text stringlengths 49 10.4k | source dict |
|---|---|
ros, eband-local-planner
Title: how to set parameters (publish_voxel_map)
I'm trying to navigate a turtlebot with eband_local_planner on hydro. I have already navigated a turtlebot with base_local_planner. With eband_local_planner, next error is displayed on a terminal.
load_parameters: unable to set parameters (las... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "ros, eband-local-planner",
"url": null
} |
Eigenvalues of a Matrix and its Transpose are the Same
Problem 508
Let $A$ be a square matrix.
Prove that the eigenvalues of the transpose $A^{\trans}$ are the same as the eigenvalues of $A$.
Proof.
Recall that the eigenvalues of a matrix are roots of its characteristic polynomial.
Hence if the matrices $A$ and $A^... | {
"domain": "yutsumura.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.989671849308438,
"lm_q1q2_score": 0.8181733837449688,
"lm_q2_score": 0.8267117876664789,
"openwebmath_perplexity": 100.83858060636113,
"openwebmath_score": 0.9450052380561829,
"tags": ... |
If you toss $5$ times then think of it as a match1 as described above that is followed by an extra toss of you, and call the whole thing match2.
Now apply that:
$$\Pr\left(\text{you win match2}\right)=$$$$\Pr\left(\text{you win match1}\right)+\Pr\left(\text{match1 ends in a tie}\wedge\text{extra toss is a head}\right... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9850429151632046,
"lm_q1q2_score": 0.8076301173961211,
"lm_q2_score": 0.8198933315126791,
"openwebmath_perplexity": 576.4229639967353,
"openwebmath_score": 0.8813685774803162,
"tag... |
Yes, it is correct. The same conclusion can be obtained by finding the rank matrix of the following matrix which gives the dimension of $V_1+V_2$: $$\left( \begin{array}{ccccccccc} 1&1&1&0&0&0&0&0&0\\ 0&0&0&1&1&1&0&0&0\\ 0&0&0&0&0&0&1&1&1\\ \hline 1&0&0&1&0&0&1&0&0\\ 0&1&0&0&1&0&0&1&0\\ 0&0&1&0&0&1&0&0&1 \end{array}\ri... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.991014570185918,
"lm_q1q2_score": 0.9054667500516212,
"lm_q2_score": 0.9136765263519308,
"openwebmath_perplexity": 109.75095484750638,
"openwebmath_score": 0.9558939337730408,
"tag... |
terminology, continuum-mechanics, stress-strain
Title: What is the name of the principle that replaces a history functional by internal/state variables? I just need to know the correct expression:
When narrowing down constitutive equations for the mechanics solids in continuum mechanics, one has in the very general ca... | {
"domain": "physics.stackexchange",
"id": 42435,
"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": "terminology, continuum-mechanics, stress-strain",
"url": null
} |
navigation
If I replace the "global_frame" parameter from "/odom" to whatever (like "/map") in the "local_costmap_params.yaml" configuration file, the error disapears but it does not work...
My tf tree seems good :
image description http://i45.tinypic.com/2lt0cua.png
And a tf_echo seems good :
psykokwak@robot:~/ros/wo... | {
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"id": 10473,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "navigation",
"url": null
} |
newtonian-mechanics, forces
You can see from the inclined plane's geometry that the resultant force on the object is $mgsinθ$, and it is constant. Therefore, by Newton's second law, the acceleration is also constant and equal to $gsinθ$.
And the normal force, always perpendicular to the contact surface, will have mag... | {
"domain": "physics.stackexchange",
"id": 53698,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "newtonian-mechanics, forces",
"url": null
} |
turing-machines
For example, let's look at input #101100# (# here means the edges of the input). The read head is at the first #.
Input starts as # 1 0 1 1 0 0 # (leaving room for markers)
Mark the first two inputs, write a 0 at the end: # 1'0'1 1 0 0 # 0
Mark the next two inputs, write a 0 at the end: # 1'0'1'1'0 0 ... | {
"domain": "cs.stackexchange",
"id": 15106,
"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": "turing-machines",
"url": null
} |
c#, interview-questions, interval
Title: Time schedule intersection I had a job interview one of the questions was the following
Given an api - you submit a name of a person and it gives back a sorted list of all the free time slots this person has. the list might be very long.
List<TimePeriod> GetTimesAvail(String pe... | {
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "c#, interview-questions, interval",
"url": null
} |
quantum-computing, it.information-theory, quantum-information, st.statistics
However, there are several known upper and lower bounds on the probability of error (i.e. 1 minus the average success probability). In terms of pairwise fidelities, the probability of error in your setting is known to be lower bounded by $\fr... | {
"domain": "cstheory.stackexchange",
"id": 1564,
"lm_label": null,
"lm_name": null,
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"lm_q1q2_score": null,
"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "quantum-computing, it.information-theory, quantum-information, st.statistics",
"... |
c++, beginner, c++11, bitwise, number-guessing-game
if (answer == 'r')
goto Reset;
guessNum |= my::getUpdateForGuessNum(myVar::bitFlag[counter],num,answer);
system("cls");
}
std::cout << "\n Your number is \n";
std::cout << "\n" << std::setfill('-') << std::setw(81) << "\n";
std::cout << std::setfi... | {
"domain": "codereview.stackexchange",
"id": 23607,
"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": "c++, beginner, c++11, bitwise, number-guessing-game",
"url": null
} |
ruby, finance
def transfer_funds
puts <<-START.gsub(/^\s*>/, ' ')
>
>Transfer from Savings to Checking '1'
>Transfer from Checking to Savings '2'
>
START
input = gets.chomp
case input.to_i
when 1
puts <<-START1.gsub(/^\s*>/, ' ')
>
>Yo... | {
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"id": 17049,
"lm_label": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "ruby, finance",
"url": null
} |
javascript, ecmascript-6, vue.js
<div class="row post-grid" v-if="posts">
<div class="col-sm-6 post" v-for="post in posts">
<div class="post-container">
<h2 class="display-4 post-title">{{post.title | titlecase}}</h2>
<div class="short-desc">
{{post.body | capitalize}}
... | {
"domain": "codereview.stackexchange",
"id": 42647,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "javascript, ecmascript-6, vue.js",
"url": null
} |
Thus the distance d betw… In the figure given below, the distance between the point P and the line LL can be calculated by figuring out the length of the perpendicular. We know that the slopes of two parallel lines are the same; therefore the equation of two parallel lines can be given as: $$y$$ = $$mx~ + ~c_1$$ and $$... | {
"domain": "eneacoaching.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9719924761487654,
"lm_q1q2_score": 0.8099852428681781,
"lm_q2_score": 0.8333246015211009,
"openwebmath_perplexity": 377.3788341689554,
"openwebmath_score": 0.7322174906730652,
"... |
java, interview-questions, stack
}System.out.println("want to continue");
First, never put unrelated commands after a closing }. The only statements that should appear on the same line as a } are things like else and catch which are directly related to the block.
