text stringlengths 49 10.4k | source dict |
|---|---|
b) For this part I used $$I=\frac{1}{3}ML^{2}+mL^{2}$$, since one ball is on the axis of rotation and does not contribute to the moment of inertia. The answer I got:
$$I=\frac{1}{3}(4.00kg)(2.00m)^{2}+(.500kg)(2.00m)^{2}=7.33 kgm^{2}$$
c) Zero, since the rod/balls are not given a radius; their distance from the axis o... | {
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• @user419669: The whole idea of RREF works with numbers (or elements of a field), but not necessarily with functions which do not form a field because we can't always divide by a function. For example, imagine $I=(-2,2)$, and you have $x^2$ in the upper-left corner of the Wronskian. It's a non-zero element as a functi... | {
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Complex Analysis: Liouville's theorem Proof
I'm being asked to find an alternate proof for the one commonly given for Liouville's Theorem in complex analysis by evaluating the following given an entire function $f$, and two distinct, arbitrary complex numbers $a$ and $b$: $$\lim_{R\to\infty}\oint_{|z|=R} {f(z)\over(z-... | {
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"lm_q2_score": 0.8267117983401363,
"openwebmath_perplexity": 366.3043084407449,
"openwebmath_score": 0.8780144453048706,
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rosjava, android
Title: Building Android App Chooser with ROSJava
Is it currently possible to build android_app_chooser from source on fuerte?
Does it use the current build of ROSJava or does it need the JNI-based Java client library?
Should we just wait until the new version of ROSJava is a bit more stable?
Origina... | {
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# What is the difference between the dot product and the element-by-element multiplication?
What is the different between the dot product "$$\cdot$$" and the element-by-element multiplication notation $$\odot$$ in Statistics? I referred to Hamilton's Time-Series Analysis, and these seem to have the same definition. Fo... | {
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standard-model, representation-theory, quantum-chromodynamics, quarks
$$
\delta q^i_\alpha = i \phi_M \tau^M_{ij} q^j_\alpha ~,
$$
where Γ, Μ are the color, weak respective adjoint indices.
Representing these as as 6×6 matrices, you may either stick the τ blocks in each entry of the 3D identity for a weak isorotat... | {
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"url": n... |
Example, and comparison with OP's biSection:
Needs["GeneralUtilities"];
func[t_?NumericQ] := 1 + NIntegrate[Sin[x^2] - x, {x, 0, t}];
(op = biSection[func, {1, 2.20}, 10^-14]) // AccurateTiming
(me = biSection2[func, {1, 2.20}, 10^-14]) // AccurateTiming
op - me
(*
0.530108
0.186535
{0.*10^-20, 0.*10^-20}
*)
### 2... | {
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"openwebmath_score": 0.2574217617511749,
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c++, performance, collections, skip-list
if (!node_added) // case new node could not be added if new key == key in table
delete new_node;
}
bool Skiplist::erase(int key)
// starts search on the highest lvl of the skiplist
// if a node with the erase key is found the algo... | {
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"tags": "c++, performance, collections, skip-list",
"url": null
} |
optics, waves, electromagnetic-radiation, visible-light, lenses
Title: Paraxial Rays and Coma In these slides it is stated that:
Coma is an abberration that afflicts off-axis light bundles in a
similar manner to the way in which spherical aberrations affects the
axial bundles.
About Coma, my questions are:
1) Does i... | {
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thermodynamics, pressure, entropy
How can one reach such conclusion using the characteristic equation in terms of entropy?
$$dS=(1/T)dU+(p/T)dV-(μ_B/T)dn_b$$
and lets assume there is no change in molecular mass, so we use only the first 2 clauses.
Can we prove, without making any other assumptions like ideal gas or ot... | {
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"tags": "thermodynamics, pressure, entropy",
"url": null
} |
quantum-mechanics, solid-state-physics, discrete
I am looking for a general way to do this process.
I have read some articles that lead me to pessimistic conclusions that this might be complicated, for example Wilkinson (1998). You do not necessarily need Bloch states with the full translational symmetry to construct ... | {
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"tags": "quantum-mechanics, solid-state-physics, discrete",
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} |
gazebo-9
Set a finite minimum allowable interpenetration depth (min_depth) of 0.001 [m] (more generally a small value relative to the scale of the colliding objects. [Source]
If that doesn't make a difference, you may also try decreasing the physics simulation step size to get a better solution as explained here. Thi... | {
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____________________________________________________________________
$\copyright \ 2017 \text{ by Dan Ma}$
# kappa-Dowker space and the first conjecture of Morita
Recall the product space of the Michael line and the space of the irrational numbers. Even though the first factor is a normal space (in fact a paracompact... | {
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# Die roll, value of 4 must follow value of 1 to win
I came across a "die roll" probability question that has me stumped.
