphasize over @logan's answer that both helium and nitrogen are inert and non-flammable. That makes them as safe to use as could be (the only dangers coming from the cryogenic properties itself, i.e. suffocation, explosion, and frostbite.) In contrast, liquid hydrogen or oxygen are extremely dang... | https://physics.stackexchange.com |
270,697 | [
"https://softwareengineering.stackexchange.com/questions/270697",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/115216/"
] | In "Pattern Oriented Software Architecture - Vol 1" (p. 131), the author said that <code>View</code> is responsible for creating <code>Controller</code>. But in "Head First Design Patterns" (p. 562) it is the <code>Controller</code> that creates the <code>View</code>. In some other references I see that nor <code>View<... | Well, I can only assume this changes along different platforms.
On the android library, you create the view from the controller.
i.e., in your <code>Activity</code> you call <code>setContentView...</code> to "awake" you XML (The view) and create it.
On the other hand, in the iOS world, you would ask the View (<code>... | Does it really matter what creates what though? It depends imo, as long as business logic and view are separated it's alright. Controller should have a reference to both of them and provide means to translate data from the logic to the view and vice versa. But honestly, in real world applications, no matter how hard yo... | https://softwareengineering.stackexchange.com |
152,619 | [
"https://electronics.stackexchange.com/questions/152619",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/66009/"
] | 1) If I connect my mobile charger to a wall socket and it is switched on, but I don't connect my mobile to the charger, does the charger still use electricity?
2) If I connect an extension box to a wall socket and connect my mobile charger to my extension box, but again I don't connect my mobile to the charger, does t... | <blockquote>
i need to make sure my electricity bill is not going up
</blockquote>
Don't plug it in is the only answer. Even without a phone on charge, some power will be taken by the charger and you will be billed for it. It will only be pennies per week but if you want to avoid extra cost then don't do it.
A powe... | If you don't connect a charger to the device it's meant to charge, there will be very little electricity flowing through the charger. (There will be a little bit leaking through, but it's usually not significant.)
As a rule of thumb, if your charger doesn't feel warm, it's probably not using enough current to affect y... | https://electronics.stackexchange.com |
112,256 | [
"https://chemistry.stackexchange.com/questions/112256",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/34362/"
] | The reaction
<span class="math-container">$$\ce{2 A + B + C -> D + 2 E}$$</span>
is found to follow the rate law as
<span class="math-container">$$r = k[\ce{A}][\ce{B}]^2[\ce{C}]^0$$</span>
If the concentration of <span class="math-container">$\ce{A}$</span>, <span class="math-container">$\ce{B}$</span> and <spa... | You would change the reaction speed, but not the order.
The order of the reaction can be changed by reagent concentration, if it is result of multiple reaction steps with different orders. By variation of concentrations you can manipulate the relative reaction speed,
as the order is often ruled by the slowest reaction... | You shouldn't be able to change the order of the reaction or the powers of the concentrations in the rate equation (which lead to the overall order). Those powers correspond to the rate determining step, so changing the rate equation would mean you have a different mechanism and potentially a different reaction.
Your ... | https://chemistry.stackexchange.com |
34,028 | [
"https://softwareengineering.stackexchange.com/questions/34028",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/11107/"
] | What kind of problems arise from installing a new program while other programs are running? I'd imagine the GAC solved a lot of the old problems of shared dll's being locked. So what kind of issues still arise? I can see issues with upgrading a single program for sure, but outside of this its hard to see why apps wo... | GAC only helps with .NET assemblies. There a lot of other applications which are not written in .NET.
What else problems exist?
<ul>
<li>Other applications holding files open</li>
<li>Other applications holding network connections open</li>
<li>Other applications holding devices open</li>
<li>Other applications slowi... | maybe the installer is just overly paranoid?
in all honesty, I have never ever closed all programs when an installer asked me to do so and never ever got into trouble. Might just be luck though.
| https://softwareengineering.stackexchange.com |
471,655 | [
"https://physics.stackexchange.com/questions/471655",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/223029/"
] | For finding electric potential energy of a uniformly charged sphere, we can assemble the sphere by brining charges from infinity to that point. So to make a uniformly charged sphere of radius <span class="math-container">$R$</span> and total charge <span class="math-container">$Q$</span>, at some instant, charge will b... | "Angular velocity" can be used inter-changably with "angular frequency", but you want to distinguish clearly between those and "cyclic frequency" which is the thing usual just termed "frequency".
