text stringlengths 49 10.4k | source dict |
|---|---|
newtonian-mechanics, friction, string
Title: Why the capstan equation is exponential? Does anybody knows any intuitive explanation about the reason that the capstan equation is exponential and not, as expected, linear? At any point, the friction force is proportional to the tension in the rope, and the friction force ... | {
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In math terms, we denote this operation as: We then define (a|b)≡ a ∗ ∗ 1b + a2b2. complex-numbers inner-product-space matlab. %PDF-1.2 %���� 2. hu+v,wi = hu,wi+hv,wi and hu,v +wi = hu,vi+hu,wi. The inner productoftwosuchfunctions f and g isdefinedtobe f,g … Of course if imaginary component is 0 then this reduces to dot ... | {
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"tags": ... |
homework-and-exercises, newtonian-mechanics, forces, gravity
Applying Newton's second law gives $$\vec F_{\rm net} = T \,\hat d + mg \,\hat d = m a_{\rm c} \,\hat d \Rightarrow T + mg = m a_{\rm c}$$ where $T$ is the component (ie it can be either positive or negative) of the tension in the $\hat d$ direction.
On... | {
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"tags": "homework-and-exercises, newtonian-mechanics, forces, gravity",
"url": null
} |
antimatter, warp-drives, exotic-matter
Title: Exotic Matter -- What is it? I have a conceptual understanding of some theoretical physics concepts, so without getting into the math, what is exotic matter?
I have read some articles that say it is anything not normal, while others say it has a negative mass (is that anti... | {
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"tags": "antimatter, warp-drives, exotic-matter",
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In order that (a, b, c) be a Pythagorean triple, they must be of the form a= n^2- m^2, b= 2nm, and c= n^2+ m^2 for some integers m and n. In order that (b, c, d) also be a Pythagorean triple, they must be of the form b= p^2- q^2, c= 2pq, and d= p^2+ q^2 for some integers p and q. That means we must have b= 2nm= p^2- q^... | {
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"openwebmath_score": 0.8100404739379883,
"tags... |
geophysics, earth-rotation, earth-system, solar-terrestrial-physics, time
(image from Wikipedia commons, originally here)
But as a consequence of these tiny variations, almost every year one or two (leap seconds) are added to our clocks to keep them aligned with the rotation of the Earth. In the long run (millennia), ... | {
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"tags": "geophysics, earth-rotation, earth-system, solar-terrestrial-physics, time",
... |
fluid-dynamics, pressure
Title: Why do trains have to slow down when crossing in a tunnel? When two trains cross inside a tunnel, the velocity of the air around the train increases so the pressure decreases (Bernoulli's Principle). Using that logic, the windows are pushed outwards because the pressure outside is infer... | {
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"tags": "fluid-dynamics, pressure",
"url": null
} |
quantum-mechanics, bells-inequality, locality, foundations, quantum-foundations
https://arxiv.org/abs/quant-ph/9810080
Violation of Bell's inequality under strict Einstein locality conditions (1998)
Gregor Weihs, Thomas Jennewein, Christoph Simon, Harald Weinfurter, Anton Zeilinger
"We for the first time fully enforc... | {
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"tags": "quantum-mechanics, bells-inequality, locality, foundations, quantum-foundations",
... |
ros2, image-transport
Originally posted by William with karma: 17335 on 2018-03-21
This answer was ACCEPTED on the original site
Post score: 1
Original comments
Comment by paulbovbel on 2018-03-24:
connect/disconnect callbacks alone would go a long way towards enabling data processing pipelines and lazy pub/sub. IMO ... | {
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homework-and-exercises, solid-state-physics, electronics
$$
The similar small parameter is $\lambda_0=T/E_\mathrm{F_0}$, which, with taking into account the formulas above, is
$$
\lambda_0=\frac{T}{E_\mathrm{F}}\left(1+\frac{\pi^2}{8}\lambda^2\right)^{-2/3}=\lambda+\mathcal{O}(\lambda^3),
$$
so $\mathcal{O}(\lambda^n)... | {
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"url": null
} |
c++, c++11, reinventing-the-wheel, vectors
#include "Vector.cpp"
}
}
Implementation:
/* Vector.cpp */
/******************************************************************************/
/* Static *********************************************************************/
/************************************************... | {
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This method can also be used if $p\neq\frac12$.
• Oh but why the constant value of 3 and 2 in front? – ys wong Aug 24 '15 at 16:56
• For HHH, the "elements" are 3H, T, T to fill 3 "positions": 3H can fill any one of the 3. For HHHH, the "elements" are 4H, T to fill 4 "positions": 4H can fill either of the 2. – hyperge... | {
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"openwebmath_score": 0.8700507283210754,
"tags"... |
generics, vb.net
My concern is over the implementation of GetHashCode(obj As T), which should somehow account for what the delegate focuses on.
Am I right to be concerned? Any ideas for a fix?
So far I was thinking of replacing the delegate signature by Func(T, IList(Of String)): the delegate would be invoked on both... | {
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also have a clearance (play) vertical to tooth depth. 14 * 5 2 * ((4/3) * 5 +10) Volume (V) = 1309 m 3. The Tank Capacity Calculator below allows you to type in your desired tank diameter and height and provides an estimated volume by gallon amount. White & blue vertical tanks are translucent for convenient product lev... | {
"domain": "piano1on1.nl",
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"lm_q1_score": 0.9817357221825194,
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"lm_q2_score": 0.8175744717487329,
"openwebmath_perplexity": 1520.8449906701846,
"openwebmath_score": 0.6385908722877502,
"tags... |
philosophy, research, theory-of-computation, incompleteness-theorems
Inference with first-order-logic is semi-decidable. This is a big disappointment for all the folks that wanted to use logic as a primary AI tool.