Two fair die are being rolled by players A and B, who alternate, with A rolling first (ie. A then B then A then B...so long as the game hasn't been won). In order to win the game, a player must ro... | {
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"openwebmath_score": 0.9125372171401978,
"tags"... |
$$B=2mk\implies k=\frac{B}{2m}\qquad\text{for}\qquad \bigg\lfloor \frac{1+\sqrt{2B+1}}{2}\bigg\rfloor \le m \le \frac{B}{2}$$ The lower limit ensures $$m>k$$ and the upper limit ensures $$m>1$$ $$B=52\implies\qquad \bigg\lfloor \frac{1+\sqrt{105+1}}{2}\bigg\rfloor =5 \le m \le \frac{52}{2}=26\\ \text{and we find} \quad... | {
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"lm_q2_score": 0.8333245932423308,
"openwebmath_perplexity": 273.90307318156545,
"openwebmath_score": 0.6703463196754456,
"ta... |
electrochemistry, redox
Title: Cell notation of all aqueous solutions If some redox reaction happened with no solid anode or cathode, like all aqueous solutions, something like the unbalanced reaction
$$
\ce {MnO4^- (aq) + C2O4^-^2 (aq) -> Mn^+^2 + CO2 (aq)}
$$ What would an electrochemical cell notation represent in... | {
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lua
end
end
Where
db = The "Setting" table
SetChecked(enable) = True to check the button; false to uncheck (boolean)
SetText("text") = Text to be placed in the edit box (string)
Could you help me to make the code less repetitive and more clean and elegant? On a cursory glance, you can change the statement:
if (enab... | {
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If we express the same transfer function $H(z)$ in terms of its poles we get
$$H(z)=k\frac{1-z^{-2}}{\left(1-re^{j\omega_p}z^{-1}\right)\left(1-re^{-j\omega_p}z^{-1}\right)}= k\frac{1-z^{-2}}{1-2r\cos(\omega_p)z^{-1}+r^2z^{-2}}\tag{2}$$
where $k$ is some gain constant to be determined, $0<r<1$ is the pole radius, and... | {
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# In how many ways can I select 4 groups from 10 indistinguishable items where each selected group only contains either 0 or an odd number of items
If this question asked instead to select groups of even number of items, then I know how to approach it.
The even approach is: there is a bijection to a sequence of 8 bit... | {
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# Ratio of areas determined by a square inscribed in the corner of a right triangle
I’m having trouble working out how to algebraically get to the answer of this question. (See original image below.)
A square is drawn in the corner of a right-angled triangle with side lengths $a$, $b$, and [hypotenuse] $c$, as shown.... | {
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"tags... |
In any event, the quest for simplicity and clarity has pitfalls. Merely making something appear simple is not a sure path to understanding. Go deeper.
### Two Negatives Make a Positive
Why it's bad: It is a false statement. If I stub my toe and later hit my thumb with a hammer it is not a good thing, it is cumulative... | {
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"openwebmath_score": 0.5754119753837585,
"tags": n... |
c++, object-oriented, c++17, networking, web-services
class Connection {
public:
explicit Connection(Looper *looper, std::unique_ptr<Socket> socket);
};
You put so much effort into making Socket movable and now you are using a unique_ptr?
Both are viable strategies, but you should decide wich aproach you want to t... | {
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"tags": "c++, object-oriented, c++17, networking, web-services",
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} |
fourier-series, gibbs-phenomenon
Title: Gibbs phenomenon in Hamming's digital filters In 'Digital Filters' by Hamming there is a cryptic section where he describes how the Gibbs phenomenon can be viewed as the displacement between the centers of two functions as they are convolved together. This is on pages 112 - 113 ... | {
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"tags": "fourier-series, gibbs-phenomenon",
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ros, rosserial, parameters
Title: Parameter support in rosserial?
I'm developing a rosserial node for reading some sensor values, and I was hoping to pull in a few parameters. There seems to be support in the code, and there's an old documentation page here (which isn't actually linked-to from the main documentation)... | {
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= 1, we have a/d = 1. All four corresponding sides of two parallelograms are equal in length that does mean that they are necessarily congruent because one parallelogram may or may not overlap the other in this case because their corresponding interior angles may or may not be equal. If two squares have equal areas, th... | {
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"t... |
Note that introducing the "imaginary" triangular portion below the base of the trapezoid doesn't affect the analysis because when you take the derivative of the area, the constant area of that portion vanishes.
If you find the above hard to imagine, you can work out the actual area of the fluid filled cross-section of... | {
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"openwebmath_score": 0.8024490475654602,
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python, ai, neural-network
def test(nodes, tset):
for i,t in tset:
nodes[0].input = i[0]
nodes[1].input = i[1]
for n in nodes:
n.evaluate()
output_nodes = [node for node in nodes if len(node.output_map) == 0]
first = min(node.node_index for node in output_nodes... | {
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terminology-and-notation
But - sorry to contradict you - "multiple-controlled" does sound wrong to me! Even so, it's still perfectly clear what the phrase means, so my discomfort with it is really just a manifestation of linguistic puritanism. ;)
One More Note
Please note that the adverb "multiply", pronounced "mul-ti... | {
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quantum-mechanics, homework-and-exercises, momentum, potential-energy, wavelength
and then I'm in doubt whether I was correct to have dropped the coefficient $C$ above in my derivations of equations.
