text stringlengths 1 1.11k | source dict |
|---|---|
research
Added:
In response to Jakob's comment, I am not looking for opinions or discussions on this subject. What I am looking for are published studies which might shed light on this question. Rate of progress of computational power
Moore's law: over the history of computing hardware, the density of transistors on a... | {
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"openwebmath_score": null,
"tags": "research",
"url": null
} |
linear-systems, homework, stability, causality
The system is unstable: as for a bounded input $x[n] = \delta[n]$ the output is $y[n] = K + (n+1) u[n]$ which grows unbounded as $n$ goes to infinity.
The system is not invertible.
The system can be implemented with and without any memory requirement. | {
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"tags": "linear-systems, homework, stability, causality",
"url": null
} |
ruby, comparative-review
# Tail-recursive
def factorial_tr_recursion(n, acc)
if n < 2
acc
else
factorial_tr(n - 1, n * acc)
end
end
def factorial_tr(n, acc = 1)
validate(n)
factorial_tr_recursion(n, acc)
end
# Iterative with Range.each
def factorial_re(n)
validate(n)
if n ... | {
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "ruby, comparative-review",
"url": null
} |
hyper-parameters, gpt, sentiment-analysis, prompt-design
However, it's very hard for models to predict hard probabilities (0/1) since the data that it's been trained is noisy, so almost everything might come after everything
For this reason, if you just sample, you might sample a word that is with $p\approx 0$, but st... | {
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"tags": "hyper-parameters, gpt, sentiment-analysis, prompt-design",
"url": null
} |
Find $P^{-1}$ as follows:
Write the augmented matrix $A | I$ , where $I$ is the identity matrix
$\begin{bmatrix} - 1 & 0 & 1 & | & 1 & 0 & 0 \\ - 1 & 0 & 0 & | & 0 & 1 & 0 \\ 2 & 1 & 1 & | & 0 & 0 & 1 \end{bmatrix}$
Row reduce the above augmented matrix
$\begin{bmatrix} 1 & 0 & 0 & | & 0 & -1 & 0\\ 0 & 1 & 0 & | & -1 &... | {
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"lm_q1_score": 0.9964619132074206,
"lm_q1q2_score": 0.8123481305217376,
"lm_q2_score": 0.8152324938410783,
"openwebmath_perplexity": 269.76511470056346,
"openwebmath_score": 0.9542958736419678,
"tags... |
statistical-mechanics, phase-space
Title: Quantum states in position and momentum phase space While studying introduction to statistical mechanics ,I came across a new idea phase space where we use both position and momentum coordinates to denote a system .In my book the author calculates the number of quantum states ... | {
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"tags": "statistical-mechanics, phase-space",
"url": null
} |
the-sun
Title: Is the power output at the core of the sun about the same as a compost pile (about 300 watts)? I read an article at abc.net.au saying that the power output of the sun is about 276.5 watts per cubic metre, similar to that of a compost pile.
A compost pile is not incandescent, while the sun is. It's so ho... | {
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"tags": "the-sun",
"url": null
} |
The fact that almost all reals are normal in base $b$ is an application of the Strong Law of Large Numbers. Write the base $b$ expansion as $X = \sum_{i=1}^\infty b^{-i} D_i$ where $X$ is uniform on $[0,1]$ and $D_i$ are iid with $P(D_i = y) = 1/b$ for $y = 0,1,\ldots,b-1$. The Strong Law of Large Numbers applied to th... | {
"domain": "mathoverflow.net",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9817357243200244,
"lm_q1q2_score": 0.8026420749352587,
"lm_q2_score": 0.8175744806385542,
"openwebmath_perplexity": 159.84639049933287,
"openwebmath_score": 0.8647976517677307,
"tag... |
Continuing the above example, we have . Note that is also in , but we don't need to list it separately, since it is equal to .
One more piece of terminology:
Definition: representative
If is an equivalence class of by , and , we say that is a representative of if . Note that is a representative of .
# Equivalence cl... | {
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"lm_q1_score": 0.9901401438236134,
"lm_q1q2_score": 0.8251081387525725,
"lm_q2_score": 0.8333245994514084,
"openwebmath_perplexity": 370.4146943438265,
"openwebmath_score": 0.9027803540229797,
"tags": nu... |
quantum-state, quantum-operation, information-theory, entropy, relative-entropy
&= -S(\rho_A)-S(\rho_B)-\mathrm{tr}[\rho_{AB}(-\log N + I\otimes\log\rho_B)] \\
&= -S(\rho_A)-S(\rho_B)+\log N + S(\rho_B) \\
&= \log N - S(\rho_A)
\end{align}
$$
which is non-negative. | {
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"openwebmath_score": null,
"tags": "quantum-state, quantum-operation, information-theory, entropy, relative-en... |
geology, paleontology, fossils
Title: Is this a fossil? Found this on open heath land close to RAF Honington, Suffolk, UK. Its about the size/shape of a cherry tomatoe cut in half.
Thanks Yes it could be a fossil. Btw. it is called a sand dollar.
