text stringlengths 49 10.4k | source dict |
|---|---|
neural-networks, machine-learning, proofs
$I: { i_1, \; \dots, \; i_n}$
to output bit vector
$O: { o_1, \; \dots, \; o_n}$
It was further back proven that such a mapping can be accomplished with one Boolean expressions for each output bit. For all $2^n$ possible input vector permutations, there exists a Boolean ex... | {
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"tags": "neural-networks, machine-learning, proofs",
"url": null
} |
newtonian-mechanics, classical-mechanics, kinematics, energy-conservation
Title: Why is energy not conserved in this situation Suppose there are three masses that are still relative to each other in space. They are positioned in an equilateral triangle. Let's accelerate one mass towards the other two with a force. The... | {
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"url... |
EDIT
In fact, this is the only non-zero solution for $\lambda = 0$. Apply $\partial_a$ to both sides of the functional equation, we get:
\begin{align}f'(a+b) &= \partial_a f(a+b)\\ &= \partial_a^n f(a)f(b) + (\partial_a^{n-1}\partial_b + \cdots + \partial_a\partial_b^{n-1})(f(a)f(b))\\ &= (\partial_a^{n-2} + \partial... | {
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"lm_q1_score": 0.9838471661250913,
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"lm_q2_score": 0.8152324915965392,
"openwebmath_perplexity": 151.26892732518144,
"openwebmath_score": 0.9942808151245117,
"ta... |
c++, matrix, computational-geometry, graphics, c++17
Summary
That was a fairly rushed review, but if there's a single takeaway here, I'd say that it's to use a flat architecture, and accept that the usage syntax won't be exactly what you want. (Though if you're really finicky about the syntax, you can get it, mostly. ... | {
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"tags": "c++, matrix, computational-geometry, graphics, c++17",
"url": null
} |
quantum-mechanics, quantum-optics, open-quantum-systems
Instead of semigroup property, we now have $V(t,t_1)V(t_1,t_0)=V(t,t_0)$". This actually seems to me a semigroup structure, but I think I am missing something, maybe on the mathematical side
Ok, that's actually true, this is not the semigroup property stated in ... | {
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How does the floating point implementation of the original recurrence get it so wrong? To see this, note that in the case of a small rounding error, the closed form expression for $x_n$ becomes $$x_n \approx \frac{3^{n+1}+5^{n+1}+\gamma_n 100^{n+1}}{3^n + 5^n + \gamma_n 100^n}$$ where $\gamma_n$ is a small number on th... | {
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"lm_q2_score": 0.8128673155708975,
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"openwebmath_score": 0.944542646408081,
"tags": n... |
By induction we can write $$w_1(a_1,\ldots,a_k) = a_1(a_2(\cdots(a_{k-1}a_k)\cdots))$$ so \begin{align*} w_1(a_1,\ldots,a_k)w_2(a_{k+1},\ldots,a_n) &= \Bigl(a_1\bigl(a_2(\cdots(a_{k-1}a_k)\cdots)\Bigr)\cdot w_2(a_{k+1},\ldots,a_n)\\ &= a_1\cdot\Bigl(a_2(\cdots(a_{k-1}a_k)\cdots)w_2(a_{k+1},\ldots,a_n)\Bigr) \\ &= a_1\c... | {
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"lm_q1q2_score": 0.8084514136237728,
"lm_q2_score": 0.8244619242200081,
"openwebmath_perplexity": 506.83361432083024,
"openwebmath_score": 0.9600741267204285,
"tag... |
homework-and-exercises, angular-momentum
Title: What is the meaning of change of angular momentum of a ballistic object during its flight? In a 2D world, three stones, whose magnitude of initial velocities are 5000m/s, are thrown from the North pole towards the Equator with horizontal initial angles of 15o, 30o, 45o a... | {
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"tags": "homework-and-exercises, angular-momentum",
"url": null
} |
navigation, laser, move-base, costmap-2d
Title: Costmap Laser "Smearing"
We are having a reoccuring issue with move_base's costmap.
The obstacles detected by the laser scan tend to get "smeared" through the costmap.
The obstacle stays constant in the body frame of the robot (setting the laser persistance on rviz to a... | {
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"openwebmath_score": null,
"tags": "navigation, laser, move-base, costmap-2d",
"url": null
} |
python, object-oriented, homework, pygame, snake-game
I would appreciate it if you could help me because this is my project and I have to give it to the instructor tomorrow. Your code overall is pretty structured, but here are some improvement suggestions. The acronym for them is called PBS:
1. 'P'ut DocStrings i... | {
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"tags": "python, object-oriented, homework, pygame, snake-game",
"url": null
} |
algorithm, haskell, numbers-to-words
Title: Converting numbers to words in Haskell Here's a program I wrote to convert numbers into English words using Haskell.