You're entirely correct to drop $C$ ($C=0$) for bound particles but note that not doing so wouldn't make $\psi(x)$ Com... | {
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f#, coordinate-system
EDIT: Answers to your questions:
Normally, you can't have a module and a type with the same name within a certain namespace, but the [<CompilationRepresentation(...)>] attribute I used adds "Module" to the name of the compiled module type. So in this case, the Direction module would be compiled ... | {
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lambda-calculus
$$
You want to show that $ h^\star = h$. To do that just take any two arguments $a$ and $b$. First evaluate $h^\star$ in $a$.
$$ h^\star(a) = (\lambda x. (\lambda y. x - y))(a) = \lambda y. a - y$$
This gives you a simpler one argument function $h^\prime = h^\star(a)$. | {
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quantum-mechanics, electromagnetism, classical-mechanics, energy, hamiltonian
$$
\mathbf{A} = B(0, x, 0)
$$
then $p_y$ would be conserved but $p_x$ would not be.
So, at the end of the day, this modification to the momentum allows for it to be conserved when $\mathbf{A}$ has a symmetry, but there's still an ambiguity b... | {
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... |
quantum-field-theory, condensed-matter, solid-state-physics, phonons, higgs
Finally, Phonons of various polarizations are often described as having an effective mass around certain critical points in the Brillouin zone, and can gain it around $\Gamma$ due to interactions with other excitations, but neither of these di... | {
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Combinatorial identity: $\sum_{i,j \ge 0} \binom{i+j}{i}^2 \binom{(a-i)+(b-j)}{a-i}^2=\frac{1}{2} \binom{(2a+1)+(2b+1)}{2a+1}$
In my research, I found this identity and as I experienced, it's surely right. But I can't give a proof for it. Could someone help me? This is the identity: let $a$ and $b$ be two positive int... | {
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"openwebmath_score": 0.8715867400169373,
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regression, statistics
Title: Diff. in P-value & F-Stat. Multiple linear regression Even if we have individual p-values for each predictor.
Why do we need overall F-statistic?
I read this solution but I am not sure if I get it right. Can someone please explain?
Source: "An Introduction to Statistical Learning: with... | {
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a regular polygon. Then click enter or “Calculate” button. = 3/ (2 * 0.999) The Evaluate Polygon Perimeter and Area check finds polygon features based on the area or perimeter of the entire polygon or its individual parts or segments. The figure below shows a regular octagon. AREA_GEODESIC — The shape-preserving geodes... | {
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"tags":... |
# Normal Distribution And Standard Deviation Pdf
File Name: normal distribution and standard deviation .zip
Size: 15117Kb
Published: 18.05.2021
In this lesson, we'll investigate one of the most prevalent probability distributions in the natural world, namely the normal distribution.
The NORM. For example, NORM. DIST... | {
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python, python-3.x, validation, e-commerce, checksum
First2 = CheckNumberStr[0] + CheckNumberStr[1]
#---------------------------------------------------------------------------#
if len(CheckNumberStr) > 12 and len(CheckNumberStr) < 17 :
# "Visa Card" Checking
if CheckNumberStr[0] == "4" :
CheckBool = C... | {
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"tags": "python, python-3.x, validation, e-commerce, checksum",
"url": null
} |
quantum-mechanics, hilbert-space, operators, notation, quantum-states
\langle n | \hat a^\dagger&= \big (\sqrt n|n-1\rangle \big)^\dagger\\
\langle n | \hat a^\dagger&= (\sqrt n)^* \ \langle n-1| \\
\langle n | \hat a^\dagger&= \sqrt n \ \langle n-1| \ \ \forall n\in \Re
\end{aligned}$$
More generally, the equality
$... | {
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"url": n... |
ros-melodic, ros-kinetic
ROS_IP is the IP of pi in /etc/hosts:
127.0.0.1 localhost
127.0.1.1 art
10.42.0.216 pi
I just added it to be sure. This works fine as well:
pc$ ssh pi@pi
pi$ ssh art@rosmaster
iptables on both systems:
pi# iptables -L
Chain INPUT (policy ACCEPT)
target prot opt sour... | {
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"tags": "ros-melodic, ros-kinetic",
"url": null
} |
cc.complexity-theory, linear-equations
Title: Complexity of solving linear equations What is known about the complexity of solving a system of linear equations over some finite field? I know that there exists an $O(n^3)$ algorithm (Gauss) that computes a solution and that for sparse systems there are even better algor... | {
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"tags": "cc.complexity-theory, linear-equations",
"url": null
} |
inorganic-chemistry, spectroscopy, molecular-structure, conformers
The answer given to this question is that conformer III is rotationally inactive.
