text stringlengths 1 1.11k | source dict |
|---|---|
python, performance, beginner, python-3.x
# Better to check the index,
# as None can plausibly be used as a dictionary key
if index is None:
self.values_list.append(value)
self.data[unprocessed_key] = value
else:
self.values_list[index] = value
self.data[original_key] = value # type: ignore[index]
def __getitem__(self, unprocessed_key: _K, /) -> _V:
# Catch KeyErrors and reraise them,
# to make for a more logical traceback.
try:
processed_key = self.keys_map.get_original_key(unprocessed_key)
except KeyError as err:
raise KeyError(*err.args) from err
else:
return self.data[processed_key]
def __delitem__(self, unprocessed_key: _K, /) -> None:
# Catch KeyErrors and reraise them,
# to make for a more logical traceback.
try:
original_key = self.keys_map.get_original_key(unprocessed_key) | {
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already seen the various types of beams and different types of loads on beam during our previous posts. Wx3 180EIL2. Complex Distributed Load Example Shear and Moment Diagrams Now that the shear and moment is known for each section of the beam the results can be plotted. Shear force and bending moment diagram example #5: mixed distributed and point loads. We have also discussed shear force and bending moment diagrams for a simply supported beam with a point load acting at midpoint of the loaded beam during our previous posts. then, the Shear Stress Distribution is given by: () ()()() ()It VQ It y V x Q y yt y dy It y V x top y y τxy = ∫ = = (3) where: V(x) the shear force carried by the section, found from the shear force diagram I the second moment of area t(y) the sectional width at the distance y from the N. Deflection of a beam is due to presence of load which causes bending moment and shear force. Note Loads and reactions must be a list, even when there is only one. BEAM FORMULAS | {
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regular-languages, finite-automata, logic
Title: Can a dfa return only the final state? I am given an assignment to design a tiny arithmetic unit (from 0 to 15 inclusive) start with 0 and using a DFA. The operations are as follow:
increment x+1 and if x+1 is larger than 15 then x+1 goes to 0
decrement x-1 and if x-1 is less than 0 then x-1 goes to 15
multiplication: 2*x and if 2*x is larger than 15 then we take 2*x - 16
division: we simply take the floor of (x/2) | {
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"tags": "regular-languages, finite-automata, logic",
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newtonian-mechanics, special-relativity, curvature
Title: Relativity and intertial reference frames in hyperbolic space I was watching this video (https://www.youtube.com/watch?v=zQo_S3yNa2w) about Hyperbolica, a game that is set in a non-euclidean space. On 7:47 the author mentions that in curved space, moving objects experience a "tidal force", with the magnitude of this force being dependent on the velocity of the object. In hyperbolic space, this force stretches the objects, while in spherical space it compresses them. | {
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physical-chemistry, bond, molecular-structure, energy, polymers
The tear beyond elasticity likely starts with breaking these intermolecular bonds keeping the individual molecules together; these are weaker than the covalent $\ce{C-C}$ and $\ce{C=C}$ bonds within a polymer chain. | {
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27 Dec 2017, 00:35
Bunuel wrote:
If $$\sqrt{xy} = xy$$ what is the value of x + y?
$$\sqrt{xy} = xy$$ --> $$xy=x^2y^2$$ --> $$x^2y^2-xy=0$$ --> $$xy(xy-1)=0$$ --> either $$xy=0$$ or $$xy=1$$.
(1) x = -1/2 --> either $$-\frac{1}{2}*y=0$$ --> $$y=0$$ and $$x+y=-\frac{1}{2}$$ OR $$-\frac{1}{2}*y=1$$ --> $$y=-2$$ and $$x+y=-\frac{5}{2}$$. Not sufficient.
(2) y is not equal to zero. Clearly not sufficient.
(1)+(2) Since from (2) $$y\neq{0}$$, then from (1) $$y=-2$$ and $$x+y=-\frac{5}{2}$$. Sufficient.
As for your solution: you cannot divide by $$xy$$ since $$xy$$ could equal to zero and division by zero is not allowed.
Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero. So, if you divide (reduce) by $$xy$$ you assume, with no ground for it, that $$xy$$ does not equal to zero thus exclude a possible solution.
Hope it's clear. | {
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"url": "https://gmatclub.com/forum/if-xy-xy-what-is-the-value-of-x-y-186800.html"
} |
terminology, quantum-computing
unfortunately in both cases there are other further issues:
theoretically, can one get a speedup based on the mathematics/physics of quantum computing? see eg proof of speedup with [adiabatic] qm computing tcs.se
in practice, after one builds the computer, and one applies various systems, eg error correction being one of the main ones, and decoherence being one of the main challenges to overcome, how efficient will it be? will there be any speedup over conventional computing?
QM algorithms run completely differently, they are not based on binary logic! so therefore there is not yet any way to determine what the "equivalent" or "corresponding" qm algorithm is to a "classical" algorithm that is under consideration. the best we can do is try to optimize the performance of both & see what happens but that is obviously not satisfactory and somewhat dependent on human factors. | {
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error-correction, communication
Title: Collective measurements: importance and realization I am reading the paper Polar codes for classical-quantum channels
by Wilde and Guha, and it is stated the fact that collective measurements are necessary in order to aciheve the Holevo symmetric information as it can be seen from the HSW theorem. | {
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javascript, algorithm, sorting, insertion-sort
function insertionSort(array, compare) {
compare = compare ? compare : defaultCompare;
for (let i = 0; i < array.length; i++) {
for (let currIndex = i; currIndex > 0; currIndex--) {
if (compare(array[currIndex], array[currIndex - 1]) < 0) {
swapIndices(array, currIndex, currIndex - 1);
}
else {
break;
}
}
}
return array;
} | {
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"url": null
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solid-state-physics, symmetry, dark-matter, antimatter
Title: Could dark matter possibly be anti-matter? Considering the broken symmetry after the big bang - what I understand as there being a huge surplus of matter and a lesser presence of anti matter - is it possible that dark matter could be anti-matter?
And thus explain the missing anti-matter we might expect from symmetry?
Is there data or any reliable theories that exclude this possibility?
So far our experience with anti-matter is small scale, right? We really don't have experience with anti-matter in bulk. Or are our theories reliable enough to predict bulk properties? No, we know enough of the "bulk properties" of antimatter to rule this out. Antimatter interacts with the electromagnetic field in exactly the same way as regular matter, just with the opposite charge. | {
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neural-network, rnn
This will give us the new hidden state. Essentially the point of the output gate is to decide what information we want the next part of the model to take into account when updating the subsequent cell state. The example in the blog is again, language: if the noun is plural, the verb conjugation in the next step will change. In a disease model, if the susceptibility of individuals in a particular area is different than in another area, then the probability of acquiring an infection may change.
The output layer takes the same input again, but then considers the updated cell state:
$o_t = \sigma(W_o [x_t, h_{t-1}] + b_o)$
Again, this gives us a vector of probabilities. Then we compute:
$h_t = o_t \circ tanh(C_t)$
So the current cell state and the output gate must agree on what to output. | {
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• The imaginary modulus transformation is only intended for purely imaginary moduli (or equivalently, negative parameter values). – J. M. is a poor mathematician Nov 5 '17 at 20:33
• Do you know of any references/resources on the imaginary modulus transformations that I can use? I've been looking but haven't found any good book beside the handbook for engineers. I know you have mention the website in your previous post, but I preferred books. thanks. – abc123 Nov 7 '17 at 22:53
• @abc123, "I know you have mention the website in your previous post" - the DLMF is also a book, so I don't understand the pickiness over this. – J. M. is a poor mathematician Nov 7 '17 at 22:57 | {
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gene, assembly, metagenome
How I understand your question as being one of estimating the abundance of either some specific genes (e.g. butyrate metabolism genes) or all genes in a microbial community across multiple samples for comparative purposes. In other words, not 16S or marker gene analysis for the purposes of estimating organismal abundance, which is a rather different problem (though in that case I would still not use an assembly).