Basic equivalence of two first-order logic statements is undecidable, which has implications for knowled... | {
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"tags": "philosophy, research, theory-of-computation, incompleteness-theorems",
"url": null
} |
OpenStudy (anonymous):
I needed a 40 on the final exam to get an A. So I guess? :)
OpenStudy (anonymous):
I'm also a math major though :P
Latest Questions
Spectrum: LaTeX masters UNITE!
13 seconds ago 38 Replies 1 Medal
Tonycoolkid21: help
11 minutes ago 3 Replies 0 Medals
NineTailedFox: can i please teach anyone a... | {
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• Since 5 > 0, we see that |5| = 5, which should be no surprise.
• Since -7 < 0, we see that |-7| = -(-7) = 7.
Notice that the definition of the absolute value of $$x$$ is given in two parts, one for when $$x \ge 0$$ and the other for when $$x < 0$$. This means that when attempting to prove something about absolute va... | {
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"lm_q2_score": 0.8289387998695209,
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"openwebmath_score": 0.9367097616195679,
"ta... |
arduino, rosserial
Originally posted by tejdeep on ROS Answers with karma: 1 on 2014-06-18
Post score: 0
Original comments
Comment by Wolf on 2014-06-19:\
My suggestion is to always try to recompile with arduino IDE, it occasionally fails for whatever reason... 2) if your problem persists 3 or 4 tries, please mark y... | {
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energy, magnetic-fields, fusion, neutrons
Title: Can neutron magnetic moment be used to slightly deflect the neutrons to not hit the tocamac lattice at a really small angle? Can neutron magnetic moment be used to slightly deflect the neutrons to not hit the tocamac lattice at a small angle? So part of the moment is sp... | {
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"tags": "energy, magnetic-fields, fusion, neutrons",
"url": null
} |
special-relativity, mass-energy
Title: How does matter turn to energy at the atomic level? When matter is converted to energy by means of $E=mc^2$, it produces quite a lot of "energy".
What I am having trouble understanding is exactly how the matter is transformed to energy at the atomic level. Do the atoms gain some... | {
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"tags": "special-relativity, mass-energy",
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gazebo
Title: DRC Vehicle - Handbrake functionality broken
Seems like the following code is clamping low handbrake values to high and vice versa.
So sending 0 for the handbrake doesn't disengage it - but gets set to high. - Should be reversed
if (this->handBrakeCmd < (handBrakeLow + handBrakeCmdEps) &&
this->GetH... | {
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& \frac{1}{3} & \frac{2}{3} & 0 & 0 & 0 \\ \hline \text{CC} & \frac{1}{5} & 0 & \frac{1}{5} & \frac{2}{5} & \frac{1}{5} \\ \hline \text{CD} & \frac{1}{8} & \frac{1}{8} & \frac{3}{8} & \frac{1}{8} & \frac{1}{4} \\ \hline \text{CE} & 0 & 0 & 0 & 0 & 0 \\ \hline \text{DA} & \frac{5}{9} & \frac{1}{9} & \frac{2}{9} & \frac{... | {
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"openwebmath_perplexity": 4115.875956951746,
"openwebmath_score": 0.33302542567253113,
"ta... |
machine-learning, deep-learning, ai-design, regression, loss
In terms of end results, it doesn't usually matter what loss function you end up using to train your model. What matters is how well the resulting model works in production environments where its predictions are being used for something practical.
Ultimately... | {
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"tags": "machine-learning, deep-learning, ai-design, regression, loss",
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lo.logic, type-theory, coq
Title: What's wrong with this LEAN proof? I'm learning to use the LEAN theorem prover and I got stuck in a proof of a simple fact in first-order logic:
$$ p(x) \rightarrow \forall x p(x) $$
My code is the following:
variables (A : Type) (p q : A → Prop)
example (x : A) : p x → (∀ x, p x) :=... | {
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"tags": "lo.logic, type-theory, coq",
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quantum-field-theory, scattering-cross-section
When the differential cross section has no angular dependence in some frame, it means that the particles are scattering in all directions with equal probability.
Contrast your differential cross with this one for nonrelativistic electron-electron scattering:
$$\frac{d\sig... | {
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"tags": "quantum-field-theory, scattering-cross-section",
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beginner, formatting, lisp, elisp
Title: Edis: Emacs driven indentation script Motivation
I recently picked up Emacs. As part of the process, I've started to configure the editor to fit my needs with Emacs Lisp. The Elisp indentation rules are still foreign to me, so I pretty much depend on Emacs' electric-indent-mode... | {
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"tags": "beginner, formatting, lisp, elisp",
"url": null
} |
performance, algorithm, array, swift
switch (subsetWithout, subsetWith) {
case (let s1?, let s2?): return s1.count < s2.count + 1 ? s1 : [first] + s2
case (let s1?, nil): return s1
case (nil, let s2?): return [first] + s2
case (nil, nil): return nil
}
}
In the recursion step, the shortest subsets ... | {
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Every logarithmic part cancels out, and we have
$$=4\cdot 5 \cdot 6 \cdots \color{red}{6}\cdot 65$$
$$=\color{red}{2\cdot 3} \cdot 4\cdot 5\cdot 6 \cdots 65$$
$$=65!$$
Hence $x=65$
You get $$4\cdot 5\cdot 6\cdots 65\cdot {\log 64\over \log 2}\\=1\cdot2\cdot3\cdot4\cdot5\cdots65=x!$$
Hence $x=65$
\begin{align}\df... | {
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"openwebmath_score": 0.997715175151825,
"tag... |
ros, ros-kinetic, ar-track-alvar
Title: ar_track_alvar publication rate too small
Hello!