However, what does it mean to be rotationally inactive? $\ce{H2O2}$ doesn't seem to have any steric effects that prevent it from rotating about the $\ce{O-O}$ bond. What ... | {
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"tags": "inorganic-chemistry, spectroscopy, molecular-structure, conformers",
"url": nu... |
c++, memory-management, c++17
friend std::ostream& operator<<(std::ostream&, const Storage&);
} storage;
std::ostream& operator<<(std::ostream& out, const Storage& storage) {
for (std::size_t i = 0; i < MEMSIZE; i++) {
out << (storage.free_[i] ? '*' : '_');
}
return out;
}
template<class T>
stru... | {
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"openwebmath_score": null,
"tags": "c++, memory-management, c++17",
"url": null
} |
star
Title: Is it possible that in the Local Interstellar Cloud there are undetected stars? The Local Interstellar Cloud is supposed to be around 30 light years large. Is it possible that in this region there are stars which are undetected? I would have thought that it wasn't possible, but there are stars which are ve... | {
"domain": "astronomy.stackexchange",
"id": 3517,
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"tags": "star",
"url": null
} |
atoms
Title: Why is the atomic mass unit less than the mass of both a neutron and a proton? The atomic mass unit is $1.6605 \times 10^{-27}$ kg.
This is less than the mean of the masses of 6 protons and 6 neutrons.
How do we account for the lower mass ?
My understanding is that some of the mass is in the form of energ... | {
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python, beginner, python-3.x, playing-cards
then when it comes to using it, just do:
return some_dict[condition]
You can also add a default value for when the conditions isn't handled by the dictionary: return some_dict.get(condition, default=None).
Class instead of globals:
The simplest example is to put the global ... | {
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"tags": "python, beginner, python-3.x, playing-cards",
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gazebo
Title: Gazebo simulation stopping after some time while using reinforced learning
Hi, I encounter a problem while using the gym-gazebo package. After running the example simulations the simulation ...pauses? The issue is like the ones described in issue 49 and issue 47, but the fix provided in issue 47 (reinst... | {
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"tags": "gazebo",
"url": null
} |
organic-chemistry, physical-chemistry, biochemistry, alcohols
Title: Storage of Urine Not all may be favorable to this project, but I will explain what I am trying to do. I work at home, and instead of walking a moderate distance to the bathroom and loosing my focus, I've been, at times, peeing in a 3 Quart Poland Spr... | {
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In this case, using these finite differencing options does not improve the solution.
`disp([presnorm,presnorm2])`
``` 20.0637 20.0637 ``` | {
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c, linux, shell
What if you need to add another command to this list for whatever reason? Now, you could just add another if, but then your code starts to look a little more messy.
To make your code more flexible here, you could try splitting these built-in functions into a struct which stores the name of the built-i... | {
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$$\int_0^{n+1} x^q dx \geq \sum_{k=0}^{n} k^q = 1+ 2^q + \cdots n^q$$
The next part of the question that I am mostly stumped on is to find $\lim_{n\to \infty}a_n$ where $a_n= 1/{n^{q+1}}+2^{q}/n^{q+1}+…+n^{q}/n^{q+1}$. I'm sure I need to use the result of the first part of the problem but I am not sure where to begin.... | {
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"openwebmath_score": 0.9701794385910034,
"tag... |
c++, performance, sorting, quick-sort
The image above is for elements in range [0; 100], generator: std::random_device (hardware, since intel cpu and libc++)
The following one is for elements in range [0; 100'000], std::mt19937_64, default constructed.
Do note that comparing two images doesn't make much sense due to ... | {
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conformal-field-theory, stress-energy-momentum-tensor
$^{***}$ There are many normal ordering (or regularisation) prescriptions, such as 'conformal normal ordering' (CNO), 'Weyl normal ordering' (WNO), 'geodesic normal ordering' (GNO), 'dimensional regularisation' (DR), etc. The simplest prescription that I am aware o... | {
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"tags": "conformal-field-theory, stress-energy-momentum-tensor",
"url": null
} |
statics
Title: Included angle in a semicircle I'm solving this problem in mechanics,
Two cylinders A and B, weighing 100 lb and 200 lb respectively, are connected by a rigid rod curved parallel to the smooth cylindrical surface shown in Fig. P-329. Determine the angles α and β that define the position of equilibrium.... | {
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vba, excel, formatting
' Convert all cells from non-text to text
' This is helpful in a variety of ways
' Dates and datetimes can now be manipulated by replace, RegEx, etc., since their value is now 4/7/2001 instead of 36988
' Phone numbers and zip codes won't get leading zeros deleted if we try to... | {
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$$\therefore \Bigg|b_n - L \Bigg| \leq \Bigg| b_n - a_n \Bigg| + \Bigg| a_n - L \Bigg| < \frac{1}{n} + \frac{\epsilon}{2} < \frac{\epsilon}{2} + \frac{\epsilon}{2} < \epsilon$$
If we let $$N = max\{N_1, N_2\}$$
Correct reasoning?