A more standard workflow is: | {
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finds a solution to the gluing equations but it has "negatively oriented tetrahedra". Does this mean what I think it means -- that once you've put the geometric structure on the tetrahedra, you have a tetrahedron folded-over? If you view the gluing equations from the upper half-space model, they say that the sum of a bunch of angles should be $2\pi$. Is this the case where one of those angles is negative? </p> <p>The other two triangulations SnapPea finds geometric structures with degenerate tetrahedra. In the upper half-space model this is where one of the angles is zero, I believe. Is there a way to fix this, so that I could get a Dirichlet domain, drill and fill, etc? This is my primary question. </p> <p>Here are the triangulations, both in SnapPea format and Regina format. </p> <p><a href="http://dl.dropbox.com/u/46424505/triangulations/found_hyp_tri.rga" rel="nofollow">Regina file, all triangulations</a></p> <p><a href="http://dl.dropbox.com/u/46424505/triangulations/tri11" | {
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I = matrix(QQ, [[ 1, 4, 0, -1, 0, 7, -9],
[ 2, 8, -1, 3, 9, -13, 7],
[ 0, 0, 2, -3, -4, 12, -8],
[-1, -4, 2, 4, 8, -31, 37]])
nsp = I.right_kernel(basis='pivot')
nsp
As we said, nspcontains a lot of unfamiliar information. Ignore most of it for now. But as a set, we can test membership in nsp.
x = vector(QQ, [3, 0, -5, -6, 0, 0, 1])
x in nsp
y = vector(QQ, [-4, 1, -3, -2, 1, 1, 1])
y in nsp
z = vector(QQ, [1, 0, 0, 0, 0, 0, 2])
z in nsp
We did a bad thing above, as Sage likes to use Ifor the imaginary number $$i=\sqrt{-1}$$ and we just clobbered that. We will not do it again. See below how to fix this.
nspis an infinite set. Since we know the null space is defined as solutions to a system of equations, and the work above shows it has at least two elements, we are not surprised to discover that the set is infinite (Theorem PSSLS).
nsp.is_finite() | {
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"url": "https://runestone.academy/ns/books/published/fcla/section-HSE.html"
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haskell
Found yet another improvement:
randomElemsFrom x = map (qarray !) . randomRs (bounds qarray) where
qarray = listArray' $ splitOn "~" x
main :: IO ()
main = do
setTitle "Quotes"
hideCursor -- catch ctrl+c for showCursor
liftM2 randomElemsFrom (readFile fileName) newStdGen >>= withInterval delay mapM_ outQ
This version has more separation between monadic and non-monadic code (which is good) but randomElemsFrom was a generally useful function before but now it is tied to the task at hand (which is bad). | {
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fourier-transform, dft
which in frequency domain is a constant (see DFT Pairs and Properties: pair row 2, property linearity):
$$x[N-1] - x[-1],\tag{9}$$
to be added to all elements of $Y$ calculated by Eq. 4.
For a general $x$, the condition of Eq. 6 for Eq. 5 enables to use a length $N+1$ DFT and IFT to calculate the backward difference, by shifting the input to the DFT one step to the right, and finally by shifting the output from IDFT one step to the left. With forward difference $x[n + 1] - x[n]$, the shift would not be necessary, and I think this matches your discarding of the 0th sample. For a circular convolution implementation of convolution by a finite sequence, using a longer transform is a common trick to avoid the circular effects in a sufficiently large part of the output of the IDFT. For then obtaining the DFT of a partial IDFT output, in particular a one shorter, I don't think there is any shortcut. | {
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differential-geometry, definition, representation-theory, topology, spinors
Title: What kind space does spinor lives in? I'm trying to read some differential geometry these days and I just encountered orientable manifold.
Quote: "If $M$ is nonorientable, $M$ has a two-sheeted orientable covering manifold $\tilde{M}$. If $M$ is simply connected, then $M$ is orientable."
I heard my instructor talking during the class couple of days before where he mentioned the spin/spinor lives in a spaces of two copy.
Question 1: what does orientable manifold has to do with spinor?
Question 2: what kind of space does spinor lives in? as it seemed to imply that every spinor got a "hold" or singular value inside of them.
Question 1: what does orientable manifold has to do with spinor? | {
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c#, game, tetris
for ( int ColNum = 0; ColNum < SourceArrayColumns; ColNum++ )
{
DestinationArray[DestinationRow,ColNum] = SourceArray[SourceRow,ColNum];
}
return DestinationArray;
}
private void SpawnNewPiece()
{
CurrentPiece = new TetrisPiece();
CenterNewPiece();
try
{
PlacePiece(CurrentPiece, DO_NOT_ENFORCE_TOP_OF_BOARD_BOUNDARY);
}
catch (SquareOffTheBoardException)
{
throw new BoardTooNarrowException("The board is too narrow. Unable to spawn new piece.");
}
}
private void CenterNewPiece()
{
int ColumnLocation = (int)Math.Round((BOARD_COLUMNS + 0.5) / 2 - 3, 0);
CurrentPiece.ChangeLocation(new int[2] { -2, ColumnLocation });
}
#endregion
}
} | {
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experimental-chemistry
Title: In the Gold Foil experiment, did Ernest Rutherford's alpha particles hit the same spot every time or did he direct the emitter to different spots? When reading and learning about the gold foil experiment, the alpha particles mostly go straight through the gold foil and some get deflected or bounce back but it doesn't say anything about the direction of the alpha particle emitter. Did the alpha particle emitter stay in the same spot or get directed to different areas of the foil? How could they all hit the same spot and get deflected in so many different directions? Even a small beam is very big compared to a gold atom
It seems you are making an assumption that, if the beam were perfectly focussed it would always show the same deflection (because geometry). | {
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organic-chemistry, nomenclature
Title: Can we use prefixes like iso, neo, etc in IUPAC nomenclature of organic compounds? Shouldn't the name of the compound in the picture be 5-(1-ethyl-2-methylpropyl) nonane instead of the given name? According to the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) various prefixes are retained for use in general nomenclature. However, many prefixes are no longer recommended.
Trivial, common, and traditional prefixes have always been an integral part of organic nomenclature. However, as systematic nomenclature develops and becomes widely used, many of these prefixes fall by the wayside. Accordingly, each set of IUPAC recommendations contains fewer of these traditional prefixes. | {
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optics, soft-question, terminology, conventions
For particles of size comparable to the wavelength, even if they have pure Dirichlet reflecting boundary conditions on the surface. When the scattering is of a long plane wave, the forward scattering amplitude must removes intensity from the wave to account for the reflected energy. This means that there is just as much diffraction as scattering, a phenomenon discussed in Peierl's book "Surprises in Theoretical Physics".
When the wavelength is small, the scattering object is big compared to the wavelength and to the wavepacket size, it will remove all the intensity from the forward wave, making all the energy in the wavepacket reflect. In this regime, you call it reflection of a wavepacket, and the dynamics might as well be reflection of a particle. If you have a wide wavepacket, you can decompose it into a part that reflects and a part that just misses the scattering object, with the only diffraction close to the boundary. It is the geometric optics limit. | {
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python, performance
except IndexError:
pass
return lcs
Can the code be made faster in pure Python? Is there a better option to differentiate the input strings when made into one sorted list than concatenating an ID to them? OK then: since your concern is speed, let's track our progress with actual timing data. The first step is to run the code through the Python profiler. With the addition of a bit of driver code that just calls LongestCommonSubstr().longest_common_substr 10000 times, I get the following results:
$ python3.4 -m profile lcs_profile.py abcdeffghiklnopqr bdefghijklmnopmnop
1130008 function calls in 3.083 seconds
Ordered by: standard name | {
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PC1 has 98% of the variance. (Jolicoeur and Mosimann get 97.61%; I get 97.16% if I set scale= TRUE; haven't checked for other issues [transcription errors etc.]).
Importance of components:
PC1 PC2 PC3
Standard deviation 25.3100 2.40272 2.26449
Proportion of Variance 0.9833 0.00886 0.00787
Cumulative Proportion 0.9833 0.99213 1.00000
Jolicoeur, P. and Mosimann, J. E. (1960) Size and shape variation in the painted turtle. A principal component analysis. Growth, 24, 339-354.
• +1. Maybe add that long is the turtle's length, larg its width, and haut its height, all in millimeters? Feb 13 at 9:12 | {
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"lm_q2_score": 0.8479677602988602,
"openwebmath_perplexity": 992.933348967242,
"openwebmath_score": 0.8425297141075134,
"tags": null,
"url": "https://stats.stackexchange.com/questions/605113/can-pc1-explain-more-than-90-of-variance"
} |
quantum-field-theory, symmetry, supersymmetry
It is possible, because variation due to the left- and right-chiral generators do not mix.
The generator of the variation is Hermitian | {
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ros2, urdf, ros2-control, transmission
Title: How to access URDF info inside a transmission interface? I'm trying to write a custom transmission interface for ros2 control for the robotiq 3f, and I need access to the joint limits defined by the urdf, but the Joint handle does seem to contain that info, and I can't see any way to access the URDF. Any suggestions or good workarounds? I already had the same problem as you are describing: But this is not yet possible directly from ros2_control side. I'll bring that up on the roadmap for the next LTS version Jazzy. (We recently added this for controllers in the rolling version.)
In the meantime, the only workaround is to add a node to your hardware_component and parse the URDF from a parameter or add a subscriber to the /robot_description topic.
Edit: I was wrong, this should be possible already since this PR: The full URDF is inside hardware_info.original_xml. | {
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Activity8.4.5
1. Explain why the series
\begin{equation*} 1 - \frac{1}{4} - \frac{1}{9} + \frac{1}{16} + \frac{1}{25} + \frac{1}{36} - \frac{1}{49} - \frac{1}{64} - \frac{1}{81} - \frac{1}{100} + \cdots \end{equation*}
must have a sum that is less than the series
\begin{equation*} \sum_{k=1}^{\infty} \frac{1}{k^2} \text{.} \end{equation*}
2. Explain why the series
\begin{equation*} 1 - \frac{1}{4} - \frac{1}{9} + \frac{1}{16} + \frac{1}{25} + \frac{1}{36} - \frac{1}{49} - \frac{1}{64} - \frac{1}{81} - \frac{1}{100} + \cdots \end{equation*}
must have a sum that is greater than the series
\begin{equation*} \sum_{k=1}^{\infty} -\frac{1}{k^2} \text{.} \end{equation*}
3. Given that the terms in the series
\begin{equation*} 1 - \frac{1}{4} - \frac{1}{9} + \frac{1}{16} + \frac{1}{25} + \frac{1}{36} - \frac{1}{49} - \frac{1}{64} - \frac{1}{81} - \frac{1}{100} + \cdots \end{equation*} | {
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"url": "http://faculty.gvsu.edu/boelkinm/Home/AC/sec-8-4-alternating.html"
} |
json, bash, linux, file-structure, jq
which disk images will be opened,
which files inside each disk image will be copied, and
which path inside the directory root will be used as the destination for the files being copied.