Second, when writing for a potential employer, alwa... | {
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"id": 15168,
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"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "java, interview-questions, stack",
"url": null
} |
python, comparative-review, database
Title: Two Python classes to update an RRD database The first Python class below is used in one of my current projects and is a totally different approach to how I normally would take things. Before I refactored the class I was not declaring instance-properties/variables. Instead t... | {
"domain": "codereview.stackexchange",
"id": 20306,
"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": "python, comparative-review, database",
"url": null
} |
interview-questions, swift, hashcode
Title: Hashing interview puzzle I've stumbled upon this pretty old article about a hashing interview question, and here it is converted to Swift in a more generic way:
struct CustomHasher {
/// An enum of the errors that may be thrown
enum HashingError: Error {
//... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "interview-questions, swift, hashcode",
"url": null
} |
c++, c++11, template
Title: Template data types implementation I'm preparing for an exam on C++, as part of my preparation I want to implement a generic map without using anything from the STD for educational purposes.
Before jumping into implementation of everything, I want to know that the skeleton for my Map is sol... | {
"domain": "codereview.stackexchange",
"id": 6110,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c++, c++11, template",
"url": null
} |
A relation R on a set A is symmetric if whenever (a, b) ∈ R then (b, a) ∈ R, i.e. Difference between antisymmetric and not symmetric. An antisymmetric and not asymmetric relation between x and y (asymmetric because reflexive) Counter-example: An symmetric relation between x and y (and reflexive ) In God we trust , … (a... | {
"domain": "tpicom.eu",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9678992932829918,
"lm_q1q2_score": 0.8509255257701465,
"lm_q2_score": 0.8791467580102418,
"openwebmath_perplexity": 559.41462801027,
"openwebmath_score": 0.82464998960495,
"tags": null... |
Is this because it could be possible that the element $f \in G$ which 'links' two elements in the same conjugacy classes could be in $S_n$ but not in $A_n$?
Thanks!
-
For question $1$: Counting helps! Refer to the exercises in Herstein. For question $2$: See here.. I'll write a long answer later tommorrow afternoon i... | {
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"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9766692325496973,
"lm_q1q2_score": 0.8030068313728512,
"lm_q2_score": 0.8221891348788759,
"openwebmath_perplexity": 150.88882852303465,
"openwebmath_score": 0.8889841437339783,
... |
special-relativity, reference-frames, time
But how can the observer on the platform now disagree that the two clocks are synchronized? The conclusion would be the same, but quantitative results would be harder to derive.
Why the conclusion would be the same:
The following relies on the assumption that the speed of s... | {
"domain": "physics.stackexchange",
"id": 32203,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "special-relativity, reference-frames, time",
"url": null
} |
newtonian-mechanics, everyday-life, friction
Title: Accelerate the car by static friction I asked this question about friction and slip ratio and now I still don't understand it
Why friction is zero when wheel slip is zero?
As the below graph of wheel friction vs slip ratio shows that in order for the car to has accel... | {
"domain": "physics.stackexchange",
"id": 12582,
"lm_label": null,
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"openwebmath_score": null,
"tags": "newtonian-mechanics, everyday-life, friction",
"url": null
} |
python, algorithm, bitwise
def create_bit_array(input_data, bits, signed=False):
if not isinstance(input_data, (int, long, str, unicode, BitArray)):
raise TypeError("Input must be given as binary strings or integers.")
