text stringlengths 1 1.11k | source dict |
|---|---|
ros, kinect, opencv, face-detection
</launch>
EDIT: Thanks to Dan Lazewatsky's suggestion I created a sample code that subscribes to topics /face_detector/faces_cloud and /face_detector/people_tracker_measurements_array. However, it's still not detecting faces. Here's my code:
#include <ros/ros.h>
#include <cv_bridge/cv_bridge.h>
#include <opencv/cv.h>
#include <opencv2/imgproc/imgproc.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <opencv2/objdetect/objdetect.hpp>
#include <people_msgs/PositionMeasurementArray.h>
#include <sensor_msgs/PointCloud.h>
#include <sensor_msgs/image_encodings.h>
void face_cloud_Callback(sensor_msgs::PointCloud a)
{
ROS_INFO("I received some point cloud info!");
}
void pos_meas_Callback(people_msgs::PositionMeasurementArray a)
{
ROS_INFO("I received some position info!");
}
int main(int argc, char **argv)
{
ros::init(argc, argv, "faces");
ros::NodeHandle nh; | {
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performance, primes, assembly, sse
The code is different per-prime: the code for 5 adds 4, or else subtracts 1 (they are equivalent, but you need to design your index handling to account for which direction you are going).
This approach is promising because it lets you get more reads without greatly increasing the table size. It works best for the smaller primes since the jump amounts (and hence required table padding) are smaller, while the horizontal unrolling described above works best for larger primes since the table increas is relatively less (since it is fixed to the read size and the large primes already have larger lookup tables).
Unrolling both the inner and outer loops allows you to even pick and choose different strategies for different primes.
Optimize the Lookup Tables | {
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civil-engineering, materials, rail, transportation
Rail Life
The life of a typical railroad rail is between 1300 MGT and 380 MGT depending on if the rail is on a straight (tangent) track or in a curve. There is more friction in a curve. Also, the rail on the low side of a super-elevated curve wears faster than the rail on the high side.
Friction
Because of this great difference in life of the rail, areas that have lots of curves employ machines that add lubrication to the rail. This lubrication is applied after the locomotives pass so that their traction capability is not reduced. Some photos of these machines are below: | {
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} |
homework-and-exercises, fluid-statics, volume
I think the block floats because $\rho_f<\rho_m$. Then I have thought that:
$$\rho_mVg-\rho_iV'g=0$$
where $V$ is the immersed volume in the mercury and $V'$ is the whole volume of the block.
So:
$l_{immersed}^3=\frac{\rho_i(l_{cube})^3}{\rho_m}=5.78cm^3\implies l_{immersed}=1.79cm.$
The book tells me that the result is $5.78 cm$ but I can't understand where I am doing a mistake.
Can you help me? The mass of the whole iron cube is $m_i=V_i\cdot \rho_i=7860kg$.
In case of floating, the mass $m_i$ equals the mass $m_m$ of the mercury which is displaced.
The mass of the displaced mercury is $m_m=V_m\cdot\rho_m$, where $V_m=10\cdot 10 \cdot l_{immersed} $.
Therefore, $l_{immersed} =\frac{V_i\cdot \rho_i} {A\cdot \rho_m} = 5.78 cm^3$ as written in your book. | {
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"url": null
} |
image-processing, edge-detection, canny-edge-detector
As regards to sigma, as the sigma increases, the smoothing increases and noisy edges will go away, but at the same time, the location of edges may also move little. See this document, http://www.cse.unr.edu/~bebis/CS791E/Notes/EdgeDetection.pdf and results at page 29 shows this effect. | {
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} |
python, scikit-learn, decision-trees, implementation, adaboost
# greedy search to find the best threshold and feature
for feature_i in range(n_features):
thresholds = np.unique(X[:, feature_i])
for threshold in thresholds:
# here we find the best stump
error = sum(w[y != predictions])
if error < 0.5 - gamma:
min_error = error
break | {
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"tags": "python, scikit-learn, decision-trees, implementation, adaboost",
"url": null
} |
history, autoclave
Paper on Geobacillus sterothermophilus: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1057891/
If anyone can find that Technology Quarterly paper I mentioned at the start that'd be great. Quick answer:
For historical and engineering reasons, standards for sterilization with autoclaves were developed with steam pressure and time being the operational parameters. Temperature wasn't even measured by autoclaves until decades after they were in widespread use. For human factor reasons, the most appealing combination of sufficient pressure and time was 15 pounds per square inch pressure (one rounded off Earth atmosphere) for 15 minutes. The temperature that corresponds to 15 psi steam pressure is 121°C.
Long answer:
It's all about the history of steam technology and the numbers people find easy to use and remember. | {
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imu, laserscan, pointcloud
Title: Fusing Lidar data with IMU data (please verify my understanding/plan)
Hello everyone,
I have a Neato XV-11 Lidar and a Sparkfun Razor 9DOF IMU. I have been able to get a live LaserScan, and PointCloud via laser_scan_assembler (periodic_snapshotter every few seconds). I have also used point_cloud_converter to get a PointCloud 2 and eventually an octomap. Mind you, this is all in 2D with just the Lidar.
I want to use the IMU data I am getting from razor_imu_9dof and fuse (transform) it with the Lidar data such that the point clouds that are being snappshotted end up in 3 dimensions. I don't mind if octomap is utilized. | {
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} |
coding-theory, hamming-code
Title: What is the reason behind a specific ordering of the rows in the generator matrix for Hamming codes? What order the rows are in a Hamming generator matrix are irrelevant for the Hamming coding to work, given the check matrix is built accoridngly.
In order to limit cognitive overload, it could have been decided that the "official" way of doing it should be either all data rows first then all parity rows after, all in ascending order, or just all rows in ascending order. In that case, in the description of a communications protocol it would be enough to specify the number of bits without providing the generator matrix, and everyone would know how to implement it. Very simple software libraries could be written which implement it.
However, after looking at some implementations, this is not the case. People seem to use arbitrary matrices, such as
$$\begin{pmatrix}
1 & 1 & 0 & 1 \\
1 & 0 & 1 & 1 \\
1 & 0 & 0 & 0 \\
0 & 1 & 1 & 1 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\ | {
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} |
c++, primes, c++17, sieve-of-eratosthenes
You can shorten the second loop by adding to the vector every time you find a prime in the outer loop. This way the second loop can start where the outer loop finishes.
There is also another algorithm you can use that is more highly optimised for making a list of primes, mind you it's also more complicated( sorry I can't remember the name off hand) | {
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black-hole, speed, time-dilation, visualization
Something else happens because of a quirk with relativistic gravity. An object reflects and emits light in all directions, but as it gets close enough to the black hole, the only light that can escape is almost entirely perpendicular. Light can only escape the photonsphere of a black hole if it's close to perpendicular, and maybe my wording could use improvement there. This question has a very nice answer on orbital velocity around a black hole. Tangential light gets considerably bent or trapped entirely. What this means is you pretty quickly will lose sight of anything that isn't directly perpendicular between the ship, the center of the black hole and where you are viewing from. To actually continue to see the ship you'd need numerous cameras spread around the black hole and the view would need to be reconstructed. | {
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You essentially negated: $P(z, j) \land Q(z, j)$.
So did the text.
The text applied "distribution of negation over conjunction" (one of DeMorgan's Laws):
• "It is not the case that $[(P(z, j)$ and $Q(z, j)]$" $$\iff \lnot[P(z, j) \land Q(z, j)]$$ $$\iff \lnot P(z, j) \lor \lnot Q(z, j)\tag{DeMorgan's law}$$
• which is to say: not $P(z, j)$, or, not $Q(z, j)$.
You are correct with your statement that the sentence translates to $\;\;\lnot[P(z,j) \land Q(z, j)]$;
It's logically equivalent to the text's answer: $\;\lnot P(z, j) \lor \lnot Q(z, j)$. | {
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file-system, assembly
;handle error if not found
;(to be implemented in the future)
ASSET_FOUND:
mov di, bx ;store the cluster number in di as input for
;LOAD_DATA_SECTOR
;// LOAD THE ASSET DIRECTORY, SEARCH FOR THE DATA FILES, AND STORE //
;// THEIR CLUSTER NUMBERS. //
mov bp, 1 ;bp -> file name str index of 1st file to find
lea si, aClst ;si -> first cluster number to initialize
xor dx, dx ;dx -> initial sector offset into asset dir
mov cx, 4 ;loop cntr -> number of files to find
INIT_CLST_NUMS:
call LOAD_DATA_SECTOR ;load a sector of the asset directory
cmp di, 0ffffh ;If di does not = 0ffffh, sector offset valid.
jne NOT_END_OF_DIR ;If sect offset valid, search loaded sector | {
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forward-kinematics, screw-theory
But right answer is [0,0,1,0,-L,0]. Why? If I'm understanding you correctly, you're attempting to put the position of the joint in for the translational velocity component of the screw axis. What you actually want to put in there is the velocity of a point rigidly attached to the rotating part of the joint, but currently located at the origin of the base frame,
$$
v = \begin{bmatrix} \omega_{x} \\ \omega_{y} \\ \omega_{z} \end{bmatrix} \times \begin{bmatrix} -x \\ -y \\ -z \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} \times \begin{bmatrix} -L \\ \phantom{-}0 \\ \phantom{-}0 \end{bmatrix} = \begin{bmatrix} \phantom{-}0 \\ -L \\ \phantom{-}0 \end{bmatrix}.
$$
You can interpret
$$
\begin{bmatrix} \omega \\ v \end{bmatrix} = \begin{bmatrix} \phantom{-}0 \\ \phantom{-}0 \\ \phantom{-}1 \\ \phantom{-}0 \\ -L \\ \phantom{-}0 \end{bmatrix}
$$ | {
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# multiply different residue classes
I am trying to solve a problem. Proof that $$300^{3000} \equiv 1 \bmod 1001$$ So after a bit of puzzeling I found that $$1001 = 7*11*13$$ and I have prooved that:
• $$300^{3000} \equiv 1 \;(\bmod 7\;)$$
• $$300^{3000} \equiv 1 \;(\bmod 11\;)$$
• $$300^{3000} \equiv 1 \;(\bmod 13\;)$$
Now I wish to conclude that therefore $$300^{3000} \equiv 1 \bmod 1001$$
But that hinges on the assumption that I can multiply residue classes somehow like:
$$[1]_7 * [1]_{11} * [1]_{13} = [1]_{1001}$$ or more general maybe: $$[a]_p * [b]_q * [c]_{13} = [abc]_{pqr}$$
Now we have some things that may help such as the factors $$p,r,r$$ being (co)prime in this case... but exaclty based on what can we draw such a conclusion ?
