text stringlengths 49 10.4k | source dict |
|---|---|
decidability, nfa
Title: Deciding whether a 2nfa halts on every input on every branch A 2nfa is a nondeterministic finite automaton that can move its head left or right on the input tape, or not. Is the following language known to be decidable?
$$
\textit{H}_{\mathsf{2nfa}} = \{ \langle M \rangle \mid M \textit{ is a... | {
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"tags": "decidability, nfa",
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fft, finite-impulse-response, overlap-add
Title: Frequency Domain Equivalent to Zero-Phase Filtering (`filtfilt`) Related to this question by @Molem7b5, what would be the frequency domain equivalent (filter implementation through overlap-add of DFT's) for a zero-phase filter as implemented with MATLAB/Octave/Python sc... | {
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"tags": "fft, finite-impulse-response, overlap-add",
"url": null
} |
ros, rqt-image-view, ros-kinetic, qtcreator
Title: Build RViz plugin from .ui file
My existing solution simply designs the GUI in qtcreator and then use the uic to generate the dotnect_window.h (link to plugin) which I might have to modify to derive from class ... : public rviz::Panel. How to automate this / do it a... | {
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"tags": "ros, rqt-image-view, ros-kinetic, qtcreator",
"url": null
} |
c, io, localization
int main (void){
int i = 0;
char caractere;
struct cadastro {
char cpf[20];
int idade;
char sexo;
char nome[100];
};
setlocale(LC_ALL, "Portuguese");
void grauRisco (void);
... | {
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"tags": "c, io, localization",
"url": null
} |
newtonian-mechanics, friction, free-body-diagram
Title: Can friction or normal force be undetermined? I've been studying newton-mechanics and encountered this weird situation where friction and normal force can't be decided.
It's a problem where a uniform rod is leaning on the wall at degree $\theta$.
Rod's length is ... | {
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"tags": "newtonian-mechanics, friction, free-body-diagram",
"url": null
} |
fourier-transform, linear-systems, z-transform, frequency-domain, laplace-transform
Title: Names of system functions in frequency domain I was just trying to refresh my systems theory known from long ago, and I realized that I had forgetten the name of the basic functions. Specifically, what are the names of these fu... | {
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... |
kinetics, theoretical-chemistry
Let us consider a thermodynamic system with first law $$\text{d}U = f_1\,\text{d}X_1 + f_2\,\text{d}X_2.$$ It is coupled to a reservoir, itself with first law $$\text{d}U' = f_1'\,\text{d}X_1' + f_2'\,\text{d}X_2' = -f_1'\,\text{d}X_1 - f_2'\,\text{d}X_2,$$ noting that $\text{d}X_i' = -... | {
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"tags": "kinetics, theoretical-chemistry",
"url": null
} |
astronomy, planets, stars, exoplanets
Title: What is the percentage of stars with planetary systems We have discovered quite a number of exoplanets to date. The Kepler spacecraft has examined 150,000 stars and found 1,059 exoplanets.
We know that Kepler, as well as all other exoplanet searches to date, can only find p... | {
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"tags": "astronomy, planets, stars, exoplanets",
"url": null
} |
electromagnetism, magnetic-fields, polarization, magnetic-moment, magnetostatics
Title: Ferromagnets - Permanent? When researching about the Curie-Temperature and magnets in general, something got me confused. What is the difference between a ferromagnet and a permanent magnet? In a ferromagnet the spins are already a... | {
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"tags": "electromagnetism, magnetic-fields, polarization, magnetic-moment, magnetostatics",... |
performance, beginner, c, programming-challenge, primes
1,4241,4243,4253,4259,4261,4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,4663,4673,4... | {
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"tags": "performance, beginner, c, programming-challenge, primes",
"url": null
} |
mathematics, n-body-simulations
4000 100.00001785427928 -80.90170126160325 58.77855309408762
4100 100.00001820278406 -84.43279542201651 53.58270894403392
4200 100.00001851840162 -87.6306720835148 48.17539842982273
4300 100.00001879988628 -90.48271069762764 42.577961726543805
4400 100.00001904612719 -92.97765557980723 ... | {
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"url": null
} |
python, performance, graph, dynamic-programming
and a time limit of 1, the five inner array rows designate the starting point, prisoner 0, prisoner 1, prisoner 2, and the exit door respectively. You could take the path:
Start End Delta Time Status
- 0 - 1 exit door initially open
0 4 -1 2
... | {
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cos a cos b 3 to convert the A and B back to x and y: which is Equation 2. Learn about the relationship between the sine & cosine of complementary angles, which are angles who together sum up to 90°. cos (+ β) = cos cos β − sin sin β, cos(u v) = cosucosv sinusinv tan(u v) = tanu tanv 1 tanutanv Double Angle Formulas si... | {
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"lm_q2_score": 0.8519527982093666,
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"openwebmath_score": 0.8957402110099792,
"tag... |
machine-learning, quantum-enhanced-machine-learning, kernel-methods
So to answer some of your questions
Why do I see SVM and quantum kernel methods used interchangeably - they should generally not be. A quantum kernel method describes (a) constructing the feature map $\phi$ to map input data $x_i$ into a state $\phi(... | {
