text stringlengths 49 10.4k | source dict |
|---|---|
electromagnetism, lagrangian-formalism, conservation-laws
Title: Current conservation from Euler-Lagrange equations for $A_\mu$ I need to verify the 4-current conservation from the Euler-Lagrange equations for $A^\mu$.
The Lagrangian defining electromagnetic field is:
$$L=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}-j^{\mu}A_\nu... | {
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### D — Denominatornumeric array
Denominator, returned as a numeric array. N./D approximates X.
collapse all
### Algorithms
Even though all floating-point numbers are rational numbers, it is sometimes desirable to approximate them by simple rational numbers, which are fractions whose numerator and denominator are s... | {
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"lm_q2_score": 0.8438950947024555,
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"tags": n... |
+3a2x+3ax2 +x urther,F (a+x)4 = (a+x)(a+x)4 = (a+x)(a3 +3a2x+3ax2 +x3) = a4 +(1+3)a3x+(3+3)a2x2 +(3+1)ax3 +x4 = a4 +4a3x+6a2x2 +4ax3 +x4. Depending on how many times you must multiply the same binomial — a value also known as an exponent — the binomial coefficients for that particular exponent are always the same. are ... | {
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"lm_q1_score": 0.9901401441145625,
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"openwebmath_score": 0.7703706622123718,
"tags":... |
Indeed, I disagree with that practice. The notation is used commonly in two different ways (yours, apparently, and mine). That makes it a source of confusion, and I would never recommend someone to use such a thing. I'm not saying you didn't give an answer, but I consider it not to be a useful one. My downvote firmly s... | {
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"lm_q1_score": 0.9805806512500486,
"lm_q1q2_score": 0.8448076932515587,
"lm_q2_score": 0.8615382040983515,
"openwebmath_perplexity": 588.732639416477,
"openwebmath_score": 0.9940757751464844,
"tags... |
algorithm, haskell, functional-programming
[78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92],
[16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57],
[86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58],
[19, 80, 81, 6... | {
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"tags": "algorithm, haskell, functional-programming",
"url": null
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python, object-oriented, python-3.x, file, tkinter
root.mainloop()
Review Concern(s):
My main concern is to code in an easy to read, efficient, and well-structured manner while still learning the language and concepts such as OOP. Feel free to mention the tiniest issue or improvement that comes to your mind, as I am... | {
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streams = VectorPlot[{0, Sign[f[θ, μ]]}, {μ, -2, 2}, {θ, 0, 4 π},
Verifying the behavior of the improper equilibria with NDSolve requires some trickery. Edit: My previous attempt at getting NDSolve to work was wrong, so I removed it.
StreamDensityPlot[{0, Sin[\[Theta]]/(\[Mu] + Cos[\[Theta]])}, {\[Mu], -3,3},{\[Theta]... | {
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"lm_q2_score": 0.8479677506936878,
"openwebmath_perplexity": 2806.0528467806507,
"openwebmath_score": 0.7675282955169678,
"tag... |
solubility, solvents
Title: Solubility in homogenous mixtures of solvents Alcohol and water are miscible. I am coming across some chemicals that are soluble in alcohol and insoluble in water. If I know solubility in two solvents separately, is solubility in a mixture of the two always straightforward, or are there c... | {
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"tags": "solubility, solvents",
"url": null
} |
xtion
Title: How to access and use skeleton joint coordinates using OpenNI, ASUS Xtion, and ROS?
To develop a person follower robot, I am using ASUS Xtion and OpenNI. To obtain both RGB image and skeleton joints, I am using a skeleton tracker script (https://github.com/Chaos84/skeleton_tracker). Tracker publishes joi... | {
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• thank you for your answer. But I think your first equation corresponds to the $\theta=.5$ case only while I think it should be valid for all values of $0\leq \theta \leq 1$? What do you say? – Frank Moses Feb 28 '18 at 4:20
• Yes you are right, I fixed that. – Piyush Divyanakar Feb 28 '18 at 4:25
• The inequality you... | {
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"ta... |
InterpolatingFunction[{{0., 10.}}, <>]
Finally, a plot:
Plot[sol[t], {t, 0, 10}] | {
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"lm_q2_score": 0.8705972650509008,
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"openwebmath_score": 0.4648638963699341,
"tag... |
-
If we round c to d, then c approximately equals d. If d also consists of an integer, then c lies closer to d than any other integer i. In other words for all integers i such that i does not equal d, ABS(ci-)>ABS(cd-), where ABS(ci-) indicates the number by which c and i differ by (the absolute value of the differenc... | {
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"lm_q1_score": 0.974821163419856,
"lm_q1q2_score": 0.8520690000927736,
"lm_q2_score": 0.8740772482857833,
"openwebmath_perplexity": 432.2086184790631,
"openwebmath_score": 0.8157265186309814,
"tags... |
ros, force, kdl, pr2
Can anyone advise me on how do I go about measuring the force of the tip of pr2's arm using the Jacobian function in KDL? Thank you in advance.
