text stringlengths 49 10.4k | source dict |
|---|---|
formal-languages, formal-grammars, compilers, attribute-grammars
this grammar is non-circular, but it fails the strong-non-circularity test, because in the strong-non-circularity test, you take the union of the dependency-sets for the productions of the same nonterminal. So you have the edges for both A->a and A->b to... | {
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"tags": "formal-languages, formal-grammars, compilers, attribute-grammars",
"url": null
} |
ros-melodic, roslaunch, roscore
Title: Problem with roslaunch on rc.local startup
Hello,
I tried launching some nodes on startup via rc.local, but I have the following errors on some of the startups:
[ 45.809342] rc.local[661]: RLException: ERROR: could not contact master [http://localhost:11311] ... | {
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You can use the following fact: If $H,K$ are subgroups of $G$, $H\cap K=\{1\}$ and $hk=hk$ for all $h\in H$ and $k\in K$, then $G\cong H\times K$.
Now, $hk\in hK,Hk$. Since $H$ is normal in $G$, $Hk=kH$. So, by your argument above, $\{hk\}=hK\cap kH$. But $kh\in hK\cap kH$ by a similar argument.
• Thanks for your answe... | {
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"openwebmath_score": 0.9604566097259521,
"tag... |
pressure
Title: Laplace delta pressure For an air bubble into the water the energy change due to the pressure forces on the system, changing infinitesimally the volume, is $\delta W=\Delta P dV$ where $\Delta P$ is $P_{in} - P_{out}$. Can you explain me why the work is not the classical $\delta W=-P dV$?
edit: Is it b... | {
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"url": null
} |
electromagnetism, magnetic-fields, electric-current, calculus
If I then integrate from $\theta = 0$ at $x = -\infty$ to $\theta = \pi$ at $+\infty$ that integral equals 2 so now I have $\displaystyle\mathbf{B}=-\frac{\mu_0I}{2\pi a}$ which looks like the right answer except it's negative.
Can someone please explain to... | {
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Now if $x=1$ you can use telescoping techniques
$$\sum_{k=1}^{\infty} \frac{1}{k(k+1)}.$$
You need to consider the partial sum
$$S_n = \sum_{k=1}^{n} \left( \frac{1}{k}- \frac{1}{k+1} \right)$$
and then take the limit as $n$ goes to infinity.
• @Leucippus: Thanks for the edit. I really appreciate it. – Mhenni Beng... | {
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"ta... |
## Problem #3
$$$\tag{15}\int 8x\cot x^2\csc x^2\,dx$$$
## Solution | {
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"openwebmath_perplexity": 3029.0189207745398,
"openwebmath_score": 1.0000100135803223,
"t... |
perl, linux
Title: Improved remake of the Linux 'ls' command I have written a script, introduced here, that improves the Linux terminal experience. It basically displays the content of the terminals current folder in a nicer way than the 'ls' command does. I use it all the time myself.
#!/usr/bin/perl
###############... | {
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"openwebmath_score": null,
"tags": "perl, linux",
"url": null
} |
python, generator, context-manager
def probe_context_generator(*pin_pairs, multi=False):
if multi:
yield probe_context(pin_pairs)
else:
for pin_pair in pin_pairs:
yield probe_context(pin_pair)
# Application Code
def probe_for_pulse(multi, p_level, pulse_pin_pairs):
for probe_pu... | {
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"tags": "python, generator, context-manager",
"url": null
} |
electromagnetism, special-relativity, education, maxwell-equations, vector-fields
So, this is all quite straightforward: The component of electric flux perpendicular to the direction of travel generates a magnetic flux line that is perpendicular to both that electric flux and its direction of motion. The electric flux... | {
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"tags": "electromagnetism, special-relativity, education, maxwell-equations, vector-fields",... |
javascript, jquery
//organized methods that are concerned with the view/model
{
setBg: function() {
$("#container").css('background', '#fff')
},
addHtml: function(pdf, callback) {
pdf.addHTML(document.getElementById('records'), callback || null);
},
bindToModel: function(model) {
... | {
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"openwebmath_score": null,
"tags": "javascript, jquery",
"url": null
} |
ros, colcon
Title: relocation R_X86_64_PC32 against symbol `_Py_NotImplementedStruct' can not be used when making a shared object; recompile with -fPIC
I've done this steps like 7 times. I re-install foxy like 7 times too. I fail to see why it's not working now, it was working another day. This colcon build error dri... | {
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"openwebmath_score": null,
"tags": "ros, colcon",
"url": null
} |
audio, fourier-series
Title: How to simplify the Fourier Series Using an Approximation? I have a signal, $f(t)$. I know a function that can be used to generate this signal, such that I can determine its Fourier series. I want to express this Fourier series in simpler terms so that the waveform can be rendered by a G... | {
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"tags": "audio, fourier-series",
"url": null
} |
# Eigenspace for a linear transformation + diagonalizability
I am new to linear algebra, and was asked the question below. I am just looking for some feedback regarding my proposed answer.
$$T:R_4[x] \to R_4[x]$$ is a linear transformation defined by $$T(p(x))=p(x)-3p''(x)$$.