• As a sketch - yes, it's a correct strategy. Probably you will need more formality and... | {
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"tags... |
programming-languages, compilers
Title: Can a dynamic language like Ruby/Python reach C/C++ like performance? I wonder if it is possible to build compilers for dynamic languages like Ruby to have similar and comparable performance to C/C++? From what I understand about compilers, take Ruby for instance, compiling Ruby... | {
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"tags": "programming-languages, compilers",
"url": null
} |
electromagnetism, electric-circuits, electric-fields, maxwell-equations, electromagnetic-induction
Title: Why is the closed line integral of $\oint \mathbf{E}\: d\mathbf{l}$ equal to $-d\Phi/dt$ and not $d\Phi/dt$? For example, in the case where there is a bar magnet moving through a loop of wire with some resistance,... | {
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"tags": "electromagnetism, electric-circuits, electric-fields, maxwell-equations, electroma... |
quantum-mechanics, hamiltonian-formalism, nuclear-magnetic-resonance
According to my notes however,
$$ H'=\frac{\hbar (\omega-\omega_0)}{2}Z-\frac{\hbar\omega_1}{2}X$$ which means I have made two mistakes: first, it should be $\sigma_\pm'=\sigma_\pm e^{\mp i\omega t}$, and second, there is a term $(\hbar\omega/2)Z$ I ... | {
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"url": nu... |
ros-kinetic, ubuntu, ubuntu-xenial
Originally posted by rfn123 with karma: 146 on 2020-08-19
This answer was ACCEPTED on the original site
Post score: 0
Original comments
Comment by gvdhoorn on 2020-08-19:
It could be this helped the OP, but for completeness: roslaunch does support launching .launch files not hosted ... | {
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now: y=2x+1 Clickable Demo Try entering y=2x+1 into the text box. So +1 is also needed; And so: y = 2x + 1; Here are some example values: Problem 2. In other words, if we can find two points that satisfies the equation of the line, then the line can be accurately drawn. Step 1: Find the y-intercept and plot the point. ... | {
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"openwebmath_score": 0.3519676923751831,
"tags": null,
... |
general-relativity, gauge-theory, gravitational-waves, degrees-of-freedom
Fourth, and it is related to the second point above, "charge conjugation" isn't any gauge principle of electromagnetism in any way. Electromagnetism is based on the continuous $U(1)$ gauge group. This group has an outer automorphism – a group of... | {
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"tags": "general-relativity, gauge-theory, gravitational-waves, degrees-of-freedom",
"url... |
Definition 4.21.1. Let $I$ be a set and let $\leq$ be a binary relation on $I$.
1. We say $\leq$ is a preorder if it is transitive (if $i \leq j$ and $j \leq k$ then $i \leq k$) and reflexive ($i \leq i$ for all $i \in I$).
2. A preordered set is a set endowed with a preorder.
3. A directed set is a preordered set $... | {
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"openwebmath_score": 0.8227077126502991,
"tags": n... |
logistic-regression, prediction, correlation
I would like to know if I can considerate Model2 an improvement of Model1 even if I have a p-value = 0.0 For the correlation problem, this basically sums up why I dislike univariate feature selection. Just because a feature has low correlation with your response in isolatio... | {
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Discover Resources parallelogram has adjacent angles as acute and,! Length of the triangles, both acute and obtuse are congruent ( 1 ) AC=24 //Given a if. ( diagonal x diagonal /2 ), or a rhombus the properties of the parallelogram the orange dots each! Students a day in preparation for their board … the diagonals of a... | {
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"openwebmath_score": 0.7164480686187744,
"... |
java, android
you check whether the savedInstanceState is null twice, and those two checks can be merged in to one...
you create a new FilterFragment instance, and you either add it to (if it is not there), or replace it (if there already was one). Thus, you have the filterFragement, and you do not need to findFragmen... | {
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"tags": "java, android",
"url": null
} |
ecology, mycology
Title: Is there an antagonistic association between Penicillium and Aspergillus? Some Aspergillus species appear to like walnuts. My question concerns the association of Penicillium and Aspergillus. No sooner does Aspergillus colonize a walnut (or some other challenging carbon source) than Penicilliu... | {
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"id": 4756,
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"openwebmath_score": null,
"tags": "ecology, mycology",
"url": null
} |
camera
The pylon_camera pkg does not support the Basler TOF-Camera
Originally posted by Marcel Debout with karma: 26 on 2016-07-21
This answer was ACCEPTED on the original site
Post score: 1
Original comments
Comment by est_CEAR on 2016-07-21:
Really? So why did it change with the MTU size? I still don't see the out... | {
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"tags": "camera",
"url": null
} |
analytical-chemistry, chromatography
Title: The Principle of Internal Standardization (in the context of ion chromatography) I am trying to grasp how internal standardization works in principle, and I am having some trouble wrapping my head around it. It is not the choosing of an IS I think about, orwhen it might bene... | {
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"tags": "analytical-chemistry, chromatography",
"url": null
} |
homework-and-exercises, newtonian-mechanics, potential-energy, explosions, estimation
speed of plane: 200 m/s
mass of plane: 100 tons
mass of fuel: 10000 US Gallons = 38000 L (see https://en.wikipedia.org/wiki/American_Airlines_Flight_11)
energy density of jet fuel: 35 MJ/L (see https://en.wikipedia.org/wiki/Jet_fuel)... | {
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"openwebmath_score": null,
"tags": "homework-and-exercises, newtonian-mechanics, potential-energy, explosions, estimat... |
np-hardness, linear-programming, polytope
Title: Complexity of Finding Largest Set of Intersecting Convex Polytopes I have a set of $n$ convex polytopes, and I wish to find the largest subset of those polytopes that shares at least one point in common. I think that this problem should be NP-hard, but I am struggling t... | {
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"id": 4692,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "np-hardness, linear-programming, polytope",
"url": null
} |
quantum-field-theory, s-matrix-theory, identical-particles
Title: LSZ Reduction formula and interacting identical particles I am studying the derivation of LSZ reduction formula on the book "A modern introduction to quantum field theory" by Maggiore. Here it is derived considering a single species of neutral scalar pa... | {
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"id": 67172,
"lm_label": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "quantum-field-theory, s-matrix-theory, identical-particles",
"url": null
} |
python, python-3.x, algorithm, programming-challenge, linked-list
______ ______ ______ ______ ______
| | | | | |
hash_map | 23 | 56 | 14 | 6 | 19 |
|______|______|____... | {
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"tags": "python, python-3.x, algorithm, programming-challenge, linked-list",
"url": nu... |
java, performance
If Anull and Bnull differ, run the simple check. If they are both false, run the complex check.