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"u... |
newtonian-mechanics, classical-mechanics, constrained-dynamics
Title: Understanding the rolling constraint for one cylinder rolling inside another cylinder This is the problem to find the equation of motion of 2 cylinders in which 1 cylinder is placed inside another cylinder with larger radius as shown in figure. The ... | {
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"tags": "newtonian-mechanics, classical-mechanics, constrained-dynamics",
"url": null
} |
inorganic-chemistry, experimental-chemistry, analytical-chemistry
References:
[1] https://en.wikipedia.org/wiki/Chromyl_chloride
[2] Pure Chromyl Fluoride. Alfred Engelbrecht, Aristid V. Grosse. J. Am. Chem. Soc., 1952, 74 (21), pp 5262–5264 |http://pubs.acs.org/doi/abs/10.1021/ja01141a007?journalCode=jacsat
[3] Vogel... | {
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Let $\frac\varepsilon3 > 0$. Then $\exists N \in \mathbb N,\, \forall n \ge N\space |x_n -l| < \frac\varepsilon3 \text{ and } |z_n -l| < \frac\varepsilon3$ so that
$$|z_n – x_n| = |z_n – l + l – x_n| \le |z_n – l| + |x_n – l| < \frac\varepsilon3 + \frac\varepsilon3 = \frac{2\varepsilon}3$$
By assumption,
\begin{align} ... | {
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star, earth, mass, accretion, universe-sandbox
Title: Why doesn't smashing larger and larger bodies incrementally into a rocky planet create a star? Let's start with a stationary Earth. If we smash a few Mercury-sized objects into the Earth, the Earth begins to accrete mass. Repeat this step with larger and larger obj... | {
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The Jacobian matrix of $\mathop{\nabla} f(\mathbf{x})$ is \begin{align} \mathbf{D} (\mathop{\nabla} f(\mathbf{x})) &= \begin{bmatrix} \frac{{\partial^2}f}{{\partial}x_1^2} & \frac{{\partial^2}f}{{\partial}x_2{\partial}x_1} & \cdots & \frac{{\partial^2}f}{{\partial}x_n{\partial}x_1}\\ \frac{{\partial^2}f}{{\partial}x_1{... | {
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"lm_q1_score": 0.987758725428898,
"lm_q1q2_score": 0.8472679300985858,
"lm_q2_score": 0.8577681049901036,
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"openwebmath_score": 0.9987526535987854,
"tags... |
signal-synthesis, approximation
The FFT result bin 1 will be the strength of the sine and should be about $N/2$. Now you can adjust $a_1$ to bring your 3rd harmonic distortion up and down. I would start with $a_1 \approx \tfrac{5}{\pi} - 2$ so that $a_0 \approx 1$. That's in bin 3 of the FFT results But the 5th ha... | {
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"tags": "signal-synthesis, approximation",
"url": null
} |
homework-and-exercises, angular-momentum, group-theory, representation-theory
Title: $n$-dimensional irreducible representation of $SU(2)$ I'm studying Electroweak theory and I've come across the following problem.
I want to look at the scalar in electroweak theory in a general $n$-dimensional irreducible representati... | {
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... |
spacetime, quantum-gravity
Title: If Space is continuous, why can't we go below Planck Length? I am not talking about any other attributes of particles, vacuum etc ruling out Uncertainty Principle thing. If talking about pure Space (which is continuous, not discrete, cf. e.g. this Phys.SE post), why is Planck Length l... | {
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"openwebmath_score": null,
"tags": "spacetime, quantum-gravity",
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c++, homework, compression, heap
cout << "\n\n";
system("pause");
return 0;
} Looks pretty readable and I agree with most of your formatting however there are some things that stand out.
using namespace std;
Kick this habit before it kicks you.
#define MAX_TREE_HEIGHT 1000
I'd prefer to put this into an anony... | {
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That said, there are many other (probably better) ways of thinking about this. For example, any two vectors (in any dimension) gives rise to a (potentially degenerate) triangle in the plane spanned by those vectors (which will be ambiguous if they are linearly dependent). Namely, given vectors $\mathbf u$ and $\mathbf ... | {
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"lm_q2_score": 0.8479677602988601,
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This is admittedly not as nice as the approach using the geometric series and makes heavy use of the dilogarithm and it's particular values but I think it's kinda fun.
Too long for a comment.
Making the problem more general, it is possible to compute $$I=\int \frac{\log (a x+b)}{(x+c) (x+d)}\,\mathrm dx$$ Using one i... | {
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experimental-physics, electric-circuits, voltage, classical-electrodynamics, education
This is, however, an incorrect conclusion. In general, the integration path for the Faraday-Maxwell law is arbitrary, but the circuit path is fixed. The only ambiguity in the potential around the loop is due to the nature of induced... | {
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"tags": "experimental-physics, electric-circuits, voltage, classical-electrodynamics, educa... |
quantum-mechanics, heisenberg-uncertainty-principle, fourier-transform
Title: Very simple example of the way the Fourier transform is used in quantum mechanics? According to a book I'm reading, the Fourier transform is widely used in quantum mechanics (QM). That came as a huge surprise to me. (Unfortunately, the book ... | {
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"tags": "quantum-mechanics, heisenberg-uncertainty-principle, fourier-transform",
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# Does the Gauss-Bonnet theorem apply to non-orientable surfaces?
