text stringlengths 1 1.11k | source dict |
|---|---|
quantum-mechanics, particle-physics, statistical-mechanics, fermions, density
The number is that will fit is $\mathcal{N} = V/\hbar^3$ where $\hbar$ is the reduced Planck's constant.
Now, let us assume that we have $N$ atoms (I'm going to pretend the fermions are weakly interacting like an approximately ideal gas just to keep the language easy, so I'll call them 'atoms') of diffuse gas in a non-porous container of volume $V_s$ but in contact with a thermal reservoir of temperature $T$. The average momentum of the gas particles will be $\bar{p} = \sqrt{2 m k_b T}$, where $k_b$ is Boltzmann's constant, and $m$ is the mass of a single atom. Keep in mind that the momentum distribution will have tails that run from zero up to several times the $\bar{p}$. Let's say that they occupy a total momentum volume of $V_p \approx 400\,\bar{p}^3$ (the four hundred comes from assuming a sphere of radius $3\bar{p}$). By assumption that gas is diffuse, so $N \ll \mathcal{N}$. | {
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cryptography, zero-knowledge-proofs
I highly recommend this talk from Ben Adida: https://www.youtube.com/watch?v=ZDnShu5V99s. He discusses cryptography in elections, including zero-knowledge proofs and other cryptographic primitives, at a holistic level. Zero-knowledge proofs are used to verify the correctness of decryption and that the mixnet worked correctly, and he shows an example zero knowledge proof for the latter. You might also be interested to take a look at https://crypto.stackexchange.com/q/6647/351 and https://crypto.stackexchange.com/search?q=%5Bvoting%5D+zero+knowledge, where you can find some pointers into the research literature. | {
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} |
javascript, node.js, promise, revealing-module-pattern
var refreshJSON = function() {
return new Promise(function(resolve, reject) {
request.getAsync('http://berkeleymapper.googlecode.com/svn-history/r101/trunk/web/foo.json').get(1)
.then(JSON.parse)
.then(saveJSON)
.then(function(json) {
resolve(json)
})
.catch (function(e) {
// Return empty json on error
resolve(emptyJSON())
})
})
}
return {
cachedJSON: cachedJSON,
refreshJSON: refreshJSON
}
}
module.exports = new Foo()
Where this could be utilized in a situation like this:
runFoo.js:
var foo = require("./foo")
// Refresh and return the latest json from remote
foo.refreshJSON()
.then(function(json) {
console.log('### Refresh cached json with remote and return ###')
console.log(json)
}); | {
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java, n-queens
* screen.
*/
public static boolean rekur(Chessboard cb, Figure fig, int il) {
boolean x = false;
int j = 0, i = 0;
while (x == false && j < Math.min(il, cb.getA())) {
while (x == false && i < Math.min(il, cb.getA())) {
x = Solution.rekur(i, j, cb, fig, il);
i++;
}
j++;
}
if (x) {
cb.show();
}
return x;
} | {
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particle-physics, mass, standard-model, higgs, quarks
Typically, e.g., the weak-gauge-invariant couplings responsible for the mass of the d are
$$
-y_d \overline{ \begin{pmatrix} u_{L} \\ d_L \end{pmatrix} } \cdot \Phi ~ ~d_R +\hbox{h.c.},
$$
where the v.e.v. of the Higgs amounts to
$$
\langle \Phi \rangle = \frac{v}{\sqrt{2}} \begin{pmatrix} 0 \\ 1 \end{pmatrix},$$
for v ~ 0.25 TeV . You then see $m_d=y_d v/\sqrt{2}$.
The mass of the u in the weak doublet knows nothing about that coupling, and arises out of a completely independent Yukawa,
$$
-y_u \overline{ \begin{pmatrix} u_{L} \\ d_L \end{pmatrix} } \cdot \tilde{\Phi} ~ ~u_R +\hbox{h.c.},
$$
where, of course,
$$
\langle \tilde{\Phi} \rangle =\langle i\tau_2 \Phi^* \rangle = \frac{v}{\sqrt{2}} \begin{pmatrix} 1 \\ 0 \end{pmatrix}.
$$
You write two such terms of each kind for the other four quarks, and you are done. | {
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I advise you to have a graphical view of the situation as depicted below with $f(x)=|x^2-a|$ (green curve) and $g(x)=b$ (black horizontal line), looking for values of $x$ such that
$$|x^2-a|<b \ \ \ \ \iff \ \ \ \ f(x)<g(x).$$
(graphics obtained with Geogebra, with sliders for values of $a$ and $b$).
This figure allows to consider the different cases according to resp. values of $a$ and $b$, by "sweeping" the horizontal line along the curve, and looking for cases where the line is above the curve.
For example, for the displayed case ($b=3 \leq a=4$), the line is above the curve for $-\sqrt{7}<x<-1$ and for $1<x<\sqrt{7}.$ (case of two disjoint validity intervals), with $\sqrt{7}=\sqrt{a+b}$ and $1=\sqrt{a-b}$.
Were $b>a$, it is visible that there would be a single validity interval.
And of course, if $b<0$, no solution exist.
• Is my graphical presentation understandable ? – Jean Marie Dec 14 '16 at 7:41 | {
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Let $x\in\mathbb R$. By continuity, $f(x)=\lim_{y\to x}f(y)$. Since this limit exists, it is independent of the manner of approach $y\to x$; specifically, we may assume that $y\to x$ through rational values since $\mathbb Q$ is dense in $\mathbb R$. But then $f(x) = \lim_{y\to x} 0 = 0$.
A slightly more topological approach:
Theorem: Let $(X, \tau_X)$, $(Y, \tau_Y)$ be two topological spaces. Suppose $Y$ is Hausdorff and that $D \subset X$ is a dense subset in $X$. Let $f,g: X \to Y$ be two continuous functions such that $f_{|D}=g_{|D}$. Then $f=g$ on $X$.
The theorem is proven in this question.
Now, $f_{|\mathbb Q}=0$ and $\mathbb Q$ is dense in $\mathbb R$, which is Hausdorff. By the previous theorem, $$f=0$$
Only thing that remains to show is that $f(r)=0\forall r\in \Bbb Q^c$
Since $\Bbb Q$ is dense in $\Bbb R$ so given $r\in \Bbb Q^c;\exists r_n\in \Bbb Q$ such that $r_n\to r$
$f$ is continuous so $r_n\to r\implies f(r_n)\to f(r)\implies f(r)=0$ | {
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"url": "https://math.stackexchange.com/questions/2016775/proving-that-f-is-identically-zero"
} |
# Limits Notes | {
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"url": "http://tjqe.uiuw.pw/limits-notes.html"
} |
either providing the upper bound on the distance between the two Xn and X, or, taking a limit. Remark 1. Also, let Xbe another random variable. De nition 5.10 | Convergence in quadratic mean or in L 2 (Karr, 1993, p. 136) Note that the theorem is stated in necessary and suï¬cient form. I am looking for an example were almost sure convergence cannot be proven with Borel Cantelli. Oxford Studies in Probability 2, Oxford University Press, Oxford (UK), 1992. In some problems, proving almost sure convergence directly can be difficult. Let be a sequence of random variables defined on a sample space.The concept of almost sure convergence (or a.s. convergence) is a slight variation of the concept of pointwise convergence.As we have seen, a sequence of random variables is pointwise ⦠Thus, it is desirable to know some sufficient conditions for almost sure convergence. Then it is a weak law of large numbers. Next, let ãX n ã be random variables on the same probability space (Ω, É, P) | {
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"url": "http://gianpaologonzalez.com/vlt5j98m/47c220-convergence-almost-surely-implies-convergence-in-probability"
} |
c#, game, unity3d
Title: Object pooling for a top down shooting game I have an Asteroids clone I'm working on and I want to see if my object pooling is written correctly. The code works I just want to know if there is anything else I need to change to make it more efficient.
My first class is my ObjectPoolManager.cs. This holds the bullets and the asteroids.
public class ObjectPoolManager : MonoBehaviour
{
//Setup some objects to be pooled.
public GameObject BulletObj;
public ObjectPool Bullets;
public GameObject AstroidObj;
public ObjectPool Astroids;
void Start()
{
BulletObj = new GameObject("Bullets");
Bullets = gameObject.AddComponent<ObjectPool>();
Bullets.objectToPool = (GameObject)Resources.Load("Prefabs/Bullet");
Bullets.LateStart(BulletObj);
AstroidObj = new GameObject("Astroids");
Astroids = gameObject.AddComponent<ObjectPool>();
Astroids.objectToPool = (GameObject)Resources.Load("Prefabs/Astroid");
Astroids.LateStart(AstroidObj);
}
} | {
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Not a rigorous proof at all, but you could take the $xe$th root of both sides, and then we have
$$e^{1/e} \geq x^{1/x}$$
That $x^{1/x}$ attains a maximum at $x = e$ can be shown fairly straightforwardly.
ETA2: A picture is worth—well, a lot of words, if not quite a thousand:
ETA: OK, a discussion of why $x^{1/x}$ attains a maximum at $x = e$. To obtain the actual value requires calculus, but we can get some intuition for the fact that it attains a maximum somewhere near $e$, as follows.
Let $f(x) = x^{1/x} = \sqrt[x]{x}$. For $x = 1$, we clearly have $f(x) = 1$. For $x = 2$, we have $f(x) = \sqrt{2} > 1$. So far, it's going up. | {
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steel, springs
A low-quality spring could become softer with use by the progressive growth of fatigue cracks in its surface but for a hand exerciser this is very unlikely because those cracks require a very large number of stress cycles to grow to significant size.