These days I'm trying to use ar_track_alvar to track ar tags but the publication of ar_track_poses is too slow.
I use Ubuntu 16.04 and ros kinetic. My CPU is Intel I7 with 8G memory. When I use ar_track_alvar, it onlypublish /ar_... | {
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"tags": "ros, ros-kinetic, ar-track-alvar",
"url": null
} |
general-relativity, gravity, space-expansion, dark-energy, cosmological-constant
Title: What's the definition of repulsive gravity? After asking this question, I got confused. I always thought that repulsive gravity was a consequence of dark energy, the Nature of which is unknown. Many theories are flying around about... | {
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"tags": "general-relativity, gravity, space-expansion, dark-energy, cosmological-constant",... |
ros, rostime, ros-indigo
Title: Time Sync between rosserial on Windows & RosMaster on linux
The problem is: how can I sync time between rosserial node on Windows xp and RosMaster on Linux.
A robot controlled by WinXP is communicating to ROSMaster on a ubuntu14.04. Everything was ok until I relized that there is alwa... | {
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"tags": "ros, rostime, ros-indigo",
"url": null
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# A set contained in $\varepsilon$-neighborhood of a finite dimensional subspace is totally bounded
I was thinking about the following: if $X$ is totally bounded, then we can always choose the space spanned by the centers of an $\varepsilon$-ball net so that $X$ is lies in a neighborhood of finite dimensional vector s... | {
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"ta... |
\begin{align} I & \equiv \int_{0}^{1}{\ln^{4}\pars{x} \over x^{2} + 1}\,\dd x \\[5mm] & = {1 \over 4}\,\totald[4]{}{\nu}\bracks{\Psi\pars{{\nu \over 4} + {3 \over 4}} - \Psi\pars{{\nu \over 4} + {1 \over 4}}}\qquad \pars{~\Psi:\ Digamma\ Function~} \\[5mm] & = {1 \over 4}\pars{1 \over 4}^{4}\bracks{\Psi^{\pars{\texttt{... | {
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"tags... |
beginner, html, homework
Title: Personal HTML page for beginner CS lab I'm completely new at programming and have started to study computer science this fall. Our first lab is going to require us to make a very simple web page like the picture LAB attached. I was wondering if I could get some good critique on my HTML ... | {
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"tags": "beginner, html, homework",
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} |
complexity-theory, logic, satisfiability, normal-forms
Title: DNF to CNF conversion: Easy or Hard In relation to the thread Proving that the conversion from CNF to DNF is NP-Hard (and a related Math thread):
How about the other direction, from DNF to CNF? Is it easy or hard?
On Page 2 of this paper, they seem to hint... | {
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c++, algorithm, union-find
Note that this also assumes that we declare numSets before nodes so as not to confuse the reader. (Elements are initialized in declaration order.) In C++20, one could likely use a range and make this even more efficient.
Don't hide a loop return condition
The getRepr() function has a while... | {
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"tags": "c++, algorithm, union-find",
"url": null
} |
java, pathfinding
visitedSet.remove(coor);
return false;
}
boolean isExit(int x, int y, Set<Coordinate> visitedSet) {
return ((x == 0) || (x == maze.length - 1) || ((y == maze[0].length - 1) || y == 0))
&& !visitedSet.isEmpty();
}
boolean isInBounds(int x, int y) {
... | {
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"openwebmath_score": null,
"tags": "java, pathfinding",
"url": null
} |
opencv, estimation, rosbag, pcl, opencv2
Title: find position of object in a bag
Hi guys,
I need to find(estimate) the 3D position of the 'people in the scene' -- (this is in the bag file) with respect to the camera.
My code is : (I didn't write it)
//ROS
#include <ros/ros.h>
#include <sensor_msgs/Image.h>
#include ... | {
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"tags": "opencv, estimation, rosbag, pcl, opencv2",
"url": null
} |
quantum-field-theory, dirac-delta-distributions
\end{align}
A little rewriting gives
\begin{align}
\frac{1}{2} {\hat f}(0) + \frac{1}{2} \sum_{k=1}^\infty \left[ {\hat f}(k) + {\hat f}(-k) \right] = \pi f(0) + \pi \sum_{n=1}^\infty \left[ f(2\pi n) + f(-2\pi n) \right]
\end{align}
To reproduce the formula you are int... | {
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"openwebmath_score": null,
"tags": "quantum-field-theory, dirac-delta-distributions",
"url": null
} |
general-relativity, metric-tensor, vectors, causality, linear-algebra
Title: Is a vector space automatically spacelike if it has a basis of spacelike vectors? I am studying Kerr Spacetime and I am not sure about something used in a proof I am trying to understand.
I am wondering, if you consider a 4-dimensional Lorent... | {
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"tags": "general-relativity, metric-tensor, vectors, causality, linear-algebra",
"url": n... |
solid-state-physics, crystals, glass, amorphous-solids
Title: Which factors determine whether a substance will be amorphous or crystalline on solidification? What decides whether a substance will be crystalline or amorphous when it solidifies?
I heard various folklores that the method of condensation of a liquid (fas... | {
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"tags": "solid-state-physics, crystals, glass, amorphous-solids",
"url": null
} |
rosjava, android
Title: android tutorial pubsub problem
Hi,
I have installed the pubsub android tutorial on an android device and have it connect to an external roscore on ubuntu desktop.
