text stringlengths 1 1.11k | source dict |
|---|---|
the formula for the volume of a Rectangular Prism?. Largest Pyramid top You can headfirst lay a second pyramid (green) inside a pyramid. 8\text{ cm}. Volume of these solids are depending on the area of their bases. The volume of the cube is x 3 and hence the volume of the pyramid is 1/6 x 3. Program for volume of Pyram... | {
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"lm_q1q2_score": 0.8201423244467436,
"lm_q2_score": 0.8397339616560072,
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"openwebmath_score": 0.6127729415893555,
"tags":... |
The statement is not for every positive integer but only for positive integers up to $$N$$. It is not trying to claim it is true for any positive integer greater than $$N$$.
Consider: $$P(j )=$$: If $$j \le N$$ then something, call it $$Q(j)$$ is true.
Let's say we can show that if $$k< N$$ that $$Q(k)\implies Q(k+1)... | {
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"openwebmath_score": 0.8099619150161743,
"tags... |
# If I have that $X$ is a random variable satisfying $0\leq X \leq 1$, how can I show that $P\left(X \geq \frac{E(X)}{2}\right) \geq \frac{E(X)}{2}$?
If I have that $X$ is a random variable satisfying $0\leq X \leq 1$, how can I show that $P\left(X \geq \frac{E(X)}{2}\right) \geq \frac{E(X)}{2}$? I saw a footnote whic... | {
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"tags"... |
python, python-3.x, tkinter
from tkinter import Entry
import tkinter as tk
import random as rand
import sys
import os
root = tk.Tk()
root.geometry("450x250+500+300")
root.title("Let's play Math!")
welcomeLabel = tk.Label(text="LET'S PLAY MATH!").pack()
startLabel = tk.Label(text='Select a math operation to start').p... | {
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"tags": "python, python-3.x, tkinter",
"url": null
} |
c#, performance, array
Here value is too vague; prefer count.
common exceptions
For a square matrix of side N, your test code throws
about 12 × N IndexOutOfRangeExceptions,
which seems like perhaps more than you'd prefer
since doing so takes time.
Consider expanding the array with borders,
so we have (N + 2 × distThr... | {
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"tags": "c#, performance, array",
"url": null
} |
inorganic-chemistry, nmr-spectroscopy
Title: H1 NMR Spectra of inorganic complex, Cu4OCl6(2-mepy)4 I'm having difficult interpreting the following H1 NMR I have been given for Cu4OCl6(2-mepy)4.
The NMR spectra obtained with integration trace beneath. I'm not too sure how to rationalise the 4.5:1 ratio between the pe... | {
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"tags": "inorganic-chemistry, nmr-spectroscopy",
"url": null
} |
physical-chemistry, atmospheric-science, spectroscopy
If the tiny $\mathrm{CO_2}$ signal changed, it would be difficult to disentangle the effects of $\mathrm{CO_2}$ concentration, solar activity, geomagnetic activity, upper atmosphere dynamics, the season, the location, …. We have many better ways of monitor atmosphe... | {
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"id": 93190,
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"openwebmath_score": null,
"tags": "physical-chemistry, atmospheric-science, spectroscopy",
"url": null
} |
ngs, covid-19, sars-cov-2, metagenome, virus
These are very small genomes < 30 kb. Quasi-species is a very real phenomenon (loads of mutations), however mixed infections are also well-known. In a mixed infection, producing one genome which is a mix of two genetically distinct viruses is a key concern. Under my experie... | {
"domain": "bioinformatics.stackexchange",
"id": 2111,
"lm_label": null,
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"lm_q1q2_score": null,
"lm_q2_score": null,
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"tags": "ngs, covid-19, sars-cov-2, metagenome, virus",
"url": null
} |
If we go back and remember that this is a ball that has been thrown upwards, then obviously it must "stop" shortly before falling back down. However, as I have shown, it stops for absolutely no time at all.
What is confusing me, is that both of the below statements are true;
1. The ball has a velocity of $0$ for no t... | {
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"openwebmath_score": 0.8402496576309204,
"tag... |
electric-circuits, electric-current, potential, electrical-resistance, voltage
If I am drawing a circuit of the cube above, and the potential
between, let's say, the upper far corner and all three adjacent
corners is the same, why can I depict this as three resistors in
parallel between two nodes? | {
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... |
ubuntu-precise, ubuntu, cmake
Originally posted by mysteriousmonkey29 on ROS Answers with karma: 170 on 2014-07-22
Post score: 0
Original comments
Comment by McMurdo on 2014-07-23:
As an aside, even the simple ros hello-world talker/listener is not just one source file. In the true spirit it is at least 2-3 source fi... | {
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"tags": "ubuntu-precise, ubuntu, cmake",
"url": null
} |
quantum-mechanics, observables, quantum-states, quantum-measurements, born-rule
In short, we can only use $|\langle u_i|\psi\rangle|^2$ if $|\psi\rangle$ can be written as a superposition of eigenkets of $A$. What if $|\psi\rangle$ is such that we cannot write it as a superposition of the eigenkets of the observable ... | {
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"tags": "quantum-mechanics, observables, quantum-states, quantum-measurements, born-rule",
... |
ocean, climate-change
That leads me to my question: Is the ocean really "rising", or is the floor just getting "thicker/higher". The article states that millions of tons of sediment is being deposited on the ocean floor every year. Most people say/believe that melting ice is causing the ocean level to rise. I'm no... | {
"domain": "earthscience.stackexchange",
"id": 894,
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"tags": "ocean, climate-change",
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} |
python, beginner, python-2.x, csv
Suggested solution
In addition to the main concerns above, I've tweaked the output routine a bit for maintainability.