I was thiking of that somehow we can use Bezout, which guarantees that if $$gcd(p,q)=1 => (\exists x,y \in \mathbb{Z})\;(px+qy=1)$$
but after scribbling some papers full of almosts...I want to ask you guys for some direction. Thanks! | {
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On the other hand, your solution for part (ii) has some issues. First of all, you’ve made some sign errors in your computation. $$I-2{1\over\sqrt2}{1\over\sqrt2}\begin{bmatrix}1\\0\\1\\0\end{bmatrix}\begin{bmatrix}1&0&1&0\end{bmatrix}=\begin{bmatrix}0&0&-1&0\\0&1&0&0\\-1&0&0&0\\0&0&0&1\end{bmatrix}.$$ However, you’re also making a more fundamental error (at least as far as I understand what you’re trying to do): $(n^Tv)n$ is the orthogonal projection of $v$ onto $n$, so $I-2nn^T$ is the matrix of the reflection in the hyperplane that’s the orthogonal complement of $n$, i.e., the hyperspace for which $n$ is a normal. One way to tell that neither matrix is correct is to examine their determinants. The eigenvalues of a reflection in a two-dimensional subspace of $\mathbb R^4$ are $1$, $1$, $-1$ and $-1$, which means that the determinant of the matrix should be $1$, but $\det M=-1$ for both your matrix and the correctly-computed value of $I-2nn^T$. You could also test the matrix that you | {
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• Squaring both sides may introduce invalid solutions. For example, if you have $x=1$ and your square both sides you get $x^2=1$, which adds the invalid solution $x=-1$. – Fly by Night Dec 25 '13 at 18:23
• @FlybyNight this is an important remark. However, we should always test the solutions, so we are safe. – Ian Mateus Dec 25 '13 at 18:26
• I am not keen on this approach. User2369284s solution provides the systematic way of answer this. Avoid squaring whenever possible. – Lost1 Dec 25 '13 at 21:03
• @Lost1 I don't understand your reluctance. After all, factoring $a\sin x+b\cos x$ gives the same extraneous solutions. – Ian Mateus Dec 25 '13 at 21:12
• I dont think it does, pal – Lost1 Dec 25 '13 at 21:58
Avoid squaring wherever practicable as it immediately introduces extraneous roots
Using Weierstrass substitution we have $$\frac{2t}{1+t^2}+\frac{1-t^2}{1+t^2}=1$$ where $t=\tan\frac x2$
$$\implies 2t+1-t^2=1+t^2\iff t^2-t=0\iff t=1,0$$ | {
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thermodynamics, entropy, probability, physical-chemistry
Title: How does entropy relate to energy, conceptually? Conceptually, I've always understood entropy to be a statistical idea. For example, if you have a vacuum inside of a box and you place a handful of gas atoms on one side, the molecules have a higher statistical probability to spread out, versus remain in one concentrated spot. Therefore, on average, they will spread around and entropy is increased.
Of course there's a more elaborate definition involving macrostates and microstates, where entropy is greater when a macrostate has more microstates. However, in my understanding, the idea is still the same: increasing entropy is really just a statistical likely-hood that will hold true on average.
There are many formulas that relate entropy to energy. For example, Gibbs Free Energy:
$$ΔG = ΔH - TΔS$$
Now, before I explain my confusion, I'd like to share an example from my course: hydrogen bonding (non-covalent interactions... like electrostatic interaction). | {
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homework-and-exercises, newtonian-mechanics, harmonic-oscillator, oscillators
But given that,
Simple harmonic motion can be defined by
$$x = A * \sin(\omega t) \tag{1}$$
where $A$ is the amplitude of oscillation, $\omega$ the angular velocity, $t$ the time, and $x$ the displacement from the mean position
And,
$$T = 2 \pi/\omega = 1/f \tag{2}$$
where, $T$ is the period of motion and $f$ is the frequency of oscillation.
Equation (1) can be rearranged to give
\begin{align*}
x &= A * \sin (\omega t)\\
\frac{x}{A} &= \sin(\omega ωt) \\
\arcsin\left(\frac{x}{A}\right) &= \omega t\\
\omega &=\frac{\arcsin\left(\frac{x}{A}\right)}{t}
\end{align*}
Subbing this into (2) gives the following relationship between $T$ and $A$
$$T = \frac{2 \pi t}{\arcsin(x/A)} = \frac{1}{f}$$
Doesn't the fact that both $T$ and $A$ appear in the above equation show that $T$(period) is dependent on $A$(amplitude) ? | {
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features. It's different for each problem. This means the model fit by lasso regression will produce smaller test errors than the model fit by least squares regression. Let’s first understand the cost function Cost function is the amount of damage you […] Now, linearity is not a standalone property. Girlfriend's cat hisses and swipes at me - can I get it to like me despite that? Ridge regression is an extension of linear regression where the loss function is modified to minimize the complexity of the model. while learning predictive modeling. Ridge Regression is a technique used when the data suffers from multicollinearity ( independent variables are highly correlated). Lasso Regression vs. Ridge Regression. You also need to make sure that the number of features is less than the number of observations before using Ridge Regression because it does not drop features and in that case may lead to bad predictions. Ridge regression adds just enough bias to our estimates through lambda to | {
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"url": "https://aargeestaffing.com/omnd22/2de3j.php?id=ridge-regression-vs-linear-regression-b8c4a1"
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image-processing, fft, noise
a = readim('https://i.stack.imgur.com/JaeTF.png');
a = a - mean(a); % must be zero mean
b = noise(newim(a),'gaussian', 1); % create white Gaussian noise image
c = real(ift(abs(ft(a)) * ft(b))); % multiply in frequency domain
c = c * (std(a) / std(c)); % scale to get the right std. dev. | {
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python, game, pygame
MorS = "settings"
elif choice == 3:
pygame.quit()
sys.exit()
# Set font
font = pygame.font.Font("freesansbold.ttf", 24)
bigfont = pygame.font.Font("freesansbold.ttf", 48)
if MorS == "main":
# Check for cursor
if choice == 1:
spText = "-- Single Player --"
stText = "Settings"
xtText = "Exit"
elif choice == 2:
spText = "Single Player"
stText = "-- Settings --"
xtText = "Exit"
elif choice == 3:
spText = "Single Player"
stText = "Settings"
xtText = "-- Exit --"
# Render text
# Render title text
title = bigfont.render("Bunny and Badgers", True, (0,0,0))
titleRect = title.get_rect() | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, game, pygame",
"url": null
} |
observational-astronomy, spectroscopy, spectra, exotic-matter
Regarding positronium, it is short-lived, and is not accumulated in sufficient amounts to yield readily observable spectral features. The positronium decay $\gamma$-quanta (511 keV line) $are$ observed (near the galactic center in particular; in pulsar spectra, etc.) Estimates for observing lines corresponding to transitions between different bound states of positronium are not very promising; e.g. https://ui.adsabs.harvard.edu/abs/1996A%26AS..120C.365B/abstract | {
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"tags": "observational-astronomy, spectroscopy, spectra, exotic-matter",
"url": null
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r, bioconductor
Title: Installing RnBeads via bioconductor - .onLoad failed in loadNamespace(), call: NULL I am trying to install RnBeads from bioconductor but the installation of its dependancy TxDb.Hsapiens.UCSC.hg19.knownGene fails. The error is:
biocLite("RnBeads")
BioC_mirror: https://bioconductor.org
Using Bioconductor 3.6 (BiocInstaller 1.28.0), R 3.4.3 (2017-11-30).
Installing package(s) ‘RnBeads’
also installing the dependencies ‘FDb.InfiniumMethylation.hg19’, ‘methylumi’
trying URL 'https://bioconductor.org/packages/3.6/data/annotation/src/contrib/FDb.InfiniumMethylation.hg19_2.2.0.tar.gz'
Content type 'application/x-gzip' length 38996322 bytes (37.2 MB)
==================================================
downloaded 37.2 MB
trying URL 'https://bioconductor.org/packages/3.6/bioc/src/contrib/methylumi_2.24.1.tar.gz'
Content type 'application/x-gzip' length 6178909 bytes (5.9 MB)
==================================================
downloaded 5.9 MB | {
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# What does the supremum of a sequence of sets represent?
I'm trying to understand more about the limits of sequences of sets in Measure Theory.
Given a sequence of sets $\{A_n\}_{n\in \mathbb{N}} = \{ A_1,A_2, \ldots \}$, what does $\sup_n \{ A_n \}$ represent?
The reason why I'm asking is because I'd like to derive what $\limsup_{n\rightarrow\infty}A_n$ means… and this should formally be $\lim_{n\rightarrow\infty} \sup\{A_k | k \geq n \}$ - right?