When I run rostopic list on ubuntu desktop, the "chatter" topic is listed. But when I publish data on this topic, the rosTextView ... | {
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"tags": "rosjava, android",
"url": null
} |
geography, earth-system, astronomy, orbit, geodesy
(the vertical axis is logarithmic)
We can see that around 10 km away from the subsolar point, ~10 meters are enough to be closer than it to the Sun. ~30 meters at 20 km, ~800 meters at 100 km, ~3,000 m at 200 km, and if you go further than 340 km, not even Mount Evere... | {
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"tags": "geography, earth-system, astronomy, orbit, geodesy",
"url": null
} |
the parallelogram is also base times height where the height of the parallelogram also! Line parallel to two planes and intersecting two lines 2 respectively and,. The height of the perpendicular between the parallel lines can be calculated distance varies shortest distance between two parallel lines point! Otherwise, ... | {
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"openwebmath_score": 0.7240748405456543,
"tags"... |
\sqrt{1-\zeta^2}} \exp{\left(-\frac{\zeta \, t}{\tau}\right)} \sin{ \left( \sqrt{1-\zeta^2} \frac{t}{\tau} \right) }$$ $$\frac{1}{\tau^2 s^2 + 2 \zeta \tau s + 1}$$ See 2nd Order Systems $$\frac{1}{s\left(\tau^2 s^2 + 2 \zeta \tau s + 1\right)}$$ $$\frac{df}{dt}$$ $$sF(s)-f(0)$$ $$\frac{d^nf}{dt^n}$$ $$s^n F(s) - s^{n-... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9871787834701878,
"lm_q1q2_score": 0.8138913278846487,
"lm_q2_score": 0.824461932846258,
"openwebmath_perplexity": 1273.2965445633374,
"openwebmath_score": 0.7897850275039673,
"tags": ... |
## Computing a multiplicative inverse in a finite field
The extended Euclidean algorithm can also be used to calculate the multiplicative inverse in a finite field.
### Pseudocode
Given the irreducible polynomial f(x) used to define the finite field, and the element a(x) whose inverse is desired, then a form of the ... | {
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"lm_q1_score": 0.9910145701859179,
"lm_q1q2_score": 0.8079072750367682,
"lm_q2_score": 0.815232489352,
"openwebmath_perplexity": 869.2067512343549,
"openwebmath_score": 0.7465854287147522,
"tags": null... |
concurrency, clojure
Title: Count Words in Quotes Fetched from Website I have solved the following exercise and would like to get some feedback on my implementation.
Create a function that uses futures to parallelize the task of downloading random quotes from https://www.braveclojure.com/random-quote using (slurp "ht... | {
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"openwebmath_score": null,
"tags": "concurrency, clojure",
"url": null
} |
neural-network, pytorch
Title: What loss function to use for imbalanced classes (using PyTorch)? I have a dataset with 3 classes with the following items:
Class 1: 900 elements
Class 2: 15000 elements
Class 3: 800 elements
I need to predict class 1 and class 3, which signal important deviations from the norm. Clas... | {
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"openwebmath_score": null,
"tags": "neural-network, pytorch",
"url": null
} |
singular values of a tensor General ways of building a TT-decomposition of projector! = 10 and d2 tensor work of Vasilescu et al and Large-scale Optimization: part applications! An important technique for capturing the high-order interactions among multiway data note: sometimes the internal format change... Square of t... | {
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"lm_q1_score": 0.9805806557900713,
"lm_q1q2_score": 0.8039715536387945,
"lm_q2_score": 0.8198933447152497,
"openwebmath_perplexity": 1346.538490959334,
"openwebmath_score": 0.7437449097633362,
"tags": ... |
acid-base, ph, concentration
\begin{align}
n_{HA} = (C_0V_A - X_1) + X_2 &\rightarrow
C_{HA} = \frac{(C_0V_A - X_1) + X_2}{V_A + V_e} = \frac{C_0V_A}{V_A + V_e} - Y_2 \\
n_{H^+} = X_1 - X_2 &\rightarrow
C_{H^+} = \frac{n_{H^+}}{V_A + V_e} = \frac{X_1 - X_2}{V_A + V_e} = Y_2 \\
n_{A^-} = X_1 - X_2 &\rightar... | {
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"tags": "acid-base, ph, concentration",
"url": null
} |
c#, project-euler, programming-challenge
{6,3,7,8,3,2,9,9,4,9,0,6,3,6,2,5,9,6,6,6,4,9,8,5,8,7,6,1,8,2,2,1,2,2,5,2,2,5,5,1,2,4,8,6,7,6,4,5,3,3},
{6,7,7,2,0,1,8,6,9,7,1,6,9,8,5,4,4,3,1,2,4,1,9,5,7,2,4,0,9,9,1,3,9,5,9,0,0,8,9,5,2,3,1,0,0,5,8,8,2,2},
{9,5,5,4,8,2,5,5... | {
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"openwebmath_score": null,
"tags": "c#, project-euler, programming-challenge",
"url": null
} |
javascript, performance, interview-questions, memory-optimization
function countDuplicates(original) {
const uniqueItems = new Set();
const duplicates = new Set();
for (const value of original) {
if (uniqueItems.has(value)) {
duplicates.add(value);
uniqueItems.delete(value);
} else {
un... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "javascript, performance, interview-questions, memory-optimization",
"url": nu... |
python, performance, numpy, statistics
ZVAL_A_X_WT_A = ZVAL_A * WT_A #float
ZVAL_B_X_WT_B = ZVAL_B * WT_B #float
SumofWT = (WT_A + WT_B) #float
SumofZVAL_X_WT = (ZVAL_A_X_WT_A + ZVAL_B_X_WT_B) #float
#FIXED MODEL
meanES = SumofZVAL_X_WT / SumofWT #float
Var = float(1) / SumofWT #float
SE ... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, performance, numpy, statistics",
"url": null
} |
discrete-mathematics
Title: A simple Query regarding Modulus Notation? Aren't these two Modulus equations exactly the same (seems obvious):
$ X = 0 \ (mod\ B) $
$ X = B \ (mod\ B) $
The reason for the query is the following NP Complete Problem from Garey and Jhonson:
AN2, Simultaneous incongruences.