Note that strftime() also doubles as a string formatter.
import csv, time
from datetime import date, timedelta
with open('SendJobs.csv') as f:
SendIDs = set(row[1... | {
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} |
java, game
public int currentState;
public Enemy(int x, int y)
{
this.x = x;
this.y = y;
this.speed = 3;
this.currentState = CREATED;
this.setDimenseions(40,35);
this.loadImage(ENTITY_ID);
this.createRectangle();
}
@Override
public void entityLogic(GameContainer gc, int deltaTime)
{
... | {
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"tags": "java, game",
"url": null
} |
c++, c++17
return std::array< T, ToN >{ a[I]... };
}
template< typename T, typename TupleT, std::size_t... I >
constexpr decltype(auto) TuppleToArray(const TupleT& t,
std::index_sequence< I... >) {
return std::array< T, sizeof...(I) >{ std::get< I >(t).... | {
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"tags": "c++, c++17",
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} |
general-relativity, metric-tensor, faster-than-light, physical-constants, warp-drives
Title: Alcubierre metric without geometrized units In the beginning of Alcubierre's paper, he defines his metric with the use of geometrized units ($G = c = 1$). While it makes the math simpler, it seems to hide the physical numbers ... | {
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algorithms, optimization, terminology, dynamic-programming
EDIT: Here is a C++ program for finding a maximal subsequence in $\mathcal{O}(n \log^{2} n)$. I use a segment tree for the range maximum data structure.
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
using ll = long long;
const... | {
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"tags": "algorithms, optimization, terminology, dynamic-programming",
"url": null
} |
ros-melodic
is it possible to install a ROS1 distro without removing python3-catkin-pkg
Not that I know of, as these packages conflict.
On the bright side I'd expect most of these packages to be reinstalled in their python2 variant along with ROS1.
You'll just end up with the python2 version of the executables instea... | {
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"tags": "ros-melodic",
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} |
c#, beginner, timer
Don't use the Thread class, use the Task Parallel Library class. It'll be much easier. You will need to use Task.Delay instead of Thread.Sleep
Notice that you're line-breaking outside of the loop and not inside. Also WriteLine will add a line-break at the end automatically | {
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"tags": "c#, beginner, timer",
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} |
algorithms, strings, enumeration
Title: Why isn't a binary counter used for generating $k$-combinations? I have been looking at algorithms that allow you to generate $k$-combinations of a given string.
My question is that why isn't the algorithm used to generate power sets used to generate the combinations of a given ... | {
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"tags": "algorithms, strings, enumeration",
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} |
Taylor Series Expansion Calculator computes a Taylor series for a function at a point up to a given power. Jack Taylor (TV Series 2010) cast and crew credits, including actors, actresses, directors, writers and more. and compare it to a₋n. These techniques include substitution and multiplication and division of series ... | {
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"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9890130576932457,
"lm_q1q2_score": 0.8085918259981172,
"lm_q2_score": 0.8175744695262777,
"openwebmath_perplexity": 521.1226257899933,
"openwebmath_score": 0.8538424372673035,
... |
lagrangian-formalism, differential-geometry, field-theory, variational-calculus, functional-derivatives
$$
\delta S\left[\gamma\right]=\int_{t_{0}}^{t_{1}}\gamma^{\ast}\mathscr{L}_{\dot{\Xi}}\Theta_{L}=\int_{t_{0}}^{t_{1}}\gamma^{\ast}\left(i_{\dot{\Xi}}d\Theta_{L}+di_{\dot{\Xi}}\Theta_{L}\right),
$$
where we have exp... | {
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"openwebmath_score": null,
"tags": "lagrangian-formalism, differential-geometry, field-theory, variational-calculus, f... |
rotational-kinematics, rotation
Title: Qualitative understanding of Euler rotation on gravitational vector If I choose the sequence of my Euler rotations to be $Z\rightarrow Y \rightarrow Z$ or in terms of matrix multiplication $R_x(\phi)R_y(\theta)R_z(\psi)$, a stationary $3$-axis accelerometer can measure a gravitat... | {
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"openwebmath_score": null,
"tags": "rotational-kinematics, rotation",
"url": null
} |
python, beginner, python-3.x, game, adventure-game
def present_person(people):
for individual in people:
print('\n{}'.format(individual))
load(15)
def start():
button = prompt_for_input(scavenge, ('X', 'B'))
load(5)
if button == 'X':
print('\n{}\n\n{}{}\n'.format(scavenge_resc... | {
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"tags": "python, beginner, python-3.x, game, adventure-game",
"url": null
} |
electromagnetism, electromagnetic-radiation, waves, maxwell-equations
Further, due to the superposition princpiple, if $\vec{E}_{EM}$ and $\vec{E}_{source}$ satisfy Maxwell's equations then so does $\vec{E}_T$. | {
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"tags": "electromagnetism, electromagnetic-radiation, waves, maxwell-equations",
"url": n... |
quantum-mechanics, quantum-field-theory, operators, hilbert-space, second-quantization
This interpretation is quite straightforward for the electromagnetic field, since every mode can be characterized by a momentum and polarization, so we can speak of a number of photons having this momentum and polarization. | {
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performance, c, null, portability
That version is much easier for humans to parse because of the judicious use of whitespace.
