text stringlengths 1 1.11k | source dict |
|---|---|
physical-chemistry
For closed, not isolated systems with zero non volume work:
(Non-volume work is e.g. a system charging a battery. )
For constant volume: $$\mathrm{d}U=\text{đ}Q$$
For variable volume: $$\mathrm{d}U=\text{đ} Q
- p \cdot \mathrm{d}V$$
For constant pressure and zero non volume work, $$\mathrm{d}H=\mat... | {
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according as $z$ lies in the 1st, 2nd, 3rd, or 4th quadrants. Here
1.9.6 $\omega=\operatorname{arctan}\left(|y/x|\right)\in\left[0,\tfrac{1}{2}\pi\right].$ ⓘ Symbols: $\pi$: the ratio of the circumference of a circle to its diameter, $[\NVar{a},\NVar{b}]$: closed interval, $\in$: element of and $\operatorname{arctan}... | {
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"openwebmath_score": 0.9758047461509705,
"tags": null,... |
human-physiology
(C) type 1: hair follicles and muscle cells; type 2: bones, red blood cells and epithelial cells.
(D) type 1: epithelial cells and bones; type 2: hair follicles, red blood cells and muscle cells.
I know muscle cells only grow in size. I am unsure about hair follicles, which is why I am confused betwe... | {
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soft-question
I'm thinking of going into a theoretical physics area and I'd like to know if this is par for the course for a physicist. (I'm coming from an engineering background and I found that there was nothing much to think about in engineering: the theory is very thin, at least at the Bachelors level. It's mostly... | {
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Similarly, . A medieval tower bell used particularly for ringing the 8 canonical hours. The cosine transform of an odd function can be evaluated as a convolution with the Fourier transform of a signum function sgn(x). Some … Let’s Workout: Example 1: Find the greatest integer function for following (a) ⌊-261 ⌋ (b) ⌊ 3.... | {
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"openwebmath_score": 0.7237217426300049,
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... |
slam, navigation, ros-kinetic, parameters, rtabmap
Title: Need help with passing parameters to a launch file
I would like to over ride rtabmap parameters on a rosrun command line....I want to used the unaltered rtabmap launch file overriding some of the Grid parameters. Can this be done from the command line? If not ... | {
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beginner, brainfuck
The result as seen above isn't as bad as it looks. It's very memory efficient since all operations are made on the same cell. But speed is also important. Unfortunately I do not know how to properly time Brainfuck executions (yet).
I'm fairly sure this is not the 'best'/'idiomatic' way of writing t... | {
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"tags": "beginner, brainfuck",
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quantum-mechanics, homework-and-exercises, operators
The step $\sum_P \sum_{P'} (-1)^{p+p'} \hat{P} \hat{P}' = \sum_P \sum_R (-1)^r \hat{R}$ requires recognizing that summing over the product all possible combinations of permutations $P$ and $P'$ is the same as summing over all permutations only once (because the perm... | {
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tensor-calculus
$\mathfrak{A}=a^{ij}\hat{\mathfrak{e}}_{i}\hat{\mathfrak{e}}_{i}$
$\mathfrak{B}=b^{ij}\hat{\mathfrak{e}}_{i}\hat{\mathfrak{e}}_{j}$
$\mathfrak{C}=c^{ij}\hat{\mathfrak{e}}_{i}\hat{\mathfrak{e}}_{j}$
$\mathfrak{D}=d^{ij}\hat{\mathfrak{e}}_{i}\hat{\mathfrak{e}}_{j}$
$\mathfrak{A}\cdot\mathfrak{B}\cdot\mat... | {
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This means a total of $\frac{\min\{m,n\}^2}{2} + m \max\{n-m, 0\}$ operations are more or less are all you need at worst.
-
Hm let me just check that, just realised this process wouldnt work if they span the space as it never gives a $0$ answer – muzzlator Mar 21 '13 at 11:10
After a gazillion edits, I think I have i... | {
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You have chosen a good formalization here: with the corrections from Brian M. Scott's answer, you are given that \begin{align} (0) \;\;\; & Bo \equiv Ba \land Ze \\ (1) \;\;\; & Ma \equiv Ba \land \lnot Ze \\ (2) \;\;\; & Ba \equiv Ma \land Ze \\ (3) \;\;\; & Ze \equiv Bo \land Ma \\ \end{align} Now, looking at the sha... | {
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## 2 Answers
I will suppose that $$X_1,\ldots,X_k$$ is i.i.d., $$Y_1,\ldots,Y_m$$ i.i.d. and $$X_i$$ is independent of $$Y_j$$ for every i,j. There is no reason for the intervals to be the same. They are different approaches to create a confidence interval for $$\Delta = \mu_X-\mu_Y$$.
Notice that you used the same e... | {
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cr.crypto-security, matrices, nt.number-theory, comp-number-theory
so we have exactly an instance of the discrete log problem modulo $p$ hiding in there.
If $\lambda$ is not a generator, the problem is exactly as hard as the discrete
log to the base $\lambda$.