-
The notation $\sup_n\{A_n\}$ is ambiguous, and I would avoid using it without more context. In the context of the $\limsup$ or $\liminf$ of sets, we are taking the partial order on sets by inclusion: $A \leq B$ if $A \subseteq B$. Then the supremum of a sequence $\{A_n\}_n$ is the smallest possible upper bound for every element of the sequence - the smallest set containing each $A_n$. This must be $$\sup_n A_n = \bigcup_n A_n.$$ | {
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electromagnetism, electromagnetic-radiation, acceleration, charge
Parrott, http://arxiv.org/abs/gr-qc/9303025
Poisson, http://arxiv.org/abs/gr-qc/9912045 | {
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"tags": "electromagnetism, electromagnetic-radiation, acceleration, charge",
"url": null
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slam, navigation, odometry, hector-slam
Title: hector_slam sporadic update error of /odom
Hi
We use a non-holonomic wheeled platform with two SICK s300 laser scanners, and have recently tried to apply hector_slam instead of gmapping because gmapping uses almost 100% cpu and hector_slam uses close to 0%. We run Fuerte and Ubuntu 12.04 LTS. The software is running on one computer on the platform.
However, we have one problem with hector_slam and that is sporadic updates of the odometry.
We have made a launch file with the following
<?xml version="1.0"?>
<launch>
<node pkg="hector_mapping" type="hector_mapping" name="hector_mapping" output="screen">
<!-- Frame names -->
<param name="map_frame" value="/map" />
<param name="base_frame" value="/base_link" />
<param name="odom_frame" value"/odom" />
<param name="scan_topic" value="/scan_unified/scan"/>
</node>
<!-- Tf use -->
<param name="pub_map_odom_transform" value="true"/>
</launch> | {
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discrete-signals, fourier-transform, frequency-spectrum, filter-design, time-series
subplot(2,1,2); %Plot time series
plot(t/3600,real(g)); hold on;
xlabel('Time (hours)')
ylabel('g(t)'); grid on
set(gca,'FontSize',14)
title('Inverse "Fourier Transform" of Spectrum')
Result:
Any help is appreciated! Bottom Line
OP's approach is closest to the "Frequency Sampling Method"
Use a linear frequency grid, not logarithmic.
Populate the spectrum on both the positive an negative frequency axis, with complex conjugate symmetry for real time samples.
(As MattL pointed out): bound the DC bin to a finite value. | {
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c++, beginner, algorithm
p2[i].fit = p1[i].fit;
}
}
This function is an example of an issue I frequently see in code. The last statement line, p2[i].fit = p1[i].fit;, is it meant to belong to last for()? The way it is indented, it leads the reader to believe so. A more careful look will reveal that it belongs to the first loop, being executed only s times (which is likely to be the correct). Is that the intended behavior, or did you actually mean this?
for(int i=0; i<s; i++)
{
for(int j=0; j<variable; j++)
{
p2[i].eq[j] = p1[i].eq[j];
p2[i].fit = p1[i].fit;
}
}
Or this?
for(int i=0; i<s; i++)
{
for(int j=0; j<variable; j++)
{
p2[i].eq[j] = p1[i].eq[j];
}
p2[i].fit = p1[i].fit;
} | {
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manipulator, moveit, ikfast, kdl, openrave
Original comments
Comment by Humpelstilzchen on 2017-01-05:
Welcome to the 5dof club, I also had lots of problems. Note that OpenRave is very picky about sympy version. The combination OpenRave git b89980e with sympy 0.7.1 worked for me.
Comment by t27 on 2017-01-05:
I installed Sympy 0.7.1, but i still get the same error with openrave. I've added the exact error in the above question...
Comment by Humpelstilzchen on 2017-01-05:
Have you tried a known working robot, e.g. youbot?
We have been trying to debug this issue since the past 2 days.
With no clear reason for this problem, we decided to try solving the IK of robot of the same configuration with a simple URDF file. So we wrote a urdf by hand, with the same joint and link config as our robot. The URDF we used earlier was generated from our original CAD model using the Solidworks URDF Converter plugin. | {
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vba, excel
Private Sub IFrameSorter_Initialise(SourceForm As Object)
Dim ctrl As Control
Dim tmpSubSorter As CFrameSorter
Dim vSortArray As Variant
For Each ctrl In SourceForm.Controls
If TypeName(ctrl) = "Frame" Then
Select Case TypeName(ctrl.Parent)
Case TypeName(SourceForm)
With FrameDictionary
If Not .Exists(ctrl.Name) Then
.Add ctrl.Name, ctrl
End If
End With
Case "Frame"
'Do nothing yet.
End Select
End If
Next ctrl
'Sort the frames contained in the dictionary into
'order based on their Top property.
vSortArray = FrameDictToArray(FrameDictionary)
Sort2DArray vSortArray
SortDictByArray vSortArray, FrameDictionary | {
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ros, base-global-planner, plugin, global-planner, nav-core
Originally posted by Earthgrazer on ROS Answers with karma: 11 on 2016-07-13
Post score: 0
That usually happens when you don't call PLUGINLIB_EXPORT_CLASS. Do you have the appropriate call to PLUGINLIB_EXPORT_CLASS at the end of the source code for your plugin?
Originally posted by ahendrix with karma: 47576 on 2016-07-13
This answer was ACCEPTED on the original site
Post score: 0
Original comments
Comment by Earthgrazer on 2016-07-18:
Yes, I do, it is at the beginning of my source code like in the tutorial.
Comment by cgm666 on 2021-03-08:
Hi, did you solve this problem? I also meet it:( | {
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optics, waves, visible-light, history, huygens-principle
The Treatise on Light of Huygens has, however, withstood the test of time: and
even now the exquisite skill with which he applied
his conception of the propagation
of waves of light to unravel
the intricacies of the phenomena of the double refraction
of crystals, and of the refraction of the atmosphere,
will excite the admiration of the student of Optics.
It is true that his wave theory was far from the complete
doctrine as subsequently developed by Thomas Young and Augustin
Fresnel, and belonged rather to geometrical
than to physical Optics. If Huygens had no conception
of transverse vibrations, of the principle of interference, or of the existence
of the ordered sequence
of waves in trains, he nevertheless
attained to a remarkably
clear understanding
of the principles of wave-propagation;
and his exposition of the subject marks an epoch
in the treatment of Optical problems. | {
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"tags": "optics, waves, visible-light, history, huygens-principle",
"url": null
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thermodynamics, computational-chemistry, heat
oxygen
0 3
O
O 1 1.2
(blank)
%chk=mo6qzvpp.freq.chk
%oldchk=mo6qzvpp.chk
#p M06/def2QZVPP
freq
geom=check guess=read
int(ultrafinegrid)
oxygen freq
0 3
(blank)
%chk=mo6qzvpp.chk
#p M06/def2QZVPP
opt
int(ultrafinegrid)
hydrogen
0 1
H
H 1 1.2
(blank)
%chk=mo6qzvpp.freq.chk
%oldchk=mo6qzvpp.chk
#p M06/def2QZVPP
freq
geom=check guess=read
int(ultrafinegrid)
hydrogen freq
0 1
(blank)
%chk=mo6qzvpp.chk
#p M06/def2QZVPP
opt
int(ultrafinegrid)
water
0 1
O
H 1 1.2
H 1 1.2 2 109.0
(blank)
%chk=mo6qzvpp.freq.chk
%oldchk=mo6qzvpp.chk
#p M06/def2QZVPP
freq
geom=check guess=read
int(ultrafinegrid)
water freq
0 1
(blank)
Have a lot of fun. | {
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python, python-3.x, calculator, tkinter
s: string
index: index of insertion
value: value to insert into string"""
return s[:index] + value + s[index:]
def adjust_adjacent_parentheses_int(s: str) -> str:
"""Check if provided string contains adjacent integer and parenthesis, if it does, insert an astrik in between them; returns modified string
s: string"""
# find indices where asterisk should be inserted
indices = []
for i in range(len(s)):
if isinstance(convert_to_int(s[i]), int):
if i + 1 < len(s) and s[i + 1] == "(": # if ( is immediately after an integer, plan to insert astrik
indices.append(i + 1)
elif i - 1 >= 0 and s[i - 1] == ")": # if ) is immediately before an integer, plan to insert astrik
indices.append(i)
# insert asterisks in their respective indices
if indices:
for i in range(len(indices)):
s = insert_in_string(s, indices[i] + i, "*")
return s | {
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we can't use the formula until we convert it to radians. Arc Length Formula For Degrees. Arc Measure Definition. Formula for $$S = r \theta$$ The picture below illustrates the relationship between the radius, and the central angle in radians. The radian measure of an angle is the length of the arc along the circumference of the unit circle cut off by the angle. One radian is defined as the angle formed such that the portion of the circle (or arc length) swept by that angle is equal to the radius of the circle. Definition: subtend – to be opposite to. Arc Length Example Problems: This handout contains 7 examples on finding arc length given radius and central angles. This page includes a lesson covering 'finding the length of an arc of a circle when the angle is in radians' as well as a 15-question worksheet, which is printable, editable, and sendable. The length of an arc (or arc length) is traditionally symbolized by s. In the diagram at the right, it can be said that ” AB subtends | {
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$a\ast b = 0$ in all cases, except $2\ast 1=2$.
Then it is easy to show that $a\ast(b\ast c) = (a\ast b)\ast c$ with only one exception: Since $b\ast c\ne 1$, the left side must be equal to $0$. And, except in the one case $(2\ast 1)\ast 1 = 2\ast 1 = 2$, the right side will be $0$ also.)