For each eigenvalue of $$T$$, find its e... | {
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"ta... |
python, parsing, python-2.x
In case it's not clear (as it wasn't to me at first), the line breaks are only occuring when the actual text passages contain newline characters. Otherwise all the tags just run on and on, on the same line. This is not at all ideal for parsing, especially if I want to read line by line. So ... | {
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"tags": "python, parsing, python-2.x",
"url": null
} |
magnetic-moment, nuclear-magnetic-resonance, radiometry
Title: Why does transversal magnetization decay and what is actually being measured in an MRI sequence? This may be a few questions disguised as one however this may help uncover what's the missing piece in my understanding.
$T1$ characterizes the rate at which l... | {
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"tags": "magnetic-moment, nuclear-magnetic-resonance, radiometry",
"url": null
} |
sql, sql-server
Title: Display the count of field in a view I have a table that look like this
ID NIP SHIFT DATE
289305 01000267 M 2015-12-01 00:00:00.000
289306 01000267 P 2015-12-01 00:00:00.000
289307 01000267 S 2015-12-01 00:00:00.000
289127 01020358 M 2015-12-01 00:00:00.000
289... | {
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"tags": "sql, sql-server",
"url": null
} |
5. Hello, jay1!
1) Solve: . $\tfrac{1}{4}a^2 + \tfrac{3}{4}a \:=\:1$
My answer: . $a=4,\;a=1$ . . . . no
We have: . $\tfrac{1}{4}a^2 + \tfrac{3}{4}a \:=\:1$
Multiply by 4: . $a^2 + 3a \:=\:4 \quad\Rightarrow\quad a^2 + 3a - 4 \:=\:0$
Factor: . $(a-1)(a+4) \:=\:0$
Therefore: . $a\;=\;1,\:-4$
2) Simplify: . $2ab^4 ... | {
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"openwebmath_score": 0.8691002726554871,
"ta... |
# Can every element of a finite field be written as a sum of two non-squares?
We know that any element of a finite field $\mathbb{F_{q}}$ ($q$ odd prime power) can be written as a sum of two squares - is the same true for non-squares? Can any element of a (sufficiently large) finite field be written as a sum of two no... | {
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"lm_q2_score": 0.8397339696776499,
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"openwebmath_score": 0.8777291178703308,
"ta... |
quantum-state, measurement, hadamard
This is also discussed in this video. Answer refined based on updated question
Your updated question boils down to something like “if we take a Hadamard transform of a superposition of two basis states and measure, why is our string related to the bitwise XOR of the two basis state... | {
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"tags": "quantum-state, measurement, hadamard",
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} |
computability, finite-automata, regular-expressions
Title: Can a Turing Machine decide if a regular expression matches all strings of exactly some length $l \geq 1$? Earlier I asked the question: Can a Turing Machine decide if an NFA accepts a string of prime length?. The answer introduced me to Parikh's theorem, whic... | {
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"tags": "computability, finite-automata, regular-expressions",
"url": null
} |
formal-languages, turing-machines, pushdown-automata
Title: Are 2 independent PDAs equivalent to a turing machine? I was thinking about the language $a^nb^nc^n$, which is obviously not context free, but if we run it through 2 automata at the same time (the first for $a$ and $b$ and the second for $b$ and $c$ and they ... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "formal-languages, turing-machines, pushdown-automata",
"url": null
} |
experimental-physics, astronomy, experimental-technique, binary-stars
Title: Why are binary objects so critical to astronomy? There are a lot of astronomical objects out there to study but binary objects seem to get more attention. Why is this? What makes binary objects (stars, Kuiper Belt Objects, black holes, gala... | {
"domain": "physics.stackexchange",
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"tags": "experimental-physics, astronomy, experimental-technique, binary-stars",
"url": n... |
Method four: (Horner schema) $$\begin{array}{cccccc} & a & b & 0 & 0 & -3 \\ \hline 1 & & a & a+b & a+b & a+b \\ \hline & a & a+b & a+b & a+b & \color{red}{a+b-3} \\ \hline 1 & & a & 2a+b & 3a+2b & \\ \hline & a & 2a+b & 3a+2b & \color{red}{4a+3b} & \\ \end{array}$$ Both red expressions must be zero...
Method five: Di... | {
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"lm_q2_score": 0.8289388146603365,
"openwebmath_perplexity": 201.0162110607113,
"openwebmath_score": 0.9310837984085083,
"tag... |
neural-networks, deep-learning, optimization, generative-adversarial-networks, generative-model
While putting this in code, for every step is the discriminator trained first for one step, keeping the generator constant, followed by the generator being trained for the same step, with the discriminator kept constant?
I... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "neural-networks, deep-learning, optimization, generative-adversarial-networks, generativ... |
solid-state-physics
Title: On the lattice structures of graphite My question is the following:
What causes graphite to have either a cubic lattice structure or a hexagonal lattice structure? Does it depend on how it is grown? Or is it a random process?