The angular quantities are measured in radians per second, while the cyclic frequency is "cycles per second" AKA hertz (Hz)... | Angular frequency (rad/s) and frequency (1/s=Hz) have the same physical dimensionality, as OP correctly figured out, but are related by a factor of <span class="math-container">$2\pi$</span>.
The inverse of this quantity is time, in one case the time it takes to go one radian in angle and in the other to go the full r... | https://physics.stackexchange.com |
11,302 | [
"https://electronics.stackexchange.com/questions/11302",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/1657/"
] | I can program LEDs 0 to 3 to light up, but I get an error when I try to assign LEDs 4 to 7. Why is that?
| This is really two questions in one...
<em>Firstly, what is the difference between a microcontroller and a microprocessor?</em>
<strong>Microprocessor</strong> is a purely a CPU that follows a set of instructions read from an external memory bus. It controls external peripherals (such as screen, keyboard, mouse, hard... | The difference is that the microcontroller includes on-chip memory like Flash EEPROM and RAM, and peripherals like parallel and serial I/O. With the first microprocessors those were all external devices. Instead of the I/O's microprocessors had an the address and data bus brought to their pins.<br>
The way you write co... | https://electronics.stackexchange.com |
1,131,456 | [
"https://math.stackexchange.com/questions/1131456",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/97407/"
] | During Cinco de Mayo, you shoot a bullet straight up into the sky at the speed of 500 m/s. The altitude of the bullet $y(t)$ at time $t$ seconds after being shot satisfies the differential equation $y''=-g$. What is the velocity of the bullet as it hits the ground?
The answer is $-500$ m/s. I can't figure this out. ... | If $y''(t) = -g$, then $y'(t) = y'(0) -gt$ and hence
$y(t) = y(0) +y'(0)t - {1 \over 2} g t^2$.
We want to solve $y(T) = y(0)$ (with $T>0$) to see when the bullet hits the ground.
This involves solving $y'(0)T = {1 \over 2} g T^2$, which gives
$T= { 2 y'(0) \over g}$.
Substituting into the equation for $y'$ gives... | The differential equation only takes gravity into account, not air resistance, so physically speaking it's obvious that the bullet's speed at landing is the same as that with which it was fired.
But if you want to compute, notice that if you integrate $y''(t)$ you get $y'(t)$, not $y'(t) \cdot t$. And don't forget the... | https://math.stackexchange.com |
10,689 | [
"https://chemistry.stackexchange.com/questions/10689",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/5244/"
] | <img src="https://i.stack.imgur.com/GUAe0.png" alt="enter image description here">
This is NanoBalletDancer.
How many different carbon environments are there in NanoBalletDancer – i.e. how
many signals would be seen in total in the 13C NMR spectrum?
I counted 8 signals from benzene ring carbons
4 from methyl group ... | 3 different methyl signals: (1, 16) (40, 41) (27, 28, 29, 33, 34, 35)
4 different methylene signals: (17) (2, 15) (3,14) (37, 39)
1 aliphatic CH signal: (36)
2 different aliphatic quaternary C signals: (26, 32) (38)
4 different triple bond C signals: (24, 30) (25, 31) (4, 13) (5, 12)
8 different aromatic carbons: ... | See the given figure below, where each unique signal is given a specific color and a shape which is
unique to it. Carbons 6 and 8 produce the same signal, yet they are left purposely blank, since I ran out of colours.
Counting 2 and 15 makes it 22, however, since there isn't really much difference between the two api... | https://chemistry.stackexchange.com |
89,500 | [
"https://security.stackexchange.com/questions/89500",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/76741/"
] | (Moved from Stack Overflow as other users said it was a security question)
I have a mysql database sitting on a remote server. Nothing else, ie no web site using it, no server side scripts etc, nothing except remote access from an application that I wrote myself in Depli. That application runs on about a dozen machine... | The first answer told many things. But as long as your connection to the mysql database is possible, you can be hacked. [My off-topic advice: keep searching for info about exploits and vulnerabilties for mysql actively].