Note that this case is not in $GL(2,p)$, so strictly speak... | {
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From Eli Bendersky’s site I got the code below for weighted random sampling.
from random import random
def weighted_choice(weights):
rnd = random() * sum(weights)
for i, w in enumerate(weights):
rnd -= w
if rnd < 0:
return i
Thus, weighted_choice gives an index to the chosen element of an array. With this index I c... | {
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"openwebmath_score": 0.5447880625724792,
"tags": ... |
Differentiation of implicit functions engineering math blog. Uc davis accurately states that the derivative expression for explicit differentiation involves x only, while the derivative expression for implicit differentiation may involve both x and y. Use implicit differentiation directly on the given equation. Implici... | {
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quantum-field-theory, path-integral, correlation-functions, functional-derivatives, 1pi-effective-action
Title: Functional derivative of the generating functional with respect to the source term To be specific, let us use the notations in W. Metzner et al., Rev. Mod. Phys. 84,299 (2012).
The generating functional $G[\... | {
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ros2
I guess it didn't work because I was using the pre-installed Autoware.Auto and sourcing from opt/AutowareAuto/setup.bash, it worked after building. Thanks!
Comment by xmfcx on 2021-11-25:
@hakan could you please mark the answer as correct if it solved your question? Thanks! | {
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php, beginner, object-oriented
switch($flag)
{
case 0:
$sql='SELECT * FROM contacts';
$p->setAll($sql);
Contact::printTable($p->pageQuery($sql));
break;
case 1:
echo'<a href="index.php?mode=normal"> Go back to unsorted table<br></a>';
... | {
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and 2; Heads and an even number; Tails and 7. The Venn diagram is an illustration of the relationships between and among sets, groups of objects that share something in common. What does the fact that A and B are not mutually exclusive mean about P(A and B)? Where is this probability represented on the Venn diagram you... | {
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"openwebmath_score": 0.4274599254131317,
"tags"... |
java, beginner, homework
It doesn't change much, and I would not go so far as to call that an improvement rather than an alternate solution.
Second option: only one loop per line
You obviously know how to use if-statements as well as loops, because you use four of them. You could leverage that to simplify the block yo... | {
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java, time-limit-exceeded, primes
Use the sieve of Eratosthenes to find all prime numbers from 2 to 10^6. You can leave the output of the sieve as an array of booleans, telling you which numbers are prime.
Read in the input numbers. For each input number, determine if it is a perfect square. If it is, look up the s... | {
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is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. c channel polar moment of inertia. 30670 Moment of Inertia The same vertical differential element of area is used. It should not be confused with the second moment of area, which is used in beam calculat... | {
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"lm_q2_score": 0.8740772351648677,
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"openwebmath_score": 0.6235755681991577,
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gravity, mass, definition, weight
$^1$ To illustrate that weight is indeed a force, note that $$g=\frac{GM}{r_E^2}$$ meaning $$W=mg=\frac{GMm}{r_E^2}$$ which is also Newton's law for gravitational force ($M$ is the mass of the earth, $G$ is the gravitational constant and $r_E$ is earth's radius). | {
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} |
css, sass
.purple {
background: linear-gradient(135deg, #424c9f 0%, #c16cf9 100%);
height: 100%;
& .card__header {
background: #424c9f;
&::before {
content: "";
display: inline-block;
width: 0;
position: absolute;
height: 0;
... | {
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In practice, this is not usually done by considering truth tables, but instead just by reasoning directly with the statements. For example:
Suppose $$A\subseteq B$$. Then, unioning both sides with $$B$$ and observing that this operation preserves the relation of containment, we can conclude that $$A\cup B\subseteq B\c... | {
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"lm_q2_score": 0.8376199572530448,
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"openwebmath_score": 0.8172138333320618,
"ta... |
python, linux
import sys
import os
import time
import subprocess
if len(sys.argv) == 2:
pid = sys.argv[1]
else:
print('No PID specified. Usage: %s <PID>' % os.path.basename(__file__))
sys.exit(1)
def proct(pid):
try:
with open(os.path.join('/proc/', pid, 'stat'), 'r') as pidfile:
... | {
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"tags": "python, linux",
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} |
ros, imu, sensor, ptam
I either get an error warning:
=== ERROR === update: NAN at index 0
=== ERROR === prediction p: NAN at index 0
Or I get this message:
[ WARN] [1441884003.214357239]: large time-gap re-initializing to last state
And sometimes this:
[ WARN] [1441884003.679369485]: Negative scale detected: -0.39217... | {
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electromagnetism, quantum-field-theory, klein-gordon-equation
The Klein-Gordon equation doesn't correspond to a familiar classical situation, but we deal with sources in the same way. The free equation $(\partial^2 + m^2)\phi = 0$ is a kind of wave equation; if we solve by Fourier transform, the equation says that the... | {
