text stringlengths 49 10.4k | source dict |
|---|---|
I then realized I could get the computer to count all of the $8$-digit strings that have three distinct given digits, so I wrote another program that runs through a loop for every integer from $0$ to $n$$p$ $-$ $1$. Every time through the loop, it constructs an equivalent $p$-digit string to represent the integer of th... | {
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• Wow that is great! Can you explain me what exactly is an interval method and how did you do it? – Tanuj Aug 12 '17 at 11:50
• @user38227 We need to draw the $x$- axes, and to put there points $-5$, $-3$ and $-1$. The sign of the function $f(x)=\frac{|x+3|+x}{x+2}-1$ on $(-1,+\infty)$ is $+$, which gives signs on all ... | {
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I have tested for all $$k\leq n$$ up to $$n=9$$ with the help of a computer without any counterexamples. Does anyone have an idea how this conjecture might be proven?
Here are some partial results. It is trivial that $$\det\M(n,k)$$ is zero when $$k=0$$ or $$n$$, and that it is $$1$$ when $$k=1$$. I can prove the resu... | {
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"openwebmath_score": 0.7748591303825378,
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javascript, php, html, sql
if ($result = $mysqli->query($q1)) {
while ($person_with_this_number = $result->fetch_array()) {
$id = $person_with_this_number[0];
$cnt = $mysqli->query(
"select count(*) as ... | {
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"tags": "javascript, php, html, sql",
"url": null
} |
quantum-mechanics, berry-pancharatnam-phase
Title: How can I infer the topology of a quantum state (or band) from its Chern number? Whereas I can calculate the Chern number of a quantum state (or band) from the integration of the Berry curvature in all space.
How can I infer the topology of the quantum state from this... | {
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} |
lagrangian-formalism, field-theory, symmetry-breaking, higgs
\end{equation*}
which gives:
\begin{equation*}
\begin{array}{ll}
\mathcal{H} & = \mathring{\phi^\dagger} \mathring{\phi} + \mathring{\phi^\dagger} \mathring{\phi} - ( \mathring{\phi^\dagger} \mathring{\phi} + \partial_i \phi^\dagger \, \partial^i\phi - V(... | {
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"tags": "lagrangian-formalism, field-theory, symmetry-breaking, higgs",
"url": null
} |
Step 2
Our base $100$ has two zeros. Therefore, right side of the answer has two digits and that can be obtained by taking the square of the deviation.
Hence, right side of the answer $=12^2=144.$ But right side of the answer can have only two digits because our base $100$ has only two zeros. Hence, from the obtained... | {
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"openwebmath_score": 0.6987869143486023,
"tags":... |
programming-languages
Semantics. Syntax is just describing the set of valid programs; but it doesn't say anything about what those programs mean. Semantics is a way of assigning meaning to programs. Unlike syntax, which is almost always given as a formal grammar as above, semantics can be given in at least two differe... | {
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"tags": "programming-languages",
"url": null
} |
# Use $\operatorname{ord}_{11}3$ to find remainder when..
Find $\operatorname{ord}_{11}3$. Then use what you found to find the remainder when you divide $3^{82}$ by $11$.
Work thus far:
$$\operatorname{ord}_{11}3=\ ?$$ $$3^1\equiv3\pmod{11}$$ $$3^2\equiv9\pmod{11}$$ $$3^3\equiv5\pmod{11}$$ $$3^4\equiv4\pmod{11}$$ $$... | {
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"openwebmath_score": 0.8721483945846558,
"tag... |
astronomy, terminology
Title: What is the precise definition of “cadence” in astronomy? I'm finding it difficult to find a precise definition of "cadence" in astronomy. This term is commonly used to describe the data of astronomical surveys. For instance, one of the data products for the Kepler mission is "30-min or 1... | {
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"tags": "astronomy, terminology",
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} |
quantum-mechanics, particle-physics
The strings like $I^G(J^P) = 1^-(0^-)$ represent the quantum numbers of the particle. $I$ is isospin: the pion, with isospin 1, is a member of an isospin triplet ($\pi^+,\pi^0,\pi^-$). $J$ is spin: the pion is spinless. $P$ is spatial parity: the pion wavefunction changes sign under... | {
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"tags": "quantum-mechanics, particle-physics",
"url": null
} |
solid-state-physics, partition-function
An edit to include a discussion from comments:
Self-Made Man: Does it also hold for the classical Einstein solid?
Yes, because to solve $Z=\int d\mathbf{p}\int d\mathbf{r}\exp(-\beta\mathcal{H}(\mathbf{p},\mathbf{r}))$ for the Hamiltonian of the harmonic oscillator, you have $... | {
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c++, object-oriented, tetris
return 0;
}
bool Utils::doesPieceFit(const Tetromino& tetromino, const int rotation, const int x, const int y)
{
for (int px = 0; px < 4; px++)
for (int py = 0; py < 4; py++) {
int pi = rotate(px, py, rotation);
int fi = (y + py) * playingField.fieldWid... | {
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ros-hydro, ubuntu-precise, ubuntu
once launching shell command 'gradle installApp' I get the following error:
20:12:25.603 [ERROR] [org.gradle.BuildExceptionReporter] FAILURE: Build failed with an exception.