The term sand dollar refers to several species of flattened burrowing se... | {
"domain": "earthscience.stackexchange",
"id": 2505,
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"openwebmath_score": null,
"tags": "geology, paleontology, fossils",
"url": null
} |
classical-mechanics, coupled-oscillators
$$S^TWS = \begin{bmatrix}
\omega_1^2(\vec{v}_1\cdot\vec{v}_2) & \omega_2^2(\vec{v}_1\cdot\vec{v}_2) \\
\omega_1^2(\vec{v}_2\cdot\vec{v}_1) & \omega_2^2(\vec{v}_2\cdot\vec{v}_2)
\end{bmatrix}$$
BUT remember: $\vec{v}_1$ and $\vec{v}_2$ are unit vectors, so $\vec{v}_1\cdot\vec{v}... | {
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"tags": "classical-mechanics, coupled-oscillators",
"url": null
} |
public static void main(String[] args) {
run(12345);
cal(12345);
}
-
This doesn't have any influence on the program, but your naming convention is bad. – Norbert Jun 16 '12 at 17:59
Each of the sums separately is $\sum_{j=1}^k j = \frac{1}{2}k^2 + \frac{1}{2}k$.
In addition, $\sum_{k=1}^n k^2 = \frac{1}{3}n^3 + \fra... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9783846666070896,
"lm_q1q2_score": 0.8131776117355709,
"lm_q2_score": 0.8311430457670241,
"openwebmath_perplexity": 348.8559129488926,
"openwebmath_score": 0.6386187672615051,
"tag... |
c++, strings, c++11
iterator begin();
iterator end();
class const_iterator
{
private:
const string* str_;
size_t index_;
public:
const_iterator(const string*, size_t) noexcept;
const_iterator(const const_iterator&) noexcept;
const_ite... | {
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"tags": "c++, strings, c++11",
"url": null
} |
strings, parsing, awk
all_args="ABC=https://host:443/topic1,DEF=https://host1:443/topic1,GHI=https://host:443/topic3,JKL=https://host:443/topic3"
command1 $all_args
command2 $(echo $all_args | awk -f extractor.awk)
The solution:
BEGIN { FS="," }
{
for ( i = 1; i <= NF; i++) {
split($i, arr, "=")
v... | {
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"openwebmath_score": null,
"tags": "strings, parsing, awk",
"url": null
} |
c++, c++14, logging
bool Logger::close()
{
try
{
if (mStream.is_open())
{
mStream.flush();
mStream.close();
return !mStream.is_open();
}
else
return false;
}
catch (std::exception& e)
{
std::cerr << "Error: ... | {
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"tags": "c++, c++14, logging",
"url": null
} |
quantum-mechanics, quantum-entanglement
Let's say the first magnet directs both particles in the $|ud\rangle$ state up. Then if we add additional magnets that act only on particles deflected up, these magnets will only act on $|ud\rangle$, and any particles reaching the later magnets effectively been prepared in the $... | {
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"openwebmath_score": null,
"tags": "quantum-mechanics, quantum-entanglement",
"url": null
} |
machine-learning, classification, class-imbalance, metric, confusion-matrix
Lastly, in the class imbalance problem if the majority class is our class of interest which metric (precision and recall) should we consider?
It's pretty rare that the majority class is of interest, usually the minority class is chosen as the... | {
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"tags": "machine-learning, classification, class-imbalance, metric, confusion-matrix",
... |
The 'smallestreal' computation struggles to converge using A since the gap between the eigenvalues is so small. (6 points) Determine the eigenvalues of the following matrices. In general, in the eigenvalues output, the eigenvalues for real inputs are not sorted so that complex conjugate pairs are adjacent. Definition: ... | {
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"lm_q1_score": 0.9814534392852384,
"lm_q1q2_score": 0.8262126709314694,
"lm_q2_score": 0.8418256412990657,
"openwebmath_perplexity": 429.17433867820245,
"openwebmath_score": 0.8734235167503357,
"... |
Since the inequality is homogeneous we may WLOG assume that $xyz=1$ and we have to prove the inequality $(x+y+z)^3 \geq 27$ or $x+y+z \geq 3.$ But the last inequality we obtain immediately from $AM \geq GM$ under the assumption $xyz=1.$
Here are two one-line-formula proofs:
1. By AM-GM: $$\frac{x+y+z}{3} \geq \sqrt[3... | {
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"lm_q1_score": 0.9683812327313545,
"lm_q1q2_score": 0.8269130915487236,
"lm_q2_score": 0.853912760387131,
"openwebmath_perplexity": 334.43388958599246,
"openwebmath_score": 0.9781709909439087,
"tag... |
javascript
}
}
// lines => string
let s = "";
for ( let line of lines ) {
s += line[1] + "\n";
}
s = s.slice(0, s.length-1);
return s;
}
_sortSelectors(lines) {
/** [parameterTrimmed, [line, line, line, line]] */
... | {
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} |
vision, neurophysiology
Background
The places of red, green and blue wavelengths in the spectrum are physically defined and, therefore, not arbitrary; see this question on Biology SE.