Given a collec... | {
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"tags": "discrete-mathematics",
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} |
java, graph
/**
* Creates an edge between {@code tailNodeId} and {@code headNodeId} with
* the default weight of 1.0. This method is a shortcut for constructing
* (virtually) unweighted graphs.
*
* @param tailNodeId the tail node of the edge.
* @param headNodeId the head node of the edge... | {
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"openwebmath_score": null,
"tags": "java, graph",
"url": null
} |
audio, nyquist, non-linear
Title: Is there a way to compute the spectrum effect of a non-linear function? I'm interested in developing audio software. I've read the books by Will Pirkle and there's something I'm struggling to understand about how non-linear functions affect the frequency spectrum of a signal. Particul... | {
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"tags": "audio, nyquist, non-linear",
"url": null
} |
# Find the sin and cos of 5pi/12
There are multiple ways to find the $\sin$ and $\cos$ of $\frac{5\pi}{12}$:
$\sin(&space;\frac{5\pi}{12})&space;=&space;\sin(\frac{\pi}{4}+\frac{\pi}{6})$
$=&space;\sin(\frac{\pi}{4})&space;\cos(\frac{\pi}{6})+&space;\cos(\frac{\pi}{4})\sin(\frac{\pi}{6})$
$=&space;\frac{\sqrt{2}}{2}\... | {
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"lm_q2_score": 0.8152324960856177,
"openwebmath_perplexity": 1942.9516211242021,
"openwebmath_score": 0.24274055659770966,
"tags": null... |
c#, .net, email
private readonly List<string> _invalidEmails = new List<string>()
{
"Abc.example.com",
"A@b@c@example.com",
@"a""b(c)d,e:f;g<h>i[j\k]l@example.com",
"just\"not\"right@example.com",
@"this is""not\allowed@example.com",
@"thi... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c#, .net, email",
"url": null
} |
robotic-arm, rotation
I'm confused about the sequence:$\underline{A}^{32} \underline{A}^{21}$, does this mean you go from frame $1$ to $2$ and then from $2$ to $3$ or should the order be reversed? There's also an expresison for $\underline{A}^{10}$ but I don't think that has to be used here.
I'm confused and the read... | {
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"tags": "robotic-arm, rotation",
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} |
then Thomas described how to break it a = c = 0 deserves mention. Popular method of creating random numbers U ( 0,1 ) a possibility may be shared with the author of specific! Seed, there is some such that k in equation ( 3.1 ) an... Discontinuous piecewise linear equation Project Published: March 7 2011 powered by Wolf... | {
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"lm_q2_score": 0.8128673246376008,
"openwebmath_perplexity": 1138.7314856987532,
"openwebmath_score": 0.5947360396385193,
... |
We know that $$T$$ is nilpotent. Now, let $$B_{11 \times 11}=T^2$$ and $$B^2=T^4=0$$, then the rank of $$B$$ can be found using this fact Matrix algebra: If $A^2=0$, Proof rank(A) $\le \frac{n}{2}$ . We get, rank$$(T^2)\leq \frac{11}{2}$$. In this way we can tell possibilities of the dimension of Kernel of $$T^2$$.
Ca... | {
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"lm_q1_score": 0.9787126469647338,
"lm_q1q2_score": 0.8024399791742697,
"lm_q2_score": 0.8198933381139645,
"openwebmath_perplexity": 157.84590018820063,
"openwebmath_score": 0.9429561495780945,
"ta... |
arithmetic, number-theory, integers
Title: Counting an integer's divisors without just enumerating them (or estimating if not possible)? I'm trying to count the number of divisors an integer $n$ has. The simple way to do this is to just enumerate all integers from 1 to $\sqrt{n}$, and count how many integers evenly d... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "arithmetic, number-theory, integers",
"url": null
} |
javascript, beginner, json, steam
Title: Steam API JSON function Upon coming face to face with the mighty cross-origin request block, and needing to get a JSON file from an external source, I decided to use the Yahoo Query Language in order to achieve this.
I'm starting to wonder however whether this code is really th... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "javascript, beginner, json, steam",
"url": null
} |
physical-chemistry, quantum-chemistry, orbitals
To properly understand this, it is necessary to go back to the fundamentals. The complex d-orbitals are obtained by solution of the Schrödinger equation. In general, these d-orbitals are made up of a radial part $R(r)$ and an angular part $Y(\theta,\phi)$. The radial par... | {
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"openwebmath_score": null,
"tags": "physical-chemistry, quantum-chemistry, orbitals",
"url": null
} |
c++, reinventing-the-wheel
Title: shared_ptr alternative with no dependencies An alternative to shared_ptr to minimize compile time. Intrusive. Reference count changes are not thread safe.