import Data.Char
import Data.List
type WordNum = String
ones :: (Integral a, Show a) => a -> WordNum
ones 1 = "one"
ones 2 = "two"
ones 3 = "three"
ones 4 =... | {
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"tags": "algorithm, haskell, numbers-to-words",
"url": null
} |
statistical-mechanics, entropy, hamiltonian-formalism, phase-space, reversibility
Above, I have assumed that one has waited for the system to reach equilibrium, but the same discussion also applies if you look at what happens at a time $t$ before equilibrium has been reached: the system will find itself in another mac... | {
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"tags": "statistical-mechanics, entropy, hamiltonian-formalism, phase-space, reversibility"... |
computability
I find Rice-Shapiro easier to use if I think about it as two separate results:
One is a monotonicity result, telling us that if $f \in \Gamma$ and $f \subseteq g$ with $g$ partial recursive, then $g \in \Gamma$. I.e. recursive extensions of functions in $\Gamma$ must belong to $\Gamma$ -- otherwise, $R_... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "computability",
"url": null
} |
pressure, fluid-statics
There are more molecules (but all the molecules are the same)
they have the same temperature (which means the average speed is the same)
leading to the idea that there are more collisions per area on the high-pressure side
If one side has a thousand molecules and one has a million molecules, t... | {
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"tags": "pressure, fluid-statics",
"url": null
} |
java, benchmarking
public BenchmarkRunner(Object target) {
this.target = target;
Class<?> clazz = target.getClass();
Benchmark annotation = clazz.getAnnotation(Benchmark.class);
if (annotation != null) {
defaultIterations = annotation.iterations();
defaultWarmUp... | {
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Overview and Key Difference 2. A forward difference is an expression of the form [] = (+) − (). The floor exerts a reaction force forward on the professor that causes him to accelerate forward. Newton’s Forward Interpolation Formula with MATLAB Program In everyday life, sometimes we may require finding some unknown val... | {
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"lm_q1_score": 0.9857180685922242,
"lm_q1q2_score": 0.8081836820353325,
"lm_q2_score": 0.8198933425148213,
"openwebmath_perplexity": 1146.4404937222164,
"openwebmath_score": 0.764614224433... |
programming-challenge, swift
// loop through numOfQueries
for _ in 0..<numOfQueries {
// each query is given in format [1, x, y] or [2, x, y]
let query = readLine()!.componentsSeparatedByString(" ").map { Int($0)! }
// check to see if query[0] is 1 or 2
switch query[0] {
case 1:
// formula ... | {
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"tags": "programming-challenge, swift",
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} |
python, python-3.x, morse-code
where InvalidMorseLetter is:
class InvalidMorseLetter(Exception):
pass
Read here and here.
In the code, I wrote to catch a KeyError because that is the error that would be raised if an invalid dictionary key is used.
You should use a custom exception because it specifically describe... | {
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"tags": "python, python-3.x, morse-code",
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} |
Hope this helps!
Last edited: Jan 19, 2016
6. Jan 20, 2016
### DaTario
I would like to express gratitude to you all for the answers.
Very interesting, spamanon, the observation that torque can be thought as Joule per radian. In fact, the equation:
$\tau = I \alpha$
makes it clear.
This makes the two questions very... | {
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performance, c, multithreading, pathfinding
Parallelizing the code
Not all algorithms lend themselves to be parallelized. Most require that the steps are done in a well-defined order, and having multiple threads work at the same time on the same problem might prevent that.
You can add mutexes to prevent multiple threa... | {
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"tags": "performance, c, multithreading, pathfinding",
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} |
ds.algorithms, big-list
Title: Polynomial-time algorithms with huge exponent/constant Do you know sensible algorithms that run in polynomial time in (Input length + Output length), but whose asymptotic running time in the same measure has a really huge exponent/constant (at least, where the proven upper bound on the r... | {
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parametric equations of basic curves, such as a line and a circle. The parametric equations of a circle with the center at and radius are. We give four examples of parametric equations that describe the motion of an object around the unit circle. Figure 9.32: Graphing the parametric equations in Example 9.3.4 to demons... | {
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"lm_q1_score": 0.9869795102691455,
"lm_q1q2_score": 0.8092179188093223,
"lm_q2_score": 0.8198933315126792,
"openwebmath_perplexity": 333.98548530394413,
"openwebmath_score": 0.8086267709732056,
"tags... |
c, file, console
if (!isdigit(c)) {
// We have a x.y. followed by a non-digit
int chars_printed = sprintf(state->output + state->output_index, "%zu.%zu.", major, minor);
if (chars_printed < 1) {
return "Error occurred while trying to write to output buffer";
}
state->o... | {
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"tags": "c, file, console",
"url": null
} |
machine-learning, regression, svr, rfe
Title: Why do I get an ValueError for an SVR model with RFE, but only when using pipeline? I am running five different regression models to find the best predicting model for one variable. I am using a Leave-One-Out approach and using RFE to find the best predicting features.
Fou... | {
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"tags": "machine-learning, regression, svr, rfe",
"url": null
} |
java, object-oriented, game, snake-game
Okay, so generally, I'd suggest not carrying around a set of empty
spaces. Keeping the taken coordinates for the snake and for the food is
fine. Using those you can immediately see which coordinates are empty
... all the ones that aren't taken. Given the few food items and th... | {
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"tags": "java, object-oriented, game, snake-game",
"url": null
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structural-engineering, beam, reinforced-concrete
With Model 1, this isn't a risk because the vertical steel from the beam ("stirrups") will resist these forces.