Spring alloy design and spring manufacture are both quite mature technologies and the materials used in them are not a significant cost-driver in a business model; the most probable way that a "low quality" spring would fail is due to a flaw hidden inside the spring (like a slag or scale inclusion) - but these would cause prompt and catastrophic failure of the spring within tens or hundreds of flexure cycles out-of-the-box. | {
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c++, game, c++11, wordle
Another example of repetition is readSolutions() and readGuesses(). These two functions do exactly the same thing, the only difference is the filename they use. So consider creating one function that takes the filename as a parameter:
std::vector<std::string> readFile(const std::string& filename, int length) {
⋮
std::ifstream fin(filename);
⋮
}
⋮
auto all_solutions = readFile("../words/solutions.txt", LENGTH);
auto all_sguesses = readFile("../words/guesses.txt", LENGTH); | {
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control, pid
Title: Robots Following Robots with Safety Distance Planning and Coordination I have two robots, I wish for the second robot to follow the first one while keeping a constant distance d_safe between them. I am trying to implement a PID controller that takes as input the current distance between the second robot and the first one and then returns the second robot's velocity. I need help with the mapping of the information provided by the PID to the velocity. I can measure the current distance between the two robots at any time. Approaches I have tried in vain:
using the error, e(t) provided by the PID as the acceleration of the following robot over time. This seemed to me as the most appealing approach, however, its main flaws include the second robot reversing when the acceleration turns out to be negative for a given period. I wish to avoid reversing and backward motion. However, stopping is fine. So let's say it's a stop-go system.
used velocity equation: | {
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newtonian-gravity, angular-momentum, galaxies
Title: How Galaxy is formed? Given the distance among stars (the most massive objective in the space) is so huge, the difference of order of magnitude is about 7.
And also, since gravity is such a weak force, how is it likely for gravity to shape galaxy the way it is?
Would it make more sense to say galaxy is collapsing?
I would like to know if my reasoning is improper, where goes wrong,
and how to test my reasoning or your reasoning with experiment? Actually, most research suggests that interactions of two galaxies (i.e., "mergers" or collisions) is what determines the shapes of galaxies, and not necessarily gravity alone. This Astronomy Now article from a few years ago goes a bit more into the details. | {
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$$\begin{eqnarray} S_1\{\}&:&\boxed{1\ 2\ 3\ 4\ 5\ 6\ 7\ 8\ 9\ 10\ 11\ 12\ 13}\\ S_2\{3,4,7,8,13\}&:&\color{red}{\boxed{1\ 2\ 5\ 6\ 9\ 10\ 11\ 12}}\\ S_3\{1,10,11\}&:&\color{red}{\boxed{3\ 4\ 7\ 8\ 13}\boxed{2\ 5\ 6\ 9\ 12}}\\ S_4\{4,5,6,7\}&:&\color{red}{\boxed{1\ 10\ 11}\boxed{2\ 9\ 12}\boxed{3\ 8\ 13}}\\ S_5\{11,12,13\}&:&\color{red}{\boxed{56}\boxed{47}\boxed{38}\boxed{29}\boxed{1\ 10}}\\ S_6\{1,2,3,4,5\}&:&\color{red}{\boxed{13}\boxed{12}\boxed{11}\boxed{10}\boxed{9}\boxed{8}\boxed{7}\boxed{6}}\\ S_7\{\}&:& \color{red}{\boxed{1}\boxed{2}\boxed{3}\boxed{4}\boxed{5}\boxed{6}\boxed{7}\boxed{8}\boxed{9}\boxed{10}\boxed{11}\boxed{12}\boxed{13}} \end{eqnarray}$$ | {
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• What I love about this is that not only will $n^1,5,9,...$ end in $n$, but if you observe the in between powers, there is always a four number cycle. e.g. for $3^k, k->\infty$, we observe the numbers $3, 9, 27, 81, 243, 729, 2187, 6561, 19683, ...$, rendering the cycle $3, 9, 7, 1$. Aug 20, 2012 at 19:30
• @KenB: the periodicity of the digits must divide $5-1=4$ so that $1^k\to 1,1,\cdots$, $2^k \to 2,4,8,6,2\cdots$ but $4^k\to 4,6,4\cdots$ (period $1,2,4$ are possible). You may too change the rules a little and compute $\pmod{33}$ for example (the table of powers will be $1,11,21\cdots$) or better play directly with Group Theory (it's fun too !). Aug 20, 2012 at 20:06
If $\gcd(a, n) = 1$ then by Euler's theorem,
$$a^{\varphi(n)} \equiv 1 \pmod{n}$$
From the tables and as @SeanEberhard stated, $$\varphi(10) = \varphi(5*2) = 10\left( 1 - \frac{1}{5} \right) \cdot \left(1 - \frac{1}{2} \right)$$
$$= 10\left(\frac{4}{5} \right) \cdot \left(\frac{1}{2} \right) = 4$$ | {
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"url": "https://math.stackexchange.com/questions/184609/why-is-the-last-digit-of-n5-equal-to-the-last-digit-of-n"
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quantum-mechanics, spectroscopy
$$
\frac{x}{\sqrt{x^2-(1-x)^2}}|3p\rangle |E_{4s}-E_{3p}\rangle
+\frac{1-x}{\sqrt{x^2-(1-x)^2}}|3s\rangle |E_{3p}-E_{3s}\rangle
$$
where the first ket is the state of the electron and the second is the state of the photon, labeled by its energy. If we measure the energy of either the electron or the photon then their combined state will collapse into one or the other of the two product states in the superposition. | {
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Your variable $X$ is simply a sum of two randoms $$x=b+e$$, where the randoms are from uniform distributions $b\sim U(b_l,b_h)$ and $e\sim U(-\varepsilon,\varepsilon)$
If $b_h-b_l=2\varepsilon$, then $X$ is from a triangular distribution. Otherwise, it'll be a trapezoidal distribution. It must very easy to come up with CDF.
UPDATE
Her's one way of calculating the CDF. Start with a PDF $f(x)$, which is easily defined as follows:
• $\frac{x-b_l+\varepsilon}{(b_h-b_l)2\varepsilon}$, when $x\in [b_l-\varepsilon,b_l+\varepsilon]$
• $\frac{1}{b_h-b_l}$, when $x\in [b_l+\varepsilon,b_h-\varepsilon]$
• $\frac{-x+b_h+\varepsilon}{(b_h-b_l)2\varepsilon}$, when $x\in [b_h-\varepsilon,b_h+\varepsilon]$
Obviously, these are when $2\varepsilon\le b_h-b_l$.
Now, to get the CDF simply take the integral $\int_{b_l-\varepsilon}^{b_h+\varepsilon}f(x)dx$, which is easy but too long for me to type | {
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visualization, clustering, multiple-sequence-alignment
Finally, regardless of their relationship, you can always do a dendrogram based on a similarity matrix, but for that, you need to define similarity. That will be usually something kmer-based. I am not following this field very closely lately, but there are some recent papers about kmer-based clusterings, like this one.
When looking for the paper I also run into this one, which proposes genome clustering using "Inter-nucleotide Covariance". No idea how useful/sound it is. Just found the abstract quite interesting.
Long story short, it really depends on what you are after and what are your sequences! If you can build a reliable tree, it is the most powerful way to determine the relationships among sequences. | {
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quantum-mechanics, atomic-physics, photon-emission, half-life
continuously into $|g\rangle$ when $a(t$) changes with time from 1 to 0 while $b(t$) changes from 0 to 1. And during this, the electromagnetic wave (the photon) is emitted meaning the longer it takes (the more stable the excited level is) the longer the emitted wave train (more coherent light is emitted). | {
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scheduling, loops
Scheduling tasks in an operating system is different. Less science, more practical engineering. The scheduler doesn't know in advance what resources will be requested in the future, so it cannot make optimal decisions. Often a notion of optimality doesn't exist at all, the scheduler just needs to be 'good enough' i.e. not violate any deadlines on the critical tasks.
Strictly speaking, scheduling tasks is also 'scheduling the order of operations' as in my matrix example above, but in practice it's a very different problem: 'find a solution that fulfills all constraints' versus 'unconstrained optimization for least amount of floating point operations.' The goal is different, the constraints are different and the information you have is different. | {
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ros, ar-pose, ros-fuerte, roboearth, vision-opencv
And with ar_pose:
[ rosmake ] Last 40 lines_vision: 61.0 sec ] [ ar_pose: 9.1 sec ] [ 2 Active 47/103 Complete ]
{-------------------------------------------------------------------------------
make[3]: Leaving directory `/home/sasha/ros/stacks/ccny_vision/ar_pose/build'
[ 70%] Built target rosbuild_precompile
make[3]: Entering directory `/home/sasha/ros/stacks/ccny_vision/ar_pose/build'
make[3]: Leaving directory `/home/sasha/ros/stacks/ccny_vision/ar_pose/build'
make[3]: Entering directory `/home/sasha/ros/stacks/ccny_vision/ar_pose/build'
Linking CXX executable ../bin/ar_multi
CMakeFiles/ar_multi.dir/src/ar_multi.o: In function `ar_pose::ARSinglePublisher::arInit()':
/home/sasha/ros/stacks/ccny_vision/ar_pose/src/ar_multi.cpp:140: undefined reference to `cvCreateImage'
CMakeFiles/ar_multi.dir/src/ar_multi.o: In function `CvBridge': | {
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c++, performance, primes
}
}
return sum;
}
bool isPrime(int n)
{
// Corner case
if (n <= 1)
return false;
// Check from 2 to n-1
for (int i = 2; i < n; i++)
if (n % i == 0)
return false;
return true;
} There are several issues, but here goes. Firstly, your indentation is all wonky. Some of this may be due to trying to input stuff here, but either way, indentation helps legibility.
