text stringlengths 49 10.4k | source dict |
|---|---|
homework-and-exercises, electrostatics, polarization, dielectric
Title: Charge in a layered ball A ball (radius $R$) has three layers. For $0<r<a$ it is a conductor with free charge $+Q$. For $a<r<b$ it is a linear dielectric $\epsilon$ with free charge embedded in it with density $\rho_{free}(r) = \left(\frac{\rho_0}... | {
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"openwebmath_score": null,
"tags": "homework-and-exercises, electrostatics, polarization, dielectric",
"url": null
} |
energy, particle-physics, standard-model, symmetry-breaking, electroweak
The weak interactions in the data, followed the symmetry of SU(2) with the massive exchange bosons and the electromagnetic of U(1), with the zero mass photon.
Ever since Maxwell unified electricity and magnetism, the goal of seeking unification... | {
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"tags": "energy, particle-physics, standard-model, symmetry-breaking, electroweak",
"url"... |
quantum-mechanics, quantum-field-theory, special-relativity, quantum-electrodynamics
The setup
Let $|\mathbf{p} \rangle$ be unit-normalized momentum eigenstates for a relativistic particle. In standard relativistic quantum field theory textbooks, one begins with field operators
$$\hat{\psi}(\mathbf{x}) = \int_{\mathbf... | {
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"tags": "quantum-mechanics, quantum-field-theory, special-relativity, quantum-electrodynami... |
cc.complexity-theory, sat, counting-complexity
I realize that this problem is somewhat arbitrary; computing the average or mode number of clauses satisfied by each variable assignment seems to capture the same quality. Probably many other problems do too.
Has this problem been studied, perhaps under a different guise?... | {
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"tags": "cc.complexity-theory, sat, counting-complexity",
"url": null
} |
ros, add-dependencies
Title: Undefined reference to ros::init
Most of the similar questions pointed to the package's CMakeList.txt . As far as I can tell, it's as it should be:
cmake_minimum_required(VERSION 2.8.3)
project(random_walk)
find_package(catkin REQUIRED COMPONENTS
roscpp
geometry_msgs
sensor_msgs
)
m... | {
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"tags": "ros, add-dependencies",
"url": null
} |
electric-current, wave-particle-duality, photoelectric-effect
Title: Photocurrent in Photoelectric effect and its misconceptions This question has been asked many times on this site before with different doubts in each question but I am conflicted with the vast amount of sources stating contradictory things.
There are... | {
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"tags": "electric-current, wave-particle-duality, photoelectric-effect",
"url": null
} |
terminology, reference-request, education
Title: Looking for a dictionary of math/CS notation There is an at-times dizzying array of symbols used in math and CS papers. Yet many assume basic familiarity that seems rarely taught in one place. I am looking for a dictionary something like the following, especially from a... | {
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"openwebmath_score": null,
"tags": "terminology, reference-request, education",
"url": null
} |
newtonian-mechanics, forces, friction, free-body-diagram
Title: Inclined Plane and Center of Mass Say there is a block sliding down an inclined plane that rests on a frictionless table. There is kinetic friction between the block and inclined plane. If the block slides downhill, then the kinetic friction acting on it ... | {
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"tags": "newtonian-mechanics, forces, friction, free-body-diagram",
"url": null
} |
c++, c++11
void append(const char* buf, std::size_t buf_size)
{
//If we are aleady using _v, forget about the stack
if (!_v.empty())
{
_v.insert(_v.end(), buf, buf + buf_size);
}
//Try use the stack
else
{
if (_stack_size + buf_size <=... | {
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"openwebmath_score": null,
"tags": "c++, c++11",
"url": null
} |
javascript, beginner, jquery, calculator, jquery-ui
Title: Retirement Calculator I created a program that determines how many years you have left before retiring, and in a year when you can retire.
This is my code below: | {
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"tags": "javascript, beginner, jquery, calculator, jquery-ui",
"url": null
} |
newtonian-mechanics, rotational-dynamics, torque, rotation
Title: Why does rotation occur? So it sounds like a dumb question, as it is very intuitive why rotation occurs. However, can you give me a scientific explanation as to why whenever I exert a force on a body it tends to move, but when it is tied to something or... | {
"domain": "physics.stackexchange",
"id": 36353,
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"tags": "newtonian-mechanics, rotational-dynamics, torque, rotation",
"url": null
} |
python, c++, strings
}
There's no reason to make a reversed copy. Just index from the back.
Nor to delay comparing the differences. It just means you have to save them.
Following the above two points ensures the function never throws. So, in C++ mark it noexcept.
Next, there's no need to go over the string from begin... | {
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"tags": "python, c++, strings",
"url": null
} |
general-relativity, orbital-motion
Title: Kinetic, potential and total orbital energy in General Relativity In Schwarzschild geodesics the total orbital energy $E$ is
$$E = \dot{t} \left( 1 - \frac{r_{\rm s}}{r} \right) m \, c^2$$
with the time dilation factor $\dot{t}$ in dependence of the local velcity $v$
$$\dot{t}... | {
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"openwebmath_score": null,
"tags": "general-relativity, orbital-motion",
"url": null
} |
graph-theory, pl.programming-languages, term-rewriting-systems
Title: Graph rewriting with one-to-many pattern matching? In the single-pushout approach to graph rewriting, many nodes in a pattern graph can be matched to a single node of a target graph.