EDIT: Thanks Peter, I appreciate any help as I am not very familiar with coding or robotics. Anyway, I realised I made a very silly mistake. The code shou... | {
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you have an for. Probably because I was only having two disconnected graph adjacency matrix in my adjacency matrix of a directed graph about. Set { v1, v2, v3, the graph for n2 elements for a graph is defined! Recommended for you the primary ways to create a boolean array, mark the … which the. Such matrix representati... | {
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"lm_q1q2_score": 0.8076268219486424,
"lm_q2_score": 0.8652240843146881,
"openwebmath_perplexity": 391.1555318715774,
"openwebmath_score": 0.5457404255867004,
"tags": null,
... |
Find an injection $M_1 \to M_2$ of $A$-modules such that $M_1\otimes N \to M_2 \otimes N$ is not injective in the following cases: \begin{enumerate} \item $A = k[x, y]$ and $N = (x, y) \subset A$. (Here and below $k$ is a field.) \item $A = k[x, y]$ and $N = A/(x, y)$. \end{enumerate} \end{exercise} \begin{exercise} \l... | {
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"lm_q1_score": 0.9873750529474512,
"lm_q1q2_score": 0.8026049065130083,
"lm_q2_score": 0.8128673133042217,
"openwebmath_perplexity": 113.17356744429497,
"openwebmath_score": 0.9986513257026672,
"tags"... |
javascript, sass
Title: Simple modals in vanilla JS Recently I was looking for some really simple modal/popup solution in vanilla JS, but nothing popped. So I wrote mine component. It works great so far, have all the options I need, but I don't know if I can improve the code itself.
JS:
/* A very simple modal componen... | {
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education
One reasonably good challenge presents a sentence encoded with a Caesar cipher, then asks the students to decode it. The person running the station give a short explanation of what a Caesar cipher is, then leave the teams to decode the text. Time penalties are awarded based on correctness -- each incorrect c... | {
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python, beginner, python-3.x, tic-tac-toe
elif compchoice == 3 and coords[0][2] == "[3]":
coords[0][2] = "[O]"
goodroll = 'yes'
elif compchoice == 4 and coords[1][0] == "[4]":
coords[1][0] = "[O]"
goodroll = 'yes'
elif compchoice == 5 and coords[1][1] =... | {
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"tags": "python, beginner, python-3.x, tic-tac-toe",
"url": null
} |
quantum-state, textbook-and-exercises, terminology-and-notation
Title: Is it wrong to say that $a$ and $b$ are the square roots of the detection probabilities in a qubit state $|\psi \rangle = a|0 \rangle +b|1 \rangle $? Is it wrong to say in $a$ and $b$ are the square roots of the probability of the qubit being in th... | {
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quantum-mechanics, quantum-computer
H^{\otimes 2} \frac{|0\rangle|+\rangle-|1\rangle|+\rangle}{\sqrt{2}}
\\& =
H^{\otimes 2} \frac{|0\rangle-|1\rangle}{\sqrt{2}}|+\rangle
\\ & = |10\rangle.
\end{align}
As such, under the standard conventions, the equality is false.
On the other hand, it is true that
$$
H^{\otimes ... | {
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fourier-transform, conformal-field-theory, dimensional-analysis, scaling
Title: Conformal primaries in momentum space Consider the Fourier transform of a conformal primary $O$
$$\tilde{O}(k) = \int d^dx e^{ik\cdot x} O(x)$$
Now consider the transformation of the momenta $k \to \lambda k$, so that the above reads
$$\ti... | {
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ros, lidar
But when I run my rosbag,op_motion_predictor doesn't show the topic"/predicted_trajectories_rviz".
the error info is "scale.y and scale.z of LINE_LIST or LINE_STRIP are ignored.
Points should not be empty for specified marker type.
At least two points are required for a LINE_STRIP marker".
Looks like predic... | {
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(iii) y(1 + log x) $$\frac{d x}{d y}$$ – x log x = 0, when x = e, y = e2.
Solution:
∴ from (1), the general solution is
log |x log x| – log |y| = log c, where c1 = log c
∴ log |$$\frac{x \log x}{y}$$| = log c
∴ $$\frac{x \log x}{y}$$ = c
∴ x log x = cy
This is the general solution.