I would also like to know if anyone has any good reading on the so... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "solid-state-physics",
"url": null
} |
mechanical-engineering, terminology, flywheels
Title: What do you call a mechanism where rotation is transfered in one direction only? I have the following to wheels that rotate on the same axis:
Assuming that they are stuck together, if I rotate the green one the red one rotates at the same speed and when I stop the... | {
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"openwebmath_score": null,
"tags": "mechanical-engineering, terminology, flywheels",
"url": null
} |
condensed-matter, quantum-entanglement, topological-order, topological-phase, topological-entropy
Title: A naive question about topologically ordered wavefunction? Topological entanglement entropy (TEE, proposed by Levin, Wen, Kitaev, and Preskill) is a direct characterization of the topological order encoded in a wav... | {
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"tags": "condensed-matter, quantum-entanglement, topological-order, topological-phase, topo... |
ros, navigation, subscribe, publisher
geometry_msgs::Twist getCommandMsg() {
geometry_msgs::Twist msg;
// body coordinates
// x is forward linear motion
msg.linear.x = DefaultVelocityCmd;
// rotation around the Z axis
msg.angular.z = DefaultTurnRateCmd;
// all other parameters are ignored in the Twist message
// N... | {
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"id": 23620,
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"tags": "ros, navigation, subscribe, publisher",
"url": null
} |
javascript
/* pageOptions:
This variable contains per-page options for skipHeadings and
headingSubstitution. The values above are used as defaults if a value is
set here, it completely overrides the default value. As with the onlyShowOn
option, the page name must match the name of your page in Squaresp... | {
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"openwebmath_score": null,
"tags": "javascript",
"url": null
} |
= ut , 0 < x < L, t > 0, (1) the boundary conditions u(0,t)=0, u(L,t) =0, t > 0, (2) and the initial condition u(x,0)=f(x), 0 x L. with boundary conditions and. In this section we go through the complete separation of variables process, including solving the two ordinary differential equations the process generates. 5 ... | {
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"lm_q1_score": 0.9777138138113965,
"lm_q1q2_score": 0.8210195020805188,
"lm_q2_score": 0.83973396967765,
"openwebmath_perplexity": 512.9019421213272,
"openwebmath_score": 0.8403221964836121,
"tags": nul... |
beginner, object-oriented, ruby, playing-cards
def update_funds(amount)
@funds += amount
end
def calculate_score
@score = 0
ace_in_hand = false
@hand.each do |h|
face_value = h.get_value[1]
if face_value.is_a? Integer
@score += face_value
... | {
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"tags": "beginner, object-oriented, ruby, playing-cards",
"url": null
} |
electric-fields, complex-numbers
It turns out that you can use the complex representation if you redefine what you mean by the average, using a complex conjugate representation. (See these notes for a review of phasor notation.) Thus, the average of the product of two waves $\mathbf{A}$ and $\mathbf{B}$ is given by: $... | {
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"tags": "electric-fields, complex-numbers",
"url": null
} |
So the only possible eigenvalues of $T$ are $\lambda=0$ and $\lambda=1$. (Note: This is true of any linear transformation $T$ such that $T=T^2$; these are called "projections").
Now that we know the possible eigenvalues, it's a bit easier to check. If $A$ is an eigenvector corresponding to $0$, then we must have $0 = ... | {
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"openwebmath_score": 0.9926109910011292,
"ta... |
java, algorithm, hash-map
}
}
}
Result :
> nakra karan
> tentak takten
> xew wex xwe
> marza maraz
> for fro rof
> aks kas
> simple mislep calcProduct
You don't need the L on these lines:
long res = 1L;
return -1L;
Instead of explaining what 65 is in a comment:
if (c < 65) { // ASCII A = 65
You can u... | {
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"tags": "java, algorithm, hash-map",
"url": null
} |
c++, c++11, programming-challenge
Title: Project Euler 23: Non Abundant Sums Here is my solution to Project Euler 23: Non Abundant Sums. I know I'm doing the Divisors function brute force, but I can't seem to get it to work any other way. Any improvements are welcome.
#include <iostream>
#include <vector>
//Calculate... | {
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"tags": "c++, c++11, programming-challenge",
"url": null
} |
star, constellations, naming, brightness
Title: Why are sometimes the brightest star of a constellation not named alpha? From the Wikipedia page of Alpha Ursae Majoris:
Alpha Ursae Majoris, Latinised from α Ursae Majoris, formally named Dubhe /ˈdʌbiː/, is, despite being designated "α" (alpha), the second-brightest ob... | {
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"id": 6926,
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"tags": "star, constellations, naming, brightness",
"url": null
} |
To obtain $(X'X)^{-1}$, we use the formula for block inverses, \begin{align} (X'X)^{-1} &= \begin{pmatrix} \hspace{2cm}A &\hspace{4.3cm}B\\ \hspace{2cm}B' &\hspace{7cm}D \hspace{2.8cm}\end{pmatrix}^{-1} \\[5pt] &=\begin{pmatrix} (A-BD^{-1}B')^{-1}&-(A-BD^{-1}B')^{-1}BD^{-1}\\ -D^{-1}B'(A-BD^{-1}B')^{-1}&D^{-1}+D^{-1}B'... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9736446517423792,
"lm_q1q2_score": 0.8216539570563882,
"lm_q2_score": 0.843895106480586,
"openwebmath_perplexity": 977.4933365618135,
"openwebmath_score": 0.954590380191803,
"tags"... |
python, python-3.x
Title: Returning postal codes between the ones that are given I have a function that returns postal codes between the ones given. It works but I feel like I made this over-complicated and there's easy way to make it more simple but I have no idea how.
Inputs are two strings that represents postal co... | {
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"id": 22097,
"lm_label": null,
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"lm_q1_score": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, python-3.x",
"url": null
} |
cc.complexity-theory, np-hardness, approximation-hardness
Does the hitting set problem remain NP-hard when the elements of $\mathcal{S}$ pairwise intersect?