The first parameter defaults to the current directory when not given. The second one defaults to a file named steps.json located at the current directory. If the first parameter is not given, the second one can't be either.
Prerequisites
This script requires the following external programs to work correctly (installation instructions for Ubuntu are between parentheses):
The JSON parsing program jq (sudo apt install jq).
The disk image manipulation utility udisksctl (sudo apt install udisks2)
Script
The complete script is below. It's name is imgdisk-copy.sh and should be marked as executable. It can be in any directory where it can be executed. For the purpose of the test below, it is placed in a directory where it can read and write.
#!/bin/bash | {
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java, graph
}
if (!graph.containsKey(source) || !graph.containsKey(destination)) {
throw new NoSuchElementException("Source and Destination, both should be part of graph");
}
/* A node would always be added so no point returning true or false */
graph.get(source).put(destination, length);
} | {
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"tags": "java, graph",
"url": null
} |
quantum-field-theory, general-relativity, cosmological-constant, qft-in-curved-spacetime
(2) How to derive the equation $\langle 0|T_{\mu\nu}|0\rangle=-\langle \rho\rangle g_{\mu\nu}$ from Lorentz invariance or in any other way?
EDIT: I again tried to solve it and got this . Am I correct here? What am I doing wrong? And the question (2) remains. The updated calculation contains a mistake. Here, $i$ is not a dummy index but a fixed index, thus sumover is not implied in the fourth line of the calculation for the vacuum expectation of $ii$-th component of energy-momentum tensor. \begin{array}
e \langle\hat{T}^{ii}\rangle_0 &=& \int\frac{\mathrm{d}^3\vec{k}}{(2\pi)^32\omega_{\vec{k}}}k^ik^i\\
&=& \int\frac{\mathrm{d}^3\vec{k}}{(2\pi)^32\omega_{\vec{k}}}\eta^{ij}k_jk^i\\
&=& -\int\frac{\mathrm{d}^3\vec{k}}{(2\pi)^32\omega_{\vec{k}}}\delta^{i}_{j}k_jk^i \\
&=& -\int\frac{\mathrm{d}^3\vec{k}}{(2\pi)^32\omega_{\vec{k}}}k_ik^i \qquad\quad\text{not summed over},\\ | {
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ros
Error C4430 missing type specifier - int assumed. Note: C++ does not support default-int TrafficProject d:\unreal projects\trafficproject\source\ros_lib\ros\node_handle.h 490
Error C2059 syntax error: ')' TrafficProject D:\Unreal Projects\TrafficProject\Source\ros_lib\rosserial_msgs\Log.h 23
Error C2059 syntax error: 'constant' TrafficProject D:\Unreal Projects\TrafficProject\Source\ros_lib\rosserial_msgs\Log.h 20
Error C2059 syntax error: '}' TrafficProject D:\Unreal Projects\TrafficProject\Source\ros_lib\rosserial_msgs\Log.h 64
Error C2143 syntax error: missing ';' before '{' TrafficProject D:\Unreal Projects\TrafficProject\Source\ros_lib\rosserial_msgs\RequestParam.h 9
Error C2143 syntax error: missing ';' before '}' TrafficProject D:\Unreal Projects\TrafficProject\Source\ros_lib\rosserial_msgs\Log.h 20 | {
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plugin, rqt
Original comments
Comment by aland_t on 2014-01-30:
I'm running groovy on Ubuntu 12.04 if that helps.
Comment by ahendrix on 2014-01-30:
Have you set your script as executable? Try chmod +x /home/alan/catkin_ws/src/rqt_mypkg/src/rqt_mypkg
Comment by aland_t on 2014-01-31:
I tried this, but I received the message "chmod could not access" ...."No such file or directory".
However, I did not notice this before, but if I run "rqt" the default rqt gui comes up. My plugin is listed under the Plugins tab. It throws a lot of errors when I click it though.
Comment by aland_t on 2014-01-31:
Ok, I have the plugin working if I just run "rqt" and open it from the plugins menu. "rosrun rqt_mypkg rqt_mypkg" still does not work.
Comment by 130s on 2014-02-02:
@atland_t you can modify your post to paste the error you got.
Comment by Dorian Scholz on 2014-09-12: | {
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ros
Midfield, XTD is on the order of an inch or two, and the desired heading changes very little, resulting in small steering changes.
On the ends, the AB line is suddenly flipped and an offset (of 15 feet in this case) is added. Tractobot01 directs full steering to turn toward the new line. It (thankfully) can not turn tight enough to simply intercept the new line. Instead it overshoots and eventually circles around and captures the line. The result is a sort of "keyhole" pattern. | {
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complexity-theory, time-complexity, polynomial-time
Title: Does P=NP imply polynomial solutions to #P? Is it true that $\#P$-complete problems could possibly be solved in polynomial time if P=NP? I know that even some counting problems related to polynomial time decision problems are $\#P$-complete, so even if P=NP it may not necessarily be true. My confusion is over how we write the answer to a $\#P$-complete problem since it may be exponential in the size of the input (for example up to $2^n$ truth assignments to a SAT instance on $n$ variables). Therefore, I cannot understand how, even if we find a fast way for computing something like the permanent of a matrix, we could still expect to write the answer in polynomial time. Am I missing something about the definition of $\#P$? Your confusion is that the class #P only asks you to count the solutions, not to enumerate them, and you only need $n$ bits to write down the number $2^n$. This means that to express the number of satisfying assignments to a formula of $n$ variables, you need | {
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python, logging, mongodb
Methods
-------
__init_logger__()
Initializes the logger.
connect_to_client( host=None, port=None, timeout=3000, username=None, password=None)
Connects to the Mongodb instance using MongoClient from PyMongo.
connect_to_database(database_name=None)
Connects to the collection in the mongodb instance.
connect_to_collection(collection_name=None)
Connects to the collection in the mongodb database.
perform_bulk_operations(list_operations_to_perform_in_bulk=None)
Executes the operations against MongoDB in bulk.
"""
def __init__(self, conf, verbose=5):
self.conf = conf
self.client = None
self.database = None
self.collection = None
self.verbose = verbose
self.logger = self.__init_logger__() | {
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interstellar-medium
The intergalactic medium (IGM) is the gas (and small amounts of dust) in between galaxies. It is mostly ionized gas with densities $\sim 10^{-6}$ particles per cm$^{3}$ and temperatures ranging from $\sim 10^{5}$ to $\sim 10^{7}$ K. Due to this temperature range, it is sometimes referred to as the "warm-hot" intergalactic medium. There is, however, evidence for some regions of neutral hydrogen with temperatures of $\sim 10^{4}$ K.
The intracluster medium is a subset of the IGM that makes up the IGM inside galaxy clusters (in between the galaxies in the cluster). This means that it is somewhat denser than the general IGM (densities of $\sim 10^{-3}$ per cm$^{3}$, denser towards the centers of clusters) and hotter as well, with temperatures of $\sim 10^{7}$ to as much as $10^{8}$ K. | {
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fluid-dynamics, flow
$\mathcal{D_{ij}} = \frac{1}{2} (u_{ij} + u_{ji}), \quad \mathcal{D}^T = \mathcal{D} \equiv \frac{1}{2}(2\cdot u_{rr} + 2\cdot u_{\theta \theta} + 2\cdot u_{xx})$
And that if I show that this equation is equal to zero the fluid flow is incompressible? The continuity equation in cylindrical coordinates is $$\frac{1}{r}\frac{\partial (ur)}{\partial r}+\frac{1}{r}\frac{\partial v}{\partial\theta}+\frac{\partial w}{\partial z}=0$$ | {
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quantum-mechanics, photons, higgs
Is the Higgs wave (if exists) a herd of Higgs bosons, and is there any experiment where we try to detect Higgs waves?
No and no, as explained above. There is no Higgs wave , as the Higgs boson has a mass, in contrast to the photon and the graviton (if it exists). The Higgs boson is an excitation of the Higgs field, and its discovery is important because it validated the standard model of particle physics, which needs the Higgs field for the generation of masses.
Edit after comment by OP:
What makes me confused is when they say that an electron can behave like a wave. But the electron has rest mass. Is that just a mathematical description for the propagation of the electron that we call wave in that case? – Árpád Szendrei | {
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$\{\underbrace{\alpha}_{\mbox{scalar}},\qquad\underbrace{e_{1},e_{2},e_{3}}_{\mbox{vectors}},\qquad\underbrace{e_{12},e_{23},e_{13}}_{\mbox{bivectors}},\qquad\underbrace{e_{123}}_{\mbox{trivector}}\}$
Cl() creates the algebra and returns a layout and blades. The layout holds information and functions related this instance of G3, and the blades is a dictionary which contains the basis blades, indexed by their string representations,
[2]:
blades
[2]:
{'e1': (1^e1),
'e2': (1^e2),
'e3': (1^e3),
'e12': (1^e12),
'e13': (1^e13),
'e23': (1^e23),
'e123': (1^e123)}
You may wish to explicitly assign the blades to variables like so,
[3]:
e1 = blades['e1']
# etc ...
Or, if you’re lazy and just working in an interactive session you can use locals() to update your namespace with all of the blades at once.