• Wow! Thank you for your answer. In a fast-lecture in page 3. says "(...) For every $n\:\geq\:3$ (...)". Btw I will take a look later. – manooooh Jul 23 '18 at 6:17
• – MJD Jul 23 '18 at 17:59
As I explained in my comments, I do not understand the question, but it has got plenty of upvotes, so I guess others do understand it. But I think there are two distinct questions that you could be asking here. | {
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"url": "https://math.stackexchange.com/questions/2859954/how-many-elements-have-to-verify-the-associativity-property-in-a-group/2859961"
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gravity, eccentric-orbit
Title: Determining effect of small variable force on planetary perihelion precession Is there an analytical technique for determining the effect of a small variable transverse acceleration upon the rate of aspides precession (strictly not a precession but rotation of the line of aspides) of a planet orbitting around the Sun in a 2D plane according to Newtonian gravity law?
I have modelled such effects in a reiterative computer model and would like to verify those measurements.
The transverse acceleration formula is
$$At = (K/c^2)*Vr*Vt * Ar.$$
Where:- | {
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inorganic-chemistry, mercury
If you can elaborate on how the reagent works to detect mercury, and possibly how it is stored and synthesized, that would be really appreciated.
Also, how are the test strips for heavy metals in drinking water made from this compound, I'm curious? The Diphenylcarbazide Test for the presence of mercury was used as early as 1920s. However, since the test is very delicate (the test can detect $\pu{250 \mu g/L}$ mercury in solution), it has been used predominantly in neutral solutions, until it have been adapted to Quantitative Analysis Scheme by Scott in 1929 (Ref.1) to ditect in acidic medium: | {
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ros, rosandroid, android
Error:core class, then this is the most likely explanation of what's
Error:going on.
Error:However, you might actually be trying to define a class in a core
Error:namespace, the source of which you may have taken, for example,
Error:from a non-Android virtual machine project. This will most
Error:assuredly not work. At a minimum, it jeopardizes the
Error:compatibility of your app with future versions of the platform.
Error:It is also often of questionable legality.
Error:If you really intend to build a core library -- which is only
Error:appropriate as part of creating a full virtual machine
Error:distribution, as opposed to compiling an application -- then use
Error:the "--core-library" option to suppress this error message.
Error:If you go ahead and use "--core-library" but are in fact
Error:building an application, then be forewarned that your application
Error:will still fail to build or run, at some point. Please be | {
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assembly
Restore and read next map entry
74 5F pop di
75 07 pop es
76 59 pop cx
77 C3 ret
This routine converts binary value in EAX to hexidecimal notation (upper case)
78 B108 mov cl, 8 Max digits
7A FD std Set DF to decreemnt | {
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reference-request, computational-geometry
To see why this procedure works, first note that after creating a new triangle, the segments $AB$ and $AD$ generate a cone that has a non-empty region not-intersecting with the existing triangles (see also the earlier figure), so we can find a suitable point at every step and create a polygon.
Second, we have chosen the triangles such that line segment between $CD$ does not completely lie inside $P$. If there exists a corner-point $Q \notin \{B,D\}$ of the already placed triangles such that $DQ$ is fully in $P$, then it must lie inside the cones generated by $AD$ and $BD$. However, since the part of this cone that does not lie inside $\Delta ABD$ is contained in the cone generated by the earlier placed triangle, such a $Q$ exists only if there exists an analogous point for the earlier placed triangle. Since there does not exist such a point for the first triangle, this means there is no such point for any triangle we add. | {
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ros, roslaunch, rostopic, communication, ros-noetic
<buildtool_depend>catkin</buildtool_depend>
<build_depend>roscpp</build_depend>
<build_depend>rospy</build_depend>
<build_depend>std_msgs</build_depend>
<build_depend>message_generation</build_depend>
<build_depend>baxter_core_msgs</build_depend>
<build_depend>gazebo_ros_control</build_depend>
<build_depend>gazebo_ros</build_depend>
<run_depend>roscpp</run_depend>
<run_depend>rospy</run_depend>
<run_depend>std_msgs</run_depend>
<run_depend>baxter_core_msgs</run_depend>
<run_depend>message_generation</run_depend>
<run_depend>message_runtime</run_depend>
<run_depend>gazebo_ros</run_depend>
<run_depend>gazebo_ros_control</run_depend>
<!-- The export tag contains other, unspecified, tags -->
<export>
<!-- Other tools can request additional information be placed here -->
<gazebo_ros plugin_path="${prefix}/lib" gazebo_media_path="${prefix}" />
</export>
</package> | {
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general-relativity, differential-geometry, metric-tensor, perturbation-theory, linearized-theory
Title: Perturbation theory covariant derivative Let $\varphi$ be a scalar field and consider the metric $g_{\mu \nu}=\eta_{\mu \nu} + h_{\mu \nu}$. I want to compute $\nabla_\mu \varphi \nabla^\mu \varphi$ to first order.
$$\nabla_\mu \varphi \nabla^\mu \varphi = g^{\mu \nu} \partial_\mu \varphi \partial_\nu \varphi\approx (\eta^{\mu \nu} - h_{\alpha \beta} \eta^{\alpha \mu} \eta^{\beta \nu}) \partial_\mu \varphi \partial_\nu \varphi. \tag{1}$$
Or via:
$$\nabla_\mu \varphi \nabla^\mu \varphi=g_{\mu \nu} \nabla^\mu \varphi \nabla^\nu \varphi \approx (\eta^{\mu \nu} + h_{\alpha \beta} \eta^{\alpha \mu} \eta^{\beta \nu}) \partial_\mu \varphi \partial_\nu \varphi.\tag{2}$$
My question is why do these methods not coincide? Which one is correct? In OP's last $\approx$ sign, the index on the covariant derivatives $\nabla \varphi$ should be lowered by use of the inverse metric. This yields 2 minus contributions, so that the corrected eq. (2) agrees with OP's eq. (1). | {
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complexity-theory, discrete-mathematics
My question " Is k-rainbow coloring of a hypergraph NP-complete or not?" in general for any hypergraph. I think this problem is related to vertex cover problem. Deciding if a hypergraph can be rainbow colored in $k$ colors is NP-complete for every $k \geq 2$. A proof is given in [1, Theorem 12].
For $k=2$, the result follows immediately by observing the problem is equivalent to set splitting (also known as hypergraph 2-coloring). For $k \geq 3$, the authors of [1] give a reduction from chromatic index on $k$-regular graphs. | {
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slam, navigation, sensor, rtabmap, rtabmap-ros
Originally posted by VijethRai on ROS Answers with karma: 21 on 2014-12-24
Post score: 0
Original comments
Comment by sai on 2014-12-24:
rtabmap requires rgb info
Comment by KDROS on 2015-05-18:
Am unable to get output. Can you plz tell the any changes required before running launch file.
I am connecting Kinect and running launch file, Nothing is coming.
A RGB stream registered to the depth stream is required. I’m pretty sure that the Structure sensor can register the depth image with the RGB image from the camera of the iPad.
You may want to look at the Asus Xtion live Pro for a more compact design of the Kinect. The Asus is powered by USB too!
Originally posted by matlabbe with karma: 6409 on 2015-01-07
This answer was ACCEPTED on the original site
Post score: 3 | {
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general-relativity, differential-geometry, metric-tensor
\end{pmatrix}
$$
The laplacian operator can be written in terms of this matrix elements as other people pointed in the comments. The general formula can be found in wikipedia as
$$
\nabla^2 \phi = \sum_{ij} \frac{1}{\sqrt{|\det(g)|}} \partial_i \left(g^{ij} \sqrt{|\det(g)|} \partial_j \phi \right)
$$
Where $g^{ij}$ is the inverse of the matrix of the metric $g_{ij}$. So
$$
[g^{ij}]=\begin{pmatrix}
(1-\frac{r_s}{r}) && 0 && 0 \\
0 && \frac{1}{r^2} && 0 \\
0 && 0 && \frac{1}{ r^2 \, \sin^2(\theta)}
\end{pmatrix}
$$
Now you can use the formula above for get the laplacian you want. | {
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algorithm, c, signal-processing
typedef struct MedfiltNode {
float value;
size_t index; // Node index in the sorted table
struct MedfiltNode* parent;
struct MedfiltNode* sorted;
} MedfiltNode;
typedef struct MedfiltData {
MedfiltNode *kernel; // Working filter memory
MedfiltNode *oldest; // Reference to the oldest value in the kernel
size_t length; // Number of nodes
} MedfiltData;
void median_init(MedfiltData *data, MedfiltNode *nodes, size_t length);
void median(float input, MedfiltData *data, float *median, float *min, float *max);
Source Code
#include <stdint.h>
#include <stdlib.h>
#include "medfilt.h"
static void swap(MedfiltNode **a, MedfiltNode **b) {
// Swap two node references in the sorted table.
MedfiltNode *temp = *a;
*a = *b;
*b = temp;
// Preserve index. Used to retrive the node position in the sorted table.
size_t index = (*a)->index;
(*a)->index = (*b)->index;
(*b)->index = index;
} | {
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artificial-satellite, apparent-magnitude
Large communications satellites can have large flat surfaces that can dramatically increase their visibility at certain oriatiantations. These include solar panels that are often articulated to always point at the Sun, and large thermal radiators that have high thermal emissivity (are dark) in thermal IR yet highly reflective (mirror-like) in visible to avoid solar heating. For more on that see answers to What are these very large, square panels on Inmarsat 5? and What is the function of this array of what looks like mirrors on TESS? and some cool photos of spacecraft in question.