(#include<memory> pulls in 17k lines of code)
This satisfies my needs, but I'm curious how it could be improved (without adding an... | {
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"openwebmath_score": null,
"tags": "c++, reinventing-the-wheel",
"url": null
} |
javascript, jquery, html, css
Title: Displaying an image in a lightbox Please review my first query project. It achieves the desired result, but am I doing it right?
window.onresize = centreBoxInViewport;
function displayLightBox(obj) {
// Get the path to the image
var path = obj.getAttribute("href");
/... | {
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"tags": "javascript, jquery, html, css",
"url": null
} |
javascript, jquery, css, animation
.slide-item-wrapper {
width: 300px;
height: 84px;
overflow: hidden;
}
.slide-item-wrapper > * {
transition: .5s ease-in-out;
}
.box-item {
display: flex;
justify-content: center;
align-items: center;
background: red;
color: white;
width: 300px;
height: 84px;
... | {
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"id": 29250,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "javascript, jquery, css, animation",
"url": null
} |
haskell, state-machine
nfa.hs:
module NFA (NFA(..), evalNFA) where
import Data.Maybe (Maybe(..))
data NFA s i = NFA {
startState :: s,
delta :: s -> i -> [s],
epsilon :: s -> [s],
isFinal :: s -> Bool
}
step :: NFA s i -> s -> i -> [s]
step (NFA _ delta epsilon _) s i = [s] >>= forward >>= consumeIn... | {
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"tags": "haskell, state-machine",
"url": null
} |
the attractor stable! 2 CB CC D0, just like s1 and s2 curve, point! Material, see Chapter 5 of Paul 's Online Notes on ODEs values with negative part... Suppose x 1 ( t ) + iw ( t ) solves x0= Ax and s2, but as. X 1 ( t ) = u ( t ) = u ( t ) solves x0= Ax of... -2 + 5i ), the attractor is a geometric representation of ... | {
"domain": "classicfilmschool.com",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9744347920161262,
"lm_q1q2_score": 0.8077468173397291,
"lm_q2_score": 0.8289388104343892,
"openwebmath_perplexity": 862.9253682009972,
"openwebmath_score": 0.6724164485931396... |
$r_1 + r_2 + r_3 + r_4 = -\frac{b}{a} \\ r_1r_2 + r_1r_3 + r_1r_4 + r_2r_3 + r_2r_4 + r_3r_4 = \frac{c}{a} \\ r_1r_2r_3 + r_1r_2r_4 + r_1r_3r_4 + r_2r_3r_4 = -\frac{d}{a} \\ r_1r_2r_3r_4 = \frac{e}{a}$
One thing to notice is that 1 term makes up the coefficient of $x^4$, 4 terms make up the coefficient of $x^3$, 6 ter... | {
"domain": "imt-decal.org",
"id": null,
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"lm_q1_score": 0.9958012048531366,
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"lm_q2_score": 0.8104789063814616,
"openwebmath_perplexity": 286.4531621307538,
"openwebmath_score": 0.9999642372131348,
"tags": n... |
python, python-2.x, django
STATE = (
('ALABAMA', 'Alabama'),
('ALASKA', 'Alaska'),
('ARIZONA', 'Arizona'),
('ARKANSAS', 'Arkansas'),
('CALIFORNIA', 'California'),
('COLORADO', 'Colorado'),
('CONNECTICUT', 'Connecticut'),
('DELAWARE', 'Delaware'),
... | {
"domain": "codereview.stackexchange",
"id": 14153,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, python-2.x, django",
"url": null
} |
algorithms, graphs, reference-request, trees
Title: Given a tree, find a vertex which maximizes the minimum distance to any leaf If I am given a graph which forms a tree, I am interested in finding a vertex which maximizes the minimum distance to any leaf.
I am sure this problem has been studied before.
Does anybody k... | {
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"id": 1267,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "algorithms, graphs, reference-request, trees",
"url": null
} |
algorithms
Title: In the Gas-Up problem, how is the amount of gas the same up to a cyclic shift regardless of starting city? I'm working through Elements of Programming Interviews as practice for finding a job. I've spent a ridiculous amount of time on Problem 18.7.
In the gas-up problem, $n$ cities are arranged on a... | {
"domain": "cs.stackexchange",
"id": 7321,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "algorithms",
"url": null
} |
black-holes, entropy, information, holographic-principle, unitarity
Title: Why is information indestructible? I really can't understand what Leonard Susskind means when he says in the video Leonard Susskind on The World As Hologram that information is indestructible.
Is that information that is lost, through the incre... | {
"domain": "physics.stackexchange",
"id": 47892,
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"tags": "black-holes, entropy, information, holographic-principle, unitarity",
"url": nul... |
So you will certainly also include $\tau\sigma$; and you will also have $\sigma\tau\sigma\tau = (132)(132) = (123)$
Perhaps you are confusing $\langle \sigma,\tau\rangle$ with the set $\langle\sigma\rangle\langle\tau\rangle$, which consists of all products $\phi\psi$, where $\phi\in\langle \sigma\rangle = \{e,\sigma\}... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9674102542943774,
"lm_q1q2_score": 0.8163927795581645,
"lm_q2_score": 0.8438951064805861,
"openwebmath_perplexity": 129.5532991659496,
"openwebmath_score": 0.9556190967559814,
"tag... |
javascript, asp.net, url
getUrlPairs({
dirty: "&%[]?",
nullable: null,
numberProp: 123,
now: new Date(),
boolProp: true,
obj: {
objProp1: "objStr",
objProp2: false,
nullable: null,
objInObj: {
aa:"aa",
bb: true
}
},
arr: [{
arrProp11: ... | {
"domain": "codereview.stackexchange",
"id": 33455,
"lm_label": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "javascript, asp.net, url",
"url": null
} |
black-holes, mass-energy
EDIT
Of course, the full relativistic problem has to be considered more carefully. First of all, what is exactly the mass of a black hole? One of the postulates of relativity is that a freely falling observer never feels gravity - so a freely falling observer will judge the black hole to be pr... | {
"domain": "physics.stackexchange",
"id": 43177,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "black-holes, mass-energy",
"url": null
} |
roboearth
Title: Question about roboearth network
Hello,
I have a small question about using roboearth with ROS. I want to use the roboearth with turtlebot kinect for object detection.