20:12:25.606 [ERROR] [org.gradle.BuildExceptionReporter]
20:12:25.607 [ERROR] [org.gradle.BuildExceptionReporte... | {
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"tags": "ros-hydro, ubuntu-precise, ubuntu",
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} |
python, game, template, tkinter
Title: Mad Libs program My code creates a Mad Libs program. Its a prewritten story that you fill in blindly. There are 4 pages of 7 entry boxs and labels. When the inputs are in and next is pressed it saves inputs as variables that it puts in the story and changes the labels. When all b... | {
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"tags": "python, game, template, tkinter",
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} |
java, object-oriented, programming-challenge, unit-testing, roman-numerals
public RomanNumeralsTest(int input, String expectedOutput) {
this.input = input;
this.expectedOutput = expectedOutput;
}
@Test
public void convertArabicNumberalToRomanNumeral() {
RomanNumeral romanNumeral = ... | {
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... |
elements, radioactivity
What is meant by "occur on Earth" and "extinct" here? I take "extinct" to mean "decayed to the point that it cannot be detected". If I am using that word correctly, then in what sense does an extinct element "occur on Earth"? Defintions
Occur on Earth differentiates between all isotopes in the ... | {
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"tags": "elements, radioactivity",
"url": null
} |
newtonian-mechanics, forces, collision, elasticity, stress-strain
Title: Deformation of a ball when it falls on a rigid surface Suppose, we drop a rubber ball on the floor. The ball collides with the floor, comes to rest and often bounces back up to lower height. I'm trying to look at this from the force perspective, ... | {
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"tags": "newtonian-mechanics, forces, collision, elasticity, stress-strain",
"url": null
... |
structural-engineering, structural-analysis, structures, aerospace-engineering, aerodynamics
Many of the above questions can be answered with Drela's Flight Vehicle Aerodynamics book. Then you have to figure out how to engineer and build the thing.
The way you approach this in practice is to rank order these effects a... | {
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"tags": "structural-engineering, structural-analysis, structures, aerospace-engineering,... |
electromagnetism, special-relativity, speed-of-light, one-way-speed-of-light
There's no point in asking what's the true value of $\epsilon$. There is no true value. In some ways, it's like asking what's the true velocity of the Earth. Velocity is always relative, a velocity only has meaning relative to some reference ... | {
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"... |
c++, design-patterns, c++11, smart-pointers
return 0;
}
The requirements of the design is that the fully constructed objects of the WidgetContainer and Widget "final" types should be immutable: properties of these classes must only be settable during construction and unchangeable thereafter. In order to construct ins... | {
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"tags": "c++, design-patterns, c++11, smart-pointers",
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} |
quantum-chemistry
&\times \sum_{k_{1}k_{2}t_{1}t_{2}w} B_{k_{1}k_{2}t_{1}t_{2}w}(n_{1}, n_{2}, A_{z}, B_{z}, P_{z}, \gamma_{1} | n_{3}, n_{4}, C_{z}, D_{z}, Q_{z}, \gamma_{2}) F_{\nu}(\overline{PQ}^{2}/4\delta),
\label{tho-2.22-1}\tag{THO eq. 2.22 part 1}
\end{align*}
with
\begin{align*}
&B_{i_{1}i_{2}r_{1}r_{2}u}(l_{... | {
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navigation, ekf, ros-kinetic, robot-localization, ekf-localization-node
Title: Robot_localization result is unpredictable
Hello,
I very recently posted a question about the robot_localization package, and received some very good insight. I managed to fuse my wheel odometry with my IMU readings, but the result is not ... | {
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"url"... |
complexity-theory
Title: W[1]-hardness of Steiner tree w.r.t. number of non-terminal vertices This is an exercice is Rolf Niedermeier's book "Invitation to fixed-parameter algorithms", Chapter 13.
Show that the following problem is W[1]-hard:
Steiner Tree in Graphs with respect to the parameter "number of non-termin... | {
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"tags": "complexity-theory",
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moveit, ompl, rosparam, ros-kinetic
[ERROR] [1528993777.331185690]: Could not find the planner configuration 'PRMkConfigDefault' on the param server
[ERROR] [1528993777.331821514]: Could not find the planner configuration 'PRMstarkConfigDefault' on the param server
[ERROR] [1528993777.332365152]: Could not find the pl... | {
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"tags": "moveit, ompl, rosparam, ros-kinetic",
"url": null
} |
general-relativity, orbital-motion
with
$$ V(r) = \left(1-\frac{2M}{r}\right)\left(1+\frac{l^2}{r^2}\right)$$.
Being a circular orbit requires two things. First of all the radius must not change, i.e. $\frac{dr}{d\tau}=0$. Second, this condition must be maintained over time meaning that $\frac{d^2r}{d\tau^2}=0$ as wel... | {
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"tags": "general-relativity, orbital-motion",
"url": null
} |
rotational-dynamics, rotation, rotational-kinematics, rigid-body-dynamics, angular-velocity
The composition of $\alpha\hat{l}$ and $\beta\hat{m}$ (where the second rotation is applied and then the first is applied) is given by $\gamma\hat{n}$, where $\cos\frac{\gamma}{2} = \cos\frac{\alpha}{2}\cos\frac{\beta}{2} - \si... | {
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"tags": "rotational-dynamics, rotation, rotational-kinematics, rigid-body-dynamics, angular... |
java, android, sqlite
Title: Inserting data into an SQLite database I've execute this code in Android for inserting 100+ rows in SQLite database.