[4]:
locals().update(blades)
Now, all the blades have been defined in the local namespace
[5]:
e3, e123
[5]:
((1^e3), (1^e123))
## Basics¶
### Products¶ | {
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# What exactly do we call a linear equation?
I know there's a difference between the linear algebra "linear function" and the "affine function", but it confused me about what we consider a "linear equation" -precisely how many variables allowed, what order could a variable carry?
• A linear equation is an equation of the form $\sum_{k=1}^n a_kx_k = c$ for variables $\{x_k\}_{k=1}^n$ and constants $\{a_k\}_{k=1}^n$ and $c$. – Michael L. Aug 22 '17 at 15:05
• Thanks a lot, what does "c" means in the sum? is it a parameter? – lun Aug 22 '17 at 16:48
• As I said, it is an arbitrary constant. – Michael L. Aug 22 '17 at 20:33
• I don't know what "what order could a variable carry" means. – Gerry Myerson Aug 27 '17 at 2:54
Here are various comments on linear functions versus linear equations.
First there is the idea of a linear combination. Essentially, linear combination means a "sum of multiples" of something. For example
$$3x-2y+4z$$ | {
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kinetics, free-energy
Note that $\Delta G_{AB}> \Delta G_{BC}>\Delta G_{BD}$.
According to transition state theory, rates are determined by the rate-limiting step. So the rate of each process will be the same,
\begin{align}
r_{A\to C}&=r_{A\to B} \\
r_{A\to D}&=r_{A\to B}
\end{align}
from which it follows that the number of transitions made during some large $\Delta t$ will also be the same,
\begin{align}
N_{A\to C}&=r_{A\to B}\Delta t \\
N_{A\to D}&=r_{A\to B}\Delta t
\end{align}
However, if we were to consider the two pathways collectively then we would predict more transitions to be made to state $D$ than $B$ since $\Delta G_{BD}<\Delta G_{BC}$.
How do we resolve this apparent discrepancy? In transition state theory (TST, goldbook) one of the necessary assumptions is that reactants and products are in equilibrium. In principle this gives us
\begin{align}\ce{
A &<=> [AB]^{$\ddagger$} -> B\\
B &<=> [AB]^{$\ddagger$} -> A\\
A &<=> B,
}\end{align}
and in addition to this, also
\begin{align}\ce{ | {
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quantum-mechanics
Nevertheless, there are places where $C(t)$ vanishes. If we just consider the amplitude $|C(t)| \propto \left|\frac{\sin(N \omega t/2)}{\sin(\omega t/2)}\right|$, then the amplitude will be largest when the numerator and denominator are both small and have approximately the same size (near $t \approx 0, 2\pi/\omega, 4\pi/\omega, ...$), and smallest when the denominator is "large" (the most extreme cases being $t\approx \pi/\omega, 3\pi/\omega, ... $. Here is a plot showing the behavior of $|C(t)|$ for $N=\{3,10,100\}$ | {
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ros, gazebo, turtlebot, camera, multiple
</launch>
Originally posted by kedarm on ROS Answers with karma: 86 on 2013-06-22
Post score: 1
Original comments
Comment by Martin Günther on 2013-06-23:
The "tried to advertise a service" warnings can be ignored, they always pop up (I think). Don't confuse tf_prefix with remapping, you need to get both right. If remapping works, rostopic list should show sth like /robot1/camera/... and not just /camera/....
Comment by kedarm on 2013-06-30:
I thought so too initially, but i still don't see any camera feed from either of the two turtlebots. Also, these are not merely warnings, they pop up as "ERRORS". I tried to see if /robot_1/camera/.. gets published, but its not. And all i see is /camera/...
OK, I have finally been able to find a solution to this problem. The problem here was two-fold. | {
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compilers, pushdown-automata, functional-programming
Title: Is it possible to write an HTML compiler with no mutable state? That's probably a vague question but allow me to try and give an example:
My compiler does transformations on HTML (from HTML to HTML). It scans a flattened DOM tree, and relies on lookbehinds (on elements pushed onto a stack) to decide what transformation to apply. I can give more detail if necessary but I don't want to lose the reader.
Can such logic be alternatively implemented with no mutable state? I have become a big believer in functional programming and have made it a point to make my code as functional-style as possible. I don't like loops that perform actions based on the content of a previous iteration, by saving the information from a previous iteration in stacks or booleans. I need to augment the functionality of this routine and will probably tip the code from being "just about understandable" to "only the author will understand this, everyone else don't touch". | {
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quantum-mechanics, bosons
Bose condensation of atoms is only a sensible notion when the size of the wavefunction is much larger than the electronic radius. What happens, really, is that on the scale of the wavefunction each of the atoms has approximately the same distribution of possible positions, but this approximation (and it is an approximation) would break down if you confined the atoms' wavefunctions to not much larger than the electronic radius. At that point, you can no longer treat the atoms as point-like effective bosons, and must instead study the system in terms of their internal structures. | {
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vb.net, cryptography, aes
End Class It seems you did a good job getting the same functionality using AES. The problem is that Microsoft is not using good practices themselves.
They confuse a password with a key, and they do not use a good key derivation function such as PBKDF2 (implemented in .NET by the class RFC2898DeriveBytes). This you should only use if you do not have access to a shared AES key, which can just consist of 16 cryptographic random bytes.
Furthermore, they did not use a random IV. The IV has the right size (the block size of the block cipher) but it has been set to a constant value. This means all the security benefits of having an IV are negated. The IV should be a cryptographic random (or at least fully unpredictable to an adversary), and could be written in front of the ciphertext (e.g. by supplying it to the unencrypted stream). Static IV's are only secure if the AES key is randomized or if the plaintext is sufficiently random itself. | {
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c, generics, collections, hash-map, set
PFX - Functions prefix, or namespace;
SNAME - Structure name (typedef SNAME##_s SNAME;);
FMOD - Functions modifier (static or empty, edit: not sure if works with inline);
V - Your data type to be worked with.
Or you can generate each part individually using HASHSET_GENERATE_STRUCT, HASHSET_GENERATE_HEADER and HASHSET_GENERATE_SOURCE.
hashset.h
#ifndef CMC_HASHSET_H
#define CMC_HASHSET_H
#include <stdlib.h>
#include <stdbool.h>
#include <string.h>
#ifndef CMC_HASH_TABLE_SETUP
#define CMC_HASH_TABLE_SETUP
typedef enum EntryState_e
{
ES_DELETED = -1,
ES_EMPTY = 0,
ES_FILLED = 1
} EntryState; | {
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Solution (a) '" p: 2 + 3 is not greater than I. That is, '" p: 2 + 3 is false. (b) "' q: It is nOl cold.
s
I. Since p is true, .-...- p
The statements p and q can be combi ned by a number of logical connectives to form compound statements. We look at the most important logical connectives. Let p and q be statements. I. The statement "p and q"' is denoted by p A q and is called the conj unction of p and q . The statement p /\ q is true only when both p and q are true. The truth table giving the truth values of p /\ q is given in Table C2. 2. The statement "p or q" is denoted by p v q and is called the disjunction of p and q. The statement p v q is true o nl y when either p or q or both are true. The tmth ta ble giving the truth values of p v q is given in Table C.3.
TABLE C.2
EXAMPLE 3
TABLE C.3
p
q
PAq
p
q
---
T
T
T
T
T
T
F
F
T
F
F
T
F
F
T
T T T
F
F
F
F
F
F
p vq
Form the conjunctio n of the statements p: 2 < 3 and q: - 5 > - 8.
Solution p
EXAMPLE 4 | {
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"url": "https://silo.pub/elementary-linear-algebra-with-applications-9th-edition.html"
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statistical-mechanics, phase-transition
$$
u(\beta) = \frac{\varepsilon e^{(a-\beta\varepsilon)\lambda}}{1+e^{(a-\beta\varepsilon)\lambda}}.
$$
In the limit of infinite $\lambda$ this has a transition point at $\beta = a/\varepsilon$, with $u$ being zero if $\beta$ is greater than this value, and $\varepsilon$ if it is below it. the "free energy" $\log Z(\beta)$ changes in a similar way, becoming piecewise linear with a discontinuity in its first derivative at $\beta = a/\varepsilon$. | {
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"url": null
} |
newtonian-mechanics, energy, work, power
Title: Does gravity exert more "power" when an object is traveling faster? So, this question arose when I was pondering the meaning of horsepower and torque in cars. I thought of the following question:
There is a 1 kilogram weight on planet M. Planet M has no atmosphere and has a gravitational constant of 1 meter per second per second. The weight is raised to a height of 2 meters and dropped. The weight will fall through the first meter in 1 second and the second meter in 0.4 seconds (rounding a bit).