Next, the biggest thing you can change to speed thing up is to replace for (int i = 2; i < n; i++) with for (int i = 2; i*i <= n; i++). This works because if \$a \cdot b = n\$, one of them is at most the square root of \$n\$. This change will probably make your code fast enough on its own.
That said, the much better solution to this type of problem is to use a prime sieve such as the Sieve of Eratosthenes which will generate all of the primes less than 1,000,000 faster by using addition and multiplication instead of modulo operations which are slower. | {
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An alternate approach is to prove that $0 \leq \sum_{k=i}^j a_{n_k} \leq \sum_{k=n_i}^{n_j} a_k$. Now go back to the definition of the limit and take advantage of the fact that $i \leq n_i$.
• This was what my comment was getting at. Nice formalisation. – The Count Feb 15 '17 at 2:16
HINT Remember that the limit of the series is defined as the limit of the sequence of partial sums. In the case where the series only has non-negative terms, the sequence of partial sums is monotonically increasing. If you take away terms, you can only decrease the value of the sum and it's still monotonic. Now remember something about monotone and bounded sequences....
Start from the definition of "converges" which says that there exists an $L$ such that for $\epsilon > 0$ there is an $n_0(\epsilon)$ such that for any $m>n_0$, $$\left| \sum_{k=1}^m a_k - L \right| < \epsilon$$ Since the terms in the series are non-negative, $L$ is certainly an upper bound for all the partial $\sum_{k=1}^m a_k$. | {
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N, Z and D are included in the set Q (because all these numbers can be written in fraction). For K-12 kids, teachers and parents. Calculator Use. This free number sequence calculator can determine the terms (as well as the sum of all terms) of an arithmetic, geometric, or Fibonacci sequence. This type of activity is required in a mathematics discipline that is known as combinatorics; i.e., the study of counting. Our combination calculator will allow you to calculate the number of combinations in a set of size n. A combination describes how many sets you can make of a certain size from a larger set. This includes the natural numbers( 1,2,3 ...), integers (-3) rational (fractions) and irrational numbers (like √2 or π). This combination calculator (n choose k calculator) is a tool that helps you not only determine the number of combinations in a set (often denoted as nCr), but it also shows you every single possible combination (permutation) of your set, up to the length of 20 elements. | {
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digital-communications, modulation, demodulation
$$
\begin{array}{|c|c|c|c|c|c|}
\hline
(b_I,b_Q) & \text{normal value} ~k & \text{Gray code value} ~\ell &\text{phase-modulated signal}\\
\hline
(0,0) & 0 & 0
& \sqrt{2}\cos\left(2\pi f_c t - 0\frac{\pi}{2}\right)\\
(0,1) & 1 & 1
& \sqrt{2}\cos\left(2\pi f_c t - 1\frac{\pi}{2}\right)\\
(1,1) & 3 & 2
& \sqrt{2}\cos\left(2\pi f_c t - 2\frac{\pi}{2}\right)\\
(1,0) & 2 & 3
& \sqrt{2}\cos\left(2\pi f_c t - 3\frac{\pi}{2}\right)\\
\hline
\end{array}
$$
That is, we can say that the QPSK modulator input
$(b_I,b_Q)$ is regarded as the Gray code representation
of the integer $\ell \in \{0,1,2,3\}$ and the modulator produces the
output
$$\sqrt{2}\cos\left(2\pi f_c t - \ell\frac{\pi}{2}\right).$$
In differential QPSK (DQPSK), the input dibit Gray-code value
is subtracted (differential, get it?) from the previous transmitted dibit Gray-code value (left-handed folks can use addition if they prefer) to get
the next transmitted dibit Gray code value. That is, with $\ell$ | {
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ros, gazebo-plugin
Originally posted by kaldo on Gazebo Answers with karma: 13 on 2017-01-12
Post score: 0
Original comments
Comment by chapulina on 2017-01-12:
When you say Gazebo displays no error, do you mean you're running it with the --verbose flag and no error messages come up? If the plugin is not loaded, you should get an error...
Comment by kaldo on 2017-01-12:
Thanks for the input! I have modified the launch file to run in verbose mode, and an error came up! I have edited the question.
As a workaround, I set the GAZEBO_PLUGIN_PATH directly in my launch file, adding an <env> tag at the beginning :
<launch>
<!-- Set up env variable so plugin are found -->
<env name="GAZEBO_PLUGIN_PATH" value="$(find car_gazebo)/plugins"/>
Originally posted by kaldo with karma: 13 on 2017-01-24
This answer was ACCEPTED on the original site
Post score: 1 | {
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programming-challenge, functional-programming, clojure
... using quot instead of / for integer division. For example,
(prime-factors 24651)
;[3 3 3 11 83]
The biggest is the last:
(last (prime-factors 24651))
;83
Or, by starting with () instead of [], we accumulate the factors LIFO, so the biggest is the first.
Or we can adapt the function to retain only the last element:
(defn largest-prime-factor [n]
(loop [n n, ans 1, candidates (prime-seq)]
(case n
1 ans
(let [candidates (drop-while #(not (divides-by? n %)) candidates)
divisor (first candidates)]
(recur (quot n divisor)
divisor
candidates))))) | {
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logic, database-theory, first-order-logic, relational-algebra
Title: Max() in Domain Relational Calculus I was looking through my notes on domain relational calculus, and noticed an interesting result in a question about finding the most expensive pizza(s), given a pizza table with schema $\text{pizza}(\underline{id}, size)$. The first idea that came to me was:
$$\{id1\ |\ \exists size1, \forall id2, \forall size2 \ (\text{pizza}(id1, size1) \land \text{pizza}(id2, size2) \land size1 \ge size2)\}$$
i.e. A pizza which is at least at big as every other pizza is the most expensive. But the answer given was instead:
$$\{id1\ |\ \exists size1, \forall id2, \forall size2 \ (\text{pizza}(id1, size1) \land (\text{pizza}(id2, size2) \to size1 \ge size2))\}$$ | {
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ros
... do more stuff here. Use tf_ptr as a regular pointer for the most part ...
return 0;
}
The comments in this thread also explain the same answer.
Originally posted by piyushk with karma: 2871 on 2013-03-12
This answer was ACCEPTED on the original site
Post score: 2
Original comments
Comment by MartinW on 2013-03-12:
Thanks for the quick reply piyushk! I tried this but now I am back to getting the error: reference to ‘transform’ is ambiguous. candidates are: tf::StampedTransform transform. Do I need to make StampedTransform a shared_ptr too? the variable transform is what I need in my callback
Comment by dornhege on 2013-03-12:
Can you give the code sample producing that.
Comment by MartinW on 2013-03-12:
Hey dornhege, I put the code into another answer (forgetting that I could edit my own question haha) | {
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optics, experimental-physics, diffraction
Edit: As a partial answer to the extension, what is meant by resolution here is how precisely you can measure the slit width. If you use a 700nm laser, you can't do much better than 700nm on this precision: so if the slit is, say, 10 microns this could be a limiting factor if you need very high precision. So if this is your limiting case, you need to use a shorter wavelength light source: blue, ultraviolet or even X-ray light to get a very precise (though harder to measure) measurement. | {
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multiclass-classification, class-imbalance, smote
SMOTE creates new observations of the minority class by randomly sampling from a set of "similar" minority class observations. Synthesized observations are computed based off adding a random percentage of the difference between two randomly chosen "similar" observations, for each coordinate (i.e. column). Similar observations are defined typically using the k most closest neighbours to a particular observation of the minority class. This means that, depending on the value of k chosen, as well as numerous other factors such as how similar your observations are in general, the distance measure, etc. SMOTE may or may not be useful for your particular problem. | {
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graphs, trees
In all other cases, since $H$ satisfies $(P)$ and contains strictly less edges than $G$, it is a tree. By deleting the dummy vertices, it stays a tree. That means that $G[C_i]$ is a tree and contains at least two vertices of degree $1$. This is absurd given the hypothesis on $C_i$. | {
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So you have $\lfloor\frac{n}{2}\rfloor+1$ such solutions (to include $0$); then you get to choose the "odd man out" in $3$ different ways. So we have $3\lfloor\frac{n}{2}\rfloor+3$ possibilities. However, you have overcounted a solution with $a=b=c$ if there is one; there is one if and only if $n\equiv 0\pmod{3}$. So the number of solutions with at least two of the numbers equal is \begin{align*} 3\left\lfloor\frac{n}{2}\right\rfloor+1&\qquad\text{if }n\equiv 0\pmod{3}\\ 3\left\lfloor\frac{n}{2}\right\rfloor+3 &\qquad\text{otherwise.} \end{align*}
For example, take $n=11$. The solutions with duplicates have $(0,0,11)$, $(1,1,9)$, $(2,2,7)$, $(3,3,5)$, $(4,4,3)$, and $(5,5,1)$, and each of them can be assigned to $a$, $b$, and $c$ in three different ways. This gives 18 solutions; $\lfloor\frac{n}{2}\rfloor = \lfloor\frac{11}{2}\rfloor = 5$, and since $11$ is not divisible by $3$, the formula gives $3(5)+3 = 18$. | {
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c++, xml, stack
Always prefer C++ casts over C-style casts. Use the correct operators: static_cast, reinterpret_cast, etc. This will prevent you from accidently casting away things you don't mean to without being explicit.