I am also interested in the approximation hardness (or tractability) of this problem. The answer is yes - the problem is still NP-Complete. for every set $S_i$ c... | {
"domain": "cstheory.stackexchange",
"id": 799,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "cc.complexity-theory, np-hardness, approximation-hardness",
"url": null
} |
quantum-mechanics, scattering, perturbation-theory, second-quantization, x-rays
Title: Photon scattering final state I'm looking through the linked paper
on x-ray scattering. The Section $5$ says that the expression $(67)$ (which contains an error but the editor mentions the correct variant at the beginning of the pap... | {
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"id": 67006,
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"tags": "quantum-mechanics, scattering, perturbation-theory, second-quantization, x-rays",
... |
signal-analysis, covariance, stationary
Title: Why does it mean that the process/signal is not stationary when its variance varied with time? Why does it mean that the process/signal is not stationary when its variance varied with time? that is,
$VAR[X(t)]= \alpha \times t$,$t$ is time,and $\alpha$ is a constant,then ... | {
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"id": 6398,
"lm_label": null,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "signal-analysis, covariance, stationary",
"url": null
} |
energy, nuclear-physics, physical-chemistry, molecules, binding-energy
Title: Why does splitting a nucleus release energy but breaking molecular bonds requires energy? The title pretty much says it all. Why is it that energy is required to break molecular bonds but energy is released when the bonds within the atomic n... | {
"domain": "physics.stackexchange",
"id": 77325,
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"tags": "energy, nuclear-physics, physical-chemistry, molecules, binding-energy",
"url": ... |
## Benford's Law
Also called the First Digit Law, First Digit Phenomenon, or Leading Digit Phenomenon. In listings, tables of statistics, etc., the Digit 1 tends to occur with Probability ~ 30%, much greater than the expected 10%. This can be observed, for instance, by examining tables of Logarithms and noting that th... | {
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"lm_q1q2_score": 0.8041153067075599,
"lm_q2_score": 0.8152324983301568,
"openwebmath_perplexity": 944.9230081708579,
"openwebmath_score": 0.5224636197090149,
"tags": null,
... |
homework-and-exercises, measurements
Title: Percent uncertainty confusion
Here is a problem where you have to calculate percent uncertainty for an angle and its sinus function. It calculates the uncertainty for its angle using the well known formula, then calculates uncertainty for sinus by subtracting maximum and mi... | {
"domain": "physics.stackexchange",
"id": 72721,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "homework-and-exercises, measurements",
"url": null
} |
inorganic-chemistry, synthesis, purification
The $\ce{Na2WO4}$ was prepared by heating the dihydrate at 200° in a vacuum.
References
Hoermann, F. Beitrag zur Kenntnis der Molybdate und Wolframate. Die binären Systeme: $\ce{Li3MoO4-MoO3},$ $\ce{Na2MoO4-MoO3},$ $\ce{K3MoO4-MoO3},$ $\ce{Li2WO4-WO3},$ $\ce{Na2WO4-WO3},$... | {
"domain": "chemistry.stackexchange",
"id": 14851,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "inorganic-chemistry, synthesis, purification",
"url": null
} |
quantum-gate, hadamard, qiskit-runtime
Title: Where can I find runtime of ibm quantum gates? I'm looking for the runtime of IBM quantum gates. For instance how long does it take to apply an Hadamard gate to a qubit ? and a CNOT gate to two qubits ?
I didn't find any answers in the documentation but it's possible that ... | {
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"tags": "quantum-gate, hadamard, qiskit-runtime",
"url": null
} |
programming, qiskit
Which will output:
┌───┐
q_0: ┤ X ├
└───┘
┌───┐┌─────┐┌───┐
q_0: ┤ H ├┤ qc1 ├┤ Z ├
└───┘└─────┘└───┘
New circuit with controlled:
q_0: ───■───
┌──┴──┐
q_1: ┤ qc2 ├
└─────┘
Decomposed new circuit:
┌────────┐ ... | {
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"tags": "programming, qiskit",
"url": null
} |
c++, programming-challenge
ranges& rs = (style ? forward : backward);
rs.ranges.push_back({start, size});
rs.total += size;
i += size;
}
}
void speak_commands(std::vector<range> const& ranges)
{
for (auto const& r : ranges)
{
if (r.size == 1)
std::cout << "Pers... | {
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"tags": "c++, programming-challenge",
"url": null
} |
ros, include, ros-kinetic, xacro
<joint name="rplidar_joint" type="fixed">
<parent link="${parent}"/>
<child link="rplidar_link"/>
</joint>
<gazebo reference="rplidar_link">
<material>Gazebo/Blue</material>
<turnGravityOff>false</turnGravityOff>
... | {
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"id": 31836,
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"tags": "ros, include, ros-kinetic, xacro",
"url": null
} |
javascript, html, websocket
<li role="separator" class="divider"></li>
<li class="mythos-font">Mythos</li>
<li class="mythos-font"><a href=#>Game rules</a></li>
<li class="mythos-font"><a href=#>Cards</a></li>
</ul>
... | {
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"tags": "javascript, html, websocket",
"url": null
} |
algorithms, pseudo-random-generators
If $f$ is not known but derived from part of the seed, then the procedure depends on the details of how it is derived. There are $2^{2^n}$ possible feedback functions $f:\{0,1\}^n \to \{0,1\}$. If we use $2^n$ bits from the seed so we can sample uniformly at random from the set o... | {