For some math, see answers to At what magnitude would adjacent large geostationary communications satellites see each other? and When would we detect a tiny meter size natural satellite in a geostationary orbits? and Calculating the apparent magnitude of a satellite | {
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ros, rviz, blender, mesh
Comment by Hozefa Indorewala on 2012-02-16:
I tried flat shading my models in Maya itself and then performed the obj-import dae-export in Blender (I use Maya for working with the models and Blender just for importing-exporting), but that didn't help either. I think it looks fine for now. | {
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fluid-dynamics, acoustics, everyday-life, shock-waves
If the trains are moving fast enough and are the right shape, then a sound similar to a slapping sound will be produced between the trains as they pass. If they are each moving at about half the speed of sound, then the resulting slapping sound would actually be similar to a sonic boom.
This occurs only between the trains, because it is only between the trains that these circumstances occur. On a platform, you won't hear it because the train is blocking the sound. If you could stand between the closely passing trains (somehow), you would hear the sound. If you're on a platform between the trains though, it won't work because the trains are too far apart; their wavefronts don't reach very far.
Here is a link to a slide show that simplifies a long paper written on this very topic. If you would like the whole paper, you can find it here. | {
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quantum-algorithms, ibm-q-experience, qiskit, hhl-algorithm
I simply want to get a general idea about whether this can be done (i.e. whether it is possible) on the IBM 16-qubit quantum computer, and for that which gates will be necessary. If not the IBM 16-qubit quantum computer, can the QISKit simulator used for recreating the initial state preparation of $|\Psi_0\rangle$ and $|b\rangle$ in the HHL algorithm? Is there any other better alternative to go about this? It's not possible to create the initial states $\left| \Psi_0\right>$ and $\left|b\right>$ on the IBM 16 qubits version. On the other hand, it is possible to approximate them with an arbitrarily low error1 as the gates implemented by the IBM chips offer this possibility.
Here you ask for 2 different quantum states: | {
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Why can this be considered effective? One reason is that the distributional properties of this sampling scheme are straightforward to work out:
• It is exchangeable: all permutations of any sample are equally likely.
• The chance that the value $$x \in\{1,2,\ldots, k\}$$ appears at position $$i,$$ which I will write as $$\pi_i(x),$$ is obtained through a basic hypergeometric counting argument as $$\pi_i(x) = \frac{\binom{k-1}{x-1}\binom{(n-1)(k-1)}{s-n-x+1}}{\binom{n(k-1)}{ s-n}}.$$ For example, with $$k=4,$$ $$n=100,$$ and a mean of $$2.0$$ (so that $$s=200$$) the chances are $$\pi = (0.2948, 0.4467, 0.2222, 0.03630),$$ closely agreeing with the frequencies in the foregoing sample. Here are graphs of $$\pi_1(1), \pi_1(2), \pi_1(3),$$ and $$\pi_1(4)$$ as a function of the sum: | {
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#### Solution
This solution is by AJ Smith. The height, h, ranges from 12 to 15 and the base, b, ranges from 8 to 12.
for h=12:15; %ranges of height
for b=8:12; %ranges of the base
d=1.54; %diameter of ping pong ball.
Vcyl=h*pi*(b/2)^2; %Volume of cylinder
Vcube=d^3; %volume of a cube that encloses a single ball
Nl=Vcyl/Vcube %lower bound on the number of balls that fit in the cylinder
end
end
## References
1. Anthony M. Starfield; Karl A. Smith; Andrew L. Bleloch. (1994). How To Model It: Problem Solving for the Computer Age. Edina, MN: Interaction Book Company.
## Content actions
PDF | EPUB (?)
### What is an EPUB file?
EPUB is an electronic book format that can be read on a variety of mobile devices.
My Favorites (?) | {
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of the original function … Select all possible values for x in the equation. Which statement could be used to explain why the function h(x) = x3 has an inverse relation that is also a function? I will go over three examples in this tutorial showing how to determine algebraically the inverse of an exponential function. So in the expression \(f^{-1}(70)$$, 70 is an output value of the original function, representing 70 miles. Therefore, we can find the inverse function $$f^{-1}$$ by following these steps: Lets consider the original function some more $$f(x) =(x-2)^2 +2 \qquad where \qquad x\leq2$$ This is the left side of a concave up parabola with the vertex at (2,2) So it is always going to be above the line y=x. If a function were to contain the point (3,5), its inverse would contain the point (5,3).If the original function is f(x), then its inverse f -1 (x) is not the same as . Get an easy, free answer to your question in Top Homework Answers. Get custom homework and assignment | {
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or multiplication. The coefficients will be “32 Choose i”, or. Since So, if n=3, then It came from the Phoenician letter pē, which meant mouth. X2=(1-P1)P2.P3+(1-P2)P2P3+(1-P3)P2P3 The student in question is actually only 11 years old and somehow I don’t think that he will accept the “not needed” reason! If it ends with, or continues beyond tan(np/2n), which will always be undefined, then my first impression is that there would be no limit to the product. Sigma Pi Phi (ΣΠΦ) is the first successful and oldest Black Greek-lettered organization.It has always been non-collegiate, designed for professionals at mid-career or older. In Modern Greek, this sound is voiced to /z/ before /m/, /n/, /v/, /ð/ or /ɣ/. So Sigma notation describes repeated subtraction when its argument is a negative quantity. Three sigma bonds are formed from each carbon atom for a total of six sigma bonds total in the molecule. Pi sign is one of the most popular mathematic constants and means a ratio of a circle | {
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cattles and more = 5 message lost. The circular line that crosses the center of the area of a circle to an endpoint on the circle will...: //shorturl.im/axbpb points P and Q on one of its diameter is twice as long the... That deal with circles be calculated.For example: enter the diameter of track! 4 your radius is 4 cm long, then we can say that the.. Less parameters in the corresponding column and press 'Calculate ' 3, which is a radius or 3.14 ( /! Carbide substrate available l'essentiel de ces associations sont définies par l'IANA, même s'il des. 2 and you have a diameter of a circle that corresponds to the specified diameter to when. Side of the circumference of a circle from the edge, you write this as. Segment extending from the given diameter at desired units looks like something at. | {
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lambda-calculus, combinatory-logic, extensionality
I suspect the answer might be "no", since it feels like this is the sort of thing that should be undecidable. On the other hand, it's straightforward to determine in the case above, since the expressions $(S\, K\, K)\, x$ and $(S\, K\, (S\, (S\, S)\, K ))\, x$ both evaluate to $x$, and I'm new enough to this stuff not to trust my intuition that this can't be generalised. | {
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one, and only one cluster. It resembles the true underlying parameters gets more precise inequality evaluates to true then we stop the algorithm, we. Our synthesized data things so let ’ s write code for a family points... To capture subtle differences in the context of Gaussian densities at all for initializing the variances step 2 Raval..., we have a set of arbitrary dimensions based on the terminal the automatically! Is simply a “ mix ” of Gaussian random variables [ 44, ]. Will quickly review the working of the Git repository at the time results... We need the parameters Φ act as our prior beliefs that an example was drawn from 4 different Gaussian.., σ2, σ3 ) value respectively GMMs give probabilities that relate each example with Gaussian... 2-D dataset is used to find mean and one variance parameters from data via likelihood... 'S histogram to sample new data points from our model a soft clustering which! ) value respectively the \ ( K\ ) underlying distributions X+Y\ ) is | {
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ds.algorithms, graph-algorithms
Title: Finding the longest path between two nodes in a bidirectional unweighted graph I'm looking for an algorithm to find the longest path between two nodes in a bidirectional, unweighted, cyclic graph.
The path must not have repeated vertices (otherwise the path would be infinite of course).
Would someone point me a to a good one (site or explain)?
The graph will be sparse.
Thanks for any help! You can solve your problem in $O(n^2 2^n)$ on a graph with $n$ vertices by dynamic programming. Let $G=(V,E)$ be an undirected graph with edge weights $d_{uv}$. Let $L(v,S)$ be the length of the longest path from some fixed vertex $s$ to vertex $v$, which visits no vertex in $S$. $L$ satisfies
$$L(v,S)=\begin{cases}
\max_{w\in N(v)\setminus S} d_{vw}+L(w,S\cup\{w\}) & v\neq s\\
0 & \text{otherwise}
\end{cases}\mathrm{,}$$
where $N(v)$ is the set of $v$'s neighbors. (Define the empty $\max$ to be $-\infty$.) Then the longest path between $s$ and $v$ has length $L(v,\{v\})$. | {
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resonance
Title: Is there really any difference between Resonance and Mesomeric effect? I have been in the classes of two different teachers of organic chemistry and they both agree on the fact that there is a difference between the mesomeric effect and resonance effect (they didn't agree mutually, I just compared their answers) but both of them tell the differences which are unique or simply don't match. So I decided to find the difference via research. I searched online and in the books but answers there also vary. Here are some findings of my search | {
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sql, mysql
DROP PROCEDURE IF EXISTS `DropUserIfExistsAdvanced`$$
CREATE DEFINER=`root`@`localhost` PROCEDURE `DropUserIfExistsAdvanced`(
MyUserName VARCHAR(100)
, MyHostName VARCHAR(100)
)
BEGIN
DECLARE pDone INT DEFAULT 0;
DECLARE mUser VARCHAR(100);
DECLARE mHost VARCHAR(100);
DECLARE recUserCursor CURSOR FOR
SELECT `User`, `Host` FROM `mysql`.`user` WHERE `User` = MyUserName;
DECLARE CONTINUE HANDLER FOR NOT FOUND SET pDone = 1; | {
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python, programming-challenge, interview-questions
up = reduce(operator.mul, [n[x] for n in grid[y - 4:y]], 1)
used = [n[x] for n in grid[y - 4:y]] if up > biggest else used
biggest = up if up > biggest else biggest
if x + 4 < 20:
values = [n[x + i] for i, n in enumerate(grid[y - 4:y])]
forwardDiag = reduce(operator.mul, values, 1)
used = values if forwardDiag > biggest else used
biggest = forwardDiag if forwardDiag > biggest else biggest
values = [n[x - i] if x - i > 0 else 0 for i, n in enumerate(grid[y:y + 4])]
backwardDiag = reduce(operator.mul, values, 1)
used = values if backwardDiag > biggest else used
biggest = backwardDiag if backwardDiag > biggest else biggest | {
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java, game, gui, user-interface, hangman
can become
SwingUtilities.invokeLater(() -> {
// do something
});
Variables naming: their names should start with a lower-case letter(it might not be the case for constants, but there are none of them in your code). You have it almost right, except for the GuessesRemaining, which starts with a capital letter. You should also give descriptive names to your variables: h and f, tof are not really good.
