text stringlengths 1 1.11k | source dict |
|---|---|
electricity, electric-current, voltage, power
Say, if the heat was unable to leave the filament for some reason
Remember that it's not just heat. It's any form of radiation. The purpose of the filament is to emit light, so you know some energy is leaving. The more you prevent it from leaving, the hotter it gets inside, but the power has to balance. Bulbs are also made to operate at a particular temperature. If you raise it too much, the filament will lose strength and fail (and then the energy input stops).
Taken to an extreme, see the xkcd what if... archive.
re you saying that the light bulb isn't going be brighter at a lower power because energy is being radiated away at the same time?
All bodies with a temperature radiate. The hotter the body, the more radiation per area is radiated. If the total power output equals total power input, then the temperature will be maintained. | {
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} |
chemical-engineering, manufacturing-engineering
Also, do not mislead yourself to believe it necessarily needs to look like a sponge to the naked eye. The particles can be powders after all when they are, the pores may be so small that it might just look like a solid mass. For example, sintered bronze bushings looks just like a solid piece of bronze. | {
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"tags": "chemical-engineering, manufacturing-engineering",
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} |
javascript, image, ecmascript-6
const preloadAll = sources =>
Promise.all(
sources.map(
preload));
const sources = [
'https://i.picsum.photos/id/1000/5626/3635.jpg',
'https://i.picsum.photos/id/10/2500/1667.jpg',
'https://homepages.cae.wisc.edu/~ece533/images/cat.png',
'https://homepages.cae.wisc.edu/~ece533/images/airplane.png'];
preloadAll(sources)
.then(images => console.log('Preloaded all', images))
.catch(err => console.error('Failed', err));
Preload to your hearts desire. | {
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"tags": "javascript, image, ecmascript-6",
"url": null
} |
python, performance, recursion, file-system
Title: Alternate method of iterating than os.walk Recently, I became tired of how slowly os.walk seems to run (really, it should be called os.crawl), and made something recursive which moves much faster. I was using it to take directories I wanted and add them to an array, but this time I need to add all files to an array that aren't in an 'exclude array.' Does anyone have any advice?
import os | {
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"tags": "python, performance, recursion, file-system",
"url": null
} |
space-expansion, solar-system
http://www.scienceminusdetails.com/2012/06/is-solar-system-tilted-sideways.html )
A nice way to confirm this with your own eyes is to go outside tonight at about 1am (NB this was written 22/11/2014) and look towards the East (assuming the sky is clear and you are in the northern hemisphere). You should be able to spot the planet Jupiter rising and it is between the zodiac constellations of Leo and Cancer. If the solar system plane was lined up with the galactic plane, two things would be true. (i) The planets would always be seen against the background of the Milky Way, which marks the disk of our Galaxy and (ii) the signs of the zodiac, marking the path of the Sun around the sky over the year (the ecliptic) would follow the Milky Way. Neither of these things are true; you should see that the Milky Way rises up into the sky from the south and lies about 50 degrees from Jupiter and well away from Leo and Cancer. (Leo is quite easy to spot).
Top view | {
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"tags": "space-expansion, solar-system",
"url": null
} |
c, gui
//Return an allocated copy of Dynamic_String content
char *ds_content_copy(const Dynamic_String *ds)
{
size_t length = ds_length(ds);
char *temp = malloc(length + 1);
if(temp == NULL)
return NULL;
return memcpy(temp, ds->content, length + 1);
}
//Reduce storage to the minimum, and return content as C string
char *ds_to_cstring(Dynamic_String *ds)
{
//Assume reducing storage will work, if it doesn't return with extra space
ds_shrink_to_fit(ds);
return ds->content;
}
//Join a list of Dynamic_Strings and return their contents as C string
//The list must be delimited by NULL
char *ds_join_list_to_cstring(Dynamic_String **ds_list)
{
//If all have length 0, return an string with '\0'
size_t total_size = 1;
for(size_t i = 0; ds_list[i] != NULL; ++i)
total_size += ds_length(ds_list[i]); | {
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"tags": "c, gui",
"url": null
} |
newtonian-mechanics, energy, rotational-dynamics, energy-conservation, work
friction acts is instantaneously at rest in the inertial frame of reference. For a detailed discussion of both of these reasons see Consistent Approach for Calculating Work By Friction for Rigid Body in Planar Motion and Is work done by torque due to friction in pure rolling?. An answer by @Dale in the second reference provides a very simple way to determine whether or not friction does net work; this is a much clearer answer than many confusing answers given elsewhere. | {
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"url": null
} |
coordinate-systems, inertial-frames, scattering, scattering-cross-section
+\frac{f_{22}}{(u-m^2)^2}
\right)
\tag{1}
\end{equation*}
where
\begin{equation*}
\begin{aligned}
f_{11}&=-8 s u + 24 s m^2 + 8 u m^2 + 8 m^4
\\
f_{12}&=8 s m^2 + 8 u m^2 + 16 m^4
\\
f_{22}&=-8 s u + 8 s m^2 + 24 u m^2 + 8 m^4
\end{aligned}
\tag{2}
\end{equation*}
Recall the Mandelstam variables are
\begin{align*}
s&=(p_1+p_2)^2
\\
t&=(p_1-p_3)^2
\\
u&=(p_1-p_4)^2
\end{align*}
Compton scattering experiments are typically done in the lab frame where the electron is at rest.
Define Lorentz boost $\Lambda$ for transforming momentum vectors to the lab frame.
\begin{equation*}
\Lambda=
\begin{pmatrix}
E/m & 0 & 0 & \omega/m\\
0 & 1 & 0 & 0\\
0 & 0 & 1 & 0\\
\omega/m & 0 & 0 & E/m
\end{pmatrix}
\end{equation*}
The electron is at rest in the lab frame.
\begin{equation*}
\Lambda p_2=\begin{pmatrix}m \\ 0 \\ 0 \\ 0\end{pmatrix}
\end{equation*}
Mandelstam variables are invariant under a boost.
\begin{equation*}
\begin{aligned}
s&=(p_1+p_2)^2=(\Lambda p_1+\Lambda p_2)^2
\\ | {
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combustion
In the "Properties" section of the same Wikipedia article there is a subheading named "Solvent properties" which has the weird statement: "Ammonia does not burn readily or sustain combustion, except under narrow fuel-to-air mixtures of $15–25\%$ air." The statement is weird both because of the placement of the sentence as well as the wording. It should be that the fuel-to-air mixture is $16-25\%$ of ammonia, not $15–25\%$ air. | {
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quantum-mechanics, history, measurement-problem, wavefunction-collapse, decoherence
If you want to understand what Copenhagen interpretation actually was the shortest way is to read Chapter 3 of the book by Werner Heisenberg "Physics and Philosophy" which is entitled... "The Copenhagen interpretation of quantum theory".
