text stringlengths 49 10.4k | source dict |
|---|---|
signal-analysis, audio, algorithms
so, what you've not specified is "logarithmic scale" to what, or what the perceived quantity is.
And the answer is perceived volume is logarithmic to power. The fact that this relation is logarithmic doesn't really matter here – it's only important that to achieve the same perceived ... | {
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"tags": "signal-analysis, audio, algorithms",
"url": null
} |
navigation, mapping, ros-hydro
Title: how to edit the map (.pbm) built by gmapping pkg
Hello All,
I need to edit the map that built by gmapping pkg. Is there any software that supports this format? almost all software open this format but they don't save changes under this format? Do you have any suggestion?
Origina... | {
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"tags": "navigation, mapping, ros-hydro",
"url": null
} |
physical-chemistry, gas-laws, equation-of-state
Title: Why is the ideal gas law so ubiquitous? Why is the ideal gas law usable in most gas problems?
For example, in a problem like this: "Suppose you have $1.00\: \mathrm{mol}$ of a gas at $0\:^\circ \mathrm{C}$, occupying a container which is $500\: \mathrm{mL}$ in siz... | {
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"tags": "physical-chemistry, gas-laws, equation-of-state",
"url": null
} |
php, javascript
function RemoveParent() {
$(this).parent().parent().remove();
}
function AddNewEvent() {
var today, html, temp, datestring;
today = new Date();
datestring = (today.getYear()+1900) + '-' + (today.getMonth()+1) + '-' + today.getDate();
html = '<li class="u... | {
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"tags": "php, javascript",
"url": null
} |
7 ] 1 is diagonalizable. We have step-by-step solutions for your textbooks written by Bartleby experts! a. matrix in #10a b. By solving A I x 0 for each eigenvalue, we would find the following: Basis for 2: v1 1 0 0 Basis for 4: v2 5 1 1 Every eigenvector of A is a multiple of v1 or v2 which means there are not three l... | {
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"lm_q2_score": 0.8633916064586998,
"openwebmath_perplexity": 456.0104119494225,
"openwebmath_score": 0.8566790819168091,
"tag... |
experimental-chemistry, photochemistry, radioactivity
Title: Excited helium gas from the colision of alpha particles with beta particles? As alpha particles are made out of 2 protons and 2 neutrons, they are the same as the helium atom with a +2 charge, but with a certain speed. The beta particles are made out of 1 el... | {
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"tags": "experimental-chemistry, photochemistry, radioactivity",
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} |
php, html, css, object-oriented
for($startdays; $startdays <= $numberofdays; $startdays=$startdays+1) {
$returndays .= $startdays.',';
}
return rtrim($returndays, ',');
// return substr($returndays, 0, -1);
}
//Define the type of dropdown
public function dropdown($ty... | {
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"tags": "php, html, css, object-oriented",
"url": null
} |
java, performance, object-oriented, multithreading, concurrency
public Person (final String name) {
this(name, null);
}
/**
* Every person is {@code SIT} greedy by default.
*
* @param name of this person
* @param room this person is currently in or {@code null}
*/
public P... | {
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"tags": "java, performance, object-oriented, multithreading, concurrency",
"url": null... |
image-processing, fft, filters, python, sampling
plt.imshow(x_truncated, cmap=plt.cm.hot)
plt.colorbar()
plt.show()
Fx_truncated_recontructed = np.fft.fftshift(np.fft.rfft2(x_truncated), axes=0)
Ferror = Fx_truncated - Fx_truncated_recontructed
Ferror.real[Ferror.real == 0] = np.abs(Ferror.real[Ferror.real != 0]).min... | {
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"tags": "image-processing, fft, filters, python, sampling",
"url": null
} |
newtonian-gravity, surface-tension, bubbles, space-mission
Title: How long would a bubble made in the ISS last? It seems to me that if on Earth soap bubbles pop, it is because the gravity makes the water and soap go to the bottom of it. When there is not enough water at the top of the bubble, it pops.
But what if we ... | {
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"tags": "newtonian-gravity, surface-tension, bubbles, space-mission",
"url": null
} |
mobile-robot, localization, mapping, planning
Title: Converting a 2D array of bits to a connectivity map (Code Debugging) I'm working on an robot that would be able to navigate through a maze, avoid obstacles and identify some of the objects (Boxes in which it has to pot the balls) in it. I have a monochromatic bitma... | {
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"tags": "mobile-robot, localization, mapping, planning",
"url": null
} |
c, file-system, linux, posix, c99
To print types lacking a printf specifier, cast to the widest available integer of matching sign-ness. In this case, "ino_t shall be defined as unsigned integer" Ref and How to print types of unknown size like ino_t?
// printf("%ld ", (long)sb.st_ino);
printf("%ju ", (uintmax_t) sb.... | {
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"tags": "c, file-system, linux, posix, c99",
"url": null
} |
formal-languages, turing-machines, finite-automata, undecidability, finite-sets
Title: Finite languages are Turing decidable - contradiction Let's say that I define the language $L$ over the alphabet $\{0, 1\}$ to be a language containing only one word, $w$, where:
$$ w =
\begin{cases}
1 & \text{if the contin... | {
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"tags": "formal-languages, turing-machines, finite-automata, undecidability, finite-sets",
"url... |
compilers
Title: Why doesn't my object code/machine code contain 1's and 0's I know when I compile my C program to machine code it gets compiled into something that specific computer can understand
But I thought computers can only understand 1's and 0's (high/low) so why doesn't my program look like a bunch of strange... | {
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"tags": "compilers",
"url": null
} |
matlab, audio, audio-processing
Title: Use of "Audacity"for teaching undergraduate labs of digital signal processing for electrical engineering students? Can we use"audacity"for teaching undergraduate labs/practicals of digital signal processing? or only MATLAB/Octave should be used?