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"id": 8304,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "algorithms, pseudo-random-generators",
"url": null
} |
foundations, category-theory
There are at least two results which I can point to, which represent ways in which the CQM community has developed results which I would judge to be broadly relevant to the interests of the quantum information community, and in which the results are entirely new: | {
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"id": 148,
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"tags": "foundations, category-theory",
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u = np.array([1.5, 0.75])
v = np.array([0.25, 1])
diamond = np.array([[0,0], u, u+v, v]).T
ax = dm.plotSetup()
dm.plotSquare(diamond)
ax.text(u[0]+.25,u[1],r'$\bf{u}$',size=20)
ax.text(v[0],v[1]+.25,r'$\bf{v}$',size=20)
ax.text(u[0]+v[0]+.25,u[1]+v[1],r'$\bf{u + v}$',size=20)
rotation = np.array([[0, -1],[1, 0]])
up =... | {
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"lm_q1_score": 0.9833429595026214,
"lm_q1q2_score": 0.8453442930680223,
"lm_q2_score": 0.8596637469145054,
"openwebmath_perplexity": 2465.0135183133702,
"openwebmath_score": 0.806428074836731,
"tags": null,
... |
ros, object-detection, 3d-object-recognition, roboearth
Title: Which is the easiest way to do Object Detection
Right now ive been searching the web and got that th best packages are roboearth and tabletop_object_detector, but I have to do the specific of recognizing doors and people, so im no sure this are the best s... | {
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"tags": "ros, object-detection, 3d-object-recognition, roboearth",
"url": null
} |
Added 26 January 2014: I should have looked at the linked pdf in the question before posting. There the identity is further generalized to $$\binom{n - r}{m - s} \binom{n}{m + r} \binom{n + s}{m} = \binom{n}{m - s} \binom{n - r}{m} \binom{n + s}{m + r},\qquad\qquad(*)$$ which corresponds to a hexagon with side lengths ... | {
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"lm_q1_score": 0.978712645102011,
"lm_q1q2_score": 0.802439969032687,
"lm_q2_score": 0.8198933293122507,
"openwebmath_perplexity": 295.65221679273634,
"openwebmath_score": 0.9460882544517517,
"tags... |
Let $U \subset \mathbb{R}$, let $f : U \to \mathbb{R}$ be a function, and suppose $x_0 \in U$. Then $f$ is right (resp. left) continuous at $x_0$ when for all sequences $\{x_n\}_{n=1}^{\infty}$ in $U \setminus \{x_0\}$ which converge to $x_0$ from the right (resp. left) it holds that $\lim\limits_{n \to \infty} f(x_n) ... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9724147169737825,
"lm_q1q2_score": 0.8082157316478721,
"lm_q2_score": 0.8311430478583168,
"openwebmath_perplexity": 79.71966527244044,
"openwebmath_score": 0.9661905169487,
"tags":... |
general-relativity, differential-geometry, curvature, coordinate-systems
Title: Riemann normal chart and special relativity When you pick Riemann normal coordinates at a point, then the Christoffel symbols vanish and the metric is flat, but the Riemann curvature tensor does not necessarily vanish. Since Einstein said ... | {
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"tags": "general-relativity, differential-geometry, curvature, coordinate-systems",
"url"... |
c, regex
// (start, end) of the full match is the zero'th entry
int end_position = offset_vector[1];
return end_position;
}
int main(void)
{
PCRE2_SPTR8 pattern = (const unsigned char*) "he[al](lo)";
PCRE2_SPTR8 string = (const unsigned char*) "add ello a healo b hello c";
// 1. Compile the pat... | {
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"openwebmath_score": null,
"tags": "c, regex",
"url": null
} |
algorithms, graphs, shortest-path
I know that without destroying the walls this could be easily solved with the use of Dijkstra. But how to take into account the fact I can destroy one wall?
The only solution I could come up with was to remember two distances for each node: one distance is the "real" shortest path, t... | {
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"id": 16068,
"lm_label": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "algorithms, graphs, shortest-path",
"url": null
} |
fluid-dynamics, operators, integrable-systems, solitons
Title: Differentiation of an operator equation in paper by Chen, Lee, Pereira 1979 This 1979 paper by Chen, Lee, and Pereira gives an operator $L$ satisfying
$$\dot L = [A, L],\tag{1}$$
where $A$ is another operator, and the dot denotes time differentiation. They... | {
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"tags": "fluid-dynamics, operators, integrable-systems, solitons",
"url": null
} |
Next, using the Prosthaphaeresis Identity, $\sin(x)-\sin(y)=2\cos\left(\frac{x+y}{2}\right)\sin\left(\frac{x-y}{2}\right)$ along with $|\cos(\theta)|\le 1$ and $|\sin(\theta)|\le \theta$ reveals
$$|\sin(x)-\sin(y)|\le |x-y|\tag 3$$
Finally, using $(3)$ in $(2)$, we obtain the coveted inequality
$$\bbox[5px,border:2p... | {
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"openwebmath_score": 0.964253306388855,
"tag... |
The only proper subgroups of $\mathbb{Z}_{10}$ are $H_1 = \{0, 5\}$ and $H_2 = \{0, 2, 4, 6, 8\}\text{.}$ They are both cyclic: $H_1= \langle 5 \rangle\text{,}$ while $H_2 = \langle 2 \rangle = \langle 4 \rangle = \langle 6 \rangle = \langle 8 \rangle\text{.}$ The generators of $\mathbb{Z}_{10}$ are 1, 3, 7, and 9.