<blockquote>
Can any expert programmers out there tell me if allowing access from any IP addres... | An attacker would need one of the following:
<ul>
<li>No known user / password
<ul>
<li>A vulnerability for the mysql version you use.</li>
<li>the IP of your mysql server (if it runs on a default port chances are its already known to the criminal world)</li>
</ul></li>
<li>Sniffed User name / password / ip
<ul>
<li>N... | https://security.stackexchange.com |
74,113 | [
"https://stats.stackexchange.com/questions/74113",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/9162/"
] | I'm writing a paper on making probability estimates, and it's been asserted to me that I should take the median of the estimates given by my participants, rather than the mean. I've been told I should do this because the mean is more affected by sampling error than the median.
Why is this? Is this something that is al... | Imagine that a variable takes values 0 and 1 with probability both 0.5. Sample from that distribution and most of the medians will be 0 or 1 and a very few exactly 0.5. The means will vary far less. The mean is much more stable in this circumstance.
Here is a sample graph of results. The plots are quantile plots, i.e... | Where did you hear this? The usual reason for preferring the median is that it is less affected by extreme values than the mean. However, it is in general less sensitive to changes in the data.
I ran a tiny example in <code>R</code>
<pre><code>set.seed(1234)
true <- rnorm(1000)
smallerror <- true + rnorm(1000... | https://stats.stackexchange.com |
423,571 | [
"https://mathoverflow.net/questions/423571",
"https://mathoverflow.net",
"https://mathoverflow.net/users/163893/"
] | I would like an example of the following situation, or a proof that no such example exists.
<span class="math-container">$\textbf{Situation}$</span>: Two connective (EDIT: I'm fine with dropping this condition) spectra <span class="math-container">$X$</span> and <span class="math-container">$Y$</span> such that the spa... | For this we can use a swindle-type technique.
Let <span class="math-container">$B = \bigoplus_{n=2}^\infty H\Bbb Z/2$</span>, and <span class="math-container">$A = \bigoplus_{n=2}^\infty \Sigma^{-n} H\Bbb Z/2$</span>. We can construct maps <span class="math-container">$A \to B$</span> by specifying their effect on each... | I am pretty sure that it will be rather delicate to find an example like you want. Here are some thoughts:
Let <span class="math-container">$X_n$</span> denote <span class="math-container">$\Omega^{\infty} \Sigma^n X$</span>. One is assuming an equivalence <span class="math-container">$X_n \simeq Y_n$</span> for all <... | https://mathoverflow.net |
154,714 | [
"https://physics.stackexchange.com/questions/154714",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/41974/"
] | I have a problem in understanding the diffraction phenomenon. At first, it is described in simple way
<blockquote>
If a wave encounters a barrier that has an opening of dimensions
similar to the wavelength, the part of the wave that passes through the opening
will flare (spread) out —will diffract—into the regio... | Let's examine more attentively what says Huygens' principle: that each point on the wave-surface that gets inside the slit, becomes a source by itself, emitting around itself a spherical wave. As see that you work in the 2D geometry, but 3D is better (I got once an explanation why but I don't remember right now). Anywa... | The way your pictures show is only one-way of explaining why we see the pattern on the screen. But you are right. It does not make much sense. Because interference is a non-localized phenomenon. If you think the rays arriving at point P you will get confused. It even fails to obey the conservation of energy, if you thi... | https://physics.stackexchange.com |
128,675 | [
"https://security.stackexchange.com/questions/128675",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/116109/"
] | I am required to submit personal information as part of a form. I looked under developer tools and found this:[![screenshot of item displayed in developer tools][1]][1]
<blockquote>
Mixed Content: The page at <code>https://example.com</code> was loaded over a secure connection, but contains a form which targets an i... | <strong>Danger Will Robinson, Danger!</strong>
The form on the site is <em>not secure</em>, and any data sent through that form will be in plain text. This means anyone listening to this communication will have a plain text copy of any data sent to that address.