Model 1 also has an advantage in that it makes the beam itself stronger, since it allows the beam to behave as a much taller beam (including the height of th... | {
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"tags": "structural-engineering, beam, reinforced-concrete",
"url": null
} |
rust, tcp, redis
key.to_string(),
value.as_bytes().to_vec(),
Some(duration.parse::<u64>().unwrap()),
))
} else {
Err(())
}
}
... | {
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"tags": "rust, tcp, redis",
"url": null
} |
peak <- function(x, y, alpha=0.05) {
#
# Estimate the peak of a quadratic logistic fit of y to x
# and a 1-alpha confidence interval for that peak.
#
logL <- function(b) {
# Log likelihood.
p <- sapply(cbind(rep(1, length(x)), x, x*x) %*% b, logistic)
sum(log(p[y==1])) + sum(log(1-p[y==0]))
}
f <- function(gamma) {
# D... | {
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"openwebmath_perplexity": 1893.9101154811324,
"openwebmath_score": 0.6975759267807007,
"ta... |
organic-chemistry, reaction-mechanism
Title: Reaction of ethene with ammonia and sodium Is the following sequence of reactions correct?
$$\ce{CH2CH2 ->[][\ce{NH3},\,\ce{Na}] NaHC=CHNa}$$
$$\ce{NaCH=CHNa + 2CH3CH2Br-> CH3CH2CH=CHCH2CH3}$$ No, because for ethene, $\mathrm{p}K_\text{a} = 44$. You won't be able to abstrac... | {
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"tags": "organic-chemistry, reaction-mechanism",
"url": null
} |
forces, classical-mechanics, lagrangian-formalism, constrained-dynamics
Title: Force of constraint for particle constrained to a surface In Goldstein's Classical Mechanics, he wrote
If a particle is constrained to move on a surface, the force of constraint is perpendicular to the surface.
Why must the force of cons... | {
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"tags": "forces, classical-mechanics, lagrangian-formalism, constrained-dynamics",
"url":... |
special-relativity, vectors, tensor-calculus
Title: 4-velocities in different frames We have an observer in an inertial frame $S$ who measures a particle's 4-velocity as $U$. We then have another inertial frame $S'$ with $X'=\Lambda{X}$, where $\Lambda$ is a matrix representing a Lorentz transformation. (To be clear, ... | {
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"openwebmath_score": null,
"tags": "special-relativity, vectors, tensor-calculus",
"url": null
} |
quantum-gate, circuit-construction, quantum-circuit
Title: Constructing a two 3-qubit state involving either X, Y or Z rotation gate The goal is to construct the state
$|\psi\rangle = \frac{1}{2}|010\rangle + \frac{\sqrt{3}}{2}|101\rangle$
Two issues I am facing:
What is a good choice for initial state?
What is a goo... | {
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Putting it all together
The volume of the holes is $6$ times the sum of the volumes of the cylinder and cap, plus the volume of the intersection:
$$V_{\text{holes}} = 6 \pi (2 \sqrt{2}-1) + \left (108- 76 \sqrt{2}\right )\pi + 8 (2-\sqrt{2})= (102-64\sqrt{2})\pi + 8 (2-\sqrt{2})$$
The volume left over after drilling... | {
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"openwebmath_score": 0.951598048210144,
"tags"... |
newtonian-mechanics, newtonian-gravity, energy-conservation, orbital-motion, potential-energy
I know it's actually the work done by the object as it goes towards the earth. That's consistent with the formula W=Fd (gravity would be doing positive work, hence negative work by the object itself)
This doesn't make sense... | {
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so this is consistent with your observation that $2$ is the inverse of $11 \bmod 3$ also.
• I now understand why this is correct from algorithmical point of view, but I don't understand why −1 ≡ 2 mod 3. I miss some math-related thing. – Danetta Jun 18 at 9:12
• Presumably you have no problem with $11 \equiv 8\equiv 5... | {
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"tag... |
slam, navigation, ros2, service, rtabmap
Title: Getting error after calling a service in eloquent
Hi!
I`m trying to use a Rtabmap service, which is defined as follows:
#request
bool global
bool optimized
bool graph_only
---
#response
Then, I call:
ros2 service call /publish_map rtabmap_ros/srv/PublishMap "{gl... | {
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"url": null
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binary-star, keplers-laws
$$ G=4\pi ^{2}\mathrm {\ AU^{3}{\cdot }yr^{-2}} \ M^{-1}\approx
> 39.478\mathrm {\ AU^{3}{\cdot }yr^{-2}} \ M_{\odot }^{-1}$$ | {
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graphs, approximation, linear-programming, integer-programming
Now suppose you want to compute a solution (not necessarily optimal) to the IP system. Using the LP relaxation, a way to do it is the following:
compute an optimal solution $X =\{x_v\mid v\in V\}$ to the LP relaxation;
consider $y_v = \left\{\begin{array}... | {
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"tags": "graphs, approximation, linear-programming, integer-programming",
"url": null
} |
c, makefile, cmake, integration-testing
/usr/bin/make -f CMakeFiles/openshell.dir/build.make CMakeFiles/openshell.dir/build
make[3]: Entering directory '/home/dac/.CLion2016.1/system/cmake/generated/openshell-69ebaaf9/69ebaaf9/Debug'
[ 25%] Building C object CMakeFiles/openshell.dir/util.c.o
[ 50%] Building C object C... | {