So, in terms of work, gravity does 1 Joule of work on the weight over each 1 meter interval. However, in terms of power, gravity exerts 1 watt of power over the first interval and 2.5 watts over the second interval. Why does it seem that gravity is magically more powerful when the object is travelling faster? | {
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"url": null
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quantum-field-theory, condensed-matter, research-level, gauge-theory, gauge-invariance
The original BCS Hamiltonian has $k=k'$ and $U\left(k,k'\right) \rightarrow -g$ a constant, and so the $s$-wave interaction is both local and global U(1) invariant. $H_{\text{BCS}}$ is only U(1) symmetry global invariant, as far as I can see.
The Hamiltonian $H_{\text{BCS}}$ given above is particularly useful to describe some non-conventional effects ($d$-wave pairing for instance) and can be further generalise. I have not doubt about the validity of the results obtained using this Hamiltonian (some of them are even justified experimentally). | {
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"url": null
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beginner, haskell, functional-programming, lambda, collatz-sequence
I wrote "function" since now it's been revealed that what we really have is just a value, which appears to be 730.
I see no reason why it couldn't be a function proper. Instead of hard-coding 666, we could take that as an argument.
invNumLongChains2 :: Int -> Int
invNumLongChains2 numChains = go 0 []
where
go :: Int -> [[Int]] -> Int
go n chains
| length (filter (\ys -> length ys > 15) chains) == numChains = n
| otherwise = humanNumLongChains (n + 1) (chains ++ [chain (n + 1)]) | {
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• There are two general approaches for curve fitting: • Least squares regression: Data exhibit a significant degree of scatter. 1}\) and adding Gaussian noise with standard deviation $$\sigma = 0. This 4-hour interactive online course is a presentation of the curve fitting in the sense of least squares. An important feature of this program is that you can use the general and powerfull (non-linear) Levenberg-Marquardt method to fit your data to any continuous function you define. Curve fitting encompasses methods used in regression, and regression is not necessarily fitting a curve. A First Order Fit to the data used to construct a working curve follows the equation:. This option allows you to use "c" as a parameter without varying the value during least squares adjustment. Data to fit, specified as a matrix with either one (curve fitting) or two (surface fitting) columns. values of a dependent variable ymeasured at. The original purpose of least squares and non-linear least squares | {
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"openwebmath_score": 0.7048426866531372,
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"url": "http://zepn.from.bz/curve-fitting-least-square-method-example.html"
} |
polymers
Title: Abundant substances which I may use like coupling agents What is the most abundant substances which I may use like coupling agent for Wood plastic composite with HDPE polymer? I don't want maleated polyolefin because they are not so abundant in my country. If you don'y want to use maleated polyolefin (the best coupling agent for this composite), you can use oxidized polyethylene, ethylene propylene rubber, ethylene-co-glycidyl methacrylate or polyolefin elastomer. | {
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quantum-mechanics, condensed-matter, solid-state-physics, quantum-spin, ferromagnetism
In antiferromagnets, there is no spontaneous magnetization. Accordingly, there are two independent types of (linearly polarized) magnons with linear dispersion relation, owing to the fact that the dynamics is now of second order in time. The general property that distinguishes ferromagnets from antiferromagnets is the presence of nonzero density of a conserved charge in the ground state, which makes two would-be Goldstone degrees of freedom canonically conjugate by the symmetry group commutation relations. | {
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complexity-theory, approximation
I think as follow:
$\mathcal{P}$ is at least hard as $\mathcal{P}'$ so if there is a constant factor approximation algorithm for $\mathcal{P}$ then for each feasible solution $\mathcal{I}$ of $\mathcal{P}$, then $\mathcal{I}$ is a solution for decision version of $\mathcal{P}'$ hence we solve decision version of $\mathcal{P}'$ in polynomial time and hence $P=NP$. Finally, we conclude that $\mathcal{P}$ has no constant factor approximation algorithm. Here is a similar example. Let $\mathcal{Q}$ be the problem of maximizing the number of satisfied clauses in an input CNF given that the assignment is the FALSE assignment. Let $\mathcal{Q'}$ be the problem of maximizing the number of satisfied clauses in an input CNF, without any other constraints. It is known that $\mathcal{Q'}$ has no PTAS (unless P=NP). Does it follow that $\mathcal{Q}$ has no PTAS? | {
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c++, matrix, c++14, template, vectors
You have a copy object.
void setMatrix(const std::vector<T>& val);
void setElement(const size_t row, const size_t col, const T& val);
You might as well have also have a move version!
void setMatrix(std::vector<T>&& val);
void setElement(const size_t row, const size_t col, T&& val);
You forgot the reference here:
// Passing by value is going to cause a copy of the array
void setRow(const size_t row, const std::vector<T> val);
void setCol(const size_t col, const std::vector<T> val);
When getting a value return by const reference to avoid an unnecessary copy.
T getElement(const size_t row, const size_t col) const; | {
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memory-management, virtual-memory, memory-allocation
Title: Why not space out memory allocations? In ext4 file system, the files are spaced out as far apart as reasonably possible to allow for efficient reallocation. Why do we not do this in memory?
Why not allocate one memory as page 20, and the next large allocation as page 100 to allow for excess expansion before and after the current allocation? I feel that makes sense for large frequently changing-in-size buffers. For smaller buffers, doing so would probably be a drain on memory because we have to allocate each page for a small amount of bytes(but perhaps do it within a block too in the malloc impl). This would also provide greater memory corruption prevention, allowing segfaults(or windows equivalent) to happen quicker(specifically for larger buffers).
Why don't we do this? I get it on modern 32-bit systems because of limited address space, but why not on 64-bit? Why is memory different from a hard disk?
Because hard disks have different performance characteristics than RAM. | {
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organic-chemistry
Otherwise (taking into account your profile name, too), especially if you aim to isolate otherwise volatile materials by steam distillation, you may seal the joints with sleaves of PFTE / Teflon. Nothing will drop into your distillation; but after the concluded distillation, start to dissamble carefully the still warm glass ware. | {
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Urumqi 830 046, P.R A matrix is A diagonal matrix diagonally. N matrix A is called strict diagonal dominance, depending on the main diagonal −|aij| for i 9=j 046 P.R. Factorization ) non-negative diagonal entries is positive semidefinite that arise in finite element methods are diagonally dominant A! Are nonsingular and include the family of irreducibly diagonally dominant and irreducible strictly! It ( A ) ≥ 0 { \displaystyle A }, the first third. … Let A ∈ R n× be A diagonally dominant real matrix with real nonnegative diagonal entries positive! Nonsingular M-matrix ( e.g., see [, Lemma 3.2 ] ) is non-singular beann. Any arbitrary scalar A cyclically diagonally dominant, Preconditioned techniques can be proved, for strictly diagonal dominant [..., H-matrix, inverseM-matrix, strictly diagonally dominant matrices, using the Gershgorin theorem! Of diagonally dominant matrix is called column diagonal dominance an eigenvalue of is. ; norm 1 dominance condition many matrices that have only | {
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python, algorithm, strings, python-2.x
Title: Solving jumbled letters using a given dictionary Given a dictionary, a method to do lookup in dictionary and a M x N board where every cell has one character. Find all possible words that can be formed by a sequence of adjacent characters.
Example:
Input: dictionary[] = {"GEEKS", "FOR", "QUIZ", "GO"};
boggle[][] = {{'G','I','Z'},
{'U','E','K'},
{'Q','S','E'}};
Output: Following words of dictionary are present
GEEKS, QUIZ
Below is my code:
dictSize=int(raw_input())
dictionary=raw_input().split(' ')
m,n=map(int,raw_input().split(' '))
boggle=[[0 for x in range(n)] for y in range(m)]
#print dictionary
bString=raw_input().split()
for i in range(0,m):
for j in range(0,n):
boggle[i][j]=bString[(i*n)+j]
#print boggle
lookUp={}
for i in range(0,m):
for j in range(0,n):
lookUp[boggle[i][j]]=lookUp.get(boggle[i][j],0)+1 | {
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rosbag, transform
Title: How to save static transforms in bag files?
How do I save a static transform in a bag file so I get a self contaned bag file that can be replayed?
Not it seems like for example rviz do not understand a static transform in a bag file.
Originally posted by TommyP on ROS Answers with karma: 1339 on 2015-04-21
Post score: 6
Original comments
Comment by lucasw on 2016-06-02:
https://github.com/ros/ros_comm/issues/706 is a related issue- the tf_static is only recorded in the first bag when splitting bags.
Finally a nice option exists a few years later :)
This is covered by this issue on Github. The corresponding PR has been merged over a year ago and Noetic is shipped with the feature. It does so by repeating the latched topics (e.g. static TFs) for each bag.
The option you are looking for while recording is --repeat-latched, so e.g.:
rosbag record -a --repeat-latched --duration 5 --split
Cheers | {
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It is from the alligation method
As shown in the post above, per the alligation method, the distrbution will be:
50 10 (=40-30) parts
40
30 10 (=50-40) parts
Thus, you see that you need 10 parts out of 20 (=(10+10)) parts of 50% solution, giving you 10/20 = 1/2 or 50% as your answer.
Hope this helps.
Moderator
Joined: 22 Jun 2014
Posts: 1030
Location: India
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE: Information Technology (Computer Software)
Re: Some part of a 50% solution of acid was replaced with an [#permalink]
### Show Tags
09 Apr 2016, 00:38
chrissy28 wrote:
Some part of a 50% solution of acid was replaced with an equal amount of 30% solution of acid. If, as a result, 40% solution of acid was obtained, what part of the original solution was replaced?