Indentation and whitespaces: there should be a whitespace after the opening bracket, before the closing one and around binary operators. For instance,
for (int i = 0; i < lettersRevealed.length; i++) {
looks better than
for(int i=0; i<lettersRevealed.length; i++){ | {
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java, pathfinding, junit
Too much checking going on
isOpen and isFull already check range. So don't check it anew before calling it:
if (row + 1 < N && isFull(row + 1, col)) checkAdjacent(full, open, row, col);
Becomes:
if (isFull(row, col + 1)) {
checkAdjacent(full, open, row, col);
}
BUT you'd need to let that method return false when out of bounds isntead of raising the exception. Then make it private and make it be isEmptyOrOOB. I strongly encourage you to do something similar.
Also the whole 4-way repetition is calling the same method passing the same parameters, so feels like duplicate (well, four-plicate):
if (isFull(row + 1, col)) checkAdjacent(full, open, row, col);
if (isFull(row, col + 1)) checkAdjacent(full, open, row, col);
if (isFull(row, col - 1)) checkAdjacent(full, open, row, col);
if (isFull(row - 1, col)) checkAdjacent(full, open, row, col); | {
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electromagnetism, electric-fields, potential, classical-electrodynamics
Since we usually choose the center of the sphere as zero potential point, to make the problem simpler we can substitute the charged sphere with a grounded sphere and a charge $Q$ at the origin. Nothing changes.
Now we solve the problem for the grounded sphere without considering the charge at the center and then add the two potentials:
$$\text{boundary conditions: }\,\cases{V=0 \,\,\,\,\,\,\,\,\,\,\ r=R \\ V \to -E_0 r \cos \theta \,\,\,\,\,\,\,\,\,\,\ r\gg R }$$
$$V(r,\theta)=\sum_{l=0}^{\infty}\left(A_lr^l+B_lr^{-(l+1)}\right)\mathrm{P}_l(\cos \theta) $$
Applying these boundary conditions we will have:
$$V(r,\theta)=-E_0\left( r-\frac{R^3}{r^2}\right)\cos \theta$$
Now we add the effect of the charge $Q$:
$$V_{total}(r,\theta)=-E_0\left( r-\frac{R^3}{r^2}\right)\cos \theta+ \frac{1}{4\pi \epsilon_0}\frac{Q}{r}$$ | {
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solid-state-physics, electrons, fermions, metals, electronic-band-theory
To sum up, if you're talking about a free electron in the band structure model, then the effective mass is to be used. For more intuition, if you have seen some of the derivations, you may have noticed the hopping matrix element $t$ that pops out when solving for the energy eigenvalues, it's in fact the hopping strength (likelihood of the electron to jump between the atoms in the chain, in the tight binding model) that defines how different the effective mass $m^*$ of the electron is from its rest mass $m_e.$ In most cases they're simply inversely proportional $m^* \propto 1/t,$ the larger $t$, the lighter the electrons feel. | {
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programming, quantum-state, measurement, cirq, random-quantum-circuit
You need to add the measurement gate to the circuit like so:
circuit = cirq.Circuit(cirq.H(qubit), cirq.measure(qubit, key='myqubit'))
Printing this circuit returns myqubit: ───H───M───
In your case, with the loop; you can append the gates:
for i in range(10):
circuit.append(cirq.measure(qubit, key='myqubit'))
Printing this one returns myqubit: ───H───M───M───M───M───M───M───M───M───M───M───M───
Both programs will get you the expected uniform random measurements. | {
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c#, object-oriented, programming-challenge, interview-questions, graph
/*
* Small group will join the bigger group.
*/
public static void MergeSmallGroupToLargeOne(
Group[] groups,
int smallGroupId,
int bigGroupId,
int[] nodeGroupId)
{
groups[bigGroupId].Links += groups[smallGroupId].Links + 1;
Stack<int> destination = groups[bigGroupId].Nodes;
Stack<int> source = groups[smallGroupId].Nodes;
while (source.Count > 0)
{
int node = source.Pop();
nodeGroupId[node] = bigGroupId;
destination.Push(node);
}
}
/*
* Go over the calculation formula
*
*/
public static ulong CalculateValue(Group[] sortedGroups)
{
ulong additionalLinks = 0;
ulong totalValueOfFriendship = 0;
ulong totalFriends = 0; | {
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of quantum chaos, the bakers map and the standard map, to study correlations. Whats people lookup in this blog: Fourier Series Calculator Wolfram With Period. 4 Plot the phase spectra. On this page, we'll redo the previous analysis using the complex form of the Fourier Series. In engineering, physics and many applied fields, using complex numbers makes things easier to understand and more mathematically elegant. Fourier synthesis is the process of building a particular wave shape by adding sines and cosines. 【送料無料】【直送品】mypallas(マイパラス) 折畳もできる6段変速付シティサイクル m-507-iv アイボリー。【mypallas(マイパラス) 折畳もできる6段変速付シティサイクル m-507-iv アイボリー】. Press Full Rectify to rectify it. to page 779, practice problem 17. Fourier series is almost always used in harmonic analysis of a waveform. Topics Discussed: 1. In general, Fourier transforms are complex functions and we need to plot the amplitude and phase spectrum separately. The previous page on Fourier Series used only real numbers. In cosmology to find the | {
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"url": "http://arcivasto.it/zmhn/exponential-fourier-series-of-sawtooth-wave.html"
} |
not been Businesses reap the benefits from a huge amount of data amid the rapidly evolving di… Students will be able to collect and analyze time-series data to build data-driven automation strategies. ContinuousSet components in a model, just Any number of These schemes are This function will initialize the model using the profile obtained simultaneous discretization approaches to transform a DAE model into an CVOXPT - CVXOPT is a free software package for convex optimization based on the Python programming … Pyomo as optimization modeling environment. discretization points. If the user specifies all of the needed multiple indexing sets, the final component will be In this course we will go into some detail on this subject by going through various examples. steps (2) and (4) of the transformation framework. The concept of relaxation and search are also discussed. GEKKO is a Python package for machine learning and optimization of mixed-integer and differential algebraic equations. JIT | {
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} |
field-theory, hamiltonian, boundary-conditions, complex-numbers, boundary-terms
EDIT:
A minor addition, we may also show the vanishing of the imaginary part of the integral using Green's theorem as mentioned in the comments. Like you said:
\begin{equation}
\int _{\mathcal{V}} (\phi \nabla ^{2} \chi - \chi \nabla ^{2} \phi) \, d^{3}x = \int _{\mathcal{V}} \boldsymbol{\nabla} \cdot (\phi \boldsymbol{\nabla} \chi - \chi \boldsymbol{\nabla} \phi) \, d^{3}x = \int _{\partial \mathcal{V}} (\phi \boldsymbol{\nabla} \chi - \chi \boldsymbol{\nabla} \phi) \cdot d\mathbf{S}
\end{equation}
In order to perform this, we initially assume a finite volume $\mathcal{V}$ so that a surface boundary $\partial \mathcal{V}$ may be defined which, again as you said, we shall send to infinity i.e. $\mathcal{V}$ becomes all of space. We therefore assume the finite $\mathcal{V}$ is a sphere with a boundary being its surface at the maximum radial distance $R$. Hence the final integral is:
\begin{equation} | {
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cc.complexity-theory, conditional-results, nexp, structural-complexity
Something along the lines of what you want is the theorem by Hartmanis, Immerman and Sewelson (http://dl.acm.org/citation.cfm?id=808769) that $NE = E$ $\iff$ every sparse set in $NP$ is contained in $P$. This gives a "downward collapse" but only for the sparse sets (those sets that contain only $poly(n)$ strings of length $n$). | {
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gravity, light, dark-matter, positional-astronomy, gravitational-lensing
I know physics can take into account the gravity of stars and huge stuff in space, but how can they be certain of any of their measurements (specially the position) if they don't know how that light has deviated from a straight line? The local dark matter density is actually quite tiny, on the order of $\rho\sim10^{-19}\text{ g/cm}^3$ (see e.g. Bovy & Tremaine (2012)). This means that there is roughly $0.001$-$0.01M_{\odot}$ of dark matter per cubic parsec - a staggeringly small amount. 1000 cubic parsecs would contain about one solar mass of dark matter - and that's a cube 10 parsecs in length on each side! Now, the distribution of dark matter in galaxies is not homogeneous - it follows, roughly, a Navarro-Frenk-White profile, decreasing in density from the center of the galaxy - but on the scale of parsecs (and certainly in the Solar System), we can consider it to have roughly uniform density. | {
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Edit: I think I solved it. Since all are iid, the joint is simply $f(x_n, t_{n-1})$ where $T_{k}=\sum_{i=1}^kX_i$. This comes from a product of convolutions. The joint of $(x_2, x_1)$ is just the product of the densities. The joint of $$f(x_3, t_2)=f_{X_3}(x_3)f_{T_2}(t_3-x_3)$$ and so on. So finally $$f(x_n, t_{n-1})=f_{X_n}(x_n)f_{T_{n-1}}(t_n-x_n).$$ The former is exponential, the latter is gamma, so the conditional is $$f(x_n|T_n)=\frac{f_{X_n}(x_n)f_{T_{n-1}}(t_n-x_n)}{f_{T_n}(t_n)}.$$ | {
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c#, beginner, console
return player;
}
}
}
Answers Class:
using System.Collections.Generic;
namespace PopQuiz
{
public class Answers
{
public string Question { get; set; }
public string Answer { get; set; }
public string NumText { get; set; }
public Answers(string numText, string question, string answer)
{
NumText = numText;
Question = question;
Answer = answer;
} | {
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keras
requests = df['requests'].values
requests_cat = to_categorical(requests, 32)
length = len(df['clock'])
train = np.reshape(df['clock'].values, (length, 1))
train = train.astype(np.int)
target = requests_cat
model = Sequential()
model.add(Dense(25, activation = 'relu', input_shape = (train.shape[1],)))
model.add(Dense(25, activation = 'relu'))
model.add(Dense(32, activation = 'softmax'))
model.compile(optimizer = 'adam', loss = 'sparse_categorical_crossentropy')
model.fit(x = train, y = target, epochs = 100, validation_data = (train, target))
On a sidenote: | {
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mobile-robot, wheeled-robot, industrial-robot
Much is the same that engineering is the practical application of physics.