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"tags": "c, makefile, cmake, integration-testing",
"url": null
} |
ros, multi-robot, multimaster, multi-machine
Originally posted by roboviz with karma: 26 on 2011-07-26
This answer was ACCEPTED on the original site
Post score: 0
Original comments
Comment by Per Lenander on 2011-12-21:
I have the exact same problem you had (with foreign relay, not wifi_comm) and I've tried the above... | {
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python, console, hangman
src/hangman/_lax_enum.py
import re
from collections.abc import Generator
from re import Pattern
from typing import ClassVar
class LaxEnum(type):
'''
Despite its name, a LaxEnum is no different from
a normal class except for that it yields every
item that is not a dunder when b... | {
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"url": null
} |
homework-and-exercises, newtonian-mechanics, newtonian-gravity, orbital-motion, planets
$$
or you can write them in spherical reference frame
$$
\vect{r} = r\uvec{r}
$$
or in cylindrical reference frame ($\ldots$). Regardless of the system of coordinates you dediced to describe the particle with, you can always calcul... | {
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"tags": "homework-and-exercises, newtonian-mechanics, newtonian-gravity, orbital-motion, pl... |
quantum-mechanics, heisenberg-uncertainty-principle, measurement-problem, commutator, observables
Title: From uncertainty to commutation relations Consider the famous problem of measuring both the position and momentum of an electron. We start with two photographs at different times, then worry about the momentum of t... | {
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Now the set of intervals assigned to $$J_i$$ covers $$J_i$$, except possibly for an interval at the left of length $$\le\frac{i-1}m|A|\le\frac{i-1}m$$, and an interval at the right of length $$\le\frac{m-i}m|A|\le\frac{m-i}m$$. Therefore, the sum of the lengths of intervals assigned to $$J_i$$ is $$\ge\frac sm-\frac{i-... | {
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"openwebmath_score": 0.9442065954208374,
"tag... |
javascript, ecmascript-6, bootstrap-4
ageInput.setAttribute('value', userAge);
//assemble age column
ageInputGroupPrepend.appendChild(ageInputGroupText);
ageInputGroup.appendChild(ageInputGroupPrepend);
ageInputGroup.appendChild(ageInput)... | {
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"tags": "javascript, ecmascript-6, bootstrap-4",
"url": null
} |
c#, design-patterns, .net, converting, framework
Am I reinventing the wheel? I couldn't find anything like it in the .NET framework but I also did not look very hard.
As I understand it, yes.
I believe all you're trying to do here is to register a 'mapping' between types. Provide an instance of one type, get back an... | {
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} |
-
Well, you lost me at "each term is n+1...". As far as I can see, if you add the two equations term by term it will be: n+n + (n-1)+(n-1) + ... + 2+2 + 1+1. How did you get (n+1) + (n+1) + ... + (n+1)? – b1_ Aug 12 '10 at 18:27
I got it! It's 2S = (1+2+...+(n-1)+n) + (n+(n-1)+...+2+1) - so you write one backwards, th... | {
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"openwebmath_score": 0.9920458197593689,
"tag... |
machine-learning, python, keras, cnn, image-classification
Title: ValueError: Error when checking input: expected conv2d_1_input to have 4 dimensions, but got array with shape (142, 1) I'm trying to pass all my images (71 for each class) from folder 'train' to model.fit.
The method ReadImages get these images and resi... | {
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} |
• First multiply with the denominator (that's $\neq 0$),
• then add $1 + \tan\alpha\tan\beta$ to both sides,
• then write $1 + x + y + xy$ as the product $(1+x)(1+y)$.
-
Thank you. I had got as far as $1 - \tan\alpha\tan\beta = \tan\alpha + \tan\beta$ but didn't think to rearrange to $1 = \tan\alpha +\tan\beta +\tan\al... | {
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"lm_q1q2_score": 0.8262034807078332,
"lm_q2_score": 0.8438951045175643,
"openwebmath_perplexity": 1010.8130883686238,
"openwebmath_score": 0.9707325100898743,
"ta... |
gazebo
Title: surface material colors from URDF and COLLADA
Gazebo 1.2.5 no longer seems to be picking up the material tag from the URDF file. This can be seen through the following commands (from this tutorial on the ROS wiki).
roslaunch gazebo_worlds empty_world.launch
roslaunch gazebo_worlds table.launch
A screen... | {
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"tags": "gazebo",
"url": null
} |
string-theory, mathematical-physics, research-level, topological-field-theory, category-theory
Title: About the Atiyah-Segal axioms on topological quantum field theory Trying to go through the page on Topological quantum field theory - The original Atiyah-Segal axioms - "Let $\Lambda$ be a commutative ring with 1, At... | {
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"tags": "string-theory, mathematical-physics, research-level, topological-field-theory, cat... |
newtonian-mechanics, string
Title: Vertical circular motion/How can tension be negative?
This is a rock tied to a string spinning vertically.
Here,
$T+mgsin\theta = mv_1^2/r => T = mv_1^2/r-mgsin\theta$
Suppose I give it a velocity $v$ at the bottom.
1) At what angle $\theta$ will the tension become zero?