elif isinstance(input_data, BitArray):
return input_data
elif isinstanc... | {
"domain": "codereview.stackexchange",
"id": 8753,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "python, algorithm, bitwise",
"url": null
} |
• I would define the $r$th harmonic number for a real number $r$ which is not a negative integer for example by $H_r = \gamma +\psi(r+1)$, where $\gamma$ is the Euler-Mascheroni constant and $\psi$ is the digamma function – Maximilian Janisch Feb 13 at 22:29
• Things are even more complicated. Suppose you have a functi... | {
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"id": null,
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9850429147241161,
"lm_q1q2_score": 0.8676229178895667,
"lm_q2_score": 0.8807970748488297,
"openwebmath_perplexity": 373.008033976001,
"openwebmath_score": 0.9237313270568848,
"tags... |
c++, performance, integer
char carry = 0;
char adder = 0;
for(int cnt = 0; cnt < max_size; ++cnt)
{
adder = result[cnt] - '0' + carry;
if(cnt < min_size)
{
adder += addend[cnt] - '0';
}
result[cnt] = adder%10 + '0';
carry = adder/10;
}
... | {
"domain": "codereview.stackexchange",
"id": 32787,
"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": "c++, performance, integer",
"url": null
} |
plasma-physics, radio-frequency
Title: Radiofrequency attenuation in cold plasma The missile plume can be considered a cold plasma. If a radio signal passes across the plume it's attenuated. Obviously the attenuation depends on the frequency of the signal. Where can I find some information about the behaviour of the R... | {
"domain": "physics.stackexchange",
"id": 12670,
"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": "plasma-physics, radio-frequency",
"url": null
} |
electrostatics, potential, method-of-images
The basic justification for the method of images is the uniqueness theorems for BVPs with Neumann boundary conditions--it doesn't matter how you find a solution to Poisson's equations with given boundary conditions, so long as you find a potential that solves Poisson's equat... | {
"domain": "physics.stackexchange",
"id": 22929,
"lm_label": null,
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"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "electrostatics, potential, method-of-images",
"url": null
} |
mechanical-engineering, fluid-mechanics, chemical-engineering, mechanical
Title: What kind of magnetic water conditioner can industrial sinter plant use? As you can see in the below shematic, the magnetic water conditioners can be used for the pipes of incoming process water on sinter plants to reduce surface tension ... | {
"domain": "engineering.stackexchange",
"id": 3185,
"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": "mechanical-engineering, fluid-mechanics, chemical-engineering, mechanical",
"... |
Bottom line: If $$\phi$$ is not continuous (or $$C^1$$, but that would be rarer) on the interval, then split the interval up.
BONUS: In this case we could also have taken a common short cut. We can notice that $$f(x) = \frac{e^{-\frac{1}{x}}}{x^2(1+e^{-\frac{2}{x}})}$$ is an even function (i.e. $$f(x)= f(-x)$$). There... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9572778048911612,
"lm_q1q2_score": 0.8367347354139146,
"lm_q2_score": 0.8740772335247532,
"openwebmath_perplexity": 217.2301750543745,
"openwebmath_score": 0.9683943390846252,
"tag... |
4. This indicates how strong in your memory this concept is. Highest Common Factor and Lowest Common Multiple; 7. Customize Customize … Chapter List. 1800-212-7858 / 9372462318. View solution Prove that the area of a regular polygon of 2 n sides inscribed in a circle is a mean proportional between the areas of the regu... | {
"domain": "formascirculares.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9724147201714923,
"lm_q1q2_score": 0.8245763267413366,
"lm_q2_score": 0.8479677545357568,
"openwebmath_perplexity": 1284.0060880995668,
"openwebmath_score": 0.5869511365890503,
... |
homework-and-exercises, kinematics, rotational-dynamics, moment-of-inertia
Title: Moment of inertia of 4 particle system Four particles are connected by rigid rods of negligible mass. The origin is at the center of the rectangle. The system rotates in the $xy$ plane about the z axis with an angular speed of $6$ rad/s.... | {
"domain": "physics.stackexchange",
"id": 30524,
"lm_label": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "homework-and-exercises, kinematics, rotational-dynamics, moment-of-inertia",
"ur... |
ros
Title: narf and kdtree flann search
Hi,
I'm not sure if I should ask this here or in the PCL mailing list but I'll ask here anyways.
I am trying to use kdtree_flann to match narf descriptors. I am extracting the descriptors in a similar way to the NARF PCL tutorial. The problem is when I try perform the NN search... | {
"domain": "robotics.stackexchange",
"id": 6259,
"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": "ros",
"url": null
} |
algorithms, integers, subsequences
Title: Test if there exists an integer k to add to one sequence to make it a subsequence of another sequence Suppose that sequence $A$ contains $n$ integers $a_1,a_2,a_3,\ldots,a_n$ and sequence $B$ contains $m$ integers $b_1,b_2,b_3,\ldots,b_m$. We know that $m \geq n$. We assume wi... | {
"domain": "cs.stackexchange",
"id": 15071,
"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": "algorithms, integers, subsequences",
"url": null
} |
So if we consider a g2 not in <g1> then <g2> will be another DIFFERENT subgroup, by 'different' i mean <g1> and <g2> are NOT the same set.
We know that both <g1> and <g2> are finite sets. However I am still a bit lost on how to complete the proof.
First why don't we also consider elements IN <g1>? Since these element... | {
"domain": "mathhelpforum.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9799765604649331,
"lm_q1q2_score": 0.8057260847199247,
"lm_q2_score": 0.8221891392358015,
"openwebmath_perplexity": 535.7785059264891,
"openwebmath_score": 0.8960572481155396,
"tag... |
gravity, speed
Title: What is the Maximum Speed that can be acheived Because of Acceleration Due to Gravity? Planets and other bodies in the universe have different ranges of gravitational fields. What is the maximum speed that can be achieved because of acceleration due to gravitational field.