My question is if there is a notion of graph rewriting where the i... | {
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"tags": "graph-theory, pl.programming-languages, term-rewriting-systems",
"url": null
} |
thermodynamics
Title: Temperature Gradient While writing the Fouriers Equation of Heat Transfer, some textbooks write the Temperature Gradient in terms of partial derivative while some other write it in terms of total derivative?
What is the difference between these two? Is there some kind of a difference during thei... | {
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"tags": "thermodynamics",
"url": null
} |
special-relativity, momentum, speed-of-light, hamiltonian-formalism
I could have messed up with rest/invariant vs relativistic/total quantities (I know that many people get $E=mc^2$ wrong, comparing total energy with rest mass without the gamma in non-stationary cases), but it really doesn't look like I did; also, I r... | {
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"tags": "special-relativity, momentum, speed-of-light, hamiltonian-formalism",
"url": nul... |
python, algorithm, array, dynamic-programming
Title: Finding the max product of a 2D array Given a 2D array of unsigned integers and a maximum length n, find a path in that matrix that is not longer than n and which maximizes the product of the elements in the path. The output should consist of both the path and the p... | {
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"tags": "python, algorithm, array, dynamic-programming",
"url": null
} |
python, python-3.x, comparative-review, configuration
if section == 'section1' and item == 'url':
ret = _normalize_url(ret)
return ret
# Provide items on a module level that has defaults.
# If they don't have defaults, you must go through get() so a good error would
# be thrown if the item is not found.
u... | {
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"openwebmath_score": null,
"tags": "python, python-3.x, comparative-review, configuration",
"url": null
} |
formal-languages, regular-languages, pumping-lemma, check-my-answer
Title: Using pumping lemma to show $L = \{a^i b^j a^k \ | \ k > i + j\}$ cannot be accepted by an FA
$L = \{a^i b^j a^k \ | \ k > i + j\}$
Use the pumping lemma to show that this language cannot be accepted by an FA.
Proof:
Suppose $L$ can be accept... | {
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"tags": "formal-languages, regular-languages, pumping-lemma, check-my-answer",
"url": null
} |
Square Roots; Square Root of 5 or 6. Newton’s Method (popular) - a very fast approximating sequence. n the number or quantity whose cube is a given number or quantity: 2 is the cube root of 8 n. Sqrt decomposition can be applied in a similar way to a whole class of other problems: finding the number of zero elements, f... | {
"domain": "centroesteticamente.it",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9766692284751636,
"lm_q1q2_score": 0.8242063844775828,
"lm_q2_score": 0.8438951084436076,
"openwebmath_perplexity": 514.8281387669324,
"openwebmath_score": 0.7013413906097412,
... |
ros
Title: Waypoints with orientation + Smooth trajectory
Hello,
I have a ground robot ( 4 wheels like a car) a I have my missions defined by a set of waypoints ( x, y, yaw (position and orientation)). I want that my robot moves through these waypoints with the specified orientation in each waypoints. The path should... | {
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"id": 11581,
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"tags": "ros",
"url": null
} |
# Find Laplace Transform of the function
$$f_T(t)=\begin{cases}2, & 0\leq t < T \\ 1, & t\geq T \end{cases}$$
-
Hello @SF, welcome to Math.SE! I've edited to include TeX so that your function displays well. But please, start to become used to include more information, what have you tried and so on so that you get bet... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9648551515780319,
"lm_q1q2_score": 0.818166056335881,
"lm_q2_score": 0.8479677545357568,
"openwebmath_perplexity": 621.6089525761411,
"openwebmath_score": 0.8893885612487793,
"tags... |
python, python-3.x, algorithm, programming-challenge, factors
My Solution
This is my solution for problem 5 of Project Euler using Python:
def LCM(a, b):
'''Return the least common multiple of
the specified integer arguments
'''
return a // gcd(a, b) * b
N = int(input("The LCM for numbers 1 thr... | {
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"tags": "python, python-3.x, algorithm, programming-challenge, factors",
"url": null
} |
solar-system, celestial-mechanics, tidal-forces, tidal-locking, io
Title: How can Io be tidally heated while it is in tidal lock? According to its Wikipedia page:
Rotation period: synchronous
Eccentricity: 0.0041
But also
...extreme geologic activity is the result of tidal heating...
How is it possible? It should ... | {
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"id": 6012,
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"tags": "solar-system, celestial-mechanics, tidal-forces, tidal-locking, io",
"url": nul... |
python, interview-questions
Title: LZW Decompression Library I've been asked to write a decompressor library for an interview process. It's a LZW decompression library. I've got it working and tried it out. I'm looking for any feedback on structure, presentation, readability from professionals who've worked as softwar... | {
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"tags": "python, interview-questions",
"url": null
} |
• OK, since my edits seem to keep getting rejected, the last part should be "I've spent lots of time looking for a counterexample but didn't find one. Can someone maybe find one?", have "High School" (gāo zhōng), have "similar to" and end with "I feel this problem looks like it was brought up by Erdös, is that right?".... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.990874360724436,
"lm_q1q2_score": 0.8278592218116152,
"lm_q2_score": 0.8354835432479661,
"openwebmath_perplexity": 349.8022243947813,
"openwebmath_score": 0.8331632018089294,
"tags... |
c, parsing, reinventing-the-wheel, integer
Where do you declare multiplier? I assume that since it is not declared within the method, it is declared as a global variable. Try to avoid global variables.
