text stringlengths 1 1.11k | source dict |
|---|---|
organic-chemistry, reaction-mechanism, aromatic-compounds, carbocation
Then the reaction follows analogously to the pathway you deduced for the 6 membered ring: First a π to atomic orbital interaction between the aromatic ring and the tertiary carbocation, which I believe to be the Rate Determining Step since it break... | {
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"url"... |
performance, haskell, file
Other general comments on the coding style or practice is also welcome. I think you've missed the forest for the trees. While the origin of your list might be IO, there's no need to carry values around inside the IO monad just because that's where you found them.
Write your functions as thou... | {
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"tags": "performance, haskell, file",
"url": null
} |
fluid-dynamics, pressure, fluid-statics, flow, bernoulli-equation
Can some one explain with equations? (please also describe symbols used.)
Note:
I see that this can be partly simplified to "bottle with two holes" problem (related paper ) It is clear that the water tap works by regulating the air supply through bubbl... | {
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"tags": "fluid-dynamics, pressure, fluid-statics, flow, bernoulli-equation",
"url": null... |
to be mutually! Question is not orthogonal with are eigenvectors always orthogonal of the eigenfunctions have the same eigenvalue? Then, our proof does work. Was constructed as a running example, we will take the matrix is symmetric, and Let... And unit circle are eigenvectors always orthogonal the eigenvalues for eige... | {
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"lm_q2_score": 0.8354835432479661,
"openwebmath_perplexity": 630.5071021837142,
"openwebmath_score": 0.8961015939712524,
"tag... |
Substitute Form 3520-a, Maharani College Second Cut Off List 2020, Corian Or Quartz For Bathroom, Clusters Of Light-gathering Pigments In A Photosystem, Cheap Marine Setup, | {
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"id": null,
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"lm_q1_score": 0.9465966762263736,
"lm_q1q2_score": 0.8190182424032914,
"lm_q2_score": 0.8652240843146881,
"openwebmath_perplexity": 1160.5609386310566,
"openwebmath_score": 0.5272994637489319,
"tags"... |
immunology
Title: How does your body ultimately recover from a cold? Is it the eradication of the virus (assuming rhinovirus) by white blood cells? Or does your body somehow adapt to presence of the virus? Great question.
Rhino Virus
For the rhinovirus in particular, it is eradicated.
Integrase
However for some of the... | {
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"openwebmath_score": null,
"tags": "immunology",
"url": null
} |
organic-chemistry, reaction-mechanism, molecular-structure, alcohols
Intermediates 2, 3, and 4 are tertiary carbocations with possibility to form both Zaitsev and Hofmann products. In one glance, one might think all would give favorable Zaitsev products under the conditions. However, in reality, they have given almost... | {
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"tags": "organic-chemistry, reaction-mechanism, molecular-structure, alcohols",
"url": ... |
Problem 3. Let $\{a_n\},\{b_n\}$ be the sequences defined in Problem 1 and Problem 2, respectively. It is clear that $b_n=a_n+1$ and so since, by Problem 2, $\{b_n\}$ satisfies the recurrence relation $b_{n+1}=b_n+nb_{n-1},$ for all $n \ge 2,$ the sequence $\{a_n\}$ satisfies
$a_{n+1}=a_n+na_{n-1}+n \ \ \ \ \ \ \ \ \ ... | {
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"openwebmath_score": 0.969171941280365,
"tags": n... |
php, strings, palindrome
For example:
function isPalindrome($text) {
$length = strlen($text);
for ($i = 0; $i < $length / 2; $i++) {
if ($text[$i] != $text[$length - 1 - $i]) {
return false;
}
}
return true;
}
function test_isPalindrome($text) {
printf("isPalindrome(%s)... | {
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} |
The paper of Anning and Erdös addressed the case that all the distances between two points in ${S}$ were integer rather than rational in the affirmative.
The Erdös-Ulam problem remains open; it was discussed recently over at Gödel’s lost letter. It is in fact likely (as we shall see below) that the set ${S}$ in the ab... | {
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"lm_q1_score": 0.9905874104123901,
"lm_q1q2_score": 0.8075590360644194,
"lm_q2_score": 0.8152324848629214,
"openwebmath_perplexity": 4622.61496713103,
"openwebmath_score": 1.0000090599060059,
"tags": n... |
molecular-genetics
In outline I understand the idea of the DNA construct but wonder physically how the stem cell initially acquires the knock-in construct.
Thanks for any enlightenment.
Edit: I see that there are several ways to do this and that the paper's "Materials and Methods" section focuses on the molecular ... | {
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"openwebmath_score": null,
"tags": "molecular-genetics",
"url": null
} |
quantum-algorithms, deutsch-jozsa-algorithm
Title: Probability estimate in classical Deutsch-Jozsa problem I have already posed the question on Math SE but I hope that people from QC community can help. I am starting studying QC, but first, I want to understand the classical view of algorithms. So in the following my ... | {
"domain": "quantumcomputing.stackexchange",
"id": 1098,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "quantum-algorithms, deutsch-jozsa-algorithm",
"url": null
} |
complexity-theory, partitions
Let $S$ be a set for which we seek a subset whose sum is $k$. Without loss of generality, we can assume that $\Sigma S \le 2k$ (because a solution for $k' = \Sigma S - k$ leads directly to a solution for $k$ using the set difference from $S$.) If $\Sigma S = 2k$ then a solution to the mul... | {
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"openwebmath_score": null,
"tags": "complexity-theory, partitions",
"url": null
} |
If you think your function is a series of sines, you could write a Fourier series expansion, and perform a least squares fit on the Fourier series coefficients.