My question is
Do you need the robot laptop and workstation to be connected to internet in order to use the roboearth features?
I am... | {
"domain": "robotics.stackexchange",
"id": 16429,
"lm_label": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "roboearth",
"url": null
} |
python, algorithm, python-3.x, tree, computational-geometry
for item in items:
if heuristic == 'best_fit':
self.best_fit(item)
elif heuristic == 'next_fit':
self.next_fit(item)
def _check_oversized(self, item: bintree.Item) -> bool:
"""
Catch... | {
"domain": "codereview.stackexchange",
"id": 28906,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, algorithm, python-3.x, tree, computational-geometry",
"url": null
} |
newtonian-mechanics
Title: When to balance torque about centre of rotation as opposed to an instantaneous axis of rotation When we consider a solid cylinder rolling down an incline we consider IAOR to be center of rotation but when the same cylinder is dragged across a rough horizontal surface by a horizontal force th... | {
"domain": "physics.stackexchange",
"id": 70855,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "newtonian-mechanics",
"url": null
} |
javascript, algorithm
I see 2 things that I'd do differently with this, if possible:
data[i + 0] += ((red + data[i + 0])) * il;
data[i + 1] += ((green + data[i + 1])) * il;
data[i + 2] += ((blue + data[i + 2])) * il;
Don't use offsets in an array to represent differe... | {
"domain": "codereview.stackexchange",
"id": 13846,
"lm_label": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "javascript, algorithm",
"url": null
} |
quantum-mechanics, homework-and-exercises, angular-momentum, vectors, commutator
$$
R(\omega)= \exp\left(-i \vec{\omega} \cdot {\vec J} \right)
$$
and you can recover
$$
[V_m,J_b]=i\frac{\partial}{\partial \omega_b} R(\omega)V_m R^{-1}(\omega)\Bigl\vert_{\vec{\omega} =0}\, .\tag{1}
$$
In this way you can then verify t... | {
"domain": "physics.stackexchange",
"id": 39217,
"lm_label": null,
"lm_name": null,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "quantum-mechanics, homework-and-exercises, angular-momentum, vectors, commutator",... |
java, parsing, swing
if (diff.hasDifferences())
return 0;
else
return 1;
}
@Override
public ArrayList<String> getDifferences(InputStream fileA, InputStream fileB) throws IOException {
ArrayList<String> differences = new ArrayList<>();
Diff diff = DiffBuilder... | {
"domain": "codereview.stackexchange",
"id": 26886,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "java, parsing, swing",
"url": null
} |
matlab, algorithms, demodulation, qpsk, timing
Title: Practical Gardner timing error implementation I'm trying to demodulate a QPSK communication.
For the moment I do:
Signal detection by computing the ratio between the power of the carrier wave compared to the signal power.
Initial clock synchronization with a pream... | {
"domain": "dsp.stackexchange",
"id": 1031,
"lm_label": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "matlab, algorithms, demodulation, qpsk, timing",
"url": null
} |
quantum-mechanics, homework-and-exercises, wavefunction, schroedinger-equation
Here’s my work:
Solving the stationary state SE is a routine job. I get :
$\psi(x) = A \sin(rx) + B \cos(rx)$, where $r= \frac{\sqrt{2mE}}{\hbar}$. I now want to enforce the boundary conditions $\psi(a)= \psi(-a) =0$.
(1): $\psi(a) = A \s... | {
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"id": 65517,
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"tags": "quantum-mechanics, homework-and-exercises, wavefunction, schroedinger-equation",
... |
# Row-wise matrix multiplication
I have a matrix $A=\{a_{ij}\}$ of dimensions $n$ rows by $m$ columns, and I would like to multiply each row of the matrix by a constant $b_i$, $i=1,\ldots,n$, and store the result in the same variable. In linear-algebra speak, I basically would like to do $A=\mathrm{diag}(b_1,\ldots,b_... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9664104924150546,
"lm_q1q2_score": 0.8135491459580912,
"lm_q2_score": 0.8418256551882382,
"openwebmath_perplexity": 3908.839130811123,
"openwebmath_score": 0.36293676495552063,
"ta... |
ros, arduino, rosseral-arduino
Title: Arduino (rosserial) node hangs during I2C reading + PWM
I've been trying to troubleshoot a strange problem for a few days now. I've got a ROS Kinetic node running on a Raspberry Pi 3 (Ubuntu Mate). I'm utilizing the rosserial_arduino package to handle communication between the Ar... | {
"domain": "robotics.stackexchange",
"id": 26524,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "ros, arduino, rosseral-arduino",
"url": null
} |
ocean, ocean-currents, tides
Physical effects, then, are likely to include direct effects on current speed, sediment, and stratification.