My current approach takes more time to initialize the database.
private void getInitialization() {
try {
dao = new IdentifyImageDao(MainActivity.this);
d... | {
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"openwebmath_score": null,
"tags": "java, android, sqlite",
"url": null
} |
homework-and-exercises, newtonian-mechanics, home-experiment
Title: Why dont we consider centripetal force in the expression for net force in specific circular motion problems? I came across a problem in a circular motion which includes a stone tied to the end of a string. They asked for the net force at the highest p... | {
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"tags": "homework-and-exercises, newtonian-mechanics, home-experiment",
"url": null
} |
coding-theory
This gives me a simple probability distribution on $S'$: $p(a) = p(A) + p(B)$.
By the Kraft inequality, again, there is a coding that corresponds to this distribution, so that I can use an algorithm like arithmetic coding to achieve acode of length $- \log p(a) = - \log p(A) + p(B)$. | {
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"url": null
} |
javascript, algorithm, programming-challenge, palindrome, circular-list
for (let i = limit1 + equalsLength, j = limit1 + equalsLength; i < limit2; i++, j++) {
if (j >= largest.length) j = i % largest.length;
if (largest[j] < length) largest[j] = length;
length += 2;
}
}
console.log(circula... | {
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"ur... |
will scale $m$ linearly into $[t_{\text{min}},t_{\text{max}}]$ as desired.
To go step by step,
1. $m\mapsto m-r_{\text{min}}$ maps $m$ to $[0,r_{\text{max}}-r_{\text{min}}]$.
2. Next, $$m\mapsto \frac{m-r_{\text{min}}}{r_{\text{max}}-r_{\text{min}}}$$
maps $m$ to the interval $[0,1]$, with $m=r_{\text{min}}$ mapped ... | {
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"lm_q2_score": 0.865224070413529,
"openwebmath_perplexity": 384.40801525891055,
"openwebmath_score": 0.8846097588539124,
"tag... |
c, circular-list
/***************************************************************************
* Returns the index'th element of the list. Returns NULL if the index is *
* out of range. *
**********************************************************... | {
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"tags": "c, circular-list",
"url": null
} |
cc.complexity-theory, reference-request, parameterized-complexity
Title: Name for "uniformly polynomial" subclass of XP? Suppose $L$ is a parameterized language with respect to some alphabet $\Sigma$.
The $k$-slice of $L$ is $L_k = L \cap \{(x,k) \mid x \in \Sigma^{*}\}$, the set of instances in $L$ which have paramet... | {
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... |
. . This is closest to their answer-choice (2).
• March 23rd 2009, 04:34 AM
siddscool19 | {
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"tags... |
c++, performance, io
Title: Enabling stack overflow protection with Y/N prompt This asks the user if they would like to enable stack overflow protection. If they enter yes (Y or y), then a Boolean SOProtection is set to true. If they enter no (N or n), then SOProtection is set to false.
If neither Y, y, N nor n is ent... | {
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# Value of $\sum\limits_n x^n$
Why is $\displaystyle \sum\limits_{n=0}^{\infty} 0.7^n$ equal $1/(1-0.7) = 10/3$ ?
Can we generalize the above to
$\displaystyle \sum_{n=0}^{\infty} x^n = \frac{1}{1-x}$ ?
Are there some values of $x$ for which the above formula is invalid?
What about if we take only a finite number ... | {
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"openwebmath_score": 0.9880840182304382,
"tag... |
e1 && e2 && ... is the logical AND function . Properties of Matrix Operations . State the statement is True or False. Matrix multiplication is commutative. Additive identity of all m*n matrices. State the statement is True or False. The answers is false. The corresponding elements of the matrices are the same (These ar... | {
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"lm_q2_score": 0.8198933403143929,
"openwebmath_perplexity": 922.1060456872423,
"openwebmath_score": 0.5299260020256042,
"t... |
formal-languages, programming-languages, compilers
Title: Is there a programming language that is not a formal language Are out there, any programming languages that are not defined algorithmically so that we can call them "constructed languages" but not "formal languages"? Are there any discussions or papers on that ... | {
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"url": null
} |
reductions, np-hard, search-problem
The other thing that's going on in your example is that, the way you defined 3-COL-SEARCH, it's a promise problem. A promise problem is one where we have a promise that the input will be within some set -- and the algorithm is allowed to do anything it likes on other inputs. Promi... | {
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"tags": "reductions, np-hard, search-problem",
"url": null
} |
Your determinant is not wrong in the sense you can still use it test for singularity, as long as you never scale by zero. It does not however possess other nice, elegant and important properties of the standard determinant.
