text stringlengths 1 1.11k | source dict |
|---|---|
climate-change, arctic
Title: Why does the Arctic warm so fast despite being so white? It may be a silly question but why does the Arctic warm so fast despite being so white ("albedo" is the word, I believe)? Isn't all that whiteness supposed to deflect all those pesky sun rays back into space (or wherever)? I heard o... | {
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"openwebmath_score": null,
"tags": "climate-change, arctic",
"url": null
} |
fluid-dynamics, drag, aerodynamics, viscosity, turbulence
Why does turbulent flow "stick" to the surface longer?
Flow around a three-dimensional object will accelerate in the forward region and decelerate where the object's cross-section contracts again. Since the energy transfer across the stratified flow in the lami... | {
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"tags": "fluid-dynamics, drag, aerodynamics, viscosity, turbulence",
"url": null
} |
c#, linq, file-system, wpf, xaml
btn_Submit.IsEnabled = false;
}
private void btn_AddDir_PreviewKeyDown(object sender, KeyEventArgs e)
{
if (e.Key == Key.Return)
{
if (Directory.Exists(txt_AddDir.Text.Trim()))
{
Direct... | {
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"openwebmath_score": null,
"tags": "c#, linq, file-system, wpf, xaml",
"url": null
} |
$$\frac{m v^2}{2} = \frac{kh^2}{2}$$
In other words, it looks exactly like we could forget about gravity and initial elongation of the spring altogether: the answer is the same as it would have been for a horizontal spring. This is not a coincidence: what we have derived means that the total (gravitational+elastic) po... | {
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"lm_name": "Qwen/Qwen-72B",
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"lm_q1q2_score": 0.8511046750447819,
"lm_q2_score": 0.8902942283051332,
"openwebmath_perplexity": 513.1419705121123,
"openwebmath_score": 0.7946702241897583,
"tag... |
gazebo, teleop
This starts gazebo and spawns the erratic model. Then run
rosrun erratic_teleop erratic_keyboard_teleop
You can now move the robot using the keys WASD.
Originally posted by Sabrina with karma: 285 on 2011-11-10
This answer was ACCEPTED on the original site
Post score: 2
Original comments
Comment by ... | {
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"openwebmath_score": null,
"tags": "gazebo, teleop",
"url": null
} |
photons, acceleration
So the photon, in leaving the atom, can be thought to partly comprise an analogy of the antenna near, evanescent field. It is this evanescent field which would make our thought experiment seem to say that the photon is accelerating.
"But don't things moving at less than $c$ always have a nonzero ... | {
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"tags": "photons, acceleration",
"url": null
} |
spacetime
This not asking how space-time can be emergent. The question is asking whether the view that space-time is emergent is considered orthodox, or to what extent it is endorsed by physicists. It is the prevailing view among high-energy physicists that spacetime should be emergent from some more basic structure b... | {
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"tags": "spacetime",
"url": null
} |
Let $X_j$ be a sequence of independent random variables with uniform distribution in the interval $[-r,r]$ (i.e. you are picking an infinite sequence of random numbers from the interval). The probability that $(X_1, \ldots, X_d)$ lies in your hypersphere, i.e. that $R_d = X_1^2 + \ldots + X_d^2 \le r^2$, is $V(r,d)/(2r... | {
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"lm_q1q2_score": 0.8418125921136481,
"lm_q2_score": 0.8558511488056151,
"openwebmath_perplexity": 235.3146041047291,
"openwebmath_score": 0.8841640949249268,
"tag... |
moveit, joint-state-publisher
<node name="pi_hardware_interface" pkg="pi_hexapod_control" type="pi_hexapod_control_node" output="screen" required="true">
<rosparam command="load" file="$(arg hexapod_params)" />
<param name="using_tcp_ip_connection" type="bool" value="$(arg using_tcp_ip_connection)" />
... | {
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"id": 38452,
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"openwebmath_score": null,
"tags": "moveit, joint-state-publisher",
"url": null
} |
rotational-dynamics, reference-frames, rigid-body-dynamics, moment-of-inertia
Since we are adding the symmetric matrix ${\rm I}_C$ to a symmetric matrix for parallel axis contribution, the result is also a symmetric matrix and hence diagonalizable.
But you can go a step further and look at the combined translational/... | {
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"tags": "rotational-dynamics, reference-frames, rigid-body-dynamics, moment-of-inertia",
... |
differential-geometry, metric-tensor, tensor-calculus, differentiation, variational-calculus
Title: On varying a tensor with respect to the metric Upon learning about the Lagrangian formulation of GR, where varying an action with respect to a metric (in order to, for instance, arrive at the Einstein field equations) i... | {
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"tags": "differential-geometry, metric-tensor, tensor-calculus, differentiation, variationa... |
Sorry I don't know how to do tex on websites, but I'm trying to learn.