In other words which i... | {
"domain": "astronomy.stackexchange",
"id": 1307,
"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": "gravity, speed",
"url": null
} |
c++, iterator, sqlite
/* returns rowid of last successfully inserted row. If no rows
inserted since this database connectioned opened, returns zero. */
int last_insert_rowid();
/* UPDATE contacts SET col1 = value1, col2 = value2, ... WHERE rowid = therowid;
table_name is table to updat... | {
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"tags": "c++, iterator, sqlite",
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In the original two-daughter question, we have to be very careful to get the information we get in such a way that we have an unbiased sample of one family from the space of all two-child families in which at least one child is a girl. Essentially, we want something equivalent to where we ask a yes-no question whose an... | {
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"lm_q1_score": 0.9783846691281407,
"lm_q1q2_score": 0.8373516394498828,
"lm_q2_score": 0.8558511451289037,
"openwebmath_perplexity": 838.9512699130639,
"openwebmath_score": 0.8090196251869202,
"tag... |
newtonian-mechanics, kinematics, energy-conservation
Note: When the spring is fully unwound it is disengaged from the wheels so that the car rolls forward freely instead of winding the spring back up. That's like the catapult which releases the stone; otherwise the stone would stretch the elastic again and keep oscill... | {
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"tags": "newtonian-mechanics, kinematics, energy-conservation",
"url": null
} |
quantum-algorithms, experimental-realization
Title: Which is the highest number factorized by QC in a non-specific experiment? Since the original experimental contribution using the Shor's factoring algorithm to factorize the integer 15 some experiments have been performed in order to calculate the largest factorized... | {
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[1 mark]
d.
(A1)(A1)(A1)(A1)(A1)(A1) (C6)
Note: Award (A1) for each number correctly placed.
Award (A0) for any entry in more than one region.
[1 mark]
e.
(A1)(A1)(A1)(A1)(A1)(A1) (C6)
Note: Award (A1) for each number correctly placed.
Award (A0) for any entry in more than one region.
[1 mark]
f.
##... | {
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"lm_q2_score": 0.817574471748733,
"openwebmath_perplexity": 4675.25584131319,
"openwebmath_score": 0.8237906694412231,
"tags"... |
# PA = LU Decomposition with Row Exchange
I am not sure how to deal with the L with we do row exchange in PA = LU decomposition. Here's my example:
$A = \left[ {\begin{array}{ccc} 1 & 1 & 1\\ 0 & 0 & 1\\ 2 & 3 & 4\\ \end{array} } \right]$
Step 1: Swap row 1 and row 3
$U = \left[ \begin{array}{ccc} 2 & 3 & 4\\ 0 & 0... | {
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"openwebmath_score": 0.7158042192459106,
"tag... |
algorithms, optimization, computational-geometry, check-my-answer
Title: Find a unit square containing most of the points Given points $p_1,\ldots,p_n$ in $\mathbb{R}^2$, the task is to find an axis-aligned unit square containing the maximum number of points. I came up with and $O(n^3)$ algorithm as follows.
Observati... | {
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"openwebmath_score": null,
"tags": "algorithms, optimization, computational-geometry, check-my-answer",
"url": null
} |
magnetic-fields, angular-momentum, differential-geometry, tensor-calculus, mathematics
In two dimensions, there is clearly rotation, imagine a one-dimensional "rod" spinning in a plane. You might be tempted to describe the rotation as the 3d vector of angular momentum perpendicular to the plane, but this is an extrins... | {
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"tags": "magnetic-fields, angular-momentum, differential-geometry, tensor-calculus, mathema... |
linear-systems, random-process, stochastic
Title: expected value of two LTI output signals multiplied (cross correlation) I have an input signal x (assumed to be iid Gaussian with $\mu=0$, $\sigma^2$) which is fed into two linear systems:
$y_1 = h_1 * x$
$y_2 = h_2 * x$ | {
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(where all sums are over $n$ items).
For reference, the elementary proof of $Var(X) = E[X^2] - E[X]^2$ is just symbol pushing: $$\begin{eqnarray} Var(X) &=& \frac{1}{n}\sum (x_i - E[X])^2\\ &=& \frac{1}{n}\sum (x^2_i - 2 E[X]x_i + E[X]^2)\\ &=& \frac{1}{n}\sum x^2_i - \frac{2}{n} E[X] \sum x_i + \frac{1}{n}\sum E[X]^2... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9748211641513499,
"lm_q1q2_score": 0.8285698983590242,
"lm_q2_score": 0.8499711832583695,
"openwebmath_perplexity": 338.28284259050065,
"openwebmath_score": 0.9555947184562683,
"ta... |
c++, pointers
template <typename O>
class slave_ptr {
private:
std::weak_ptr<O> m_ptr;
public:
slave_ptr() {}
slave_ptr(std::shared_ptr<O> ptr) : m_ptr(ptr) {}
O& operator*() const {
if (m_ptr.expired())
throw ObjectInvalid();
return m_ptr.lock().operator*();
}
O... | {
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quantum-mechanics, condensed-matter, solid-state-physics, fermions, time-reversal-symmetry
\end{equation}
where the operators $\hat{\psi}^{\dagger}_{A}/\hat{\psi}_{A}$ satisfy the usual anticommutation relations and $H$ is the first quantized Hamiltonian (basically just an $N\times N$ matrix). If the second quantized ... | {
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"tags": "quantum-mechanics, condensed-matter, solid-state-physics, fermions, time-reversal-... |
algorithms, graphs, shortest-path
If you are not using a consistent heuristic function, then you should store along each node in the hash table its value $g(n)$ ---i.e., the cost of the path from its corresponding root node, either $s$ or $t$. Doing so, the previous procedure is just slightly modified by selecting the... | {
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"openwebmath_score": null,
"tags": "algorithms, graphs, shortest-path",
"url": null
} |
programming-languages, type-theory, type-checking, types-and-programming-languages
Title: Dynamic testing of down casts as explained in TAPL On page 195 of Pierce's TAPL book, he states that one can replace a down-cast operator by some sort of dynamic type test. Then he gives the following rules:
T-Typetest:
$\dfrac{\... | {
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"tags": "programming-languages, type-theory, type-checking, types-and-programming-languages",
... |
arithmetic
However, the last line of the demonstration assumes that $\ll$ distributes over $\oplus$. Is this assumption true or does it only work for my specific use case? Yes, bit shifts distribute over all bitwise logical operations $\odot$ for which $0 \odot 0 = 0$,* in the sense that: $$(a \odot b) \ll n = (a \ll ... | {
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"openwebmath_score": null,
"tags": "arithmetic",
"url": null
} |
waves, interference, wavelength, superposition
Title: Why is the phase difference an "odd number of half-wavelengths" when two waves interfere destructively? Excerpt from the Feynman Lectures, Volume III, Quantum Behavior (emphasis mine):
At those places where the two waves arrive at the detector with a phase differe... | {
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"tags": "waves, interference, wavelength, superposition",
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} |
c++, template-meta-programming, c++20
template <string_constructible... T>
string(const T&...) // input)
// -> string<((sizeof(detail::to_string(input).elems) - 1) + ... + 1)>; // original
// -> string<((decltype(detail::to_string(input))::size_static() - 1) + ... + 1)>; // avoiding external sizeof and accessi... | {
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"tags": "c++, template-meta-programming, c++20",
"url": null
} |
convolution
Title: Applications or physical interpretation of auto-convolution? I wonder if anyone has any experience with auto-convolution. In particular i'm interested in understanding the physical interpretation of it.