Use better names
The code has an odd characteristic in that every variable names begins with either p or l rendering the names unprounceable and impeding readability. I can only guess that the... | {
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Mat.(x = y);; (* is x equal to y *)
Mat.(x <> y);; (* is x unequal to y *)
Mat.(x > y);; (* is x greater to y *)
Mat.(x < y);; (* is x smaller to y *)
Mat.(x >= y);; (* is x not smaller to y *)
Mat.(x <= y);; (* is x not greater to y *)
All aforementioned infix have their corresponding functions in the... | {
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"lm_q2_score": 0.8333245973817158,
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"openwebmath_score": 0.3930170238018036,
"tags": ... |
ros-kinetic
But again: in general I would try to maintain a consistent up-to-date system.
Originally posted by gvdhoorn with karma: 86574 on 2018-11-15
This answer was ACCEPTED on the original site
Post score: 1
Original comments
Comment by kevin.kuei.0321@gmail.com on 2018-11-18:
Thanks for the reply.
I encountered... | {
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} |
c#, rational-numbers
if (upperFormat[0] == 'M')
{
innerFormat = format.Replace('M', 'G');
var integerPart = rational.IntegerPart.Numerator;
if (integerPart != 0)
{
var fractionalPart = rational.Frac... | {
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"tags": "c#, rational-numbers",
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} |
mechanical-engineering, mechanisms, metalwork
Title: Making a basic sprung mechanism that can withstand moderate percussive force I'm making a game where you have to hit targets, kind of like whack-a-mole except the targets aren't actively actuated. I'd still like an element of mechanical "feel" to it, so I'm aiming t... | {
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"id": 5283,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "mechanical-engineering, mechanisms, metalwork",
"url": null
} |
general-relativity, cosmology, energy-conservation, space-expansion, universe
Title: Energy extraction from universe expansion? I recently learned that energy is not conserved according to general relativity. Inspired, I went looking for a way to harness this interesting feature of the theory and came across an idea t... | {
"domain": "physics.stackexchange",
"id": 82712,
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"tags": "general-relativity, cosmology, energy-conservation, space-expansion, universe",
... |
that has at least one double bond is called as alkene with the general formula C n H 2 n. ffmpeg reads from an arbitrary number o. Therefore, vavg m s m/s. RMS voltage of a half wave rectifier, VRMS = Vm / 2 and Average Voltage VAVG= Vm/π, Vm is the peak voltage. If acceleration is constant the Vavg occurs at 1/2 the t... | {
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"lm_q2_score": 0.894789454880027,
"openwebmath_perplexity": 1900.9799295418693,
"openwebmath_score": 0.6601222157478333,
"tags": ... |
physical-chemistry, mole
Title: How to apply the Principal of Atom Conservation (POAC) 27.6 g $\ce{K2CO3}$ was treated by a series of reagents so as to convert all of its carbon to $\ce{K2Zn3(Fe(CN)6)2}$. Calculate the weight of the product.
I am asking here is that, why we are applying POAC only on Carbon atom not o... | {
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"tags": "physical-chemistry, mole",
"url": null
} |
kalman-filter
The correction step mostly works the same way. This time you have a measurement model that looks something like
$$
z_k = h(x)
$$
where $h(x)$ may be nonlinear. So how do we get calculate our predicted measurement $z$? You guessed it, we use an unscented transformation again. I won't go into details on ho... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "kalman-filter",
"url": null
} |
c, file-system, io, winapi, arduino
char *fin = strstr(SerialBuffer, word); //Find 'search' in SerialBuffer and assign to 'fin'
//if fin has data then close Serial and close/save file
if (fin != NULL){
printf("Results Successfully logged \n \r \n \r");
fclose(fp... | {
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"openwebmath_score": null,
"tags": "c, file-system, io, winapi, arduino",
"url": null
} |
special-relativity, terminology, aether
In that 1920 talk, Ether and the Theory of Relativity Einstein points out that Lorentz had already stripped the concept of Ether of almost all physical properties.