2) If the... | {
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(2) angle at the vertex C(x,y) equals to 90 degrees --> ABC is a right triangle with hypotenuse AB --> consider AB to be diameter of a circle and in this case C could be anywhere on the circle and it will be right angle (if the diameter of the circle is also the inscribed triangle’s side, then that triangle is a right ... | {
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"openwebmath_perplexity": 2198.3319928084566,
"openwebmath_score": 0.6977137923240662,
"tags": null,
"url": ... |
r, roc
#> rsample * 1.1.0 2022-08-08 [1] CRAN (R 4.1.0)
#> rstudioapi 0.13 2020-11-12 [1] CRAN (R 4.1.0)
#> scales * 1.2.0 2022-04-13 [1] CRAN (R 4.1.0)
#> sessioninfo 1.2.2 2021-12-06 [1] CRAN (R 4.1.0)
#> stringi 1.7.8 2022-07-11 [1] CRAN (R 4.1.0)
#> stringr ... | {
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"tags": "r, roc",
"url": null
} |
linear-programming, network-flow
Title: How are vertex capacities defined in a flow network? I'm new to network flows and I'm reading this topic from Cormen's Algorithms book (3rd edition) from 26 chapter. I came across this problem from the 26.1 section
Suppose that, in addition to edge capacities, a flow network ha... | {
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is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. Let us take the base and height of the triangle be x cm. One of the angles is straight (90 o ) and the other is the same (45 o each) Triangular obtuse isosceles angle : two sides are the sam... | {
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"openwebmath_perplexity": 493.65826513452413,
"openwebmath_score": 0.6773985028266907,
"tags": nul... |
graph-theory, graph-algorithms, graph-classes
Title: Is it necessary to call matrix multiplication $n$ times to find a claw A claw is a $K_{1,3}$. A trivial algorithm will detect a claw in $O(n^4)$ time. It can be done in $O(n^{\omega+1})$, where $\omega$ is the exponent of fast matrix multiplication, as follows: take... | {
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"openwebmath_score": null,
"tags": "graph-theory, graph-algorithms, graph-classes",
"url": null
} |
water, aqueous-solution, solubility, home-experiment
Title: Does the salt in the ocean act as a binding agent on sand? When I walk on the beach, there appears to be an upper layer of the sand that is 'crusty'.
This appears to be the opposite of what you see in sand in a dessert setting, where the individual particle... | {
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"tags": "water, aqueous-solution, solubility, home-experiment",
"url": null
} |
ros, imu, gazebo, simulation, gazebo-plugins
Title: Interpretation of IMU data from the gazebo_ros_imu plugin
We want to use the gazebo_ros_imu plugin for the simulation of our quadrotor and other vehicles in Gazebo. When looking at the output and source file of the plugin, several questions arise:
When the platform... | {
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"tags": "ros, imu, gazebo, simulation, gazebo-plugins",
"url": null
} |
ruby, markov-chain
Title: Name/word generator using DTMC in Ruby I just wrote a basic DTMC algorithm focused on generating names, though it could be used to generate lots of other things. It's designed to be run from the command line, so input is taken from a file, with a couple of options specified on the command lin... | {
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"tags": "ruby, markov-chain",
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} |
c++, c++11, recursion, boost, static
return calcedSize;
}
// ...
} Don't Repeat Yourself
Your looping code appears twice. Once in the body of size() and once in the body of GoRec::size(). You only need it once. In fact, the entire structure of GoRec is kind of weird and unnecessary. I also don't like how you ... | {
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When the goal is prediction, analyses begin in a similar way to exploratory analyses. You might want to come up with a list of candidate models you want to test, which can either be based on an exploratory analysis of the data or informed by theory or the literature as to which variables might be useful for predicting ... | {
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"openwebmath_perplexity": 431.8432274751122,
"openwebmath_score": 0.5763149261474609,
"tags": n... |
statistical-mechanics, atoms
Title: Was Lord Kelvin correct when he postulated the size of atoms? In What is Life? published in 1944, physicist Erwin Schrodinger writes the following:
Why are atoms so small? To begin with, they are very small indeed.
Every little piece of matter handled in everyday life contains an
e... | {
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### Standard#
FORTRAN 77 and later
## hypot#
### Name#
hypot(3) - [MATHEMATICS] returns the distance between the point and the origin.
### Syntax#
result = hypot(x, y)
real(kind=KIND) elemental function hypot(x,y) result(value)
real(kind=KIND),intent(in) :: x, y
where x,y,value shall all be of the same kind.
... | {
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"openwebmath_score": 0.5095717906951904,
"tags":... |
thermodynamics, rotational-kinematics
Title: Will rotational kinetic energy of an object ultimately dissipate due to internal energy loss? First time to physics Stack Exchange and I'm about to show my extreme lack of physics knowledge. I've only been through Physics 121, particle physics. So, bear with me!
So an obje... | {
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Any element of $H\cap K$ distinct from $e_G$ will have both order $3$ and $5$, but no such element of $g$ exists. To be more precise, if $g\in G$ is such that $g^3=g^5=e_G$, then $g=e_G$.