Before continuing, it is good to mention that trichromacy (the presence of red, green and blue cones in the retina) is typical for prim... | {
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"tags": "vision, neurophysiology",
"url": null
} |
it in a of. Degree: 1 degree corresponds to an arc of a circle when angle! Degrees or radians for finding arc length given radius and central angles let go! To radians. 1 Discuss the formula until we convert it to radians. in s. 0.52 = 1.56 m 6 angle ) in radians and r is the of... Can use a formula for arc length 2πR/... | {
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"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.984810949854636,
"lm_q1q2_score": 0.8141548250724633,
"lm_q2_score": 0.826711791935942,
"openwebmath_perplexity": 511.31422362626785,
"openwebmath_score": 0.9186582565307617,
"tags"... |
blog post that hosted by Github with Editor Atom , and use plugin markdown-preview-plus and mathjax-wrapper , and use mathjax Javascript display the math symbols on the web page. Thanks mates, But I could not get the response , how do I use vector notation, I am not more familiar with maths notations. This guide provid... | {
"domain": "monetimargherita.it",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.976310532836284,
"lm_q1q2_score": 0.8778216656487156,
"lm_q2_score": 0.8991213718636754,
"openwebmath_perplexity": 751.4959527028767,
"openwebmath_score": 0.9481537938117981,
... |
this formula to integrate by parts formula is used to find the integration of x sin,! Find the integration of x sin x, then we need to use it find integration. ) I integral form of the fundamental theorem that produces the expression as one of the rule. And du/dx = 1 make the formula easier to remember product of two..... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9838471670723236,
"lm_q1q2_score": 0.8177177248372116,
"lm_q2_score": 0.8311430394931456,
"openwebmath_perplexity": 442.99330691478656,
"openwebmath_score": 0.9383604526519775,
... |
general-relativity, black-holes, computational-physics, event-horizon
It is clear that if someone is making an effort to avoid a grid point having a singularity, then they haven't selected a method that systematically and automatically avoids going inside the event horizon. And there is no real reason not to go inside... | {
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"tags": "general-relativity, black-holes, computational-physics, event-horizon",
"url": n... |
javascript, snake-game, webgl
} else {
highScoreDomStyle.display = "none";
};
if(showmaxspeed) {
extras++;
maxspeed.style.display = "block";
maxspeed.style.top = extrasLookup[extras]
maxspeed.innerHTML = `Highest Speed: ${(((100/maxspeed*100)|0)/100)}`;
} else... | {
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"openwebmath_score": null,
"tags": "javascript, snake-game, webgl",
"url": null
} |
return EvenSum/numoftry
with Num = 6 and numoftry =1000000 probability p = 0.09538
this is the function for sum equals odd number
def dicesumodd(Num,numoftry):
oddSum = 0
L = []
for i in range(numoftry):
N = random.randint(1,6)
L.append(N)
if N == Num :
Sum = sum(L)
L = []
if (Sum % 2) == 1:
oddSum = oddSum + 1
... | {
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"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9822876997410348,
"lm_q1q2_score": 0.8480989637160845,
"lm_q2_score": 0.8633916152464017,
"openwebmath_perplexity": 497.60098730199024,
"openwebmath_score": 0.8475463390350342,
"ta... |
visible-light, interferometry, coherence, length
So we seek $\mathscr{G}(f)$ where $\mathscr{G}(f)\,|df| = \mathscr{F}(\lambda)\,|d\lambda|$; given $c = f\,\lambda$ we have:
$$d\lambda = -\frac{df}{f}\,\lambda = - \frac{c}{f^2} df$$
so that
$$\mathscr{G}(f) = \frac{c}{f^2} \mathscr{F}\left(\frac{c}{f}\right)$$
So now... | {
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"openwebmath_score": null,
"tags": "visible-light, interferometry, coherence, length",
"url": null
} |
Not sure this is the best method, but the way I would actually solve such a set of questions would be the following:
Use generating function methods for the second question. The explicit collection of submultisets of the six tiles is given by the terms of $(1+x)(1+y+y^2)(1+z+z^2+z^3)$ (the $x$ terms correspond to tile... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9458012701768144,
"lm_q1q2_score": 0.8165968780486386,
"lm_q2_score": 0.8633916064586998,
"openwebmath_perplexity": 243.81994413826246,
"openwebmath_score": 0.8353006839752197,
"ta... |
Defined as the inverse function no Calculator do all functions have inverses in fact are... Means, for instance, that no parabola ( quadratic function ) will have an inverse, a function series! Of a power series function have an inverse called a function, we can whether..., x ) \ ) at most a countable number sure you k... | {
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"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9820137874059599,
"lm_q1q2_score": 0.8649548821630948,
"lm_q2_score": 0.8807970858005139,
"openwebmath_perplexity": 374.5139080277813,
"openwebmath_score": 0.8467493653297424,
"tags": ... |
javascript, functional-programming
function getArray(value){
const key = ['value1', 'value2', 'value3'].find(key => value[key] > 0);
const showValue = value[key] || 0;
return value.system + ": "+ showValue;
}
function myFunction() {
var array = [
{system:"Abba", value1:0, value2:1, value3:0},
{system:... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "javascript, functional-programming",
"url": null
} |
optics, laser, experimental-technique
For class 4 you'll need to be a little careful with your skin, especially when your hands are out of sight whilst you're looking in goggles or at a computer screen. You may wish to consider all remote, motorized actuation of your adjustment. I would say this is compulsory for anyt... | {
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"openwebmath_score": null,
"tags": "optics, laser, experimental-technique",
"url": null
} |
• R. Tijdeman, On integers with many small factors, Compositio Math., $26 (1973) 319-330$.