The problem with global variables is that since every function has access to these, it becomes increasingly hard to... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
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"tags": "c, parsing, reinventing-the-wheel, integer",
"url": null
} |
beginner, sql, sql-server, t-sql, stackexchange
This is definitely a much clearer way to express your desired logic than the CASE statement in the original post. For me, the reason it's clearer is that it maps quite easily to reading in plain English:
Show me rows where the max body length is 0 or more and the lengt... | {
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"tags": "beginner, sql, sql-server, t-sql, stackexchange",
"url": null
} |
python, python-3.x, error-handling, number-systems
Title: Interactive command-line binary to decimal converter Is this the most efficient way to write this piece of code? Is there a better way of handling errors inside of a while/for loop, instead of calling back to the original function? I have tried using break or c... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, python-3.x, error-handling, number-systems",
"url": null
} |
electromagnetism, charge, polarization
Title: Polarization surface charge density on spherical surface - electromagnetics Problem
A charged metal sphere of radius $a $ gives rise to a $\mathbf{D} $-field given by $\mathbf{D}=\mathbf{a_R} \frac{C}{R^2} $ in the surrounding medium with permittivity $\varepsilon $. What... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "electromagnetism, charge, polarization",
"url": null
} |
quantum-field-theory, path-integral, boundary-conditions
$\varphi_0(x,t_i) =\varphi_0(x, t_f)$ for all $t_i, t_f$. So, why doesn't the above integral vanish? More generally, how do we implement boundary conditions in the path integral? I think you are confused that the upper and lower limits of the integral are the sa... | {
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"openwebmath_score": null,
"tags": "quantum-field-theory, path-integral, boundary-conditions",
"url": null
} |
javascript, jquery, beginner, backbone.js, underscore.js
var _this = this;
var success = function (json) {
_this.onApiSuccess(json);
};
var error = function (jqXHR, textStatus, errorThrown) {
_this.onApiError(url, jqXHR, textStatus, errorThrown);
};
$.aj... | {
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"openwebmath_perplexity": null,
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"tags": "javascript, jquery, beginner, backbone.js, underscore.js",
"url": null
} |
javascript, array, coldfusion
Title: Converting a list to an array when list has quotes and embedded comma This function converts a list to an array when list has quotes and embedded comma:
array function convertRow(required string lstRow) {
var arResult = [];
var arTemp = ListToArray(arguments.lstRow, ',', t... | {
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"openwebmath_score": null,
"tags": "javascript, array, coldfusion",
"url": null
} |
neural-network, nlp, naive-bayes-classifier
Solution 2 This solution begins to touch the fence of Deep Learning. This solution is a comparison of the attention encodings within the source utterance and the target utterance. The source utterance is, a phrase like "need janitor". Now you should train an attention model ... | {
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"tags": "neural-network, nlp, naive-bayes-classifier",
"url": null
} |
c#, reinventing-the-wheel, ip-address
/// <summary>
/// Creates a new Ip4Address from a well formed IP address. i.e. "10.10.1.255"
/// </summary>
/// <param name="address"></param>
/// <exception cref="ArgumentNullException"></exception>
/// <exception cref="ArgumentException">I... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c#, reinventing-the-wheel, ip-address",
"url": null
} |
lagrangian-formalism, symmetry, field-theory, action, noethers-theorem
Title: Transformation of coordinates in Noether's Theorem I am confused, in the proof of Noether's theorem, by the change of boundary in the action integral during the transformation of coordinates. I have seen on Wikipedia
that along with the cha... | {
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"tags": "lagrangian-formalism, symmetry, field-theory, action, noethers-theorem",
"url": ... |
performance, vba, excel, search
.VerticalAlignment = xlCenter
With Selection.Font
.Name = "Arial"
.FontStyle = "Regular"
.Size = 10
End With
i = 2
' Begin looping:
' We are checking all the Worksheets in the Workbook
For Each wks In ActiveWorkbook.Worksheets
If wks... | {
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"openwebmath_score": null,
"tags": "performance, vba, excel, search",
"url": null
} |
exoplanet, observational-astronomy
I know that at times B and A would overlap and appear as a single sun,
but what about when they don't?
Well, do they? Do we know that for sure? For the overlap to happen, the orbit of Bb would have to be relatively coplanar to the mutual orbits of A and B. This seems likely, but I... | {
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c++, c++17
if(moduleId < module_count)
{
return modules_[moduleId];
}
else
{
return std::nullopt;
}
Look at the code generated when you call this!
Writing it to allow NVRO is much cleaner.
std::optional<ConfigurationModule> retval;
if (moduleId < module_count)
retval.emplace(mo... | {
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classical-mechanics, fluid-dynamics
Second: Your first equation is not the equation of energy conservation in the fluid. It is not written in conservative form $dw/dt=-\vec{\nabla}\vec{\jmath}$, where $w$ is a suitable density, and $\jmath$ is a current. It also does not include the internal energy density, which expl... | {
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- x2) + abs(y1 - y2), where abs(x) is the absolute value of x. Manhattan distance for numeric attributes : If an attribute is numeric, then the local distance function can be defined as the absolute difference of the values, local distances are often normalised so that they lie in the range 0 . Usually Euclidean distan... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
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"lm_q1_score": 0.9752018354801187,
"lm_q1q2_score": 0.80401678598899,
"lm_q2_score": 0.8244619285331332,
"openwebmath_perplexity": 821.909100899805,
"openwebmath_score": 0.7825772762298584,
"tags": nu... |
ros-kinetic, dynamic-reconfigure
Title: dynamic_reconfigure: Why don't many ROS Navigation Plugins have add_dependencies() for gencfg in CMakeLists.txt
I was following this tutorial to get dynamic_reconfigure to work on my own nav_stack plugin.