So use that!
if ((noteObjectFromUser.getStartDateTimestamp() == null)
!= (databaseNoteObject.getStartDateTimestamp() == null)) {
if (!noEdit) {
gantt = true;
}
noEdit = true;
} else ... | {
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "java, performance",
"url": null
} |
quantum-gate, linear-algebra
Those controlled operations $C$ and $V$ act on $(n+m)$-qubit space. You can consider first $n$ qubits as control register and last $m$ qubits as target register. Now, $C_n^j(U_{2^m})$ applies unitary operation $U_{2^m}$ on the target register if control register is in the state $|j\rangle... | {
"domain": "quantumcomputing.stackexchange",
"id": 693,
"lm_label": null,
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"openwebmath_score": null,
"tags": "quantum-gate, linear-algebra",
"url": null
} |
javascript, performance, react.js, react-native
newtext[37] += normal[indexed] + '̳';
newtext[38] += normal[indexed] + '̈';
newtext[39] += normal[indexed] + '̾';
newtext[40] += normal[indexed] + '͓̽';
newtext[41] += normal[indexed] + '̸';
newtext[42] += normal[indexed] + '҉ ';
newtext[43] += ... | {
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"id": 37905,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "javascript, performance, react.js, react-native",
"url": null
} |
thermodynamics, entropy, heat-engine
(Question 1) Where does the energy required for the compression come from?
This is supplied externally. After completing the cycle, the Carnot engine produces net work, but some work is needed to keep it going in some parts of the cycle. This can be done e.g. by using a motor with... | {
"domain": "physics.stackexchange",
"id": 32944,
"lm_label": null,
"lm_name": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "thermodynamics, entropy, heat-engine",
"url": null
} |
c++, performance, c++11, collections, skip-list
EXPECT_TRUE((std::is_same_v<typename Skip_list<K, V>::value_type, expected>));
}
TYPED_TEST_P(SkipListTypesTest, SizeTypeIsCorrect)
{
using K = std::tuple_element_t<0, TypeParam>;
using V = std::tuple_element_t<1, TypeParam>;
EXPECT_TRUE((std::is_integral_v... | {
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"openwebmath_score": null,
"tags": "c++, performance, c++11, collections, skip-list",
"url": null
} |
python, python-3.x, programming-challenge
def test8(self):
exp_8 = [["W","W","D","A","W","W","S","A","A"],
["A","D","D","A","D","D","D","A","A"],
["S","S","S","S","S","W","A","A","S"],
["W","W","W","D","D","S","W","S","D"]]
colours = ["W", "A", "S",... | {
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"tags": "python, python-3.x, programming-challenge",
"url": null
} |
Another example is expressions like $\displaystyle\lim_{h\to0}\frac{(x+h)^3-x^3}h=3x^3$. The value of this expression depends on the value of the free variable $x$, but not of the bound (or "dummy") variable $h$. We could have said $\displaystyle\lim_{k\to0}\frac{(x+k)^3-x^3}k=3x^3$ and it would still be $3x^2$. | {
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"id": null,
"lm_label": "1. YES\n2. YES",
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"lm_q1_score": 0.9814534398277177,
"lm_q1q2_score": 0.8644613096875166,
"lm_q2_score": 0.8807970654616711,
"openwebmath_perplexity": 215.07206600184705,
"openwebmath_score": 0.892816960811615,
"tag... |
special-relativity, lagrangian-formalism, variational-principle, action, geodesics
More importantly, the corresponding Euler-Lagrange (EL) equations for the action (B) are the null/light-like condition
$$ 0~\approx ~\frac{\delta S}{\delta\lambda}~=~\dot{x}^2, \tag{C}$$
and the geodesic equations
$$ 0~\approx ~-\fr... | {
"domain": "physics.stackexchange",
"id": 25489,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "special-relativity, lagrangian-formalism, variational-principle, action, geodesics... |
acid-base, redox, metal
The given answer is (C), $\ce{HNO3} $ but I don't understand why.