Weblink of "audacity"
https://www.... | {
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"tags": "matlab, audio, audio-processing",
"url": null
} |
drag, aerodynamics, lift
Title: what causes airborne bodies to tilt? Imagine a Helium-inflated oblate spheroid floating still (A).
Buoyancy force cancels gravity force on Y axis. Object is tied to ground with a rope.
If a wind force is applied on X axis, why does the spheroid tilt , thus inducing an aerodynamic lift &... | {
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"tags": "drag, aerodynamics, lift",
"url": null
} |
reference-request, regular-expressions
Title: Succinctness of regular expressions with empty word Consider regular expressions on some alphabet $\Sigma$, without the empty word: $$e,f:=a\in\Sigma\mid e\cdot f \mid e+f\mid e^+$$
These $\varepsilon$⁻free expressions can define all regular languages that do not contain t... | {
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} |
gazebo, laser, urdf
Originally posted by Airuno2L with karma: 3460 on 2014-10-03
This answer was ACCEPTED on the original site
Post score: 5
Original comments
Comment by Robot on 2014-10-03:
thanks a lot.. it is working..
Comment by Airuno2L on 2014-10-03:
Nice, glad to help. If that answers everything please mark it... | {
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php, object-oriented, mvc, controller
// Instantiate CartTable and CartItemTable for database queries
$cartTable = new CartTable($connection);
$cartItemTable = new CartItemTable();
// If a cart already exists for the current session
if($doesCartExistForCurrentUser) {
// Get cart id in th... | {
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positive matrices is a subset of all non-negative matrices. I want to run a factor analysis in SPSS for Windows. Today, we are continuing to study the Positive Definite Matrix a little bit more in-depth. Conversely, some inner product yields a positive definite matrix. A symmetric matrix is defined to be positive defin... | {
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"openwebmath_score": 0.8304567933082581,
"tags": null... |
special-relativity, energy, mass, mass-energy, matter
As for cosmology, it's just like in the sun. Different forms of energy can move differently. And that's the only things that makes the situation change when mass is created or destroyed. The energy can move around differently when it converts to different forms. | {
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homework-and-exercises, special-relativity, doppler-effect
in order that the wavelength of one photon be twice that of the other?
So given the formula above, the remainig mathematical task is to solve
$2 = \lambda_{\text{towards}} / \lambda_{\text{away}} = \left(\lambda_s \sqrt{ \frac{1 + \beta}{1 - \beta} } \right) ... | {
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"tags": "homework-and-exercises, special-relativity, doppler-effect",
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$(\sin \theta + \cos \theta)(\tan \theta + \cot \theta)=\sec \theta + \csc \theta$
- 2 years, 11 months ago
Can you hear the Proving Trigonometric Identities Wiki page calling out your name?
Staff - 2 years, 11 months ago
Thank You, it is a good practice for we beginners!
- 2 years, 11 months ago
yes
- 1 month, ... | {
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javascript
ILw2ceM1kHsMAOFYei6LsdxDMOkE6RBfKd+tmN+p5KNzPd9y7IIIaIo0hcW0CpHuW3bLMuucpQnQGCMr6+vo3tiNptVFOX4+JjuMJlMwEajvRDz9fv7e13XgyBACBUKhYuLC3oPLythOgzDgJtqEAS6rnueB61hGPZ6PfBEQsjNzQ29uj3PAwKEkOM4uq6nECRD0CYdcdi2DaHruvS9FyGEMXZdF0LbtoEgMeFKEMtzzHFcYjlxSPrwVSFqtRodFgoF2rYZhgE/jVStVukHS5K0t7eXknBZyWZ1d3c3GAwIIZIkNZvN2... | {
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computer-vision
Convolution x0,y0 in the input will be mapped to x0,y0 in the output
Pooling x0,y0 will be mapped to x0/2,y0/2
Converting x0,y0 in image to x0^,y0^ in the output feature map
So if we have a CNN with Conv->Conv->Pool->Conv->Conv->Pool ....
The pixel x0,y0 in the input will be mapped to the pixel floor(... | {
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# shifting and reversing the signal
Say I have a signal $x[n]$.
What is $x[3-n]$?
My solution #1.
$x[-n]$, reverse first. Then, $x[-(n-3)]$, shift to the right by 3.
My solution #2.
$x[n-3]$, shift right by 3. Then $x[-(n-3)]$, reverse the entire shifted signal.
Both of my solution is incorrect. Why?