However, I notice that in ros navigation stack plugins, for example the g... | {
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"openwebmath_score": null,
"tags": "ros-kinetic, dynamic-reconfigure",
"url": null
} |
gazebo
Title: Problem to install GAZEBO in Synaptic
Hi!
when i "Mark" "ros-fuerte-simulator-gazebo" in "Synaptic" when this package "is not installed" (in status!), wanna "to be removed" some ROS packages in list, when i click "mark". it gave me this error:
Can't Mark All Packages For Installation Or Upgrade
ros-fu... | {
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"tags": "gazebo",
"url": null
} |
math, norm
Title: How to prove this norm inequality? $$
\left( \sum |z_i|^a \right)^b \geq \left( \sum |z_i|^b \right)^a, \quad \forall a\in [1,2], b\in [2,+\infty)
$$
Actually this is equivalent to
$$
\|z\|_a \geq \|z\|_b \quad \forall a\leq b
$$ Although the question could belong to SE.math, mastering inequalities ... | {
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"tags": "math, norm",
"url": null
} |
machine-learning, python-3.x, market-basket-analysis
Title: How to present Market Basket Analysis Results? I am working on a Retail Company's in-store transactions for 3 months. I have performed the Market Basket Analysis on the same and I'm getting hundreds if not thousands of association rules. I am using the aprior... | {
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"tags": "machine-learning, python-3.x, market-basket-analysis",
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There are at least two optimizations you could make.
First of all, you are performing r multiplications and r divisions for each value of C(k,r) you compute for r < k/2. You should only need at most one multiplication and one division per value of C(k,r) that you compute, because at the time you want to compute C(k,r)... | {
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"lm_label": "1. YES\n2. YES",
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"lm_q1_score": 0.9390248225478307,
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"openwebmath_perplexity": 1297.1675396423818,
"openwebmath_score": 0.6181367039680481,
"ta... |
quantum-mechanics, hamiltonian-formalism
Title: Eigenstates & eigenvectors of the vector potential $\mathbf{A}$ In the presence of a magnetic field $\mathbf{B} = \nabla \times \mathbf{A}$, the Hamiltonian of a classical system is modified to :
$$ H = \frac{(\mathbf{p}-\frac{e}{c}\mathbf{A})^2}{2m}, $$
which is usually... | {
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"tags": "quantum-mechanics, hamiltonian-formalism",
"url": null
} |
Let $w_j$ denote the approximation to $u'\bkt{x_j}$, the derivative of $u$ at $x_j$. The standard second-order finite difference approximation is
\begin{align} w_j = \dfrac{u_{j+1}-u_{j-1}}{2h} \label{eqn_central_difference} \end{align}
which can be derived by considering the Taylor expansions of $u\bkt{x_{j+1}}$ and... | {
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"tags": nu... |
homework-and-exercises, thermodynamics, entropy, thought-experiment
This is a homework question but I believe it touches on something very general. The lake is a heat bath and the water added is our small thermodynamic system. We need to calculate the change in entropy of both system and surroundings and then add them... | {
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"url": nul... |
As Ant said in the comments, in both cases, the answer is $\frac{4}{52} = \frac{1}{13}$. Your first equation simplifies to this: \begin{align*} \left(\frac{4\cdot 3}{52 \cdot 51}\right) + \left(\frac{48 \cdot 4}{52 \cdot 51}\right) &= \left(\frac{4}{52}\right)\left( \frac{3}{51} + \frac{48}{51}\right) \\ &= \left(\frac... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
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"openwebmath_score": 0.9508559107780457,
"ta... |
electromagnetism, waves, vectors, calculus, superposition
z+\omega t)}=\frac{1}{2}$, and $\overline{\cos(2\omega t)}=0$, we obtain: $\overline{E^2}=\frac{1}{4}(\frac{1}{2}E_i^2+\frac{1}{2}E_r^2+E_i E_r\cos(2\delta z))$. Therefore, $\overline{E^2}$ is maximum when $\cos(2\delta z)=1$ and minimum when $\cos(2\delta z)=-... | {
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"tags": "electromagnetism, waves, vectors, calculus, superposition",
"url": null
} |
Substitution method. converts the recursion into a tree whose Solutions to exercise and problems of Introduction to Algorithms by CLRS (Cormen, Leiserson, Rivest, and Stein) Divide (line 2): (1) is required to compute q as the average of p and r. Conquer (lines 3 and 4): 2 T ( n /2) is required to recursively solve two... | {
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"id": null,
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"lm_q1_score": 0.9777138196557983,
"lm_q1q2_score": 0.8511949741121726,
"lm_q2_score": 0.8705972616934408,
"openwebmath_perplexity": 630.4070380938905,
"openwebmath_score": 0.7153167724609375,
"... |
special-relativity, spacetime, reference-frames, lorentz-symmetry
Fun exercise: Apply the same reasoning to a symmetrical setup using buoys in both Alice's and Bob's frame.