Taking the standard as a reference, you computation breaks one rule: Multiplying the row (or co... | {
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For the last part, a simple continuous function whose integral over circles doesn't vanish is the conjugation. We have
$$\int_{\lvert z-a\rvert = r} \overline{z}\,dz = 2\pi ir^2,$$
so
$$L(z \mapsto \overline{z}) = 2\pi i \Biggl(1 - \sum_{n = 1}^\infty r_n^2\Biggr).$$
In the construction above, it is easily seen tha... | {
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"openwebmath_score": 0.9735835194587708,
"tag... |
The remainder is $5$ because the remainder of $17$ is $5$.
It's no different with polynomials.
There remainder is $-9$ because the remainder of $5x + 1$ is $-9$.
\ \ \begin{align}p\ &\equiv\,\ 5\,\ x\,\ +\ 1\!\!\pmod{\!(x + 2)f}\quad\ \ [\,f = x + 1\rm \ \ in\ OP\,]\\ \Rightarrow\ \ p\ &\equiv\,\ 5\ \,\color{#c00}x\... | {
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"lm_q2_score": 0.8267118026095991,
"openwebmath_perplexity": 434.9738756010734,
"openwebmath_score": 0.8650945425033569,
"tag... |
solid-state-physics
To determine the density of space what we generally do is determinate the number of possible quantum states(possible values of quantum numbers) from energy $E$ to $E+dE$.
This corresponds to the volume element for a "shell" in $m$ dimensions of radius $n = \sqrt{\sum^{i=m}_{i=1}{{n_i}^2}}$ which i... | {
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Alternatively, if you want faster convergence, you can use the more sophisticated and extremely powerful Gaussian Quadrature. More complicated but well worth knowing. Here, too, you divide the domain to intervals. For each interval, you sample the function at a few carefully chosen points to obtain surprisingly high ac... | {
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"lm_q2_score": 0.8596637487122111,
"openwebmath_perplexity": 335.2277592628072,
"openwebmath_score": 0.9098044633865356,
"tag... |
java, game, swing
int len;
while ((len = in.read(buffer)) > 0) {
zos.write(buffer, 0, len);
}
in.close();
zos.closeEntry();
// remember close it
zos.close();
if (new File(Game.logFilePath).exists()) new File(Game.log... | {
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"tags": "java, game, swing",
"url": null
} |
human-biology, immunology, infection, immune-system
Question 3: there is no mechanism for directly transfering information between lymphocytes. Lymphocytes cannot read and write their DNA at will, and they are not able to simply copy sequences from each other. Rather, their diversity comes from first randomly re-shuff... | {
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} |
c#, performance, linq, set
And with a single collection:
result1: 00:00:02.9254441
result2: 00:00:04.8505489
controlResult: 00:00:00.2102433
I have to apologize, I have changed my review as I wrote this due to some details I overlooked as I was writing. Thank you mjolka for pointing out my mistake.
For m... | {
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"tags": "c#, performance, linq, set",
"url": null
} |
water, phase
Title: Does autoionization occur in steam? It is well known that H2O spontaneously autoionizes to H+ and OH- when it is in liquid phase. I was wondering whether it does the same in gas phase, either to the same extent as in liquid phase or at all. Yes, water is ionized to some extent in all phases. One st... | {
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"id": 4888,
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"openwebmath_score": null,
"tags": "water, phase",
"url": null
} |
ros, rosbridge, rostopic, topics
Title: How to get topic list from ROSBridge?
I've beem unsing ROSBridge 2.0 to communicate with ros, and i'm trying to get the topic list using the following JSON message:
{
"op": "call_service",
"service": "/rosapi/topics"
}
but i get an error on ros with the following text : "call_s... | {
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} |
c, wrapper, c++-cli
Image(int nb_hints) {
this->init(nb_hints);
}
Image() {
this->init(0);
}
You can use delegating constructor for this:
Image(int nb_hints) {
// actual initialization code here
}
Image() : Image(0) {
}
Consider changing the type of Hints to something like List<Frame^>^ or `IList^. Th... | {
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"tags": "c, wrapper, c++-cli",
"url": null
} |
c++, algorithm, sorting, c++14
template<typename Iterator>
auto operator-(const group_iterator<Iterator>& lhs, const group_iterator<Iterator>& rhs)
-> typename group_iterator<Iterator>::difference_type
{
return (lhs.base() - rhs.base()) / lhs.size();
}
/////////////////////////////////////////////////////////... | {
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"tags": "c++, algorithm, sorting, c++14",
"url": null
} |
work yourself and up to 35,000 if you're hiring a contractor to finish your basement. Virtual tour of 43 Woodbine Crescent including panoramic scenes, photo gallery, map view, property brochure and property information Virtual tour of 43 Woodbine Crescent, Hamilton, Ontario L8R1Y2. The expected value of the random vari... | {
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"id": null,
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"lm_q1_score": 0.9669140177976359,
"lm_q1q2_score": 0.8015125557055082,
"lm_q2_score": 0.8289388104343893,
"openwebmath_perplexity": 1101.7371464684404,
"openwebmath_score": 0.6746727824211121,
"tags": null... |
electromagnetism
Title: Motional emf and induced electric fields A book i am referring to states:
"..When the loop moves toward the magnet,it is the magnetic force which drives the charge to flow.But what causes the induced current in a stationary loop when a magnet moves towards it?A magnetic field cannot exert force... | {
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} |
They are based on two different properties. Minimum spanning tree is based on cut property whereas Shortest path is based on the edge relaxing property.