The obvious possible biological effect is from collisions. This is not my field, but as I understand it no effect is likely on small fish populations from collisions, although indiv... | {
"domain": "earthscience.stackexchange",
"id": 668,
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"openwebmath_score": null,
"tags": "ocean, ocean-currents, tides",
"url": null
} |
$\Leftrightarrow\sin^2C=4\sin^2\frac{C}{2}\cos^2\fr ac{C}{2}$
which is true.
3. Hi,
I'll write a solution that can definitely be simplified, I'm not happy it uses two other triangle identities, but they are well known and I included links to their proofs below.
First, note that $b-a \neq 0$ (otherwise $\beta-\alpha=... | {
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"id": null,
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"lm_q2_score": 0.8438951084436077,
"openwebmath_perplexity": 1213.2294344485817,
"openwebmath_score": 0.9204145073890686,
"ta... |
The trigonometric function $\tan x$ is an invertible function from $(-\pi/2,\pi/2)$ to $\mathbb{R}$. Also to find an invertible function from $(0,1)$ to $(-\pi/2,\pi/2)$ find the equation of the straight line joining the points $(0,-\pi/2)$ and $(1,\pi/2)$. Now compose the two functions together. You can likewise find ... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9825575116884779,
"lm_q1q2_score": 0.801012799569138,
"lm_q2_score": 0.8152324826183822,
"openwebmath_perplexity": 231.61522538609447,
"openwebmath_score": 0.9460605978965759,
"tag... |
mechanical-engineering
Title: How this engine time its ignition of spark?
HI all, do these nitro power engine use flywheel with one magnet on one side to time the ignition of the spark plug or do they use other mechanism? Thank you The ignition source in this type of engine is a glow plug, here is how it works.
The i... | {
"domain": "engineering.stackexchange",
"id": 4572,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "mechanical-engineering",
"url": null
} |
lagrangian-formalism, field-theory, renormalization, effective-field-theory, locality
Title: Why does the Lagrangian Density have to be a polynomial of the field? In a lecture, a professor appeared to have said that the Lagrangian can only contain terms that have powers of $\phi$ and a term with $\partial_\mu \partial... | {
"domain": "physics.stackexchange",
"id": 54580,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "lagrangian-formalism, field-theory, renormalization, effective-field-theory, local... |
random-forest, accuracy, overfitting, hyperparameter-tuning
Title: Hyperparameter tunning for Random Forest- choose the best max depth I'm trying to choose the best parameters for random forest model.
For that goal I hae run my model in loop with only one parameter and each time I have changed the number for the param... | {
"domain": "datascience.stackexchange",
"id": 8806,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "random-forest, accuracy, overfitting, hyperparameter-tuning",
"url": null
} |
quantum-mechanics, momentum, time-reversal-symmetry
Title: Time reversal in momentum space So I'm trying to find the wave function in momentum representation for the state $\hat{T}|\psi⟩$, where $\hat{T}$ is the time-reversal operator.
First, we know that the time reversal operator acts on momentum as follows:
$$ \hat... | {
"domain": "physics.stackexchange",
"id": 99817,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "quantum-mechanics, momentum, time-reversal-symmetry",
"url": null
} |
data-mining, nlp, information-retrieval, language-model
Title: How to create a good list of stopwords I am looking for some hints on how to curate a list of stopwords. Does someone know / can someone recommend a good method to extract stopword lists from the dataset itself for preprocessing and filtering?
The Data:
a ... | {
"domain": "datascience.stackexchange",
"id": 2022,
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"tags": "data-mining, nlp, information-retrieval, language-model",
"url": null
} |
python, performance, beginner
# Read all lines in ralease body whihc start with '-'
def read_lines_start_with_dash(self, lines_in_release_body, sheet, tag_name):
# Counter for updating rows in google sheet file
row = 2
for line in lines_in_release_body:
if (line[:1]).encode('utf... | {
"domain": "codereview.stackexchange",
"id": 33352,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, performance, beginner",
"url": null
} |
cc.complexity-theory, reference-request, quantum-computing, query-complexity
Before that question can be answered, we have to make the model precise. We can think of Grover's algorithm as solving the following problem: $\exists x\; \varphi(x)$?
In this model you only have access to $\varphi(\cdot)$ through an oracle ... | {
"domain": "cstheory.stackexchange",
"id": 1695,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "cc.complexity-theory, reference-request, quantum-computing, query-complexity",
"... |
slam, imu, calibration, visual-odometry, vio
Title: Why do we need to know the translation between Camera and IMU? In Visual Inertial Odometry, assuming the camera and the IMU are attached to the same rigid body, why isn't it enough to know just the relative rotation between the camera and the IMU? Why do we need to k... | {
"domain": "robotics.stackexchange",
"id": 2641,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "slam, imu, calibration, visual-odometry, vio",
"url": null
} |
kinect
Title: Getting started with ROS and Kinect?
Hi all!
I'd consider myself a pretty decent programmer, but I have no idea how to get started with ROS and Kinect. Does ROS have anything that makes it easier - For example, the ability to work with a 3d model of the world around the Kinect with programming? Right no... | {
"domain": "robotics.stackexchange",
"id": 23109,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "kinect",
"url": null
} |
option C is correct, you have to just select any n number from m which can be done in C(m,n) ways, and coming to the arrangement, that chosen n numbers should be in strictly increasing order, so you have just 1 way to arrange them. Hence if you do selection followed by arrangement it will be C(m,n) * 1, which will be s... | {
"domain": "gateoverflow.in",
"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9835969713304754,
"lm_q1q2_score": 0.8898115327590297,
"lm_q2_score": 0.904650541527608,
"openwebmath_perplexity": 653.5775049227947,
"openwebmath_score": 0.911790132522583,
"tags": ... |
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