You just made a small mistake on the final step. In the second to last step, we actually have our full equation as:
$\frac{-b}{2a}\pm \sqrt{\frac{b^{2}-4ac}{4a^{2}}}=\frac{-b}{2a}\pm \frac{\sqrt{b^{2}-4ac}}{2a}$
Now we can collect the common fact... | {
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"lm_name": "Qwen/Qwen-72B",
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"openwebmath_score": 0.96335768699646,
"tags... |
lambda-calculus, functional-programming, combinatory-logic
$$
\bot \sqsubseteq F(\bot), F(G(\bot)) \sqsubseteq F(G(F(\bot))), \ldots
$$
estabilishing that $(1)\sqsubseteq(2)$. Further,
$$
F(\bot) \sqsubseteq F(G(\bot)), F(G(F(\bot))) \sqsubseteq F(G(F(G(\bot)))), \ldots
$$
estabilishing that $(2)\sqsubseteq(1)$, con... | {
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"tags": "lambda-calculus, functional-programming, combinatory-logic",
"url": null
} |
homework-and-exercises, newtonian-mechanics, work
$$W = - (mg \sin(\theta)) \cdot d = K_f - K_i = \frac{1}{2} mv_f^2 - \frac{1}{2} mv_0^2.$$
Hence
$$-2g d \sin(\theta) = v_f^2 - v_0^2,$$
and therefore
$$v_f = \sqrt{v_0^2 - 2gd \sin(\theta)}.$$
This is the same as before, as it should be. | {
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"tags": "homework-and-exercises, newtonian-mechanics, work",
"url": null
} |
c#, entity-framework, database, search, repository
query = FilterGuids(query, searchParameters);
return query;
}
internal static IQueryable<Company> FilterCompanyQuery(IQueryable<Company> query, ClientSearchParameters searchParameters)
{
if (searchParameters == null) return query;
... | {
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"tags": "c#, entity-framework, database, search, repository",
"url": null
} |
pcl, catkin, ros-groovy
CMakeFiles/example2.dir/src/example2.cpp.o:(.rodata._ZTVN3pcl11KdTreeFLANNINS_15FPFHSignature33EN5flann9L2_SimpleIfEEEE[vtable for pcl::KdTreeFLANN<pcl::FPFHSignature33, flann::L2_Simple<float> >]+0x10): undefined reference to `pcl::KdTreeFLANN<pcl::FPFHSignature33, flann::L2_Simple<float> >::s... | {
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"id": 16245,
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"openwebmath_score": null,
"tags": "pcl, catkin, ros-groovy",
"url": null
} |
-
Here's a sketch of a combinatorial proof. For fixed $k$ we want to count how to partition a set of some size into $k$ nonempty partitions. Order the set and mark each point in the order at which a new partition occurs; this is the factor $t^k$ in the generating function. Between the appearance of partition $i$ and pa... | {
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"lm_q2_score": 0.8267118026095991,
"openwebmath_perplexity": 282.72839640172896,
"openwebmath_score": 0.9418739080429077,
"tag... |
plate-tectonics, earth-history, planetary-formation
Why would only that portion of the Earth be above water? Is there something significant about where Pangaea was located which made it different from the rest of the Earth? The formation and break up of supercontinents have happened throughout Earth's history in almos... | {
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"tags": "plate-tectonics, earth-history, planetary-formation",
"url": null
} |
Vice versa rule for Perfect Square
Author Message
TAGS:
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Joined: 11 Feb 2015
Posts: 5
Vice versa rule for Perfect Square [#permalink]
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04 Jun 2015, 02:21
1
KUDOS
Perfect square has the following properties:
1) The number of distinct factors of a perfect square is ALWAYS ODD.
2) The sum of ... | {
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"openwebmath_score": 0.6620155572891235,
"tags": nu... |
quantum-computer
The error correction method has been made more efficient since, by Shor and collaborators, and the upshot is that if you make a small quantum computer which is coherent for long enough time, and you can encode some dozens of qubits robustly so that you can reverse the errors faster than they occur, yo... | {
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"tags": "quantum-computer",
"url": null
} |
ros, ros2, tf2, joint-state-publisher, robot-state-publisher
But more to the point of my original question, the authority is meant to be the source of the transformation information. Presumably this is meant to be the name of the node that is publishing the transformation (e.g. your joint_state_broadcaster).
The "Auth... | {
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"tags": "ros, ros2, tf2, joint-state-publisher, robot-state-publisher",
"url": null
} |
human-biology, pathology, medicine, treatment, clinical-trial
Title: What is overdiagnosis? What is overdiagnosis ?
I have searched this Wiki result but didn't understood at all.
Can you please explain the first two line of Wikipedia :
Overdiagnosis is the diagnosis of "disease" that will never cause symptoms or deat... | {
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"tags": "human-biology, pathology, medicine, treatment, clinical-trial",
"url": null
} |
fft, frequency-spectrum, self-study
apply(X, 2, fft) does the fft of the columns.
Note that the use of .row or .col is my convention. I could have used x, y , or z because that's just a dummy variable from apply's point of view.
Also, you can type ? apply in R in order to obtain the help for apply. Sometimes they can... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "fft, frequency-spectrum, self-study",
"url": null
} |
thermodynamics, kinetic-theory
Why do some substances undergo sublimation while others do not?