A cut splits a graph into two components. It may involve multiple edges. In MST, we select the edge with the least weight.
Edge relaxing says that given I know dista... | {
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"openwebmath_score": 0.5299387574195862,
"tags... |
gas-laws, pressure, kinetic-theory-of-gases, ideal-gas, van-der-waals-behavior
$$P_\text{eff}V_\text{eff} = nRT$$
which looks exactly like the ideal gas law, but corrected for additional factors. | {
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Figure 2: Conical pendulum The conical pendulum, shown in Figure 2, con-sists of a mass m at the end of a …. 2:50 Breaking the force of tension into its components. Conical pendulum – measuring g Number 13573 0-EN Topic Me ch anics , two -dimensional motion Version 201 7-02-17 / HS Type Student exercise Suggested for g... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9755769085257165,
"lm_q1q2_score": 0.8576752917655135,
"lm_q2_score": 0.8791467738423873,
"openwebmath_perplexity": 513.4436833255314,
"openwebmath_score": 0.6579096913337708,
"tags... |
Python and Matplotlib This guide assumes that you have already installed NumPy and Matplotlib for your Python distribution. It is obtained by the replacement of e^(-2piik/N) with an nth primitive unity root. Sure, you can use Python as a simple calculator, but did you know that Python can help you learn more advanced t... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9755769063954521,
"lm_q1q2_score": 0.8232845715573548,
"lm_q2_score": 0.8438951005915208,
"openwebmath_perplexity": 889.6016044723806,
"openwebmath_score": 0.4872167706489563,
"tags":... |
c++, c++11, recursion, template, stl
// for pedagogical purposes only
Holder() {
cache_.insert(std::make_pair("alpha", std::make_unique<int>(1)));
cache_.insert(std::make_pair("beta", std::make_unique<int>(2)));
cache_.insert(std::make_pair("gamma", std::make_unique<int>(3)));
cache... | {
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"tags": "c++, c++11, recursion, template, stl",
"url": null
} |
programming-challenge, rust
The product of these numbers is \$26 × 63 × 78 × 14 = 1788696\$.
What is the greatest product of four adjacent numbers in the same
direction (up, down, left, right, or diagonally) in the 20×20 grid?
I'm doing the #ProjectEuler100 challenge to learn Rust. I still have lots of places where... | {
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java, algorithm, graph
How could I implement this so that I increase its adaptability? As it is right now, it only accepts Node 0 and the source and it breaks when I try any other Node. Negative weights are also a no go.
Also, feel free to comment on anything else, i.e formatting, variable names, redundancy. int [] pr... | {
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"tags": "java, algorithm, graph",
"url": null
} |
meteorology, geology, seismology, precipitation, enso
Title: Is there any correlation between La Niña/El Niño and seismic activity? I've read in the past that extreme precipitation levels may have an effect on seismic activity, and wondered if anyone has ever analysed the La Niña / El Niño cycles to see if there is an... | {
"domain": "earthscience.stackexchange",
"id": 129,
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"openwebmath_score": null,
"tags": "meteorology, geology, seismology, precipitation, enso",
"url": null
} |
image-processing, wavelet, normalization, orthornormal
Title: Obtaining normalized matrix for the Haar Wavelet Transform I've been reading this article: http://aix1.uottawa.ca/~jkhoury/haar.htm which explains the Haar Wavelet Transform.
At a certain point, the author says:
... Since the transformation matrix $W$ is ... | {
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"tags": "image-processing, wavelet, normalization, orthornormal",
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Going back to $9- x^2= (3- x)(3+ x)= -(x- 3)(x+ 3)\ge 0$, another and perhaps simpler way to see that is this: $a- b> 0$ if and only if $a> b$ and $a- b< 0$ if and only if a< b. If x< -3 then it is also less than 3 so both of x- 3 and x+ 3= x-(3) are negative. Their product (the product of two negative numbers) is posi... | {
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"lm_q2_score": 0.8479677545357569,
"openwebmath_perplexity": 272.50361983417446,
"openwebmath_score": 0.8143748641014099,
"ta... |
multithreading, perl
Title: Perl mutiple children creation My program will fork, launching $n children. When a child finishes, the parent will launch a new one, if we have more to launch.
#!/usr/bin/perl
use strict;
use warnings;
use POSIX ":sys_wait_h";
#function, that every child will run
sub func
# {{{
{
my... | {
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"tags": "multithreading, perl",
"url": null
} |
quantum-computer
Title: Why Do Multiple Hadamard Gates Return to Base State? Reading through IBM's intro to quantum computing and gates and I'm confused about the Hadamard gate. When you use an H gate it appears to rotate the qubit along the X axis pi/4 putting it in a superposition.
If my base state was |0> and I pas... | {
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"tags": "quantum-computer",
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# Is there an irrational number arbitrarily close to another irrational number?
I know that there is a rational number arbitrarily close to an irrational, due to the density of real number. But what about an irrational number? Thanks!