Note following comments: As @dmckee observed, the phenomenon is independent of a particular choice of time origin, in either frame. Alice and Bob ... | {
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"url": null
... |
performance, algorithm, c, random, ascii-art
There are at least multiple functions in main().
//TODO: Implement program input and conditional commands
Set up the screen
The contents of the while (1) loop also seem to be multiple functions
Default Cases for switch Statements
While it isn't necessary in the current co... | {
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"openwebmath_score": null,
"tags": "performance, algorithm, c, random, ascii-art",
"url": null
} |
optics, interference, hologram
Title: Sampling theorem for in-line digital holography In digital holography, the image sensor must have a sufficient pixel density. The book New Techniques in Digital Holography by Pascal Picart and others, the following condition is given:
Considering the maximum angle $\theta_{max}$... | {
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"tags": "optics, interference, hologram",
"url": null
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# 2021 JMPSC Sprint Problems/Problem 1
## Problem
Compute $\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{9}\right)(3+6+9)$.
## Solution
Solving the right side gives $3 + 6 + 9 = 18$. Distributing into the left side gives $\frac{18}{3}+\frac{18}{6}+\frac{18}{9}$, so the answer is $6 + 3 + 2 = \boxed{11}$.
## Solution 2
$... | {
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"openwebmath_score": 0.9273114204406738,
... |
c#, wpf, mvvm, rubberduck, xaml
private DeclarationType DeclarationType
{
get
{
DeclarationType result;
if (!DeclarationTypes.TryGetValue(ComponentType, out result))
{
result = DeclarationType.Class;
}
return result;
... | {
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"tags": "c#, wpf, mvvm, rubberduck, xaml",
"url": null
} |
4. Jul 12, 2013
vanhees71
One can use differentiation to check, where the function has an extremum, and then it's easy to check where it takes a maximum for natural numbers.
I'd also take the logarithm before, i.e., setting $f(x)=x^{1/x}$, I'd investigate
$$g(x)=\ln[f(x)]=\frac{\ln x}{x}.$$
5. Jul 12, 2013
Ray Vic... | {
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"openwebmath_score": 0.8836337924003601,
... |
dot product of two vectors and two... Vectors representing adjacent sides by its height leaning rectangular box is a two-dimensional figure with four sides weights! With initial point and terminal point, Online calculator between the input by... To create the area of this page dimensional space are given a triangle wit... | {
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"lm_q1_score": 0.989986427013312,
"lm_q1q2_score": 0.8719771444067899,
"lm_q2_score": 0.8807970701552504,
"openwebmath_perplexity": 302.8607392057107,
"openwebmath_score": 0.7798196077346802,
"tags": null,... |
Do you know the derivatives of trig functions? If so: first, write $\tan x = \sin x/\cos x$. Then simplify the resulting fraction and multiply by $1 = \frac{x - 0}{x - 0}$, and use the limit you already know and a particular interpretation of what remains to see that the limit is indeed $0$. To start you off: \begin{al... | {
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"lm_q1_score": 0.9637799462157138,
"lm_q1q2_score": 0.8248521777080732,
"lm_q2_score": 0.8558511524823263,
"openwebmath_perplexity": 564.0530901219649,
"openwebmath_score": 0.9720847010612488,
"tag... |
Solution to Understanding Analysis 2nd Edition Exercise of Chapter 2.6
Exercise 2.6.1
Let $\varepsilon > 0$ be arbitrary. Since $(x_n)$ converges to $x$, there exits $N\in\mathbf N$ such that $$\label{eq2.6.1.1}|x_n-x|<\frac{\varepsilon}{2}$$ for all $n\geqslant N$.
Whenever $n,m\geqslant N$, we have\begin{align*}|x... | {
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"openwebmath_score": 0.9975311160087585,
"ta... |
P(true-negative result) is $$P(H-)=(1-p)f;$$
P(false-negative result) is $$P(D-)=p(1-v);$$
the false omission rate (complement of the NPV) is $$P(D|-)=\frac{P(D-)}{P(D-)+P(H-)}=\frac{p(1-v)}{p(1-v)+(1-p)f};$$
the false discovery rate (complement of the PPV) is $$P(H|+)=\dots.$$
$$P(\text{False Negative Result}) = P... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9857180635575531,
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"lm_q2_score": 0.8289388083214156,
"openwebmath_perplexity": 447.18414788248447,
"openwebmath_score": 0.6292878985404968,
"ta... |
a square root if it has a factor that's a perfect square. Now I do have something with squares in it, so I can simplify as before: The argument of this radical, 75, factors as: This factorization gives me two copies of the factor 5, but only one copy of the factor 3. Denominator separately, reduce the fraction and chan... | {
"domain": "labonska.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9683812318188365,
"lm_q1q2_score": 0.8230961304135535,
"lm_q2_score": 0.8499711718571774,
"openwebmath_perplexity": 632.3590035240143,
"openwebmath_score": 0.8792956471443176,
"tags": n... |
general-relativity, spacetime, differential-geometry, metric-tensor, geodesics
Title: Geodesic equation (free particle) How to find a coordinate system whose geodesic equation does not have the "Christoffel symbol" term? (i.e. free particle - generalized Newton's second law.) Suppose you're in a coordinate system wher... | {
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"tags": "general-relativity, spacetime, differential-geometry, metric-tensor, geodesics",
... |
java, beginner, snake-game, javafx
fruit = new Fruit(Color.RED);
fruit.moveToRandom(emptyTiles);
pane.getChildren().add(fruit);
emptyTiles.remove(fruit.getPoint());
}
@Override
public void close() {
pane.getChildren().removeAll(snake.getRectangles());
pane.getChildr... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "java, beginner, snake-game, javafx",
"url": null
} |
qiskit, programming
Title: Jordan-Wigner $\leftrightarrow$ Bravyi-Kitaev transformation in Qiskit A couple of questions regarding the conversion between Jordan-Wigner (JW) and Bravyi-Kitaev (BK) states in Qiskit.