I understand what convolution, correlation and auto-correlation are, also i'm aware that the def... | {
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"tags": "convolution",
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pharmacology, cardiology, toxicology, electrophysiology, electrocardiography
In a study in patients with therapeutic nontoxic digitalis levels determined that these patients may safely undergo electrical cardioversion without reducing or withholding the dose of digitalis. Thus, the cardioversion is not contraindicated... | {
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"tags": "pharmacology, cardiology, toxicology, electrophysiology, electrocardiography",
"u... |
Hence $$A+B+C+7=\dfrac{4}{9}(10^{2m}-1)+\dfrac{2}{9}(10^{m+1}-1)+\dfrac{8}{9}(10^{m}-1)+7=$$$$=\dfrac{1}{9}(4\cdot 10^{2m}+28\cdot 10^m+49)=\dfrac{1}{9}(2\cdot 10^{m}+7)^2=\left(\dfrac{2\cdot 10^m+7}{3}\right)^2$$ but $$2\cdot 10^m+7\equiv 0 \pmod{3}$$ since $10^m\equiv 1 \pmod{3} \Rightarrow 2\cdot 10^m\equiv 2 \pmod{... | {
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"openwebmath_score": 0.6336814165115356,
"tag... |
In both ratios, it is Length-to-Width.
. . That is, .the longer side : the shorter side.
If you don't "line them up" correctly, you're asking for trouble.
Code:
* - - - - - - - - - *
| | * - - *
| | | |
40 | | 3 | |
| ... | {
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"openwebmath_score": 0.759093701839447,
"tag... |
With $B$ I would have done pretty much the same thing, subtracting row 1 from both row 2 and row 3: $B \sim \left( \begin{array}{ccc} 1 & x & x^{2} \\ 1 & y & y^{2} \\ 1 & z & z^{2} \end{array} \right) \sim \left( \begin{array}{ccc} 1 & x & x^{2} \\ 0 & y - x & y^{2} - x^{2} \\ 0 & z - x & z^{2} - x^{2} \end{array} \ri... | {
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"lm_q1_score": 0.9688561667674652,
"lm_q1q2_score": 0.8115332747375046,
"lm_q2_score": 0.8376199714402812,
"openwebmath_perplexity": 220.30148697447768,
"openwebmath_score": 0.8335779905319214,
"ta... |
# Trivial question about nested quantifiers.
Reading my textbook, I came across exercises for nested quantifiers.
The question: Let $L(x, y)$ be the statement “$x$ loves $y$,” where the domain for both $x$ and $y$ consists of all people in the world. Use quantifiers to express each of these statements.
i) Everyone lo... | {
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"openwebmath_score": 0.9342421889305115,
"tag... |
quantum-chemistry, computational-chemistry
What physically is going on is the list you generate is the list of basis functions which have a significant overlap. Thus for a given $a$ the list of associated $b$ will be those basis functions in some sense close to $a$ in space. For a very large system this is independent... | {
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"tags": "quantum-chemistry, computational-chemistry",
"url": null
} |
camera
Title: Problem with camera while running SVO live
hi everybody,
I'm trying to launch the live of SVO, but it gives me immediately this type of error:
[ INFO] [1418401675.780991894]: SVO initialized
[ INFO] [1418401675.791371920]: Found parameter: svo/cam_topic, value: /ardrone/front/image_raw
[ INFO] [14184017... | {
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c++
At least officially, you're supposed to prefer to use <cstdint> instead. I have a hard time getting very excited about it though.