I would like to present the following excerpts, make from them what you want. | {
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newtonian-mechanics, forces, torque
So far, my idea was: No, because when we place the cube on the water, a same amount of water equal to the submerged volume will be displaced. (My guess is) That will keep the centre of mass fixed, so there will be no extra torque about the contact point.
But the answers I got to these questions made me confused over my opinion: Can the fish topple the bowl and What is the rower actually doing? Pushing the water or pushing the lake?. ( Read them only if you are interested. I expect an answer for this question.)
Is the cube still able to change the CoM of the system? You are right, the bowl doesn't lean. From Archimedes' principle we know that the mass of the displaced fluid is the same as the mass of the cube. This means that the weight of the cube is the same as the weight of some water that would occupy the submerged part of the cube. In other words, if you substitute the cube with a volume of water equal to the volume of the submerged part, the force is the same. | {
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"url": null
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quantum-mechanics, quantum-field-theory, particle-physics
...I know that $\exists$ a whole theory on this, Quantum Electrodynamics (thanks Feynman!!!), but I have not studied it. I have only ever taken an intro QM class as an undergraduate.
Edit: If the position eigenstate causes problems, let B be in an arbitrary eigenstate as well. The question is rephrased: if the positions are indeterminate, how is the force, which depends on them, calculated? Note that the problem you pose is non-realistic. If at a certain moment B is in a position eigenstate, $\delta (\vec r)$, at an extremely short time after , B can be everywhere is the universe with equal probability. You will see the effect of this, below.
But let's first calculate the force $<\vec F>$. In QM, the influence of between A and B goes as follows: let $\psi_A(\vec r)$ be the wave-function of the electron A, where the vector $\vec r$ connects A, wherever A is, with B.
Then the force of interaction is
$\vec F(\vec r) = -\frac {e^2 \vec r}{4 \pi \epsilon_0 |r|^2}$. | {
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c++, beginner, object-oriented, reinventing-the-wheel, sfml
return m_active;
}
void clickableRect::reset()
{
m_active = false;
}
bool clickableRect::isInside(const sf::RenderWindow & window) const
{
return sf::Mouse::getPosition(window).x > getPosition().x
&& sf::Mouse::getPosition(window).x < getPosition().x + getSize().x
&& sf::Mouse::getPosition(window).y > getPosition().y
&& sf::Mouse::getPosition(window).y < getPosition().y + getSize().y;
}
I would love any and all feedback on all aspects of the code provided but request specifically to know about:
Is this a good use of inheritance and am I doing it right? Should I use a component pattern instead?
Can I clean up the logic itself inside the click function. It seems a bit messy to me and also requires me to call reset on the objects immediately after returning a true value.
Compile with all warnings | {
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thermodynamics, heat-conduction
I'm trying to write a differential equation that will give me $T(x,t)$ when both of these mechanisms are accounted for so I could answer things like what the equilibrium temperature will be for a certain material at various $P$ and $x$, but that is proving to be beyond my ability. Is this function even analytically obtainable? The only thing I could find anywhere was the math for a fully insulated rod and I was unable to implement Newton's law into that. It seems like you want to treat this as a time-dependent problem. If you do a heat balance on the portion of the rod between x and $x+\Delta x$, you have that the rate of change on internal energy with respect to time is equal to the axial heat flow in minus the axial heat flow out minus the rate of heat loss through the surface:$$\rho\pi r^2\Delta x C\frac{\partial T}{\partial t}=\pi r^2q(x)-\pi r^2q(x+\Delta x)-2\pi r\Delta x h(T-T_0)$$where C is the heat capacity of the rod material. If we divide this equation by the volume of the | {
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• @qbert: For example, in $5$-adic analysis, $3$ and $53$ are 'nearby' integers. Some people like to emphasize the arithmetic statement: $3 \equiv 53 \pmod{5^2}$. Some people like to measure the distance: $d(3, 53) = 5^{-2}$. Others prefer to express the that they are the same up to some amount of precision: $3 = 53 + O(5^2)$. And each of these ways of thinking themselves have several ways they could be notated. – user14972 Jul 31 '16 at 1:53 | {
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"openwebmath_score": 0.9015369415283203,
"tags": null,
"url": "https://math.stackexchange.com/questions/1876350/ways-of-showing-sum-limitsn-1-infty-ln11-n-to-be-divergent/1876352"
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c#, algorithm, object-oriented, design-patterns, graph
var smallest = queue[0];
queue.Remove(smallest);//Removing the optimized Node at every Iteration
if (smallest == finish)//Meaning we have calculated the shortest path upto destination node, so no need to calculate shortest path for remaining nodes like in original Dijkstra
{
path = new Stack<string>();
while (previous.ContainsKey(smallest))
{
path.Push(smallest);
smallest = previous[smallest];
}
path.Push(start);
path.Push(": " + distances[finish].ToString());//Adding the shortest path distance as last element
break;
}
if (distances[smallest] == int.MaxValue)
{
break;//This corner-case scenario can happen if the remaining nodes are Un-reachable.
} | {
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special-relativity
Title: Relativity struggle Ok so there is something that I don't really understand , suppose we have the proper time A :8 years and gamma factor 2. Now I understand that the time slow downs for the relative time (t') so the relative time (dilated time) is 16 years. However guy who is moving in the t' frame is actually 8 years old and the guy in proper frame is 16 years which is opposite from what is said above so why do we say that t' is 8 years old if his dilated time is 16 ? How can we transform between the age and time ? Maybe my misunderstanding is the fact that I don't interpret t and t' in the good way ?
What I understand from this is that A: 16(t')=2x8(t) so in john frame after 16 years Mary age by 8 years ? Isn't t' the dilated time or is it the age what is it specifically and what do they mean in the book exactly I think what you don't understand is symmetry of relativity.
If John's time (t) ticks 2 times faster then Mary's (t2), then John will age 2 times faster then Mary. | {
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special-relativity, field-theory, probability, density, klein-gordon-equation
6.2 Probability currents and densities
One of the reasons that Schrödinger wasn't happy with the Klein-Gordon equation after he'd derived it was that something rather nasty happens when you think about the flow of probability density. The probability of a particle being located somewhere depends on $\phi^{*}(x)\phi(x)$
and so if this quantity is time-dependent then particles must be sloshing around. The probability density $\rho$ and probability current density5 $\boldsymbol{j}$ obey a continuity equation
\begin{equation}
\dfrac{\mathrm d\rho}{\mathrm dt}+\boldsymbol{\nabla} \cdot \boldsymbol{j}=0,
\tag{6.9}\label{6.9}
\end{equation}
which is more easily written in four-vector notation as
\begin{equation}
\partial_{\mu}j^{\mu}=0.