Wi... | {
"domain": "discretemath.org",
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"lm_q1_score": 0.9919380101400315,
"lm_q1q2_score": 0.8200468456171953,
"lm_q2_score": 0.8267117876664789,
"openwebmath_perplexity": 1615.108769389095,
"openwebmath_score": 0.9999842643737793,
"tags... |
resource-recommendations, standard-model, quarks, weak-interaction
Weak Interactions of Leptons and Quarks,
by Eugene D. Commins & Philip H. Bucksbaum (Cambridge University Press, 1983)
ISBN-13 : 978-1423446637
Elementary Particles and Their Currents, by Jeremy Bernstein (W. H. Freeman and Co., 1968) ASIN : B0000CO... | {
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"tags": "resource-recommendations, standard-model, quarks, weak-interaction",
"url": null... |
c++, recursion, template, constrained-templates, c++23
Title: recursive_find and recursive_find_if_not Template Functions Implementation in C++ This is a follow-up question for A recursive_find_if Template Function with Unwrap Level Implementation in C++ and recursive_invocable and recursive_project_invocable Concept ... | {
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"tags": "c++, recursion, template, constrained-templates, c++23",
"url": null
} |
rviz, macos, homebrew, macos-lion, osx
{'__file__':setup_script, '__name__':'__main__'}
File "setup.py", line 8, in <module>
version = '0.0.0'
ImportError: No module named rospkg
CMake Error at ros/CMakeFiles/safe_execute_install.cmake:5 (message):
Error executing process with arguments
Call Stack (most recent... | {
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"tags": "rviz, macos, homebrew, macos-lion, osx",
"url": null
} |
performance, php, array, tree, database
$data =
[
[
"countryID" => 1,
"countryName" => "USA",
"regionID" => 10,
"regionName" => "Indiana",
"cityID" => 100,
"cityName"=> "Indianapolis",
],
[
"countryID" => 1,
"countryName" => "USA",
"re... | {
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"id": 43644,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "performance, php, array, tree, database",
"url": null
} |
java, beginner, classes
Title: Class for formatting topics using BBCodes I'm developing a program for users from a VBulletin's forum. This forum has a lot of people interested in write good articles but some of them don't know how to use the formatting bar in his favor. Sometimes, the others members don't read this th... | {
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} |
Alternatively, one could use contour integration to evaluate the integral of interest or evaluate the integral on the right-hand side of $$(1)$$.
• The Weierstrass substitution is going to fail if you apply it to this integral. You have to do something first (integrate on $[-\pi,\pi]$ and split, for instance). – Jean-... | {
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"openwebmath_score": 0.9907956123352051,
"tag... |
volcanoes, pyroclastic-flows
Edit: In a research* it is suggested that a turbidite current can flow over barriers, if the thickness of the flow exceeds %65 of the barrier. One may interpret this that, after a pyroclastic current dives to shallow water it may come back to the surface again. | {
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"tags": "volcanoes, pyroclastic-flows",
"url": null
} |
information-theory, capacity
Title: When channels are in a cascade and are independent is the capacity the sum? Just wondering if two channels are independent then is the overall capacity, the sum of the individual capacities?
For example suppose I have two BEC where the probability of erasure is $\varepsilon$ and $\... | {
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"openwebmath_score": null,
"tags": "information-theory, capacity",
"url": null
} |
complexity-theory, formal-languages, sets
Title: How to apply "verification" and "decision" for the SUBSET SUM problem? The SUBSET SUM problem states that:
Given finite set S of integers, is there a subset whose sum is exactly t?
Can someone show me why verification is simpler than decision for this problem? If anybo... | {
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"tags": "complexity-theory, formal-languages, sets",
"url": null
} |
javascript, css, api, event-handling, dom
function arrPrevBtn() {
if (currentSlide == 0) {
currentSlide = carouselImages.length - 1;
} else {
currentSlide--;
}
addRemoveHideClass();
}
function addRemoveHideClass() {
carouselImages.filter(function (img) {
if (img == foundIma... | {
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"id": 40624,
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"url": null
} |
So, we thought we were departing into some new territory and found ourselves looking back at earlier work from a different angle. What a nice surprise!
One more added observation: We got a little lucky in guessing the angle of rotation, but even if it wasn’t known, it is always possible to compute an angle of rotati... | {
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"tags": n... |
c, parsing, floating-point
static const int max = sizeof strings / sizeof strings[0];
for (int i = 0; i < max; ++i)
printf("%20s = > %.9g\n", strings[i], extended_atof(strings[i]));
}
(I changed the function name to extended_atof() so as to be safely distinct from the standard library atof().)
Your impl... | {
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"tags": "c, parsing, floating-point",
"url": null
} |
javascript, node.js
Logging/consoleLogger.js
module.exports = function consoleLogger() {
return {
log: function log(message) {
console.log(buildString(message));
},
error: function error(message) {
console.error(buildString(message));
}
};
}
function buildString(message) {
var time =... | {
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"tags": "javascript, node.js",
"url": null
} |
of these stresses will be discussed in detail as follows. Now always remember that we will have to first determine the reaction forces at each support. So, remembering here we can also think of that In terms of this equation. numericals 8. It also explains step by step equilibrium moments and forces, and it gives you a... | {
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"openwebmath_score": 0.6833874583244324,
"tags": nul... |
Example : Consider the sequence : 2, 6, 12, 20, 30, ...