If that fails, you could configure a neural network to give you the result as a series of sines. (Actually, this might not work without pre-multiplying each s... | {
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"lm_q2_score": 0.8267118026095991,
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"openwebmath_score": 0.7313056588172913,
"tags... |
python, python-3.x, numerical-methods
NB_POINTS = 10**5
def in_circle(x, y):
return x**2 + y**2 < 1
def compute_pi(nb_it):
inside_count = sum(1 for _ in range(nb_it) if in_circle(random.random(),random.random()))
return (inside_count / nb_it) * 4
if __name__ == "__main__":
print(compute_pi(NB_POINTS... | {
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"tags": "python, python-3.x, numerical-methods",
"url": null
} |
catkin-make, roscpp
If it is an external library
find_package( PkgConfig REQUIRED)
pkg_check_modules( mylib REQUIRED mylib )
or
FIND_LIBRARY(mylib_LIBRARIES mylib /path/to/lib)
then link the library to your node
add_executable(mynode src/mynode.cpp)
target_link_libraries(mynode ${mylib_LIBRARIES})
hope this helps
... | {
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"url": null
} |
those since you're going to run into this kind of thing when you do real-world work. First, City-Data.com calls this "Distribution of median household income...", but that isn't right and doesn't make sense. This is the distribution of household income, not the distribution of median household income. Each household ha... | {
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"id": null,
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"lm_q1_score": 0.9715639694252315,
"lm_q1q2_score": 0.8352183188300522,
"lm_q2_score": 0.8596637433190939,
"openwebmath_perplexity": 846.8181001137721,
"openwebmath_score": 0.3196735382080078,
"tags": ... |
c1x1 + c2x2 + + cnxn = z Subject to a11x1 + a12x2 + + a1nxn = b1. Learn exactly what happened in this chapter, scene, or section of Inequalities and what it means. What makes it linear is that all our constraints are linear inequalities in our variables. Linear Programming Problem Complete the blending problem from the... | {
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"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9861513873424045,
"lm_q1q2_score": 0.8585407040574128,
"lm_q2_score": 0.8705972684083609,
"openwebmath_perplexity": 606.6295555419894,
"openwebmath_score": 0.5247300267219543,
"... |
arduino, motor, line-following
As the edge is only a line, the behaviour depends more or less only on the distance of the sensors, not the ratio between the distance of the sensors and the thickness of the line. I'd give it a go and see how the behaviour changes.
A ratio that you can change more continuously is that o... | {
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"tags": "arduino, motor, line-following",
"url": null
} |
organic-chemistry, nomenclature
Title: How is 2-hydroxy-ethoxy named? 2-hydroxy-ethoxy is $\ce{HO-CH2-CH2-O}$.
I have a couple of confusions regarding this substituent.
Ethoxy is $\ce{-HO-CH2CH2}$ or $\ce{-OC2H5}$. So the $\ce{HO}$ in the above formula probably belongs to ethoxy.
Hydroxy (prefix for alcohol group) is ... | {
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"url": null
} |
point for any system of linear differential equations with coefficient matrix A because A * o = o. Find the eigenvalues and eigenvectors of the following matrices. To find the eigenvalues and eigenvectors of a matrix: (I first define the matrix given in Problem 19, Section 6. In quantum physics, if you're given an oper... | {
"domain": "osteriarougeroma.it",
"id": null,
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"lm_q1_score": 0.9814534392852384,
"lm_q1q2_score": 0.8262126709314694,
"lm_q2_score": 0.8418256412990657,
"openwebmath_perplexity": 429.17433867820245,
"openwebmath_score": 0.8734235167503357,
"... |
quantum-mechanics, solid-state-physics, quantum-chemistry, density-functional-theory
2. $v$-Representability:
As you've pointed out already, the discussion basically takes places for a fixed interaction $U$ (say e.g. Coulomb interaction) and kinetic energy $T$ (and particle number $N$). For a fixed $U$, we are interes... | {
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One more example, using a very familiar group, the additive group $\mathbb Q$ of rational numbers. For any set $S$ of primes, consider the subgroup of $\mathbb Q$ consisting of those numbers that can be written as fractions (integer over integer) in which all the prime divisors of the denominator belong to $S$. (So, fo... | {
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"lm_q1_score": 0.9838471684931717,
"lm_q1q2_score": 0.8439127159524495,
"lm_q2_score": 0.8577680995361899,
"openwebmath_perplexity": 207.11658112225055,
"openwebmath_score": 0.9011984467506409,
"ta... |
electromagnetism, special-relativity, maxwell-equations
This is because of two things: first, the Lorentz transformations do not affect the components of $E_\parallel$ and $B_\parallel$ in the direction of the boost. Second, the Lorentz transformation is linear on the perpendicular components $\vec{E}_\perp$ and $\v... | {
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"id": 55683,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "electromagnetism, special-relativity, maxwell-equations",
"url": null
} |
swift, networking
}, &context)
SCNetworkReachabilityScheduleWithRunLoop(reachability, CFRunLoopGetMain(), kCFRunLoopCommonModes)
}
}
But I did something different. Instead of having two functions for the network status and the type, I consolidated the functionality of both functions into one. I also add... | {
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"openwebmath_score": null,
"tags": "swift, networking",
"url": null
} |
fft, matlab, frequency-response, frequency-domain
Keep in mind that whatever the information in the negative-frequencies part is, it is needed to be able to convert your signal from the frequency domain back to the time domain, whether it will lie on the right or left of the positive-frequencies part (which you seem t... | {
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"tags": "fft, matlab, frequency-response, frequency-domain",
"url": null
} |
• How would you suggest approaching this, showing that the interior of the closed ball is equal to the open ball? Jan 31, 2018 at 0:15
• ... where a "normed linear space" means over some field with an archimedean valuation. The result is not true e.g. over $p$-adics where that $1-1/n$-construction fails. -- Also, note ... | {
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"lm_q1_score": 0.9820137879323496,
"lm_q1q2_score": 0.860034891538952,
"lm_q2_score": 0.8757869819218865,
"openwebmath_perplexity": 300.67503388137794,
"openwebmath_score": 0.997844398021698,
"tags... |
c#, unit-testing
if (!String.IsNullOrWhiteSpace(path))
{
client.DownloadFile(addr, path);
}
}
}
} Here's how I would do it, with comments!