\tag{6.10}\label{6.10}
\end{equation}
If, as is usual in non-relativistic quantum mechanics,6 we take the spatial part to be
\begin{equation} | {
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java, playing-cards
default: return null;
}
}
}
Card(Rank rank, Suit suit)
{
this.rank = rank;
this.suit = suit;
}
Rank getRank()
{
return rank;
}
Suit getSuit()
{
return suit;
}
@Override
public String toString()
{
return "rank: " + rank + "\t suit: " + suit;
}
}
CardDeck.java
import java.util.ArrayList;
public class CardDeck
{
private ArrayList<Card> cards;
CardDeck()
{
cards = new ArrayList<>();
for(Card.Suit s: Card.Suit.values())
{
for(Card.Rank r: Card.Rank.values())
{
cards.add(new Card(r,s));
}
}
}
public static void main(String[] args)
{
CardDeck deck = new CardDeck();
System.out.println(deck);
} | {
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ros, rviz, urdf, load
Original comments
Comment by zakizadeh on 2016-12-01:
thanks a lot !
i can load urdf in rviz while have same error !!!
Comment by gvdhoorn on 2016-12-01:
So did you resolve the issue? Or are you still having the same error?
Comment by zakizadeh on 2016-12-01:
i still have same error but this time urdf loading correctly !!
Comment by gvdhoorn on 2016-12-01:
well, what is the output of ls -al /home/zakizadeh/catkin_ws3/src/wrist/meshes/m2_1.stl? Does the file actually exist?
Comment by zakizadeh on 2016-12-01:
problem is solved . thanks a lot .
Comment by gvdhoorn on 2016-12-02:
Please tell us what you did to solve the problem. That way future readers might be able to avoid the same / similar problems.
Comment by trashperson on 2020-01-16:
It was after all this error pointed out by gvdhoorn, thanks a bunch. I changed the $(find package) to //package and it worked. sorta dumb and unexpected, weird flex but ok
Comment by Teo Cardoso on 2020-03-29: | {
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of Mathematics Studies (105)) on Amazon. Thanks for contributing an answer to Mathematics Stack Exchange! Please be sure to answer the question. Free multiple integrals calculator - solve multiple integrals step-by-step This website uses cookies to ensure you get the best experience. Similarly, a double integral allows you to measure the signed volume between a function z = f(x, y) and the xy-plane as bounded by any two. A multiple integral is a definite integral of a function of more than one variable. You can solve double integrals in two steps: First evaluate the inner integral, and then plug this solution into the outer integral and solve that. Multiple Integrals 4. quad (func, a, b, args = (), full_output = 0, epsabs = 1. Evaluate the double integral ZZ R 2xy dA. To the best of the authors' knowledge, for the researches referring to the triple integral term in the LKFs, most literature directly applied the Jensen-based double integral inequality (JBDII) (see (17) for details) to | {
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ros-hydro, ubuntu-precise, ubuntu
Title: simple method to detect node crashes
Hey guys,
I am searching for a simple way to detect a node crash. I saw this already and the answer looks pretty simple to implement. However, the project I am working on has around 15+ nodes running at the same time and it looks like I would have to set a watchdog for each one of them. | {
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c, integer
hugeint *hugeint_create(void)
{
hugeint *self = xmalloc(sizeof(hugeint)
+ HUGEINT_INITIAL_ELEMENTS * sizeof(unsigned int));
memset(self, 0, sizeof(hugeint)
+ HUGEINT_INITIAL_ELEMENTS * sizeof(unsigned int));
self->n = HUGEINT_INITIAL_ELEMENTS;
return self;
}
hugeint *hugeint_clone(const hugeint *self)
{
hugeint *clone = xmalloc(sizeof(hugeint) + self->n * sizeof(unsigned int));
memcpy(clone, self, sizeof(hugeint) + self->n * sizeof(unsigned int));
return clone;
}
hugeint *hugeint_fromUint(unsigned int val)
{
hugeint *self = hugeint_create();
self->e[0] = val;
return self;
}
hugeint *hugeint_parse(const char *str)
{
char *buf;
hugeint *result = hugeint_create();
size_t bcdsize = copyNum(&buf, str);
if (!bcdsize) return result;
size_t scanstart = 0;
size_t n = 0;
size_t i;
unsigned int mask = 1;
for (i = 0; i < bcdsize; ++i) buf[i] -= '0'; | {
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special-relativity, symmetry, conservation-laws, noethers-theorem
Quantum mechanically, the bracket is replaced by $1/i\hbar$ times the commutator which is nonzero. The ket vectors simply transform as
$$|\psi\rangle \to \exp(i\lambda N)|\psi\rangle$$
under the symmetry you're looking for. This is just the overall change of the phase which doesn't change the physical (measurable) properties of the ket vector. Because the number of particles is conserved so perfectly, any complete enough measurement of the system will find it in an eigenstate of $N$. The conservation law implies that the final state will be an eigenstate, too. So after one complete enough measurement, the subspaces of the Hilbert space with different eigenvalues of $N$ are pretty much separated from each other – we say that they live in different superselection sectors. | {
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In Pari-GP you can get the desired result like this:
? \p=501
? sqrt(2) The answer is:
1.41421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147010955997160597027453459686201472851741864088919860955232923048430871432145083976260362799525140798968725339654633180882964062061525835239505474575028775996172983557522033753185701135437460340849884716038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723724
If you like programming I suggest trying to solve some of the Project Euler problems.
-
Actually, I think this probably is for a Project Euler problem. Not sure I can blame anyone for looking this one up though. Most computer languages don't do that kind of precision normally. It took quite a while to find an algorithm just about made for a computer. – Mike Apr 23 '12 at 18:00 | {
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In the second solution:
You choose (R1,R2,R3) first then assign the suits. But using $\binom{13}{3}$ means the order of the three ranks do not matter. In other words, you are treating the three hands (R1,R1,R2,R2,R3), (R3,R3,R2,R2,R1), (R1,R1,R3,R3,R2) as one hand only. Thus you undercount 3 times.
Your first method is to count ways to choose two from thirteen ranks for the pairs, two from four suits for each of those, and one from fourty-four cards to be the loner (or one from eleven ranks and one from four suits). That is okay. $$\binom{13}2\binom 42^2\binom{44}1 \\\binom{13}2\binom 42^2\binom {11}1\binom 41$$
Your second method is to count ways to choose three from thirteen ranks, two from four suits for the pairs, one from four suits for the singleton, and—wait—which two from those three selected ranks are to be the pairs? Ah, that is better.$$\binom {13}3\binom 42^2\binom 41\binom 32$$ | {
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} |
atmosphere, clouds, ice, atmospheric-optics
half-width of the diffraction lobe around the specular direction $10^{-2}$ or on the order of a degree [Crawford, 1968, p.486]. This is broader than the angular width of a pixel but narrower than change in the zenith direction over the area covered by a pixel (0.1°). Is this collective horizontal alignment a known effect at even 1 degree, much less 0.1 degrees? Has this ever been measured to be true over such large areas, or even calculated? | {
"domain": "earthscience.stackexchange",
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"tags": "atmosphere, clouds, ice, atmospheric-optics",
"url": null
} |
cosmology, universe, space-expansion, space
Title: How does a particular galaxy's apparent recessional velocity CHANGE as the universe expands? By this I mean will the light from distant galaxies continue to show red shift (i.e. if you look at light from a particular galaxy now and in 10000 years time, the spectra will have been shifted again), or is there a certain red shift which always corresponds to a certain set of galaxies (those which are the same distance away from Earth)? I think the answer lies in the apparent recessional velocity from Earth, but I'm struggling to interpret how it will change, if at all. | {
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ros-kinetic
Edit: i appreciate your answered, it will help me to reorganize and modify my code. i forgot say that im quite new to python too, but i need to finish it in a record time. tnx again for your time. i'll verify all again y to tell you as soon as possible. greets.