Independen... | {
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For the groups of order 8 for example, $D_4$ is $f(x)=x^4-2$, for $\mathbb{Z}_8$ my guess would be the cyclotomic $\phi_8=x^4+1$ and what's left is $\mathbb{Z_2}\times \mathbb{Z_4}$, $\mathbb{Z_2}\times\mathbb{Z_2}\times\mathbb{Z_2}$, which are abelian and the quaternion $Q_4$ which is non-abelian. I 'd like to think t... | {
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"lm_q1_score": 0.9752018376422666,
"lm_q1q2_score": 0.8209499123692285,
"lm_q2_score": 0.8418256412990658,
"openwebmath_perplexity": 94.2527629044901,
"openwebmath_score": 0.8190231919288635,
"tags... |
$$f^*(y) \supseteq \{x\} \iff \{y\} \supseteq \{f(x)\}$$
This can be used to prove:
Proposition. For all subsets $B$ of $Y$ and all subsets $A$ of $X$, we have:
$$f^*(B) \supseteq A \iff B \supseteq f_*(A)$$
Once you've proved this, your problem becomes a one-line proof:
$$f^{*}(f_*(A)) \supseteq A \iff f_*(A) \su... | {
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"openwebmath_score": 0.9023452401161194,
"tag... |
Distance measure space is the length of a line segment between the two points as. Output raster contains the measured distance from every cell to the square of. Case ) there is only 1 Dimensional space every cell to the nearest source used to find Euclidean! '19 at 10:04. fu DL fu DL fu DL fu DL fu DL )... Given by the... | {
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"lm_q2_score": 0.8376199653600372,
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"openwebmath_score": 0.8368810415267944,
"tags": n... |
star, stellar-evolution
As far as I know, that claim is made only through rough estimates of evolutionary tracks, not precise calculations. We do know that UY Scuti is certainly in the later period of its hydrogen-burning phase, if it is indeed at that point in its life. Arroyo-Torres et al. (2013) believe observation... | {
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"tags": "star, stellar-evolution",
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} |
ros, message
Title: How to use msgs in ros
Hi dear
I want to write a program that is tell me how many msgs that one node has published
How can I write this program
I wrot this program but it's not worked
#include "ros/ros.h"
#include "std_msgs/String.h"
int i=0;
void chatterCallback(const std_msgs::String::ConstPtr... | {
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c, parsing, functional-programming, lazy
test_regex: u = regex( "ab|cd|ef" ) = _
test_regex: parse( u, chars_from_string( "ab" ) ) = _
test_regex: parse( u, chars_from_string( "cd" ) ) = _
test_regex: take( 1, parse( u, chars_from_string( "cd" ) ) ) = _
test_regex: parse( u, chars_from_string( "ef" ) ) = _
test_r... | {
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"tags": "c, parsing, functional-programming, lazy",
"url": null
} |
robots, multi-agent-systems
In practice, these models can collapse if the environment implementation is not reliable. It can be difficult for robots or, say, self-driving cars, if they expect some transponders put on their way, as these devices are expensive to set and maintain, and they can be broken or stolen. It wo... | {
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"tags": "robots, multi-agent-systems",
"url": null
} |
thermodynamics, statistical-mechanics, probability, partition-function
&= -N\beta^{-1} Z_{\mathrm{sp}}^{-1} \frac{\partial}{\partial \epsilon_j} Z_{\mathrm{sp}} \\
&= N Z_{\mathrm{sp}}^{-1} g_j e^{-\beta \epsilon_j}
\end{align}
and everything checks out. | {
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"tags": "thermodynamics, statistical-mechanics, probability, partition-function",
"url": ... |
electricity, conductors, lightning
Title: Will putting a rubber cap on a steel bar prevent it from getting struck by lightning? Let's say there's a stainless steel bar pointing to the sky from the ground.
Like this there's a possibility it gets struck by lightning.
Now would putting a rubber cap on top of the bar chan... | {
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"openwebmath_score": null,
"tags": "electricity, conductors, lightning",
"url": null
} |
ros
Title: How display pointcloud messages in browser using rosjs?
Hi guys,
I have found the same question but the answer seems to be obsolete.
Concerning, this link. I can't find some JavaScript files used in this tutorial. Especially visualization.js.
They are not included in rosbridge nor wviz packages. I can't f... | {
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"id": 11002,
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"tags": "ros",
"url": null
} |
beginner, php, array, statistics
for ($i = 0; $i < $num; $i++) {$sum = $sum + ST::productMeanDeviation($arr1, $arr2, $i);}
return $sum;
}
/**
*
* @return a number equal to product mean deviation of each array values
*/
public static function productMeanDeviation($arr1, $arr2, $item)... | {
"domain": "codereview.stackexchange",
"id": 34513,
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"openwebmath_score": null,
"tags": "beginner, php, array, statistics",
"url": null
} |
$$\sum_{n=1}^{\infty} (-1)^n p_n^{-s}$$ converges. To do this, we estimate
$$p_{2n}^{-s}-p_{2n+1}^{-s} = s^{-1}\int_{p_{2n}}^{p_{2n+1}} x^{-1-s} dx = O_s(G_{2n}\cdot p_{2n}^{-1-s})$$ where we define $G_n= p_{n+1}-p_n$.
Now note that by the PNT we have $p_n\sim n\log n$ and $\displaystyle\sum_{n=X}^{2X-1} G_n = p_{2X}... | {
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"lm_q1_score": 0.9840936082881853,
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"openwebmath_score": 0.9874736070632935,
"tag... |
java, complexity, heap
public class ArrayHeapMinPQ<T> {
private PriorityNode<T>[] items;
public class ArrayHeapMinPQ<T> {
private PriorityNode<T>[] items;
Don't write comments that state the obvious. It's polluting the source code. Write comments for when they would really make sense.