A. $$\frac{1}{5}$$
B. $$\frac{1}{4}$$
C. $$\frac{1}{2}$$
D. $$\frac{3}{4}$$
E. $$\frac{4}{5}$$
M25Q30 | {
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c#, object-oriented, game, interview-questions, console
private int GetLetterPoints()
{
int score = 0;
foreach (char letter in this.Letters)
{
switch (letter)
{
case 'a':
case 'e':
case 'o':
case 's':
score += 1;
break;
case 'c':
case 'f':
case 'g':
case 'i':
case 'l':
case 'r':
case 't':
case 'u':
score += 2;
break;
case 'd':
case 'h':
case 'k':
case 'm':
case 'n':
score += 3;
break;
case 'j':
case 'p':
case 'w':
case 'y':
score += 5;
break;
case 'q':
score += 7; | {
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c#, linq, lookup
public FastCollection(IList<T> data)
{
_items = data;
_lookups = new List<Expression<Func<T, object>>>();
_indexes = new Dictionary<string, ILookup<object, T>>();
}
public void AddIndex(Expression<Func<T, object>> property)
{
_lookups.Add(property);
_indexes.Add(property.ToString(), _items.ToLookup(property.Compile()));
}
public void Add(T item)
{
_items.Add(item);
RebuildIndexes();
}
public void Remove(T item)
{
_items.Remove(item);
RebuildIndexes();
}
public void RebuildIndexes()
{
if (_lookups.Count > 0)
{
_indexes = new Dictionary<string, ILookup<object, T>>();
foreach (var lookup in _lookups)
{
_indexes.Add(lookup.ToString(), _items.ToLookup(lookup.Compile()));
}
}
} | {
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On the other hand, mediawiki even without MJ seems to always reload page for preview and AFAIK nobody objects (I agree: reloading is an annoyance but rather minor).
1333
##### MAT244 Announcements / Re: Tests (all sections)
« on: February 11, 2013, 06:56:33 PM »
For TT1, MT and TT2:
The night lectures start as usual and continued without any break until 30-25 min before test; then we go to EX | {
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gravity, speed-of-light, orbital-motion
Update: After reading the below answers, here's my reasoning to why I thought it would be in the nanometre range.
I thought that if light was as close as possible to Earth (like, a planck length away or something), Earth's gravity would make it hit Earth immediately, but I forgot that the pull of gravity gets weaker when one is further away from Earth (i.e. at the surface of Earth is still somewhat "far away"). You can take the Newtonian expression for the orbital speed as a function of orbital radius and see what radius corresponds to an orbital speed of $c$, but this is not physically relevant because you need to take general relativity into account. This does give you an orbital radius for light, though it is an unstable orbit.
If the mass of your planet is $M$ then the radius of the orbit is:
$$ r = \frac{3GM}{c^2} $$
where $G$ is Newton's constant. The mass of the Earth is about $5.97 \times 10^{24}$ kg, so the radius at which light will orbit works out to be about $13$ mm. | {
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fluid-dynamics, rotational-dynamics, collision, earth
Could an asteroid have hit at an angle to slow the Earth in its revolution or rotation also creating more tilt on Earth axis giving birth to seasons?
Could an asteroid pass through the crust into the magma changing its flow in the Earth and the crust following after?
Could an asteroid hit on a polar cap or a deep ocean causing it to rain and flood the World?
http://physics.stackexchange.com/q/269617/ If I understand correctly, you are asking if a meteor impact could (i) slow the Earth's rotation on its axis or revolution around the Sun enough to account for the 8 to 12-fold decrease in longevity of human-kind measured in Earth days/years; and (ii) cause 40 days of torrential rain, resulting in sufficient inland flooding to float a large wooden boat. | {
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print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.
print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$
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I was getting the answer as 36.
My cases were similar to that of Deeparaj.
Case 1: When (4,8) is one of the selected pair.
Among the remaining 6 numbers only (2,6) have GCD=2. We can select any 3 pairs from the remaining 6 numbers in ((6C2)(4C2)(2C2)/3!)=15 ways( Note that we have to only select the pairs, hence the factor of 3! in the denominator). From this we need to subtract the ways where (2,6) is one of the pairs. Hence the answer of case 1 is 15-3=12.
Case 2: When (4,8) is not of the pairs. | {
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human-biology, skin, heat
A burn is an injury which is caused by application of heat or chemical
substances to the external or internal surfaces of the body, which
causes destruction of tissues. The minimum temperature for producing a
burn is about 44°C for an exposure of about 5-6 hours or about 65°C
for two seconds are sufficient to produce burns.
Thermal injuries
I. With the object of producing standard low-temperature burns in
animals, and of studying the area of tissue only partly damaged in a
burn, a burning iron has been made capable of applying temperatures
from 45°-80°C. to the skin; with this the amount of heat and
temperature causing skin damage has been studied, and the macroscopic
and microscopic damage due to graded temperatures have been
delineated. | {
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physical-chemistry, water
My attempt:
I have read this: Liquid water below freezing temperature. So, I understand that the small piece of ice is only added to provide a nucleation site to promote the freezing of water.
But, all physical processes must follow the Law of Calorimetry, right? So, for water below $0$ degrees to freeze, it must first accept heat from somewhere, to reach zero degrees. But, the container is at an even lower temperature, so it won't provide water with any heat (negative temperature gradient). We have also not been given the mass of ice added, so we can't calculate the amount of heat the water will gain from the ice (the latter is at a high temperature than water). The system is isolated, so there is no other possible heat source... | {
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and identification of key features of graphs of the following functions: – power functions ( if on exam one- know general shape and plot points). Read each question carefully and choose the answer that you think is most likely to be correct. 5 Graphing Sine and Cosine Functions - PRACTICE TEST. Cannot exceed 1 since always lies between -1 and 1. Trigonometric Functions. REVIEW SHEETS. 4 Trigonometric Functions and their Graphs 12. Definition of Inverse Trig Functions: Reciprocals also have Function Domain Range. MS 115 PRECALCULUS ALGEBRA AND TRIGONOMETRY. We have seen that once a graph of a function is determined we can obtain the graphs of related functions through scaling and shifting. Review of Trigonometric, Logarithmic, and Exponential Functions In this tutorial, we review trigonometric, logarithmic, and exponential functions with a focus on those properties which will be useful in future math and science applications. I am hoping students will be motivated to work hard on the | {
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(b) What is the type of correlation?
(c) What is the strength of the correlation?
(a) This graph will be shown during the grind!
(b) Negative correlation
(c) Perfect with $$r=-1$$
## Question 2
The price of five second-hand bikes is shown below.
\begin{align}\{100,85,60,40,20\}\end{align}
The first bike is one years old, the second bike is two years old etc.
(a) Represent this information on a scatter graph.
(b) What is the type of correlation?
(c) What is the strength of the correlation?
(a) This graph will be shown during the grind!
(b) Negative correlation
(c) Strong with $$r$$ close to $$-1$$
## Question 3
The price of five second-hand bikes is shown below.
\begin{align}\{100,85,90,80,85\}\end{align}
The first bike is one years old, the second bike is two years old etc.
(a) Represent this information on a scatter graph.
(b) What is the type of correlation?
(c) What is the strength of the correlation?
(a) This graph will be shown during the grind! | {
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javascript, algorithm, html5, cache
for (var tmpKey in tmpData) {
var tmpExp = JSON.parse(localStorage.getItem(tmpKey)).expirationTime;
if (tmpExp > expTime) {
delete tmpData[tmpKey];
tmpData[key] = expTime;
break;
}
}
}
for (var deleteKey in tmpData) {
this.destroyItem(deleteKey);
}
return true;
}; | {
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"tags": "javascript, algorithm, html5, cache",
"url": null
} |
covering 100+ topics in Mathematics... Are unblocked penny is tossed 60 times yielding 45 heads and 15.! Out of n objects in a previous video possible from a set of objects$! These five people in five chairs is five factorial does matter it is a of... 2 } =10 $types of such pairs permutations ; Home safe 472. Matter it is the permutation formula which we use of the statements in these questions 17! Distinguish between permutations and Combinations: permutation: any arrangement of these 120 permutations and... The Binomial Theorem Subsection 2.4.1 Combinations Combinations involve counting the number of arrangements... Give a different permutation of a set and forming subsets: 3600 the information that determines ordering. To know how to count are 10 questions on a Discrete Mathematics for each of these 120 permutations Combinations. 40 Discrete Mathematics CHAPTER TWO permutations, there are 10 questions on a Discrete Mathematics Mathematics. Daily for 2-3 months to learn and | {
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"openwebmath_score": 0.5296341180801392,
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"url": "http://neuropsychologycentral.com/k0jdv3cp/discrete-math-combinations-and-permutations-a63cd2"
} |
c++, c++11, file, image, serialization
Title: Writing a bitmap image from C++ Here's my function that creates a bitmap file from an array of pixels. It can write a bitmap both with transparency and without transparency. Please review my code and give constructive criticism on how to increase the overall quality of it. :)
typedef unsigned char BYTE;
inline int bmpEncoder(const std::string &location,
const unsigned __int32 &width, const unsigned __int32 &height,
const std::vector<BYTE> &buffer,
const bool &hasAlphaChannel = true) {
std::ofstream fout(location, std::ios::out | std::ios::binary);
if (fout.fail()) {
return 0;
}
//Padding
const unsigned __int8 padding = hasAlphaChannel ? 0 : (4 - (width * 3) % 4) % 4;
//Bitmap file header.