Yes, consider $\alpha + \frac{1}{n}$ where $\alpha$ is irrational and $n$ is an int... | {
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"openwebmath_score": 0.9146267771720886,
"ta... |
ros, rosmaster, roscpp
~rosConnectionHandler_t ()
{
delete nh;
}
ros::NodeHandle *nodeHandle() { return nh; };
private:
ros::NodeHandle *nh;
};
Originally posted by techno74 with karma: 90 on 2015-02-05
This answer was ACCEPTED on the original site
Post score: 1
Orig... | {
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"tags": "ros, rosmaster, roscpp",
"url": null
} |
electrostatics
\end{equation}
so that
$$
\iint_S Y_n\sin\theta d\theta d\phi = 2\pi P_n(\cos\theta^\prime)\int_0^\pi P_n(\cos\theta)\sin\theta d\theta
$$
Using the usual substitution $x = \cos\theta$, we get
\begin{equation}\tag{18}\label{e18}
\iint_S Y_n\sin\theta d\theta d\phi = 2\pi P_n(\cos\theta^\prime)\int_{-1}^... | {
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"openwebmath_score": null,
"tags": "electrostatics",
"url": null
} |
Math Help - Prove the following equasion:
1. Prove the following equasion:
Hey guys,
I have a question to prove the following equation:
$Sin^2aCos^2B - Sin^2Bcos^2a = Cos^2B - Cos^2a
$
What I mean by 'proving' is that you have to take one side of the equation and reach the other side...
Usually its easier to take th... | {
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"openwebmath_score": 0.9350670576095581,
"ta... |
c++, game, c++11, proxy, mediator
template <typename T>
struct Summoned : SummonedMonster, T { // Adapter Pattern
template <typename... Args>
Summoned (LivingBeing* summoner, const LivingBeing::Data& data, Args&&... args) : SummonedMonster(summoner, data), T(data, std::forward<Args>(args)..., SummonedTag{}) {... | {
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"tags": "c++, game, c++11, proxy, mediator",
"url": null
} |
proof-theory, automated-theorem-proving, program-verification
Title: Why is Proof Checker required in Proof Carrying Code In the classical PLDI'98 paper by Necula, "The design and implementation of a certifying compiler", the high-level verifier uses:
VCGen to generate verification conditions (safety predicates)
Firs... | {
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"tags": "proof-theory, automated-theorem-proving, program-verification",
"url": null
} |
radiation
It's true that since the Earth is not a point, an observer in the upper atmosphere directly above that point on the surface would not be at exactly the same radius from the Sun as the radius of Earth's orbit (defined in terms of the position of the center of the Earth), but if you actually do the calculation... | {
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"openwebmath_score": null,
"tags": "radiation",
"url": null
} |
optimization, c, linked-list, circular-list
modify the list, so it should be passed const. Parameter list_tail is
inaccurate - a circular list has no tail. Call it just list.
Also, putting main last avoids the need for prototypes, all functions except
main should be static and the names of struct ll_core and c_ll w... | {
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"tags": "optimization, c, linked-list, circular-list",
"url": null
} |
newtonian-mechanics, forces, computational-physics, discrete
ax.set_xlim((-4, 4))
ax.set_ylim((-4, 4))
ax.set_zlim((-4, 4))
ax.plot(x[:,0], x[:,1], x[:,2], 'r-')
ax.plot(x[0,0], x[0,1], x[0,2], 'bo')
ax.plot(x[-1,0], x[-1,1], x[-1,2], 'go')
plt.show()
Starting point $[3, 0, 0]$ and direction vector $[0, 1, 1]$
Star... | {
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"tags": "newtonian-mechanics, forces, computational-physics, discrete",
"url": null
} |
c++, datetime
int TimeOnly::GetSecond() const
{
return secondsInDay % 60;
}
inline bool operator==(const TimeOnly& lhs, const TimeOnly& rhs) {return lhs.equal(rhs);}
inline bool operator!=(const TimeOnly& lhs, const TimeOnly& rhs) {return !lhs == rhs); }
inline bool operator< (const TimeOnly& lhs, const TimeOnl... | {
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[ (2,3)(4,5), (2,4)(3,5) ] ) )
gap> length := Size( cl );
5
gap> rep := Representative( cl );
Subgroup( Group( (1,2,5), (2,3,5), (3,4,5) ),
[ (2,3)(4,5), (2,4)(3,5) ] )
gap> order := Size( rep );
4
gap> IsAbelian( rep );
true
gap> abel := Filtered( classes, cl -> IsAbelian( Representative( cl ) ) );
[ ConjugacyClassSub... | {
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"openwebmath_score": 0.5242224335670471,
... |
ros-indigo
def project(msg):
#x = np.array([[msg.position.z, msg.position.z], [msg.position.y, msg.position.y]])
#np.savetxt('text.txt', x)
## Initialize moveit commander
print "============ Starting setup"
moveit_commander.roscpp_initialize(sys.argv)
#rospy.init_node('project1', anonymous=True)
## Inst... | {
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"openwebmath_score": null,
"tags": "ros-indigo",
"url": null
} |
ds.algorithms, np-hardness, sorting
No choices are made during the computation, so the complexity of the algorithm is $O(N^3)$
CODE
This is a working Java implementation of the algorithm:
public class StrangeSort {
static int PEG = 0xffffff, HOLE = 0x0;
static int M = 0, N = 0, choices = 0, aux = 0, end;
s... | {
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"tags": "ds.algorithms, np-hardness, sorting",
"url": null
} |
$\sum\limits_{n = N}^\infty {\left| {{a_n}} \right|}$
is convergent. However since,
$\sum\limits_{n = 1}^\infty {\left| {{a_n}} \right|} = \sum\limits_{n = 1}^{N - 1} {\left| {{a_n}} \right|} + \sum\limits_{n = N}^\infty {\left| {{a_n}} \right|}$