Quote:
As to the mechanical nature of the Lorentzian ether, it may be said of it, in a somewhat playful spirit, th... | {
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"tags": "special-relativity, terminology, aether",
"url": null
} |
-
Excellent answer! – jyim Oct 21 '12 at 15:58
@jonathan: Glad it helped! – Brian M. Scott Oct 21 '12 at 16:01
Both answers are good, but the $(B \land C)$ term is not necessary. If both $B$ and $C$ are true, then one of $(A \land C)$ or $(B \land \neg A)$ are satisfied too, depending on whether $A$ is true or not. ... | {
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"lm_q2_score": 0.8289388125473629,
"openwebmath_perplexity": 2141.915384942747,
"openwebmath_score": 0.9999700784683228,
"tag... |
quantum-mechanics, black-holes, astrophysics, hawking-radiation
This will be the fate of all evaporating black holes, but most will take a very long time to get to this stage (even supposing they do not accrete any matter).
The evaporation time is only less than the age of the universe for $M < $ a few $10^{11}\ \text... | {
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"id": 19070,
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"tags": "quantum-mechanics, black-holes, astrophysics, hawking-radiation",
"url": null
} |
thermodynamics
The heat of denaturation is small but not completely negligible. Since you start with 100C water, and want to end around 65C, for the small amount of water you mention (40 mL), it's around a 10% error.
Yes, if you're trying to hit it right at 63C, you'll need to account for the heat going into denatura... | {
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"tags": "thermodynamics",
"url": null
} |
force on the object then is. In specifying the transient-response characteristics of a control system to a unit-step input, it is common to specify the following: 1. Oscillations are the resulting solutions to the spring-mass system given by the differential equation. Abstract: This paper deals with the behaviour of an... | {
"domain": "gremium-franconia.de",
"id": null,
"lm_label": "1. YES\n2. YES",
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"openwebmath_score": 0.795654296875,
"tags... |
GALAXY EXPRESS 999 MOVIE BAKABT
sequences and series – Why does this converge to $\pi/4$? – Mathematics Stack Exchange
Iterative algorithms for computing approximations to the number PI through infinite series using double and arbitrary precision. The computer was designed with numbers represented and binary fraction... | {
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"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9905874109681435,
"lm_q1q2_score": 0.8028502083186545,
"lm_q2_score": 0.810478913248044,
"openwebmath_perplexity": 1145.5005775699653,
"openwebmath_score": 0.800981342792511,
"tags"... |
javascript, jquery
Title: Displaying text on button click I have some JS code that when the user clicks the "add" button, some text is displayed to a textarea.
The code seems to be working OK. However, I realize I must refactor the code so that I am using only the one on click function instead of the six that I have f... | {
"domain": "codereview.stackexchange",
"id": 16941,
"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": "javascript, jquery",
"url": null
} |
acid-base, everyday-chemistry
Title: Is it possible to neutralize acids with vinegar (e.g. when experiencing heartburn)? I would like to know if it is possible to neutralize heartburn with a shot of vinegar, or if one should only use basics (like edible soda). What I know from high school, is that you can neutralize a... | {
"domain": "chemistry.stackexchange",
"id": 9368,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
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"tags": "acid-base, everyday-chemistry",
"url": null
} |
quantum-mechanics, operators, harmonic-oscillator
$$\langle \hat{H}\rangle=\langle\Psi|\alpha\hat{x}^2+\beta\hat{p}^2|\Psi\rangle=\alpha\langle\Psi|\hat{x}^2|\Psi\rangle+\beta\langle\Psi|\hat{p}^2|\Psi\rangle=\alpha\langle\hat{x}^2\rangle +\beta\langle \hat{p}^2\rangle$$
We can calculate the expectation of $\hat{p}^2$... | {
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"tags": "quantum-mechanics, operators, harmonic-oscillator",
"url": null
} |
c++, iterator, sqlite
/* SELECT col1, col2 FROM table_name WHERE col1 = x;
table_name is table to select,
name_begin and end are iterators to a collection of column name strings in table to select
where_clause is the sql WHERE clause
where_bindings_begin and end are iterators to a colle... | {
"domain": "codereview.stackexchange",
"id": 41260,
"lm_label": null,
"lm_name": null,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "c++, iterator, sqlite",
"url": null
} |
java, object-oriented
private Optional<Command> findCommand(String identifier) {
return getAllCommands().stream().filter(c -> c.isIdentifier(identifier)).findAny();
}
private Set<Command> getAllCommands() {
Set<Command> commands = cli.getCommands();
commands.addAll(commandLineInteracti... | {
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"tags": "java, object-oriented",
"url": null
} |
ros, navigation, odometry, encoders, phidgets
n.setParam(reset_topic, false);
ros::Publisher odom_pub =
n.advertise<nav_msgs::Odometry>(name, 50);
tf::TransformBroadcaster odom_broadcaster;
// get encoder indexes
encoder_index_left = -1;
nh.getParam("encoderindexle... | {
"domain": "robotics.stackexchange",
"id": 28892,
"lm_label": null,
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"tags": "ros, navigation, odometry, encoders, phidgets",
"url": null
} |
"P implies Q" and "Q implies P"
? If you do agree, then notice what happens when P and Q swap places: We prove: "Q implies P" and "P implies Q", which is exactly the same as in the line above. So, it does not matter which statement is called "P" and which is called "Q".