public void DownloadFile(string host, string file, string user, string pass, string path)
{
// Inverted if-statement to redu... | {
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• That said, this discussion really takes us close to the concept of forecastability, which is a frequent topic in Foresight. If your supermarket sales are well described by a Poisson distribution, there is a lower limit for your forecast's MSE - although we could probably improve on it if we knew all shopping lists in... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551596627306,
"lm_q1q2_score": 0.8482493069529616,
"lm_q2_score": 0.8791467801752451,
"openwebmath_perplexity": 688.1923195249794,
"openwebmath_score": 0.8175317049026489,
"tag... |
python, python-3.x, object-oriented, design-patterns
def get_presigned_url(self, key: str, download_name: str, expiration: int = 10):
"""Generate a presigned URL to share an S3 object
:param key: string
:param download_name: The name of the file when downloaded
:param expiration: Time i... | {
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"tags": "python, python-3.x, object-oriented, design-patterns",
"url": null
} |
Attempt #2
Number of ways of drawing $$1$$ black ball out of $$3$$ black balls $$\binom{3}{1}=3$$ Now, we have to draw two more balls, we can choose those balls from the $$8$$ remaining balls $$\binom{8}{2}=28$$ Since both the above events are associated with each other, by fundamental principle of counting, the number... | {
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"lm_q1_score": 0.9805806518175514,
"lm_q1q2_score": 0.8571032249968491,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 154.21553549898297,
"openwebmath_score": 0.8001653552055359,
"ta... |
HINT $\$ By Wilson's theorem $\$ mod $19\::\ -1 \ \equiv\ 18\:!\ \equiv\ 18\cdot17\cdot 16\:!\ \equiv\ (-1)\ (-2)\cdot 16\:!$
Similarly we have the Wilson reflection formula $\rm\displaystyle\ (p-1-k)\:!\ \equiv\ \frac{(-1)^{k+1}}{k!}\ \ (mod\ p)\:,\$ $\rm\:p\:$ prime
-
@Bill Dubuque: Thank you! – Chan Feb 26 '11 at... | {
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"lm_q2_score": 0.8723473763375643,
"openwebmath_perplexity": 362.9958573576288,
"openwebmath_score": 0.9255539178848267,
"tags... |
particle-physics, experimental-physics, resource-recommendations, scattering-cross-section, data
Title: Where to find cross section data for $e^{-}$ + $p$ $\longrightarrow$ $p$ + $e^{-}$? Where to find cross section data for $e^{-}$ + $p$ $\longrightarrow$ $p$ + $e^{-}$ ?
PDG's cross-section data listing does not incl... | {
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"tags": "particle-physics, experimental-physics, resource-recommendations, scattering-cross-... |
# DeMoivre's Theorem
• December 25th 2010, 06:22 AM
ironz
DeMoivre's Theorem
I need to find the real and imaginary values of z^5, when z = 2-2i
I got r = 2 sqrt(2) and theta = -pi/4
However now I am stuck. I tried to put it into the form r^k e^(i k theta)
and got (2 rt(2)) ^5 * e^(-5pi/4) but then I don't know what... | {
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"openwebmath_perplexity": 512.6315302996521,
"openwebmath_score": 0.8884896636009216,
"tag... |
c++, ros-melodic
pnh.getParam("dominant_axis_mode", dominant_axis_mode_);
pnh.getParam("scale_linear", scale_linear_);
pnh.getParam("scale_angular", scale_angular_);
pnh.getParam("sub_topic", sub_topic_);
pnh.getParam("controller_enabled", controller_enabled_);
twist_sub_ = nh.subscribe(sub_topic_, 10, &Twis... | {
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"openwebmath_score": null,
"tags": "c++, ros-melodic",
"url": null
} |
classical-mechanics
If the object has a mass $m$, then the rate of change of momentum is
$$\dot p = m \dot v = F$$
With $m=\frac43 \pi r^3 \rho_s$, we rewrite as
$$\frac43 \pi r^3 \rho_s \dot v =\frac12\rho v^2 \pi r^2 C_D$$
Rearranging, we get a differential equation for velocity:
$$\frac{dv}{v^2} = \frac{3}{16}\frac... | {
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In the case that , Theorem 7.9 yields the following corollary.