const char signature[2] = { 'B', 'M' };
const unsigned __int32 fileSize = buffer.size() * sizeof(BYTE) + padding * (height - 1) + 14 + 124;
const unsigned __int32 offset = 14 + 124; | {
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c++, c++11, sorting, stl
std::move_backward(sortPosition, elem, std::next(elem));
*sortPosition = std::move(current);
}
}
template <typename FwdIt>
void insertionSort(FwdIt begin, FwdIt end)
{
insertionSort(begin, end, std::less<typename std::iterator_traits<FwdIt>::value_type>());
}
template <typename BiDirIt, typename Comparer>
void quickSort(BiDirIt begin, BiDirIt end, Comparer compFunc)
{
detail::QuicksortStack<BiDirIt> ranges;
ranges.push(std::make_pair(begin, end));
while (!ranges.empty())
{
const auto current(ranges.top());
ranges.pop();
const auto last(std::prev(current.second));
const auto pivot(std::partition(current.first, last, [=](const typename std::iterator_traits<BiDirIt>::value_type& val){ return compFunc(val, *last); }));
std::iter_swap(pivot, last);
ranges.push(std::make_pair(current.first, pivot)); | {
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# When an airbag is inflated the nitrogen gas has a pressure of 1.30 atmospheres, a temperature of 301 K, and a volume of 40.0 liters. What is the volume of the nitrogen at STP?
Jun 27, 2016
$\text{47.8 L}$
#### Explanation:
You can actually use two approaches to solve this problem.
You can use the ideal gas law to find the number of moles of gas present in that sample, then use the known molar volume of a gas at STP conditions to find the new volume.
As a way to double-check the result you get by using this approach, you can use the combined gas law equation to find the new volume of the gas without finding out how many moles it contains.
So, the ideal gas law equation looks like this
$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} P V = n R T \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$
Here you have | {
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} |
cosmology, universe, curvature, cosmological-inflation, observable-universe
My concern The constant $k$ in the FRW metric can be rescaled to have values $k=0,\pm 1$. How is this a problem when $k$ can always be rescaled and not a measurable parameter? The physical quantity is $k/a^2$. Rescaling $k$ must be accompanied by a corresponding redefinition of $a$. If we take $k = -1,0,1$ as is standard, then $a$ gives the radius of curvature. | {
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algorithms, concurrency, deadlocks
the actions performed are:
Ph_i gives his left fork to its predecessor Ph_{i-1}
the post-conditions are as follows:
Ph_{i+1} becomes the new altruistic philosopher
Ph_{i-1} is now holding two forks and can eat
After eating, Ph_{i-1} puts down both forks.
The important invariant is that the predecessor of the altruistic philosopher is guaranteed to eat after a deadlock situation.
Given N philosophers, the round robin policy guarantees that each philosopher becomes altruistic exactly once in a sequence of N deadlocks.
Hence, each philosopher is guaranteed to eat (at least) once every N deadlocks (because it is the predecessor of an altruistic philosopher exactly once every N deadlocks).
This is, of course, the analysis of the worst-case possible outcome. Depending on the work-load, deadlocks may not arise so frequently and in this case each philosopher would have the chance to eat pretty much anytime it wants. | {
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javascript, datetime, formatting
Title: Simple elapsed time counter I've written a simple JavaScript function based off some existing code that takes a specific UNIX time string (in the snippet: 1491685200). It shows an alert if the specified time is still in the future. When that date has passed, it shows the elapsed days, hours and minutes whenever the function is called in-page.
I'm don't have much JavaScript object experience so it works just fine as-is, but I think it can be optimized further before I migrate my other stuff over to ES6.
function ElapsedTime () {
var nTotalDiff = Math.round((new Date()).getTime() / 1000) - 1491685200;
if (nTotalDiff >= 0) {
var oDiff = {};
oDiff.days = Math.floor(nTotalDiff / 86400);
nTotalDiff -= oDiff.days * 86400;
oDiff.hours = Math.floor(nTotalDiff / 3600);
nTotalDiff -= oDiff.hours * 3600;
oDiff.minutes = Math.floor(nTotalDiff / 60);
nTotalDiff -= oDiff.minutes * 60;
oDiff.seconds = Math.floor(nTotalDiff);
return oDiff;
} else { | {
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special-relativity, spacetime
Title: How can it be that Doppler Factor $k=\frac{1}{k}$? I am currently studying special relativity mainly using this paper which uses spacetime diagrams to derive the formulas for the properties of special relativity (Time dilation, length contraction etc.).
In chapter II, the "Doppler k-Factor" is derived as $$k=\sqrt{\frac{1+\beta}{1-\beta}} \tag{9}$$ where $\beta=\frac{V}{c}$ ($V$ is the speed of which an inertial frame of reference $K'$ is receding from a "stationary" frame $K$.
(I use the same tags for equations here as used in the linked paper to avoid confusion).
Earlier in the paper, $k$ has been defined as
$$k=\frac{cT_2}{cT'}=\frac{cT'}{cT_1}\tag{7}$$
You can get from here to euquation $9$ by multiplying the two "versions" of $k$ and then taking the square root.
$cT_2$, $cT_1$ and $cT'$ are different "events" that happen when a ligght ray is sent from $K$ to $K'$ and reflected from $K'$ back to $K$: | {
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squares function -- and can be computed as such. compute_ak: calculate the set of normalization constants, needed for exact pattern probabilities. n, k. integers with k between 0 and n. Value integer, the Binomial coefficient $({n \over k})$. It calculates the binomial distribution probability for the number of successes from a specified number of trials. Also, if Y N ( 0.5 n, 0.25 n), it is not hard to see that. (n - k)!). Stepwise regression is a sequential feature selection technique designed specifically for least-squares fitting. Dimension too large., this was due to the calculation of the binomial coefficient.) In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Examples to Implement Polynomial in Matlab. But that doesn't give me that happy feeling that comes with understanding. Yes, @Bruno, you are right. binomial coefficient. k = 1:n; The logistic regression coefficient associated with a predictor X is the | {
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"lm_q2_score": 0.863391599428538,
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#### JeffM
##### Elite Member
Thanks for help. I'm aware that my language is sloppy, hopefully it will improve in time as my ability to think clearly develops ( I hope!). I think I was just trying to note that I had realised that the operation works both ways, so that, in the case of f(x) = 1/x applying a power of minus one creates the output and applied to the output gives you the input ( for that value of x). I've probably dug myself in deeper with imprecise language-apologies. I've got a long way to go before I can use language with the rigour required by mathematics! I think I now get it even though it might sound like I don't linguistically. I can now grasp that when f(x) = ff(x) then it is an involution.
Thanks for the help-really valuable.
One way to avoid the problems of natural language is to formulate your thoughts in mathematical symbols immediately. If you are told that an involution is a function that is its own inverse, put the definition of an inverse down first. | {
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mri
Title: Bloch equation: adding gradients I have a bloch simulation that I have implemented in Python. The implementation is very simple as:
import numpy as np
GYRO = 267538030.3797 # in radians / s / T
T1 = 0.3
inv_T1 = 1.0/0.3
T2 = 0.05
inv_T2 = 1.0/0.05
M0 = 1.0
# This function is called at various time steps
def bloch(self, M, B):
# Solve bloch equation in rotating frame.
# M: Magnetization vector
# B: Effective magnetic field
return GYRO * np.cross(M, B) - [M[0] * inv_T2,
M[1] * inv_T2,
inv_T1 * (M[2] - M0)] | {
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c++, csv
offset = end_offset + 1;
item += 1;
}
return result;
}
}
}
#endif A few observations:
I would never write x += 1; if I wanted to increment x. I think this is confusing and more prone to error than writing ++x;. Of course, there should be no difference for the compiler.
In count_items, do you really want to return 1 even if there are no matches? Be as it may, you don't have to write an explicit loop as this is equivalent to using std::count, i.e., you could just write
std::size_t count_items(const std::string &line, char separator) {
return std::count(line.cbegin(), line.cend(), separator) + 1;
}
I find your split function parse_line quite difficult to read. There are several alternatives to this including many in Boost (Tokenizer, boost::algorithm::split, ...). | {
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newtonian-mechanics, momentum
and you should also see at the general formula of momentum in which force is inversely proportional to the time taken and directly proportional to the change in momentum according to your fictional scenario it will result in a very large amount of force in a very small time which will nearly tend to zero and according to the basic mathematical principles any ratio between any non-zero number with zero will result in infinity and it is mere impossible for any man or machine in this world to apply infinitive force
and if you take an example of very minute elementary particles like electrons whose weight is very small but moves with a very high velocity the result will be the same
so in short answer to your question is practically impossible but theoretically possible | {
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differential-geometry, resource-recommendations, vector-fields, mathematics, calculus
$$ d \omega = (n+1)\partial_{[\mu_{n+1}}\omega_{\mu_{1}\cdots \mu_{n}]} dx^{\mu_{1}} \cdots dx^{\mu_{n}}dx^{\mu_{n+1}}.$$ Let us note, then, that it makes sense to integrate an $n$ form over an $n$ dimensional manifold, and an $n+1$ form over an $n+1$ dimensional manifold.