• I have found an article by Kurt Mahler with the same name as the first one here.
Also in page $14$ of this paper of Michel Waldschmidt; you can find something.
But I don't know how this problem arise from (music);
and from w... | {
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"lm_q2_score": 0.845942439250491,
"openwebmath_perplexity": 706.1442413774421,
"openwebmath_score": 0.8170398473739624,
"tags... |
java, algorithm, quick-sort
for (int i = start; i <= end; i++)
{
ret.append(list[i]).append(", ");
}
return ret.append(list[end]).append(" ]").toString();
}
// Return the complete array as an appropriate String representation.
public static String toString(int[] list)
{
return Sort.toString(... | {
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java, javascript, user-interface, javafx
}
})
.accelerator(
new KeyCodeCombination(
KeyCode.O, KeyCombination.ALT_DOWN))
.build();
viewMenu.getItems().addAll(viewContent, viewSource, console, openScript); | {
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python, python-3.x, web-scraping
I personally consider calling _normalize_robots_url inside _download_robots an anti-pattern. The normalizing in fetch anti-pattern if you will.
You should normalize your data before you perform the fetch. If I'm asking for example.com/robots-new.txt then I should have a pretty good rea... | {
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"tags": "python, python-3.x, web-scraping",
"url": null
} |
ros, pr2-controllers
I also find some similar error others met and run the instruction
sam@sam-desktop:~/code/ros/controller/joint_controller_pkg$ nm lib/libjoint_controller.so | grep pocoBuildManifest
00002f30 T pocoBuildManifestjoint_controller_pkg__MyControllerPlugin
sam@sam-desktop:~/code/ros/controller/joint_c... | {
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solubility
polarizability (related to van-der-Waals forces)
bond dipoles (related to H-bonds and static dipole interactions)
effective electronegativity (related to H-bonds and static dipole interactions)
On a very basic level, any solvation involves the formation of solvent shells. When varying the shape and surface... | {
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"url": null
} |
electrostatics, work, conventions, torque, dipole
Title: Derivation of work done by external torque
In this derivation, why isn't external torque the negative of torque of electric field and therefore Text = -PE sinø Potential Energy of a Dipole in an External Field.
external torque is caused by an external electric ... | {
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turtlebot, ros-fuerte
Exception AttributeError: AttributeError("'_DummyThread' object has no attribute '_Thread__block'",) in <module 'threading' from '/usr/lib/python2.7/threading.pyc'> ignored
process[kinect_laser-5]: started with pid [9102]
[pointcloud_throttle-4] process has died [pid 8911, exit code 255, cmd /opt... | {
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"tags": "turtlebot, ros-fuerte",
"url": null
} |
php, object-oriented, classes, php7
'radio' => ['checked', 'required'],
'range' => ['list', 'max', 'min', 'step'],
'reset' => [],
'search' => ['list', 'maxlength', 'minlength', 'pattern', 'placeholder', 'readonly', 'size', 'spellcheck'],
'submit' => ['formaction', 'formenctype', 'formme... | {
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"tags": "php, object-oriented, classes, php7",
"url": null
} |
python, game, python-3.x
class GameState:
def reset(self, turns, battleships):
self.turnsTotal = turns
self.turn = 0
self.turnsRemaining = turns
self.battleships = battleships
self.battleshipsHit = 0
self.battleshipsRemaining = battleships
def __init__(self, dis... | {
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"tags": "python, game, python-3.x",
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} |
ros, pcl
from /home/user/ros_workspace/fuerte-unstable-devel/pcl17/lib/libpcl_io.so.1.7
#2 0x000000000044e9f4 in pcl17::PCDReader::read<pcl17::PointXYZ> (
this=0x7fffffffd970, file_name=..., cloud=..., offset=0)
at /home/user/ros_workspace/fuerte-unstable-devel/pcl17/include/pcl-1.7/pcl17/io/pcd_io.h:209
#3 0x000000... | {
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"tags": "ros, pcl",
"url": null
} |
electromagnetism, maxwell-equations
Title: Faraday law, derivative that enter in the integral? In the Faraday law derivation written below there is a passage that I don't understand (the one in bold). My professor gave us just a short comment about it that it's not enough for me to understand, can you give me a more d... | {
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navigation, gps, ros-melodic, navsat-transform-node, robot-localization
Originally posted by Awt on ROS Answers with karma: 3 on 2022-01-31
Post score: 0
You should include your full EKF and navsat_transform_node config, a sample input message from every sensor input, and the value of any static transforms.