// Declaring a const... | {
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"tags": "java, complexity, heap",
"url": null
} |
work to be done!. 5 log (9 ) 2 2. Logarithmic Rules Logarithm log b a = m bm = a log 4 16 = 2 42 = 16 Definition: Common Logarithm: log 10 = log Natural Logarithm: log e = ln Change of Base: log b a = log 5 13 = Product Rule: log b (xy) = log b x + log b y log 3 (4x) = log 3 4 + log 3 x Quotient Rule: log b = log b M -... | {
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"id": null,
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9854964211605606,
"lm_q1q2_score": 0.812504271451398,
"lm_q2_score": 0.8244619199068831,
"openwebmath_perplexity": 2107.3554604779924,
"openwebmath_score": 0.5253328084945679,
"tag... |
c++, memory-management, template, lambda, heap
//***************
// eHeap::ReplaceByKey
// emplace and move
// search keys can differ from compare keys
// returns false if item not found
//****************
template<class type, class lambdaCompare>
template<typename DataMember, typename lambdaEquals>
inline bool eHeap<... | {
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"openwebmath_score": null,
"tags": "c++, memory-management, template, lambda, heap",
"url": null
} |
pr2
Title: Keyboard controller for PR2 arm
Hi, I am currently trying to write a pr2 arm controller that will allow me to control all the arm joints of pr2 by keyboard
I'm basing my code on this
which will let me control r_arm_controller.
I tried modifying it but I still cannot achieve what I want. The keyboard contro... | {
"domain": "robotics.stackexchange",
"id": 11972,
"lm_label": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "pr2",
"url": null
} |
visible-light, photons, atoms, spectroscopy
Title: photon absorption by atoms causes heat? I have came up with a weird doubt: photon absorption by atoms causes heat? I mean, I was always told that if the photon's frequency is the magic one, the atoms absorbs the photon and goes to an excited state. So I have to suppos... | {
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"openwebmath_score": null,
"tags": "visible-light, photons, atoms, spectroscopy",
"url": null
} |
rviz
Title: How to set Z axis in RVIZ?
Hi all. I'm using a drone and to be display in RVIZ, I need to have a Z axis to see the height of the drone to ground.
However, my RVIZ got only the X and Y axis. Only views in 2D. My robot's frame does not go up or down, only can navigate around the 2D plane. Anyway I can set?
... | {
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"tags": "rviz",
"url": null
} |
we can rearrange the sum to find:
\begin{align*} a(n) &= \sum_{i=1}^{n} \sum_{\substack{1 \leq j \leq n \\ 1 \leq k \leq n}} \mathbf{1}\{ij \leq n\}\mathbf{1}\{ik \leq n\} = \sum_{\substack{1 \leq j \leq n \\ 1 \leq k \leq n}} \sum_{i=1}^{n} \mathbf{1}\Big\{i \leq \frac{n}{\max\{j,k\}}\Big\} \\ &= \sum_{\substack{1 \l... | {
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"lm_q2_score": 0.8807970748488297,
"openwebmath_perplexity": 336.1803810455722,
"openwebmath_score": 0.999997615814209,
"tags... |
lambda-calculus
(The converse is false, as $(\lambda x.xx)(\lambda a.a)$ satisfies this via inclusion of $xx$ but does not diverge) This is essentially the criterion used by type systems to avoid divergence. Take, for instance, the simply typed lambda calculus. In order for $f\ x$ to be well typed, we must have:
$$f :... | {
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"tags": "lambda-calculus",
"url": null
} |
quantum-mechanics, special-relativity, path-integral, action, virtual-particles
Title: Can the mass-shell equation be derived from the path integral formulation I've recently been trying to wrap my head around the notion of virtual particles, which as far as I understand live in quantum histories which can never be ob... | {
"domain": "physics.stackexchange",
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"openwebmath_score": null,
"tags": "quantum-mechanics, special-relativity, path-integral, action, virtual-particles",
... |
c#, performance, .net
public void Execute()
{
lock (_lock)
{
if (ShuttingDown)
{
return;
}
StartMonitoring();
}
}
}
In the constructor we are going to the DB via the SettingsService (Injected via IoC Container) and then s... | {
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"openwebmath_score": null,
"tags": "c#, performance, .net",
"url": null
} |
machine-learning, neural-network, deep-learning, dataset, cross-validation
Title: How to properly apply CrossValidation and/or split the dataset? I have a particular problem and do not really now how to properly validate my experiments in this scenario.
There is one big data set with 100.000 samples, 99.000 y=0, 1.00... | {
"domain": "datascience.stackexchange",
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"tags": "machine-learning, neural-network, deep-learning, dataset, cross-validation",
... |
java, bloom-filter
Title: Counting Bloom filter library in Java See also the next iteration.
This snippet is a counting Bloom filter supporting removal of elements as well. Instead of a bit vector it maintains a vector of "bucket counters". Also, the API supports well taking your customised hash functions.
Inserting: ... | {
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"tags": "java, bloom-filter",
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} |
digital-communications
The only caveat that needs to be stated is that baseband data
communication will always have a zero imaginary component, while for
bandpass communication the imaginary component of the complex envelope
might be nonzero.