The JW $\rightarrow$ BK conversion matrix I refer to below is the one from equation (29) here. (I'm not re... | {
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"tags": "qiskit, programming",
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equilibrium
I have the answers for this, and this is the step I got to:
$$\frac{[0.5]^2}{[0.5]^2[0.75]}$$
So, I know in the top part of the fraction, it is given that at equilibrium $\pu{0.5 mol}$ of water is present. I get that.
But it also says that $\pu{1 mol}$ of $\ce{H2S}$ and $\pu{1 mol}$ of $\ce{SO2}$ reacted. ... | {
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"tags": "equilibrium",
"url": null
} |
c++, reinventing-the-wheel, memory-management, overloading
//QUATRO
friend DynString operator+ (char* x, DynString& y) {
DynString newString;
newString.c = new char[strlen(x) + strlen(y.c) + 1];
strcpy(newString.c, x);
strcat(newString.c, y.c);
return newString;
}
/... | {
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"tags": "c++, reinventing-the-wheel, memory-management, overloading",
"url": null
} |
navigation, turtlebot, ros-hydro, slam-gmapping, gmapping
<param name="xmin" value="-30.0"/>
<param name="ymin" value="-30.0"/>
<param name="xmax" value="30.0"/>
<param name="ymax" value="30.0"/>
<!--
<param name="xmin" value="-1.0"/>
<param name="ymin" value="-1.0"/>
<param name="xmax" value=... | {
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"id": 19562,
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"tags": "navigation, turtlebot, ros-hydro, slam-gmapping, gmapping",
"url": null
} |
special-relativity, spacetime, inertial-frames, coordinate-systems, lorentz-symmetry
From Figure 02:
Lorentz Transformation from $\:\mathrm{S_{1}}\equiv \{x_{1}y_{1}\eta_{1}, \eta_{1}=ct_{1}\}\:$ to $\:\mathrm{S_{2}}\equiv \{x_{2}y_{2}\eta_{2}, \eta_{2}=ct_{2}\}\:$
\begin{equation}
\begin{bmatrix}
x_{2}\\
... | {
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"tags": "special-relativity, spacetime, inertial-frames, coordinate-systems, lorentz-symmet... |
c#, beginner, game, wpf, xaml
private void Save()
{
SaveWindow saveWindow = new SaveWindow();
saveWindow.ShowDialog();
}
private void Exit()
{
bool? proceed = true;
Confirm confirm = new Confirm();
proceed = confirm.ShowDialog... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c#, beginner, game, wpf, xaml",
"url": null
} |
you should note that
i) this is only true for each connected component of $U$
ii) strictly speaking $u*\rho_\epsilon$ is only defined on $U_\varepsilon = \{x\in U: d(x,\mathbb{R}^n\backslash U)>\varepsilon\}$, so you first get the result for any such domain, but then it it true for $U$ if $\varepsilon$ tends to $0$. | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9811668695588647,
"lm_q1q2_score": 0.8067047268298045,
"lm_q2_score": 0.822189121808099,
"openwebmath_perplexity": 243.8495989098854,
"openwebmath_score": 0.9688162207603455,
"tags... |
ros, ros-melodic
That should print more information to the terminal.
You should see some confirmation of connection, or errors / warnings in case it couldn't connect.
Comment by zahid990170 on 2022-07-06:
thanks @gvdhoorn, yes, it printed the following
[ INFO] [1657115166.352950658]: Added message handler for message ... | {
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"url": null
} |
vba, type-safety
End Sub
Insertion
Public Sub Emplace(ByVal index As Long, ByVal element As Variant)
TypeCheck element, TypeName(Me) & ".Emplace"
this.Emplace index, element
End Sub
Public Sub Insert(ByVal index As Long, ByVal sequence As Variant)
TypeCheckSequence sequence, TypeName(Me) & ".Insert"
... | {
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"openwebmath_score": null,
"tags": "vba, type-safety",
"url": null
} |
thermodynamics, visible-light, lenses
I forgot to mention that you can't heat the sample beyond about $5500\,K$ (which is the temperature of a black body that best fits the spectrum we receive at sea level). Of course, you need to know what you're doing to get anywhere close to this temperature. | {
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"tags": "thermodynamics, visible-light, lenses",
"url": null
} |
pca, matplotlib
Title: Ploting eigenvectors I've generated two clouds of 3d points from multivariate_normal
data = np.random.multivariate_normal([2,2,2],[[1,0,0],[0,5,0],[0,0,10]],
size=500)
data = np.vstack((data, np.random.multivariate_normal([-2,-2,-2], [[1,0,0],[0,5,0],[0,0,10]], size=500)))
data = data - data.m... | {
"domain": "datascience.stackexchange",
"id": 4391,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "pca, matplotlib",
"url": null
} |
to that particular variable. Implicit Differentiation (7:55) The Rate of Change (6:53) Related Rates (8:31) All videos are closed captioned. Beyond Calculus is a free online video book for AP Calculus AB. Related rates problems can be solved using by computing. Extrema on an Interval; Rolle’s Theorem; Mean Value Theore... | {
"domain": "wm-20-10.de",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9763105245649665,
"lm_q1q2_score": 0.8499732708877084,
"lm_q2_score": 0.8705972633721708,
"openwebmath_perplexity": 860.0567509387288,
"openwebmath_score": 0.7438331246376038,
"tags": nu... |
newtonian-mechanics, classical-mechanics, rotational-dynamics, reference-frames
The last part of the puzzle is equating net force $\boldsymbol{F}$ to the rate of change of linear momentum and net torque about the center of mass $\boldsymbol{\tau}_{\rm COM}$ to the rate of change of angular momentum.