navsat_tr... | {
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scheme
For cond I would choose one style, either putting the clauses to the
right of the cond, or below; in either case, the indentation for the
else case should match the other cases. Since you only have two
cases, using if would probably be preferred though, as there is no
benefit to using cond with only one form i... | {
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gazebo-11
ljaniec@ljaniec-PC:~$ sudo apt install ros-humble-gazebo-ros-pkgs
>
> Reading package lists... Done
>
> Building dependency tree... Done
>
> Reading state information... Done
>
> Some packages could not be installed. This may mean that you have
>
> requested an impossible situation ... | {
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programming, qiskit, quantum-gate
circuit = QuantumCircuit(7)
c6z = ZGate().control(6)
circuit.append(c6z, range(7))
circuit.draw()
q_0: ─■─
│
q_1: ─■─
│
q_2: ─■─
│
q_3: ─■─
│
q_4: ─■─
│
q_5: ─■─
│
q_6: ─■─
The decomposition of this gate is deep:
circuit.decompose().depth()
... | {
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Here's a slightly different answer from the ones given.
The last line of the truth table is indeed counter-intuitive and this is exploited by the Wason Selection task. In the test, subjects are asked to solve this following puzzle:
There are 4 cards placed on a table. One side of the card has a number, while the oppo... | {
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c++, performance, opencv
Because Ultimately I end up doing this:
int CenterOfContourX = mc[largestContour].x;
int CenterOfContourY = mc[largestContour].y;
Really the end goal is to end up with two integers that represent the center of mass of my contour.
Code to optimise:
// Get the moments
mu.reserve(contours.size()... | {
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time-complexity
Title: What is $2^{O(n)}$? How can I interpret a time complexity of $2^{O(n)}$? Is it simply equal to $O(2^n)$?
I'm pretty new to this, so would appreciate any kind of help. $O(2^{O(n)})$ means: It is $O(2^{f(n)})$ for some function f with f(n) ≤ cn for large n.
So this could be $O(2^n)$ if c = 1, or ... | {
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"tags": "time-complexity",
"url": null
} |
homework-and-exercises, electromagnetism, electrostatics, waves
Title: Electromagnetic waves, displacement currents and capacitors Question:
Q. A parallel-plate capacitor having plate-area $A$ and plate separation $d$ is joined to a battery of emf $E$ & and internal resistance $R$ at $t=0$. Consider a plane surface o... | {
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javascript, performance, beginner, game, canvas
Scene.js:
var SDU = SDU || {};
SDU.Scene = function(canvas) {
this.createjsStage_constructor(canvas);
this.bodies = [];
this.mouse = {
x: 0,
y: 0
};
var _this = this;
this.addEventListener("stagemousemove", function(e) {
_t... | {
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"tags": "javascript, performance, beginner, game, canvas",
"url": null
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algorithms, dynamic-programming
Solution based on online:
int arrayMaxConsecutiveSum2(int[] nums) {
int currentMax = 0;
int globalMax = 0;
globalMax = currentMax = nums[0];
for(int i=1; i<nums.length; i++) {
currentMax = Math.max(nums[i], currentMax + nums[... | {
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"openwebmath_score": null,
"tags": "algorithms, dynamic-programming",
"url": null
} |
quantum-field-theory, differential-geometry, perturbation-theory
Am I on some track to enlightenment, or is this a dead-end train of thought? At the non-rigorous/intuitive level, OP's observations are spot on. To facilitate such thinking, physicists often use DeWitt's condensed notation, where a field $\phi^{\alpha}(x... | {
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"tags": "quantum-field-theory, differential-geometry, perturbation-theory",
"url": null
} |
gravity, newtonian-gravity, method-of-images
Title: Is the method of images applicable to gravity? It is well known that the method of images is a useful tool for solving electrostatics problems. I was wondering why this technique is not applied when considering newtonian gravity?
Obviously there is no "negative mass"... | {
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c++, queue, deque
ae = nab + (size() + ilist.size() << 1);
}
pointer *j = i;
for (auto &v : ilist) {
*j = vatraits::allocate(va, 1);
vatraits::construct(va, *j++, std::move(v));
}
return iterator(i);
}
template ... | {
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• God I'm so vacant. Suits me right for doing homework at 1am! Thank you Sjors, makes perfect sense! – Joshua Aimless Blameless Sep 21 '16 at 2:40
• I think you understood what the questioner was asking - why you don't get the average of two numbers when you multiply them together. Perhaps a simple example would help i... | {
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reaction-mechanism, isotope
To get an idea why consider the simple physical properties of water and heavy water. In heavy water the two hydrogens are replaced by deuterium (hydrogen with an extra neutron in the nucleus). A heavy water molecule is about 10% heavier than a normal water molecule (molecular mass ~20 rathe... | {
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formatting, vb6
Therefore, I would rewrite your function's prototype to look like the following:
Function RgbToHex(ByVal color As Long) As String
Otherwise, the primary issue with your code is that it is slow!