• Thanks, but you missed a part of my question. $H$ is isomorphic to $\Bbb Z_{3}$ and $K$ is isomorphic to $\Bbb Z_{5}$. But then $\... | {
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c#, generics, enum
/// <summary>Gest the hash code for the current object.</summary>
/// <returns>A hash code for the current object.</returns>
public override int GetHashCode() =>
base.GetHashCode();
}
RestrictedEnum is not the best name, as it does not really tell me anything about what this class d... | {
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} |
where
$$\beta^{(ij)}_k = \begin{cases} 1, & k = i, \\ -1, & k = j, \\ 0, & \text{otherwise}. \end{cases}$$
Obviously, for this choice of $u$, we have $\alpha_k = 1$ for all $k$. Notice that $\langle u, w_{ij} \rangle_1 = 1 - 1 = 0$ for all $i < j$. Therefore,
$$\langle u, w_{ij} \rangle_2 = 0$$
for all $i < j$. Let... | {
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"openwebmath_score": 0.9873944520950317,
"ta... |
$$\chi_p^2 \equiv \sum_{i=1}^p Z_i^2 \sim \text{ChiSq}(p).$$
Now, the random variables $$Z_1^2,Z_2^2,Z_3^2, ...$$ are IID with mean $$\mathbb{E}(Z_i^2) = 1$$ and variance $$\mathbb{V}(Z_i^2) = 2 < \infty$$, so we have $$\mathbb{E}(\chi_p^2) = p$$ and $$\mathbb{V}(\chi_p^2) = 2p$$. Applying the classical central limit ... | {
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"openwebmath_score": 0.8971330523490906,
"ta... |
newtonian-gravity, lagrangian-formalism, statics, variational-principle
Solving the equation and reversing the variable substitution gives
$$r(\phi) = \frac{GM\rho}{\lambda}\frac{\alpha^2 - 1}{\alpha\bigl(\alpha - \cosh\bigl[\sqrt{\alpha^2 - 1}(\phi - \phi_0)\bigr]\bigr)}\tag{cf. 23}$$
Note: I'm not convinced the most... | {
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"url": ... |
c++, constructor
or eliminate side-effects until you have one side-effect per line:
throw std::invalid_argument("Failed to initialize Kafka configuration. Caused by " + m_errstr);
I would also caution that rd_kafka_conf_set can probably fail for plenty of reasons that would not be best described as "invalid argument.... | {
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$$ii 9, 18, 31, 48, 69, 94,...$$
$$iii 14, 11.5, 9, 6.5, 4, 1.5,...$$
Consider the following sequence. $$\displaystyle{s}_{{n}}={2}{n}−{1}$$ (a) Find the first three terms of the sequence whose nth term is given. $$\displaystyle{s}_{{1}}={N}{S}{K}{s}_{{2}}={N}{S}{K}{s}_{{3}}=$$ (b) Classify the sequence as arithmetic, ... | {
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"lm_q1_score": 0.9899864281950694,
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"lm_q2_score": 0.8289387998695209,
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"openwebmath_score": 0.7760883569717407,
"tags":... |
We'll introduce our approach by proving the uniqueness up to
automorphisms of the projective planes of order at most 5
and identifying their automorphism groups. In each case we
do this by showing that all (hyper)ovals are equivalent, i.e.
by showing that a combinatorial projective plane Π must have a
(hyper)oval O an... | {
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"lm_q1_score": 0.9907319853876677,
"lm_q1q2_score": 0.8277402594148112,
"lm_q2_score": 0.8354835330070839,
"openwebmath_perplexity": 2557.5821634393883,
"openwebmath_score": 0.8611697554588318,
"tags": n... |
cross-validation, smote
Title: Is it necessary to use stratified sampling if I am using SMOTE already? I have already applied SMOTE to my imbalanced dataset with more than 300K observations. Does it still make sense to use stratified K-fold cross validation rather than simply ordinary K-fold cross validation (seems un... | {
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"tags": "cross-validation, smote",
"url": null
} |
c++, beginner, c++17, lexical-analysis
7,What Changes,68853 / 2,MChoice,TRUE,0.414285714,1,1:52,,"Harrison, D"," L01 - Introductory, BT01 - Recall (remembering and understanding), Protein Structure-Function, B01 Biochemistry"
8,Secondary Structure,68854 / 1,MChoice,TRUE,0.357142857,1,1:33,,"Harrison, D"," L01 - Introd... | {
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"tags": "c++, beginner, c++17, lexical-analysis",
"url": null
} |
c++, c++14, statistics
int main(int argc, char** argv) {
double bad_array[]{1.0};
try
{
sd(bad_array, bad_array);
}
catch (std::runtime_error& error)
{
cout << "ERROR: " << error.what() << "\n";
}
try
{
sd(bad_array, bad_array + 1);
}
catch (std::... | {
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"id": 20815,
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"lm_q1q2_score": null,
"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "c++, c++14, statistics",
"url": null
} |
Since $B(0,r_m) \supset B(0,r_c)$, the map $\frac{\vec{\nabla}V}{|\vec{\nabla}V|}$ will be surjective over the hyper-torus $$\bigg\{ (x_1,\ldots,x_n) : x_1^2 + \left(\sqrt{x_2^2 + x_3^2 + \cdots + x_n^2} - (r_m+1)\right)^2 \le r_m^2 \bigg\}$$ Since $U(x,y) = x$ whenever $x^2 + y^2 \ge r_m^2$, $V(x_1,\ldots,x_n)$ equals... | {
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"id": null,
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9736446486833801,
"lm_q1q2_score": 0.8510406225542377,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 282.0459992361244,
"openwebmath_score": 0.9861288070678711,
"tag... |
computer-vision, edge-detection
Title: Get histogram of edge lengths/orientations in an image using OpenCV In the process of trying to estimate whether a ROI contains [Japanese] text, I need to get a rough count of edges, hopefully binned by length and/or orientation... I think this would give me strong-enough feature... | {
"domain": "dsp.stackexchange",
"id": 175,
"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": "computer-vision, edge-detection",
"url": null
} |
javascript, object-oriented, opengl, webgl
this.detail.gl.attachShader(this.detail.webGLProgramObj, webGLVertexShaderObj);
this.detail.gl.attachShader(this.detail.webGLProgramObj, webGLFragmentShaderObj);
// Bind the vertex attributes, if any.