The answer lies in thermodynamics, specifically the triple point of the substance. If this occurs at a large pressure compared to STP, then it is possible for a material to sublimate. For instance, if you look at the phas... | {
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"tags": "thermodynamics, kinetic-theory",
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} |
energy, magnetic-fields, work
that gets to what I am trying to understand. What is happening that recovers energy? | {
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} |
• looks nice, but isn't it somewhat overkill to invoke the Minkowski theorem here? May 19 '11 at 17:05
• This is really misleading since it makes the question look like complicated, while is almost obvious that $\det(A+B) = \det(A) \det(1+A^{-1/2}BA^{-1/2}) \geq \det(A) (1+\det(A^{-1/2}BA^{-1/2})) = \det(A) + \det(B)$.... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9859363746096915,
"lm_q1q2_score": 0.8216050385373651,
"lm_q2_score": 0.8333246035907933,
"openwebmath_perplexity": 218.6506590117626,
"openwebmath_score": 0.9629952907562256,
"tags... |
python, optimization, performance, csv
for row in self.rows:
if set(row).isdisjoint(set(titles)):
row.insert(0, '')
def write_csv(self, rows, name_to_write):
"""Writes a csv based on a list of lists as data for the rows, and a
name of the file to write (string).
... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, optimization, performance, csv",
"url": null
} |
error-correction, stabilizer-code, pauli-group
$^1$ There is a subtlety here: the normalizer $N(S)$ of $S$ is defined with respect to the group containing $S$. In particular, the normalizer $N_{\mathcal G_n}(S)$ of $S$ in $\mathcal G_n$ is generally different from its normalizer $N_{U(2^n)}(S)$ in $U(2^n)$. In our cas... | {
"domain": "quantumcomputing.stackexchange",
"id": 5095,
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"openwebmath_score": null,
"tags": "error-correction, stabilizer-code, pauli-group",
"url": null
} |
The operation $Ae_1$ is the first column of $A$. $Ae_2$ is the second column. Thus $A(e_1 + e_2)$ is the vector that results from the addition of the first and second columns. The vector of all 1's is given by $e_1 + e_2 + \cdots + e_n$. Applying $A$ to this vector yields $$Ae_1 + Ae_2 + \cdots + Ae_n$$ which is the ve... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.986979510652134,
"lm_q1q2_score": 0.804617763408358,
"lm_q2_score": 0.815232489352,
"openwebmath_perplexity": 158.04777564990792,
"openwebmath_score": 0.901796281337738,
"tags": nu... |
bandwidth
Title: Is the constant signal $x(t)=1$ bandwidth limited? A quick question I was asked by a friend for homework.
We have an LTI system and we needed an example for reconstruction and such...
Anyway, he asked me if the constant signal is bandwidth limited.
Since the Fourier Transform of a constant is $\delta(... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "bandwidth",
"url": null
} |
protein-structure
In a mol file and its sdf/mol2 derivatives, a tabular representation is used to store coordinates (properties) of the atoms of the small molecule (top part below), while the connectivity has an edge-node relationship, i.e. are edges. Note that the index of the properties in the first block is the id ... | {
"domain": "bioinformatics.stackexchange",
"id": 1905,
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"openwebmath_score": null,
"tags": "protein-structure",
"url": null
} |
general-relativity, black-holes, gravitational-waves, event-horizon, information
Firstly, in general relativity when you say an object has mass $M$, you do not mean that if you summed up the mass $m_i$ of each part, they add up to $M.$ In fact $$M\neq m_1+m_2+\dots +m_N.$$
Secondly, energy and mass aren't conserved, ... | {
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"openwebmath_score": null,
"tags": "general-relativity, black-holes, gravitational-waves, event-horizon, information",... |
standard-model, neutrinos, weak-interaction, chirality, helicity
Title: Are massless antineutrinos in the Standard Model right-handed or right-chiral? For massless fermions, their chirality (determining under which representation of the Lorentz group they transform) and their helicity (projection of spin onto three-mo... | {
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"openwebmath_score": null,
"tags": "standard-model, neutrinos, weak-interaction, chirality, helicity",
"url": null
} |
ros, ros-kinetic, laserscan
Title: [python] output of a code be called in another python code automatically
Hi everyone,
I have a robot equipped with different sensors. one of them is 3d lidar. i have used the pointcloud and converted them into lasersacn. now i have written a simple python code which do object detcti... | {
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"tags": "ros, ros-kinetic, laserscan",
"url": null
} |
@robjohn: Thank you very much for your crystal clear explanation. The proof is valuable, and I really appreciate it. – C. Y. Cheng Apr 9 '14 at 4:10 | {
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"tag... |
c#, search
Title: Search arrays for values I implemented a search function like this:
private static void GetResults(ref ObservableCollection<string> resultTitles, ref string[] query, ref ObservableCollection<int> weight)
{
int position = -1;
foreach (string[] r in SearchKeys.Keys)
{
position++;
... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c#, search",
"url": null
} |
For a generic $$n\ge3$$, I don't know if there is an algorithmic method to find a basis for $$\Lambda=S\cap \Bbb Z^n$$ and if such a basis can be always complete to a basis for $$\Bbb Z^n$$, like in the $$n=2$$ case. | {
"domain": "mathoverflow.net",
"id": null,
"lm_label": "1. YES\n2. YES",
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"openwebmath_score": 0.8254910111427307,
"tags": ... |
possible to carry out far from trivial calculations at compile time. The trapezoidal rule is equivalent to averaging the left-endpoint and right-endpoint approximations, Tn D Ln CRn =2: (2) Creating a MATLAB script We first write a M ATLAB script that calculates the left-endpoint, right-endpoint, and trapezoidal approxi... | {
"domain": "lucacaponedesign.it",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9932024684496266,