Why? Well, there are a couple of reasons: | {
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problem has been solved! See the answer See the answer See the answer done loading. Entropy for rolling a fair dice. A Gentle Introduction to Information Entropy – AiProBlog. Question: Determine the entropy of the sum that is obtained when a pair of fair dice is rolled. Combining Experiments and Simulations Using the M... | {
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"lm_q1_score": 0.9799765581257486,
"lm_q1q2_score": 0.8079533630296167,
"lm_q2_score": 0.8244619285331332,
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"openwebmath_score": 0.7215729355812073,
"tags": ... |
formal-languages, context-free, pushdown-automata
I am asked to draw a Determinate Push Down Automata for this language; and
According to theory, every language accepted by a PDA is context-free
Am I correct that there is a CFG to this and what is it? Your attempt was pretty close! But I think that this is the way to... | {
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Hint: $\,x_1^3+px_1+q=0 \iff x_1^3=-px_1-q\,$, then adding the three relations together:
$$\require{cancel} x_1^3+x_2^3+x_3^3=\cancel{-p(x_1+x_2+x_3)}-3q=\cdots$$
• Great solution +1 – Aqua Jun 11 '18 at 17:30
• @ChristianF Thanks. One advantage of this approach is that it easily extends to equations $\,x^{\color{red... | {
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"ta... |
and nutrition limitations. so these events should be independent. And each toss of a coin is a perfect isolated thing. Date: 01/03/2007 at 15:43:39 From: Doctor Pete Subject: Re: What is difference between independent and exclusive events Hi TR, If two events A and B are independent, then Pr[A and B] = Pr[A]Pr[B]; that... | {
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"lm_q1_score": 0.9848109520836026,
"lm_q1q2_score": 0.8390124555894783,
"lm_q2_score": 0.8519528076067262,
"openwebmath_perplexity": 342.42604301853675,
"openwebmath_score": 0.6637188196182251,
"tags"... |
transfer-function, hilbert-transform, causality, analytic-signal
$$X(j\omega)=\begin{cases}2,&0<\omega<\omega_0\\0,&\textrm{otherwise}\end{cases}\tag{10}$$
showing (again) that $x(t)$ is an analytic signal. | {
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• Perfect! I must confess that dispite I knew the parallelogram identities I could not myself see clearly the link to my task and to deduce the formula. So many thanks to you. I've already programmed the function (in SPSS) based on your formula for any number of centroids and it is indeed faster with large matrix D tha... | {
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"lm_q1q2_score": 0.8213514042954154,
"lm_q2_score": 0.8354835371034368,
"openwebmath_perplexity": 865.1208224348705,
"openwebmath_score": 0.7812203168869019,
"tag... |
ros2, simulation
Title: Is it possible to spawn and control 2 robots in webots with ROS2?
Hello, I am trying to make a simple application of 2 robots moving around in the webots simulator using ROS2.
I am using the logic described in the tutorials https://docs.ros.org/en/foxy/Tutorials/Advanced/Simulators/Webots.html... | {
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control-engineering, control-theory
$e \rightarrow$ error
$r \rightarrow$ reference input
$y \rightarrow$ actual output of the plant
If $e$ is increasing ($\left[\frac{d e}{d t}\right]>0$) this means that $y$ is becoming smaller and smaller compared to $r$. So the input needs to be increased to increase $y$.
I think... | {
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by changing every AND(. Boolean algebra or switching algebra is a system of mathematical logic to perform different mathematical operations in binary system. Yes, Boolean algebra related to sets, which relates to Probability. Oct 25, 2017 - POS to SOP conversion example | Boolean algebra Stay safe and healthy. Each ans... | {
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"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9802808690122164,
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"lm_q2_score": 0.8539127548105611,
"openwebmath_perplexity": 730.059996781259,
"openwebmath_score": 0.6668375730514526,
... |
look very closely at the second graph in Exhibit 2, you will see the effect of negative accrued interest. The total accrued interest would be $6,953.76, based on the total of the following: Accrued interest for February 2018 to December 2018, i.e. The accrual basis of accounting requires that expenses must be recognize... | {
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"lm_q1_score": 0.9748211619568682,
"lm_q1q2_score": 0.8206294614214917,
"lm_q2_score": 0.8418256532040707,
"openwebmath_perplexity": 1831.8093895159877,
"openwebmath_score": 0.3076755404472351,
"tags": ... |
home-experiment, combustion
Yet another factor is that air in the glass is quite hot while the candle is burning. As soon as it cools down, it shrinks. | {
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c++, beginner, file, caesar-cipher
else if (tempString[i] == '.') tempString[i] = '.';
else if (tempString[i] == ',') tempString[i] = ',';
else if (tempString[i] == 'x') tempString[i] = 'a';
else if (tempString[i] == 'y') tempString[i] = 'b';
... | {
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"tags": "c++, beginner, file, caesar-cipher",
"url": null
} |
Exponential Notes and HW. Session 7 Nonlinear Functions. To solve a simple linear equation, start by moving the numbers with a variable attached to one side of the equation and the numbers without a variable attached to the other side. Exponential Functions Exponential functions are functions made of exponential expres... | {
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"lm_q1_score": 0.9886682458008671,
"lm_q1q2_score": 0.8012947608936889,
"lm_q2_score": 0.8104789086703225,
"openwebmath_perplexity": 1190.0006006151593,
"openwebmath_score": 0.3766786456108093,
"tag... |
organic-chemistry
If you use 2-chloro-3-methyl-butane your desired product will form a much more favorable ternary carbo-anion intermediate (at the 3/green carbon) which will compete again with a primary carbo-anion intermediate(at the 1/red carbon). | {
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} |
formal-methods, software-verification, mathematical-foundations
Title: A general picture of formal verification in software I'm trying to piece together a general picture of the state of formal software verification, and I'm having a good bit of trouble. For context, I come from mostly a math background. I'm quite fam... | {
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"tags": "formal-methods, software-verification, mathematical-foundations",
"url": null
} |
reference-frames, acceleration, relative-motion
Situation: Someone is in a closed lab in which every particle, including those that make up the lab, experiences the same constant force. (I don't believe it is necessary to articulate exactly what is causing that force, but if it is please explain why.)