First off, what does it mean by reduction product -- is it the product that is formed when the acid is reduced in the redox reaction between the metal and the acid?
Second, why is the answer $\ce{HNO3} $? Whenever any metal is ad... | {
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"id": 960,
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"openwebmath_score": null,
"tags": "acid-base, redox, metal",
"url": null
} |
terminology, celestial-mechanics, thermodynamics
When the system has settled on $\ddot I =0$, and therefore $2K = - V$, the system is said to be virialized. The system as reached a particular kind of statistical equilibrium.
In astrophysics is important to know whether a system is virialized, because we usually want t... | {
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"id": 5851,
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"openwebmath_score": null,
"tags": "terminology, celestial-mechanics, thermodynamics",
"url": null
} |
asymptotics, combinatorics, upper-bound
$$
In turn, we can simplify this down to
$$
w(a, b) = b \times \frac{1}{1 - (b + ba)}
$$
This tells us that the language $w$ is isomorphic to the language $b(b \mid ab)^*$ (whose direct translation is already $\frac{b}{1 - b - ba}$) without ever having to resort to any language-... | {
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "asymptotics, combinatorics, upper-bound",
"url": null
} |
microcontroller, can
Title: Making high CAN baud rates work I'm dealing with a board that no matter what I do I can't seem to make CAN work over 125 kbit/s. I'll give some detail about the board on the bottom, but I'm going to keep this question generic.
First of all, regarding hardware. From what I've gathered, there... | {
"domain": "robotics.stackexchange",
"id": 256,
"lm_label": null,
"lm_name": null,
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"lm_q2_score": null,
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"openwebmath_score": null,
"tags": "microcontroller, can",
"url": null
} |
ros, roslaunch, sicktoolbox-wrapper
started roslaunch server http://constructor-pc:38491/
SUMMARY
========
PARAMETERS
* /robot_description: <?xml version="1....
* /rosdistro: indigo
* /rosversion: 1.11.21
* /sicklms/baud: 500000
* /sicklms/port: /dev/ttyUSB0
NODES
/
jimmy_state_publisher (j_robot_state_publisher/ji... | {
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"id": 29353,
"lm_label": null,
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"openwebmath_score": null,
"tags": "ros, roslaunch, sicktoolbox-wrapper",
"url": null
} |
quantum-mechanics, fourier-transform, superposition
Most simply, if you add two plane waves with different relative phases, you obviously get different functions:
$$e^{ikx}+e^{-ikx}=2\cos{kx}$$
but
$$e^{ikx}+e^{i\pi}e^{-ikx}=2i\sin{kx}$$
Cleaning up some misconceptions | {
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"id": 24569,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "quantum-mechanics, fourier-transform, superposition",
"url": null
} |
classical-mechanics, lagrangian-formalism
Title: Non-uniqueness of the Lagrangian Goldstein, 3rd ed
$$
\frac{d}{d t}\left(\frac{\partial L}{\partial \dot{q}_{j}}\right)-\frac{\partial L}{\partial q_{j}}=0\tag{1.57}
$$
expressions referred to as "Lagrange's equations."
Note that for a particular set of equations of mo... | {
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"id": 82003,
"lm_label": null,
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"tags": "classical-mechanics, lagrangian-formalism",
"url": null
} |
Let one woman complete the job in $$w$$ days and one man in $$m$$ days.
First equation:
It takes 6 days for 3 women and 2 men working together to complete a work:
As the rate of 1 woman is $$\frac{1}{w}$$ job/day, then the rate of 3 women will be $$\frac{3}{w}$$ job/day. As the rate of 1 man is $$\frac{1}{m}$$ job/day... | {
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"id": null,
"lm_label": "1. Yes\n2. Yes",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9678992932829918,
"lm_q1q2_score": 0.820747397779396,
"lm_q2_score": 0.8479677622198946,
"openwebmath_perplexity": 1275.580241492516,
"openwebmath_score": 0.6380464434623718,
"tags": nu... |
navigation, move-base, amcl
Title: Problem with Autonomous robot motion: amcl
My robot has been set up for autonomous motion using amcl & move_base from ROS navigation stack. The robot performs correctly using teleop; and the motors follow the velocity values published by move_base well enough. The problem is that, a... | {
"domain": "robotics.stackexchange",
"id": 24494,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "navigation, move-base, amcl",
"url": null
} |
mobile-robot, kinematics, matlab, geometry
For starters, some of your code uses variables that I didn't see mentioned anywhere, such as (confusingly) tk and kt. Furthermore, there are some magic numbers that I can't understand, such as the assignments for tk and kt - they're both set to 2 despite the comment beside tk... | {
"domain": "robotics.stackexchange",
"id": 1062,
"lm_label": null,
"lm_name": null,
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"lm_q2_score": null,
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"tags": "mobile-robot, kinematics, matlab, geometry",
"url": null
} |
# Maximum number of guaranteed coins to get in a “30 coins in 3 boxes” puzzle
There are a total of 30 gold coins in three wooden boxes (but you do not know how many in each individual box). However, you know that one box has exactly 4 coins more than another box.