Now, y = e2, when x = e
e log e = ce... | {
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"openwebmath_score": 0.742913544178... |
what is subgroup
Prove that: (2cos&+1)(2cos&-1)(2cos2&-1)=2cos4&+1
e power cos hyperbolic (x+iy)
10y
Michael
tan hyperbolic inverse (x+iy)=alpha +i bita
prove that cos(π/6-a)*cos(π/3+b)-sin(π/6-a)*sin(π/3+b)=sin(a-b)
why {2kπ} union {kπ}={kπ}?
why is {2kπ} union {kπ}={kπ}? when k belong to integer
Huy
if 9 sin theta + ... | {
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"openwebmath_score": 0.9361161589622498,
"tags": nu... |
laser, laboratory-safety
Then, the spotsize $s$ of a perfectly focussed, unaberrated beam is of the order of $\frac{\lambda}{\eta}$. For maximum efficiency, you need the beam to focus to a point of diameter smaller than the heat diffusion length. Note that this implies a minimum numerical aperture. Then you can calcul... | {
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"tags": "laser, laboratory-safety",
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python, database, data-retrieval, cheminformatics
Title: Sql query slow on Chembl postgres database Doing complex sql query on Chembl database and it takes 40 minutes on the machine from lab.
I was thinking using dask, extract each table and export to parquet, when do the data processing .
Is this a good approach or t... | {
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"tags": "python, database, data-retrieval, cheminformatics",
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newtonian-mechanics, energy-conservation, reversibility, perpetual-motion
Consider weight-lifting machines—machines which have the property that they lift one weight by lowering another. Let us also make a hypothesis: that there is no such thing as perpetual motion with these weight-lifting machines. (In fact, that th... | {
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"url... |
Finally, we want to simplify each piecewise condition with Reduce:
ReducePiecewise[expr_, x_, assum_: True] :=
FullSimplify[
expr /. HoldPattern[Piecewise][l_, r___] :>
Piecewise[Transpose[{#1, Reduce[# && assum, x]& /@ #2}& @@ Transpose[l]], r],
assum
]
ReducePiecewise[rigor, x, 0 < x < 1]
-(-1 + x) x
## In summa... | {
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"lm_q2_score": 0.822189134878876,
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"openwebmath_score": 0.513802707195282,
"tags... |
complexity-theory, time-complexity, reductions, polynomial-time
Is it required that A is non-trivial as stated on wikipedia? Some places seem to suggest that the requirement is only B has to be non-trivial, and A doesn't matter if trivial or non-trivial. Based on this question.
Can someone provide me a concrete exampl... | {
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"tags": "complexity-theory, time-complexity, reductions, polynomial-time",
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functional-programming, matrix, f#
Title: Probabilistic Matrix Inspection - Suggested by a paper, implemented by me I have read this paper and I actually found it interesting.
This is an attempt to implement the proposed algorithm. I would like to know:
Is my algorithm correct by what is discribed in the paper?
Is my... | {
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ros, household-objects-database
To integrate the database with tabletop object detector, you should create a launch file(in this example, I created a package named ricky_tabletop_object_detector, I put my_server.yaml in ricky_tabletop_object_detector/yaml/, and put this launch file in ricky_tabletop_object_detector/la... | {
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"openwebmath_score": null,
"tags": "ros, household-objects-database",
"url": null
} |
javascript, performance, algorithm, tree, json
{"d":4,"t":"div","a":{"class":"bx-1 s10 fw-6 ml-5 di-1"}},
{"d":4,"t":"div","a":{"class":"tg-up"}}, | {
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} |
structural-engineering, structural-analysis, structures, moments
All we have to do is start by pretending the beam only has one of those supports (let's say it's the one to the left). We can then calculate the result for this cantilever beam, which is easy enough.
But a cantilever beam dips and bends all the way to it... | {
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"tags": "structural-engineering, structural-analysis, structures, moments",
"url": nul... |
homework-and-exercises, electromagnetism, special-relativity, energy-conservation
Title: Energy conserved... or not? Confused! I am confused. Could someone kindly explain what's going on in this question?
A particle of mass $m$ and charge $e$ moves in the $x,y-$ plane. There is a constant magnetic field $B$ that poin... | {
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ros2, rosdep
File "/usr/local/lib/python3.10/dist-packages/adafruit_platformdetect/chip.py", line 90, in id
import hid
ModuleNotFoundError: No module named 'hid'
[ros2run]: Process exited with failure 1 I should have added --as-root pip:false as an extra argument to rosdep. This is described at github. | {
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integration quiz with answers. MATH 105 921 Solutions to Integration Exercises Solution: Using direct substitution with u= sinz, and du= coszdz, when z= 0, then u= 0, and when z= ˇ 3, u= p 3 2. We could not evaluate the integral until it had only the one variable $$u$$. Integration by substitution Introduction Theorem ... | {
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"openwebmath_score": 0.9461153745651245,
... |
sun
Title: Is there an instance where the sun sets or rises partly, then return back? I am reading Longest Sunset from XKCD. At first, I've thought that he mentions these phenomena just for fun, but it turns out to me that it might happens, based on the level of somewhat seriousness that I perceive from his writing. H... | {
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string-theory
\end{align}
The first thing we note is that because of momentum conservation and mass-shell condition
\begin{align}
0= k_1^2 =(-k_2-k_3)^2 = k_2^2+k_3^2 + 2 k_1\cdot k_2 \Rightarrow k_1\cdot k_2 =0
\end{align}
We now add the ghost contribution $\langle ccc\rangle = C_{D_2}^g y_{12} y_{13} y_{23}$, the po... | {
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quantum-gate, quantum-state, unitarity
Title: Can we always find a unitary operation connecting qubit states with given eigendecompositions? Consider the density matrices $\rho_0 = |0 \rangle \langle 0|$ and $\rho_1 = |1 \rangle \langle 1|$. Let $\{p_1, p_2\}$, and $\{p_3, p_4\}$ be two probability distributions, that... | {
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Claim 3: $f(2n) = 25 \cdot10^{2n - 2} + 10^{n}$.