I found statements of the Gauss-Bonnet theorem here, here, here, here, here, here, here, and here. None of them require that the surface be orientable. However, Ted Shifrin claims in a comment to this question that the Gauss-Bonnet theorem actually only... | {
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"openwebmath_score": 0.9532164931297302,
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spacetime, time
Observation of change is important to defining a concept of time. If there are no changes, no time can be defined. But it is also true that if space were not changing, no contours, we would not have a concept of space either. A total three dimensional uniformity would not register.
In special relativit... | {
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"tags": "spacetime, time",
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entomology, ethology, behaviour
Title: What is this grasshopper doing? I spotted a grasshopper standing on a pavement with a long sting placed in asphalt. I also recorded a video of it moving:
https://youtu.be/JoDdg2yUuYo
What is it doing? It's its ovipositor & it's trying to dig a hole to lay its eggs.
"How Do Grass... | {
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"tags": "entomology, ethology, behaviour",
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electromagnetism, photons, quantum-electrodynamics, virtual-particles, pions
What I am getting at is that a single electron doesn't produce any EM field until it meets another charged particle! Actually, this should make sense if you think about it for a while. How do you detect there is an electron if nothing else at... | {
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"tags": "electromagnetism, photons, quantum-electrodynamics, virtual-particles, pions",
"ur... |
quantum-mechanics, hilbert-space, quantum-entanglement, density-operator, quantum-states
is still separable. This is completely independent of $\tau$.
k=n: This means we have essentially a maximally mixed state. To properly normalize it, we should write $|\Psi_0\rangle=\frac{1}{\sqrt{n}} \sum_{i=1}^n |x_i\rangle|y_i\r... | {
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"tags": "quantum-mechanics, hilbert-space, quantum-entanglement, density-operator, quantum-... |
cosmology, space-expansion
3 questions in one post may be a bit too much, so a general explanation how the expansion of space relates to (a) the size of physical objects, e.g. the typical diameter of atomic particles (1) above, and to (b) speed, wave length and frequency of light would be great. Space does expand, but... | {
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"id": 19708,
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"tags": "cosmology, space-expansion",
"url": null
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javascript, jquery
As you can see, I use $("body") 3 times to execute 3 different actions. Is there any way to use it only once so I can reduce my code? Like many jQuery methods, .on() returns jQuery object which you can use for chaining purpose.
Sidenote: You should take into account that prompt method may return nul... | {
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cc.complexity-theory, derandomization, space-bounded, pseudorandomness
An interesting subproblem may be the following: suppose we just want to fool symmetric functions over all n indices, do we have a nice space? By the above observations, we just need to fool the threshold functions over $n$-bits, which is just a fam... | {
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feature-scaling, mse
# Ludwig
from ludwig.api import LudwigModel
final_training_dataframe = training_dataframe
# Neural Net: 4 hidden layers
model_definition = {'input_features': [{'name': 'incomeBeforeTax', 'type': 'numerical'},
{'name': 'netIncome', 'type': 'numerical'},
{'name': 'sellingGeneralAdministrative',... | {
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"openwebmath_score": null,
"tags": "feature-scaling, mse",
"url": null
} |
algorithm, c, file, image, memory-management
Title: Two dimensional gaussian image generator in C This is a follow-up question for Image Processing Median Filter in C. I am attempting to create a two dimensional gaussian image like below in C.
The formula is as follows.
The experimental implementation
base.h: Conta... | {
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"openwebmath_score": null,
"tags": "algorithm, c, file, image, memory-management",
"url": null
} |
r
Title: Calculate regression coefficients for specific conditions in a data frame I have a data set where leaf mass (MASS) was measured in 30 different tanks (TANK) on 3 dates (DATE). The tanks were also assigned to 5 different treatments.
I want to calculate the regression slope of the mass loss for each tank so I w... | {
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"id": 24279,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "r",
"url": null
} |
For the forward direction, suppose there is a partition of $\{a_1, \ldots a_n\}$ into two sets $L$ and $R$ such that $\sum_{a_i \in L} a_i = \sum_{a_i \in R} a_i$. Set $L' = \{a_i' : a_i \in L\} \cup \{b_i' : a_i \notin L\}$ and $R' = \{a_i' : a_i \in R\} \cup \{b_i' : a_i \notin R\}$. This is a partition with the same... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9658995742876885,
"lm_q1q2_score": 0.8321593931559061,
"lm_q2_score": 0.8615382129861583,
"openwebmath_perplexity": 226.92639743186146,
"openwebmath_score": 0.688023567199707,
"tag... |
marine-biology, vestigial
Title: Modern Whales with Vestigial legs Myth? Is it a myth that modern whales have been found with hind legs sticking out of their sides and full formed tibias, fibias, and toe bones? I keep finding assertions, but no citations. For example, the wikipedia page has no citation for it.