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"tags": "electromagnetism, quantum-field-theory, klein-gordon-equation",
"url": null
} |
c++, multithreading
ThreadGroup<vector<double>&> pool(number_of_threads,[&](tuple<vector<double>&>& inputs, int thread_index){
double sum = 0;
vector<double>& used_buffer = std::get<vector<double>&>(inputs);
size_t length = (used_buffer.size() / number_of_threads) + 1u;
size_t start = length * thread_i... | {
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"tags": "c++, multithreading",
"url": null
} |
quantum-mechanics, operators, representation-theory, quantum-optics, lie-algebra
$$
K_+= \sqrt{2} \begin{bmatrix} 0&1&0\\0&0&1\\0&0&0\end{bmatrix}; \\
K_-= -\sqrt{2} \begin{bmatrix} 0&0&0\\1&0&0\\0&1&0\end{bmatrix}; \\
K_0= \begin{bmatrix} 1&0&0\\0&0&0\\0&0&-1\end{bmatrix} ? \\
$$ | {
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"tags": "quantum-mechanics, operators, representation-theory, quantum-optics, lie-algebra",... |
algorithm, computational-geometry, rust
#[test]
fn test_triangle() {
let p2 = Point::new(0.0, 0.0);
let p1 = Point::new(0.0, 1.0);
let p0 = Point::new(1.0, 1.0);
let t = Triangle::new(p0, p1, p2);
assert_eq!(t.range_x(), (0.0, 1.0));
assert_eq!(t.range_y(), (0.0, 1.0... | {
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"tags": "algorithm, computational-geometry, rust",
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} |
homework-and-exercises, kinematics, probability
Likewise, in early calculus courses, we learn that the average value of a function $f(x)$ is $\langle f(x) \rangle = \frac{1}{b-a}\int_a^b f(x)dx.$ This is because the probability density function of $x$ is simply the constant probability density function $1/(b-a)$. It's... | {
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"tags": "homework-and-exercises, kinematics, probability",
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} |
c++, random, simulation, statistics
[...] a return from the initial call to the main function is equivalent to calling the exit function with the value returned by the main function as its argument; reaching the } that terminates the main function returns a value of 0.
For C++, since the first standard in 1998; see I... | {
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"tags": "c++, random, simulation, statistics",
"url": null
} |
general-relativity, gravity, visible-light, black-holes, photons
Title: Can photons form a black hole? Can photons form black holes the same way as other matter? If there happens to be enough of them concentrated in an area of space so that enough energy exists within a radius to form an event horizon, will an actual ... | {
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"tags": "general-relativity, gravity, visible-light, black-holes, photons",
"url": null
} |
group-theory, lie-algebra
My construction of matrix for simple roots seems to be wrong. How to verify the linear dependence correctly? Below follows the proof which Howard Georgi seems to have in mind. Let us call the root vector(s) in the Dynkin diagram $(a)$ corresponding to | {
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"tags": "group-theory, lie-algebra",
"url": null
} |
# HP Forums
You're currently viewing a stripped down version of our content. View the full version with proper formatting.
.
InvH:
« .577215664902 - InvPsi 1. -
»
InvPsi:
« DUPDUP DUP InvP InvP DUP InvP InvP DUPDUP InvP InvP DUP InvP DUP EXP .5 + Psi OVER - - EXP .5 +
»
InvP:
« DUP EXP .5 + Psi OVER - - EXP .5 + ... | {
"domain": "hpmuseum.org",
"id": null,
"lm_label": "1. YES\n2. YES",
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"lm_q1_score": 0.9820137910906878,
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"tags": n... |
optics, laser, refraction, vision
So a uniform illumination is modulated by an exponential intensity distribution. For a non-uniform image, this is a multiplicative factor (hence it is sometimes called multiplicative noise).
The most probably value is $I=0$, hence all the dark spots, and the maximum brightness is unbo... | {
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"tags": "optics, laser, refraction, vision",
"url": null
} |
scikit-learn, svm, multiclass-classification
# training a linear SVM classifier
from sklearn.svm import SVC
svm_model_linear = SVC(kernel = 'linear', C = 1).fit(X_train, y_train)
svm_predictions = svm_model_linear.predict(X_test)
# model accuracy for X_test
accuracy = svm_model_linear.score(X_test, y_test)
# cre... | {
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"tags": "scikit-learn, svm, multiclass-classification",
"url": null
} |
machine-learning, classification, class-imbalance, kaggle
Title: AUC ROC metric on a Kaggle competition I am trying to learn data modeling by working on a dataset from Kaggle competition. As the competition was closed 2 years back, I am asking my question here. The competition uses AUC-ROC as the evaluation metric. Th... | {
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"tags": "machine-learning, classification, class-imbalance, kaggle",
"url": null
} |
python, algorithm, performance, combinatorics
760 else:
761 n10 += 1
762
763 1 5 5.0 0.0 return n11, n00, n10, n01 If I understood w... | {
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"tags": "python, algorithm, performance, combinatorics",
"url": null
} |
na.numerical-analysis, sparse-matrix
Title: Graph sparsification and eigenspaces I am currently trying to understand whether I can make some claims about the relation between eigenspaces of a sparsifier and the original matrix. In this context, let me first define a couple of entities.