The equations belo... | {
"domain": "physics.stackexchange",
"id": 69966,
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"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "newtonian-mechanics, classical-mechanics, rotational-dynamics, reference-frames",
... |
ros, turtlebot, hokuyo, ros-indigo
and
$ lsof | grep /dev/ttyACM0
lsof: WARNING: can't stat() fuse.gvfsd-fuse file system /run/user/1000/gvfs
Output information may be incomplete.
lsof: WARNING: can't stat() fuse.gvfsd-fuse file system /run/user/1001/gvfs
Output information may be incomplete.
lsof: WARNING... | {
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"id": 32118,
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"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "ros, turtlebot, hokuyo, ros-indigo",
"url": null
} |
single-cell, atac-seq, pcr, duplications
Title: How is PCR duplication rate computed in scATAC-seq? Reading Cusanovich et al. (2015) I encountered the sentence:
We mixed pairs of cell lines (HEK293T or HL-60 versus GM12878), performed combinatorial cellular indexing, and sequenced the resulting libraries to saturatio... | {
"domain": "bioinformatics.stackexchange",
"id": 652,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "single-cell, atac-seq, pcr, duplications",
"url": null
} |
classical-mechanics, precession
Since $L$ points along the axis of the top, we see that this axis moves to the right... (Giancoli, 2008)
I just don't understand why you can assume that it will always be true that $L$ and the axis of the top will always lie on top of one another.
The book doesn't address this, but is ... | {
"domain": "physics.stackexchange",
"id": 845,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "classical-mechanics, precession",
"url": null
} |
c++, performance, programming-challenge, c++14
This form allows us to parallelize the computation to (possibly) eke out a tiny bit more speed:
#pragma omp parallel for reduction(+:sum)
On my system, this makes it much slower - you'd need a larger problem space to benefit, I think.
Reduce the search space
Instead of t... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c++, performance, programming-challenge, c++14",
"url": null
} |
python, beginner, python-2.x, role-playing-game
There is commenting (although basic). Commenting code is a MUST, even if it's for yourself. It will help you understand your own code and help anyone else who uses it, even if it's just to show different parts of the program.
The code is broken down into functions, which... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, beginner, python-2.x, role-playing-game",
"url": null
} |
c#, array, extension-methods
return sourceArray.CalculateTrim( false, false, true, false );
}
/// <summary>
/// Trims the outer bottom layers of null objects;
/// </summary>
/// <typeparam name="TSource">A <see cref="Nullable"/> type object.</typeparam>
/// <param name="sourceArray">The source ... | {
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"id": 25776,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c#, array, extension-methods",
"url": null
} |
quantum-mechanics, energy, angular-momentum, schroedinger-equation, spherical-harmonics
In both cases, the additional symmetry is related to the fact that the $n=-1$ and $n=2$ cases are the only ones to support closed orbits.
Also, in both cases, you can go out of your way to define "radial" quantum numbers (basically... | {
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"openwebmath_score": null,
"tags": "quantum-mechanics, energy, angular-momentum, schroedinger-equation, spherical-harm... |
python, pandas, dataframe, jupyter
Title: Calculate all days for each years between two dates in a pandas dataframe I'm new in python and coding. I'm doing a university project exercise. Last question is :
"
For each year, compute the total amount of loans. Each loan that has planned expiration time and disburse time ... | {
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"id": 8214,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, pandas, dataframe, jupyter",
"url": null
} |
vba, excel
Title: Key on a Header and Offset I have a section of code that I've been attempting to clean up and hopefully speed up. The section of code where I pass values in order to generate a key and update a table on a different sheet I think is my biggest problem. However I would like any suggestions/modification... | {
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"id": 12323,
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"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "vba, excel",
"url": null
} |
distributed-systems, arithmetic
Title: Overflow of integer counter in distributed systems I've just been introduced to Paxos.