// This must happen BEFORE linking the program.
if (vertex... | {
"domain": "codereview.stackexchange",
"id": 13720,
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"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "javascript, object-oriented, opengl, webgl",
"url": null
} |
general-relativity, differential-geometry, metric-tensor, tensor-calculus, vector-fields
$\delta_\xi\equiv {\cal L}_\xi$ is a Lie-derivative wrt. the vector field $\xi$ in the active picture, or a general coordinate transformation in the passive picture.
The terminology Einstein transformation yields (at the time of ... | {
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"id": 19040,
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"tags": "general-relativity, differential-geometry, metric-tensor, tensor-calculus, vector-... |
Once you've done that you will probably be able to find other families of intervals covering $\mathbb Q$ whose total length is as small as you may want.
Let $\{r_n\}=\mathbb Q$ be an enumeration of rationals. For each fixed positive integer $k$, consider the collection $E_k= \{ [r_n, r_n +1/2^{k+n}):n\ge 1\}$, then $E... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.986571747626947,
"lm_q1q2_score": 0.81114857597576,
"lm_q2_score": 0.8221891392358015,
"openwebmath_perplexity": 292.7279845953763,
"openwebmath_score": 0.7609784007072449,
"tags":... |
c#, uwp
};
}
catch (FormatException ex)
{
return null; // TODO log;
}
return platform;
}
Stations and Lines are sets that have been constructed in the exact same way (only without fk's). Hirarchy-wise I want the Stations to include a list of plattforms and each ... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c#, uwp",
"url": null
} |
cosmology, symmetry, quantum-gravity, big-bang
Title: Why isn't our universe symmetric? Why were random variations introduced in the spherically symmetric universe after Big Bang which made it non-symmetrical. Since the outcome of a coin toss depend on factors such as torque applied, air resistance etc. By the same lo... | {
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"lm_q2_score": null,
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"tags": "cosmology, symmetry, quantum-gravity, big-bang",
"url": null
} |
Anyway, those highest points tend to be saddles. The very, very highest point-- where's that in Alaska or somewhere-- that's a max, of course, by definition. But there are a lot of saddle points in other places. And those would be maxima of minima or minima of maxima.
Good. I'm stopping there. We might see this again ... | {
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"lm_q2_score": 0.8289388019824946,
"openwebmath_perplexity": 610.2312734417585,
"openwebmath_score": 0.7315199971199036,
"tags": null,
... |
quantum-mechanics, operators, momentum, vectors
on the left hand side we get a vector, but on the right hand side we get a scalar?
It would make sense for me to apply $\hat{p}_x$, $\hat{p}_y$ and $\hat{p}_z$ to the wavefunction separately and put the results into a vector getting $\bar{p} = (p_x, p_y, p_z)$, but I don... | {
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"tags": "quantum-mechanics, operators, momentum, vectors",
"url": null
} |
php, svg
Or even:
$y = 100 + 20*$start2 + 20; // + 20 for initial loop where $i = 0
for(...) {
$y = $y - 20;
}
You already have quite a lot of variables, but if performance really matters, you could save constant results in further variables (such as (($max + $max10) / 4, $y - 12, 5 - 82/5, etc; see also my note ... | {
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"tags": "php, svg",
"url": null
} |
a complicated matrix product in moving a particle from one point to another now let 's look some! Force makes an angle theta with the displacement some of the vector projection of b onto a vector projections ''! N and let x be a subspace of R n and let be! Let 's look at some examples regarding vector projections compl... | {
"domain": "com.ua",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9626731158685838,
"lm_q1q2_score": 0.8311638880043787,
"lm_q2_score": 0.8633916064586998,
"openwebmath_perplexity": 540.020270122964,
"openwebmath_score": 0.7926164269447327,
"tags": null... |
discussed the problem of finding out whether a given graph is Eulerian or not. }$$ Then at any vertex other than the starting or ending vertices, we can pair the entering and leaving edges up to get an even number of edges. Graf yang mempunyai lintasan Euler dinamakan juga graf semi-Euler (semi-Eulerian graph). Is ther... | {
"domain": "uoa.gr",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9678992932829917,
"lm_q1q2_score": 0.8187870797104523,
"lm_q2_score": 0.8459424295406088,
"openwebmath_perplexity": 524.4225499700382,
"openwebmath_score": 0.48435333371162415,
"tags": nu... |
python, game, rock-paper-scissors
while intro_loop == True:
#Valid name input is stored inside the player_name variable (was formerly blank)
player_name = input("\nWelcome to Rock Paper Scissors, PYTHON REMASTERED!\n What is your name?\t")
if player_name != "": #If statement forces the name to not be blank... | {
"domain": "codereview.stackexchange",
"id": 36255,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, game, rock-paper-scissors",
"url": null
} |
-
\begin{align} \sin(z)^2 &= (\sin x \cos (iy))^2 +(\cos x \sin(iy))^2 \\ &=\sin^2x \cosh^2y+\cos^2x \sinh^2y \\ &= \sin^2x (1+\sinh^2y )+(1-\sin^2x ) \sinh^2y \\ &=\sin^2 x+\sin^2 x \sinh^2y+ \sinh^2y-\sin^2x \sinh^2y \\ &=\sin^2x+\sinh^2y \end{align}
- | {
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"id": null,
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"lm_q1_score": 0.9833429595026213,
"lm_q1q2_score": 0.8396890863329848,
"lm_q2_score": 0.8539127455162773,
"openwebmath_perplexity": 595.664883251431,
"openwebmath_score": 0.9977002143859863,
"tags... |
navigation, move-base
Hovever when I am using rviz it seams that it is able to work
correctly sometimes.