Is this statement incorrect or am I misconstruing it somehow? In signal pro... | {
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"tags": "digital-communications",
"url": null
} |
So, it can be more than one and it can be anything.
For further discussion please ask me through gmail.
Continuous random variables can lead to confusion.
First, note that if $$X$$ is continuous then $$P(X = x) = 0$$ for every x. Don’t try to think of $$f(x)$$ as $$P(X = x)$$. This only holds for discrete random var... | {
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"lm_q1_score": 0.9796676430955553,
"lm_q1q2_score": 0.8287424394600162,
"lm_q2_score": 0.8459424431344437,
"openwebmath_perplexity": 211.8678882699808,
"openwebmath_score": 0.9467018246650696,
"tag... |
mechanical-engineering, structural-engineering, civil-engineering, structural-analysis
Title: Understanding out of plane principal stresses Consider that the state of stress at a point is given by an element taken at that point as shown,
The principal stresses in the x-y plane are given as,
$$\sigma_{1} = {\sigma_{x}... | {
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"tags": "mechanical-engineering, structural-engineering, civil-engineering, structural-a... |
By definition of set equality:
$\ds \bigcap_{i \mathop \in I} F_i = S$
$\blacksquare$ | {
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"id": null,
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"lm_q1_score": 0.9884918516137419,
"lm_q1q2_score": 0.801151790337851,
"lm_q2_score": 0.8104789018037399,
"openwebmath_perplexity": 342.49927868219544,
"openwebmath_score": 0.9963005781173706,
"tags": ... |
homework-and-exercises, vectors, moment-of-inertia, rigid-body-dynamics
Title: Rigid Body Motion and defining $\vec{L}$ and $\vec{\omega}$ This is a study question I have been struggling with, I would appreciate help defining initial vectors to start the question.
We consider a thin circle shaped disk (mass m, radius ... | {
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"tags": "homework-and-exercises, vectors, moment-of-inertia, rigid-body-dynamics",
"url":... |
## Tag Archives: direct sum
### Facts about power series of matrices
Let $G(x) = \sum_{k \in \mathbb{N}} \alpha_k x^k$ be a power series over $\mathbb{C}$ with radius of convergence $R$. Let $A$ be an $n \times n$ matrix over $\mathbb{C}$, and let $P$ be a nonsingular matrix. Prove the following.
1. If $G(A)$ conver... | {
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"lm_q1q2_score": 0.8106575848061016,
"lm_q2_score": 0.8267117855317474,
"openwebmath_perplexity": 46.50295748534041,
"openwebmath_score": 0.9932059049606323,
"tags": ... |
performance, bash, checksum
Title: Bash script to perform LUHN check The following Bash script takes a single parameter (the PAN) and exits with 1 if the PAN does not satisfy a LUHN check.
#!/bin/bash
pan=$1
panlen=${#pan}
for i in $(seq $((panlen - 1)) -1 0); do
digit=${pan:$i:1}
if [ $(((panlen-i) % 2)) -eq 0... | {
"domain": "codereview.stackexchange",
"id": 28962,
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"openwebmath_score": null,
"tags": "performance, bash, checksum",
"url": null
} |
This is already very close to a claim that can be directly resolved by the Bombieri-Lang conjecture, but ${V}$ is affine rather than projective, and also contains some singularities. The first issue is easy to deal with, by working with the projectivisation
$\displaystyle \overline{V} := \{ [X,Y,Z,R_1,R_2,R_3,R_4] \in... | {
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"openwebmath_score": 1.0000090599060059,
"tags": n... |
The recent paper by Homlin, Jones, Kurlberg, McLeman, and Petersen (Experimental Math., to appear) is devoted to these questions especially in the context of imaginary quadratic fields. One should expect that every natural number arises as the class number of an imaginary quadratic field. Refining an earlier conjecture... | {
"domain": "mathoverflow.net",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9828232930001334,
"lm_q1q2_score": 0.853903189930967,
"lm_q2_score": 0.8688267728417087,
"openwebmath_perplexity": 267.0133536510818,
"openwebmath_score": 0.7085285782814026,
"tags"... |
mathematical-physics, commutator, phase-space, wigner-transform, deformation-quantization
=i\frac{\partial}{\partial y^\alpha} g(y)$$
Alltogether we derived,
$$y_\alpha \star g(y)=(y_\alpha+i \partial_\alpha)g(y)$$
which for example gives
$$y_\alpha \star y_\beta=y_\alpha y_\beta+i \partial_\alpha y_\beta=y_\alpha y_\... | {
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"id": 9337,
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"openwebmath_score": null,
"tags": "mathematical-physics, commutator, phase-space, wigner-transform, deformation-quanti... |
Accelerating the pace of engineering and science
# trapz
Trapezoidal numerical integration
## Description
example
Q = trapz(Y) returns the approximate integral of Y via the trapezoidal method with unit spacing. The size of Y determines the dimension to integrate along:
• If Y is a vector, then trapz(Y) is the app... | {
"domain": "mathworks.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9724147209709196,
"lm_q1q2_score": 0.8377724409867199,
"lm_q2_score": 0.8615382129861583,
"openwebmath_perplexity": 1336.9735775095755,
"openwebmath_score": 0.8684871196746826,
"tags":... |
python, programming-challenge, interview-questions, matrix, median
Title: Calculate median of a matrix I am solving interview questions from here.