NEVER cast away const from a pointer. In this case you don't have to. This is the most dangerous thing you can do and leads to potentially crashing code. Your could have declared the pointer as const char *.
Don't store the content of string::c_str() in a variable:
If the std::string is modified in any way, the pointer that was returned is invalidated. If you try to use that pointer, you have undefined behavior. So storing the pointer is dangerous. The best place to use the value is to pass it directly as a parameter to the function:
std::ifstream checkFile(fileName.c_str()); // Perfectly fine.
// There is no chance of altering
// filename and invalidating the | {
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javascript
function ajax_tweet(server_response_text,html_div)
{
var first_split,second_split,tweet_count,return_string='';
var aml_status=check_aml(server_response_text.slice(0,6));
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return_string=return_string+'<div class="Bb2b"><img class="a" src="pictures/' + second_split[0] + '.jpg" alt=""/><a class="a" href="javascript:void(0)\">' + second_split[1] + ' posted ' + view_date(second_split[2],second_split[3]) + '</a><br/><p class="c">' + second_split[4] + '</p></div>';
}
fill_id(html_div,return_string);
}
else if (aml_status===aml_status_type.fail)
{/*add code here when ready */}
else if (aml_status===aml_status_type.undefined)
{ | {
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lagrangian-formalism, symmetry, action, noethers-theorem, variational-calculus
\begin{equation}\tag{5}
\Delta(\partial_{\mu}\phi^a) = \partial_{\mu}(\Delta\phi^a) + \partial_{\mu}(\delta x^{\sigma})\partial_{\sigma}\phi^a(x)\,.
\end{equation}
After the detour, we come back to Noether. I decided to proceed by using the invariance of the action:
\begin{equation}
S[\phi^a(x),\partial_{\mu}\phi^a(x)]=\int_{\Omega}d^4x\;\mathcal{L}(\phi^a(x),\partial_{\mu}\phi^a(x))\,.
\end{equation}
To shorten the following expressions, I'll choose to abuse the notation: $S[\phi^a(x),\partial_{\mu}\phi^a(x)]=S[x]$ and $\mathcal{L}(\phi^a(x),\partial_{\mu}\phi^a(x))=\mathcal{L}(x)$. We need our transformation to produce a variation of the action of maximum a boundary term, which is the integral of the divergence of a smooth field $W^{\mu}$, satisfying $\left.W^{\mu}\right|_{\partial\Omega}=0$, which is our condition for a well behaved variational principle. In summary, we need that:
\begin{align}
\delta S &= \tilde{S}[\tilde{x}]-S[x]\\ | {
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supernova, pulsar
Alternatives are that there are instabilities in the final phases of nuclear burning, just prior to the core collapse. These instabilities cause the core to wobble back and forth and when the supernova happens, the core just happens to be travelling one way or another. There have also been suggestions that asymmetric radiation from the pulsar itself could gradually accelerate it to the speeds observed. | {
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c++, windows, embedded
auto rc = RegSetValueEx(hKey, regValueName.c_str(), 0, REG_SZ, (BYTE*)regValue.data(), cbData);
if (rc != ERROR_SUCCESS){
throw std::runtime_error("Windows system error code: " + to_string(rc));
}
}
else if(rc != ERROR_SUCCESS){
DEBUG_PRINT("Error setting key.\n")
}
else {
DEBUG_PRINT("UNKNOWN ERROR: Key does not exist, and a new key was not created.")
}
}
catch (std::exception& e)
{
DEBUG_PRINT(e.what())
}
}
//DEBUG_PRINT("BYTE*: " + to_string(sizeof(BYTE*)));
//DEBUG_PRINT("BYTE: " + to_string(sizeof(BYTE)));
//DEBUG_PRINT("char*: " + to_string(sizeof(char*)));
//DEBUG_PRINT("char: " + to_string(sizeof(char)));
//ASSERT(sizeof(BYTE*) == sizeof(char)); | {
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For every complete orthonormal system $\Phi$ there is an $L^2$ function $Y$ whose $\Phi$-Fourier series can be rearranged to diverge almost everywhere.
So we can finish as follows. Take the Haar functions as above (a complete orthonormal set) and the function $Y$ defined above. We write this function's $\Phi$-Fourier series as $$\sum_{n=1}^\infty \langle Y, X_n \rangle X_n$$ Now there exists a rearrangement $\sigma$ of the indices of sum such that it diverges almost everywhere. Now let $Y_n = \langle Y, X_{\sigma(n)} \rangle X_{\sigma(n)}$ be this rearrangement of terms. We can see $$\sum_{n=1}^\infty Y_n$$ satisfies the requirements of the problem. Indeed $$\sum_{n=1}^\infty\operatorname{Var} (Y_n) = \operatorname{Var}(Y) < \infty.$$ Furthermore, $\sum Y_n$ diverges almost everywhere. | {
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newtonian-mechanics, forces, reference-frames
Title: Fictitious Forces in a car crash Do we actually feel fictitious forces acting on our bodies? My conclusion is that yes we do, since when I am accelerating upwards in an elevator, I feel a lot of pressure on my knees. I have an example though (that certainly has some logical error in it) that proves the opposite:
A car is moving at constant velocity u=100km/h with a passenger on the back seat. The passenger is sitting on ice so that the friction between the car and passenger is 0. The car crashes on a wall, and stops completely in t=0.1s.
Inertial frame of reference:
An observer outside of the car, sees the passenger moving at constant speed of u=100km/h after the crash, so the net force acting on him continues to be 0. When the passenger eventually hits the wall he stops moving as well.
Non inertial frame of reference: | {
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• First of all let me tell you a bog "thank you". Among all the definitions and descriptions of extensionality and intentionality in every book, blog, etc I have read, yours was the best and cleared out a lot of things. Regarding your last paragraph, where from do we conclude that one can not state two values are not definitionally equal unless one is certain there is no proof $P$? Does it come from $(Id-DefEq)$ elimination rule? – al pal Aug 9 at 2:05
• @alpal yes it comes from that rule. Notice that P is free in the premise but not in the conclusion, meaning it's interpreted existentially. The rule says "anytime there exists a proof P that two values are equal, then we can consider them definitionally equal." So to prove that they are not equal, we must rule out the existence of any proof. – jmite Aug 10 at 6:36 | {
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scala, generics, collections, type-safety
We know that the last line won't ever do anything useful, so in my mind it would be kinder to prevent it from compiling so as to prevent any client of the API from making a mistake.
Happy to discuss the code more, but didn't want to go into too much detail if you're no longer interested. | {
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z. Wilkinson and T. Predator, which deals with objective functions, will also be placed on the same lattice randomly. Modified Model with "Limits to Growth" for Prey (in Absence of Predators) In the original equation, the population of prey increases indefinitely in the absence of predators. % the purpose of this program is to model a predator prey relationship % I will be using. In the last section we make a review of the paper and share with the future plans. To find the ratios of the errors, we will. We present an individual-based predator-prey model with, for the first time, each agent behavior being modeled by a fuzzy cognitive map (FCM), allowing the evolution of the agent behavior through the epochs of the simulation. The prey still relies on the food source, but the predator relies solely on the former competitor. This lesson allows students to explore the interactions of two animal populations (wolves and moose) within an ecosystem. Represent and interpret data on a line graph. | {
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"url": "http://gunb.nomen.pw/predator-prey-model-simulation-matlab.html"
} |
symmetry, group-theory, higgs, lie-algebra, symmetry-breaking
Title: Peskin Schroeder Higgs mechanism for an $SU(3)$ gauge theory with a scalar field $\varphi$ in the adjoint representation In Peskin Schroeder pag.696 a Higgs mechanism for an $SU(3)$ gauge theory with a scalar field $\phi$ in the adjoint representation is presented. The covariant derivative of $\phi$:
$$ D_{\mu}\phi_{a} = \partial_{\mu}\phi_{a}+ g f_{abc}A^{b}_{\mu}\phi_{c}\tag{20.32}$$
defining the quantity
$$\Phi=\phi_c t^c\tag{20.34}$$
We consider the expansion of $\Phi$ around two vacuum choice:
$$1) \,\,\,\Phi_0 = v \begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & -2
\end{bmatrix}$$
$$2) \,\,\,\Phi_0 = v \begin{bmatrix}
1 & 0 & 0 \\
0 & -1 & 0 \\
0 & 0 & 0
\end{bmatrix}$$
In the first case the unbroken generators are: $T_1,T_2,T_3,T_8$
In the second case the unbroken generators are: $T_3,T_8$
Where $T_i$ are Gell-Mann matrices according to the normalization which here is $T_i = \lambda_i/2$. | {
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"url": null
} |
# Cardinality of cofinite topology
Does it make sense to ask about cardinality of closed finite topology defined on the set of Natural Numbers? Is it countable or uncountable? Is it possible to prove that it is countable?
Further, if it countable, is every closed finite topology (cofinite topology) defined on countable set again countable?
- | {
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navigation, catkin-make, move-base, ros-kinetic
Originally posted by mateusguilherme on ROS Answers with karma: 125 on 2020-06-15
Post score: 0
Navigation Stack on GitHub
ROS will search your ROS_PACKAGE_PATH in order, so packages in your own workspace will be found before the ones in /opt/ros... . Your self-compiled move_base will thus be used automatically instead.