http://... | {
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"id": 1521,
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"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "marine-biology, vestigial",
"url": null
} |
discrete-signals, sampling
Title: Examples of digital signals occurring in Nature In Chapter 1 of Oppenheim & Schafer's Digital Signal Processing, the authors state that not all discrete-time signals are the result of sampling continuous-time signals, and thus they are making the choice not to "force results from anal... | {
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"id": 12104,
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"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "discrete-signals, sampling",
"url": null
} |
haskell, recursion
Title: Naïve optimization by stepping until the error falls below a threshold As an exercise, I wanted to rewrite this toy Python code in Haskell:
def f(x):
return abs(42-x)**2
def improve(x):
newX = x + 0.1
return newX, f(newX)
def optimize(f, goal):
x = 0
err = f(x)
while... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "haskell, recursion",
"url": null
} |
simulation, laser, stage, ros-fuerte, pioneer
# load an environment bitmap
floorplan
(
name "cave"
size [16.000 16.000 0.800]
pose [0 0 0 0]
bitmap "cave.png"
)
# set the resolution of
# throw in a robot
my_block( pose [ 5 4 0 180.000 ] color "green")
define pioneer_base position
(
color "red" # Def... | {
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"id": 9511,
"lm_label": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "simulation, laser, stage, ros-fuerte, pioneer",
"url": null
} |
sql, sql-server, t-sql
IF @first_procstep_id IS NOT NULL
AND @procstep_config_id IS NOT NULL
BEGIN
IF @steps_ort_id BETWEEN 1 AND 7
SELECT @result = COALESCE((
SELECT TOP 1 c.Gehaeuse
FROM CompanyDB.dbo.Config AS c
INNER JOIN CompanyDB... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "sql, sql-server, t-sql",
"url": null
} |
algorithms
Sketch
USAGE = { # map day to number of opens for that day
"A": {0: 2, 1: 2, 2: 2, 3: 2, 4: 2},
"B": {0: 10, 1: 0, 2: 0, 4: 0},
"C": {0: 0, 1: 3, 2: 3, 4: 3},
"D": {0: 0, 1: 0, 2: 0, 3: 5},
"X": {0: 3, 1: 3, 2: 3, 3: 3, 4: 0},
"Y": {0: 0, 1: 0, 2: 0, 3: 0, 4: 3},
"Z": {0: 0, 1: ... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "algorithms",
"url": null
} |
### Show Tags
15 Dec 2017, 12:22
Bunuel wrote:
In the rectangular coordinate system above, if the equation of m is y = x, and m is parallel to n, what is the shortest distance between m and n?
(A) √2
(B) 1
(C) √2/2
(D) 1/2
(E) 1/4
[Reveal] Spoiler:
Attachment:
The attachment 2017-12-15_1259.png is no longer availab... | {
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"lm_q1_score": 0.9637799441350253,
"lm_q1q2_score": 0.8338856079221376,
"lm_q2_score": 0.865224072151174,
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"openwebmath_score": 0.7717209458351135,
"tags"... |
All other $$A_k$$ must not contain $$1$$ and must contain $$2$$ but not $$3$$. Thus wlog $$A_{n-3} = \{2 \} \cup [5, n]$$.
All other $$A_k$$ must not contain $$1$$ nor $$3$$, and must contain $$2$$ and $$4$$ (otherwise they are a subset of $$A_{n-3}$$). Thus wlog $$A_3 = \{2, 4, 5\}$$.
All other $$A_k$$ must contain ... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9830850897067341,
"lm_q1q2_score": 0.8060249136865121,
"lm_q2_score": 0.8198933359135361,
"openwebmath_perplexity": 177.3675552820519,
"openwebmath_score": 0.9907485842704773,
"tag... |
observational-astronomy, observable-universe, sky-survey, hydrogen, gas
Gas lit up in this way manifests itself as so-called Lyman α blobs, and shows you the "knot" part of the cosmic web. But recently, more filamentary structures have been observed to larger distances from the overdensities (Umehata et al. 2019). And... | {
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"openwebmath_score": null,
"tags": "observational-astronomy, observable-universe, sky-survey, hydrogen, gas",
"url"... |
# Real numbers $r$ and $1/r$ whose decimal representations contain the same digits
I was wondering idly this morning about real numbers $r$ with the property that the decimal representations of $r$ and $1/r$ both contain the same nonzero digits (not necessarily the same number of times or in the same order). Some obvi... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9875683498785867,
"lm_q1q2_score": 0.8186337227374787,
"lm_q2_score": 0.8289387998695209,
"openwebmath_perplexity": 204.1731042360283,
"openwebmath_score": 0.8220124244689941,
"tag... |
c++, beginner, makefile, sdl, make
Title: Makefile and object file directory Ok this is the first makefile I've ever written. I it works and that's about it. Things that I was wondering if if I can specify where the object files go. It looks really bad with all the .o files cluttering the working folder. I was thinkin... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c++, beginner, makefile, sdl, make",
"url": null
} |
java, performance
If it is anything different than this, then here's what I expect to see...
Unit tests verifying it produces the same result as the above code.
Unit tests verifying it is faster than the above code.
A pile of comments explaining the exact logic of this non-obvious approach (or as a minimum, a link to... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "java, performance",
"url": null
} |
python, scikit-learn, hyperparameter-tuning, grid-search, gridsearchcv
x = iris.drop('species', axis=1)
y = iris.species
max_depths = [5, 10, 15]
scores = []
for i in range(len(max_depths)):
rfc = RandomForestClassifier(max_depth=max_depths[i])
scores.append({'max_depth':max_depths[i], 'scores':[]})
for... | {
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"id": 5872,
"lm_label": null,
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"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "python, scikit-learn, hyperparameter-tuning, grid-search, gridsearchcv",
"url... |
performance, php, array, json
$_POST['otherdata']='otherdata';
//Execution of Function hover $_POST Variable.