Proof of Claim 3: Because of claim 2, $x_n$ is $5 \cdot 10^{2n-1} + 10^n$. Note that $g_n(x_n)$ and $g_n(x_n - 1)$ are the first numbers written that will differ by at least 2. Thus, $f(2n) = g_n(x_n - 1) + 1 = 25 \cdot 10^{2n-2} + 10^n$$\blacksquare$
Thus, $f(2) + f(4... | {
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... |
imu, navigation, gps, robot-localization
Originally posted by EdCherie on ROS Answers with karma: 33 on 2017-03-01
Post score: 0
Original comments
Comment by Tom Moore on 2017-03-01:
Please post sample input messages from all sensors.
Comment by EdCherie on 2017-03-06:
Updated the initial question
Comment by EdCherie... | {
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ros, ros-kinetic, image-view, image, filesystem
started roslaunch server http://nils-ros:35825/
SUMMARY
========
PARAMETERS
* /mix_image/camera_info_url: file:////home/nil...
* /mix_image/flip_horizontal: False
* /mix_image/flip_vertical: False
* /mix_image/frame_id: my_camera
* /mix_image/publish_rate: 10
* /... | {
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"tags": "ros, ros-kinetic, image-view, image, filesystem",
"url": null
} |
gazebo, simulation, turtlebot, turtlebot-simulator, turtlebot-gazebo
e = sqrt(xx + yy);
//Υπολογισμός γραμμικής ταχύτητας - u
u2 = u1 + (egcsa);
//Υπολογισμός γωνιακής ταχύτητας - ω
w2 = w1 + (ka + ((gcsasna(a + h*th))/a));
//fprintf(file,"\nDx = %f",x);
//fprintf(file,"\nDy = %f",y);
//fprintf(file,"\nDf = %f",f);
//... | {
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"tags": "gazebo, simulation, turtlebot, turtlebot-simulator, turtlebot-gazebo",
"url": nu... |
beginner, io, go
Title: Golang Video stream Input/Output multiplexing I wrote a camera client that will read a video stream and write to a player for playback.
I have some basic keyboard controls for recording the stream.
I coded the client with a single video stream in mind.
I refactored the code so I can have playb... | {
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"tags": "beginner, io, go",
"url": null
} |
classification, nlp, clustering, unsupervised-learning, sentiment-analysis
Title: Sentiment analysis of tweets (Train model on a labelled dataset and use on some other unlabelled data) I have a huge amount of tweets on a particular topic say 'ABC' and the data is not labelled. I want to perform multi-class sentiment a... | {
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"tags": "classification, nlp, clustering, unsupervised-learning, sentiment-analysis",
... |
It remains to show ${\cap_{k=1}^\infty C_k}$ is nonempty. Assume it is empty, then ${\cup_{k=1}^\infty (X \setminus C_k ) = X \setminus (\cap_{k=1}^\infty C_k) = X}$. Since metric space is Hausdorff, ${C_k}$ is closed for all ${k}$ and ${\{ X \setminus C_k \}}$ is an open cover for ${C_1}$. Since ${C_1}$ is compact, th... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9766692284751636,
"lm_q1q2_score": 0.8007645939676922,
"lm_q2_score": 0.8198933381139646,
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"openwebmath_score": 0.9738972783088684,
"tags":... |
moveit
Originally posted by v4hn with karma: 2950 on 2017-02-01
This answer was ACCEPTED on the original site
Post score: 0
Original comments
Comment by Rahndall on 2017-02-01:
Actually, it becomes a problem since RViz seems stuck waiting for this function, and no planning is allowed
Comment by v4hn on 2017-02-01:
Ah... | {
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c#, linq, recursion
public class RecursiveObject
{
public int Id { get; set; }
public int ParentId { get; set; }
public List<RecursiveObject> Children { get; set; }
}
I am aware of some Linq alternatives to solve the foreach loop but that does hardly not change the approach of this.
private static List<Re... | {
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"tags": "c#, linq, recursion",
"url": null
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acoustics, resonance, vibrations
Title: How does a guitar work? Here are four different possible ways:
The plucked string vibrates longitudinally, vibrating the air around it. This vibrating air then causes the air inside the sound box to vibrate also, which vibrates the outside air also.