Originally posted by asmigox on ROS Answers with karma: 5 on 2018-10-19
Post score: 0 | {
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newtonian-mechanics, kinematics, velocity
And likewise for conditions for leaving the circle, why should tension be zero and velocity not 0?
If we are back to the complete circular swing here then think of it like this:
As long as the object is being swung around, the tension in the string is what keeps it in place and keeps it in a circle. The tension in the string is what makes the body change its direction all the time so the path is circular. If in the highest point the rope is not tight, then the body was not swung outwards hard enough. So if the rope is not tight then we have the possibility of slacking.
This is the situation where the circular path can be "flattened". Only if the rope is not tight all the time can the body take another path. If the rope is tight always, then the only possible path is the circular path. So that is a clear condition to look for.
What really is meant by leaving the circle? Is it like following a different parabolic path for some time? | {
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c++, c++11, boost, portability, dynamic-loading
RpnDLData DLCloseData(Library, GetObjectDebugLevel());
if (!DLCloseData.IsLibraryOpen())
{
ShowOnlyIfLevelGreaterThan(LEVEL3, "Can't open shared library : %s\n", Library.c_str());
return Added; // If errors occur then ignore this library
}
const OpTableEntry *TableEntry = DLCloseData.GetOperationTableData();
if (!TableEntry)
{
ShowOnlyIfLevelGreaterThan(LEVEL3, "Can't find symbol rpnhub_plugin in : %s\n", Library.c_str());
}
else
{
m_OpenedLibraries.push_back(DLCloseData);
m_Operations[TableEntry->name] = TableEntry;
Added++;
}
return Added;
}
Note that this change also assumes that the m_OpenedLibraries becomes an array of objects rather than an array of pointers. That is, it would be declared like this:
std::vector<class RpnDLData> m_OpenedLibraries; | {
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c++, beginner, reinventing-the-wheel, computational-geometry
inline Vector &Vector::operator-=(const Vector &v)
{
x -= v.x;
y -= v.y;
z -= v.z;
return *this;
}
inline Vector &Vector::operator*=(float scalar)
{
x *= scalar;
y *= scalar;
z *= scalar;
return *this;
}
inline Vector &Vector::operator/=(float scalar)
{
assert(!EqualsZero(scalar));
scalar = 1.0f / scalar;
x *= scalar;
y *= scalar;
z *= scalar;
return *this;
}
inline Vector &Vector::operator-()
{
x = -x;
y = -y;
z = -z;
return *this;
}
inline float &Vector::operator[](int i)
{
if (i == 0) {
return x;
} else if (i == 1) {
return y;
} else if (i == 2) {
return z;
} else {
assert("[] Access error!");
}
}
inline float Vector::X()
{
return x;
}
inline float Vector::Y()
{
return y;
}
inline float Vector::Z()
{
return z;
}
inline void Vector::Set(float x, float y, float z)
{
this->x = x;
this->y = y;
this->z = z;
} | {
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"tags": "c++, beginner, reinventing-the-wheel, computational-geometry",
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} |
c++, datetime
public:
WeekLine()
: year(-1)
, month(0)
, dayOfMonth(0)
{}
WeekLine(int year, WeekDay firstDayOfWeek)
: year(year)
, isLeap(isLeapYear(year))
, month(0)
, dayOfMonth(0)
, firstDayOfWeek(firstDayOfWeek)
, offset(getOffsetOfFirstDay(year, 0))
, linesPrinted(0)
{} | {
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electromagnetism, electric-circuits, terminology
Title: What is reactive power? I am trying to understand what is reactive power. I have read that it has a relation with voltage, that is has a relation with the creation of a magnetic field in a motor, that it is coming and going between consumption and generators. But what exactly is the physical meaning of reactive power?
But what exactly is the physical meaning of reactive power? | {
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particle-physics, nuclear-physics, radiation, elementary-particles
Yes, the weak interaction is "the same" between pairs of quarks or leptons of various kinds. That's a key symmetry and organizational principle in understanding the standard model particles. In all cases using W, one particle changes to its partner with the different charge. With Z it's just like electrtic force in that it doesn't change the types or move the charge around. | {
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time, spacetime-dimensions
Physically, this would be very weird. Without the clean separation between future and past the causal structure is gone. There would be nothing in such a universe that we would recognize as causality. You could have closed timelike curves (time travel) just as easily as you can now walk in a circle. Although the idea of such a universe being able to contain life that could walk is probably pretty impossible. It would be truly bizarre. | {
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quantum-mechanics, angular-momentum, symmetry, molecules
Why is this so? I actually don't know how to explain this intuitively, but I can demonstrate it with a concrete wavefunction. Let's label the two lower-energy $\pi_\mathrm g$ orbitals by $\psi_{a+}$ and $\psi_{a-}$, and the two higher-energy $\pi_\mathrm g$ orbitals by $\psi_{b+}$ and $\psi_{b-}$. The sign $\pm$ indicates the direction of the angular momentum projection along the internuclear axis: $\pi$-type orbitals come in pairs of $+1$ and $-1$ units of these angular momentum. Now consider the following wavefunction (I ignore normalisation).
$$\Psi = \psi_{a+}(1)\psi_{b-}(2) - \psi_{a-}(1)\psi_{b+}(2) + \psi_{b-}(1)\psi_{a+}(2) - \psi_{b+}(1)\psi_{a-}(2)$$ | {
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genetics, molecular-biology, molecular-genetics
Title: Chromosomomal walking I'm having a great deal of trouble understanding chromosomal walking, especially in regards to this article:
Control of male sexual behavior and sexual orientation in Drosophila by the fruitless gene.
I can get the fact that you can use recombination frequency analysis with chromosomal markers to assess the relative position of a gene, but I'm just stumped as to what it exactly it means when they say that they cloned the gene using DNA segments flanking the two insertions (fru3 and fru4) as a basis for the chromosomal walk. How to perform a chromosomal walk
I believe that the first publication to describe this approach was Bender et al., Science, 1983. In that paper they explain how they "walked" along the chromosome to reach the Bithorax Complex (BX-C).
This approach requires two reagents: | {
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experimental-physics, cold-fusion
Transmutations
The transmutation products in deuterium forced through Pd presented by show peaks at mass +8,+12. Bombardment by alphas cannot produce this, as there is absolutely no chance of the same atom being hit twice by two different alphas.