# Corollary.
The dimension of is . Hence in a Jordan canonical form of T, the number of Jordan blocks corresponding to equals the dimension of .
# Proof.
Exercise.
We are now able to devise a method for describing the dot diagram in terms of the rank... | {
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"tags": nul... |
# A useful lemma for proving normality
In this post we discuss a lemma (Lemma 1 below) that is useful for proving normality. In some cases, it is more natural using this lemma to prove that a space is normal than using the definition of normality. The proof of Lemma 1 is not difficult. Yet it simplifies some proofs of... | {
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Proof of the lemma: Since the space is Hausdorff, for every $$y\in Y$$ there is a neighborhood $$U_y$$ of $$y$$ and a neighborhood $$V_y$$ of $$x$$ such that $$U_y\cap V_y=\varnothing$$. We have that $$\bigcup_{y\in Y} V_y$$ is an open cover of Y and since compact, there exists a finite subcover $$V_{y_1},V_{y_2},...V_... | {
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"openwebmath_score": 0.9812362194061279,
"tags... |
quantum-field-theory, quantum-electrodynamics, renormalization
$$ (p'-p)_{\mu} \Gamma^{\mu} (p, p') = S(p')^{-1} - S(p)^{-1}$$
where all momenta are off-shell.
I guess that in QED textbooks authors put these fermions on-shell to discuss quantum corrections to form factors (such as Schwinger's $\alpha/2\pi$ correction... | {
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Example $$\PageIndex{2}$$:
1. Find the exact values of the following.
• $$\arctan(\sqrt{3})$$
• $$\mbox{arccot}(-\sqrt{3})$$
• $$\cot(\mbox{arccot}(-5))$$
• $$\sin\left(\arctan\left(-\frac{3}{4}\right)\right)$$
1. Rewrite the following as algebraic expressions of $$x$$ and state the domain on which the equivalence is ... | {
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"tags":... |
c#, .net, mvp
var convertedList = (from rw in dt.AsEnumerable()
select new Earning()
{
EmployeeID=Convert.ToInt32(rw[0]),
WorkDays= Convert.ToInt32 (rw[2]),
... | {
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} |
algorithm, strings, haskell, complexity
Your base cases should be simpler.
countSubsequences [] _ = 1
countSubsequences _ [] = 0
The recursive case is correct, but could be written more clearly with a more idiomatic convention for parameter names, and using guard clauses.
countSubsequences needle@(n:ns) haystack@(h:h... | {
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"tags": "algorithm, strings, haskell, complexity",
"url": null
} |
organic-chemistry, photochemistry, dye
In molecules with a dipole it may additionally be the case that in a polar solvent the stabilisation due to the solvent polarity brings the initially formed excited state closer to a crossing to a charge-transfer state and this non-radiative process will lower fluorescence yield.... | {
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"tags": "organic-chemistry, photochemistry, dye",
"url": null
} |
java
BigDecimal has a constant for this, BigDecimal.ZERO. Use it here and below.
for (Company c : trn) {
Another unnecessary abbreviation - call the loop variable company.
counter = new BigDecimal("0");
Is this actually a counter? It seems like a summation, and should be called something like totalPrice accordingly.... | {
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ros, openni, rosbag
Title: using openni_camera to play a bag problem
I have a .bag file from a kinect which is writing the topics:
camera/depth/image
camera/rgb/camera_info
camera/rgb/image_color/commpresed
/clock
/rosout
/rosout_agg
/tf
I am trying to use openni nodelet to play it back ( I need to conect the data to... | {
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The way I went about starting this problem is to use the definitions where the definition of the dot product on real numbers is: the sum with k from 1 to n of ak * bk and the definition of matrix multiplication for the entries of Ax would each be of the form: sum from k=1 to k=n of Aik * xk1.
Hopefully that was clear ... | {
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"openwebmath_score": 0.9281216263771057,
"ta... |
error-correction, resource-request, fault-tolerance, state-distillation, magic-states
The website of Earl Campbell has a nice didactic, higher-view introduction on 'magic'. There are some good references in there, too.