we know that $$\sum\limits_{n = 1}^\infty {\left| {{a_n}} \right|}$$ i... | {
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"lm_q2_score": 0.847967764140929,
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"openwebmath_score": 0.9078403115272522,
"tags": null,... |
homework-and-exercises, classical-mechanics, torque, moment-of-inertia
Title: Torque with 2D center of mass
A cube of mass M rests tilted against the wall as shown (see below). There is no friction between the wall and the cube, but the friction between the cube and the floor is just sufficient to keep the cube from ... | {
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"tags": "homework-and-exercises, classical-mechanics, torque, moment-of-inertia",
"url": ... |
quantum-state, quantum-operation
so you can see that the linear combination $\sum_{i}p_i \Lambda_i$ is the Choi state of the map $\sum_{i}p_i \mathcal E_B^i$. It remains to see whether this map is a channel. It is trace preserving because
$$\mathrm{Tr} \left(\sum_{i}p_i \mathcal E_B^i(\rho)\right)=\sum_i p_i=1$$
and c... | {
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"openwebmath_score": null,
"tags": "quantum-state, quantum-operation",
"url": null
} |
electrical-engineering, consumer-electronics
Power LEDs are sometimes just a LED and resistor connected in series across the input power. These LEDs don't need to be particularly bright, so are often run at less than their maximum current rating. Many common indicator LEDs are rated for 20 mA, but are still plenty b... | {
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"id": 595,
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"openwebmath_score": null,
"tags": "electrical-engineering, consumer-electronics",
"url": null
} |
• The question is exactly about the integration constant. Does it really need to be real? Does the constant play any role in your application (after using initial or/and boundary conditions)? – user Jun 16 '20 at 8:30 | {
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"lm_q2_score": 0.8757869819218865,
"openwebmath_perplexity": 230.17815960976293,
"openwebmath_score": 0.878878116607666,
"tag... |
ros, vslam
Originally posted by Tien Thanh on ROS Answers with karma: 231 on 2011-02-27
Post score: 1
Original comments
Comment by Homer Manalo on 2011-03-02:
Ooops, now I can also see this error on my system! This works in cturtle (actually not fully cause I still have some problems (http://answers.ros.org/question/... | {
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cosmology, resource-recommendations, cosmic-microwave-background
(ii) way of inferring things like curvature of universe or baryonic/dark matter content by looking at the CMBR spectrum,
The way this is done in practice is to do a giant Bayesian fit by computing the spectrum associated with a set of cosmological param... | {
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"tags": "cosmology, resource-recommendations, cosmic-microwave-background",
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# What do we actually prove using induction theorem?
Here is the picture of the page of the book, I am reading:
$$P_k: \qquad 1+3+5+\dots+(2k-1)=k^2$$ Now we want to show that this assumption implies that $P_{k+1}$ is also a true statement: $$P_{k+1}: \qquad 1+3+5+\dots+(2k-1)+(2k+1)=(k+1)^2.$$ Since we have assumed ... | {
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"lm_q1_score": 0.987946222258266,
"lm_q1q2_score": 0.8565846932763611,
"lm_q2_score": 0.8670357494949105,
"openwebmath_perplexity": 166.37486381312206,
"openwebmath_score": 0.8577460646629333,
"tag... |
ros-kinetic
Originally posted by raequin on ROS Answers with karma: 368 on 2018-04-24
Post score: 0
The following package-installation commands took care of this problem.
sudo apt install ros-kinetic-position-controllers ros-kinetic-effort-controllers ros-kinetic-joint-trajectory-controller ros-kinetic-robot-state-pu... | {
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} |
programming, qiskit
/.error-footer -->\n\n\n </div><!-- /#cf-error-details -->\n </div><!-- /#cf-wrapper -->\n\n <script type="text/javascript">\n window._cf_translation = {};\n \n \n</script>\n\n</body>\n</html>\n'``` The explanation is in the body of the message (after some scrolling): | {
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17, 2012 Definion! If(something(pushes(the(minute(hand(where(-me(passes(correctly,(then(itis(moving(the. Assume we have a matrix [R0] which defines a rotation about the origin:. xz yz z xy y zy x yx zx ij τ τ σ τ σ τ σ τ τ σ σ For static equilibrium τxy= τyx, τxz= τzx, τzy= τyz resulting in s ix independent scalar quant... | {
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"lm_q1_score": 0.9822876992225169,
"lm_q1q2_score": 0.8206851953639296,
"lm_q2_score": 0.8354835309589074,
"openwebmath_perplexity": 643.2726873535121,
"openwebmath_score": 0.6907839775085449,
"... |
in agreement with Accidental's answer. With this approach, you can obtain the series expansions of g just using Series:
Series[g[t], {t, 0, 4}] //TeXForm
$$g(0)-g(0) t x+\frac{1}{2} t^2 \left(g(0) x^2+g(0)\right)+t^3 \left(-\frac{1}{6} g(0) x^3-\frac{1}{2} g(0) x\right)+\frac{1}{24} t^4 \left(g(0) x^4+6 g(0) x^2+3 g... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9615338101862455,
"lm_q1q2_score": 0.831942217139224,
"lm_q2_score": 0.865224091265267,
"openwebmath_perplexity": 2166.384833893749,
"openwebmath_score": 0.603827953338623,
"tags":... |
[4 marks]
a.