For each box, you can ask for a number of coins from t... | {
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"id": null,
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"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.965899577232538,
"lm_q1q2_score": 0.83394958766458,
"lm_q2_score": 0.8633916064586998,
"openwebmath_perplexity": 474.9852205823485,
"openwebmath_score": 0.5937708616256714,
"tags":... |
In this case, `pchip` and `makima` have similar behavior in that they avoid overshoots and can accurately connect the flat regions.
Perform a second comparison using an oscillatory sample function.
```x = 0:15; y = besselj(1,x); xq2 = 0:0.01:15; p = pchip(x,y,xq2); s = spline(x,y,xq2); m = makima(x,y,xq2); plot(x,y,'... | {
"domain": "mathworks.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9830850906978876,
"lm_q1q2_score": 0.8170843406426309,
"lm_q2_score": 0.8311430499496096,
"openwebmath_perplexity": 1127.7523160579976,
"openwebmath_score": 0.8469887375831604,
"tags":... |
combinatorics, data-mining
$$
Indeed, either element $n+1$ is in a partition of its own, or it joins one of the other $k$ parts. The initial conditions are $\genfrac{\{}{\}}{0pt}{}{0}{0} = 1$ and $\genfrac{\{}{\}}{0pt}{}{0}{n} = \genfrac{\{}{\}}{0pt}{}{n}{0} = 0$ for $n > 0$. In other words, if $n = k = 0$ then there ... | {
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"id": 6438,
"lm_label": null,
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"lm_q1_score": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "combinatorics, data-mining",
"url": null
} |
electrostatics, electric-fields, metric-tensor, vector-fields, covariance
The idea is:
$$ \nabla F = \frac{\partial F}{\partial Z^i} e^i =( \frac{\partial F}{\partial Z^i} g^{i \alpha}) e_{\alpha}$$
The bracketed term you identify as the component of the gradient as a vector.
In Cartesian coordinate none of this matte... | {
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"id": 88237,
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"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "electrostatics, electric-fields, metric-tensor, vector-fields, covariance",
"url... |
cosmology, energy-conservation, space-expansion, dark-energy, virtual-particles
This isn't how the expansion works. The expansion rate is described by the Hubble parameter, $H$, and the Hubble parameter tells us the (average) recession velocities at a distance $d$. The equation is simply:
$$ v = H d \tag{1} $$
The Hub... | {
"domain": "physics.stackexchange",
"id": 46449,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
"lm_q1q2_score": null,
"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "cosmology, energy-conservation, space-expansion, dark-energy, virtual-particles",
... |
cosmology, wavelength, doppler-effect
Title: Is the cosmological Doppler effect more effective at long wavelengths? When observing the Doppler effect of a particular galaxy, is the wavelength change greater for long wavelengths?
According to the simple Doppler effect formula, the wavelength change is proportional to t... | {
"domain": "physics.stackexchange",
"id": 79550,
"lm_label": null,
"lm_name": null,
"lm_q1_score": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "cosmology, wavelength, doppler-effect",
"url": null
} |
condensed-matter, solid-state-physics
Title: Debye model and Debye temperature The Debye model yields the following temperature dependence of specific heat:
$$C = \frac{12\pi^4Nk_B}{5\theta_D^3} T^3 \,,$$
where $\theta_D$ is the Debye temperature.
From this answer, the argument is that a lower Debye temperature will i... | {
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"id": 39496,
"lm_label": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "condensed-matter, solid-state-physics",
"url": null
} |
machine-learning, image-classification, computer-vision, image-recognition
Title: Machine learning algorithms for identification and classification of Microorganisms https://www.google.com/search?q=Viruses+images&tbm=isch&ved=2ahUKEwiB9-fsoL3sAhUJyHMBHWRZB-sQ2-cCegQIABAC&oq=Viruses+images&gs_lcp=ChJtb2JpbGUtZ3dzLXdpei... | {
"domain": "datascience.stackexchange",
"id": 8464,
"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": "machine-learning, image-classification, computer-vision, image-recognition",
... |
c++, regex, file-system, c++20
return newFiles;
}
static void searchAllDirectoriesForFiles(std::string partialFileSpec)
{
for (auto currentDir : subDirectories)
{
if (currentDir.discovered && !currentDir.searchedFiles)
{
std::vector<std::string> newFiles =
searchDir... | {
"domain": "codereview.stackexchange",
"id": 44183,
"lm_label": null,
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"lm_q2_score": null,
"openwebmath_perplexity": null,
"openwebmath_score": null,
"tags": "c++, regex, file-system, c++20",
"url": null
} |
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