Originally posted by pcoenen with karma: 249 on 2020-06-15
This answer was ACCEPTED on the original site
Post score: 1 | {
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"tags": "navigation, catkin-make, move-base, ros-kinetic",
"url": null
} |
units to the right. Certainly the graph is optional; the beauty of the slope formula is that we can obtain the slope, given two points, using only algebra. Data Visualization, Data Mining and Tableau. We're hoping to bring back a new tool to graph equations, but for the moment, we'd recommend GraphSketch, which is a free tool to produce nice multi-function graphs. Naomi showed a slope graph in her Forbes blog post. Finding Slope from a Graphed Line Worksheets These Linear Functions Worksheets will produce problems for practicing finding the slope from a graphed line. You have all the needed averages and SDs. Linear Regression Formula To clear the graph and enter a new data set, press "Reset". For this equation y = 3x + 2 is in slope intercept form. This can be done by calculating the slope between two known points of the line using the slope formula. Key Questions. In this example we have not bothered plotting the points, because this is not necessary. Answer Key You don’t need to add | {
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"url": "http://metstrategies.com/sztvzsd/oofapob.php?khdtkqcnx=graph-slope-formula"
} |
quantum-mechanics, condensed-matter, many-body, second-quantization, anyons
Title: Is it possible to make statements about bosonic/fermionic systems by taking the limit $\theta\to \pi$ or $\theta\to 0$, of an anyonic system? One might naïvely write the (anti-)commutation relations for bosonic/fermionic ladder operators as limits
$$
\delta_{k,\ell} = \bigl[ \hat{b}_{k}, \hat{b}_{\ell}^\dagger \bigr]
= \hat{b}_{k} \hat{b}_{\ell}^\dagger
- \hat{b}_{\ell}^\dagger \hat{b}_{k}
= \lim_{\theta\to\pi} \Bigl( \hat{b}_{k} \hat{b}_{\ell}^\dagger
+ e^{i\theta}\cdot\hat{b}_{\ell}^\dagger \hat{b}_{k} \Bigr)
$$
$$
\delta_{k,\ell} = \bigl\{ \hat{c}_{k}, \hat{c}_{\ell}^\dagger \bigr\}
= \hat{c}_{k} \hat{c}_{\ell}^\dagger
+ \hat{c}_{\ell}^\dagger \hat{c}_{k}
= \lim_{\theta\to 0} \Bigl( \hat{c}_{k} \hat{c}_{\ell}^\dagger
+ e^{i\theta}\cdot\hat{c}_{\ell}^\dagger \hat{c}_{k} \Bigr).
$$ | {
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homework-and-exercises, electromagnetism, special-relativity, tensor-calculus
Title: Components of electromagnetic tensor in a moving frame I need to find the electric and magnetic components of electromagnetic tensor in an inertial frame S' moving in the +x direction with a speed $\beta$ relative to frame S. Electromagnetic tensor in S frame $F_{\mu\nu}$ is given below.
$$F_{\mu\nu}=\begin{pmatrix}
0 & -E_x & -E_y & -E_z \\
E_x & 0 & B_z & -B_y \\
E_y & -B_z & 0 & B_x \\
E_z & B_y & -B_x & 0\end{pmatrix}$$
Since$$F_{\mu'\nu'}=\Lambda_{\mu'}^{\mu}\Lambda_{\nu'}^{\nu}F_{\mu\nu}$$ Is it correct to use lorentz transformation matrix
$$\Lambda_{\mu'}^{\mu}=\begin{pmatrix}
\gamma & -\gamma\beta & 0 & 0 \\
-\gamma\beta & \gamma & 0 & 0 \\
0 & 0 & 1 & 0 \\ | {
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javascript, html, angular.js, fizzbuzz, twitter-bootstrap
I'm looking for a general review here, particularly focusing on best practices, since I'm fairly new to HTML and JS and completely new to AngularJS and Bootstrap. Very nice. I can't really see any major issues here, just some nits to pick. Note, though, that my knowledge of Angular is near-nil, so perhaps there's something there that someone else will be better equipped to comment on.
Markup
The markup is all-Bootstrap, so it's pretty by-the-book already.
There's a lot of it though, making it a hard to skim. To get a good look I copied it to my editor, and basically add more whitespace to separate things. In general, you seem to skimp on whitespace (both in markup and JavaScript) a little too much for my tastes.
You can also leave some things out, and combine others; some classes work fine on non-div elements. | {
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fluid-dynamics, gauss-law, flow
You are correct, but it is irrelevant to the derivation of buoyancy force on the body. Here's how the argument goes:
Buoyancy force is determined solely by the force exerted by the fluid on the body's surface. In other words it depends only on the state of stress in the fluid (when evaluated at the body's surface).
If the solid body were replaced by fluid which is the same as the ambient fluid, then that replacement-fluid-body would be in equilibrium.
Therefore to find buoyancy force on the solid body, replace the solid body by ambient fluid and do your calculations.
Thus the manner in which divergence theorem has been used makes sense. | {
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javascript, node.js, async-await, eslint
return ticker;
};
const getCurrencyData = () => {
getOrderBook().then(orderBook => ([buyOrders, sellOrders] = [orderBook.buys, orderBook.sells] )); //eslint-disable-line
getTicker().then(ticker => ([bid, ask, lastBuy] = [ticker.Bid, ticker.Ask, ticker.Last])); //eslint-disable-line
};
setInterval(() => {
getCurrencyData();
}, 5000); | {
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Chung's definition is the same as Rudin's. Any expectation they say does not exist does not exist in Wikipedia's definition either: an example would be a discrete approximation to the Cauchy distribution. As Chung and Rubin do accept some infinite expectations, some other statements would need to be qualified, such as the expectation of the sum of a finite number of random variables being the sum of the expectations of the random variables; Wikipedia's definition avoids this issue.
- | {
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python, beginner, programming-challenge, python-3.x, playing-cards
#check 2 pair
elif(mostcommonfreq == 2 and nextcommonfreq == 2):
vallist.remove(mostcommon)
vallist.remove(mostcommon)
vallist.remove(nextcommon)
vallist.remove(nextcommon)
if mostcommon>nextcommon:
vallist.insert(0,nextcommon)
vallist.insert(0,nextcommon)
vallist.insert(0,mostcommon)
vallist.insert(0,mostcommon)
else:
vallist.insert(0,mostcommon)
vallist.insert(0,mostcommon)
vallist.insert(0,nextcommon)
vallist.insert(0,nextcommon)
val = [hands.index('two pair')] + [i for i in vallist] | {
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experimental-physics, error-analysis, statistics
So how are we dealing with these? By measuring the distributions when necessary and by using either numerical statistics packages that can calculate true error distributions for the non-normal case or, and this is more commonly used in very complex bias scenarios, by using Monte-Carly simulations where we include the measured error distributions into the simulation of our experiments from the get-go and we just simulate e.g. the experiment a million times with the measured distributions for the errors. Is this complicated? Yes. It is complicated and necessary whenever you are doing a real experiment in science. | {
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atmosphere-modelling, humidity
However, there are other sources for relative humidity profiles. You can obtain them from reanalysis data. If you want probabilities, you could calculate them from reanalysis. I have not used probabilities, but I have used profiles from Anderson et al. (1986) in the past:
Anderson, G. P., S. A. Clough, F. X. Kneizys, J. H. Chetwynd, and E. P. Shettle (1986), AFGL atmospheric constituent profiles (0–120 km), AFGL, TR-86-0110. | {
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matlab, estimation, linear-algebra, least-squares, parameter-estimation
Recursion without auxiliary state variables
For what it's worth, I also found a recursion that doesn't require auxiliary state variables (such as $A$ and $B$), but requires remembering the previous two $m$ and the previous $y$:
$$m_n = \frac{2m_{n-1}(n - 2)}{n + 1} - \frac{m_{n-2}(n - 2)(n - 3)}{n^2 + n} + \frac{6y_{n-1}(n - 3)}{n^3 - n} - \frac{6y_{n-2}(n - 3)}{n^3-n}.\tag{13}$$
Slope from the most recent $N$ samples
Earlier I had thought that you want to calculate the slope based on $N$ most recent samples. I will keep the following stub of an analysis about that, in case it might be useful for someone. | {
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error in using the trapezium rule with six ordinates. Use this area of trapezoidal prism calculator to find the area by using length of the top, length of the bottom and height values of trapezoidal prism. Simpson's (Parabolic) Rule. Starting with (3, 12) and using y = ax2 + bx + c, you could write: 12 = a(3)2 + b(3) + c 12 = 9a + 3b + c. A similar but more accurate numerical method is the trapezoidal method: y n+1 = y n + h 2 [f (x n;y n) + f (x n+1;y n+1)]; n = 0;1;::: (6) It is derived by applying the simple trapezoidal numerical integration rule to the equation Y(x n+1) = Y(x n) + Z. To find the area under a curve, we have to split the space into very thin strips and look at them individually. After reading this chapter, you should be able to: 1. Z b=x 1 a=x0 f(x)dx = Z x 1 x0 P1(x)dx + 1 2 Z x 1 x0 f00(ξ)(x− x0)(x−x1)dx = Z x 1 x0 x−x1 x 0. Example: Let's approximate this definite integral with n = 5. In mathematics, and more specifically in numerical analysis, the trapezoidal | {
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"url": "http://danieledivittorio.it/jobz/trapezium-rule.html"
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algorithm, c, multithreading, matrix, portability
#ifdef _WIN32
HANDLE* threads = calloc(num_threads, sizeof(HANDLE));
#else
pthread_t* threads = calloc(num_threads, sizeof(pthread_t));
#endif
for (i = 0; i < num_threads - 1; ++i)
{
#ifdef _WIN32
threads[i] = CreateThread(NULL,
1000000,
ThreadProc,
(void*) &thread_info_structs[i],
0,
NULL);
#else
pthread_create(&threads[i],
NULL,
thread_func,
(void*)&thread_info_structs[i]);
#endif
}
#ifdef _WIN32
ThreadProc((void*) &thread_info_structs[num_threads - 1]);
#else
thread_func((void*)&thread_info_structs[num_threads - 1]);
#endif | {
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bolzano theorem. Functions continuous on a closed interval attain there a maximal and a minimal value. If is some number between f (a) and f (b) then there must be at least one c : a 0, det(A + el) ¥= 0 where I is the identity matrix. While it is not true that a bounded sequence is convergent, the Bolzano-Weierstrass theorem tells us that we can at least find a convergent subsequence. Prove that the polynomial function. The Monotone Subsequence Theorem Fold Unfold. Use the Bolzano Weierstrass Theorem to prove that if f is a continuous function on [a, b), then f is bounded on [a, b] (that is, there exists M> 0 such that |f(r)| < M for all r E [a, b). Then {x n} ∞ n=1has a convergent subsequence. The Nested Intervals Theorem We begin by proving the seemingly unrelated nested intervals theorem (Theorem 6). Recently, it has been demonstrated that the Bolzano-Weierstrass theorem re sults from a definition. topic/Bolzano-Weierstrass-property. It is the fabled Bolzano-Weierstrass theorem. | {
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powershell, web-services, ip-address
Just something to be mindful of.