If you don't know what data is sent there then you can'... | Look at the actual request that is sending the form data. That link is HTTP, hence you are in danger. "Mixed content" warnings are given when a website supports HTTPS ony partially, that is it fetches/sends some contents over HTTP, which can be intercepted, sniffed or changed by an attacker.
| https://security.stackexchange.com |
416,627 | [
"https://softwareengineering.stackexchange.com/questions/416627",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/376120/"
] | I do not know how to properly formulate this question, but I am trying to find the best algorithm to get the nearest integer number where every set of numbers (including decimals) give an integer number when doing multiplication. Example:
Assuming:
<pre><code>X = 232
Y = [2, 5, 1, 0.1, 0.0625]
</code></pre>
The final n... | How to you write the word "<em>computer</em>" in ancient latin language? Nobody knows, because for sure, there were no computers in the roman empire ;-)
The MVC architectural model was designed in the 70s to address a clean separation of responsibility and decoupling the "application" logic (Model) ... | Your question is rife with "if A then B" and "A XOR B" suppositions, where there is no logical connection between A and B.
It's so persistently present in your question that it pretty much invalidates or otherwise distracts from the arguments you're trying to make.
Don't get me wrong, it's good that... | https://softwareengineering.stackexchange.com |
260,578 | [
"https://electronics.stackexchange.com/questions/260578",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/125146/"
] | I have done a previous project where I used an Arduino Mega to control a Three-phase industrial metal pattern scrolling machine (bender), and I faced many problems with noise voltage spikes being read as interrupts on Arduino pins.
I am now doing another project of similar requirements but I am looking into using Cat5... | I have dealt with noise and spikes on industrial equipment that was problematic even with opto-isolated I/O points. First off, are you running these wires directly from the I/O pins around the machine? If so, this is what needs to be addressed. Tell us what these pins are connected to such as relays, analog points, etc... | You'll find doing this will give little benefit to you. This is because you are not creating a faraday's cage around your signal wire so EMI can still be induced in your wire.
You should either create a proper differential pair at the point of the relay or you should use a shielded cable that's correctly grounded on b... | https://electronics.stackexchange.com |
602,719 | [
"https://physics.stackexchange.com/questions/602719",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/103229/"
] | I have been reading about raising and lowering operators, but I am a bit unsure of one thing. If you have a string of raising and lowering operators (or any kind of operator), do you apply them in order of right to left or left to right?
An example would be
<span class="math-container">$$A^{\dagger}A^{\dagger}A^{\dagge... | In the usual situation, where the quantum state is on the right (a ket), like <span class="math-container">$A^{\dagger}A^{\dagger}A^{\dagger}A|\psi\rangle$</span>, you do indeed apply the (annihilation) operator on the far right first, and then successively to the left. If you have trouble remembering this, think of i... | With any operators acting on a ket <span class="math-container">$| \psi \rangle$</span>, you apply the one farthest to the right first. So in your case <span class="math-container">$A$</span>.
| https://physics.stackexchange.com |
10,803 | [
"https://datascience.stackexchange.com/questions/10803",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/16024/"
] | I have read that distributional representation is based on distributional hypothesis that words occurring in similar context tends to have similar meanings.
Word2Vec and Doc2Vec both are modeled according to this hypothesis. But, in the original paper, even they are titled as <code>Distributed representation of words ... | The reply from Andrey Kutuzov via google groups felt satisfactory
<blockquote>
I would say that word2vec algorithms are based on both.
When people say <code>distributional representation</code>, they usually mean the
linguistic aspect: meaning is context, know the word by its company and
other famous quo... | Effectively, Word2Vec/Doc2Vec is based on <code>distributional hypothesis</code> where the context for each word is its nearby words. Similarly, LSA takes the entire document as the context. Both techniques solve the <code>word embedding</code> problem - embed words into a continuous vector space while keeping semantic... | https://datascience.stackexchange.com |
3,772,362 | [
"https://math.stackexchange.com/questions/3772362",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/679552/"
] | I find symmetry very appealing so I would politely ask you for some of the best resources (books, courses, articles, etc.) you know on this topic.