The plucked string vibrates ... | {
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"tags": "acoustics, resonance, vibrations",
"url": null
} |
fluid-dynamics, pressure
Title: Can atmospheric pressure hinder a pump to lift water? I have this small submersible pump that ironically runs but not lift water when it is fully submerged. The only two ways I can make it lift water the way it's intended to run is to submerge the pump only halfway its intake and to cov... | {
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"tags": "fluid-dynamics, pressure",
"url": null
} |
doppler-effect
$$c*(HiFreq - LoFreq) = V*(HiFreq + LoFreq)$$ and finally.
$$V = \frac{(HiFreq - LoFreq)}{(HiFreq + LoFreq)} * c$$ | {
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"tags": "doppler-effect",
"url": null
} |
quaternion, ros-groovy, transform
Title: TF not compiling under Groovy?
I am trying to implement some TF under groovy, but ran into compilation errors quickly. I just installed a fresh Ubuntu 12.04 with ROS Groovy. To be sure, I tried to implement the tutorial (http://wiki.ros.org/tf/Tutorials/Introduction%20to%20tf)... | {
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"tags": "quaternion, ros-groovy, transform",
"url": null
} |
ros, ros-melodic, rosdep, wstool
Title: How to depend on apt install that requires a source list file?
I'm looking for the "ros correct" way (wstool or rosdep compatible) way to depend on a debian package that is installed via a addition to the source lists? Here is the dependency I'm trying to add: https://docs.ope... | {
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"tags": "ros, ros-melodic, rosdep, wstool",
"url": null
} |
quantum-mechanics, operators, quantum-information, commutator, quantum-states
It is this statement I don't follow. Why is it impossible for an operator which commutes with $R$ to give us the requisite information?
I know that, for any such commuting $A$, since $R$ is nondegenerate we have $A|r_n\rangle = \lambda |r_n\... | {
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"tags": "quantum-mechanics, operators, quantum-information, commutator, quantum-states",
... |
product law for limits the limit law $\lim_{x→a}(f(x)⋅g(x))=\lim_{x→a}f(x)⋅\lim_{x→a}g(x)=L⋅M \nonumber$
principal unit tangent vector a unit vector tangent to a curve C
principal unit normal vector a vector orthogonal to the unit tangent vector, given by the formula $$\frac{\vecs T′(t)}{‖\vecs T′(t)‖}$$
power series a... | {
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"lm_q2_score": 0.8152324960856175,
"openwebmath_perplexity": 141.3882769672332,
"openwebmath_score": 0.9248999357223511,
"ta... |
c++, c++11, mathematics, template
bool operator!=(const DistanceExpression& other) const
{
return !(*this == other);
}
private:
T _data;
};
My new distance function is implemented as such:
template<std::size_t N, typename T>
auto distance(const Point<N, T>& lhs, const Point<N, T>& rhs)
-> Di... | {
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"tags": "c++, c++11, mathematics, template",
"url": null
} |
homework-and-exercises, newtonian-mechanics, forces, friction
Title: Ropes and Pulleys - Really unintuitive answer I usually don't want to do this, but please go to this link, the solution is too big to post it here
http://engineering.union.edu/~curreyj/MER-201_files/Exam2_2_26_09_Solution.pdf
And go to page 5 of the... | {
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"tags": "homework-and-exercises, newtonian-mechanics, forces, friction",
"url": null
} |
acceleration, water, speed, distance
Title: Modeling a waterfall I'm modeling a waterfall, the water streams out of a rectangular box with a width of $\text{W}$, a length of $\text{L}$ and a hight of $\text{H}$, so the volume of the water that is streaming from a higher point to the lower point equals $\text{V}_\text{... | {
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"tags": "acceleration, water, speed, distance",
"url": null
} |
assembly, x86, nasm
push r15
call _free
add rsp, 16 ;clear the stack
mov rax, 60 ;SYSCALL_EXIT
mov rdi, 0
syscall
;(first)last argument pused onto the stack must be the amount of bytes
;if successfull then rax will contain pointer to the memory
_mal... | {
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"tags": "assembly, x86, nasm",
"url": null
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# Solve a system of equations
#### anemone
##### MHB POTW Director
Staff member
Solve the following system for real values of $a$ and $b$:
$2^{a^2+b}+2^{a+b^2}=8$
$\sqrt{a}+\sqrt{b}=2$
#### mente oscura
##### Well-known member
Solve the following system for real values of $a$ and $b$:
$2^{a^2+b}+2^{a+b^2}=8$
$\... | {
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"openwebmath_score": 0.9368056058883667,
"ta... |
The operations $+$, $*$, and so on are all carried out by appropriate manipulation of trigonometric representations. Here we compute and plot the maximum, minimum, and roots of $f$:
[maxval, maxpos] = max(f);
[minval, minpos] = min(f);
r = roots(f);
plot(f, LW, lw), grid on, hold on
plot(r, f(r), '.r', MS, 18)
plot(ma... | {
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"lm_q1_score": 0.9911526449170697,
"lm_q1q2_score": 0.8237896364075763,
"lm_q2_score": 0.831143054132195,
"openwebmath_perplexity": 1450.5721992579056,
"openwebmath_score": 0.911601722240448,
"tags":... |
the-sun, declination, sun-rays
Title: Is there a difference between the solar elevation angle and sun declination? I need to use the sunrise equation but one of the variables is the sun declination. On the other hand, I have the values for solar elevation angle that I need. Are they the same thing? Elevation and Decli... | {
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"tags": "the-sun, declination, sun-rays",
"url": null
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# Calculating the solar power hitting Earth
I'm trying to calculate the amount of power from the sun hitting the earth, but I am getting a number which is off by a factor of ~4.