This requires that a fusion fragmented Pd ejected a Be8 as it's fusion fragmentation product, and that this Be8 then was absorbed by another nucleus in transit, giving 8 units of mass to another nucleus by absorption. If this is so, there are sum rules for the transmutation elements: the amount of light element X produced is equal to the difference of (Pd+X) and (Pd-X), where Pd+X means add all the protons and neutrons in X to Pd, and Pd-X means subtract all the neutrons and protons in X from Pd. This sum rule is a stringent test of the theory. | {
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value. For a given circle center, we compute the optimum circle radius ˆr by solving: (5) ¶J ¶r n r=rˆ =0 )rˆ = å i=1 d i n This means that both d i and ˆr can be considered as functions of the circle center coordinates x and y which from now on will be the free parameters of our model. Let ∅ be the angle between Do not mix r, the polar coordinate, with the radius of the circle. Move the center of the circle a small distance toward point P (call this new center. Let us put a circle of radius 5 on a graph: Now let's work out exactly where all the points are. Google Classroom. By the definition of a circle, any two radii have the same length. The y coordinate of the point to check. Use the midpoint formula to find the midpoint of the line segment. For example, some will have a negative r value, some will have the angle in radians, and some will have the angle in degrees. Given the centre and radius of a circle, to find the equation of Circle K?. But circle equations are often given in | {
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17. anonymous
okay, so its A, C, or D lol.... so lets try to rule out A...
18. anonymous
@jim_thompson5910
19. jim_thompson5910
what did you get so far in checking choice A?
20. anonymous
that A is, in fact NOT the answer!?
21. jim_thompson5910
if x = 1, then what is f(1) ?
22. anonymous
f
23. anonymous
Wait, so it IS A!!!!!
24. jim_thompson5910
$\Large f(x) = 3(2)^x$ $\Large f(1) = 3(2)^1$ $\Large f(1) = \underline{ \ \ \ \ \ \ \ } \text{ (fill in the blank)}$
25. anonymous
6
26. jim_thompson5910
27. anonymous
12
28. jim_thompson5910
Good. Choice A is definitely the answer. As practice, why not go through C and D and eliminate them. With choice C, if x = 1, then what is f(x) equal to? | {
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fluid-mechanics
Title: Confused with supercritical airfoil transonic condition analysis I am a high school student learning to analyze aircraft models in Autodesk CFD for the first time.
My current project is analyzing a supercritical airfoil on Autodesk CFD (that was designed in Autodesk Fusion360).
Can I get help with the following :
I researched several turbulence models(https://knowledge.autodesk.com/support/cfd/learn-explore/caas/CloudHelp/cloudhelp/2019/ENU/SimCFD-UsersGuide/files/GUID-E9E8ACA1-8D49-4A49-8A35-52DB1A2C3E5F-htm.html#:~:text=Turb.%20model%20%20%20Turbulence%20Model%20%20,model%20wi%20...%20%206%20more%20rows) and I chose the SST k omega turbulence model, with a 250 m/s inlet velocity, 0 gauge pressure , unknown outlet and a compressible flow , I am getting a lift to drag ratio of approx. 4.3.I think the lift to drag ratio is too low. I am suspecting the analysis conditions are to blame. Are these the correct input parameters? Am I missing anything else?
Thank you. | {
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c#
if (args.HasFlag(Args.Campaigns))
{
GetAndSaveResources(urls.ListAdvertisers, true);
}
if (args.HasFlag(Args.Advertisers))
{
GetAndSaveResources(urls.ListAdvertisers, true);
}
if (args.HasFlag(Args.CampaignGroups))
{
GetAndSaveResources(urls.ListCampaignGroups, false);
}
}
catch (Exception e)
{
Console.WriteLine(e.InnerException);
Console.WriteLine(e.StackTrace);
}
} | {
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c, serialization, arduino
Code slave Arduino
#include <Arduino.h>
#include <SoftwareSerial.h>
#include "Protocol.h"
#include "Slave.h"
SoftwareSerial serial(SLAVEPINS); // RX, TX
void setup()
{
// Multiple LED outputs
pinMode(REDLED1, OUTPUT);
pinMode(YELLOWLED1, OUTPUT);
pinMode(GREENLED1, OUTPUT);
pinMode(REDLED2, OUTPUT);
pinMode(YELLOWLED2, OUTPUT);
pinMode(GREENLED2, OUTPUT);
serial.begin(BAUDRATE); // SoftwareSerial connection (baudrate 9600)
serial.setTimeout(TIMEOUT); // Maximum wait time
}
void loop()
{
static String readString; // String containing serial data
static long counter = 0; // Counter
static bool setLight = false; // Turn lights on once
unsigned long currentTime = millis(); // Set current time
static unsigned long previousTime = 0; // Set previous time | {
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newtonian-mechanics, forces, newtonian-gravity, potential-energy, weight
When you started lifting the object, necessarily the force of your hand was bigger than the weight. Otherwise, there would be no acceleration for the object's velocity changes from zero to pointing upwards. Only after this small moment, we can assume the resulting force is zero. In this situation, the acceleration of the object is zero, but the velocity isn't. Therefore, it keeps moving upwards due to Newton's First Law of Motion (the Principle of Inertia). Be careful, you don't need forces to keep something moving (though the greeks thought so). | {
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ibm-q-experience
Result from the simulator:
Result from the real IBM quantum hardware: Yes, the cause of unexpected results in your measurement is noise (due to different kind of effects as qubits decoherence, gate operations imperfections, etc). There are many kinds of error correction and error mitigation techniques available (see Qiskit - Measurement Error Mitigation as ax example) that can reduce (or remove, in some cases) the impact of noise.
The quantum devices from IBM Quantum that you can experiment on for free are the following:
As you see in the picture, ibm_nairobi has 7 physical qubits. To access larger and more powerful computers you need Premium account on the IBM Quantum platform. | {
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} |
fourier-transform, frequency-spectrum, frequency-response, linear-phase
I tried to observe the magnitude and phase responses for different values of M and observed a similar pattern.
Is there any reason behind this pattern? Is there any significance for this? The significance is a constant time delay for all frequencies. Time delay is the derivative of phase with respect to frequency, so given a linear phase as shown, the time delay is constant. Notice that the abrupt steps in phase actually only occur when the magnitude goes through zero so does not effect the nature of it being a "linear phase" filter.
An M-point moving average filter will have a time-delay (for all frequencies) of $M/2$, so if you increase the number of points, the phase slope versus frequency will increase.
Why do we like linear phase filters so much? Please see this post on that:
Why is a linear phase important?