Function Naming Conventions
PowerShell suggests that you name your functions in the basic for of Verb-Noun(s) among other convention standards. This is not super important for personal code but consistency should be. Some of your function names have hyphens and others don't. Hyphens are present in all of the MS cmdlets so it would make sense to follow suit. Again, just be consistent.
Function Names and Calls
You are using the param keyword which is good for your simple functions. However it is also a good practice when calling your functions to use the parameter keywords and not rely on positional argument matching. It is not a question of functionality but of readability. Looking at:
ConfigureServers 'officetwo' 'officeone' | {
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cc.complexity-theory, lo.logic, sat
Context
The reliable assignments appear in the context of Partial Distributive Expansion
Detailed examples are available at Prime Implicants and Reliable Assignments.
The full context is an integrated SAT algorithm for a complete set of solutions. Here is an informal rationale on what I have to cover eventually. Any hints welcome. Answer to your primary question: You have posed a Yes/No question. By definition, a Yes/No answer suffices. There is no requirement to produce any kind of assignment as an answer. If you modify the problem to require a certificate for the Yes/No answer, the answer will depend on what constraints you impose on the certificate and the certification algorithm (should it be linear-time verifiable, etc.). | {
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backpropagation, definitions
case Functions.LossFunction.MSE:
changes = Functions.MSEDerivative(outputs, answers);
break;
}
for (int i = 0; i < changes.Length; i++) {
Neuron neuron = network[network.Length - 1][i];
double act = neuron.activation;
switch(neuron.activationFunction) {
case Functions.ActFunction.Sigmoid:
changes[i] *= Functions.sigmoidDerivative(Math.Log(act / (1 - act)));
break;
case Functions.ActFunction.Linear:
changes[i] *= Functions.LinearDerivative(act);
break;
}
}
for (int i = network.Length - 1; i > 0; i--) {
for (int j = 0; j < network[i].Length; j++) { | {
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "backpropagation, definitions",
"url": null
} |
beginner, android, kotlin
<LinearLayout
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:orientation="horizontal">
<Button
android:id="@+id/button_cancel"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_weight="1"
android:text="@android:string/cancel" />
<Button
android:id="@+id/button_ok"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_weight="1"
android:text="@android:string/ok" />
</LinearLayout>
</LinearLayout> | {
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Posted 4 months ago
873 Views
|
3 Replies
|
14 Total Likes
| | {
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"openwebmath_score": 0.5392575263977051,
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"url": "http://community.wolfram.com/groups/-/m/t/1340126?sortMsg=Votes"
} |
Functions y = |x| Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. The graph may or may not intersect the horizontal axis, depending on how the graph has been shifted and reflected. One of the fundamental things we know about numbers is that they can be positive and negative. The ABSOLUTE function in Excel returns the absolute value of a number. To see why, let's consider the following example: This equation looks similar to what we've seen before; it doesn't look particularly much more complicated than the others. absolute value functions. You can apply the unary minus (negation) operator. The Overflow Blog Episode 304: Our stack is HTML and CSS Join Date: Oct 2010. No credit card required 37 Sophia partners guarantee credit transfer. From the hardware perspective, it is easier to flip the sign bit on a signed integer type. (I could have done the "plus" and the "minus" on the left-hand side, but I'm a creature of habit.) | {
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"url": "https://communitylibrariesnetwork.org/cq6bv/6c8d10-how-to-flip-an-absolute-value-function"
} |
thermodynamics, fluid-dynamics, flow, turbulence
This means that tiny perturbations right at the at the start of the rising air column get magnified, and after a while those perturbations grow so big that the column is disrupted in ways that are extremely complex and changing from moment to moment. This makes the system behavior very hard to predict after a while- and the smooth predictable rise of the air column switches into random, misshapen vortices.
The growth of those vortices is an extremely complex phenomenon that got its first mathematical treatment by a guy named Von Karman in the late 1940's. | {
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"tags": "thermodynamics, fluid-dynamics, flow, turbulence",
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} |
homework-and-exercises, kinematics, velocity, vectors
Your runner must have a speed of -4m/s in the y direction in point B, you get the velocity:
$V_B = -4 \, \text{m/s} \, \hat{y} + 0 \, \text{m/s} \, \hat{x}$
The speed in the x direction is unchanged.
Regardless of choice of axis the equation should be: $V_A + change = V_B = -V_A$, so the change in this case must always be equal to $-2 \cdot V_A$
You initial guess of -8m/s, with regard to the magnitude of the velocity change, is correct if you place your initial vector along with one of the axes of your coordinate system of choice. | {
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| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com
Originally posted by EgmatQuantExpert on 04 Jul 2018, 05:50.
Last edited by EgmatQuantExpert on 07 Jul 2018, 06:13, edited 3 times in total.
Intern
Joined: 27 Feb 2018
Posts: 36
Location: India
WE: Engineering (Real Estate)
Re: The average of 6 numbers is 8. One new number is now added [#permalink]
### Show Tags
04 Jul 2018, 05:55
EgmatQuantExpert wrote:
Solve any Mean and Standard deviation question under a minute- Exercise Question #2
2- The average of 6 numbers is 8. One new number is now added to the set of 6 numbers and the arithmetic mean of the 7 numbers is now calculated.
Is the arithmetic mean of 7 numbers greater than 10?
1. The additional number is at least 23.
2. The additional number is a multiple of 4.
Options | {
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"url": "https://gmatclub.com/forum/the-average-of-6-numbers-is-8-one-new-number-is-now-added-269695.html"
} |
newtonian-mechanics, forces, differentiation
$$\mathbf{F}(x) = \frac{1}{2m} 2m\mathbf{v}(x)m\mathbf{a}(x)$$
Which turns out to be
$$\mathbf{F}(x) = m\mathbf{v}(x)\mathbf{a}(x)$$
Which is obviously not equal to the classic formula. Where is my mistake? Is the treatment correct at all? Thanks in advance. Simple: $\vec{p}^{\prime}(\vec{x})$ is not $m\vec{a}$. In particular, $\vec{p}^{\prime}$ is the space derivative of $\vec{p}$, but $m\vec{a}=m\partial_t\vec{v}=\partial_t(m\vec{v})=\partial_t\vec{p}$.
You can correct your argument by noting that $\partial_t\vec{x}=\vec{v}$ and applying chain rule. | {
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java, combinatorics
if (tmpSp1.length > 1)
{
if (tmpRaw1.contains("not "))
{
isKnight1 = tmpRaw1.contains("knight") ? false : true;
}
else
{
isKnight1 = tmpRaw1.contains("knight") ? true : false;
} | {
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"tags": "java, combinatorics",
"url": null
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everyday-life
Title: Despite of so much assumptions and approximations,why physics work so well? I always believe that physics can explain everything happening around us.Our every single action can be defined by physical laws.
Now I m coming to the question(as I have mentioned the laws), the assumptions are the base of physics( I apologise if someone disagree) and still these assumptions work so well in general.
Now,Let's talk like gentleman,The kinetic theory of gases is completely based on certain assumptionsthese assumptions are so helpful in understanding gaseous phenomena.
Whenever I read about gravity I always find an assumption that assume earth to be a sphere(actually it is not),but still the effect of rotation of earth on value of g,effect of height and depth on g(acceleration due to gravity)
works well.
Edit:After reading the disappointing comments I have tried to compress this question. | {
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zoology, entomology
Both males and females produce a sound when flying but not at the same frequency. I would think of the male sound as mainly an artefact of flying and don't really know if it has any usefulness. I would note though that before mating both gender tend to synchronize their sound (Gibson and Russel 2006). On the other hand males are very attracted toward the sound of females.
In nature, mosquitoes make swarms. Male's job in the swarm is find find female, courtship and mate. This means that males need a cue to detect them from far away and this cue is their sound. Males evolved large and fluffy antennas (with which they hear) while females only have small antennas Charlwood and Jones 2008.