I calculate the "area" of the earth, as seen from the sun, and then divide that by the surface area of a sphere of radius 1 AU, to get the p... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9658995733060719,
"lm_q1q2_score": 0.8321593820085315,
"lm_q2_score": 0.8615382023207901,
"openwebmath_perplexity": 375.91630737161677,
"openwebmath_score": 0.8320827484130859,
"ta... |
c#, multithreading, reinventing-the-wheel, thread-safety
/// <summary>
/// Sets the index of the specified child control in the collection to the specified index value.
/// </summary>
/// <param name="child">The child <see cref="Control"/> to search for.</param>
/// <par... | {
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"tags": "c#, multithreading, reinventing-the-wheel, thread-safety",
"url": null
} |
dct, dft
As you can see, transformed image is represented in DCT by magnitude spectrum with no problem. In a more compact and denser way, and look at the magnitude of coefficients. It is bigger than two times of DFT. DFT is symmetric, you could just divide it into two. One part is redundant. And one more thing, DCT ca... | {
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"openwebmath_score": null,
"tags": "dct, dft",
"url": null
} |
quantum-field-theory, lagrangian-formalism, path-integral
Title: Is the physics of a Quantum Field Theory dependent on the choice of Lagrangian? A Quantum Field Theory can be obtained by quantising a Classical Field Theory through to a procedure. The procedure involves starting with a set of equations of motion that ... | {
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"openwebmath_perplexity": null,
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"tags": "quantum-field-theory, lagrangian-formalism, path-integral",
"url": null
} |
electrons, atoms, neutrons, protons
Title: Why are atomic nuclei protons and neutrons, and not electrons and neutrons or protons and neutrons Wouldn't proton-electron nuclei be more stable since they attract each other and aren't just neutral to each other? What is the reason for this? I tried searching for an answer ... | {
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"tags": "electrons, atoms, neutrons, protons",
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So we get $\mathbf{1} \cdot \mathbf{s} \leq \sqrt{N}\sqrt{M + \mathbf{1}\cdot \mathbf{s}}$.
So we have $A \leq \sqrt{N} \sqrt{M+A}$. Squaring we get $A^2 \leq N (M+A)$. So we have $(A - N)A \leq NM$. Thus $A-N \leq \sqrt{NM}$. Thus $A \leq \sqrt{NM}+N$.
Thus $\sum_k s_k \leq \sqrt{N} \sqrt{N(N-1)} + N \approx N \sqrt... | {
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"lm_q2_score": 0.8479677506936878,
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"openwebmath_score": 0.8934245705604553,
"tag... |
c++, object-oriented, design-patterns
Be consistent
I see different variable names for exactly the same thing, like volatilityPrc, vol and v. I see both float and double being used, if the result of GetPrice() is going to be a float, why use doubles? Why does OptionPriceDollars have a default constructor but the other... | {
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Otherwise on the Prime you can also use this one liner that you can define as a user function to reverse the number N:
EXPR(CHAR(REVERSE(ASC(STRING(N)))))
It works with integers and also with positive decimal numbers, for example for 67.28 it returns 82.76
To reverse both positive and negative numbers you need:
SIG... | {
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electrostatics, charge, electromagnetic-induction
$$
As you can see, the induced charge will be equal to the inducing in magnitude if the latter is infinitely close to the surface of the sphere.