I would also dare to pose a challenge for the most intuitive explanation of some complex practical case symmetry is addressing.
I'm not that well versed with the subject, so... | OK, let's give the jumbo post of all of the proofs that a group of order <span class="math-container">$30$</span> has normal <span class="math-container">$3$</span>- and <span class="math-container">$5$</span>-subgroups.
<h2>Proof 1: Element Counting</h2>
Suppose that <span class="math-container">$G$</span> does not ha... | Here's one more Proof.
Let <span class="math-container">$G$</span> act on <span class="math-container">$G$</span> by left multiplication. Then there is an induced homomorphism <span class="math-container">$\varphi:G\to\operatorname{Sym}(G)\simeq S_{30}$</span>. Let <span class="math-container">$g\in G$</span> be an ele... | https://math.stackexchange.com |
154,027 | [
"https://math.stackexchange.com/questions/154027",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | I am suppose to use partial fractions
$$\int \frac{5x+1}{(2x+1)(x-1)}$$
So I think I am suppose to split the top and the bottom. (x-1)
$$\int \frac{A}{(2x+1)}+ \frac{B}{x-1}$$
Now I am not sure what to do.
| But $$\frac{5x+1}{(2x+1)(x-1)}\ne\frac{5x+1}{2x+1}+\frac{5x+1}{x-1}\;,$$ as you’ll see if you combine the fractions on the righthand side over a common denominator: you get
$$\begin{align*}
\frac{5x+1}{2x+1}+\frac{5x+1}{x-1}&=\frac{5x+1}{2x+1}\cdot\frac{x-1}{x-1}+\frac{5x+1}{x-1}\cdot\frac{2x+1}{2x+1}\\\\
&=\f... | Suppose $\frac{5x+1}{(2x+1)(x-1)} = \frac{A}{2x+1} + \frac{B}{x-1}$. Then $5x+1 = A(x-1)+B(2x+1) = (A+2B)x + (B-A)$. So by comparing coefficients, we get $A+2B = 5$ and $B-A = 1$. Solving this gives $A = 1$ and $B = 2$.
| https://math.stackexchange.com |
67,109 | [
"https://math.stackexchange.com/questions/67109",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/2109/"
] | In the Euler formula, for counting the number of faces, we count <strong>the regions bounded by edges, including the outer, infinitely-large region</strong>, so in the graph $K_1$ there is only one face which is outer (if I have understood it properly); similarly for $K_3$, there are two faces one bounded by edges and ... | First, your typical looking cube graph or whatever it's called. Then, you put the graph on a sphere (use your imagination for the other side), with the gold dot representing the "point at infinity" under stereographic projection. Oh, but let's put it in the plane - where'd the back face go I wonder?
<img src="https://... | Here's a graphical elaboration of what I was talking about in the comments, using the dodecahedron as an example:
<img src="https://i.stack.imgur.com/ZGM0e.gif" alt="expanding dodecahedron">
(I might consider doing animations for the other polyhedra if asked nicely...)
| https://math.stackexchange.com |
4,126 | [
"https://mechanics.stackexchange.com/questions/4126",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1803/"
] | I am looking for an aftermarket device that turn off the engine when the car is in rest and turn on the engine when the throttle is pushed. Which are the producer? Where i can find it on internet?
| I don't know of an aftermarket system out there currently. But it wouldn't be that difficult to do. General Motor's "Green Line" Hybrids have removed the starter and replaced the alternator with a generator/starter much like some older farm tractors. The have a 36 volt battery to handle the additional power requirement... | Auto start/stop requires design changes to the starter, flywheel, solenoid, charging system, among other things. A traditional starter isn't rated for the duty cycle that a start/stop system requires. The flywheel and starter are also changed do that the engine can start faster. The solenoid has a higher duty cycle. Th... | https://mechanics.stackexchange.com |
28,794 | [
"https://dsp.stackexchange.com/questions/28794",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/18333/"
] | This is a very common example in most Signal Processing books I have come across.
x(n) = cos($\frac{n}{6}$) is a non-periodic discrete signal because it doesn't satisfy the periodicity condition for discrete time signals i.e, it is not of the form 2$\pi$($\frac{m}{N}$).