Any finite impulse response (FIR) filter with symmetric or anti-symmetric coefficients (The OP's case with coefficients all 1 is symmetric) will be a linear phase filter. | {
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sun, plasma-physics, thermal-conductivity, convection
The core
A central area with pressures high enough to induce hot fusion of atomic nuclei
The radiative zone
A spinning ball of somewhat solid material surrounding the core, through which energy is conducted via radiation
Semi-observable:
The convective zone
A layer of plasma surrounding the radiative zone, through which energy is conducted thermally via convection flows - millions of degrees in temperature
This is the subject of some 2012 studies by NASA in coordination with various other reputable institutions, which observed that the sun's convection appears to be "anomalously weak"
http://arxiv.org/pdf/1206.3173.pdf
Observable:
The surface of the photosphere
The border between the convective zone and the corona - temperature in the ballpark of 5-10 thousand degrees
The corona
The outer plasma atmosphere, where flares take place - millions of degrees in temperature You've actually identified a key area of ongoing research known as the coronal heating problem. | {
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java
coupons left.
Write a program that inputs a value for N and outputs how many
chocolate bars we can eat and how many coupons we would have left
over. Use a loop that continues to redeem coupons as long as there are
enough to get at least one chocolate bar. | {
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cell-culture, safety
Agents: serious or lethal diseases transmissible via aerosols, e.g.,
M. tuberculosis, SARS. Recombinant DNA activities using genetic
material from BSL-3 organisms or such organisms as host cells.
Why then, does the CDC classify cell line work, including work with viral production cells, as a BSL-2 activity requiring only BSL-2 containment levels, when the act of immortalising the cells would involve working with viral agents that can cause cancer? | {
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ofdm, symbol-timing
https://dspillustrations.com/pages/posts/misc/schmidlcox-synchronization-for-ofdm.html Yes it can, for time advances relative to the ideal selection but not for time delays. Since the Cyclic Prefix (CP) is taken from the end of the exact same OFDM symbol, it is circularly invariant, up to the shift equal to the length of the circular prefix, such that the resulting DFTs for any advance offset will all be related by a linear phase. (With an advance we circularly rotate through the same data, up to the CP length, with a delay we start using data from the next OFDM symbol). | {
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derivative formulas, Chain Rule, Implicit differentiation) A Puzzle by David Pleacher Solve the 26 derivative problems below and place the answer in the corresponding cell ld be integers from 1 to 9 inclusive. Linear multi-step methods: consistency, zero-. 1 Verify by substitution that the given function is a solution of the given differential equation. Differentiation formulas (sums, differences, products, and quotients) The chain rule Derivatives of trigonometric functions Implicit differentiation Rate of change in the natural and social sciences, including position, velocity, acceleration, and rectilinear motion— includes an oral presentation. Course Hours per Week: Class, 3. Implicit differentiation is also crucial to find the derivative of inverse functions. If y =f(x), the variable y is given explicitly (clearly) in terms of x. Such a function is referred as in implicit function. Find the derivative of f ()g()x Chain Rule f ′(g(x))⋅g′(x). o Verify the derivative of an implicit | {
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computability, undecidability, proof-techniques, reference-question, turing-recognizable
Why does this work?
If $(\langle M \rangle,x)\notin HP$ then 1.1 never halts, and $M'$ accepts exactly all the inputs that are being accepted at step 1.2, so $L(M')=L_1$.
On the other hand, if $(\langle M \rangle,x)\in HP$ then, at some point step 1.1 halts and $M'$ accepts exactly $L_2$. It may happen that $1.2$ accepts beforehand, but since $L_1 \subseteq L_2$, this doesn't change the language of $M'$ in this case.
If (2) does not hold, then $L_S \notin RE$.
Again, we will assume $L_S\in RE$ and show that $HP$ becomes decidable, which is a contradiction.
If condition (2) doesn't hold, then there exists $L_1\in S$, all its finite subsets $L_2 \subseteq L_1$ satisfy $L_2 \notin S$ (note that $L_1$ must be infinite, since $L_1\subseteq L_1$). | {
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c#, finance
public void CreateAccount(string name)
{
BankAccount account = new BankAccount();
CalculateIBAN calculateIban = new CalculateIBAN();
try
{
if (!String.IsNullOrEmpty(name))
{
account.Name = name;
account.IBAN = calculateIban.IBAN();
_accounts.Add(account);
Console.WriteLine("Account created - Name: {0}, IBAN: {1}", account.Name, account.IBAN);
}
else
{
Console.WriteLine("Account name is null or empty.");
}
}
catch (NullReferenceException ne)
{
Console.WriteLine(ne.StackTrace);
}
}
public float Deposit()
{
string iban = rv.EnterIban();
BankAccount account = rv.GetAccountByName(iban, _accounts); | {
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slam, navigation, turtlebot, ros-fuerte, hector-slam
<param name="pub_map_odom_transform" value="true"/>
<!-- Map size / start point -->
<param name="map_resolution" value="0.050"/>
<param name="map_size" value="$(arg map_size)"/>
<param name="map_start_x" value="0.5"/>
<param name="map_start_y" value="0.5" />
<param name="map_multi_res_levels" value="2" />
<!-- Map update parameters -->
<param name="update_factor_free" value="0.4"/>
<param name="update_factor_occupied" value="0.9" />
<param name="map_update_distance_thresh" value="0.4"/>
<param name="map_update_angle_thresh" value="0.06" />
<param name="laser_z_min_value" value = "-1.0" />
<param name="laser_z_max_value" value = "1.0" />
<!-- Advertising config -->
<param name="advertise_map_service" value="true"/>
<param name="scan_subscriber_queue_size" value="5"/>
<param name="scan_topic" value="hokuyo_scan"/>
<!-- Debug parameters -->
<!-- | {
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the same length and all the angles are the same), each of the exterior angles will have size 360 ÷ the number of sides. Therefore we now have two triangles within one Quadrilateral. (The terms “main diagonal” and “cross diagonal” are made up for this example.) Become a member and unlock all Study Answers Try it risk-free for 30 days Yes. Abhinav. Let us look at the properties of quadrilaterals. Yes, because all the angles in any quadrilateral (4-sided polygon) add up to 360. Kite; That does not seem to many does it. For example, when you have a triangle in which the tip is at the 45 degree angle ( pi / 4 rad), the leg from the tip to the base is perpendicular, and the other angle is 45 degrees. If you were to walk around a four sided shape until you reach the start you will have rotated by 360 degrees. The angles in a parallelogram will always add up to 360°. The opposite angles at the endpoints of the cross diagonal are congruent (angle J and angle L). Which type of angle is between | {
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} |
quantum-mechanics, wavefunction, hilbert-space, schroedinger-equation
Well, there is a way to make them useful, but of course it only really does a good job when $\hat H_1$ and $\hat H_2$ have some sort of nice relationship. A Schrödinger equation $i \hbar \partial_t |\Psi\rangle = \hat H |\Psi\rangle$ can be phrased purely as a unitary operator $|\Psi(t)\rangle = \hat U(t) |\Psi_0\rangle.$ The condition is that $i\hbar \partial_t \hat U = \hat H \hat U,$ but this is no problem in theory. This means that all of our expectation values in the second case take the form $$A(t) = \langle \Psi(t)|\hat A |\Psi(t)\rangle = \langle \Psi_0|\hat U_2^\dagger \hat A \hat U_2|\Psi_0\rangle.$$ Now since a unitary operator is defined by $U^\dagger U = 1$ we will insert strategic $\hat U_1^\dagger \hat U_1$ terms to rewrite this same expectation value as $$A(t) = \langle \Psi_0|\hat U_1^\dagger ~\Big(\hat U_1 \hat U_2^\dagger \hat A \hat U_2 \hat U_1^\dagger\Big)\hat U_1 |\Psi_0\rangle.$$Note that now there is some complicated time dependence for this parenthesized | {
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performance, julia
Next, I modified logpredictive() in conjugate.jl such that
function logpredictive(me::Gaussian1DGaussian1D, xx::Float64)
gg = posterior(me)
mu = gg.mu
vv = gg.vv
# ll = exp(-(xx - mu)^2 / (2*(vv + me.vv))) / sqrt(2*pi * (vv + me.vv))
# return log(ll)
#>>> modified part (start)
tmp = vv + me.vv
val = -(xx - mu)^2 / (2 * tmp) - 0.5 * log( 2*pi * tmp )
return val
#<<< (end)
end
Then the result becomes
iteration: 1, number of components: 20, elapsed time: 0.009714609
iteration: 1, number of components: 20, elapsed time: 0.009562715
iteration: 2, number of components: 20, elapsed time: 1.409258263
...