18. Aug 9, 2016
### Mr Davis 97
Alright, I th... | {
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"openwebmath_score": 0.7066720724105835,
"... |
Case 2: -4x + 3 > 0
x < 3/4 ------(2)
Now think, is it possible that x is < than 3/4 and greater than 5/2? No! So this case doesn't give any solutions.
Hence, the only solution is x >= 5/2
and yes, don't try to learn up Mathematical concepts. Try to understand them. That way, you will never forget them.
_____________... | {
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"id": null,
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"lm_q2_score": 0.8807970732843033,
"openwebmath_perplexity": 4824.547883777812,
"openwebmath_score": 0.6306199431419373,
"tags": n... |
python, python-3.x, game, chess
return sorted(pos_moves)
class Rook(ChessPiece):
def __init__(self, pos='a1', color=None, num='_'):
ChessPiece.__init__(self, pos, color, num, self.__class__.__name__)
self.demo_moves = ('a1', 'a8', 'h8', 'h1', 'a1')
def possible_moves(self):
pos_moves ... | {
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"tags": "python, python-3.x, game, chess",
"url": null
} |
python, performance, number-guessing-game
mycm=col_mask[:]
myfm=field_mask[:]
if not self.check_groups(self.rows, myrm, self.cpr, mysol):
break
if not self.check_groups(self.cols, mycm, self.cpc, mysol):
break
if no... | {
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"openwebmath_score": null,
"tags": "python, performance, number-guessing-game",
"url": null
} |
quantum-mechanics, electromagnetism, polarization
Corollary: suppose I send in light along the $x$-axis polarized along the $y$-axis. Then it is again a superposition of $\sigma^+$ and $\sigma^-$. Does anything change? i.e. does it drive all three? The answer to this question is contained within Jagerber48's answer to... | {
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"tags": "quantum-mechanics, electromagnetism, polarization",
"url": null
} |
A set is dense/closed in a given topological space.
$[0,1]$ is closed in $\mathbb{R}$ but it is not dense in $\mathbb{R}$ since there are real numbers that can not be approached arbitrarily close by elements of $[0,1]$.
$[0,1]\setminus\{\frac{1}{2}\}$ is dense in $[0,1]$ but it is not closed in it.
Take $\mathbb R$ ... | {
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"openwebmath_perplexity": 151.26199863167778,
"openwebmath_score": 0.8905569314956665,
"ta... |
# Limit of quotient involving floor function and identity function
How can I prove that $$\lim_{x\to +\infty}\frac{\left \lfloor{x}\right \rfloor}{x}=1$$
L'Hôpital's rule seems to fail here, since the floor function is not differentiable for integers. What other ways are there to prove this?
• Try squeezing it. – ki... | {
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"lm_q2_score": 0.8267117962054048,
"openwebmath_perplexity": 415.67637359315546,
"openwebmath_score": 0.9518313407897949,
"ta... |
newtonian-mechanics, newtonian-gravity, reference-frames
Title: The chronology of taking approximation changes the answer? The problem is to find the time it takes a particle dropped from a height $h_0$ above the surface of the earth to reach the surface (exactly, not approximately i.e. $g$-value is not constant, in t... | {
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"openwebmath_score": null,
"tags": "newtonian-mechanics, newtonian-gravity, reference-frames",
"url": null
} |
Well, now you find all the partitions sets (=equiv. classes) one by one. After all, there're only 8 subsets here...
Tonio
5. Yeah a little, I guess im not really seeing the difference between equivalence class and partition. Are you able to have equivalence classes in a partition of something like the powerset of A b... | {
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"openwebmath_score": 0.8663439750671387,
... |
c#, converting
array.Add(value);
div = div / 26;
}
div -= getOne;
if (div > 0) array.Add(div);
var letters = array.Select(s => (char)('A' + s - 1)).Reverse().ToArray();
return new string(letters);
Now I wonder if there is a better way write this. You could slightly simplify the code as follows:
Reduce the n... | {
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"tags": "c#, converting",
"url": null
} |
observational-astronomy, supernova
According to an article on the Portal to the heritage of astronomy it wasn't until the 12th century that astronomy got a more modern scientific twist:
Chronologically, the Middle Ages are conventionally divided into an Early Medieval and a Later Medieval period. A chief marker of th... | {
"domain": "astronomy.stackexchange",
"id": 1790,
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"openwebmath_score": null,
"tags": "observational-astronomy, supernova",
"url": null
} |
special-relativity, speed-of-light, inertial-frames, galilean-relativity
$$
\begin{pmatrix}
t^{'} \\
x^{'}
\end{pmatrix} =
\begin{pmatrix}
\cos \theta & \sin \theta \\
-\sin \theta & \cos \theta
\end{pmatrix}
\begin{pmatrix}
t \\
x
\end{pmatrix}
$$
Look, for example, at the first row. After defining $v = \tan \theta$... | {
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"tags": "special-relativity, speed-of-light, inertial-frames, galilean-relativity",
"url"... |
gravitational-waves, instruments
Distance. The amplitude of gravitational waves decreases roughly with the inverse of the luminosity distance $\propto D^{-1}$. So sources that are further away will be more difficult to observe and at some point they will be less/not visible.