#include <cstring>
From the looks of the code, you really wanted to include <string> here instead. You use an std::string in one place anyway (and I don't any use of anything from <cst... | {
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} |
the triangle is 9, find the area of the circle.-----My first thought was to use πr^2 to get the diameter then the radius and use that as the hypotenuse of the right triangle, but since one of the legs is 9, that got me really confused. Color Palette From Image, Christina Murphy Instagram, 39, p. 564 Theorem 10.13 Inscr... | {
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"lm_q1_score": 0.9664104924150546,
"lm_q1q2_score": 0.8115277171957763,
"lm_q2_score": 0.8397339676722393,
"openwebmath_perplexity": 814.5840034889102,
"openwebmath_score": 0.5601709485054016,
"tags": null,
... |
parsing, validation, kotlin
for (rule in rules) {
var index = 0
val dates = rule.dates
if (dates != null) {
Assert.assert(dates.size == 1)
val start = dates[0].startDate
val end = dates[0].endDate ?: start
index = getIn... | {
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"openwebmath_score": null,
"tags": "parsing, validation, kotlin",
"url": null
} |
ros, joint
[ 1.22460635e-16, -1.00000000e+00, 0.00000000e+00,
0.00000000e+00],
[ -0.00000000e+00, 0.00000000e+00, 1.00000000e+00,
0.00000000e+00],
[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
1.00000000e+00]])
>>> transformations.euler_from_matrix(m,'sxyz')
(0.0, 0.0, ... | {
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"tags": "ros, joint",
"url": null
} |
computability, undecidability, proof-techniques, reference-question, turing-recognizable
2. Closure properties
Sometimes we can use closure properties to show some language is not decidable, based on other languages we already know not to be decidable.
Specifically,
if $L$ is not decidable (we write $L\notin R$), then... | {
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"tags": "computability, undecidability, proof-techniques, reference-question, turing-recognizable... |
javascript, jquery, userscript, wikipedia
/**
* Prepend the thumbnail with clicked body text
* @param {string} text Body text
*/
function prependText(text) {
$(".infobox .vcard .plainlist").addClass($(".infobox tbody").prepend(text));
} Nice idea.
Here's a solution that breaks down each of the steps into tiny,... | {
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"tags": "javascript, jquery, userscript, wikipedia",
"url": null
} |
Consider the convergent series $$1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} - \frac{1}{6} + \ldots$$ and one of its rearrangements $$1 + \frac{1}{3} - \frac{1}{2} + \frac{1}{5} + \frac{1}{7} - \frac{1}{4} + \frac{1}{9} + \frac{1}{11} - \frac{1}{6} + \ldots$$ in which two positive terms are always followe... | {
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"lm_q1_score": 0.97241471777321,
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"lm_q2_score": 0.863391617003942,
"openwebmath_perplexity": 233.22227212056484,
"openwebmath_score": 0.8296274542808533,
"tags"... |
homework-and-exercises, newtonian-mechanics, energy, projectile, drag
Under this model, the ball eventually reaches a terminal speed that we can find from Newton's second law (working on a single axis, say $y$):
$$
\sum F_y=-mg+Dv^2=ma_y
$$
where for convenience I have defined $D=1/2\rho C_DA$. Terminal speed ($v_t$) ... | {
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"tags": "homework-and-exercises, newtonian-mechanics, energy, projectile, drag",
"url": n... |
There are different approaches to compute the requested auto-correlations but I would like to provide the simplest that suits to your case provided that.
• The difference equation is an LCCDE type indicating an LTI system.
• The input to the system $$v[n]$$ is WSS (wide sense stationary) random process.
Both of which... | {
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"lm_q1_score": 0.959762057376384,
"lm_q1q2_score": 0.8018653945429689,
"lm_q2_score": 0.8354835330070839,
"openwebmath_perplexity": 361.9283243712944,
"openwebmath_score": 0.9670982956886292,
"tags... |
electromagnetism
Title: Derivation of Magnetic Energy and Ohm's Law I am currently reading section 10.1 of Classical Electricity and Magnetism by Panofsky and came across their derivation for magnetic energy stored in current systems.
Consider a process in which a battery with a nonelectrostatic field E' is feeding e... | {
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"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "electromagnetism",
"url": null
} |
6. ## Re: Solve f (x) = 0
Originally Posted by gilagila
Is it meaning that the x = 3, -2 and (5+√(-19))/2 or (5- √(-19))/2 <- using formula calculation ?
meaning if f(x) = 0, then x = { 3, 2, (5+√(-19))/2 and (5- &√(-19))/2}
am i right ?
Both x = (5+√(-19))/2 and x = (5- √(-19))/2 are solutions, although, as HallsofIv... | {
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"openwebmath_score": 0.8372477293014526,
"t... |
php, security, pdo
public function results() {
return $this->_results;
}
public function first(){
return $this->results()[0];
}
public function count(){
return $this->_count;
}
private function ExceptionLog($message, $type, $sql = "") {
if(!empty($sql)) {
... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "php, security, pdo",
"url": null
} |
Primality testing for 64 bit numbers
For very small numbers, say 32 bits unsigned, testing all divisors up to the square root is a very decent approach. Some optimizations can be made to avoid trying all divisors, but these yield marginal improvements. The complexity remains $O(\sqrt n)$.
On the other hand, much fast... | {
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"lm_q1q2_score": 0.8179225622530906,
"lm_q2_score": 0.8311430499496096,
"openwebmath_perplexity": 643.6228530696061,
"openwebmath_score": 0.70257169008255,
"tags"... |
c++, quick-sort
Title: Quick Sort on C++ vector I've seen other implementations around, but they seem pretty complicated. This seems to work for me, but is there anything I'm missing? Also, any tips on how I can improve the quality of the code is appreciated.
#include <iostream>
#include <vector>
template<typename It... | {
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"openwebmath_score": null,
"tags": "c++, quick-sort",
"url": null
} |
newtonian-gravity, dark-matter, galaxies, milky-way, galaxy-rotation-curve
Title: What is a reasonably accurate but simple model of the Milky Way's gravitational field? I am putting together a toy program which shows how stars move around in the galaxy.
To run the simulation I need to know strength of the Milky Way's ... | {
"domain": "physics.stackexchange",
"id": 19279,
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"openwebmath_score": null,
"tags": "newtonian-gravity, dark-matter, galaxies, milky-way, galaxy-rotation-curve",
"ur... |
python, python-3.x, web-scraping
Title: DeliciousSoda: A simple parser for robots.txt files This is my first big project that I've decided to release publically. It's available on my Github, and through pip3: pip3 install delicioussoda.