$_POST=buildVirtualData($_POST);
$_POST=reduArray($_POST);
echo var_dump($_POST); | {
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"id": 39044,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "performance, php, array, json",
"url": null
} |
quantum-field-theory, hilbert-space, operators, mathematical-physics
They are not enough even for flat spacetime. They are enough in both cases as far as you restrict your interest to the free theory. As soon as you switch on a quantum interaction the $C^*$ formalism turns out to be insufficient to describe the obser... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "quantum-field-theory, hilbert-space, operators, mathematical-physics",
"url": nu... |
meteorology, snow, radar
Radar beams increase in height with distance from the radar. They really don't tell you what is actually happening at the ground, but instead up at some height aloft... this may mean that, especially further from the dish, light precipitation shown on radar can actually be evaporating before ... | {
"domain": "earthscience.stackexchange",
"id": 1293,
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"lm_q1q2_score": null,
"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "meteorology, snow, radar",
"url": null
} |
PART-I: I would like to provide the general proof considering the title of the question and imposing no specific properties on the signal $$x(t)$$ other than having a CTFS representation.
The following is a simple analysis to conclude that the CTFS coefficients of any signal $$x(t)$$ and that of the DC removed signal ... | {
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"lm_q1_score": 0.9763105307684549,
"lm_q1q2_score": 0.8883517884371317,
"lm_q2_score": 0.9099070023734244,
"openwebmath_perplexity": 743.008559337098,
"openwebmath_score": 0.9961004853248596,
"tags... |
ros, moveit, movegroup
/opt/ros/hydro/include/moveit/move_group_interface/move_group.h:69:7: note: candidate expects 1 argument, 0 provided | {
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"id": 19740,
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"openwebmath_score": null,
"tags": "ros, moveit, movegroup",
"url": null
} |
quantum-mechanics, schroedinger-equation
I understand the idea: if the probability decreases in any region, it must flow outside, so that the total probability is always one. But how such a flow relates to the vector difference in the brackets?
I mean: the left side is a known subject, the square of the wave function... | {
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"tags": "quantum-mechanics, schroedinger-equation",
"url": null
} |
special-relativity, inertial-frames
&&&&\\
&(\gamma-1)s_{31}s_{11}&\ \ (\gamma-1)s_{31}s_{21}\ \ &1+(\gamma-1)s_{31}^{2}&
\end{bmatrix}\\
&\\
& \stackrel{(B-12)}{=}
\begin{bmatrix}
&1+(\gamma-1)n_1^{2}&\ \ (\gamma-1)n_1n_2\ \ &(\gamma-1)n_1n_3&\\
&&&&\\
... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "special-relativity, inertial-frames",
"url": null
} |
electric-circuits, electric-current, electrical-resistance, voltage, batteries
Title: Voltage drop across battery with internal resistance Consider a battery with internal resistance connected to an external voltage source; there is a voltage difference along the battery
The voltage source is not drawn in the pictur... | {
"domain": "physics.stackexchange",
"id": 50098,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "electric-circuits, electric-current, electrical-resistance, voltage, batteries",
... |
quantum-spin, fermions, hamiltonian, pauli-exclusion-principle
Title: How would Hamiltonian for several fermions with spin look? All discussions of Pauli exclusion principle I read usually talked about antisymmetric wavefunctions, from which the princinple appears. But I would like to see a Hamiltonian for multiple fe... | {
"domain": "physics.stackexchange",
"id": 12915,
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"lm_q1_score": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "quantum-spin, fermions, hamiltonian, pauli-exclusion-principle",
"url": null
} |
noise, snr
subplot(312)
plot(sigma_N_t)
xtitle('$\mbox{\rm Level of noise,}\ \sigma$')
subplot(313)
plot(s_N_t, 'r')
xtitle('$\mbox{\rm Signal to noise ratio,}\ SNR$') | {
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"id": 3055,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "noise, snr",
"url": null
} |
molecular-biology, cell-biology
This rate decreases dramatically as radius of the cell increases. For example a cell with double the diameter (2 micrometers) has a volume eight times larger, so collisions between any two molecules take 8 times ($2^3$) as long to occur (in other words, it takes molecules 8 times longer... | {
"domain": "biology.stackexchange",
"id": 5584,
"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": "molecular-biology, cell-biology",
"url": null
} |
algorithm-analysis, probability-theory
Title: Why is adding log probabilities faster than multiplying probabilities? To frame the question, in computer science often we want to calculate the product of several probabilities:
P(A,B,C) = P(A) * P(B) * P(C)
The simplest approach is simply to multiply these numbers, and ... | {
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"id": 9226,
"lm_label": null,
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"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "algorithm-analysis, probability-theory",
"url": null
} |
standard-model, quantum-anomalies, effective-field-theory, hadron-dynamics
$$
where $L_{i} \equiv U\partial_{i}U^{-1}$ and $U$ is the goldstone bosons matrix.