Power of the source. The stronger the sourc... | {
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"tags": "gravitational-waves, instruments",
"url": null
} |
unique up to a factor of $\rm\;h \in ker(\sigma-1) = \{h: \sigma\:h = h\:\} = \;$ constants, i.e. $\rm deg\;h = 0 \ \$ QED
Remark $\;$ This reformulation of my prior answer is intended to dramatically illustrate the innate symmetry. Its striking simplicity arises precisely from the simple structure of the orbits of th... | {
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"lm_q2_score": 0.8519528076067262,
"openwebmath_perplexity": 939.5338640697898,
"openwebmath_score": 0.9513248801231384,
"tag... |
c++
// override all functions (in fact, only == and !=)
template<typename F>
bool comp(F f, const reverse &b) const { return f(tup(), b.tup()); }
// override remaining functions, each separately
bool comp(op::lt, const reverse &b) const { return tup() > b.tup(); }
bool comp(op::gt, const reverse ... | {
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"tags": "c++",
"url": null
} |
In article <1992Sep14.133741.34561@watson.ibm.com> you write:
>Title: Cliff Puzzle 1: Can you beat the numbers game?
>From: cliff@watson.ibm.com
>
>If you respond to this puzzle, if possible please include your name,
>address, affiliation, e-mail address. If you like, tell me a little bit
>about yourself. You might als... | {
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"id": null,
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"lm_q1_score": 0.969785412932606,
"lm_q1q2_score": 0.8459897509268901,
"lm_q2_score": 0.8723473663814338,
"openwebmath_perplexity": 1260.6151974306902,
"openwebmath_score": 0.7816751003265381,
"tags": nul... |
python, fixed-point
should_be('1', 1)
should_be('10', 1)
should_be('100', 1)
should_be('1004', 4)
should_be('10004', 5)
should_be('105', 3)
should_be('01', 1)
should_be('1.2035', 5)
should_be('001.09508', 6)
should_be('0.00110', 3)
Of course, a proper test suite is probably better.... | {
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"openwebmath_score": null,
"tags": "python, fixed-point",
"url": null
} |
mathematical-physics, condensed-matter, research-level, topology, topological-insulators
In general, consider two Hamiltonians $H_1(\bf k)$ and $H_2(\bf k)$ of the same size. It might be true they do not belong to the same homotopy class, and thus cannot be deformed into each other. However, by adding a few trivial ba... | {
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"tags": "mathematical-physics, condensed-matter, research-level, topology, topological-insu... |
of time to a function of frequency. e jwt Cos wt jSen wt Time Fourier transform, DTFT) Matlab y uso de función òfft código aquí) (c) P. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. 1 shows how increasing the period does indeed lead to a cont... | {
"domain": "agenzialenarduzzi.it",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.981735721648143,
"lm_q1q2_score": 0.8678929482289481,
"lm_q2_score": 0.8840392878563336,
"openwebmath_perplexity": 1078.9064028815767,
"openwebmath_score": 0.8407778143882751,
"... |
molecular-biology, dna, molecular-genetics
However the 4rth nucleosome will be exactly parallel to the 3rd, and thus the same amount of degrees off-center from the 2nd nucleosome as the 3rd nucleosome is to the 1st, maintaining the pattern.
This forms a more 3-D tubular strucuture than an actual shoelace on a shoe wo... | {
"domain": "biology.stackexchange",
"id": 5230,
"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": "molecular-biology, dna, molecular-genetics",
"url": null
} |
quantum-mechanics, hilbert-space, wavefunction, time-evolution, unitarity
does not depend on $t_0$. We require that the evolution in a span $t_1 + t_2$ is the same as the evolution in $t_1$ followed by the evolution in $t_2$, and is also equal to the evolution in $t_2$ followed by the evolution in $t_1$, $$ U(t_2)U(t_... | {
"domain": "physics.stackexchange",
"id": 65421,
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"lm_name": null,
"lm_q1_score": null,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "quantum-mechanics, hilbert-space, wavefunction, time-evolution, unitarity",
"url... |
python, python-2.x, comparative-review, formatting
else:
template = ' Record GLB {logical_address} {physical_address} {module:34}{var_name}' \
'(0..{last_element})\n 0 {width:7}{var_type}'
module = line.partition('.')[0].rpartition('\t')[2]
logical_address = line... | {
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"tags": "python, python-2.x, comparative-review, formatting",
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usb-cam, camera, ros-kinetic
Originally posted by gvdhoorn with karma: 86574 on 2018-07-30
This answer was ACCEPTED on the original site
Post score: 0 | {
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homework-and-exercises, optics, lenses
This means that the reference system is different for $o$ and $i$, which can be confusing.