Definition 1: Partial Ordering ... | {
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"url": null
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terminology, symmetry
What's the correct term for the relationship between $A_1$/$B_1$ and $A'$, and between $A_2$/$B_2$ and $A''$? Are they subspecies? Does $A_1$ imply $A'$? | {
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"tags": "terminology, symmetry",
"url": null
} |
electromagnetic-radiation, symmetry, goldstone-mode
Title: Skin depth and Mermin-Wagner theorem I recently became aware of the Coleman-Mermin-Wagner theorem presented in [1802.07747] for higher-form symmetries and I have a question about how it might be applied to electromagnetism.
The theorem states: continuous $p$-f... | {
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"tags": "electromagnetic-radiation, symmetry, goldstone-mode",
"url": null
} |
# Computing a complex integral potentially using residues
The question is:
Compute:
$$\mbox{p.v.}\int_{-\infty}^{\infty}\frac{x\sin4x}{{x^2}-1}dx$$
Initially I thought it was straight forward and I could just use residues. However, the Residue Theorem requires the poles to be in the upper plane ($y > 0$), and in th... | {
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"lm_q2_score": 0.8705972549785203,
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"openwebmath_score": 0.9720173478126526,
"tags... |
navigation, ros-melodic
rosparam get /move_base/global_costmap
footprint: '[]'
footprint_padding: 0.01
global_frame: map
height: 10
inflation_layer: {cost_scaling_factor: 10.0, enabled: true, inflate_unknown: false,
inflation_radius: 0.5}
obstacle_range: 7
obstacles_layer: {combination_method: 1, enabled: true, foot... | {
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"id": 34719,
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"openwebmath_score": null,
"tags": "navigation, ros-melodic",
"url": null
} |
bash, shell, installer
if [[ "${active_gpu}" == 'true' ]]; then
if [[ "${version}" == 'dev-gpu' ]]; then
pip install "${version}"
else
pip install package-gpu=="${version}"
fi
else
if [[ "${version}" == 'nightly' ]]; then
pip install "${version}"
else
pip install p... | {
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"tags": "bash, shell, installer",
"url": null
} |
c#, unit-testing, asynchronous
namespace ThrottlingReview
{
public abstract class BindableBaseWithThrottling : BindableBase
{
private readonly TimeSpan _throttleLimit;
private readonly TaskScheduler _taskScheduler;
private readonly ConcurrentDictionary<string, Task> _cooldownTasks;
... | {
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"tags": "c#, unit-testing, asynchronous",
"url": null
} |
1. $$(a + b)^2 = a^2 + b^2$$, for all real numbers a and b.
2. There are integers $$x$$ and $$y$$ such that $$2x + 5y = 41$$.
3. If $$x$$ is an even integer, then $$x^2$$ is an even integer.
4. If $$x$$ and $$y$$ are odd integers, then $$x \cdot y$$ is an odd integer.
Add texts here. Do not delete this text first.
##... | {
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"lm_q2_score": 0.8397339656668286,
"openwebmath_perplexity": 132.42719216959972,
"openwebmath_score": 0.7440686821937561,
"tags"... |
thermodynamics, physical-chemistry, ideal-gas
However, on Wikipedia, it states that p is the pressure of the gas and work can be represented by:
W=-pdV=-nR*dT (isobaric case)
Using the pressure of the system itself to calculate work doesn't make much sense to me to be honest. And it doesn't fit the description of work... | {
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"tags": "thermodynamics, physical-chemistry, ideal-gas",
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} |
So, then: "In problems like these does one just do a bunch of trial and error, as I have done for quite a while now, or is there a more clever way to go about it?".
Here are three approaches to finding the sums of series before starting to prove the result. It's good to have all of them available. | {
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"lm_q2_score": 0.8596637469145053,
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"openwebmath_score": 0.8615207076072693,
"ta... |
homework-and-exercises, newtonian-mechanics, experimental-physics, newtonian-gravity
is correct (taken from two independent sources), following formula is correct as well
$$g=\frac{\ell\pi^2(\cos(\alpha)-9)^2}{16T_m^2}$$
This suggests my experiment alone was not very accurate, thus resulting in the error seen in my or... | {
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"tags": "homework-and-exercises, newtonian-mechanics, experimental-physics, newtonian-gravi... |
python, snakemake, github
Thanks The answer for any testing purpose is generally to put together a small and minimal dataset so the test completes in seconds or minutes while still being representative. It makes (to me) limited sense to have a Actions/CI running using for example the entire human genome as input. The ... | {
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"tags": "python, snakemake, github",
"url": null
} |
robotic-arm, trajectory
As you point out, there are many curve options. Curves are chosen to eliminate discontinuities in position, velocity, and acceleration. And when possible, minimizing acceleration.