Problem : Given a N cross M matrix in which each row is sorted, find the overall median of the matrix. Assume N*M is odd.
Note: No extra memory is allowed.
For example:
... | {
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"tags": "python, programming-challenge, interview-questions, matrix, median",
"url": n... |
c++
for (int i = 0; i < cols; i++)
data[std::slice(i, rows, cols)] = filler * i;
// show the data:
for (int i = 1; i <= t.size(); i++) {
std::cout << t[i-1] << "\t";
if (i % cols == 0)
std::cout << "\n";
}
The result should look like this:
0 1 2 3 4... | {
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"openwebmath_score": null,
"tags": "c++",
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} |
work and the inclined plane doesn't. Using slot weights, add a 200 g load to the cart. P12 Inclined Planes. The inclined plane is one of the six classical simple machines defined by Renaissance scientists. Just plug this information into the following equation: The figure shows an example of a cart moving down a ramp... | {
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"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.983342958526322,
"lm_q1q2_score": 0.8215668551893897,
"lm_q2_score": 0.8354835391516133,
"openwebmath_perplexity": 396.8773525954262,
"openwebmath_score": 0.5151293873786926,... |
$$p = 0.2 + 0.8^2p,$$
yielding $p = \frac59$. So $P$ has either a $\frac59$ or $\frac49$ chance of winning, depending on who starts.
Here is a diagram that might help:
So if we start in the $P$ square, there's a $0.2$ chance of winning immediately. There's also a $0.8^2$ chance of moving to $Q$ then right back to $P... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9814534392852383,
"lm_q1q2_score": 0.8380756100583576,
"lm_q2_score": 0.8539127548105611,
"openwebmath_perplexity": 456.86048636970344,
"openwebmath_score": 0.7569027543067932,
"ta... |
filter-design, z-transform, transfer-function
$$A_{LP}(\omega)=1-A_{HP}(\omega)\tag{3}$$
The corresponding complex frequency is then given by
$$H_{LP}(e^{j\omega})=A_{LP}(\omega)e^{-j\omega (N-1)/2}\tag{4}$$
and the filter coefficients are
$$h_{LP}[n]=-h_{HP}[0],-h_{HP}[1],\ldots,1-h_{HP}[(N-1)/2],\ldots,-h_{HP}[N-1]\... | {
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"id": 10294,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "filter-design, z-transform, transfer-function",
"url": null
} |
# Mean distance between 2 points in adjacent voxels (cubes)
Let's imagine our central unit voxel $$V_1=[0,1]^3$$.
We allow the second one to be in $$V_2=[-1,2]^3 \setminus [0,1]^3~$$, the surrounding voxel (center removed).
My question:
What is the mean distance between a point in $$V_1$$ and a point in $$V_2$$?
O... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9890130583409235,
"lm_q1q2_score": 0.8502186768145958,
"lm_q2_score": 0.8596637523076225,
"openwebmath_perplexity": 1239.5758415108808,
"openwebmath_score": 0.992321789264679,
"tag... |
filters, finite-impulse-response
Title: Purpose of FIR Filter Structure I read Digital Signal Processing of author G.Proakis and see this FIR Filter Structure. I understand all about this but I wonder that what is purpose of classification to 4 structures?
Here is this section: These are just different ways to implem... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "filters, finite-impulse-response",
"url": null
} |
fluid-dynamics, cosmology, thermodynamics
Title: Perfect fluids in cosmology? In cosmology, it is often assumed that the equation of state of a cosmological fluid is of the form $p=w\rho$. Why is this? Is it the equation of a perfect fluid?
Why does $w=0$ for matter $1/3$ for radiation and $-1$ for a cosmological cons... | {
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "fluid-dynamics, cosmology, thermodynamics",
"url": null
} |
waves, velocity, speed
Title: What is the interpretation of speed of a travelling wave, based on $\frac {\partial x}{\partial t}$ formula Motion satisfies the wave equation if the following holds true
$$\nu^2 * \frac {\partial ^2 \psi} {\partial x^2} = \frac {\partial ^2\psi} {\partial t^2}$$ where $\psi$ is the vert... | {
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neural-network, cnn
EDIT
The confusion I had was that I didn't consider that if a weight is shared, its parameter $h_j^l$ appears several times in the loss function. When differentiating for $h_j^l$, several terms (considering the according inputs) will "survive". Therefore the updates will be the same. I think you're... | {
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the picture, that $$\angle A and \angle B$$ are not congruent. 5) 6) 7) regular octagon 8) regular 15-gon 9) regular 11-gon 10) regular pentagon. In Figure 4, notice that in order for a regular polygon to tessellate the plane, the sum of the interior angles that meet at a common point must equal 360 degrees. For exampl... | {
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"openwebmath_score": 0.2936362624168396,
"tags":... |
php, mysql, mysqli
function __destruct()
{
$this->close();
}
public function runQuery()
{
$this->ping(); // reconnects if connection is closed
$args = func_get_args();
$cnt = count($args);
if ($cnt === 1){
return $this->query($args[0]);
... | {
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"tags": "php, mysql, mysqli",
"url": null
} |
c++, comparative-review
test1 will be calculated at compile-time and test2 at runtime.