iteration: 5, number of components: 20, elapsed time: 1.40165818
7.022493 seconds (5.00 M allocations: 1.043 GB, 0.43% gc time) | {
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slam, navigation, ros-kinetic, slam-gmapping, gmapping
I am unable to figure out how do I solve this problem. My environment variables are properly defined in the bashrc.
Thanks
Edit 1:
dpkg -l | grep gmapping
dpkg -l | grep gmapping
ii ros-kinetic-gmapping 1.3.10-0xenial-20181117-012312-0800 amd64 This package contains a ROS wrapper for OpenSlam's Gmapping.
ii ros-kinetic-openslam-gmapping 0.1.2-0xenial-20180809-134859-0800 amd64 ROS-ified version of gmapping SLAM.
ii ros-kinetic-slam-gmapping 1.3.10-0xenial-20181117-032709-0800 amd64 slam_gmapping contains a wrapper around gmapping which provides SLAM capabilities.
Edit 2:
My environment is set as follows:
all binary packages installed in
/opt/ros/kinetic/share
and my custom package are inside
~/catkin_ws/src | {
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This is a well-known problem. See here, with solution, published in 1996.
Summarizing: Having put [1501,3000] into our set, the interval [751,1500] is excluded, so we need 500 from [1,750]. Having then added [376,750] to our set, the interval [188,375] is excluded, so we need 125 from [1,187]. And recurse until done.
• Forgive me my ignorance, but I cannot see why this method would give us the largest possible set having the property $2x \in A \implies x \not \in A.$ Jul 3 '14 at 16:07
• @IndrayudhRoy: Because any number you add from $[750,1500]$ forces the removal of one from $[1501,3000]$ So the total number from $[750,3000]$ is no more than $1500$ Jul 3 '14 at 16:14
• So can it be done or not?
– user142299
Jul 3 '14 at 16:17
• @gnometorule Are you sure? I thought I had a way to get it up to $1999$.
– user142299
Jul 3 '14 at 16:28
– user142299
Jul 3 '14 at 16:35 | {
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(Step 4) $= \textcolor{blue}{2x}(3x+2) \textcolor{blue}{+7}(3x+2)$
$= \textcolor{blue}{(2x+7)}(3x+2)$
Example 2
$10x^2-31x-36$
(Step 1) $10 \times -36 = -360$
(Step 2) Negative; $9 \times 40 = 360$; the difference between $9$ and $40$ is $31$
(Step 3) $10x^2\textcolor{red}{-31x}-36$
$= 10x^2$ $\textcolor{red}{ + 9x - 40x} - 36$
(Be careful with minus signs!)
(Step 4) $=$ $\textcolor{blue}x(10x+9)\textcolor{blue}{-4}(10x+9)$
(Be extra careful with minus signs!!)
$=$ $\textcolor{blue}{(x-4)}(10x +9)$
At first, you may think that this method makes things more complicated - which it may do for simple cases, where there aren't many factors. But when you have lots of factors to consider, you'll find it involves much less trial and error!
Give it a try. | {
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javascript, beginner, html, html5
First, though: Don't use bracketed (aka subscripting) access to properties when regular dot notation works, e.g.:
window.Math.PI
is exactly the same as:
window['Math']['PI']
but a lot simpler.
Secondly, don't bother with window when there's no need. window is the global object in a browser's JS runtime, so you can just say
Math.PI
The exception to this is if you have variable shadowing, but that's outside the scope of this review.
Now, to tackle question 2 first, you could do this:
function calcCircleArea(r) {
if(r >= 0) {
return Math.PI * r * r;
}
return "invalid input";
} | {
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java, algorithm, tree, data-mining
private static final class RadixTreeNode {
RadixTreeNode[] children;
}
private final RadixTreeNode root;
private final LotteryConfiguration lotteryConfiguration;
/**
* Implements the main constructor.
*
* @param lotteryConfiguration the lottery configuration object.
* @param root the root node of the radix tree.
*/
private MissingLotteryRowsGenerator(
LotteryConfiguration lotteryConfiguration,
RadixTreeNode root) {
this.lotteryConfiguration =
Objects.requireNonNull(
lotteryConfiguration,
"lotteryConfiguration == null");
this.root = Objects.requireNonNull(root, "The root node is null.");
} | {
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quantum-mechanics, operators, momentum, hilbert-space, dirac-delta-distributions
$$i\hbar \langle x|x\rangle = \langle x| (\hat{x}\hat{p} - \hat{p}\hat{x})|x\rangle = x \langle x|\hat{p}|x\rangle - \langle x|\hat{p}|x\rangle x = 0$$
because $|x'\rangle$ is only defined when it is smeared a little, you need to use a seprate variable for the two occurences of x'. So write the full matrix out for this case:
$$ i\hbar \langle x|y\rangle = x\langle x|\hat{p}|y\rangle - \langle x|\hat{p}|y\rangle y = (x-y)\langle x|\hat{p}|y\rangle$$
And now x and y are separate variables which can be smeared independently, as required. The p operator's matrix elements are the derivative of a delta function:
$$ \langle x|\hat{p}|y\rangle = -i\hbar \delta'(x-y)$$
So what you get is
$$ (x-y)\delta'(x-y)$$ | {
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fft, fourier-transform, physical-units
If you look at a power density spectrum (squared), then the units above should be squared as well (mV$^2$ or T$^2$/s$^2$).