When I was a cam designer, this book: Cam Design by Clyde H. Moon was our bible. It is very old, but still pre... | {
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"tags": "robotic-arm, trajectory",
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} |
them with the help of some examples. The fundamental theorem of calculus is a theorem that links the concept of differentiating a function with the concept of integrating a function. Fundamental Theorem of Calculus Part 2 (FTC 2) This is the fundamental theorem that most students remember because they use it over and o... | {
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"openwebmath_score": 0.9256067276000977,
"tags":... |
a problem for practice having uniform density of F R, i.e. the. Bases ) bisecting lines is the centroid of a trapezoid is at the centre the. The calculator has been provided with educational purposes in mind and should be accordingly. Use below given formula kite: a trapezium of height 4.5 cm parallel! “ h ”.. centroid... | {
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"lm_q1_score": 0.9579122696813392,
"lm_q1q2_score": 0.8043914747434461,
"lm_q2_score": 0.8397339716830606,
"openwebmath_perplexity": 589.5559055863192,
"openwebmath_score": 0.7258831262588501,
"tags": null... |
c, thread-safety, queue, embedded, variant-type
Did you consider checking the return value of pthread_mutex_init() and pthread_mutex_lock()? It so happens that in your code, you can avoid checking that, since you are not using recursive mutexes, but if you didn't know that, you should have either written if-statements... | {
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"tags": "c, thread-safety, queue, embedded, variant-type",
"url": null
} |
python, algorithm, multithreading, graph, depth-first-search
def get_counts_from_dict(ddegrees):
"""Returns the degrees of the nodes in a graph via the dictionary of counts
Input: ddegrees"""
return [ddegrees[node] for node in ddegrees.keys()]
def split_nodes(ddegrees):
"""Returns shuffled list of ev... | {
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"tags": "python, algorithm, multithreading, graph, depth-first-search",
"url": null
} |
Let \eqalign{ A_1&=\text{the set of all functions from }\Bbb N\text{ to }\Bbb N. \cr A_2&=\text{the set of all non-increasing from }\Bbb N\text{ to }\Bbb N. \cr A_3&=\text{the set of all non-decreasing }\Bbb N\text{ to }\Bbb N. \cr A_4&=\text{the set of all 1-1 functions from}\Bbb N\text{ to }\Bbb N. \cr A_5&=\text{the... | {
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"lm_q1_score": 0.9825575121992375,
"lm_q1q2_score": 0.8519124991389965,
"lm_q2_score": 0.8670357598021707,
"openwebmath_perplexity": 191.6129276320447,
"openwebmath_score": 0.965313732624054,
"tags... |
c++, design-patterns, observer-pattern
switch (subtype) {
case SUB_FREE:
sub = std::make_unique<FreeSubscriber>(name);
break;
...
}
sublist.push_back(std::move(sub));
}
Although there are nicer solutions which I will show below.
In notify(), you need to ensure you use a reference:
fo... | {
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} |
in MATLAB are documented this way as well. MATLAB provides some special expressions for some mathematical symbols, like pi for π, Inf for ∞, i (and j) for √-1 etc. Mesela 5 üzeri 6 sayısının matlab de kodlanması = "5^6" şeklinde olur. Ln is the notation used in physics and engineering to denote the logarithm to base e ... | {
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"lm_q1_score": 0.9334308147331958,
"lm_q1q2_score": 0.8041863110937596,
"lm_q2_score": 0.8615382076534742,
"openwebmath_perplexity": 1246.51345888803,
"openwebmath_score": 0.6243621706962585,
... |
natural-language-processing, transformer, fine-tuning
There are different approaches for this. Some adapt the data, others prefer to transfer the model. There is a lot of research in this area. This is a good article that covers the basics and might provide you with a more specific solution you can try out. | {
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"tags": "natural-language-processing, transformer, fine-tuning",
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} |
swift, community-challenge, sprite-kit
self.anchorPoint = CGPoint(x: -minx/(maxx - minx), y: -miny/(maxy - miny))
self.scaleMode = .aspectFit
}
required init?(coder aDecoder: NSCoder) {
fatalError("init(coder:) has not been implemented")
}
func setUpScene() {
... | {
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"tags": "swift, community-challenge, sprite-kit",
"url": null
} |
newtonian-mechanics, forces
I've deliberately avoided figuring out what the radius of that circle is, because I think it's possible to answer your question without that - in fact, it may even be easier to answer the conceptual question without getting bogged down by having to calculate what the radius is. But as you s... | {
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"openwebmath_score": null,
"tags": "newtonian-mechanics, forces",
"url": null
} |
general-relativity, black-holes, speed-of-light
Title: What happens 'inside' the event horizon of a black hole, in particular to photon speed This is a follow-up question to two answers given here and here, where the speed in different coordinate systems is discussed when approaching the Schwarzschild radius. To cite,... | {
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"tags": "general-relativity, black-holes, speed-of-light",
"url": null
} |
den[, n]) Deconvolves divisor out of signal, division of polynomials for n terms. This (draft) document gives examples for white noise tests. The general autoregressive process, AR(p) Autocorrelation function B For the process to be stationary the modulus of G. With two variables (x and y), controlling for a third (z) ... | {
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"lm_q1_score": 0.981735721648143,
"lm_q1q2_score": 0.8071724351068768,
"lm_q2_score": 0.8221891261650248,
"openwebmath_perplexity": 1254.9740245179125,
"openwebmath_score": 0.8607275485992432,
"tag... |
dimensional-analysis, units, si-units
It's important to note that not every measurable quantity is inherently definable in terms of SI base units. If I count the number of people in my office building right now, and tell you that there are "12 people" in the building right now, then "people" is not expressible in ter... | {
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"tags": "dimensional-analysis, units, si-units",
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} |
• The blue-orange one, in $$(-\infty, -1)$$
• The red-orange one, in $$[-1, 1)$$
• The red-green one, in $$[1, \infty)$$.