Stokes' theorem is the spectacular result that integrating a $d-1$ form, $\omega_{d-1}$ over the $d-1$-dimensional boundary of a $d$-dimensional manifold is equal to integrating the $d$-form $\omega_{d} = d \omega_{d-1}$ over the $d$ dimensional boundary. Indeed, a $d$ form will have the form $\omega_{d\, \mu_{1} \cdots \mu_{d}} dx^{1}\cdots dx^{d} = \omega_{d\, \mu_{1} \cdots \mu_{d}} dV$ where $V$ is the volume measure; $d \omega_{d} = 0$ due to the anti-symmetrisation of $d + 1$ indices taking on only $d$ values.
Note to mathematicians | {
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ros-kinetic, gazebo-7
I would also recommend taking a look at the ODE manual and learning more about the friction model, CFM & ERP and how it relates to kp and kd: http://ode.org/ode-latest-userguide.pdf | {
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c#, asynchronous, wpf, mvvm, system.reactive
Title: A ViewModel using ReactiveUI 6 that loads and sends data Most of the Rx Compelling Examples™ load and store data locally, which I don't find that Compelling.
I spent some time coming up with how to best perform the following actions but want to make sure I am not Doing It Wrong™.
Here are the cases I am trying to solve:
Load data from cache and remote server when view model is instantiated
Save data to server when UI interaction happens (some button press)
Handle error cases (network down)
Some items I am trying to avoid:
Errors being swallowed (async in ctor for example)
Incorrect use of Rx patterns (is there a more 'correct' way)
Loss of data either through out of sync lists, not using cache correct, other.
public class CommonViewModel : ReactiveObject, IRoutableViewModel
{
private readonly RemoteHttpService _remoteClient; | {
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glaciology, ice-sheets, glaciation
It should be added the the understanding of the variations of the last ice sheet come from a series of indirect sources such as sea-level changes, paleo-climate records e.g., (ice cores) and interstadial paleoclimate reconstructions. This means that as our understanding of these indirect records are improved, we can also improve our ice sheet forcing. Add to that uncertainties about basal conditions beneath past ice sheets that affect their dynamics and it is easy to see that past ice thickness values are uncertain. We can, however, obtain reasonable estimates from the models which could be accurate to within, perhaps 500 m (my guestimate). | {
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Testing of hypothesis, and... Carried out as the applications of the MCQs on this page are covered from Estimate Estimation! The statistical inference not properly working plz resolve the errors as soon as possible $... Sir Imdad assess the relationship between the dependent and independent variables a set of sufficient. Can also update them Nts, Kppsc, Ppsc, and other test https: //itfeature.com receive! Population, based on random sampling Nts, Kppsc, Ppsc, and efficiency of the statistical inference Estimation... Sorry, your blog can not share posts by email end of post also contains answers of all at., Nts, Kppsc, Ppsc, and other test sent - your... Inference MCQs for Preparation of Fpsc, Nts, Kppsc, Ppsc and!$ T_2 $is, 15 categories are updated, 15 any I can also update them from hypothesis. Online learning concepts and enhance the knowledge too dynamic which means _______ estimator$ \hat { }! Also contains answers of all MCQs at last page will help the learner to understand the | {
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ros, pr2, ros-kinetic, grasp
Feel free to ask question if something is unclear.
Comment by timtuch96 on 2021-07-29:
Thank you very much, I will try it out asap :)
I finally managed to add custom poses, you can find the stage here : https://github.com/YannickRiou/moveit_task_constructor/blob/master/core/src/stages/generate_custom_pose.cpp
You can then use it by giving it an array with custom poses (please see the function createDropTask that use the stage "GenerateCustomPose") : https://github.com/YannickRiou/pr2_mtc/blob/4b6242d05bad952ac7b6d3f2df7e7a5df6f0afdb/src/pr2_tasks.cpp#L329
Feel free to ask question if something is unclear. | {
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homework-and-exercises, optics, interference
I assume there must be something I'm missing about the concept so I'd really appreciate it if someone explain it to me. Suppose a particular thickness of the slab to be $d$. Then for two different wavelength, the condition for constructive interference:
$$2nd=m_1\lambda_1$$
$$2nd=m_2\lambda_2$$
$$\frac{m_2}{m_1}=\frac{\lambda_1}{\lambda_2}$$
That should be a condition for constructive interference to match up. Note that the order of interference must be different. Though it's not impossible that two-wavelength can not produce constructive interference for the same width. | {
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special-relativity, astronomy, meteorites, meteoroids, asteroids
So near-luminal macroscopic bodies aren't observed. I would even go further and despite my being a believer that life in the Universe is extremely rare, I would say that an object moving by a near-luminal speed would prove the existence of an advanced civilization. I should be a bit careful: the gravitational slingshot is a process that allows the speed to be enhanced even naturally. But even if the source of the speed were a gravitational slingshot and the speed would be really high, like 99.9999% of the speed of light, chances would be high that some intelligence was behind the optimization of the gravitational slingshot because it's extremely unlikely for such an outcome to occur naturally. | {
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homework-and-exercises, newtonian-mechanics, classical-mechanics, harmonic-oscillator
Title: Harmonic oscillator with constant external force I tried to find the full derivation of the differential equations for the following problem but did not find any relevant resources that discuss external forces with harmonic motion (except damped and forced motions):
"Mass m is attached to a string (which is itself connected to the ceiling) and is a mathematical pendulum if we use a small angle approximation. a horizontal external constant force $F_0$ is applied to the mass m. write the relevant differential equations, and show the derivation for the angular frequency" (the answer is $\omega'=\sqrt{(\sqrt{g^2+(F_0/m)^2})/l}$ ).
I tried to solve this example in the following way:
I decomposed the force mg and $F_0$ to their radial and tangent component. in the tangent axis, the equation is $−mgsin(θ)−F_0cos(θ)=mlθ′′$ (1). | {
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other analytical methods have difficulty solving. This paper will be primarily concerned with the Laplace transform and its ap-plications to partial di erential equations. f(t+ T) = f(t) for all t 0. 0 Year 2012. 1 p344 PYKC 24-Jan-11 E2. Since the m. The Laplace transform is a widely used integral transform (transformation of functions by integrals), similar to the Fourier transform. These theorems are applied to most commonly used special functions to obtain many new two and three dimensional Laplace transform pairs from known one and two dimensional Laplace transforms. Applications of the Laplace Transform - Free download as PDF File (. Laplace Transform of tf(t) The video presents a simple proof of an result involving the Laplace transform of tf(t). [PDF] The Laplace Transform: Theory and Applications By Joel L. When we apply Laplace transforms to solve problems we will have to invoke the inverse transformation. We get Hence, we have. The Laplace transform pair for. With its | {
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• It is just another tool to add to your toolbox. The only potential problem the method may throw up is integrals which are either tedious or difficult to find. – omegadot Feb 6 '18 at 3:53
• Yes. But remember the sum this can be done on must first converge (try the technique on $\sum_{n =1}^\infty 1/n$ as see what happens) and the number of linear factors appearing in the denominator should not be too many since as their number grows the number of integrations that need to be performed also grows and can become very tedious. – omegadot Feb 6 '18 at 4:04
• And as an example of a sum that leads to a more difficult integral to find (unless you are familiar with special functions that is or other more advanced techniques for finding improper integrals) is $\sum_{n = 1}^\infty 1/n^2$. See what you end up with if you let $1/n = \int_0^1 x^{n - 1} \, dx$ and $1/n = \int_0^1 y^{n - 1} \, dy$. – omegadot Feb 6 '18 at 4:06 | {
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database, pathogenesis, data, host-pathogen-interaction
Pathway modules represent groups of functionally related enzymes part of the metabolic network. I think this one is easy to understand because it represents the classical understanding of "module". The modules involve metabolites (compounds with id starting with "C"), enzymes (represented by KEGG ortholog ids starting with "K") and reactions (represented by ids starting with "R"). The reactions integrate compounds and enzymes in a particular step in the chain of reactions included in that module.
Signature modules represent molecules associated with a particular phenotype. In particular, the example listed in the KEGG page points to EHEC pathogenicity signature, Shiga toxin. The two molecules in module M00363 are associated with the phenotype, which is in this case EHEC pathogenicity. But in principle they do not necessarily need to be related to each other (in this case they are, but not in the same meaning as the metabolic module). | {
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photons, laser, ionization-energy
In quantum mechanics, the totalitarian principle tells you, basically, that if something can happen, it must happen. However, it doesn't tell you how often it will happen.
For the multiphoton ionization you're asking about, your calculations show that there is a six-photon ionization process that's possible for the nitrogen molecule subjected to a 477nm laser. However, what you don't learn from that calculation is how likely that process is to happen: if your laser is weak, you're likely to have one or two electrons get ionized on occasion; that might be once per million ages of the universe, but it's still a positive rate so the process is happening.
To get the pretty sparks of laser-induced optical breakdown in air, however, you don't just need a nonzero rate, you need enough electrons to kick-start the avalanche process of dielectric breakdown. That is, you need the ionization rate be macroscopically meaningful, not just nonzero. | {
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