How do they avoid obstacles? | {
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ros-kinetic, debian
$ sudo apt-get update
Ign http://ftp.fr.debian.org jessie InRelease
Ign http://download.opensuse.org InRelease
Hit http://packages.ros.org jessie InRelease
Get:1 http://download.opensuse.org Release.gpg [481 B]
Hit http://packages.ros.org jessie/main amd64 Packages
Hit http://security.debian.org jessie/updates InRelease
Hit http://ftp.fr.debian.org jessie Release.gpg
Hit http://download.opensuse.org Release
Ign http://download.opensuse.org Release | {
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} |
organic-chemistry, nmr-spectroscopy
I "usually" understand steps 3-5, but sometimes I can't honestly figure out how many peaks I am looking at. How can I reliably tell the difference between lines within a peak due to coupling and distinct peaks when they are sometimes so close together?
Step 6 is difficult. Sometimes I can deduce an answer, and sometimes I am wondering how to tell the differences between hundreds of isomers. How can I systematically determine the right answer (or even be able to recognize IF there is single valid answer)? Of course there is a systematic approach to solving structure. The key is that it is an iterative process, and it is not uncommon to have to repeat the cycle several times. For complicated molecular structures (for example, alkaloids with C35+ frameworks) you might get 20 or more possible candidate structures that you have to work through very closely. | {
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ros, arduino, bluetooth, rosserial-python
This other one is really similar to mine:
http://stackoverflow.com/questions/18108932/linux-c-serial-port-reading-writing
Let me know if it helps.
Comment by Giovani Debiagi on 2016-10-10:
ogruiz, I've got permission to share the code now. It's up above, inside my answer. | {
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python, python-3.x, html, covid-19
# Using this as a naive, assumed-local-timezone date is dubious, but
# Worldometers has left ambiguous their date boundaries
EPOCH = datetime.fromtimestamp(0)
DAY = timedelta(days=1)
def get_chart_props(parser: Parser, script: str) -> Iterable[
Tuple[
str, # chart name
Dict[
str, # property name
Node, # property node value - an Object or an Array
],
]
]:
tree = parser.parse(script)
for node in tree.children():
if (
isinstance(node, ExprStatement)
and node.expr.identifier.node.value == 'Highcharts'
and node.expr.identifier.identifier.value == 'chart'
):
name_arg, chart_arg, *_ = node.expr.args
name = name_arg.value.strip("'")
props = {
prop.left.value: prop.right
for prop in chart_arg.properties
}
yield name, props | {
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"tags": "python, python-3.x, html, covid-19",
"url": null
} |
entropy, inertia
Title: Does Inertia "conflict" Entropy? Earth continues to spin because of inertia. Does this fact "conflict" the entropy of the universe? Since the tendence is towards disorder, how is Inertia of planets Spin related to Entropy? the earth continues to spin because of the conservation of angular momentum; the conservation of angular momentum does not conflict in any way with the entropy of the universe. The physical mechanisms at work in the earth which slowly convert angular momentum into dissipative tidal dynamics and thence into frictional heat can themselves be considered an illustration of the thermodynamic principles that describe entropy. | {
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special-relativity, experimental-physics, time-dilation
As the light splits at the beam-splitter, makes its round-trips, and returns to the beam-splitter, the resulting phase difference is
$$ \Delta\phi(v) = \frac{\Delta t_{S}(v)}{T_{S}(v)}. $$
The result of the KT experiment is that $\Delta\phi(v)$ does not depend on $v$. In particular, we have $\Delta\phi(v) = \Delta\phi(0)$, so then
\begin{align}\tag{5}
\frac{\Delta t_{S}(v)}{\Delta T_{S}(v)} = \frac{\Delta t_{S}(0)}{\Delta T_{S}(0)}
\end{align}
Now we will put all the equations $(1)$-$(5)$ together.
By $(5)$ and $(4)$,
$$ \gamma(v) = \frac{\Delta T_{S}(v)}{\Delta T_{S}(0)}. $$
By $(3)$, this is
$$ \gamma(v) = \frac{\Delta T_{S}(v)}{\Delta T_{I}(0)}. $$
By $(2)$, this is
$$ \gamma(v) = \frac{\Delta T_{I}(v)\cdot \Delta t_{S}(v)/\Delta t_{I}(v)}{\Delta T_{I}(0)} = \frac{\Delta T_{I}(v)}{\Delta T_{I}(0)}\cdot\frac{\Delta t_{S}(v)}{\Delta t_{I}(v)}. $$
By $(1)$, this is
$$ \gamma(v) = \frac{\Delta t_{S}(v)}{\Delta t_{I}(v)}, $$
and we arrive at the equation | {
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rospy, ros-hydro, ubuntu-precise, ubuntu
Then I run catkin_make, and get the following response:
CMake Error at /opt/ros/hydro/share/catkin/cmake/catkinConfig.cmake:75 (find_package):
Could not find a configuration file for package roslint.
Set roslint_DIR to the directory containing a CMake configuration file for
roslint. The file will have one of the following names:
roslintConfig.cmake
roslint-config.cmake
Call Stack (most recent call first):
nmea_navsat_driver/CMakeLists.txt:4 (find_package)
CMake Error at nmea_navsat_driver/CMakeLists.txt:23 (roslint_python):
Unknown CMake command "roslint_python".
I don't know what roslint_DIR is, and can't find anything about it online, but I did try searching my computer for both roslintConfig.cmake and roslint-config.cmake (no results for either). Anyone know what could be going wrong/how to fix it?
Originally posted by mysteriousmonkey29 on ROS Answers with karma: 170 on 2014-08-14
Post score: 0 | {
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binary-trees, search-trees
AND
If I call the successor $n$ times, the time complexity is $O(n)$ in a balanced tree.
Shouldn't tree traversal take $O(n^2)$ or $O(n\log n)$ time? Gist: The time complexity of calling the sucessor function multiple times is not merely the product of the number of calls and the worst-case bound, though that product does encompass the worst case. Rather, if the function going to be called from every node, a more sophisticated analysis can establish a tighter worst-case bound for specific trees and implementations of the successor function.
At best, tree traversal takes at $O(n)$ time: $n-1$ calls are made to the successor function, which takes constant time. One simple example of this is the traversal of a linked list, which has a successor function that immediately returns a pointer to the next node with no additional computation. | {
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Scan be deduced from a statement R if the truth table of S is True whenever. , Fs in its truth table column. The tee symbol ⊤ is sometimes used to denote an arbitrary tautology, with the dual symbol ⊥ representing an arbitrary contradiction; in any symbolism, a tautology may be substituted for the truth value "true," as symbolized, for instance, by "1. Trump, Truth and the Power of Contradiction. Tautologies []. A proposition is said to be a tautology if its truth value is T for any assignment of truth values to its components. p ∨ q Solution to EXAMPLE 2. Ø p ® c, where c is a contradiction \ p. R R • ∼ R T T F F F F F T Willard is either a philosopher or a windbag, and he’s neither a philosopher nor a windbag. Determine whether the following statement pattern is a tautology or a contradiction or contingency. That is, a statement and its negation can never have the same truth value. Definition: A compound statement is a contradiction if there is an F beneath its main connective in | {
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urdf
<child link="${prefix}_rotate_link"/>
<origin rpy="0 0 0" xyz="0.0 0.0 0.01"/>
<axis xyz="0 0 1"/>
</joint>
<link name="${prefix}_wheel_link">
<inertial>
<mass value="0.01" />
<origin xyz="0 0 0" />
<inertia ixx="1e-6" ixy="0.0" ixz="0.0" iyy="1e-6" iyz="0.0" izz="1e-6" />
</inertial>
<visual>
<origin rpy="0 0 0" xyz="0 0 0"/>
<geometry>
<mesh filename="package://mark_description/mesh/caster/caster_wheel.dae"/>
</geometry>
<material name="Yellow"/>
</visual>
<collision>
<origin rpy="0 0 0" xyz="0 0 0"/>
<geometry>
<mesh filename="package://mark_description/mesh/caster/caster_wheel.dae"/> | {
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ros2
Title: Where is the log file in ROS 2.0
I install ROS 2.0 in my computer, and run the demo programs. But I can not find the log file.
Where is the log file in ROS 2.0?
I know the default position in ROS 1.0 is ~/.ros.
Originally posted by Dragon on ROS Answers with karma: 68 on 2018-02-28
Post score: 1
The logging subsystem in ROS 2 does not createa a logfile at the moment.
Originally posted by Dirk Thomas with karma: 16276 on 2018-02-28
This answer was ACCEPTED on the original site
Post score: 1
Original comments
Comment by Dragon on 2018-02-28:
Thanks for your answer. Now if I want to log into a file, how should I do? I can not find any introduction for this.
Comment by Dirk Thomas on 2018-03-02:
For now (until that feature is being implemented) you can use "standard" features available on your system. E.g. pipe the output into a file.
Comment by Dragon on 2018-03-08:
en. en. I find the function through source code. Now, it can't log in the file through the ros2. | {
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Look at the Types
whos step1*
Name Size Bytes Class Attributes
step1In 1x1 1 logical
step1Out 1x1 1 logical
The results from step 1 are logical - are these numbers greater than low? And the answers for both of our values is yes, or true, represented in MATLAB as logical values. When we take these values as inputs in the second step, what happens is the true values are interpreted as numeric inputs with value 1. And then we ask if 1 is less than high. Which it is in both of these cases!