Do you know any solution for this issue?
This are my yaml files:
base_local_planner_params.yaml:
TrajectoryPlannerROS:
max_vel_x: 0.45
min_vel_x: 0.1
max_rotational_vel: 1.0
min_in_place_rotational_vel: 0.4
acc_lim... | {
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"id": 9278,
"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": "navigation, move-base",
"url": null
} |
Dividing into cases where there is one chocolate ball and more than one.
One chocolate ball of ice cream:
$11$ flavors left to choose from. Is combination 'with repetition' with $n=11$ and $r=4$ and then subtract all inapplicable cases. (All cases - cases where there are $3$ of $1$ flavor and $1$ of another - cases w... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9920620049598214,
"lm_q1q2_score": 0.8619300234890879,
"lm_q2_score": 0.8688267660487573,
"openwebmath_perplexity": 581.2403988490029,
"openwebmath_score": 0.7283103466033936,
"tag... |
The end result was 666666, then N=5... there IS a 5-digit number that you can multiply by (5+2) = 7 and end up with 666666 (it's 95,238 - you just have to do a little division to prove it). This IS a possibility.
The end result was 7777777, then N=6, but there is no 6-digit number that you can multiply by (6+2) = 8 an... | {
"domain": "gmatclub.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9196425267730008,
"lm_q1q2_score": 0.8038385971417774,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 1703.3075328679993,
"openwebmath_score": 0.6720051765441895,
"tags": ... |
TL;DR $$\quad f(x)=x^3+Ax^2+1\,$$ always has a simple zero on the negative axis. The other two zeros are
• real, positive and distinct, if $$\,A<-1.88988\:=\:-\dfrac{3}{\sqrt[3]{4}}\:=\:A_1$$
• merging into a double zero at $$x=\sqrt[3]{2}$$, if $$\,A=A_1$$
• non-real (thus complex-conjugate), if $$\,A>A_1$$ | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9883127416600689,
"lm_q1q2_score": 0.85146919156448,
"lm_q2_score": 0.861538211208597,
"openwebmath_perplexity": 370.22600157662055,
"openwebmath_score": 0.8927750587463379,
"t... |
python, python-3.x, tkinter
my_gui = Application()
my_gui.mainloop() Importing tkinter
Pick a single way to import tkinter. You currently have this:
import tkinter as tk
from tkinter import *
Remove the second line so that you only have this:
import tkinter as tk
That means that you have to prefix all tkinter classe... | {
"domain": "codereview.stackexchange",
"id": 16269,
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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": "python, python-3.x, tkinter",
"url": null
} |
A[0,1] = 0.000000000001
A.is_symmetric()
A.is_symmetric(tol=1.0e-13)
This is not a course in numerical linear algebra, even if that is a fascinating field of study. To concentrate on the main ideas of introductory linear algebra, whenever possible we will concentrate on number systems like the rational numbers or al... | {
"domain": "runestone.academy",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9888419690807407,
"lm_q1q2_score": 0.8014355644746147,
"lm_q2_score": 0.810478913248044,
"openwebmath_perplexity": 281.1879529503222,
"openwebmath_score": 0.9999170303344727,
"tags... |
# help factoring
#### slowle4rner
##### New member
I'm having trouble factoring the following binomial... can someone try to point me in the right direction please?
4y^3+4
It has been 7 years since I took algebra and I am trying to get my review done. This one just does not make sense to me right now...
Thanks!
#... | {
"domain": "mathhelpboards.com",
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"lm_q1_score": 0.9802808759252645,
"lm_q1q2_score": 0.8785780851794255,
"lm_q2_score": 0.8962513772903669,
"openwebmath_perplexity": 457.30777979942474,
"openwebmath_score": 0.8290965557098389,
... |
newtonian-mechanics, thermodynamics, pressure, volume
Title: Confusion on $pV$ diagrams I am extremely confused on the concept of a $pV$ diagram.
I understand that Pressure times (change in) Volume equals the Work done by a piston; however, I am confused on how volume and pressure can increase at the same time. Accord... | {
"domain": "physics.stackexchange",
"id": 94640,
"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": "newtonian-mechanics, thermodynamics, pressure, volume",
"url": null
} |
quantum-mechanics, electromagnetism
$$
\mathbf p = -i \hbar \nabla_{\mathbf r} = \boldsymbol \pi+q\mathbf A(\mathbf r).
$$
It is normal for operators to be expressible using other operators. For example, kinetic momentum can be in some scenarios expressed as constant times $\mathbf rH_0 - H_0\mathbf r$. This does not... | {
"domain": "physics.stackexchange",
"id": 96501,
"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": "quantum-mechanics, electromagnetism",
"url": null
} |
ros
Title: rosemacs error : dynamic-completion-table
After installing ros-noetic on a debian 10. I installed ros-noetic-rosemacs via apt. The installed version is : 0.4.17-1buster.20220221.094135.
When I run emacs (emacs --debug-init) I get the following error:
Debugger entered--Lisp error: (void-function dynamic-com... | {
"domain": "robotics.stackexchange",
"id": 38428,
"lm_label": null,
"lm_name": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "ros",
"url": null
} |
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