The true charge of the sphere will be equal to this image charge. Why? Due to the Gauss' law. It states that
$$
\oint_{S}\ba... | {
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Then each tangency gives a Pythagorean relation:
\begin{align} e^2+u^2 &= (e+f)^2\tag{1} \\ e^2+v^2 &= (e+h)^2 \tag{2} \\ f^2+(2e-g)^2 &= (f+g)^2 \tag{3} \\ g^2+(u+f-v)^2 &= (g+h)^2 \tag{4} \\ (u-v)^2 + (2e)^2 &= (f+h)^2 \tag{5} \end{align}
It's possible to chug through the system eliminating variables one by one, bu... | {
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called the interval of convergence). If a power series converges absolutely for all , then its radius of convergence is said to be and the interval of convergence is. and now it can be rewritten as a basic geometric series, the sum of: [16x/75]^k with the ratio as (16x)/75 and the starting value (since you said k=1 to ... | {
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\displaystyle \begin{aligned} {\rm Cov}(X,X)_{jk} &={\rm Cov}(X_j,X_k)\\ &={\mathbb E}[X_jX_k]-\mu_j\mu_k. \end{aligned}
Similarly, expressing this with matrix algebra,
\displaystyle \begin{aligned} {\rm Cov}(X,X) &={\mathbb E}[(X-\mu)(X^T-\mu^T)]\\ &={\mathbb E}[XX^T]-\mu\mu^T. \end{aligned}
For vectors ${x\in{\ma... | {
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i also have another question, what happens if a particular $$A_n$$ is finite?
Last edited: Jul 15, 2007
13. Jul 15, 2007
### CompuChip
Yeah, so for each n we can assign a natural number to each element from $$A_n$$, and in the end, have neither elements of $$A_n$$ nor natural numbers "left" (that is, there is a bije... | {
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optics, reflection, refraction, geometric-optics, dispersion
Title: A Rainbow Paradox I was studying the phenomena of the formation of a rainbow. In my book, the following diagram is given:
So, the rays at the red end of the spectrum make a larger angle with the incident ray than the rays at the violet end of the spe... | {
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• But in this problem $a^2$ is not necessarily the largest square that divides $n$. – Lone Learner May 2 '12 at 19:25
• @LoneLearner But my proof in the linked thread doesn't use that. Rather, it uses only that $\rm\:c\:$ is squarefree (necessarily true when its cofactor $\rm\:b^2\:$ is a maximal square divisor of $\rm... | {
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python, cryptography, blockchain
if isinstance(stamp, str) == False:
raise Exception("")
self.stamp_str = stamp
This should at least raise RuntimeError("expected a string"). And in reality, you shouldn't manually raise an exception at all; any operation that requires a string will eventually raise TypeErr... | {
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orbital-motion
Title: Universal formulation of Kepler problem for the hyperbolic case I'm trying to derive the universal formulation of the time-of-flight equation that appears in the Kepler problem (following Bate Fundamentals of astrodynamics and Vallado Fundamentals of astrodynamics and applications), and I don't s... | {
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• First of all: Thanks a lot, that really helped! Especially your last point provides a nice view on independence, which I haven't realized before. May 21 at 16:22
• And a quick follow-up question: We could generalize the result, so that in the same setting for measurable functions $g,h$ and $$g(a) = \mathbb{E}(h(X,a))... | {
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rviz, urdf, ros-kinetic, collada, dae
The error that i get using "rosrun rviz rviz" while running my C++ Node is:
Could not load resource [file://models/v1-01/model.dae]: Unable to open file "file://models/v1-01/model.dae".
Thank you guys for your support!
Greetings,
Alex
Originally posted by AlexROS on ROS Answers w... | {
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# Complex roots
Recently I was looking back over some of my previous posts to see if I could improve them. While doing this I noticed something; I haven't done complex roots yet. This surprised me since it's the easiest to calculate by far (at least from what I've found).
So let's get on with it.
Let: $z$ be a compl... | {
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control, robotic-arm, kalman-filter, matlab, noise
Why not this state space form:
$$
\begin{bmatrix} \dot{x} \\ \\\dot{\hat{x}} \end{bmatrix} =\begin{bmatrix} A & -BL \\ KC & [A-BL-KC] \end{bmatrix} \begin{bmatrix} x\\ \hat{x} \end{bmatrix}+\begin{bmatrix} B & I & 0\\ B & 0 & K \end{bmatrix}\begin{bmatrix} r\\ d\\ n ... | {
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signal-analysis, wavelet, continuous-signals
Title: What are the advantages and disadvantages of the Ridgelet transform? I used the continuous wavelet transform (CWT) to analyze the behavior of a 1-D smooth signal (extracting its modal property, damping and frequency components) in my research. Now someone asked:
Why... | {
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Notice that:
$$\color{Blue}{a=\sqrt{7\sqrt{2\sqrt{7\sqrt{2\sqrt{...}}}}}} \ \ \ ;$$ $$\color{Red}{b=}\sqrt{\color{Red}{2}\color{Blue}{\sqrt{7\sqrt{2\sqrt{7\sqrt{...}}}}}} \ \ \ ;$$
which implies that:
$$\color{Red}{b}=\sqrt{\color{Red}{2}\color{Blue}{a}} \ \ \ ;$$
similarly we have:
$$a=\sqrt{7b} \ \ \ .$$
So we ... | {
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## Beta Prior
• It is convenient (but not necessary) to use a Beta distribution as a model for the prior.
• We will later see the Beta distribution is conjugate to the Binomial distribution.