(i) attempt to use $$G(t) = \sum {{\text{P}}(Y = y){t^y}}$$ (M1)
$$= \sum\limits_{y = 0}^\infty {{{\text{e}}^{ – y}}(1 – {{\text{e}}^{ – 1}}){t^y}}$$ A1
Note: Accept a listing of terms without the use of $$\Sigma$$.
this is an infinite geometric series with first term $$1 – {{\text{e}}^... | {
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"lm_q1_score": 0.9908743634192695,
"lm_q1q2_score": 0.81241128293433,
"lm_q2_score": 0.8198933315126791,
"openwebmath_perplexity": 3192.680281406569,
"openwebmath_score": 0.8997789621353149,
"tags"... |
c, strings
Title: C dynamic strings In the process of writing a compiler, I wrote this dynamic string library to help with keeping track of heap allocated strings and to have an easy way to format them.
Note:
The macros ALLOC(), CALLOC(), and REALLOC() used in the implementation are equivalent to the C stdlib function... | {
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"tags": "c, strings",
"url": null
} |
shown for illustrative purposes.Anders Celsius ( °C ) the CIPM formally adopted degree to... Is an absolute absence of any thermal energy temperatures from Celsius to kelvin-K = °C... Is 273.15 K − 273.15 Celsius = 0° C. what is the temperature value can be converted Celsius... To degrees Celsius the Celsius temperatur... | {
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"lm_q1_score": 0.9732407160384083,
"lm_q1q2_score": 0.8252767520803771,
"lm_q2_score": 0.8479677622198947,
"openwebmath_perplexity": 1804.3262654793741,
"openwebmath_score": 0.7905264496803284,
"tags": nul... |
MT1988 wrote:
MT1988 wrote:
generis wrote:
Without the formula see diagram
The shortest distance between parallel lines is a line perpendicular to both parallel lines
Draw a perpendicular line from point B to point A
That creates right isosceles ∆ ABO where OA = AB
-- The line y = x makes a 45° angle with both the x-... | {
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"lm_q2_score": 0.8577680995361899,
"openwebmath_perplexity": 2976.88257315349,
"openwebmath_score": 0.8180845975875854,
"tags": null,
"url": "htt... |
mars, water, planetary-atmosphere
Title: Why wouldn't massive torrents freeze on Mars? I am currently reading the Cambridge Guide to the Solar System. In chapter 8, section 8.7, they explain that massive torrents of water created outflow channels on the surface of Mars in the past. The book goes on to state that these... | {
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"tags": "mars, water, planetary-atmosphere",
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} |
3 minutes ago. [email protected] Chapter 2 DIFFUSION 2. FEM 2D_Transient_Diffusion. Diffusion Time Calculator When considering the diffusion of ions and molecules in solutions, it is generally useful to be able to estimate the time required for diffusion over a given distance. Imperial College London, 2019. txt) or rea... | {
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"lm_q1_score": 0.9755769071055402,
"lm_q1q2_score": 0.8440926429097708,
"lm_q2_score": 0.865224091265267,
"openwebmath_perplexity": 1675.8624038387193,
"openwebmath_score": 0.5665031671524048,
"tags": nu... |
cor(x, y)
[1] 0.7454673
plot(x, y, pch=20)
Perhaps closer to a practical example, for each $$i = 1, 2, \dots, 100,$$ let $$X_i, Y_i$$ be independently distributed as $$\mathsf{Norm}(i+30, 5).$$ [We may be weighing 100 standard specimens of known weights $$i+30$$ on two different low-quality scales in order to assess ... | {
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"lm_q1_score": 0.975201841245846,
"lm_q1q2_score": 0.81053223468898,
"lm_q2_score": 0.8311430520409023,
"openwebmath_perplexity": 282.12928772914796,
"openwebmath_score": 0.9637175798416138,
"tags"... |
evolution, zoology, adaptation
One answer that came to mind is domestic animals - the horse and dog in prehistory, the cat in ancient Egypt, etc. That seems too obvious on one hand, and on the other hand may not really be an answer, as there seems to be no indication that pre-domestic animals were endangered by humans... | {
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"openwebmath_score": null,
"tags": "evolution, zoology, adaptation",
"url": null
} |
quantum-mechanics, fourier-transform, superposition
Title: Superposition of waves with different initial phase in Quantum Mechanics In Quantum Mechanics, if a particle's state is a superposition of many states, then we say that its position is well-defined (by the Heisenberg uncertainty principle, because here we have... | {
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"tags": "quantum-mechanics, fourier-transform, superposition",
"url": null
} |
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