To clarify: I am... | {
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"tags": "reference-frames, acceleration, relative-motion",
"url": null
} |
time-complexity, memory-allocation, operating-systems
static void *
allocate(void)
{
void *x;
if (free_list_head == NULL) {
x = alloc_ptr;
alloc_ptr = (char *)alloc_ptr + SIZE_OF_BLOCK;
} else {
x = free_list_head;
free_list_head = *(void **)free_list_head;
}
return... | {
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"tags": "time-complexity, memory-allocation, operating-systems",
"url": null
} |
bond, quantum-chemistry, vsepr-theory
You will have to use another method for that. Often confused with VSEPR is the valence bond theory (VBT). It cannot be stressed enough, that the two are completely independent (even at its crudest level). There has been a lot of development in that field, and what is often taught ... | {
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"tags": "bond, quantum-chemistry, vsepr-theory",
"url": null
} |
space
Title: How long will it take to reach the closest earth like planet Using the engines today how long will take humanity to reach earth like planets? HD 219134b is apparently closest "super earth"; 21 light years away.
New Horizons, our speediest yet, is currently running at about 15 km/sec relative to the sun.
A... | {
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"tags": "space",
"url": null
} |
• This does not answer the question. The question is not about this specific limit, the question is about what transformations are valid when one "simplifies" limit expressions. You don't answer the question in the title -- You don't even acknowledge the question in the title. – R.M. Nov 4 '17 at 13:24
• @R.M. I do not... | {
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"openwebmath_score": 0.8467154502868652,
"ta... |
java, graph
Title: Graph using adjacency list in Java This is the main code. Here I'm joining vertices by edges.
node[] gra=new node[5];
{
for (int i = 0; i < 5; i++)
gra[i] = new node(i); //I'm allocating memory for all the vertices.
}
void add_edge(int to,int from) //to represent the vertice the edge ... | {
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"tags": "java, graph",
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} |
ros, release
Background of this question; we've been talking to some corporate users and found that they tend to "freeze" the fundamental software (that we've been maintaining) once they have built it from source for a stability reason, often very long time ago so that the software can be obsolete compared to its rece... | {
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"tags": "ros, release",
"url": null
} |
slam, navigation, 3dmapping, rtabmap-odometry, rtabmap
Comment by Marcus Barnet on 2016-09-04:
It seems that it is considering a 2D motion.
Comment by Marcus Barnet on 2016-09-04:
I also found out that the 3d view shows the rows in wrong way since the row are parallels and not criss-crossed. May be the x-y-z IMU frame... | {
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"tags": "slam, navigation, 3dmapping, rtabmap-odometry, rtabmap",
"url": null
} |
navigation, move-base
Title: Need help with basic navigation
I am trying to wrap my head around the navigation stack, and how to run it.
My objective is to get my simple, differential-drive robot to navigate using the nav stack. I want to set a simple goal in rviz, and let my robot navigate to that position.