"lm_q1q2_score": 0.871512101787295,
"lm_q2_score": 0.8774767778695836,
"openwebmath_perplexity": 638.8632955111407,
"openwebmath_score": 0.8422544598579407,
... |
# Expected number of coin flips until all cars move to end of array?
Imagine that we have an array of length $$2n$$, where the first $$n$$ entries are a $$C$$ (representing a toy car) and the remaining $$n$$ entries are empty. Additionally, we have $$n$$ fair coins labeled $$1$$ through $$n$$, where coin $$i$$ corresp... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9805806489800367,
"lm_q1q2_score": 0.8039715394245025,
"lm_q2_score": 0.8198933359135361,
"openwebmath_perplexity": 206.18149032675737,
"openwebmath_score": 0.6821374297142029,
"ta... |
beginner, object-oriented, game, vba, excel
Private Type BoardDimensionsData
Width As Long
Height As Long
End Type
Private this As BoardDimensionsData
Public Property Let Width(ByVal Width As Long)
this.Width = Width
End Property
Public Property Get Width() As Long
Width = this.Width
End Property
P... | {
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"openwebmath_score": null,
"tags": "beginner, object-oriented, game, vba, excel",
"url": null
} |
javascript
var savedSchedules = {};
var data = [];
var layout = {
showlegend: false,
xaxis: {range: ['2020-01-01 00:00:00', '2020-01-01 23:59:59'],
showgrid: false,
zeroline: false,
showline: true,
tickformat: '%H:%M:%S'
},
yaxis: {rangemode: 'tozero',
... | {
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"id": 37837,
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"openwebmath_score": null,
"tags": "javascript",
"url": null
} |
python, game, animation, pygame
running = True
x = -200
while running:
event = pygame.event.poll()
if event.type == pygame.QUIT:
running = False
x += speed
screen.fill((255, 255, 255)) # fill the screen
screen.blit(person, (int(x), 340))
screen.blit(... | {
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"tags": "python, game, animation, pygame",
"url": null
} |
java, performance
I can solve size=9 in 18 seconds, but I tried a very different approach (starting from the top and trying to compute the rows below). For size=10, it took 50 minutes and I can see no chance that size=11 finishes this year.
I don't claim that starting from the top is better, maybe starting from the ba... | {
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"tags": "java, performance",
"url": null
} |
python, beginner, game, pygame, snake-game
def set_by_bounds(item_x, item_y, width, height):
if item_x >= display_height or item_y <= 0:
item_x = [random.randrange(0, display_width - block_size),
random.randrange(0, display_width - block_size),
random.randrange(0, displa... | {
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"tags": "python, beginner, game, pygame, snake-game",
"url": null
} |
quantum-field-theory, feynman-diagrams, greens-functions, partition-function, 1pi-effective-action
The RHS of the equation 11.43 is just the functional integral rewriting of $\langle \Omega| e^{-i T H}|\Omega\rangle$. | {
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"tags": "quantum-field-theory, feynman-diagrams, greens-functions, partition-function, 1pi-... |
homework-and-exercises, newtonian-mechanics, newtonian-gravity, energy-conservation, escape-velocity
Title: Escape velocity at an angle Comparing the work required for a mass to escape the Earth's gravity to the necessary initial kinetic energy gives us the escape velocity from the surface of the Earth of around $11\;... | {
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"id": 31621,
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"tags": "homework-and-exercises, newtonian-mechanics, newtonian-gravity, energy-conservatio... |
• Sometimes (and certainly no always) it helps to look at special cases to see if some general form becomes apparent. If $\sigma_1=\sigma_2=\sigma$, then the expectation is $\frac{\sigma (\text{$\mu $1}+\text{$\mu $2}) \text{erfc}\left(\frac{\text{$\mu $1}-\text{$\mu $2}}{2 \sigma }\right)}{\sqrt{2}-2 \sigma \text{erf}... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9597620596782468,
"lm_q1q2_score": 0.8157700935112093,
"lm_q2_score": 0.8499711832583695,
"openwebmath_perplexity": 6878.171138481237,
"openwebmath_score": 0.7091668248176575,
"tag... |
java, javascript, design-patterns, http, ajax
Is that all there is to it?