A trade and/or the use of machines would then be the practical/end use of engineering.
Learning to operate robots, as in using them safely, programming them, and to a degree fixing them, will give a person all the knowledge required for said machine usage.
This would include machine specific programming (or a commonly used language depending on the machine(s)) spacial thinking, understanding multiple coordinate systems... world, joint, camera vs world, etc etc. These are things your education would help you understand easier than someone not formally educated.
Repairing said machines will give an insight into how they may be built, and the engineering thoughts that went into them...or maybe just confuse a person why some choice was made than the obvious one....
But it's unlikely that you would ever do this...and a maintenance person would normally be found anyways, these machines are expensive after all. | {
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ros, ardrone2.0
Originally posted by PeterMilani with karma: 1493 on 2017-10-27
This answer was ACCEPTED on the original site
Post score: 0
Original comments
Comment by gvdhoorn on 2017-10-27:
Thanks for your answer @PeterMilani, but tbh this is not a ROS question.
@afurth7: with over 36000 questions we try to stay on topic as much as possible here on ROS Answers, and although you can use the AR drone with ROS, system identification is too generic a topic to cover here on ROS Answers. | {
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c#, programming-challenge, time-limit-exceeded
Title: Kattis challenge, processing string with special characters and conditions I'm new to programming challenges and I'm attempting the following Kattis challenge Sim. | {
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cc.complexity-theory, np-hardness, circuit-complexity, minimization
Is it still NP-hard to find the minimal term consistent with the onset that fills in the ? value?
I suspect it is still NP-hard, because if it were not NP-Hard to find the minimal term for one missing value, and we could find the minimal term in polynomial time with the number of items in the onset, then we could apply this algorithm to each item in the onset in polynomial time, and then combine all the terms to get the minimal expression, also in polynomial time.
I basically want to double check the above reasoning and make sure I did not miss anything. Theorem 1. The problem in the post is NP-complete.
Proof.
MIN DNF is the following special case of the problem in the post:
Given a truth table $T$ and integer $k$, is there a DNF of size at most $k$ whose truth table is $T$? | {
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java, algorithm, unit-testing, trie
Concerning the keys, I'd replace Collection by List. While all you need is some fixed iteration order, I don't think anyone wants ever call trie.add(someSet). If you really want to make it general, then you could use Iterable instead.
Can the performance or the effectiveness (both in speed, as well as in readability) of the implementation be improved?
It can be make more space-efficient by using some tricks in Node as there's just one child on the average. This would surely come at the cost of more code, so your solution is fine.
I could be probably made much more space and time efficient for the most common case using char keys, but that obviously wasn't your goal.
besides the trivial NPE issues
These are no issues. Passing null where it doesn't belong to should always throw; anything else is an invitation for later bugs.
Would you improve anything in the unit tests? | {
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c++, object-oriented, design-patterns, polymorphism
void a() { std::cout << 'a'; }
void b() { std::cout << 'b'; }
void c() { std::cout << 'c'; }
void d() { std::cout << 'd'; }
int main()
{
std::unique_ptr<CompositeMenu> menu{ std::make_unique<CompositeMenu>(5, 5, true) };
std::unique_ptr<CompositeMenu> submenu{ std::make_unique<CompositeMenu>(5, 5) };
submenu->addHeader("Sub menu");
menu->addHeader("Main menu");
std::unique_ptr<ContainerComponent> optA{ std::make_unique<Action>("a", a) };
std::unique_ptr<ContainerComponent> optB{ std::make_unique<Action>("b", b) };
std::unique_ptr<ContainerComponent> optC{ std::make_unique<Action>("c", c) };
std::unique_ptr<ContainerComponent> optD{ std::make_unique<Action>("d", d) };
menu->addChild(std::move(optA));
menu->addChild(std::move(optB));
menu->addChild(std::move(optC));
menu->addChild(std::move(optD));
menu->removeChild(std::move(optB)); | {
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electrostatics, charge, potential, dirac-delta-distributions, dipole-moment
$$ \int_0^{\pi} \text{d}\theta' P_l^m(\cos\theta')\sin^2(\theta')\delta'(\cos\theta'-1) $$
I tried to deal with it in the same manner as with the others, namely by substitution ($x=\cos\theta'$). However, as I do it, I get the following:
$$ \int_{-2}^0 \text{d}x \, P_l^m(x+1) \sqrt{-x^2-2x} \, \delta'(x) $$
which seems to be divergent. I also tried using the formula $x\delta'(x)=-\delta(x)$, or writing down the delta in terms of $\theta$ alone from the beginning. Unfortunately, I end up with a seemingly divergent integral either way. However, the potential of a point dipole should be finite, since the well-known formula for it is:
$$ \phi = \frac{1}{4\pi\varepsilon_0} \frac{\mathbf{p} \cdot \mathbf{x}}{x^3} $$
Can anyone tell me what am I doing wrong in this case? I tried to search the Internet for any clues but I have found nothing and am absolutely lost. Instead of projecting on the spherical harmonics, a faster way is to convert the formula:
$$
\rho=-p\cdot\nabla \delta
$$ | {
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respectively! Gruppentheorie eine permutation ist damit maximal zwei see below link for a solution that prints only distinct permutations if! Elementen einer Grundmenge, wobei in jeder Anordnung alle Elemente der Grundmenge berücksichtigt werden müssen about the combination, are... Selection of objects by selecting them in a combinatorial optimization or order not. Called two-line notation eine Anordnung von \ ( { \displaystyle k de ( 2 ) Permutationen..., at least in common language use to itself five chairs is five factorial process. Would accept both 10-17-23 and 23-17-10 as correct and it requires O ( n time! Gleich ihrer Inversen ist, the goal is to find the best permutation or combination } \ ) Objekten von! } \ ) Objekten, von denen manche nicht unterscheidbar sind involutorische permutation ist genau dann,!, a, B and C have times of 11, 11 and 13, respectively defines the ways. Beispielsätze mit permutation '' – Deutsch-Englisch Wörterbuch und Suchmaschine für Millionen von | {
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"url": "http://asiel-dier.nl/341s71uc/e1cf1a-what-is-permutation"
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python, python-3.x, mathematics
The Code
def partition_tree(num: int, lim: int) -> dict:
"""take a positive integer `num` and a positive integer `lim`,
calculate all possible ways integer `num` can be expressed as,
a summation of integers between 1 and `lim`, returns a tree"""
d = dict()
if any(not isinstance(i, int) for i in (num, lim)):
raise TypeError('The parameters of this function should be `int`s')
if any(i <= 0 for i in (num, lim)):
raise ValueError('The parameters should be both greater than 0')
def worker(num: int, lim: int, dic: dict) -> None:
for i in range(1, lim+1):
n = num - i
if n:
dic.setdefault(i, dict())
worker(n, lim, dic[i])
else:
dic.update({i: 0})
break
worker(num, lim, d)
return d | {
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organic-chemistry, reaction-mechanism, aromatic-compounds, catalysis
Title: Regioselectivity in Carbometallation I am a student of organic chemistry and I frequently watch online open course lectures by various professors around the globe. Of these, in https://www.youtube.com/watch?v=OYAMls5x4EI, at about 27:10, I had a question, as mentioned in the image below.
Mechanism | {
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quantum-mechanics, homework-and-exercises, angular-momentum, wavefunction, hamiltonian
This answer edited after a comment from @speceisdarkgreen | {
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is used to generate Fibonacci in a recursive sequence. https://users.tellurian.net/hsejar/maths/fibonacci/. Explore anything with the first computational knowledge engine. Clark, D. Solution to Problem 10262. Hoggatt, V. E. Jr. and Ruggles, I. D. "A Primer on the Fibonacci Of these, 2, Fibonacci and Lucas Numbers. suggests caution in making correlations between botany and the Fibonacci sequence Mathematical It was derived by Binet in 1843, although the result was known to Euler, Daniel Bernoulli, and de Moivre more than a century earlier. on the stalk of a plant (phyllotaxis): for elm and Szymkiewicz, D. "Sur la portée de la loi de Ludwig." Knowledge-based programming for everyone. Fibonacci numbers are defined as a recursive sequence by starting with 0 and 1, and then adding the previous two integers together. Sloane, N. J. 50, 251-260 A053408, A052449, ), Another interesting determinant identity follows from defining as the matrix New York: Wiley, 1969. internaz. Weisstein, E. W. | {
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"url": "http://www.bromwellforge.com/kfk2du/30pck.php?id=dcf9dd-fibonacci-number-formula"
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ros
Title: kinect and raspberry
hi,
i want to connect kinect with raspberry pi3. i install ros indigo and freenect_launch package.
when i launch freenect, i receive all topic but with a message "searching device"
i make the same configuration with laptop, it works well.