If you are a fan of (video) lectures, I can recommend the free-access(!) lecture series on quantum e... | {
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"tags": "error-correction, resource-request, fault-tolerance, state-distillation, m... |
energy
Title: Work done on a car and kinetic energy From the work energy-theorem, we know that:
$$
W_{net}=KE_{final}-KE_{0}
$$
Now, imagine that there is a car that is initially at rest. Eventially,
at some point in time, it attains kinetic energy of 1000$J.$ This
means that the work done on the car is also 1000$J.$ ... | {
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rosjava, android
W/DefaultChannelPipeline( 3678): at java.util.ArrayList.add(ArrayList.java:118)
W/DefaultChannelPipeline( 3678): at org.ros.internal.message.ListField.deserialize(ListField.java:75)
W/DefaultChannelPipeline( 3678): at org.ros.internal.message.DefaultMessageDeserializer.deserialize(DefaultMess... | {
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"tags": "rosjava, android",
"url": null
} |
optimization, performance, c, programming-challenge, bitwise
while (T--) {
scanf("%d %d", &N, &Q);
for (i = 1; i <= N; i++) {
scanf("%d", &x);
root = add_index_to_node(root, i, x, 0);
}
for (i = 0; i < Q; i++) {
scanf("%d %d %d", &a, &p, &q);
result = find_largest(root,... | {
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"tags": "optimization, performance, c, programming-challenge, bitwise",
"url": null
} |
Is there an aproach to calculate it in terms of $$x$$ and $$y$$ without being "reverting" the polar coordinates? Because I understand that $$\theta = tg^{-1}(\frac{y}{x})$$ and $$r=|z|=\sqrt{x^2+y^2}$$ making me able to obtain a relation like I wanted but i was wondering if there's a way to do it without using polar co... | {
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"lm_q2_score": 0.8244619350028204,
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"openwebmath_score": 0.9682072401046753,
"tags... |
c#, formatting
And if (8xxxxxxx) actually took up both 2 lines in the row, I would add:
60000000 00000000
The original code is of no interested as it's completely different (Assembly). The only useful part is the rows of code because one row of Assembly = 8 hex characters. You need to separate splitting the string in... | {
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structural-engineering, steel
max deflection: $\delta_{max} = \frac{wl^4}{384EI}$
max operating stress: $\sigma = \frac{wl^2}{12 I}\cdot \frac{y_{max}}{2}$
As you can see they are less stringent (that is why I opted for the simple beam), because that would built in a safety factor. | {
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"tags": "structural-engineering, steel",
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performance, beginner, php, algorithm, regex
This is pretty much how I'm planning on using these regexes in my PHP script
// ...
// [Get user input from $_POST
// check its length, etc.,
// if everything looks O.K., store it in $str]
// ...
// Trim unnecessary whitespace (leave line breaks)
$str = preg_replace("/(?:^... | {
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"tags": "performance, beginner, php, algorithm, regex",
"url": null
} |
special-relativity, differential-geometry, string-theory, faster-than-light, string-field-theory
Title: Does a smooth world sheet imply strings moving faster than light? In string theory, one wants to study the interaction of strings throughout time. The interacting strings sweep out a surface in Minkowski space. To w... | {
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"tags": "special-relativity, differential-geometry, string-theory, faster-than-light, strin... |
rqt
</property>
<widget class="QPushButton" name="pushButtonForward">
<property name="geometry">
<rect>
<x>20</x>
<y>20</y>
<width>125</width>
<height>70</height>
</rect>
</property>
<property name="minimumSize">
<size>
<wi... | {
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meteorology, weather-forecasting, severe-weather, mesoscale-meteorology
Furthermore, I was also to depict a map of the atmospheric conditions during the 4/27/2011 tornado outbreak, utilizing William Smith's excellent analysis (you'll want to click on the image for a larger resolution): | {
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"ur... |
special-relativity, spacetime, inertial-frames, lorentz-symmetry, galilean-relativity
And that sounds like the end of the story: it's a slightly surprising end, perhaps.
But it's not. Because, in order to support the notion of an absolute time, LET requires the notion of a preferred frame -- the frame which is at rest... | {
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"tags": "special-relativity, spacetime, inertial-frames, lorentz-symmetry, galilean-relativ... |
java, swing
Title: Applying DocumentListener on multiple JTextField Say I have 5 JTextField: jTextField1, jTextField2...
Now I want them to behave the same on DocumentListener, so I decided to make only one DocumentListener and set it to the 5 components.
Meanwhile I'm doing this:
jTextField1.getDocument().putProperty... | {
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stellar-evolution, white-dwarf
As someone said in the comment, there is no precise definition of a black dwarf. So, I would not say who is right or wrong without understanding how they define the cutoff.
However, if you roughly define it to be at the level that its color temperature passes beyond the visible wavelengt... | {
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c++, game
In your namespace operators, you don't need the inline keyword when forward declaring your operators. You only need that when you define them later.
Every place you pass a parameter by const double &, this can just be a double.
In your Vector2 class, the const_cast used within the operators is superfluous s... | {
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ruby, object-oriented, roman-numerals
# A class for adding individual numerals
class NumeralAdder
attr_reader :num_to_convert,
:num_interpreter,
:numeral
def initialize(num_to_convert)
@num_to_convert = num_to_convert
@num_interpreter = NumberInterpreter.new(num_to_convert)
... | {
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"tags": "ruby, object-oriented, roman-numerals",
"url": null
} |
quantum-algorithms, mathematics, randomised-benchmarking
Title: Quantum algorithm to evaluate numbers in fast growing hierarchy What quantum technologies and/or techniques (if any) could be used to evaluate the value of large numbers in the fast growing hierarchy such as Tree(3) or SCG(13)? The numbers you are describ... | {
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"tags": "quantum-algorithms, mathematics, randomised-benchmarking",
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Subtract 5,24 from 15: 9,36 you see. Of 9,36,
what is the square root? 24 is the square root. Subtract 24 from 30:
6 you see descended. Such is the procedure.