Since $U$ here acts in 5-dimensional manifold, there is no direct way to gauge the Wess-Zumino term by simple elongation of derivative. However, we know the exp... | {
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"id": 28411,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "standard-model, quantum-anomalies, effective-field-theory, hadron-dynamics",
"ur... |
thermodynamics
Title: Calculating enthalpy per gram mole of oxygen bond in haemoglobin
A solution of $\pu{5 g}$ of haemoglobin in $\pu{100 cm^3}$ of solution shows a temperature raise of $\pu{0.031 ^\circ C}$ for complete oxygenation. Each mole of haemoglobin binds $\pu{4 mol}$ of oxygen. If the heat capacity of the ... | {
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"id": 3877,
"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": "thermodynamics",
"url": null
} |
filters, lowpass-filter, infinite-impulse-response, c
...
f = 0.242: 0.782501
f = 0.250: 0.774971
f = 0.258: 0.767380
...
Aside from the inefficient code, is there something wrong with the method I am using to obtain the frequency response or am I interpreting the cut-off frequency relation incorrectly or something ... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "filters, lowpass-filter, infinite-impulse-response, c",
"url": null
} |
vcf, genomics
##GATKCommandLine=<ID=Mutect2,CommandLine="Mutect2 --alleles /add/2024-03-04_force_mutect/E200K.vcf.gz --output /add/2024-03-04_force_mutect/output//Ctrl4_E200K_frequency.vcf --intervals /add/2024-03-04_force_mutect/E200K.vcf.gz --input /add/2023-06-18_CJD_16_samples/312092_15-Ctrl4_H01_S11_R1_001.fastq.... | {
"domain": "bioinformatics.stackexchange",
"id": 2669,
"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": "vcf, genomics",
"url": null
} |
As for the exercise which prompted this question, proving that there exists some $n$ such that $n,n+1,n+2,\dots,n+200$ are all composite consider the following:
Suppose we want to force each $n+i$ to be composite. If we want to force $2\mid n$ and $3\mid (n+1)$ and $5\mid (n+2)$, etc... that would correspond to the sy... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.977022627413796,
"lm_q1q2_score": 0.8605586784015001,
"lm_q2_score": 0.8807970811069351,
"openwebmath_perplexity": 136.67351527536294,
"openwebmath_score": 0.7182556390762329,
"tag... |
quantum-field-theory, feynman-diagrams, spinors, helicity
(-)-gauge boson
$\epsilon^\mu_-(k,r)=\frac{1}{\sqrt{2}}\frac{[k\gamma^\mu r\rangle}{\langle rk\rangle}$
$\epsilon^{\mu\ast}_-(k,r)=-\frac{1}{\sqrt{2}}\frac{[r\gamma^\mu k\rangle}{[rk]}$
Here, $r$ shall be an arbitrary reference momentum with $r^2=0,rk\neq0$, a... | {
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"id": 76339,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "quantum-field-theory, feynman-diagrams, spinors, helicity",
"url": null
} |
physical-chemistry, quantum-chemistry, redox, bond, ions
For instance, assume two helium atoms approaching each other. When they get closed to each other, the electrostatic attraction force between the nucleus of first $\ce{He}$ atom with two positive charges and the two electrons in the second atom causes each atom t... | {
"domain": "chemistry.stackexchange",
"id": 15178,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "physical-chemistry, quantum-chemistry, redox, bond, ions",
"url": null
} |
java, beginner, calculator, swing, finance
panel.add(new JLabel("Total Interest Payments"));
panel.add(new JLabel("Month where principal payments > interest"));
panel.add(this.totalInt);
panel.add(this.changeMonth);
return panel;
}
public JFrame getFrame() {
return fra... | {
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"tags": "java, beginner, calculator, swing, finance",
"url": null
} |
java, dynamic-programming, change-making-problem
There is another bug in your code: The for loop that introduces int subValue will only update coinChangeCounts for that subValue index if there is at least one coin with a value that is smaller than or equal to subValue. However, if there is no coin with a value of 1, t... | {
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"openwebmath_score": null,
"tags": "java, dynamic-programming, change-making-problem",
"url": null
} |
organic-chemistry, nomenclature
P-102.3.4 Cyclic forms of monosaccharides
Most monosaccharides exist as cyclic hemiacetals or hemiketals. Two aspects of the internal cyclisation must be examined: first, the size of the ring, and secondly, the conformation of the newly created chirality center.
P-102.3.4.1 Ring size
Ou... | {
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"tags": "organic-chemistry, nomenclature",
"url": null
} |
# Math Help - Challenging "Find the Hashed Area" Question
1. ## Challenging "Find the Hashed Area" Question
See attached question. It asks: "A circle is inside a square, which is also found inside another square with with 6 meter sides. Find the hashed area".
Is the correct answer: 9pi/2 meters^2 or 9pi meters^2?
C... | {
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"tag... |
coding-theory
# plot diff
plot(range(1, p), [a-b for a, b in zip(mp, lb)])
xlabel('p')
ylabel('m')
show() There is an additional lower bound we can build, that will address cases like what @user3017842 mentioned in their comment on Yuval's answer. (Cases where $p$ is particularly small.) Suppose we knew $m$ al... | {
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"openwebmath_score": null,
"tags": "coding-theory",
"url": null
} |
python, python-3.x
print("Order Summary:")
print('Bread type: %s \t %f', choosed_bread,bread_price)
print('Protein type: %s \t %f', choosed_protein,protein_price)
print('Cheese type: %s \t %f', choosed_cheese,cheese_price)
print('Add-on type: %s \t %f', choosed_add_ons,add_on_price)
print('Total price: \t %f', total_p... | {
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"tags": "python, python-3.x",
"url": null
} |
$$\Re\left( Ae^{iat}\left(1+\frac{A}{B}e^{i(b-a)t}\right)\right)$$
I've had a go, but I just can't manage to manipulate the result into the form I want.