Putting it all together: Ctrl-F Oriented Programming
The below code snippets illustrate the pattern used throughout the application. They handle the pass function, in which a user gives up on getting their team to guess the current name, puts t... | {
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"tags": "java, javascript, design-patterns, http, ajax",
"url": null
} |
dark-matter
Just how "smoothly" dark matter is distributed on very small scales depends on what it is. It could be in lumps of mass of $10^{20}$ kg in the form of primordial black holes or it could be in the form of mass ive particles of 100-1000 times the mass of a proton, or maybe it doesn't exist at all and there i... | {
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"tags": "dark-matter",
"url": null
} |
ros, moveit, universal-robots, move-group-interface, ur10
Originally posted by srujan on ROS Answers with karma: 32 on 2020-12-07
Post score: 1
move_group.plan() and the MoveJ command are not the same. MoveJ moves directly to the target in joint space (PTP motion), while move_group.plan() submits a planning request t... | {
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"tags": "ros, moveit, universal-robots, move-group-interface, ur10",
"url": null
} |
\binom{n-1}{k}}{(2k+1)}+\dfrac{1}{2n+1}\sum\limits_{k=0}^{n-1} \dfrac{n(-1)^k \binom{n-1}{k}}{n-k}\\ &=\dfrac{2n}{2n+1}\sum\limits_{k=0}^{n-1}\dfrac{(-1)^k \binom{n-1}{k}}{(2k+1)}+\dfrac{1}{2n+1}\sum\limits_{k=0}^{n-1} \left[(-1)^k \binom{n}{k}\right]+\dfrac{(-1)^n}{2n+1}\\ &=\dfrac{2n}{2n+1}\sum\limits_{k=0}^{n-1}\dfr... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9845754499548452,
"lm_q1q2_score": 0.8536621098031294,
"lm_q2_score": 0.8670357460591569,
"openwebmath_perplexity": 1628.5546507729061,
"openwebmath_score": 0.9516960382461548,
"ta... |
java, graph
@Override
public String toString() {
if (vertexesWithAdjacents.isEmpty()) {
return "[]";
}
StringBuilder builder = new StringBuilder();
for (T key : vertexesWithAdjacents.keySet()) {
builder.append(key + ": " + vertexesWithAdjacents.get(key) + EOL... | {
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"openwebmath_score": null,
"tags": "java, graph",
"url": null
} |
quantum-computing
The article by Shiekh [cs/0507003] describes "adding quantum interference to quantum computers". This ignores the fact that: | {
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"tags": "quantum-computing",
"url": null
} |
astronomy, stars, stellar-evolution
Title: Is it possible to tell the difference between a young star that is just "big" and an older red giant? I read the Wikipedia page for one of the biggest known stars, UY Scuti, and was curious to see the age of the star isn't really known at all.
When a star's hydrogen fuel is e... | {
"domain": "physics.stackexchange",
"id": 93312,
"lm_label": null,
"lm_name": null,
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"openwebmath_score": null,
"tags": "astronomy, stars, stellar-evolution",
"url": null
} |
python, algorithm, python-3.x, sorting, mergesort
Interestingly, removing lo = hi leads a much more efficient code on my benchmark: the function returns much more quickly (because we always have lo == 0, we get out of the loop as soon as mi == upper) and the list is still fully sorted.
def natural_merge(a):
upper ... | {
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"tags": "python, algorithm, python-3.x, sorting, mergesort",
"url": null
} |
java, algorithm, programming-challenge, recursion
public static boolean[][] copyArray(boolean[][] original) {
boolean[][] copy = new boolean[original.length][];
for (int i = 0; i < original.length; i++) {
copy[i] = original[i].clone();
}
return copy;
}
public static void arrangeQueens(char[]... | {
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linear differential equations as well nonhomogeneous equations = 0 a... Column vector: 4x+7y-9 = 0, 5x-8y+15 = 0, 5x-8y+15 = 0 2.3 equations. Of equations having 2 variables is given by: Section 2.3 matrix equations ¶ permalink.... B to have the same technique as we applied to solve system of linear equations matrix co... | {
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"id": null,
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9539661015270469,
"lm_q1q2_score": 0.8070004127406513,
"lm_q2_score": 0.8459424411924674,
"openwebmath_perplexity": 446.3467371902766,
"openwebmath_score": 0.815635025501251... |
quantum-mechanics, quantum-field-theory, operators, differentiation
$$
as usual. Just like for an ordinary function, the derivative may or may not be well-defined (the limit may or may not exist or be unique), but let's only consider cases where it is well-defined.
Sometimes we write $X$ as an abbreviation for $X(t)$,... | {
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"tags": "quantum-mechanics, quantum-field-theory, operators, differentiation",
"url": nul... |
ruby, yaml
def welcome
puts "Welcome to the Translation Center! Please enter the language you would like to translate to English or you can choose from the list below:
1. Spanish
2. Russian
3. Arabic"
input = language = gets.chomp!
case language
when /spanish/i
spanish_translate
... | {
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"openwebmath_score": null,
"tags": "ruby, yaml",
"url": null
} |
javascript, beginner, programming-challenge
Title: arithmetic with numbers and letters I've started learning JavaScript last week. Today I ran into a JS exercise available at this link
codewars exercise and decided to give it a try. I've used very basic JS because I know only a small number of JS methods. Could you pl... | {
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"openwebmath_score": null,
"tags": "javascript, beginner, programming-challenge",
"url": null
} |
beginner, c, c++17
get_exit_input();
return 0;
}
load_extender_dll.cpp:
#include <string>
#include <mutex>
#include <Windows.h>
#include <easyhook.h>
#include "robin_hood.h"
// thank you for making this hash map, martinus.
// here's his github: https://github.com/martinus/robin-hood-hashing
namespace rh = robin_... | {
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"url": null
} |
and that's kind of where my ability to reason ends.
I think the rest of it will be something like:
$$w_{k+1} = w_kx$$
ie. $$w_k$$ concatenated with $$x$$ where $$x \in S^*$$
but how can I show that $$w_{k+1} \in (S^*)^*$$?
Any help to push me in the right direction would be greatly appreciated. | {
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"openwebmath_score": 0.9266244173049927,
"tag... |
# Proving inequalities with Mathematica
Question summary: I would like to learn some tips and tricks on how to prove inequalities with Mathematica.