Other common error for this kind of problems is that $o$ and $i$ is the distance to the lens, so you can't use the number you get for $i$ from the first lens as the $o$ for he second lens. ... | {
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"tags": "homework-and-exercises, optics, lenses",
"url": null
} |
c#, performance, excel, cyclomatic-complexity
public void AddEditTenant(int apartmentNumber, CRenter tenant)
{
TenantUpdates.Add(new CApartment(apartmentNumber, tenant));
worksheetChanged = UdateTenantDataTable(apartmentNumber, tenant);
}
public CRenter GetTenant(int ap... | {
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soft-question, advice-request, project-topic
Have a look at the proceedings of the conference "Fun with Algorithms": they should provide you with a good selection of "Fun" problems to work on, and a venue where to submit your results for feedback.
Check the publications of people known to consider fun problems and pr... | {
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experimental-physics
Title: If you bottle space with something inside does it still float when brought back to Earth? If you put something like a penny in a jar in space and brought it back to earth would the penny still float like in space?
would the penny still float like in space?
Your main misunderstanding is in... | {
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} |
• Oh! I should read more carefully. I derived the full probability of the roll, not the probability given that the sum was already 15. I understand your answer now. – aepound May 11 '15 at 12:35 | {
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"tags... |
discrete-signals, z-transform, transfer-function, impulse-response
Does anybody see what I might did wrong or what properties can be exploited here? We know that $\displaystyle
\frac{\sin(\theta (n+1))}{\sin(\theta)} u[n+1]$ has value $0$ for $n < -1$ since $u[n+1]=0$ for $n < -1$. At $n=-1$, $u[n+1]$ jumps to value $... | {
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"tags": "discrete-signals, z-transform, transfer-function, impulse-response",
"url": null
} |
frequency components—so that you would be able to. 3 Reference 1) 1. For a complex function f(x) which satisfies the condition that. The Fourier transform is simply a method of expressing a function (which is a point in some infinite dimensional vector space of functions) in terms of the sum of its projections onto a s... | {
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"lm_q2_score": 0.8824278556326344,
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"openwebmath_score": 0.879318118095398,
"tags"... |
general-relativity, differential-geometry, acceleration, vectors
Title: How to calculate the proper acceleration (as a 4-vector) in general relativity? I am trying to derive some equations which will let me simulate the motion of a spaceship in different geometries of spacetime. Suppose I know the metric and Christoff... | {
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"tags": "general-relativity, differential-geometry, acceleration, vectors",
"url": null
} |
c, sorting, mergesort
Title: Constructing an odd-even mergesort sorting network I was searching for a non-recursive odd-even mergesort implementation and found this one:
Sedgewick R.
The resulting sorting network is not an odd-even-merge sort network. When one draws a diagram of the pairs, it can be seen that too ma... | {
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"tags": "c, sorting, mergesort",
"url": null
} |
javascript, html5
It uses the dialog element to create the dialogs.
Async functions and promises to wait for user input.
Event listeners to get user clicks.
Defines a state machine via the object interrogation that uses named properties to connect states. The function interrogate takes a state name and use it to deter... | {
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"openwebmath_score": null,
"tags": "javascript, html5",
"url": null
} |
java, java-8, javafx
Dashboard.fxml
<?xml version="1.0" encoding="UTF-8"?>
<?import java.lang.*?>
<?import javafx.geometry.*?>
<?import javafx.scene.control.*?>
<?import javafx.scene.layout.*?> | {
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"tags": "java, java-8, javafx",
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} |
java, algorithm, programming-challenge, time-limit-exceeded, combinatorics
Title: Bovine Shuffle using a queue (USACO Dec 2017 Silver) I am working on the "Bovine Shuffle" problem from the December 2017 USA Computing Olympiad, and have got it to work for every test case beside two. When I run these two cases on my ow... | {
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... |
javascript, typescript
I was wondering if there's a way of doing this where I don't need a nested for loop.
Plunkr: https://plnkr.co/edit/FXhbCr9aaXcL61g3q7Fe?p=preview You can simplify it by using Array.prototype.some method and lazy evaluation of && operator
const pageTypes = ['dashboard', 'klantenkaart', 'complexka... | {
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then we have $$a \leq b + \frac{a-b}{2}=\frac{a+b}{2}$$
Simplifying, we have $$2a \leq a+b$$
and hence $$a \leq b$$
but we have assumed that $a>b$ which is a contradiction since we get $a < a$.
• I like this answer. It does not provide an intuitive explanation but it has to convince anybody doubting this step by us... | {
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"openwebmath_score": 0.913870632648468,
"tag... |
physical-chemistry, materials
Title: OFET vs Traditional Transistors What is the advance of OFET's (Organic Field effect transistors) over the traditional CMOS Transistors? The advantages of OFET's over traditional CMOS transistors all derive from how OFET's can be manufactured. Traditional transistors are manufactur... | {
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"tags": "physical-chemistry, materials",
"url": null
} |
homework-and-exercises, classical-mechanics, rigid-body-dynamics
Consider the following, then come to your own conclusion as to whether or not the friction forces affect one another.