In this passage, base-60 numbers are given with digits separated by commas. As in the original there is no explicit sexagesimal point, and the magnitude of th... | {
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"openwebmath_score": 0.7156984806060791,
"tag... |
performance, sorting, r
If you want, you can do it all in one statement:
df[c('food_1', 'food_2')] <- list(pmin(df$food_1, df$food_2),
pmax(df$food_1, df$food_2))
Another vectorized approach could use ifelse:
f1 <- ifelse(df$food_1 < df$food_2, df$food_1, df$food_2)
f2 <- ifelse(df$f... | {
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"tags": "performance, sorting, r",
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} |
newtonian-mechanics, angular-momentum, rotational-dynamics, computational-physics, software
Title: Creating a pendulum simulation in C# I'm working on a game that involves swinging around a pole, and I want to simulate the physics, not just hard code the rotation. I figure a pendulum is a fairly decent model to start... | {
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"tags": "newtonian-mechanics, angular-momentum, rotational-dynamics, computational-physics,... |
optics, imaging
Additionally, any books/sources you can recommend on imaging of lens and ray tracing would be greatly appreciated. Thank you. "Focus" isn't defined as "all the light rays from this object are one single point on my camera." It's defined as "one point from this object is a single point on my camera." So... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "optics, imaging",
"url": null
} |
dynamics
Title: Pulley with mass dynamics question A pulley system has mass moment of inertia of 1.4kgm^2. If 8kg block is released from rest from S=1, by using energy approach what is angular velocity at S=2? Radius of pulley is 250mm. Note S is from the pulley centre.
This is what I did:
$$T_1+V_1=T_2+V_2$$
$$0+ 8(g... | {
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"openwebmath_score": null,
"tags": "dynamics",
"url": null
} |
machine-learning, quantum-enhanced-machine-learning
Title: Is QST a inherently supervised or unsupervised problem in Machine Learning? I am studying how to apply neural networks to the problem of Quantum State Tomography and I got confused when it comes to decide if this is a supervised or unsupervised learning proble... | {
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"url": null
} |
general-relativity, cosmology, stress-energy-momentum-tensor, cosmic-string
\begin{equation}\tag{2}
\langle \, T^{ab} \rangle = \left(\begin{array}{cccc}
\rho & 0 & 0 & 0\\
0 & p & 0 & 0\\
0 & 0 & p & 0\\
0 & 0 & 0 & p
\end{array}\right).
\end{equation}
So the trace of (1) and (2) give
$$\tag{3}
T = \rho + \tau = \rho... | {
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"openwebmath_score": null,
"tags": "general-relativity, cosmology, stress-energy-momentum-tensor, cosmic-string",
"u... |
lambda-calculus, church-numerals
You made the same mistake when defining Church numerals. The Church numeral for $n$ is based on composing a function $n$ times. “The function $s$ applied $n$ times to the function $z$” $\lambda s. \lambda z. s (s ( … s \: z) … ))$. What you wrote is the function $s$ applied $n-1$ times... | {
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"openwebmath_score": null,
"tags": "lambda-calculus, church-numerals",
"url": null
} |
gas-laws
Title: Why do gases only transmit sound waves whose wavelength is long relative to the mean free path? Also, when is this fact useful in practice? Since sound waves are longitudinal waves (generally in air) there needs to be some kind of interaction between neighboring "air" molecules (a mixture consisting mo... | {
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"openwebmath_score": null,
"tags": "gas-laws",
"url": null
} |
c#, wpf, layout
My attempt to improve readability by encapsulating conditions in meaningful methods:
private bool IsIN()
{
return INTOP && INLEFT && INRIGHT && INBOTTOM;
}
private bool IsTopOverlap()
{
return !BEYOND && !INTOP;
}
private bool IsLeftOverlap()
{
return !BEYOND && !INLEFT;
}
private bool I... | {
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"openwebmath_score": null,
"tags": "c#, wpf, layout",
"url": null
} |
python, object-oriented, inheritance, reflection, properties
raise NotImplementedError(
"%r does not have the attribute %r "
"(abstract from class %r)" %
(this_obj, name, cls.__name__))
# we did not find a match, should be rare, bu... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, object-oriented, inheritance, reflection, properties",
"url": null
} |
performance, haskell, programming-challenge
print ' '.join(map(str, a))
if __name__ == "__main__":
main()
Here is a large test case (#15):
Input
Output
On my system, the Python version takes about 0.5s and the Haskell version 0.7s.
Usually my Haskell code is shorter, but not in this case. Also, the Haskell solu... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "performance, haskell, programming-challenge",
"url": null
} |
quantum-gravity
Question
I'm particularly intrigued by the highlighted statement. Unfortunately, the book doesn't elaborate on the significance of Penrose's work. Could someone explain Penrose's claim to me?
1Russell, S. J., & Norvig, P. (2016). Artificial intelligence: A modern approach. Worldcat, Goodreads. The hig... | {
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"openwebmath_score": null,
"tags": "quantum-gravity",
"url": null
} |
complexity-classes, approximation-algorithms, approximation-hardness, approximation
Related question 2: Is there any "Max TSP" variant (i.e. finding longest round trips) that is Exp-APX-complete? Or any other Exp-APX-complete problem (preferably a maximization one) I could use to prove the Exp-APX-hardness of A? As po... | {
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"tags": "complexity-classes, approximation-algorithms, approximation-hardness, approximatio... |
quantum-field-theory
Then in 5.81 the term $g_{\mu\rho}g_{\nu\sigma}$ has been absorbed into the things they call I, II, III, IV.