4. Nov 30, 2007
### Ben Niehoff
You don't need to take the real part, actually. You can draw all the necessary conclusions from the formula as it is. In particular... | {
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"openwebmath_perplexity": 641.5491739145629,
"openwebmath_score": 0.682317852973938,
"tags"... |
# Describing points in the complex plane
When describing sets of points in the complex plane such as $$|2z-i| =4$$ would it be correct to describe the set exactly as we would in the $$x,y$$ plane?
For instance, Letting $$z=x+iy$$ for some $$x,y \in \mathbb{R}$$
yields the equation $$x^2+(y-\frac{1}{2})^2=4$$
And wo... | {
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"lm_q2_score": 0.8376199633332891,
"openwebmath_perplexity": 156.99837525279648,
"openwebmath_score": 0.9050506353378296,
"ta... |
physical-chemistry, kinetics
\begin{align}
\frac{\Delta [\ce{A}]}{\nu_{\ce{A}}} = \frac{\Delta [\ce{B}]}{\nu_{\ce{B}}} = \frac{\Delta [\ce{C}]}{\nu_{\ce{C}}} \ .
\end{align}
Finally, if you divide now by the reaction time $\Delta t$ and use the values for the stoichiometric coefficients, you get the equations from y... | {
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"tags": "physical-chemistry, kinetics",
"url": null
} |
Therefore, the degree of $$P_k$$ is equal to $$1 + \sum_{\substack{ p \, \in \, \mathtt{PRIMES}\\ p \leq k }} (p - 1).$$
Further, we get that the degree of $$P_k \sim \frac{k^2}{2 \log k}$$ by applying results from: What is the sum of the prime numbers up to a prime number $n$?
We have that $$dim(V) = n$$ precisely w... | {
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"lm_q2_score": 0.8558511506439707,
"openwebmath_perplexity": 318.32853433815245,
"openwebmath_score": 0.8228177428245544,
"ta... |
to the right of the following as rational or irrational: 1 far verify..., [ latex ] \sqrt { 36 } =6 [ /latex ] therefore [ latex ] \sqrt { }... All closely related you remember what the difference is among these types of numbers you! You need any other stuff in … Transcript squares of whole numbers, you must be a geniu... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9890130554263733,
"lm_q1q2_score": 0.8834946686344102,
"lm_q2_score": 0.8933094096048377,
"openwebmath_perplexity": 396.32674951472035,
"openwebmath_score": 0.7736655473709106,
"tags": null,
... |
graphs, shortest-path
Title: shortest path tree algorithm Suppose we are given a directed weighted graph $G=(V,E)$, a source vertex $s$ and the value of the cheapest path $\delta(s,v)$ for every $v \in V$.
I want to find an algorithm for the shortest path tree rooted in $s$ with time complexity of $O(V+E)$.
We may as... | {
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"openwebmath_score": null,
"tags": "graphs, shortest-path",
"url": null
} |
navigation, odometry, gps, navsat-transform-node, ekf-localization
Navsat data. This is typically obtained from a GPS device.
The robot's orientation in an earth-fixed frame. navsat_transform_node first converts lat/lon coordinates to UTM coordinates, and then transforms them into your robot's local frame. In order to... | {
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"tags": "navigation, odometry, gps, navsat-transform-node, ekf-localization",
"url": nul... |
• Moreover, this can prove that $\frac{1}{i}+\sum_{n=1}^{i}\frac{1}{n^2}$ is an upper bound to the sequence for any $i$ (which yields arbitrarily tight bounds) – Milo Brandt Nov 1 '14 at 0:15
• Shouldn't the rigth side summation to infinity diverge? – Guerlando OCs Nov 1 '14 at 0:15
• No: we get a telescoping series – ... | {
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"lm_q2_score": 0.8418256412990658,
"openwebmath_perplexity": 465.04885171683827,
"openwebmath_score": 0.916891872882843,
"tag... |
urdf, xacro, ros-kinetic
but RVIZ, it works and shows the model without errors
this is my code :
<?xml version="1.0"?>
<robot xmlns:xacro="http://www.ros.org/wiki/xacro" name="pan_tilt">
<xacro:property name="base_link_length" value="1" />
<xacro:property name="base_link_radius" value="2" />
<xacro:property name... | {
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"id": 34664,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "urdf, xacro, ros-kinetic",
"url": null
} |
proteins, western-blot
However, here come the hidden assumptions: this is all assuming that (i) you are not experiencing significant protein loss during your preparation steps, that (ii) your antibodies are good (specific and yield the complete protein extract), that (iii) the blotting procedure is performed correctly... | {
"domain": "biology.stackexchange",
"id": 11288,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "proteins, western-blot",
"url": null
} |
javascript, node.js
const ref = obj.expires_secs
const expires_secs = ref != null ? ref : this.expires_secs
await this.mark_installed(obj.uuid)
const val = `${obj.ip}_${obj.port}_${obj.relay_ip}_${obj.relay_port}`
return redis.setex(`${this.prefix}:${obj.uuid}`, expires_secs, val)
}
// Usage
active.ping(ob... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "javascript, node.js",
"url": null
} |
discrete-signals, continuous-signals
Title: Comparing 2 sinusoids: Discrete case vs Continuous case I'm doing MIT's OCW course with Allan Oppenheim - "Signals and Systems".