The blue-orange component is when $$x < -1$$, or $$|x + 1| = -x - 1$$ and $$|x - 1| = -x + 1$$. Thus the sum of these is $$-x - 1 + (-x + 1) = -2x$$.
The red-orange component is when $$-1 \leq x <... | {
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"openwebmath_score": 0.9894774556159973,
"ta... |
linked-list, swift, generics
I would make isEmpty a computed property instead of an instance
method (similar to the isEmpty property of CollectionType etc):
var isEmpty: Bool {
return self.count == 0
}
Instead of a printList() method it is more Swifty to make the type
conform to CustomStringConvertible:
extension... | {
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"tags": "linked-list, swift, generics",
"url": null
} |
file, csv, powershell
[string]$SourceFn = 'c:\temp\raw\FlatFileSplitterTestDoc.dat'
Split-FlatFile -Filename $SourceFn -PageSize 10 #simple demo to test with before throwing huge docs at this [Reflection.Assembly]::LoadWithPartialName("System.IO") | out-null
I'm almost certain that this statement is not needed at all... | {
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"tags": "file, csv, powershell",
"url": null
} |
ros
UPDATE: ros-fuerte-robot-model is already installed. Maybe the problem is something different altogether ... the reason why I installed and compiled this and other packages to my workspace is that they were required for another package and could not be found. But $roscd robot_model works fine and takes me to /opt/... | {
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} |
This could be interpreted as an binomial distribution $$X \sim Bin(n=4, p = 1/3)$$ so what you should calculate is $$P(X \geq 2) = 1- P(X \leq 1) = 1- (P(X = 1) + P(X = 0)) \approx 0.4075$$.
• I have edited the question, 4 balls are drawn. – user121 Feb 15 '20 at 15:59
• $n=12$? No. $n$ would be the number of draws be... | {
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"tags"... |
Other inequalities for $\mathop{F\/}\nolimits\!\left(\phi,k\right)$ can be obtained from inequalities for $\mathop{R_{F}\/}\nolimits\!\left(x,y,z\right)$ given in Carlson (1966, (2.15)) and Carlson (1970) via (19.25.5). | {
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"openwebmath_perplexity": 11227.564807042425,
"openwebmath_score": 0.9508581161499023,
"tags": null,
... |
asteroids, natural-satellites, size
Title: Why haven't more captured small moons been found? Shouldn't captured moons have the same size distribution as asteroids? And asteroids are more common the smaller size they are. Moons are likely captured if they are in highly inclined orbits, and those moons should've origina... | {
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"openwebmath_score": null,
"tags": "asteroids, natural-satellites, size",
"url": null
} |
beginner, python-3.x, tic-tac-toe
# Start player is selected
def player_order():
liste = ["x","o"]
shuffle(liste)
return liste
# Input is checked for correctness
def input_verification():
while (user_input := "placeholder")not in board_fields:
try:
user_input = int(input(f"{xo} is ... | {
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"tags": "beginner, python-3.x, tic-tac-toe",
"url": null
} |
# Miscellaneous Exercise Application of Derivatives Solution - NCERT Class 12
## Chapter 6 Ex.6.ME Question 1
Using differentials, find the approximate value of each of the following.
(i) \begin{align}{\left( {\frac{{17}}{{81}}} \right)^{\frac{1}{4}}} \end{align}
(ii) \begin{align}{\left( {33} \right)^{ - \frac{1}{... | {
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"openwebmath_score": 1.0000097751617432,
"tags": nul... |
• Thank you so much for clarifying! And thanks for editing! – user6969 Jan 14 at 18:27
• so $x_n$ would be equal to $\rho^{n-1}(x_0-\mu)+\mu$? Because you defined $x_{n+1}$ to be $p^{n+1}_{11}$ – user6969 Jan 14 at 18:41
• As I wrote at the outset, "$x_n$" is shorthand for "$(P^n)_{11}.$" – whuber Jan 14 at 18:44
• I u... | {
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"lm_q2_score": 0.8267118004748678,
"openwebmath_perplexity": 211.53356762884115,
"openwebmath_score": 0.9665246605873108,
"ta... |
visible-light, photons
Title: Do photons emitted from different color filters leave varying size marks on a screen when fired? I have read that photon "size" is proportion to wavelength, but I've also read that photon "size" isn't exactly a thing. So does this mean that different colors, which have different wavelengt... | {
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"openwebmath_score": null,
"tags": "visible-light, photons",
"url": null
} |
statistical-mechanics, computational-physics, ising-model, algorithms, percolation
but only from the publication I cannot understand why this is working. I followed some sources, but obviously not the right one.