There is notion of the of value that is incremented each time a new proposal is send. To provide order for proposals, something like time. What happens when this long or integer value overflow... | {
"domain": "cs.stackexchange",
"id": 7081,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "distributed-systems, arithmetic",
"url": null
} |
$$C_2^{2} = \frac{1}{1+R} (q*C_3^{3} + (1-q)*C_3^{2}) = 1.009276*(0.5636*7.65 + 0.4363*1.03) = 4.8051$$,
My questions are:
a) is the value of $$C_2^{2}$$ correct?
b) is there a faster way to calculate the option value of the tree because this takes a lot of time (yes you can write a program but I am following the th... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9736446471538802,
"lm_q1q2_score": 0.8351613168427101,
"lm_q2_score": 0.8577680977182187,
"openwebmath_perplexity": 414.7783489167521,
"openwebmath_score": 0.8174222707748413,
"tag... |
Sign Up free of charge:. It is so named based on its resemblance to the teeth of a plain-toothed saw with a zero rake angle. Thus, if you start with 20 points you will get 20 Fourier coefficients. Here, a sine function is full-wave rectified, meaning that the wave becomes positive wherever it would be negative. trigono... | {
"domain": "amicidellacattolica.it",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9848109511920161,
"lm_q1q2_score": 0.811939131812706,
"lm_q2_score": 0.8244619242200081,
"openwebmath_perplexity": 603.0161213606915,
"openwebmath_score": 0.8685778975486755,
... |
python, python-3.x, gui, pyqt
def reset_labels(self):
"""
Delete all labels in the current session_data.
Return:
None
"""
message = QMessageBox()
answer = message.question(
self, 'Question', 'Are you sure, do you want to delete all current sessio... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, python-3.x, gui, pyqt",
"url": null
} |
telescope, optics
Title: Shouldn't this cause a fire? This website shows a telescope projecting the sun onto a blackboard: https://astronomyconnect.com/forums/articles/2-three-ways-to-safely-observe-the-sun.21/
Why isn't the board catching fire? You can easily start a fire on a sunny day by targeting the focal poin... | {
"domain": "astronomy.stackexchange",
"id": 4967,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "telescope, optics",
"url": null
} |
If $k\neq \ell$
$$(A\cdot\hat A)_{k\ell}=\sum_{i=1}^n (-1)^{i+\ell}a_{ki} \det A(\ell\mid i)=0$$
for it is the expansion of the determinant of the matrix $A^{k\ell}$ defined by $$(A^{k\ell})=\begin{cases} a_{ij} \text{ if }i\neq \ell\\a_{kj}\text{ if }i=\ell\end{cases}$$ which has two equal rows.
• I can't seem to u... | {
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"id": null,
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9817357184418846,
"lm_q1q2_score": 0.8026420635838504,
"lm_q2_score": 0.8175744739711883,
"openwebmath_perplexity": 177.7501536819416,
"openwebmath_score": 0.9739255309104919,
"tag... |
special-relativity, momentum
y' &= y \\
z' & = z,\end{align}$$ and how to apply them to resolve the "twins paradox".
If I'm right about what's confusing you, you're stuck on what is known as Galilean addition of velocities:$$\mathbf{v}' = \mathbf{v} - \mathbf{u}_o,$$ where if an object is moving with velocity $\mathbf... | {
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"id": 33876,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "special-relativity, momentum",
"url": null
} |
php
if ($day > 0)
{
if ($day < 5)
{
$start += ((5 - $day) * 86400);
}
$end += (7 - $day) * 86400;
}
$weekend['StartDate'] = date('d-F-Y', $start);
$weekend['EndDate'] = date('d-F-Y', $end);
return $weekend;
} | {
"domain": "codereview.stackexchange",
"id": 670,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "php",
"url": null
} |
turing-machines, reductions
Title: Reduction from $L$ to $L_{TM}$
Let $L$ be the language of all the words with the shape $<M_1,M_2,w>$ such that $M_1,M_2$ are turing machines that accepts $w$, show that $L$ isn't decidable.
I thought to use reduction from $L_{TM}=\{<M,w>\mid M \text{ accepts } w\}$
how can I defin... | {
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"id": 8874,
"lm_label": null,
"lm_name": null,
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"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "turing-machines, reductions",
"url": null
} |
by the vector and the positive real axis (,. Determine its magnitude and argument of the complex number in matlab defined as the argument of a consisting. Divided have a complex number sin 5 6 π ) is but as result i. Functions on them predefined types for both complex and rational numbers, determine. Can convert angle ... | {
"domain": "carfol.pl",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9835969655605173,
"lm_q1q2_score": 0.8884774407223296,
"lm_q2_score": 0.9032942067038785,
"openwebmath_perplexity": 641.9323531297422,
"openwebmath_score": 0.8969402313232422,
"tags": ... |
organic-chemistry, stereochemistry, molecular-orbital-theory, pericyclic
The top line shows the symmetry allowed disrotatory closure of trans, trans-1,6-dimethylhexatriene. There are two possible disrotatory motions - either the tops or the bottoms of the p-orbitals on carbons 1 and 6 can move towards each other in a... | {
"domain": "chemistry.stackexchange",
"id": 3358,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "organic-chemistry, stereochemistry, molecular-orbital-theory, pericyclic",
"url... |
c++, linked-list
std::cout<<"\n--------------------------------------------------\n";
std::cout<<"----------------deleting at start-----------------";
std::cout<<"\n--------------------------------------------------\n";
obj.deleteHead();
std::cout << obj << std::endl;
std::cout<<"\n---------------... | {
"domain": "codereview.stackexchange",
"id": 31521,
"lm_label": null,
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"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c++, linked-list",
"url": null
} |
python, beginner, rock-paper-scissors
if player1Move == opponentMove:
print ("Tie!" + " Please go again.")
elif (player1Move == "Rock") and (opponentMove == "Paper"): # rock loses to paper
opponentScore = opponentScore + 1
elif (player1Move == "Paper") and (opponentMove == "Rock"): # paper beats rock
playe... | {
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"id": 20182,
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"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, beginner, rock-paper-scissors",
"url": null
} |
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