• We will say $\theta \sim \text{Beta}(a,b),$ with density $p(\theta) = \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)} \theta^{a-1} (1 -... | {
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"openwebmath_score": 0.9804865121841431,
"tags": null,
... |
machine-learning, combinatorial-games, go
Title: What is the significance of move 37? (to a non go player) I have seen (and googled) information for Game 2, Move 37 in the AlphaGo vs. Lee Sedol match
However it is difficult to find information concerning this move that doesn't rely on an understanding of go (which I d... | {
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"tags": "machine-learning, combinatorial-games, go",
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ros
Title: I cannot control my fetch robot
Hi all. I am trying to move a fetch robot go straigh. For example my robot spawn in position (0,0). it cannot go straight to (-3,0) or (-3, -3). i see the code here: https://github.com/fetchrobotics/fetch_gazebo/blob/gazebo2/fetch_gazebo_demo/scripts/demo.py
I don't understa... | {
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u, v& was adjacent edges. Substituting this back into our formula for the volume of a parallelepiped we get that: We note that this formula gives up the absolute value of the scalar triple product between the vectors. Notice that we Notify administrators if there is objectionable content in this page. rev 2021.1.20.383... | {
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"lm_q2_score": 0.8519528000888386,
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"openwebmath_score": 0.9352316856384277,
"tags": null,
... |
proof-techniques, np, proof-assistants
Title: Why proving the solution of a problem is polynomial time is sufficient enough to say that it is a NP prolbem? Why proving that we can verify the solution of a problem is polynomial time is sufficient enough to say that the problem is nondeterministic polynomial time? Pleas... | {
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"tags": "proof-techniques, np, proof-assistants",
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php, object-oriented, security, mysqli
Title: Updating necessary data using just one function My objective is to update necessary data using one function instead of having different functions to update different fields. So, I've created one and I think this is not really elegant, efficient or secure. I would seriously... | {
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regular-languages, pumping-lemma
I don't think I did, but maybe, did I make any mistake?
Is there a counter-example word to the pumping lemma for $L_4$ when $|\Sigma| \geqslant 3$?
Do you know of any simpler language that is a counter-example to the converse of the pumping lemma (not regular but verifying the conclusi... | {
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"tags": "regular-languages, pumping-lemma",
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thermodynamics, energy
Title: Understanding Gibbs free energy I want to verify a thought I had about Gibbs free energy. In some ways, I'm actually wondering why we are using enthalpy instead of the internal energy $U$. Right now, I'm thinking that enthalpy is mostly useful because reactions are done at constant pressu... | {
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"tags": "thermodynamics, energy",
"url": null
} |
newtonian-mechanics, momentum, energy-conservation, conservation-laws, collision
Title: Conservation of momentum + conservation of energy + Newton's second law = Contradiction? When a body with a mass of 1 kg moves at constant velocity of 1 m/s and collide (elastic collision) with a body with the same mass that's at r... | {
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ros, roslaunch, namespace
Original comments
Comment by leblanc_kevin on 2011-11-27:
You may be right, especially if (as I suspect) one can't access absolute/parent namespaces. As I said, for now I'm using relative namespaces for topics. But if roslaunch support for namespaces were flexible enough, other approaches (... | {
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"tags": "ros, roslaunch, namespace",
"url": null
} |
coordination-compounds, electronic-configuration, molecular-structure
Title: How many electrons are around the platinum in an ethenetriplatinate complex?
In $\ce{[Pt3(C2H4)]-}$, how many electrons are there around platinum? | {
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classification, shape-analysis
Title: Classifying 2D shapes by the smoothness of their boundaries I'm doing image analysis, and I want to classify smooth objects (has smooth boundaries) from non-smooth objects (has zigzag-like boundaries). Which feature should be fed into ML framework? What are some popular techniques... | {
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"tags": "classification, shape-analysis",
"url": null
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ros, moveit, planning-scene
planning_scene.world.collision_objects.clear();
planning_scene.world.collision_objects.push_back(remove_object); //This step removes the object from the world
planning_scene.robot_state.attached_collision_objects.push_back(attached_object); //This step attaches the object to the robot... | {
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"url": null
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Thus, if ${G}$ has Kazhdan property (T), then one can find at least one compact set ${S}$ and some ${\epsilon>0}$ with the property that for every representation unitary ${\rho: G \rightarrow U(H)}$ with no non-trivial invariant vectors, and every ${v \in H}$, one can find ${s \in S}$ such that ${\| \rho(s) v - v \|_H ... | {
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• Wow, thank you for this example! It's a very simple function yet it reflects the ideas on why the Taylor series doesn't equal the function. One question though: in your example it is clear that the derivatives do not exist at $x=0$, and I can see how this acts as a "barrier". However, in the example proposed by @Huma... | {
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"lm_q2_score": 0.822189134878876,
"openwebmath_perplexity": 261.77182920690467,
"openwebmath_score": 0.8931723833084106,
"tag... |
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