My question is :
the coefficient of n, i.e, $... | The problem with your reasoning is that $\pi \ne \frac{22}{7}$; $\pi$ is an irrational number. There is no period $N$ for which $x[n] = x[n+N] \ \forall \ n \in \mathbb{Z}$. Hence, the sequence is not periodic.
| The periodicity of a signal holds if we can show <span class="math-container">$x(n)=x(n+N)$</span>, otherwise, the signal is nonperiodic. Simply start with
<span class="math-container">$$
\begin{align}
x(n+N) &= \cos( \frac{n}{6} + \frac{N}{6}) \\
&= \cos(\frac{n}{6})\cos(\frac{N}{6}) - \sin(\frac{n}{6})\sin(\... | https://dsp.stackexchange.com |
559,294 | [
"https://electronics.stackexchange.com/questions/559294",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/278572/"
] | Since the current meets the open boundary and gets reflected back does this mean that the return path has zero current always on it? Or there is also a standing wave there as well with a current with an opposite direction of propagation?
The same I would ask about a lambda/2 dipole antenna which is a standing wave line... | A transmission line doesn't have a "supply path" and a "return path". The two conductors that make up a TL are coupled throughout their length so that they always have opposite currents — this is what makes it a transmission line, and it's true even if you're "only driving one side", with ... | You're correct that, at the open end of the transmission line or antenna, the current is zero. At other points on the line, there is a nonzero current; it's at a maximum 1/4 wavelength from the open end. In your dipole, that's 1/4 wavelength from each end, putting it at the center feed point. The voltage is maximum ... | https://electronics.stackexchange.com |
1,034,519 | [
"https://math.stackexchange.com/questions/1034519",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/187578/"
] | I'm having trouble with the following proof:
<img src="https://i.stack.imgur.com/QwtDk.png" alt="enter image description here">
$\color{red}{\text{This is not the end of the proof.}}$
I'm not understanding the definition of $A_k$. For instance $A_5\nsubseteq A_6$ because $A_6$ takes $\omega$ if $|X_{n\geq6}(\omega)-... | Here is an intuitive answer. Hope it helps.
You know that $X_{n}$ converges almost surely to $X$. That is, the distance between $X_{n}$ and $X$ will be, and will remain, very small for large $n$. In other words, given a small distance, say $\epsilon = 0.00012$, then there will be at least the same, if not more, amount... | Since $X_n$ converges to $X$ almost everywhere, there exists a set $M$ of measure 1 with every $\omega\in M$ satisfying $X_(\omega)\rightarrow X(\omega)$. This translates to the usual epsilon definition of a limit for each omega. So clearly there exists a $K$ such that $A_K$ is non empty.
Fix $\epsilon>0$. Clearly... | https://math.stackexchange.com |
1,395,441 | [
"https://math.stackexchange.com/questions/1395441",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/258051/"
] | $\int\frac{x^2+x}{(e^x+x+1)^2}dx$<br>
I tried solving it but could not finish.I tried putting $e^x=t$ but not getting integrable.Please help me in solving it.
| Given, $\displaystyle I = \int\frac{x^2+x}{(e^x+x+1)^2}dx = \int\frac{(e^x+x+1)x-xe^x}{(e^x+x+1)^2}dx $
$\displaystyle I = \int\frac{x}{e^x+x+1}dx-\int\frac{xe^x}{(e^x+x+1)^2}dx$
$\displaystyle I = \int\frac{(e^x+x+1)-(e^x+1)}{e^x+x+1}dx-\int\frac{(xe^{-x})}{(1+xe^{-x}+e^{-x})^2}dx$
Now in second integral put $(1+xe... | \begin{align}
\int\frac{x(x+1)}{(1+e^x+x)^2}dx&=\int\frac{(1+e^x+x)^2-(1+e^x)(1+e^x+x)-xe^x}{(1+e^x+x)^2}dx\\
&=\int1dx-\int\frac{1+e^x}{(1+e^x+x)}dx-\int\frac{xe^x}{(1+e^x+x)^2}dx\\
\end{align}
| https://math.stackexchange.com |
144,268 | [
"https://security.stackexchange.com/questions/144268",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/116721/"
] | I am having an issue with Metasploit's search commands. When trying to search multiple keywords, the output displays only the first keyword. For example, if I use the command <code>search platform:windows type:exploit</code>, I will only receive the output of for Windows platforms, and include payloads, exploits, and p... | TL;DR - upgrade, it works like you expect now.