I'm given 2 continuous signals$$x(t)=\cos[\omega_x(t+r_x)+\theta_x]\tag1$$ and $$y(t)=\cos[\omega_y(t+r_y)+\theta_y]\tag2$$
Assuming their phases ... | {
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"tags": "discrete-signals, continuous-signals",
"url": null
} |
# Documentation
### This is machine translation
Translated by
Mouseover text to see original. Click the button below to return to the English verison of the page.
# sinc
## Syntax
``````y = sinc(x)``````
## Description
example
``````y = sinc(x)``` returns an array, `y`, whose elements are the sinc of the elemen... | {
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"tags": ... |
The last line shows we are guaranteed to have a solution if $n (\log_2 13 - \log_2 12) \geq 1$. (Any interval of length at least $1$ contains at least one integer.) This says there is a choice of $m$ for all $n \geq \dfrac{1}{\log_2 13 - \log_2 12} = 8.659\dots$. An exhaustive search will find a solution for $n = 9$ an... | {
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9715639636617015,
"lm_q1q2_score": 0.8258013570354114,
"lm_q2_score": 0.84997116805678,
"openwebmath_perplexity": 265.35974898983585,
"openwebmath_score": 0.9958269000053406,
"tags... |
Hello Mary Lou, Airbnb Kerry Dingle, Oman Currency 100 Baisa Equal To Bangladeshi Taka, First Hat-trick In World Cup, 2019 Washington Redskins, Bernardo Silva Fifa 21 Rating, Charlotte Hornets T-shirt Vintage, | {
"domain": "anemon.gr",
"id": null,
"lm_label": "1. YES\n2. YES\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9902915240915783,
"lm_q1q2_score": 0.875456613728082,
"lm_q2_score": 0.8840392878563336,
"openwebmath_perplexity": 640.4365673322267,
"openwebmath_score": 0.8737838268280029,
"tags": n... |
general-relativity, gravity, spacetime, time-dilation, observers
Title: Would time dilation increase the distance between objects? Two objects are moving towards a gravity well. They are at $x$ distance from each other and moving at a fixed speed. The gravity well is massive enough for the objects to experience signif... | {
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"tags": "general-relativity, gravity, spacetime, time-dilation, observers",
"url": null
} |
• @sasha Does this answer your question? – Norbert Schuch Jan 14 '15 at 13:55
In terms of the splitting $V=W\oplus W^{\perp}$, the projection operator $P_1=P=P_2$ and unitary operator $U$ are block diagonal
$$P ~=~ \begin{bmatrix} {\bf 1} & {\bf 0} \\ {\bf 0} & {\bf 0}\end{bmatrix}$$
and
$$U ~=~ \begin{bmatrix} U|_... | {
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"lm_q2_score": 0.8311430520409023,
"openwebmath_perplexity": 195.0223395328785,
"openwebmath_score": 0.9067228436470032,
"tag... |
joystick
Title: Handle Linear and Angular Velocity on Differential Drive Robot
Hi guys ,
I have some question about the cmd_vels ( linear , angular) -> Motor Speed Handling
since i have the differential drive robot which each wheel can do the maximum speed at 0.25 m/s
( So, Ideally, MAX Linear Velocity of Robot = 0.2... | {
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"openwebmath_score": null,
"tags": "joystick",
"url": null
} |
cc.complexity-theory, reference-request, time-complexity, space-complexity
Title: The hardness of generating an instance of a problem that is harder than the complexity of the resulting problem
In the movie Inception Cobb asks a asks Ariadne to design a maze that takes twice as much time to design. This lends itself... | {
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"tags": "cc.complexity-theory, reference-request, time-complexity, space-complexity",
"ur... |
homework-and-exercises, magnetic-fields, schroedinger-equation, eigenvalue
b) Once you have the eigenstates and eigenvalues of the Hamiltonian, you can write down an equation of motion for the eigenstates by solving the time dependent Schrodinger equation for them. Then, you can find a representation of the initial st... | {
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"tags": "homework-and-exercises, magnetic-fields, schroedinger-equation, eigenvalue",
"ur... |
frequency-spectrum, frequency
Title: How to make frequency axis for even and odd FFT length? Can I get help on how to make frequency axis going from negative frequency to positive frequency, (in Hertz), that will be the x-axis in an FFT result, but given either an even length FFT, or odd length FFT. I am having some t... | {
"domain": "dsp.stackexchange",
"id": 382,
"lm_label": null,
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"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "frequency-spectrum, frequency",
"url": null
} |
performance, sql, sql-server
Title: SQL query with nested subqueries The following query is taking over 800ms to run, and returning 300 rows. When deployed to SQL Azure, it takes much longer on an affordable price tier.
SELECT
Tests.Id,
Tests.Title,
Tests.AuthorId,
Tests.[Status],
Users.FirstName +... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "performance, sql, sql-server",
"url": null
} |
computability, time-complexity
Title: Is there an algorithm which can compute every algorithm's time complexity? I think of an algorithm which computes the time complexity. It would be great if a code editor could compute the time complexity of the selected lines and even compare two pieces of codes in order to help d... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "computability, time-complexity",
"url": null
} |
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