This is a simple parser for robots.txt files for a website. And yes, the name "Del... | {
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"id": 36770,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, python-3.x, web-scraping",
"url": null
} |
homework-and-exercises, thermodynamics, thermal-radiation, thermal-conduction
Title: Thermal radiation in hollow sphere I have been asked to calculate the time taken for a highly conducting hollow sphere to cool down from a certain temperature say $\theta_1$ to a temperature $\theta_2$ ($\theta_1, \theta_2 > \theta_s$... | {
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"tags": "homework-and-exercises, thermodynamics, thermal-radiation, thermal-conduction",
... |
gravity, astrophysics
Title: Does mass determine gravity or is it a predetermined quantity If Earth were to gain large enough mass, would it have enough gravitational force to hold the extra mass, or is there a predetermined magnitude of gravitational force for earth due to its location in space-time?
If not, would t... | {
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"id": 31344,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "gravity, astrophysics",
"url": null
} |
performance, vba, ms-access
WB.Sheets(3).Cells(i, 7) = "QLL OUT OF RANGE PA ADDED"
ElseIf WB.Sheets(3).Cells(i, 2) = WB.Sheets(3).Cells(i + 1, 2) And WB.Sheets(3).Cells(i, 6) = 4 And WB.Sheets(3).Cells(i, 7) = "New QL" _
And WB.Sheets(3).Cells(i, 2) = WB.Sheets(3).Cells(i + 2, 2) Then
WB.... | {
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"id": 43845,
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"lm_q1q2_score": null,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "performance, vba, ms-access",
"url": null
} |
ruby
def self.apply_patch(old_text, patch)
text = old_text.split("\n")
patch = StringIO.new(patch)
current_line = 1
while patch_line = patch.gets
# Grab the command
m = %r{\A(?:(\d+))?(?:,(\d+))?([acd]|s/\.//)\Z}.match(patch_line)
raise ArgumentError.new("Invalid ed command: #{patch_line.chomp}") ... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "ruby",
"url": null
} |
javascript, unit-testing, angular.js, jasmine
Method 1: Multiple Unit Tests
var mockFailureResponse;
beforeEach(function () {
mockFailureResponse = {
data: [],
};
});
it('saveFailure should set processing to false', function () {
$scope.processing = true;
$scope.saveFailure(mockFailureRespons... | {
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"id": 27006,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "javascript, unit-testing, angular.js, jasmine",
"url": null
} |
primes, sieve-of-eratosthenes, rust
Segmented Sieve
I struggled with this one the most. I wanted a .each_slice() method very badly, since that was the quickest route to the same algorithm in Ruby, and asked for it on SO.
/// A [segmented
/// approach](https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes#Segmented_sieve... | {
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"openwebmath_score": null,
"tags": "primes, sieve-of-eratosthenes, rust",
"url": null
} |
c, fibonacci-sequence
N = *prev + *prevprev; //fibonacci recurrence relation
tempseq[n] = N; //add current value of N to the temp array
}
return N;
}
EDIT: Not to step on the toes of JS1 who recently replied, but I wanted to add an image here of my cmd line execution of my f... | {
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"openwebmath_score": null,
"tags": "c, fibonacci-sequence",
"url": null
} |
beginner, parsing, haskell, homework, logging
-- Parse a whole logfile.
parse :: String -> [LogMessage]
parse s = map parseMessage (lines s)
-- Insert a L.LogMessage into a sorted L.MessageTree.
insert :: L.LogMessage -> L.MessageTree -> L.MessageTree
insert (L.Unknown _) t = t
insert m (L.Leaf) = L.Node Leaf m Leaf
... | {
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"tags": "beginner, parsing, haskell, homework, logging",
"url": null
} |
ros, filesystem, logging
Originally posted by Daniel Stonier with karma: 3170 on 2011-04-03
This answer was ACCEPTED on the original site
Post score: 7
Original comments
Comment by veltrop on 2011-04-03:
I think I will kill the logging architecture as you suggested. Back to printf() for me :( It would make sense fo... | {
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"tags": "ros, filesystem, logging",
"url": null
} |
astrophysics, neutron-star, stellar-astrophysics, x-ray, gamma-rays
How does the field decay of a magnetar power the emission of high-energy electromagnetic radiation?