As for the details of the loop, if you want to re-implement the max_element algorithm's logic, I would go with a loop over iterators, not indexes, only to make it more readable:
template <typename T, std::size_t N>
constexpr auto ma... | {
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Continue the descending pattern, the "secondary base-bloodline" $$\Gamma(1, \frac23,\cdot)$$ render two and one. Then there's the "single bloodline". $$\begin{array}{c|ccccccc} \mathbf{\Gamma(1, \frac23, \frac12) } & C & 0 & D & E & & C_X & \\ \hline \Gamma(1, \frac23, \frac12, \frac12) & C & 0 & D & E & F & C_X & \\ \... | {
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"tag... |
c, programming-challenge
Title: Find the smallest number in the first array that is not in the second one I have solved the given assignment below is the question and getting correct answer. but my question is is there any way to reduce the complexity of my code or there is any other efficient way to write the code?
... | {
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"tags": "c, programming-challenge",
"url": null
} |
functional-programming, clojure, minesweeper
Title: Clojure Minesweeper from scratch In order to exercise and learn Clojure, I decided to write a simple Minesweeper game from scratch. I'd consider myself as a Clojure novice and would be thankful if somebody could do a review or give me feedback on the code.
The full ... | {
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"openwebmath_score": null,
"tags": "functional-programming, clojure, minesweeper",
"url": null
} |
observational-astronomy, galactic-dynamics, gas, sagittarius-a, molecules
Title: How do they know the newly-spotted gas near the center of our galaxy is molecular without knowing what gas it is? Phys.org's Mystery gas discovered near center of Milky Way links to Teodoro et al 2020 in Nature Cold gas in the Milky Way’s... | {
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"tags": "observational-astronomy, galactic-dynamics, gas, sagittarius-a, molecules",
"ur... |
c++, simulation, physics
using DataSet = std::vector<Vec3D>;
The struct Trajectory does not contain a trajectory, it just contains the current state of a single particle. So Particle would have been a better name for this. I would have added a Vec3D acceleration member variable, and removed step_no and temperature: t... | {
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"tags": "c++, simulation, physics",
"url": null
} |
quantum-mechanics, wavefunction, quantum-states
Title: Proof that two wave functions represent the same state How can I proof that the following two wave functions
$$\phi_n(x)=A \sin{\frac{n\pi}{L}x},$$ and
$$\psi_n(x)=\begin{cases} B\cos \frac{n \pi}{L}x & n \text{ odd}\\ C\sin \frac{n\pi}{L}x & n \text{ even}\end{c... | {
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"url": null
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• Actually one does not have to split the interval $(0,\infty)$, see @robjohn answer. Dec 15 '17 at 19:22
For each $n,$ the integrand, which is nonnegative, is bounded above on $[0,\infty)$ by $\dfrac{e}{1+\sqrt n x^{42}}.$ Letting $x = n^{-1/84}y$ shows
$$\int_0^\infty \frac{1}{1+\sqrt n x^{42}}\, dx = n^{-1/84}\int... | {
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"openwebmath_score": 0.9982491731643677,
"ta... |
graph-theory, approximation-algorithms, bipartite-graphs
Title: Constrained version of vertex cover in a bipartite graph Let $G(V_1, V_2, E)$ be a bipartite graph such that degree of all the vertices in $V_1$ is bounded by some constant (say) $d$. Now, for given two positive integer $l$ and $k$, we wish to decide if t... | {
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$$\frac{d}{dx} x^n = nx^{n-1}$$
Which is not defined for case:
$$\frac{d^n}{dx^n}x^n = \text{ undefined}$$
The idea is to show that this recursion can be expressed in analytical form and it is valid for all $$n\in \mathbb{Z}+$$ by induction. Problem is i don't know how do you express this in recursive form and how d... | {
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"lm_q2_score": 0.8705972801594707,
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"openwebmath_score": 0.9954684972763062,
"tag... |
performance, vba, excel
Dim updateSheet As Worksheet
Set updateSheet = wsLFF
CONST_DATA updateSheet, "J", startRow, endRow, "US"
....
End Sub
CO_BUYER_CONST has Sheets(LFF_WS).Select hiding inside. A couple lines later you have Range(...) which relies on that .Select since it's implicitly using the Activ... | {
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} |
particle-physics, magnetic-fields, scattering, classical-electrodynamics, magnetic-moment
I need to confirm the results (2)-(4).
More importantly, how can I write (2)-(4) in a simple closed vectorial form, using only the vectors $\vec{\boldsymbol{\mu}}$, $\vec{\mathbf{v}}_0$ (and probably the impact vector $\vec{\math... | {
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# Finding total after percentage has been used?
Tried my best with the title. Ok, earlier while I was on break from work (I have low level math, and want to be more fond of mathematics)
I work retail, and 20% of taxes are taken out, and I am wanting to find out how much I made before 20% is taken out.
So I did some ... | {
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"openwebmath_score": 0.7463533282279968,
"tags": n... |
$$\Rightarrow x({y^{ – 1}}y){z^{ – 1}} \in H$$
$$\Rightarrow {x^{ – 1}}z \in H$$
hence R is transitive A1
hence R is an equivalence relation AG
[8 marks]
a.
(i) for the equivalence class, solving:
EITHER
$$x{(ab)^{ – 1}} = e{\text{ or }}x{(ab)^{ – 1}} = {a^2}b$$ (M1)
$$\{ ab,{\text{ }}a\}$$ ... | {
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"tag... |
ros, plugin, planner
Any thoughts?