I'm studying various inequalities in triangle that have the form $R+ar + bs\geq 0$, where $R$ is a circumcircle radius, $r$ is an incircle radius and $s$ is a semiperimet... | {
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"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9674102571131692,
"lm_q1q2_score": 0.8316475316507889,
"lm_q2_score": 0.8596637523076225,
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"openwebmath_score": 0.459581196308136,
"tags... |
$$\kappa (a_1,\ldots a_n) = (\kappa a_1,\ldots,\kappa a_n)$$
where $$\kappa\in K$$. This multiplication is also defined if $$\kappa$$ is from a subfield $$L$$. The addition of vectors doesn't change.
It is an operation known as ‘restriction of scalars’. Any $$\mathbf C$$-vector space $$V$$ is also an $$\mathbf R$$-ve... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9752018383629826,
"lm_q1q2_score": 0.8189101050984487,
"lm_q2_score": 0.839733963661418,
"openwebmath_perplexity": 101.33991687393522,
"openwebmath_score": 0.8814148902893066,
"tag... |
algorithms, sorting
Title: Lower bound on comparison-based sorting of $k$-sorted arrays In $k$-sorting array algorithms, every element is supposed to be $k$ positions from its correct positions. So with that in mind, if we used a randomized QuickSort, we will have $O(n\log{n})$. Now to prove a lower bound on this, we ... | {
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"tags": "algorithms, sorting",
"url": null
} |
entropy
as there will always be difference between the temperature however small the range might be . What is the intuition behind it? Change of entropy is measured at constant temperature,so how can it be measured in a range ? I know it is done by definite integration but can't getting the proper intuition . Also ,if... | {
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"tags": "entropy",
"url": null
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# Generate and graph the Recamán Sequence
I was surprised to see that we don't have any posts that mention the Recamán Sequence, so I figured I should post it as a challenge. By definition, $$a_0=0$$ and $$a_n=a_{n-1}-n$$ if the r.h.s. is positive and different from all previous elements, and $$a_n=a_{n-1}+n$$ otherwi... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9591542794197472,
"lm_q1q2_score": 0.8383749206517636,
"lm_q2_score": 0.8740772351648677,
"openwebmath_perplexity": 5213.820737821472,
"openwebmath_score": 0.18212491273880005,
"ta... |
audio, embedded-systems
//The data collected is in 24-bit signed format on a 32 bit frame, to do DSP we want the data to be in float format from [-1.0, +1.0]
for(int i = 0; i < BUFFER_SIZE/2; i++){
leftChannelFloat[i] = INT24_TO_FLOAT * leftChannel[i];
}
//Audio passthrough
for(int i = 0; i < ... | {
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"id": 12114,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "audio, embedded-systems",
"url": null
} |
machine-learning, ai, interpretation
ML is not magical, it needs to be fed with the right information in order to produce a meaningful and reliable answer.
The closest application to this idea is Question Answering (QA). QA is an NLP task where the system answers a question, but the system must have been trained on a ... | {
"domain": "datascience.stackexchange",
"id": 10060,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "machine-learning, ai, interpretation",
"url": null
} |
formal-languages, turing-machines, automata
f(k)[l] refers to output of Turing Machine f(k) with l as input.
Now, define Turing machine TD to give f(i)[i]+1 for each natural number i. Since f is computable and all of f's range's programs are total. TD exists. But TD is not in f's range. Because for every natural numbe... | {
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"tags": "formal-languages, turing-machines, automata",
"url": null
} |
gazebo
I use these parameters (my damping is that hight because I use strong PID controllers on my joints. You'd better take a value between 0 and 1):
friction = 0.01
damping = 6
cfm_damping = 1
implicit_spring = 1
I hope this helps.
Originally posted by debz with karma: 198 on 2016-01-13
This answer was ACCEPTED on... | {
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} |
python, python-3.x, strings
>>> data = {'foo.bar': 'baz'}
>>> assert data['foo.bar'] == 'baz'
>>> assert Path.from_str('["foo\\.bar"]').get(data) == 'baz'
You can set and delete by using those methods instead.
And you can mix all the above together to walk complex paths.
>>> d... | {
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} |
c#, object-oriented, game, console
Object-Oriented Design
I still can't figure out the purpose or need of having Hand class as suggested by some.
Your current implementation requires you to do tricks and store way too much information on your existing classes.
Card's property FaceName could be an extension method o... | {
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"tags": "c#, object-oriented, game, console",
"url": null
} |
cc.complexity-theory, approximation-hardness
Title: Are runtime bounds in P decidable? (answer: no) The question asked is whether the following question is decidable:
Problem Given an integer $k$ and Turing machine $M$ promised to be in P, is the runtime of $M$ ${O}(n^k)$ with respect to input length $n$ ? | {
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homework-and-exercises, newtonian-mechanics, vectors, relative-motion
Sorry for the horrendous image but I hope the idea is clear. $v_P$ could be any direction and the blue circle represents all possible directions of $v_p$
Anyway, my problem lies in that I do not understand why this is the necessary condition for the... | {
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"tags": "homework-and-exercises, newtonian-mechanics, vectors, relative-motion",
"url": n... |
ros
Title: Need correct syntax to call an actionlib service from a class member function
What is the correct syntax to call an actionlib service from a class member function. As it is defined below I believe the var ac goes out of scope. But I am my attempts to move it outside being weak in c++ have failed.