The figure below is a free body diagram (FBD) of the cylinder which assumes there is no kinetic friction between the piston shaft and th... | {
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} |
classification, statistics, optimization, machine-learning-model
More on it here
Much more theoretical understanding of it you could find in ISLR at page 129 4.2 Why Not Linear Regression? | {
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electrical-engineering, stepper-motor
However, i offer some advice that may prove useful to you:
If affordable, I would use double the minimum holding torque needed for the application because i usually find that my calculations don't usually account for all the true dynamics of the mechanism. When starting out with ... | {
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"tags": "electrical-engineering, stepper-motor",
"url": null
} |
ros-fuerte, ubuntu-oneiric, arm-navigation, ubuntu
error: ‘it’ was not declared in this
scope
/home/pragyan/tredext/biome/armnavigation/planning_models/src/kinematic_model.cpp:1281:65:
error: request for member ‘begin’ in
‘group_links_set’, which is of
non-class type ‘int’
/home/pragyan/tredext/biome/armnavigation/pla... | {
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"tags": "ros-fuerte, ubuntu-oneiric, arm-navigation, ubuntu",
"url": null
} |
visible-light, laser, vision, perception
This may be a source of your misunderstanding.
The way humans perceive color is by having three types of photoreceptors in their eyes. Each of them has a broadish response function which means, that the "green" receptors react well to pure green light (as in 555nm), but also ar... | {
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"tags": "visible-light, laser, vision, perception",
"url": null
} |
$$f(t_0 -)=\lim_{n\rightarrow\infty} f(t_0-1/n) \in [f(t_0)-\varepsilon, f(t_0)+\varepsilon]$$
and
$$f(t_0 +)=\lim_{n\rightarrow\infty} f(t_0+1/n) \in [f(t_0)-\varepsilon, f(t_0)+\varepsilon].$$
Consequently, we have $M(t_0)\leq\varepsilon$, and we deduce that $(x-\delta, x)$ and $\mathcal{J}(\varepsilon)$ are disjo... | {
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"lm_q1_score": 0.9777138099151277,
"lm_q1q2_score": 0.8230645569787032,
"lm_q2_score": 0.8418256432832332,
"openwebmath_perplexity": 182.55860118725187,
"openwebmath_score": 0.9111455678939819,
"ta... |
physiology, marine-biology, invertebrates, molluscs
Fig. 1. Octopus on land. Source: BBC
Your sub questions; I think small octopuses may survive longer, since passive gas exchange is the mode of survival on land. In general, an increase in diameter causes the volume to increase with a third power, while surface increa... | {
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"tags": "physiology, marine-biology, invertebrates, molluscs",
"url": null
} |
… ] when$ $... Diagonalizable, and proceed to the next step is called a matrix whose contain! Be an$ n\times n $matrix with the help of sympy.Matrix ( ) method, we explain to..., some matrices are not similar to diagonal matrices$ n\times n $matrix real... Root of a and their algebraic multiplicities from the character... | {
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"lm_q1_score": 0.9719924761487654,
"lm_q1q2_score": 0.8182481895718012,
"lm_q2_score": 0.8418256412990657,
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"openwebmath_score": 0.7855561971664429,
"tags": nul... |
homework-and-exercises, general-relativity, curvature, cosmological-constant, anti-de-sitter-spacetime
$$
Then, taking a trace of the equation above, we find
$$
R - \frac{1}{2} d R + \Lambda d = 0 ~~\implies ~~ R = \frac{2\Lambda d}{d-2}
$$
Thus,
$$
r^2 = \frac{d-2}{2\Lambda d} \, .
$$
Here, $d$ is the dimension of t... | {
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"tags": "homework-and-exercises, general-relativity, curvature, cosmological-constant, anti... |
java, object-oriented, game, libgdx
This time I wanted to separate everything tutorial related from the regular classes as much as possible. I created a TutorialGameScreen class that extends the GameScreen class. All of the conditional logic is inside that. There is still a TutorialPhase enum which contains the stri... | {
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"tags": "java, object-oriented, game, libgdx",
"url": null
} |
java, swing, audio
})
.withComponent(() -> {
saveButton = new JButton("Save Pattern...");
saveButton.setEnabled(false);
saveButton.addActionListener(new SaveButtonListener());
... | {
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"tags": "java, swing, audio",
"url": null
} |
17E. In this case and and so we have found an example where but and thus disproving the statement. Is l Dillig, CS243: Discrete Structures Mathematical. The establishment of a fact by the use of evidence. Proof: By contradiction; assume that there is a rational number r and an irrational number s where the number r + s... | {
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"lm_q2_score": 0.863391617003942,
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"openwebmath_score": 0.7791018486022949,
"tags"... |
neural-networks, machine-learning, reinforcement-learning, meta-learning
I was wondering if meta learning is the right area to look into?
In general no, but you might want to consider meta learning if:
You have too many policies to select between by testing them all thoroughly.
The policies have some meaningful low... | {
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"tags": "neural-networks, machine-learning, reinforcement-learning, meta-learning",
"url": null... |
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