A young magnetar (i.e., strongly magnetized neutron star) has two main energy components: rotational (aka. spin) and magnetic. Rotational energy has s... | {
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"tags": "astrophysics, neutron-star, stellar-astrophysics, x-ray, gamma-rays",
"url": nu... |
python, python-3.x, object-oriented, game, pygame
x += self.tile_size[0]
y += self.tile_size[1]
Is there anything that needs to be fixed? Map.tile_size seems awkward. You never use the tuple as whole, only the individual [0] and [1] components. Perhaps use two members (Map.tile_width and Map.tile_heigh... | {
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"openwebmath_perplexity": null,
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"tags": "python, python-3.x, object-oriented, game, pygame",
"url": null
} |
2, NCERT Solutions For Class 9 Maths Chapter 3, NCERT Solutions For Class 9 Maths Chapter 4, NCERT Solutions For Class 9 Maths Chapter 5, NCERT Solutions For Class 9 Maths Chapter 6, NCERT Solutions For Class 9 Maths Chapter 7, NCERT Solutions For Class 9 Maths Chapter 8, NCERT Solutions For Class 9 Maths Chapter 9, NC... | {
"domain": "minshawi.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9632305339244013,
"lm_q1q2_score": 0.8206269541286901,
"lm_q2_score": 0.8519528038477824,
"openwebmath_perplexity": 451.6143338806028,
"openwebmath_score": 0.46098050475120544,
"tag... |
and vectors the..., which also defines perpendicular lines straight angle, this one 's going from the left to addition! Chorion was breached at a right triangle that is an isosceles triangle a...... see full answer below it with the rays first any length Learning Built... Signal a character 's vulnerability see right a... | {
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"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9637799472560581,
"lm_q1q2_score": 0.8052222812968466,
"lm_q2_score": 0.8354835391516132,
"openwebmath_perplexity": 688.3798798713781,
"openwebmath_score": 0.5210673213005066,
"ta... |
tensor: the Cauchy stress tensor, usually written as $\boldsymbol{\sigma}$. What is the best way to make bold math symbols, in particular Greek letters and \nabla? fonts math-mode symbols bold. log in sign up. math by Noam D. If $$f$$ is a function of two variables, then $$\text{div}(\vecs \nabla f) = \vecs \nabla \cdo... | {
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"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9877587265099557,
"lm_q1q2_score": 0.8005576169522185,
"lm_q2_score": 0.8104789109591831,
"openwebmath_perplexity": 2008.5028412290067,
"openwebmath_score": 0.8692194223403931,
"tags": ... |
[Proof of Lemma] It is trivial for the "only if" part, since if a non-empty string s can be generated by a substring ss of s, then s can be writen as s=ss+r=r+ss, where r=s.substring(ss.length), which contains ss as a substring, while ss is non-empty since s is not.
For the "if" part, the "While" statement directly fo... | {
"domain": "leetcode.com",
"id": null,
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9877587257892505,
"lm_q1q2_score": 0.8075663206475977,
"lm_q2_score": 0.8175744739711883,
"openwebmath_perplexity": 1947.0089949612184,
"openwebmath_score": 0.8013752698898315,
"tags": ... |
performance, beginner, vba, excel
Title: VBA - If value in sheet1 found in sheet2, then delete data from sheet2 I have 2 sheets setup: Exclusions and Issues
Issues has a list of CASE ID's and Columns that list the "Issue"
Exclusions will be populated with CASE ID's that are to be excluded (and removed) from the Issues... | {
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"openwebmath_score": null,
"tags": "performance, beginner, vba, excel",
"url": null
} |
quantum-field-theory, mathematical-physics, regularization, analyticity, casimir-effect
Title: Analytical continuation as regularization in Quantum Field Theory, the remaining questions There is an old question posted (Regularization) which did not get an answer, about the validation of analytic continuation as regula... | {
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"id": 99849,
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"openwebmath_score": null,
"tags": "quantum-field-theory, mathematical-physics, regularization, analyticity, casimir-e... |
javascript, jquery, html, dom, jquery-ui
function dialog_OkCancel({
title,
message,
funk_Ok
}) {
var buttons = {
"Ok": function() {
funk_Ok();
$(this).dialog("close");
},
"Cancel": function() {
$(this).dialog("close");
}
}
dialog_Handler({
title,
message,
butto... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "javascript, jquery, html, dom, jquery-ui",
"url": null
} |
haskell, homework
Alright, so f is valid if and only if it evaluates to True for both arguments! That's what we want.
Now for contradiction:
contradiction f = (contradiction $ f True) && (contradiction $ f False)
This is the key: contradiction asks the question "Is this proposition false for all possible inputs"? To ... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "haskell, homework",
"url": null
} |
javascript, jquery, form
Not a huge change but you can see a pattern forming.
Add click event to inputs in a div with a class name selector. (.eyecolour inputs)
Set the class of the div to the value of the clicked input.
Set the class of the container item.
Set the cookie.
Numbers 2 and 3 are not done every time bu... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "javascript, jquery, form",
"url": null
} |
proximal-policy-optimization, probability-distribution, loss
I started printing the losses and it turns out that the policy loss becomes nan.
I do something like this for the policy loss:
dist, value = self.model(batchStates)
new_probs = dist.log_prob(batchActions)
ratio = torch.exp(new_probs - batchOldProbs)
clippe... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "proximal-policy-optimization, probability-distribution, loss",
"url": null
} |
+∞ ∑ k=1 b ksin(kπx). The mathematical expression of thermal condition at the boundary is known as boundary condition. (1) (I) u(0,t) = 0 (II) u(1,t) = 0 (III) u(x,0) = P(x) Strategy: Step 1. The fundamental physical principle we will employ to meet. W(r,t) < 1, with the boundary condition W = @W @r, on r =1. I simply ... | {
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"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9888419694095656,
"lm_q1q2_score": 0.836503389555895,
"lm_q2_score": 0.8459424411924673,
"openwebmath_perplexity": 466.0453277681271,
"openwebmath_score": 0.8282039165496826,
... |
homework-and-exercises, geometry, volume
So here's what I discovered:
Using integration, I was able to get the volume of a "sliced cylinder, which is the shape the water would take if the water has more than half the volume of the cylinder:
V=3.14r^2((h1+h2/2))
And for cases, for which the volume of the water is less... | {
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"openwebmath_score": null,
"tags": "homework-and-exercises, geometry, volume",
"url": null
} |
The same paper goes on in quite some detail about the process of creating Venn diagrams for higher values of n, especially for simple diagrams with rotational symmetry.
For a simple summary, the best answer I could find was on WikiAnswers:
Two circles intersect in at most two points, and each intersection creates one... | {
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"lm_q2_score": 0.8459424373085146,
"openwebmath_perplexity": 532.7736524284068,
"openwebmath_score": 0.6550043225288391,
"tags... |
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