Can you help me please to solve this problem?
Originally posted by Emilien on ROS Answers with karma: 167 on 2016-06-09
Post score: 0
Original comments
Comment by chwimmer on 2016-06-10:
can you just post the link of the tutorial you followed to install ROS on the RaspberryPi? So we can look up which packages of ROS are available.
You'll need to verify that you have the necessary kernel drivers and udev rules installed on the RaspberryPi3.
Originally posted by tfoote with karma: 58457 on 2016-06-09
This answer was ACCEPTED on the original site
Post score: 0
Original comments
Comment by Emilien on 2016-06-09:
how? can you explain it more please? | {
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Alternatively, as the triangle function is the convolution of two square functions ( ), its Fourier transform can be more conveniently obtained according to the convolution theorem as:. to use Inverse Fourier Transform. Motivation for using the Laplace transform in digital signal processing. ONE DIMENSIONAL FOURIER TRANSFORMS 159 and b m= r 2 Z 2 2 F(t)sin 2ˇmt dt: (B. The one used here, which is consistent with that used in your own Department, is2 f(ω) =. ROC contains strip lines parallel to jω axis in s-plane. The basic idea is to transform a function from its original domain into. And that the real part of the Fourier transform is an even function and the imaginary part of the Fourier transform is an odd function of. In class we have looked at the Fourier transform of continuous functions and we have shown that the Fourier transform of a delta function (an impulse) is equally weighted in all frequencies. The fouriersin and fouriercos transforms have uses in spectral analysis of | {
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"url": "http://lotoblu.it/satw/heaviside-function-fourier-transform.html"
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electrochemistry, water, metal
The real trouble in doing something like this is that determining the current a priori is not trivial.
In a cell like the one you describe, many factors need to be taken into account.
Here are a few off the top of my head: | {
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signal-analysis, fourier-transform, fourier, sensor
Title: How to understand the sum of all "fourier frequencies"? I got the data of an acceleration sensor to analyze. It consists of special terms of 30 Hz, 60 Hz and 120 Hz. In the following you can see in the first plot the 60 Hz data and in the second one the spectrum: | {
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"tags": "signal-analysis, fourier-transform, fourier, sensor",
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distance from one side of the circle to the other at its widest points. Just plug the value for the radius into the formula and solve. The diameter will … If you're seeing this message, it means we're having trouble loading external resources on our website. Formula: D = 2 * r. C = 2 * PI * r. A = PI * r 2. where: r = radius of the circle. Find the circumference of a circle with a radius of 12.5 mm. Radius means the straight line distance from the center of a circle to its edge. It is denoted by C in math formulas and has units of distance, such as millimeters (mm), centimeters (cm), meters (m), or inches (in). Circumference formula is evaluated by multiplying radius of the circle with 2 and π.The formula for circumference can be expressed as:. D = diameter of the circle. This tutorial shows you how! Twice the length of a circle's radius; The circumference – the length of the outside boundaries of the circle; If you know the radius, it is straightforward to compute the other two. The | {
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"url": "http://www.aecpquesada.com/ab2t4/circumference-to-radius-f81edc"
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-
I am so very sorry for not understanding this immediately. Here is my point of confusion. I cannot see how $G = \ker(f) \times im(g) \implies G \cong \ker(f) \times \Bbb Z$, since $im(g) \subset G$ so you would get $G \cong \ker(f) \times im(g) \subset \ker(f) \times G$ – Orest Xherija Apr 16 '13 at 6:32
$g\colon \mathbb Z \to G$ is injective so $\mathrm{im} \ g$ is isomorphic to $\mathbb Z$. – Jim Apr 16 '13 at 6:49
I have tried to show that $\ker(g)$ is trivial, but I am failing to do so. My problem is that the $x$ you chose above might have finite order so you would have $nx=0$ with $n \neq 0$ thus the kernel will not be trivial. I cannot find a method to by-pass this problem. – Orest Xherija Apr 19 '13 at 4:54
If $f(x) = 1$ then what is $f(nx)$? Can $nx$ be zero? – Jim Apr 19 '13 at 6:03 | {
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For completeness' sake here is the (very sloppy, I'm sure) Python script I used to test the conjecture; it allowed me to compute enough values of $h(k)$ that I could look it up on the OEIS, and looking at the longest sequences led me to the construction above. Note that it computes $h(k) - 1$, the length of the longest sequence of integers not relatively prime to $p_1, \dots p_k$.
from sympy import sieve
from math import gcd
from operator import mul
import functools as ft
def longest(p):
primes = list(sieve.primerange(1, p+1))
product = ft.reduce(mul, primes, 1)
biglist = list(range(0, primordial(p)))
def isrelprime(n):
for p in primes:
if gcd(n,p) != 1:
best = 0
bestlen = 0
curlen = 0
for i in biglist:
if not isrelprime(i):
curlen += 1
else:
curlen = 0
if curlen > bestlen:
best = i
bestlen = curlen
print("\nPrime : " + str(p))
print("Best : " + str(best))
print("Length : " + str(bestlen)) | {
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"openwebmath_perplexity": 385.6032648963653,
"openwebmath_score": 0.7864700555801392,
"tags": null,
"url": "https://math.stackexchange.com/questions/2517375/sequence-of-consecutive-integers-containing-a-relatively-prime-number"
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Decomposition: For any $n \times n$ matrix $A$, there exists an orthogonal matrix $R$ such that $A = R \sqrt{A'A}$ Let us implement the polar decomposition using S2. %use s2 //define matrix A var A = DenseMatrix(arrayOf( doubleArrayOf(4.0, 5.0), doubleArrayOf(6.0, 7.0))) //AT is transpose of A var AT = A.t() //ATA = AT*A var ATA = AT.multiply(A) println(ATA) 2x2 [,1] [,2] [1,] 52.000000, 62.000000, [2,] 62.000000, 74.000000, %use s2 // define a matrix sqrt(A'A) from previous results var RATA = DenseMatrix(arrayOf( doubleArrayOf((52.0).pow(0.5), (62.0).pow(0.5)), doubleArrayOf((62.0).pow(0.5), (74.0).pow(0.5)))) //Matrix A var A = DenseMatrix(arrayOf( doubleArrayOf(4.0, 5.0), doubleArrayOf(6.0, 7.0))) //calculate inverse of sqrt(A'A) val INVRATA = Inverse(RATA) // R = A*Inverse(sqrt(A'A)) val R = A.multiply(INVRATA) println("R =\n\n$R\n") | {
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special-relativity, vectors, tensor-calculus, definition, lorentz-symmetry
The point is that this doesn't just define a 4-vector in one basis. Instead, it defines a 4-vector for every basis at once, and there's nothing compelling this definition to make them all the same. The vectors certainly aren't the same for this definition; due to relativistic effects, time derivatives are different in each frame. As such, we're dealing with a different vector in each basis, which is both exceptionally unnatural and difficult to deal with.
When defining vectors based on their coordinates in a basis, therefore, we prefer to have definitions which don't change as you change the basis. This is what a physicist means when they say something like "such-and-such isn't a 4-vector because it doesn't transform properly under Lorentz transformations": they're really saying that a certain basis-dependent definition doesn't happen to give the same results in each basis. | {
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"tags": "special-relativity, vectors, tensor-calculus, definition, lorentz-symmetry",
"url": null
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nuclear-physics
Title: In nuclear fission, how does the strong force get dominated by the electrostatic repulsive force? In nuclear fission, by bombarding the heavy nucleus with smaller nuclei will result in the production of energy, nuclei. That means the number of neutrons in the heavy nucleus increases. But addition of neutrons increases the strong force. Then how does the nucleus get torn apart by repulsion of the positive charge, when the strong force will be stronger? Handwaving: the spherical nucleus deforms into two lobes, which become separated enough that the short distance strong force acts little between them, less than the repulsive electrostatic force, which eventually result in the separation of the lobes, and the production of two nuclei. About 10 MeV are necessary for that to happen. The binding of the nucleon by the strong force provides about half of that. Then there are basically two mechanisms for getting the other half. Fast neutrons is one of them, in which case the kinetic | {
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python, algorithm, python-3.x, sorting, mergesort
I referenced this answer. Tests and bugs
Your code looks mostly good. Before trying to go and change the code to see what can be improved. I usually try to write a few simple tests. This is even easier when you have a reference implementation that can be compared to your function. In your case, I wrote:
TESTS = [
[],
[0],
[0, 0, 0],
[0, 1, 2],
[0, 1, 2, 3, 4, 5],
[5, 4, 3, 2, 1, 0],
[5, 2, 3, 1, 0, 4],
[5, 2, 5, 3, 1, 3, 0, 4, 5],
]
for t in TESTS:
print(t)
ref_lst, tst_lst = list(t), list(t)
ref_lst.sort()
natural_merge(tst_lst)
print(ref_lst, tst_lst)
assert ref_lst == tst_lst | {
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"tags": "python, algorithm, python-3.x, sorting, mergesort",
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