My question: Can someone outline how percolation theory comes into play? That the algorithm is working due... | {
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"openwebmath_score": null,
"tags": "statistical-mechanics, computational-physics, ising-model, algorithms, percolation... |
php, optimization, sql
$result = strtotime($this->DtReading) + 2 * 60 * 60;
$this->time = time() + 60 * 60 - $result;
return round($this->time / 60, 2);
}
}
public function Cycle() {
$this->Arr = array();
$conn = odbc_connect('monitor', '', '');
if (!$c... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "php, optimization, sql",
"url": null
} |
c++, c++14
template<typename T>
constexpr List<T> List<T>::reverse() const
{
List<T> l;
l.length = length;
for (int i = 0; i < l.length; ++i)
{
l.array[i] = array[length - i - 1];
}
return l;
}
template<typename T>
template<typename Filter>
constexpr List<T> List<T>::filter(Filter f) const
{
List<T>... | {
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"tags": "c++, c++14",
"url": null
} |
combinatorics, dynamic-programming, recursion, divide-and-conquer
One possible configuration of the grid is one where all the cells are in state $0$:
00
00
You could swap any rows and/or columns without changing anything. So the above counts as 1 configuration.
Another configuration is where only 1 cell is in state $1... | {
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"tags": "combinatorics, dynamic-programming, recursion, divide-and-conquer",
"url": null
} |
newtonian-mechanics, forces, work, spring
Finally, what would be the correct work done by the force from point a to point b for the second image? $W_1$ or $W_2$?
Thank you. The simplified form of Hooke's law $F(x) = -kx$ only applies to 1D systems where the equilibrium point is at $x=0$. The more general form of Hooke... | {
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"tags": "newtonian-mechanics, forces, work, spring",
"url": null
} |
python, json, gui, tkinter, ftp
# filename for the JSON to be sent via FTP
self.fname_send = fname_send
# filename for the JSON to be saved locally with all results
self.fname_save = fname_save
# ftp login credentials
self.use_ftp = use_ftp
self.ftp_host = ftp_host
... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, json, gui, tkinter, ftp",
"url": null
} |
Math polygon triangle. The area of an equilateral triangle is s 2 3 4 \frac{s^2\sqrt{3}}{4} 4 s 2 3 . Calculate the height of a triangle if given two lateral sides and radius of the circumcircle ( h ) : height of a triangle : = Digit 2 1 2 4 6 10 F fem_to_triangle, a MATLAB code which reads FEM files defining a 2D mesh... | {
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"lm_q2_score": 0.8244619199068831,
"openwebmath_perplexity": 535.7041350003676,
"openwebmath_score": 0.8246050477027893,
"tags": ... |
quantum-chemistry, orbitals, atomic-structure
$$\rho=\psi\psi^*.$$
While the probability is
$$P =\int_{x_1}^{x_2}{\psi\psi^* \mathrm{d}x}.$$
(This is only in one dimension. In spherical coordinates you must integrate over the volume).
Why is there a difference between these two quantities? I think it will be easier t... | {
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"tags": "quantum-chemistry, orbitals, atomic-structure",
"url": null
} |
thermal-conductivity
The thermal conductivity $\kappa$ of a material will be the sum of all such influences: $$\kappa=\kappa_{e}+\kappa_{ph}.$$
The intuition behind it
$\kappa$ can intuitively be thought of as how much energy every second $q$ that over one square metre is transported over the thickness $\Delta x$. The... | {
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"tags": "thermal-conductivity",
"url": null
} |
inverse trigonometric functions. In previous math classes you learned some basic algebraic properties, such as the Distributive Property and Define and use inverse trigonometric functions. However, if you're going on to study calculus, pay particular attention to the restated sine and cosine half-angle identities, beca... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9891815523039175,
"lm_q1q2_score": 0.8040733530335388,
"lm_q2_score": 0.8128673155708975,
"openwebmath_perplexity": 564.1065187435921,
"openwebmath_score": 0.8320470452308655,
"tags":... |
## (i) Let A = {5, 6, 7}. Define a relation R on A as R = {(5, 6), (6, 5)}. Relation R is not reflexive as {(5, 5), (6, 6), (7, 7)} /∈R. Now, as (5,6)∈R and also (6,5)∈R, R is symmetric. (5,6),(6,5)∈R, but (5, 5) /∈R.Therefore R is not transitive. Hence, relation R is symmetric but not reflexive or transitive. R = {(a... | {
"domain": "byjus.com",
"id": null,
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9877587236271351,
"lm_q1q2_score": 0.8075663298561554,
"lm_q2_score": 0.8175744850834648,
"openwebmath_perplexity": 1508.665682359475,
"openwebmath_score": 0.8910825848579407,
"tags": ... |
Here is a recent paper written by two NIST physicists, one a Nobel winner, arguing that radians should be treated as a unit in SI and not as a dimensionless number, much as I have been using by my own discovery. This should at least makes the case that there is some room for variety here.