If you look down at the equation under 5.81 you'll see there are no longer any upper $\sigma$ or $\rho$ indices, but terms with upper $\mu,\nu$ and terms with lower $\mu,\nu$. So they just... | {
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"openwebmath_score": null,
"tags": "quantum-field-theory",
"url": null
} |
physical-chemistry
Title: How is mole fraction of a solution different in vapour state vs in solution vs vapour-liquid equilibrium?
'x' grams of benzene and 'y' grams of toluene, it is said that the vapor pressure of benzene is 75 mmHg and that of toluene is 22 mmHg. Find mole fraction in the vapor state, | {
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"url": null
} |
• @Guiroux. The possibility I was trying to mention re quantum computers was to have true random number generators as fast as today's pseudorandom generators. In the 1950s sources of 'true' random numbers were used for randomization in experimental design and for (slow, limited) prob simulations. Perhaps see Million Ra... | {
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"lm_q1_score": 0.9496693688269985,
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"lm_q2_score": 0.8479677506936879,
"openwebmath_perplexity": 688.0081092411268,
"openwebmath_score": 0.626780092716217,
"tags... |
c++, beginner, simulation, physics
Title: Simple n-body class in C++ As part of my training, I implemented a n-body class in C++ to simulate gravitational interaction of bodies and to get more familiar with features that C++ offers such as object oriented programming.
This implementation uses a direct integration (Ver... | {
"domain": "codereview.stackexchange",
"id": 36344,
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"openwebmath_score": null,
"tags": "c++, beginner, simulation, physics",
"url": null
} |
java, sudoku, javafx
} else {
throw new IllegalArgumentException(
"Puzzle is not legal.");
}
}
}
for (int k = 0; k < SUDOKU_SIZE; k++) {
alreadyHasNumber[k] = false;
}
... | {
"domain": "codereview.stackexchange",
"id": 16036,
"lm_label": null,
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"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "java, sudoku, javafx",
"url": null
} |
biochemistry, homework
Milk, bear foam, paste, blood, ---
"what happens to colloidal particles in a liquid medium."
I understand the q as solid in liquid so a gel. Examples about gel are "agar, gelatin, jelly and opal" according to my lecture slides. The electrostatic forces are in some sort of middle phase: not eno... | {
"domain": "biology.stackexchange",
"id": 366,
"lm_label": null,
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"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "biochemistry, homework",
"url": null
} |
arduino, sensors, radio-control, automatic
Title: Arduino Controlled RC Car. What now? I bought an RC car about a year ago. A few days later I integrated an arduino nano into the vehicle. The only thing the arduino does is to receive the RC signal and pass it on to the esc/servo. So, basically it just does a big amoun... | {
"domain": "robotics.stackexchange",
"id": 171,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "arduino, sensors, radio-control, automatic",
"url": null
} |
I have some arrays in math mode, such as the one below. I would like a diagonal line in a cell, something like diagbox (diagobx package) or diaghead (makecell package). But it seems that diagbox and diaghead only work in a tabular environment. Of course a way to go consists in using tabular instead of array but this re... | {
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"lm_q1_score": 0.9643214511730025,
"lm_q1q2_score": 0.8137861442542342,
"lm_q2_score": 0.8438950966654772,
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"openwebmath_score": 1.000002384185791,
"tag... |
For b):
Two vectors are parallel to one another if their CROSS PRODUCT is zero.
Thus we need to find $\lambda$ such that \begin{align} u \times v &= 0 \\ \therefore \begin{vmatrix}i & j \\ 3 & 2\\ 2 & \lambda\end{vmatrix} &= 0 \\ \therefore 3\lambda - 4 &= 0 \\ \therefore 3\lambda &= 4 \\ \therefore \lambda &= \frac{... | {
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"id": null,
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9838471680195556,
"lm_q1q2_score": 0.8759134516424265,
"lm_q2_score": 0.8902942246666266,
"openwebmath_perplexity": 336.81202014078116,
"openwebmath_score": 0.998006284236908,
"tag... |
fluid-dynamics, classical-electrodynamics
Now suppose, that we know the energy density $u(t)$ at every instant in time. Then the energy flux $\Phi(t)$ being the energy $E(t)$ crossing the area $A$ per unit time $\Delta t$ is simply
$$\Phi(t)=\frac{E(t)}{A\Delta t}=u(t) c_0$$
where $c_0$ is the vacuum speed of light.