How to Get the Expected Answer
How do we get the expected answer, and it's easy. We simply combine two logical expressions, but in a different way than above.
myExprCorrect = @(x) (low < x) & (x < high)
inResult1 = myExprCorrect(pi)
outResult1 = myExprCorrect(17)
myExprCorrect =
@(x)(low<x)&(x<high)
inResult1 =
1
outResult1 =
0 | {
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electromagnetism, electricity, magnetic-fields, electric-current, electromagnetic-induction
\begin{equation}
\Delta \vec{A} = (\vec{v} \Delta t) \times \Delta \vec{l}.
\end{equation}
This changes the flux integral by
\begin{equation}
\Delta \Phi_B = \vec{B} \cdot \Delta \vec{A} = \vec{B} \cdot (\vec{v} \times \Delta \vec{l}) \Delta t,
\end{equation}
which implies
\begin{equation}
\frac{\Delta \Phi_B}{\Delta t} = \vec{B} \cdot (\vec{v} \times \Delta \vec{l}).
\end{equation}
Now we can take the limits of small $\Delta t$ and small $\Delta \vec{l}$, then integrate up the contributions from all those little $\Delta \vec{l}$ segments around $\partial S$ to get the total derivative of the flux:
\begin{align}
\frac{d \Phi_B}{dt}
&= \int_{\partial S} \vec{B} \cdot (\vec{v} \times d\vec{l}) \\
&= \int_{\partial S} \left( \vec{B} \times \vec{v} \right) \cdot d\vec{l}.
\end{align}
To get from the first to second line, I just used the usual scalar triple product. And this is the same result as the one we got using the material derivative — again, it's nonzero. | {
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optics, power, fiber-optics, solar-cells, technology
SBS introduces the most stringent power limit for the amplification and the passive propagation of narrow-band optical signals in fibers.
That same link explains the mechanism in more depth. SBS puts an upper limit on the power you can send through a fiber, regardless of the losses you can tolerate. | {
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electromagnetism, magnetic-monopoles
also get a non-zero curl field and these are impossible. So we are only left with a radial inner field. And therefore the total charge inside the envelope is zero and there can't be any flux passing through it. So in conclusion the field outside must vanish everywhere. | {
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quantum-mechanics, homework-and-exercises, wavefunction, schroedinger-equation, harmonic-oscillator
Question 3: How was that 2 moved into the exponent? Answer to part 1: This is a common method of solving differential equations, employed by physicists to quickly extract a solution without having to make slow progress using more rigorous methods. The first step is to look for an asymptotic solution (i.e. the limit of large $\xi$ in this case), where the equation is easily solvable. Now, we know that this will not give us an exact solution, so we can't just proceed to claim $$\psi (\xi)=Ae^{-\xi^2/2}$$ However, since this solution must be exact in the limit, we can try to look for a solution of the form $$\psi(\xi)=\phi(\xi)e^{-\xi^2/2}$$ Which, we hope, may allow us to recast the original equation in a simpler or well-known form. Really, we've done nothing but use a change in variables, motivated by the asymptotic solution. Ideally, one would like to rigorously justify things like this (why exactly is it reasonable to believe that this makes things easier?) but, being a good | {
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ros, slam, navigation, compile, ubuntu
/home/toni/ros/rgbdslam_freiburg/rgbdslam/src/node.cpp:1339: error: undefined reference to 'GOMP_parallel_end'
/usr/local/include/eigen3/Eigen/src/Core/products/GeneralMatrixMatrix.h:92: error: undefined reference to 'omp_get_thread_num'
/usr/local/include/eigen3/Eigen/src/Core/products/GeneralMatrixMatrix.h:93: error: undefined reference to 'omp_get_num_threads'
/usr/local/include/eigen3/Eigen/src/Core/products/Parallelizer.h:131: error: undefined reference to 'omp_get_num_threads'
/usr/local/include/eigen3/Eigen/src/Core/products/Parallelizer.h:131: error: undefined reference to 'omp_get_thread_num'
/usr/local/include/eigen3/Eigen/src/Core/products/Parallelizer.h:131: error: undefined reference to 'omp_get_num_threads'
/usr/local/include/eigen3/Eigen/src/Core/products/Parallelizer.h:131: error: undefined reference to 'omp_get_thread_num'
/usr/local/include/eigen3/Eigen/src/Core/products/Parallelizer.h:131: error: undefined reference to 'omp_get_num_threads' | {
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Writing $\int_0^x f(x)\,dx$ is the same as $\int_0^x f(t)\,dt$. However, the former is much more ambiguous and should be avoided for sake of clarity.
This means the derivative would be,
$$\frac{d}{dx}\left[ \int_0^x (x^2-x)\,dx \right] = \frac{d}{dx}\left[ \int_0^x (t^2-t)\,dt \right] = x^2 - x$$
• $\int_0^xf(x)~\mathrm dx=\int_0^xf(t)~\mathrm dt$ is quite a bad habit, and it will become especially ambiguous when your integrals contain multiple variables. – Simply Beautiful Art Jul 15 '17 at 23:12
Let $\phi$ be a continuous, real-valued function defined in some neighborhood of $0$. Writing $$f(x) = \int_{0}^{x} \phi(x)\, dx$$ is bad syntax: it uses the single letter $x$ for both
• The input value of the function $f$;
• The dummy variable of integration.
Setting $x = 2$, for example, invites the reader to ponder the meaning of $$f(2) = \int_{0}^{2} \phi(2)\, d2,$$ which is almost surely not intended. (The problem is "$d2$".) | {
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performance, algorithm, rust, hashcode
#[cfg(not(debug_assertions))]
let loopable_words = words.iter();
#[cfg(debug_assertions)]
let loopable_words = words.iter().enumerate();
for data in loopable_words {
#[cfg(not(debug_assertions))]
let word = data;
#[cfg(debug_assertions)]
let word = data.1;
#[cfg(debug_assertions)]
let attempts = data.0;
let merged = format!(
"{}{}",
word, "........................................................!1"
);
let hash = hash_md5(hash_md5(hash_md5(hash_md5(merged.clone()))));
#[cfg(debug_assertions)]
println!(
"Attempts: {}/{}, Hash: {}, Text: {}",
attempts, word_list_length, hash, merged
);
if hash == goal_hash {
println!("We found the password: {}", merged); | {
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# How to find the point on the sphere that is closest to a plane?
Consider the plane $x+2y+2z=4$, how to find the point on the sphere $x^2+y^2+z^2=1$ that is closest to the plane?
I could find the distance from the plane to the origin using the formula $D=\frac{|1\cdot 0+2\cdot 0+2\cdot 0-4|}{\sqrt{1^2+2^2+2^2}}=\frac43$, and then I can find the distance between the plane and sphere by subtracting the radius of sphere from plane-origin distance:$\frac43-1=\frac13$. But then I am stuck here because I don't know how to convert this distance into a direction vector, so I could subtract it from the plane to find the sphere point. Any help would be appreciated.
• Have you learned the Lagrange multiplier? Feb 4, 2017 at 5:24 | {
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classical-mechanics, collision
I am pretty sure that this collision is for elastic collisions. At
least, this is what I also found on Wikipedia.
I looked at the Wikipedia article. It looks like $u$ in your equation is the velocity in the center of mass frame which does not change before and after the collision. Since you didn't state was $u$ was I assumed it was the velocity of the two masses stuck together following the collision, which would also satisfy conservation of momentum.
Regardless, I believe your equation only requires conservation of momentum. It would apply whether the collision is elastic or inelastic. So the equation does not only apply to elastic collisions, as stated.
Hope this helps. | {
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php, unit-testing, zend-framework, doctrine
Is this easily testable at the moment? How could I improve it in this
regard?
Do I really need all the getters and setters or could I use a
generic 'magic methods' __get and __set to do this job?
Should I be validating input in the setter functions or is it fine to validate
before persisting (like in my assertMinLengthUserIdNotLessThan1
function)?
Is there any better way of getting the Doctrine entity
into an array? I have a simple toArray() function so far but I there
may be better ways of doing it for more complicated objects.
Any general comments/advice would be much appreciated also!
Thanks in advance! Quick answers: | {
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general-relativity, special-relativity, thought-experiment
Let us consider a space-time domain in which no gravitational field exists relative to a reference-body K. K is then a Galileian reference-body, and the results of the special theory of relativity hold relative to K. | {
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@ramanujan_dirac, of course I've used, and in a rather very essential way, the number $\,m\,$ in my proof: it appears in both in (2) and (4)...is this what you were refering to? Of course, a subgroup $\,N\,$ is normal iff $\,N=N^x\,$ for all $\,x\in G\,$ ...so I do see a pretty direct relation. – DonAntonio Jan 21 '13 at 18:35 | {
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"openwebmath_score": 0.9204723834991455,
"tags": null,
"url": "http://math.stackexchange.com/questions/214871/any-subgroup-of-index-p-in-a-p-group-is-normal"
} |
genetics, evolution, molecular-genetics, population-genetics, mutations
The correct answer is (C). These recent conclusions about
mutations—recall that Darwin did not know of mutations—are all the
reverse of those listed in the choices, with the exception of choice
(C), the correct answer. Rates, in fact, tend to be below in
populations, mutations are generally not lethal, any gene location can
be affected, and they are felt to be the source of genetic variation.
Darwin felt over-production of offspring was the source of potential
variation.
The answer is C here. However, I didn't particularly understand why E wasn't considered a correct answer.
Could you please explain why C, and not E, is correct? Going through the possible answers
(A) Rates tend to be very high in most populations. | {
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