void ha... | {
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} |
quantum-mechanics, computational-physics
Here is a video of propagation. Crank-Nicholson method is effectively the average of forward (explicit) Euler
$\psi(x,t+dt)=\psi(x,t) - i*H \psi(x,t)*dt$
and backward (implicit) Euler method
$\psi(x,t+dt)=\psi(x,t) - i*H \psi(x,t+dt)*dt$
The backward component makes Crank-Nicho... | {
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"tags": "quantum-mechanics, computational-physics",
"url": null
} |
mechanical-engineering, fluid-mechanics, pressure
So, in general, the average pressure gives the most accurate results if used in calculations because there are many applications/cases in which the locations with $P=P_{average}$ are the best places for experimental data collection. | {
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"tags": "mechanical-engineering, fluid-mechanics, pressure",
"url": null
} |
c#, mysql, authorization
namespace Sahara.Base.Game.Permissions
{
internal class PermissionManager
{
private readonly Dictionary<int, Permission> _permissions;
private readonly Dictionary<string, PermissionCommand> _permissionCommands;
private readonly Dictionary<int, PermissionGroup> _... | {
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"openwebmath_score": null,
"tags": "c#, mysql, authorization",
"url": null
} |
organic-chemistry, cyclohexane
Now, if you put tert-butyl group in $\ce{C3}$-equotorial position on equatorial-methylcyclohexane (left hand structure, vide supra), you get cis-1,3-substituted compound (C). On the other hand, if you put tert-butyl group in $\ce{C3}$-equatorial position of axial-methylcyclohexane (right... | {
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"tags": "organic-chemistry, cyclohexane",
"url": null
} |
The complete code reads as follows :
``````#include <feel/feel.hpp>
using namespace Feel;
int
main( int argc, char** argv )
{
// Initialize Feel++ Environment
Environment env( _argc=argc, _argv=argv,
_author="Feel++ Consortium",
_email="feelpp-devel@feelpp.org" ) );
/// [mesh]
// create the mesh (specify the dimens... | {
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"id": null,
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"lm_name": "Qwen/Qwen-72B",
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"openwebmath_score": 0.26109886169433594,
"tags": nu... |
java
public int prepareCargoPacket(int count7Kg, int count2Kg, int totalKg) {
int solution = -1; // if there is no answer, or no need for 2Kgs soaps, the answer is -1
// if we have 7Kg ones many more than totalKg, we should decrease it to get from 2Kgs.
if (7*count7Kg > totalKg) {
return prepareCargoPacket... | {
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} |
javascript, optimization, performance, html
A ton of commented out code and console.log statements, please clean this up
Inconsistent indenting, you indent with 1, 4 or 0 spaces, pick one ( I suggest 2 )
The underline button, it does not work
The italics button, it does not work either
if (rtf[rtfIndex].contentDocumen... | {
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"tags": "javascript, optimization, performance, html",
"url": null
} |
c#, beginner, mvc, controller
This can be cleaned an extracted pretty quick.
public bool MustSignWaiver(tb_Student student)
{
return student.SIGNEDWAIVER != true;
}
We do this so that we can simply call MustSignWaiver(tbs) instead of declaring our x and whatnot. We end up with:
if (MustSignWaiver(tbs))
{
Sess... | {
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} |
general-relativity, lagrangian-formalism, differential-geometry, metric-tensor, variational-principle
$$
S = \int_\mathcal{M} \text{d}^n x \sqrt{|g|} \mathscr{L}(\phi^\mu(x),\nabla_\alpha \phi^\mu(x))
$$
where $\mathcal{M}$ is a region of spacetime with a fixed background metric $g$, and vary $\phi^\mu$. To do this, ... | {
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"tags": "general-relativity, lagrangian-formalism, differential-geometry, metric-tensor, va... |
Here is Tao's comment from, now deleted, post 2:
"Note that if A is strictly upper triangular, then its eigenvalues are all zero, whereas $A+A^T$ is an arbitrary symmetric matrix with zero diagonal, which constrains the trace of the matrix but otherwise imposes almost no conditions on the spectrum whatsoever (the only... | {
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"ta... |
ros
output= "Data index "+str(self.index)
min_x, max_x=self.axes.get_xlim()
min_y, max_y=self.axes.get_ylim()
self.axes.text(max_x*0.6,max_y*0.7,output,horizontalalignment='left',verticalalignment='center')
self.canvas.draw()
if __name__ == "__main__":
app = QApplication(sys.argv)
window =... | {
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} |
• The second approach goes via natural deduction to make explicit the proof steps that were described in the case of contraposition: $$\dfrac{ \dfrac{ \dfrac{\neg B, A \vdash \bot }{\neg B \vdash A \to \bot} }{\neg B \vdash \neg A} }{\vdash \neg B \to \neg A}$$ So we simply use the implication introduction rule twice, ... | {
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"lm_q1_score": 0.9585377284730286,
"lm_q1q2_score": 0.8166289035649364,
"lm_q2_score": 0.8519528019683106,
"openwebmath_perplexity": 173.8768554607002,
"openwebmath_score": 0.8441201448440552,
"tag... |
c#, datetime
StringBuilder builder = new StringBuilder();
builder.Append(utc.ToString("ddHHmm", ci)); // day, hours, minutes
builder.Append("Z"); // time zone
builder.Append(utc.ToString("MMMyy", ci).ToLower()); // month, year
return bui... | {
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"openwebmath_score": null,
"tags": "c#, datetime",
"url": null
} |
homework-and-exercises, experimental-physics, microscopy
I get two equations:
$$x^2+y^2=R^2 \\ (x-d)^2+(y+\Delta h)^2=R^2$$
However solving them lead me to nowhere:
$$\begin{align} x^2-2xd+d^2+y^2+2\Delta h y+\Delta h^2 &= R^2 \\
-2xd+d^2-2\Delta h y+\Delta h^2 &= 0 \\
x &= \frac{d}{2} - \frac{\Delta h y}{d} + \frac{\... | {
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"tags": "homework-and-exercises, experimental-physics, microscopy",
"url": null
} |
python, file-system
class FileName(NamedTuple):
Parent_Record: int
Allocated_Size: int
Real_Size: int
Name: str
class File_Record(NamedTuple):
Header: Record_Header
Attributes: tuple
def parse_file_permissions(data: bytes) -> File_Permissions:
flag = parse_little_endian(data)
return F... | {
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"tags": "python, file-system",
"url": null
} |
354
453
357
753
Now we know that 4 must divide abc, but that means for sure that abc must be even, in particular c must be even, the only one of these numbers which has c even is 453, so now we have locked in cde.