Of course you are free to do ... | {
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"lm_q1_score": 0.9697854146791214,
"lm_q1q2_score": 0.8318510026854776,
"lm_q2_score": 0.8577681104440172,
"openwebmath_perplexity": 1550.3158272210114,
"openwebmath_score": 0.8600427508354187,
"ta... |
Comment: There is a very nice book on bijective arguments called Proofs that Really Count. Maybe one should start collecting Mean Proofs.
• very interesting, sometimes I wonder, how does this world looks in the eyes of people like yourself? It must be very different from my world! Also, thanks for naming the book. Dec... | {
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"lm_q1_score": 0.9875683476832692,
"lm_q1q2_score": 0.8164343941560662,
"lm_q2_score": 0.8267117876664789,
"openwebmath_perplexity": 851.3528319938475,
"openwebmath_score": 0.9926669001579285,
"tag... |
java, jpa, jsf
css.css
@CHARSET "UTF-8";
body {
background-color: #ffffff;
font-family: Verdana, "Verdana CE", Arial, "Arial CE", "Lucida Grande CE", lucida, "Helvetica CE", sans-serif;
font-size: 12px;
color: #000000;
}
.header {
background-color: #ffffff;
font-size: 14px;
font-family... | {
"domain": "codereview.stackexchange",
"id": 10827,
"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": "java, jpa, jsf",
"url": null
} |
19320Vg + 2712Va = 9500 kg
Vg + Va = 0.9441 m3
Solving for Vg and substituting:
Va = 0.5262 m3 and Vg = 0.4179 m3
The mass of the gold would then be 8072.89 kg and the mass percent would be 80.73%
I appreciate your response. If there is a method to solve this using calculus I would like to understand how to go abou... | {
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"openwebmath_score": 0.6088011264801025,
"... |
12. Feb 28, 2009
### Staff: Mentor
Agreed that this is a simple problem, and that the limit is 0. Tiny Tim's approach is superior to mine in its simplicity. Your approach, using a computer-generated graph, is useful for gaining understanding about the behavior of this function, but that's about it. It is well-known t... | {
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"lm_q1_score": 0.981735725388777,
"lm_q1q2_score": 0.8383166595875811,
"lm_q2_score": 0.8539127566694178,
"openwebmath_perplexity": 1175.6462945508158,
"openwebmath_score": 0.5315227508544922,
... |
homework-and-exercises, electricity, electric-circuits, electrical-resistance
Title: Lamps in parallel and series circuit - which will light up? Will both lights in this circuit light up? It seems to me that the first light on the left is in series, and therefore will not light up.
Thanks for any explanation. If the s... | {
"domain": "physics.stackexchange",
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "homework-and-exercises, electricity, electric-circuits, electrical-resistance",
... |
python, regex, file
The change_configuration_options() takes a dictionary of new configuration option changes, and it uses a little trick within the inner loop to check write non-matching options to the output file. That trick is the for ... else loop. If the for loop completes normally, the else will execute, but if ... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, regex, file",
"url": null
} |
zoology, species-identification, marine-biology, arthropod
Title: Is this a saltwater millipede? I spotted this millipede-like creature in Hervey Bay, Australia at low tide, just kind of hanging out at the bottom of a small saltwater tidepool.
It's several inches long, composed of a large number of segments, each o... | {
"domain": "biology.stackexchange",
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "zoology, species-identification, marine-biology, arthropod",
"url": null
} |
navigation, turtlebot, gmapping
/kinect_laser/parameter_updates 5 msgs : dynamic_reconfigure/Config
/kinect_laser_narrow/parameter_descriptions 5 msgs : dynamic_reconfigure/ConfigDescription
/kinect_laser_narrow/paramete... | {
"domain": "robotics.stackexchange",
"id": 9502,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "navigation, turtlebot, gmapping",
"url": null
} |
energy, speed
Title: Why does it take more energy to go faster to the same place? Edit: to people asking about details, I am not asking about drag. Take it to happen in vacuum, space, no drag, no other forces. I would like a general rule of thumb. This guy with e equals mv squared answered already.
This is NOT about r... | {
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"openwebmath_score": null,
"tags": "energy, speed",
"url": null
} |
$$\mathbb{P}(|X_n-X| \geq \epsilon_n \, \, \text{i.o.})=0.$$
• You gave a counter example for a specific sequence of $\epsilon_n$. Is there a sequence of $\epsilon_n$ such that $P(|X_n-X|>\epsilon_n i.o.)=0$? Oct 5, 2018 at 13:48
• @S_Alex For the particular example which I gave you can answer this question yourself, ... | {
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"openwebmath_score": 0.9751617312431335,
"tags... |
conjugate can also be denoted using z. Forgive me but my complex number knowledge stops there. You can easily check that a complex number z = x + yi times its conjugate x – yi is the square of its absolute value |z| 2. Conjugate complex number definition is - one of two complex numbers differing only in the sign of the... | {
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"lm_q2_score": 0.8267117876664789,
"openwebmath_perplexity": 667.714821680727,
"openwebmath_score": 0.7939547896385193,
"ta... |
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