The first differences are : 4, 6, 8, 10, ...
The second differences are : 2, 2, 2, ...
Since the second differences are equal, t(n) is a quadratic in n, ie : t(n) = an^2 + bn + c.
So you can assume the sum has a cubic form : S(n) = An^3 + Bn^2 + Cn + D
Plugging ... | {
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"lm_q2_score": 0.8705972784807406,
"openwebmath_perplexity": 589.8774510717521,
"openwebmath_score": 0.8441044688224792,
"tags... |
machine-learning, artificial-intelligence, neural-networks
Title: About the behaviour of multi-layer perceptrons I have a multilayer perceptron. It has an input layer with two neurons, a hidden layer with an arbitrary number of neurons, and an output layer with two neurons.
Given that randomboolean and targetboolean a... | {
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"tags": "machine-learning, artificial-intelligence, neural-networks",
"url": null
} |
differential-geometry, tensor-calculus, differentiation
\;=\; \frac{\partial y^i}{\partial x^j} \frac{\partial}{\partial x ^i} \otimes \mathbf{d} x^j \;=\; \frac{\partial y^i}{\partial x^j} \frac{\partial}{\partial y ^i} \otimes \mathbf{d} y^j
\quad \in T_x M \otimes T^*_x M
$$
The above, if it is correct, is a (1,1)... | {
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"id": 90885,
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"tags": "differential-geometry, tensor-calculus, differentiation",
"url": null
} |
+ \sqrt{43} + \sqrt{46} + \sqrt{47} \\ & + \sqrt{51} + \sqrt{53} + \sqrt{55} + \sqrt{57} + \sqrt{58} + \sqrt{59} \\ & + \sqrt{61} + \sqrt{62} + \sqrt{65} + \sqrt{66} + \sqrt{67} + \sqrt{69} \\ & + \sqrt{70} + \sqrt{71} + \sqrt{73} + \sqrt{74} + \sqrt{77} + \sqrt{78} \\ & + \sqrt{79} + \sqrt{82} + \sqrt{83} + \sqrt{85} ... | {
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"lm_q2_score": 0.8615382094310357,
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"openwebmath_score": 0.9993078708648682,
"tag... |
newtonian-mechanics, particle-physics, statics, equilibrium, rigid-body-dynamics
With this we can define a quantity called Torque associated for a force $f$ applied to a point $\vec{r}$ of the rigid body by:
$$
\vec{\tau}=\vec{r}\times\vec{f}(\vec{r})
$$
So, if we have a force $\vec{f}_1$ applied at $\vec{r}_1$ and $\... | {
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"tags": "newtonian-mechanics, particle-physics, statics, equilibrium, rigid-body-dynamics",... |
python, python-3.x, web-scraping
a better practice is use a CONSTANT_VALUE at the beginning of the file;
QTY_THREAD_OFFSET = 3
.....threading.active_count() - QTY_THREAD_OFFSET))
(maybe you can think in a better constant name, but you get the idea right?)
The same for:
while(threading.active_count() > 2): # main th... | {
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} |
In following experiment, you will see, even you get a large sample and calcluate the empirical mean from the sample, the numbers are quite different from experiment to experiment.
set.seed(0)
par(mfrow=c(1,2))
experiments=rep(1e5,100)
mean_list_cauchy=sapply(experiments, function(n) mean(rcauchy(n)))
mean_list_normal=... | {
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"openwebmath_perplexity": 475.06411975071904,
"openwebmath_score": 0.9157067537307739,
"tag... |
homework-and-exercises, projectile, drag, estimation, weather
Thus, no matter what the wind direction is, at 1000 yards (914 m), hurricane force winds of 150 mph (67 m/s) don't even come close to reversing bullet direction. The maximum ideal range for this projectile is only 2.72 miles (4377 meters) and at 1000 yards... | {
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"tags": "homework-and-exercises, projectile, drag, estimation, weather",
"url": null
} |
java, programming-challenge, fizzbuzz, java-8
Title: The FizzBuzz challenge in Java 8 written in a short, readable and interesting way I decided to take on the FizzBuzz challenge with as twist that I would use Java 8 concepts to make it a bit modular, yet still let it be a short, readable and understandable program.
T... | {
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"tags": "java, programming-challenge, fizzbuzz, java-8",
"url": null
} |
c, strings
This seems to be a valid solution for the problem and outputs the correct answer. But I have been told that the implementation is messy and not readable because of the use of the state variable and that there are more elegant ways of doing it. I have been trying to wrap my head around it for some time and ... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c, strings",
"url": null
} |
terminology, velocity, speed
Title: Why and how does negative velocity exist? Why and how does negative velocity exist? I have read on the internet about negative velocity but I still don't understand how it can even exist since time is positive and so is length. By doing some math I came to the conclusion it can't an... | {
"domain": "physics.stackexchange",
"id": 41171,
"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": "terminology, velocity, speed",
"url": null
} |
newtonian-mechanics, rotational-dynamics, reference-frames, momentum, torque
Title: Why center of mass constant is zero? The Center of mass frame (CM) is defined in such a way that total momentum in this frame is zero. Thus
$\vec P'=\sum (m_i\vec v_i')=\sum \big[m_i(\vec v_i-\vec u)\big] =\vec P - M\vec u=0 \tag{1} $
... | {
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"id": 86925,
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"tags": "newtonian-mechanics, rotational-dynamics, reference-frames, momentum, torque",
"... |
7. Same question for the series $$\sum_{n=1}^\infty\frac{s(n)}{n^2}$$.
8. Prove that the series $\sum_{n=0}^\infty \frac{(-1)^n \, \tau(2n+1)}{(2n+1)^s}$ converges conditionally (but not absolutely) for any real number $$s>\frac{1}{2}$$, and converges absolutely for any $$s>1$$.