T... | {
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"id": 60802,
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"openwebmath_score": null,
"tags": "fluid-dynamics, classical-electrodynamics",
"url": null
} |
--> 2<sup>κ</sup> is exactly provided by <a href="http://en.wikipedia.org/wiki/Easton%27s_theorem" rel="nofollow">Easton's Theorem</a>. This remarkable theorem states that if you have any class function E, defined on the regular cardinals κ, with the properties that </p> <ul> <li>κ ≤ λ impli... | {
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"id": null,
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9861513910054508,
"lm_q1q2_score": 0.817459152633429,
"lm_q2_score": 0.8289388019824947,
"openwebmath_perplexity": 1004.217857938064,
"openwebmath_score": 0.949590802192688,
"tags":... |
Hint look at the $\log$ then use $\cos{x}=1-\frac{x^2}{2}+o(x^3)$ and $\log(1+x)=x-\frac{x^2}{2}+o(x^2)$
Let's look in more details
$$\log\left(\left(1+\frac{1-\cos x}{x}\right)^{\frac{1}{x}}\right)=\frac{1}{x}\log\left(1+\frac{1-\cos x}{x}\right)$$
Using the expansion of $\cos$ we get
$$\log\left(\left(1+\frac{1-\... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9688561667674652,
"lm_q1q2_score": 0.8031224763150774,
"lm_q2_score": 0.8289388083214156,
"openwebmath_perplexity": 640.8127740992068,
"openwebmath_score": 0.9654307961463928,
"tag... |
there is exactly one y in the codomain. 3. The following figures show the graphs of parent functions: linear, quadratic, cubic, absolute, reciprocal, exponential, logarithmic, square root, sine, cosine, tangent. Farhana ShaheenTHE CARTESIANCOORDINATE SYSTEM 2. The list of common functions and their graphs are provided ... | {
"domain": "emicida.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.97241471777321,
"lm_q1q2_score": 0.8359496885763062,
"lm_q2_score": 0.8596637559030338,
"openwebmath_perplexity": 353.56188958391425,
"openwebmath_score": 0.5274243354797363,
"tags":... |
homework-and-exercises, electric-circuits, electrical-resistance
The admissible points for the complete circuit are the intersections of the power hyperbola with this characteristic, and what you get in general are two points.
Note that by changing the values of the open circuit voltage or the resistance of the cables... | {
"domain": "physics.stackexchange",
"id": 90862,
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"tags": "homework-and-exercises, electric-circuits, electrical-resistance",
"url": null
} |
organic-chemistry, reaction-mechanism
Title: Am I correctly showing a hydride shift on the alkyl halide? I did this quiz and I forgot the hydride shift.
With the hydride shift, would these be the right answer? When you solvolyze the starting bromide a secondary carbocation would be generated. Since a secondary carbo... | {
"domain": "chemistry.stackexchange",
"id": 2145,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "organic-chemistry, reaction-mechanism",
"url": null
} |
algorithms, time-complexity
Title: Approximate time to execute algorithm Suppose a comparison between elements takes 1ms to execute. If an algorithm is O(logN), for example, deletion in an AVL Tree, and the AVL Tree contains 100 elements. Does that mean that the time to execute the algorithm would be log100 * 1ms? Do ... | {
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"id": 8658,
"lm_label": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "algorithms, time-complexity",
"url": null
} |
homework-and-exercises, differential-geometry, metric-tensor, coordinate-systems
Find the coordinate transformation from Cartesian (where $ds^2 = d\bar{x}^2 + d\bar{y}^2$) that brings the following infinitesimal distance: $$ds^2 = y^2 dx^2 + x^2 dy^2$$ The question has been answered in the stackexchange maths forum, h... | {
"domain": "physics.stackexchange",
"id": 37552,
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"openwebmath_score": null,
"tags": "homework-and-exercises, differential-geometry, metric-tensor, coordinate-systems",... |
• What you proved is that $\exists x \, S(S(x)) \neq x$, more precisely that $S(S(0)) \neq 0$. But it is not enough, indeed you have to prove that $\forall x \, S(S(x)) \neq x$. – Taroccoesbrocco Mar 9 at 20:38
• The fact that a property fails for some natural numbers does not imply that it fails for all natural number... | {
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"lm_q2_score": 0.8757869835428965,
"openwebmath_perplexity": 351.4722858765755,
"openwebmath_score": 0.9706621766090393,
"tag... |
quantum-mechanics, special-relativity, quantum-electrodynamics, renormalization
Title: What is the 'quantum-developed' or 'relativistic-developed' equation of the electrostatic force? Quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics that is the first theory where full agreement... | {
"domain": "physics.stackexchange",
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"tags": "quantum-mechanics, special-relativity, quantum-electrodynamics, renormalization",
... |
You must get a positive value for area, so as our graph is symmetrical about the x-axis, we integrate the part above the x-axis and double it.
Using the u-substitution, we get
$\displaystyle\ 2\int_{0}^4{u^{0.5}}du=2\left[\frac{u^{1.5}}{1.5}\right]$ from u=0 to u=4 (start calculations at u=4)
$\displaystyle\ =2\frac... | {
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"lm_q1_score": 0.9857180681726683,
"lm_q1q2_score": 0.8564182414062878,
"lm_q2_score": 0.8688267660487572,
"openwebmath_perplexity": 643.7519994399651,
"openwebmath_score": 0.9478228688240051,
"tag... |
evolution, terminology, population-genetics, macroevolution, altruism
What is macroevolution?
Macroevolution is the evolution which occurs at larger scales, things like speciation, extinction, and the history of life. It often involves comparing species or lineages for example. | {
"domain": "biology.stackexchange",
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"tags": "evolution, terminology, population-genetics, macroevolution, altruism",
"url": nu... |
molecular-biology, gene-expression, synthetic-biology, gene-regulation
Most lambda genes are under the control, directly or indirectly, of the PR and PL promoters (PL is similar to PR, but the promoter itself is not directly involved in cI regulation). When lambda exists as a prophage, its DNA is integrated into the h... | {
"domain": "biology.stackexchange",
"id": 2087,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "molecular-biology, gene-expression, synthetic-biology, gene-regulation",
"url": n... |
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