Originally posted by ROSCMBOT on ROS Answers with karma: 651 on 2014-11-27
Post score: 1
Original comments
Comment by ROSCMBOT on 2014-11-27:
I also checked this thread about this problem @Ken_in_JAPAN @fergs
Thanks to @fergs, I added another target_link_libraries after add_librar... | {
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c++, performance, c++11, file-system, boost
Title: Adding/changing ID3 tags to media files with "artist - title" format This code puts or changes ID3 tags to media files based on their file names. It assumes the files are in this format:
morbid angel - maze of torment.mp3
The resulting tag would be:
Artist: morbid ... | {
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"tags": "c++, performance, c++11, file-system, boost",
"url": null
} |
c#, unit-testing, asp.net-core
Title: Is this enough for unit testing a basic controller? My pet project, is a community driven lyrics archive, it is still a work in progress, and all code is open sourced on GitHub.
I have a local git branch tests/add-controller-tests where I wish to add some unit tests on my controll... | {
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ros
P.S.2 is this the only way?
If using the receipt time instead of a timestamp is acceptable (depends on your application), allow_headerless = True should work, and you can post your code for help troubleshooting. Otherwise, there's no need to modify the publisher directly. If you're really trying to synchronize ... | {
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"url": null
} |
organic-chemistry, nomenclature, ionic-compounds, erratum
Title: How to name LiN(CF2SO3)2? I found this compound in the list of inorganic lithium salts from this article on ScienceDirect.
It is said to be of the sulfonate group. Let's focus on the anion alone.
I'm not sure if it can be bis(difluoromethanesulfonyl)imid... | {
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"tags": "organic-chemistry, nomenclature, ionic-compounds, erratum",
"url": null
} |
ros
Title: Unexpected behavior when trying to set position of PR2 arm in Gazebo
Hi,
I am using Fuerte on Ubuntu 11.10.
In Gazebo, I have been using the SetModelConfiguration method suggested here to move a PR2 arm to a certain position. It was working fine for the past several months, but recently I have gotten som... | {
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A: See answers to the summer's midterm in the "Midterm Summer 2011" section
Q: g(z) = z^2 - |z|^2.Find g'(z) where it exists.
A: g(x+iy)=(x+iy)^2-|x+iy|^2=2ixy-2y^2. Cauchy-Riemann equations with u(x,y)= - 2y^2, v(x,y)=2xy read
0=2x
-4y=-2y
Hence if the complex derivative exists at some point (x,y), then by Cauchy-Ri... | {
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"lm_q2_score": 0.853912760387131,
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"openwebmath_score": 0.9511043429374695,
"tags":... |
ros, gazebo, ros2, diff-drive-controller
Title: Remapping diff drive controller to cmd_vel
Hi!
I'm looking to use nav2 with my current diff drive controller setup. My controller is currently subscribed to the /diff_drive_controller/cmd_vel_unstamped topic, while it appears nav is publishing to the /cmd_vel topic. Is ... | {
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"tags": "ros, gazebo, ros2, diff-drive-controller",
"url": null
} |
c++, multithreading
As for the parameters of main() itself, you can use the same trick, or use the other allowed form of main() that takes no parameters:
int main() {
The remaining warnings I get are about comparisons between signed and unsigned integers. Use std::size_t as the type of threads_ready.
Unconditionally ... | {
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"tags": "c++, multithreading",
"url": null
} |
quantum-mechanics, operators, commutator, observables
Title: How to recognize a Complete Set of Commuting Operators (CSCO) A question about 'completeness'. These two operators are commuting, but I want to know more about their completeness.
How do you know if {H}, {B}, {H,B} and/or {$H^2$,B} are forming (a) Complete ... | {
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"tags": "quantum-mechanics, operators, commutator, observables",
"url": null
} |
# can remove opening
if char == "(" and invalid_opening > 0:
self.valid_builder(
s, result, curr, idx+1, invalid_opening-1, invalid_closing)
# can remove closing
if char == ")" and invalid_closing > 0:
self.valid_builder(
s, result, curr, idx+1, invalid_opening, invalid_closing-1)
self.valid_builder(
s, result, curr+[... | {
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"lm_q2_score": 0.8596637487122111,
"openwebmath_perplexity": 6090.381773024074,
"openwebmath_score": 0.30743175745010376,
"tags"... |
java, optimization, android, pathfinding
public void addChild(int row, int col, TiledMap tiles, Node currentNode, Node target)
{
if((row >= 0 && col >= 0) && (row <= 14 && col <= 39))
{
if (tiles.isPassable(row, col))
{
if (!isNodeClosed(row, col))
{
doub... | {
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"tags": "java, optimization, android, pathfinding",
"url": null
} |
I think an argument could be made for keeping only one digit of precision in the answer (how precise is that "$$1\%$$" anyway?), in which case both answers round to $$0.8.$$
1. How did the author derive the equation ...
They didn't. Instead, the fact is that $$P(D\mid T_1,\ T_2) = \frac{P(T_1,\ T_2\mid D)P(D)}{P(T_1,... | {
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"lm_q2_score": 0.9219218348550491,
"openwebmath_perplexity": 311.0663614422447,
"openwebmath_score": 0.739641547203064,
"tags... |
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