9. Investigate the convergence of the ... | {
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"lm_q2_score": 0.8244619285331332,
"openwebmath_perplexity": 515.5650390839191,
"openwebmath_score": 0.9990357160568237,
"tags": ... |
fft, discrete-signals, frequency, signal-analysis, peak-detection
Title: Estimate frequency and peak value of a signal's fundamental How can I find out frequency and peak value of a signal's fundamental?
Please do consider the following:
The peak value of some harmonics might be higher than that one of the fundamenta... | {
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"id": 1284,
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"tags": "fft, discrete-signals, frequency, signal-analysis, peak-detection",
"url": null
} |
c++, rational-numbers
A bug somewhere
The very first test I wrote, failed:
int main()
{
Rational r1{1,4};
Rational r2{2,4};
return (r1 + r2 != Rational{3/4});
}
But this was a bug in the test! Rational{3/4} means Rational{0} (integer division), but I meant Rational{3,4}. I improved the test:
int verify... | {
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"tags": "c++, rational-numbers",
"url": null
} |
programming, ibm-q-experience, simulation
Title: IBMQ_Melbourne Readout error I am trying to simulate an experiment on IBM's melbourne quantum computer and here are the results
Qasm simulator :
ibmq_16_melbourne:
error
why is there such high probability of unwanted states i.e 01 and 10. Also when the circuit is tr... | {
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"openwebmath_score": null,
"tags": "programming, ibm-q-experience, simulation",
"url": null
} |
homework-and-exercises, electromagnetism, electrostatics, dipole, dipole-moment
Title: Do Dipole Moments Obey Superposition? Essentially, I have two surfaces which I know how to find the dipole moments for. I realize that
$V_{dip}(r) = \frac{1}{4\pi \epsilon_0 r^2} \mathbf{\hat{r}} \cdot \int \mathbf{r'} \rho{(\mathb... | {
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"id": 25687,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "homework-and-exercises, electromagnetism, electrostatics, dipole, dipole-moment",
... |
observational-astronomy, astrometry, betelgeuse
Title: What will it finally take to accurately measure the distance to Betelgeuse? Comments below What is the maximum distance measurable with parallax? discuss challenges associated with parallax measurements of Betelgeuse and link to Wikipedia’s Betelgeuse; Distance me... | {
"domain": "astronomy.stackexchange",
"id": 4483,
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"openwebmath_score": null,
"tags": "observational-astronomy, astrometry, betelgeuse",
"url": null
} |
genetics, biochemistry, bioinformatics, pathology, database
Title: Grouping OMIM disease codes I have ~100 sets of genes, and each set includes between 2 and 70 genes. I'd like to perform an enrichment analysis on each of these sets to test if they're enriched for OMIM disease labels. However, I'm encountering a probl... | {
"domain": "biology.stackexchange",
"id": 5323,
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"openwebmath_score": null,
"tags": "genetics, biochemistry, bioinformatics, pathology, database",
"url": null
} |
# The largest integer that divides $p^4-1$, in which p is a prime greater than $5$ [duplicate]
The question is to find the largest integer that divides all $p^4-1$, where p is a prime greater than 5. Being asked this question, I just assume this number exists. Set $p = 7$, then $p^4-1=2400$. I don't have any backgroun... | {
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"lm_q2_score": 0.8311430478583168,
"openwebmath_perplexity": 168.3203247832023,
"openwebmath_score": 0.6897412538528442,
"tag... |
solubility, geochemistry
the ppm of fluorite in pure water is zero!
$K_\mathrm{sp}=[\ce{Ca_{original}} + \ce{Ca_{added}}][2\ce{Ca_{added}}]^2 = 4[\ce{Ca_{original}} + \ce{Ca_{added}}][\ce{Ca_{added}}]^2$
Yes, this is correct and can be solved, you say you know $[\ce{Ca_{original}}]$ is $\pu{0.375E-3M}$ and $K_\math... | {
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"tags": "solubility, geochemistry",
"url": null
} |
general-relativity, special-relativity, quantum-gravity, quantum-mechanics
But if $l_P$ is a Lorentz invariant their is no question about that. $l_P$ is the same in all reference frames! Another confusing issue is that the Planck mass (from which the Planck length is derived) is often derived by setting equal the Comp... | {
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"tags": "general-relativity, special-relativity, quantum-gravity, quantum-mechanics",
"ur... |
knowledgebase, relied on by millions of students & professionals. Answer to Fourier series: Calculate the Fourier series of the wave form:. You can then use this formula to make predictions, and also to find repeating patterns within your data. The first term in a Fourier series is the average value (DC value) of the f... | {
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"id": null,
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"lm_q1_score": 0.9886682454669814,
"lm_q1q2_score": 0.8281282595168402,
"lm_q2_score": 0.8376199633332891,
"openwebmath_perplexity": 497.33143749852866,
"openwebmath_score": 0.9017105102539062,
"tags... |
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