In versions before 4.13.8, <code>search</code> used a <em>union</em> instead of an <em>intersection</em> of results. Thus your example ("search platform:windows type:exploit") would show you all modules that target Windows (including payloads, auxiliary, and post modules)... | Inside an older version of msfconsole, you could call grep immediately before calling the search command.<br /><br />
For example, to search for the 2 terms '<em>shellshock</em>' and '<em>mod_cgi</em>':
<pre><code>msf > grep mod_cgi search shellshock
auxiliary/scanner/http/apache_mod_cgi_bash_env 2014-09-24 ... | https://security.stackexchange.com |
96,811 | [
"https://datascience.stackexchange.com/questions/96811",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/50727/"
] | I'm building a recommender system where the number of products is rather low (around 50), and we can assume it'll stay the same for a long time.
I'm looking at two different way of tackling the problem:
<ul>
<li>Using a matrix factorization technique.</li>
<li>Treating it as a multi-class classification problem with a ... | <span class="math-container">$d_k$</span> is the dimensionality of the query/key/value vectors. In your example, the length of those vectors is 3, so <span class="math-container">$d_k = 3$</span>
| In addition to Noe's answer, you could consider <span class="math-container">$d_k$</span> being the equivalent of<code>hidden_state</code> dimensionality as seen in recurrent layers e.g. argument <code>units</code> in <code>tf.keras.layers.LSTM</code>.
| https://datascience.stackexchange.com |
536,382 | [
"https://physics.stackexchange.com/questions/536382",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/105209/"
] | Let me first give a sketch of how I understand band energy mathematically. It is not exactly rigorous, but probably could be made rigorous under suitable conditions.
Let <span class="math-container">$H$</span> denote the Hamiltonian on an <span class="math-container">$d$</span>-torus (finite volume with period boundar... | I think I finally understand how to mathematically interpret band energies. Please correct my if you think otherwise.
For simplicity, let me consider a 1D finite system so that the underlying single-particle Hilbert space is <span class="math-container">$\mathscr{H} \equiv L^2[0,N)$</span> where <span class="math-conta... | Your symmetry argument is completely general, but the part about the discrete energy levels assumes non-interacting atoms - you need to include hopping between them in order to get a band structure. This is called <em>tight-binding model</em> as opposed to the <em>nearly free electrons model</em>. A good way of underst... | https://physics.stackexchange.com |
24,706 | [
"https://quant.stackexchange.com/questions/24706",
"https://quant.stackexchange.com",
"https://quant.stackexchange.com/users/17810/"
] | I have daily currency returns. For each month, I have to find the return associated to the 5% lower tail quantile for each currency (the lowest return or the second lowest return).
Could you please tell me how to do it using Excel?
Thanks in advance.
| $I_{\{S_{T}-K>0\}}$ is NOT independent of $\mathcal{F}_{t}$, since
\begin{align*}
S_T=S_t \, e^{(r-\frac{1}{2}\sigma^2)(T-t) + \sigma (W_T^*-W_t^*)},
\end{align*}
where $S_t \in \mathcal{F}_t$, though $e^{(r-\frac{1}{2}\sigma^2)(T-t) + \sigma (W_T^*-W_t^*)}$ is independent of $\mathcal{F}_t$.
However, since $W_T^*-... | You can also infer the value of your binary option from the value of a European call option with the same strike and time-to-maturity by going long on a call with strike $K$ and time-to-maturity $\tau$, and short on a call with strike $K+\Delta K$ and the same time-to-maturity. If you hold $\frac{1}{\Delta K}$ of that ... | https://quant.stackexchange.com |
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