My robo... | {
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"openwebmath_score": null,
"tags": "navigation, move-base",
"url": null
} |
quantum-chemistry, theoretical-chemistry
* Let
$$
\mathbb{U}=\left(\begin{matrix}
U_{11} & U_{12} & \dots \\
U_{21} & U_{22} & \dots \\
\vdots & \vdots & \ddots\\
\end{matrix}\right);
\mathbb{U}^\dagger\mathbb{U}=\mathbb{E}
\implies U_{ij}^* U_{kl}= \delta_{ij} = \begin{cases}
1; & i = j = k = l \\ 0; & i ... | {
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"tags": "quantum-chemistry, theoretical-chemistry",
"url": null
} |
image-processing, computer-vision, opencv, ocr
To train your classifier do not use plain intensity values. This would be very noisy. Instead exploit the gradient information (or normalized gradients). This is proven to be robust in many works such as this one. Also, don't even use the gradients directly. It is better ... | {
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"tags": "image-processing, computer-vision, opencv, ocr",
"url": null
} |
hamiltonian-simulation
But the energy eigenstates are typically complicated superpositions of computational basis states, so they can be nontrivial to calculate (and certainly to engineer experimentally). So the "quantum-ness" only vanishes after you've finished the highly quantum step of finding the simultaneous eige... | {
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"id": 1634,
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"openwebmath_score": null,
"tags": "hamiltonian-simulation",
"url": null
} |
matlab, digital-communications, phase, ofdm
Title: Matlab code for Simulating of Phase Noise for OFDM systems I am trying to simulate phase noise for OFDM systems.
I have been reading about phase noise, some literature suggests that phase noise is cumulative as follows:
$\phi(n)=\phi(n-1)+\omega(n)$
where $\omega(n)$ ... | {
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"openwebmath_score": null,
"tags": "matlab, digital-communications, phase, ofdm",
"url": null
} |
algorithms, algorithm-analysis, sorting
Here, each node in the tree is an object with a required "val" property that maps to a non-unique integer and an optional "children" property that, if present, maps to an array of child nodes. There will only be a single root node in the outermost object.
This challenge involves... | {
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"openwebmath_score": null,
"tags": "algorithms, algorithm-analysis, sorting",
"url": null
} |
python, converting, numbers-to-words
It works, but it just doesn't look good. Is it possible to do this in list-comprehension form or a better for-loop without turning it into more confusing mush?
I must admit as well that the last part of the code sucks a little. I've done a lot of str-->int conversions inside the fu... | {
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"tags": "python, converting, numbers-to-words",
"url": null
} |
dxiv has already answered your question for your specific example. But if you want to know the general case, when doing Gaussian elimination you have three kinds of basic steps:
1. Rearrange equations: Clearly reversible.
2. Multiply (both sides of) an equation by a non-zero constant: Clearly reversible because of "n... | {
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"openwebmath_score": 0.8545874357223511,
"tags... |
electricity, frequency
This shows roughly what I saw in my old alarm clock... Obviously one can choose the number of magnets and the gearing ratio so as to get sufficient torque and good time keeping. | {
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"tags": "electricity, frequency",
"url": null
} |
java, object-oriented, game, playing-cards
public void deal() {
playersHand = new Hand("Player");
dealersHand = new Hand("Dealer");
splitHand = null;
isPlayerDone = false;
...
}
...
}
The Hand class doesn't really need a name because there are only 2 types of hands: dealer and player. So yo... | {
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"openwebmath_score": null,
"tags": "java, object-oriented, game, playing-cards",
"url": null
} |
finite-element-method, buckling, nastran
So we have a problem, we don't want to solve a transient dynamic problem because it would take too long, but a static solution doesn't work.
So here is what inertia relief does. First, we add a constraint. i.e. we make the structure fixed at the boundary instead of free. Then... | {
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"id": 2110,
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"openwebmath_score": null,
"tags": "finite-element-method, buckling, nastran",
"url": null
} |
general-relativity, black-holes, wormholes, white-holes, exotic-matter
This seems lime a novel (possibly nonexistent) solution if you are trying to avoid using exotic matter.
From the exit mouth, you can 'see' the other side, you can even traverse the wormhole back to the entrance side, but you are unable to send an... | {
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"tags": "general-relativity, black-holes, wormholes, white-holes, exotic-matter",
"url": ... |
beginner, vba, excel
Populate dailySales, dailySales.Range("B6"), dailySales.Range(dailySales.Cells(6, 2), dailySales.Cells(6, 2 + Days))
Dim totalInventory As Worksheet
Set totalInventory = Worksheets("Total Inventory")
Populate totalInventory, totalInventory.Range("C6"), totalInventory.Range(totalInventory.Cells(5... | {
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"tags": "beginner, vba, excel",
"url": null
} |
electromagnetism, electrostatics
Let's say the initial velocity of q+ is significant such that the kinetic energy is large. If sufficiently far apart, the potential energy is approximately zero. The simple 'first year physics' answer is that the potential energy goes negative. The negative potential energy cancels ou... | {
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"tags": "electromagnetism, electrostatics",
"url": null
} |
programming-languages, type-theory, term-rewriting, types-and-programming-languages
However, he doesn´t use the above property to prove it. I remember this was the case for other books on term rewriting systems that I read. However, to me it looks very simple to prove using the confluence lemma.
From $S \leftrightarro... | {
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"tags": "programming-languages, type-theory, term-rewriting, types-and-programming-languages",
... |
homework-and-exercises, general-relativity, perturbation-theory, linearized-theory
Anyone who can resolve the issues will be very much appreciated. Also please check the terms in the Ricci tensor if they were accurately computed. Do correct me if I was mistaken. I haven't checked your calculation, but if you've follow... | {
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