We now proceed to figure out ab4, which must be divisible by 4. Any number divisible by 4 must have the ... | {
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"lm_q1_score": 0.9895109068841395,
"lm_q1q2_score": 0.8135651164842826,
"lm_q2_score": 0.822189134878876,
"openwebmath_perplexity": 503.21277429336044,
"openwebmath_score": 0.7465418577194214,
... |
Henceforth, we shall assume that the given positive numbers are distinct, i.e., $$|\{a_1, a_2, \dots, a_n\}| = n$$
Let $${\rm A} := \mbox{diag} (a_1, a_2, \dots, a_n)$$. Note that $$\mathrm A \succ \mathrm O_n$$. Consider the following matrix equation
$${\rm A X + X A} = 1_n 1_n^\top$$
Multiplying both sides by $$-1... | {
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"lm_q1_score": 0.9626731126558705,
"lm_q1q2_score": 0.8001190729969782,
"lm_q2_score": 0.8311430562234877,
"openwebmath_perplexity": 843.7603929314433,
"openwebmath_score": 0.9891015291213989,
"tag... |
c++, c, graphics, raytracing
aabb.h
#pragma once
typedef struct aabb
{
float3 min;
float3 max;
} aabb;
internal bool aabb_hit(aabb const *this, ray const *r, float tmin, float tmax)
{
#define swap(a, b) ({__typeof__(a) temp = a; a = b; b = temp;})
for(i32 a = 0; a < 3; ++a)
{
float inv... | {
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"url": null
} |
I have no idea about the transitivity part yet.
• If $w(s)$ denotes the number of entries in $s$ set to 0, then $uRv \Leftrightarrow w(u)=w(v)$. We know $=$ is an equivalence relation, so $R$ is an equivalence relation. – wj32 Oct 31 '12 at 5:50
The first two parts are fine as they are (except perhaps the formulation... | {
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"lm_q2_score": 0.8376199572530449,
"openwebmath_perplexity": 56.343890435586786,
"openwebmath_score": 0.9526137113571167,
... |
electromagnetism, biophysics
Title: How strong is the magnetic fields generated in the human body? How strong is the magnetic field produced by the human body? I have researched the question but all I find is how strong does a magnetic field have to be to kill a human. Neuromagnetic signals are of the order of 50 to ... | {
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"id": 32720,
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"openwebmath_score": null,
"tags": "electromagnetism, biophysics",
"url": null
} |
rospy, ros-kinetic
if __name__ == '__main__':
MyNode()
I'm running my node like:
export ROS_MASTER_URI=http://robot:11311; rosrun myrobot mynode.py
and the terminal output is:
[DEBUG] [2018-05-19 19:42:14]: init_node, name[/mynode], pid[5769]
[DEBUG] [2018-05-19 19:42:14]: binding to 0.0.0.0 0
[DEBUG] [2018-05-1... | {
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"openwebmath_score": null,
"tags": "rospy, ros-kinetic",
"url": null
} |
electromagnetism, electric-circuits, electrons, batteries, electrochemistry
Title: About a battery's positive terminal Does the positive terminal of the battery mean that the concentration of electrons is more there. In some places people say that current moves from positive to negative and they call it a convention w... | {
"domain": "physics.stackexchange",
"id": 92489,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "electromagnetism, electric-circuits, electrons, batteries, electrochemistry",
"u... |
information-theory, communication, superdense-coding
When communication begins, both parties set $i=0$. Then, Alice behaves as you described, and Bob behaves as follows:
Define a variable $z\in\{0, 1, \emptyset\}$
While $b$ is unknown:
1. Check $\mathcal{C}$:
a. If no signal was received: $z \leftarrow\emptyset$... | {
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"openwebmath_score": null,
"tags": "information-theory, communication, superdense-coding",
"url": null
} |
java, object-oriented, swing, quiz
For clickA through clickD, you could do this:
private bool[] correctChoice = new bool[] {false, false, false, false};
But since there's only one correct choice at a time, why not collapse it into a single index int instead:
int correctChoice = 0;
With that out of the way, the amoun... | {
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"tags": "java, object-oriented, swing, quiz",
"url": null
} |
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