Now in general, for a given unit U, albeit in volt (V), tesla (T), whatever. The FFT sums samples $x_k$ in the original units (U) multiplied by unitless complex values (due to discretization) $e^{-2\pi j\cdot}$. Thus the units after FFT remain the same as for the original signal, i.e. U.
If you take the absolute value, the same again. For instance, the $0$-frequency index gives you the DC, or average value of your signal (or at least it is proportional, with a factor of the number of samples, or its square root depending on the normalization).
The continuous Fourier transform, in contrast, "sums" the samples times complex cisoids times a time differential (the $\mathrm{d}t$):
$$\int e^{-2\pi j\cdot}x(t)\mathrm{d}t $$
Its units would be U.s (s for seconds). Unless you normalize it by something with a unit, like in | {
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statistical-mechanics, computational-physics, ising-model
Title: Boltzmann distribution in Ising model I've written in Matlab a code for a Ising model in 1 dimension with 40 spins at $k_{B}T=1$.
I record the energy of every step in a Metropolis Monte Carlo algorithm, and then I made an histogram like this. | {
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neural-networks, topology
Analysis of Answer One of Three
It is true that every directed graph can be realized in an arbitrarily large RNN because they are Turing complete, but that doesn't mean they are a great topology for all finite algorithms.
Turing was aware that his punched tape model was not the best general purpose, high speed computing architecture. He was not intending to prove anything about computing speed but rather what could be computed. His Turing machine had a trivial topology deliberately. He wanted to illustrate his completeness theorem to others and resurrect the forward movement of rationalism after Gödel disturbed it with his two incompleteness theorems. | {
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computer-vision, visualization, optical-flow
Title: Optical-flow visualizations explained What do the arrows depict in the optical-flow visualizations such as the one below?
(image source: learnopencv)
Is it correct to say that the pixel at the tip of an arrow was at the origin of the arrow in previous frame? Yes, as your linked page shows:
the idea is that the pixels move from $(x,y)$ in the first from to $(x+\Delta x, y + \Delta y)$ in the second. I believe the image you quote is just connecting a series of $(x_i,y_i)$ with their next locations $(x_i+\Delta x_i, y_i + \Delta y_i).$ | {
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For instance, market value is 950, the face value is 1000 and the coupon interest rate is 5%. Step 3: Finally, the formula for a current yield of the bond can be derived by dividing the expected annual coupon payment (step 1) by its current market price (step 2) and expressed in percentage as shown below. The current market price of the bond is how much the bond is worth in the current market place. =8.33% For Bond B Step 1:Calculate Annual coupon payment 1. You can use the following Current Yield Calculator, This has been a guide to Current Yield Formula. Suppose, you got an offer to invest in a bond. Settlement (required argument) – This is the settlement date of the security. The company pays interest two times a year (semi-annually). Microsoft MVP Excel SalesAid Software "Gary" wrote in message ... A bond has a $1,000 par value, 12% coupon rate, interest on the bond is paid annually, the current yield to maturity on the bond is 6%, and the maturity of the bond is 10 years. Insert | {
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html, haskell, recursion
I have a working implementation, but the recursive part is a bit repetitive:
segment :: [Inline] -> [Inline]
segment [] = []
segment [el] = [el]
segment els @ (head:tail) =
case head of
Emph ch -> map (Emph . toList) (segment ch) ++ segment tail
Strong ch -> map (Strong . toList) (segment ch) ++ segment tail
Strikeout ch -> map (Strikeout . toList) (segment ch) ++ segment tail
Superscript ch -> map (Superscript . toList) (segment ch) ++ segment tail
Subscript ch -> map (Subscript . toList) (segment ch) ++ segment tail
SmallCaps ch -> map (SmallCaps. toList) (segment ch) ++ segment tail
Quoted qt ch -> map (Quoted qt . toList) (segment ch) ++ segment tail
Cite cs ch -> map (Cite cs . toList) (segment ch) ++ segment tail
Span attr ch -> map (Span attr . toList) (segment ch) ++ segment tail
_ ->
maybe [sentence els] (\i -> (sentence $ take i els) : segment (drop i els))
$ (1 +) <$> List.findIndex split els
where | {
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reinforcement-learning, policies, off-policy-methods
You can see from the pseudocode that both algorithms describe this behaviour policy as "policy derived from Q (e.g. $\epsilon$-greedy)".
The difference in the two algorithms is in which target polcy is being used: | {
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of the balloon as a function of the time t (in seconds). You multiply y or y² by a suitable term t(x), so that y becomes larger on the right side of the y-axis and smaller on the left side. Volume of Sphere = πr 3. Given James' golf ball has a radius of 1. At what rate is the surface area of the balloon increasing at the moment when its radius is 8 feet? Solution. From the Oval to the Egg Shape You can develop the shape of a hen egg, if you change the equation of a oval a little. The volume V(r) ( cubic meters) of a spherical balloon with radius r meters is given by V(r)= 4/3 pie r ^3. The volume of a container is generally understood to be the capacity of the container, i. What is the volume formula for a sphere? B. Related Rates - Homework 1. Do not enter number that look like fractions, such as 2/5. Find the radius of the tank. The problem tells us that = 400 cubic inches/min and inches. Teach classes how to find the volume of spherical solids. 56r³ = 1152000. Assuming that the | {
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# How to determine the average waiting time of an event when encountering the system at some time > 0?
In this textbook, page 82, problems 9-11, the author gives the following distribution for the time between a sequence of occurrences:
a) Exponentially distributed with $$\lambda = 1/10$$, so one occurrence every 10 minutes
b) Uniformly distributed in [5, 15] minutes
c) 3 minutes with a probability of 0.9 and 73 minutes with a probability of 0.1
The author asks that if someone encounters this system at time 100 minutes, what is the average waiting time before the next occurrence for each of these distributions.
I wrote a simulation (not sure if the result is correct) that gave me the following for the average time:
a) ~ 10min
b) ~ 5.5min
c) ~ 23min
Is the above correct? If so, what's the intuitive explanation for each result? | {
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java, interview-questions
}
/**
* O(6)
*/
public void addFriend(int customerId1, int customerId2) {
if(this.customers.containsKey(customerId1) && this.customers.containsKey(customerId2)){
//we add a key to the customers friend entry
this.customers.get(customerId1).addFriend(customerId2);
this.customers.get(customerId2).addFriend(customerId1);
}else{
throw new IllegalArgumentException("the customerId or movieId provided does not exists");
}
}
/**
* returns any movie that has been liked by a friend.
*
*
*/
public Collection<Integer> getRecommendationsFromFriends(int customerId) {
return getFriendRecommendations(customerId, 1);
} | {
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php, comparative-review
I haven't included the whole pagination script that queries the Mysql database. Just the Pagination Section that I need reviewed.
(By Pagination Section, I mean the bottom part you see on the Searchengine Result Pages that display links to other search result pages (Pages: 23456789 etc.)).
I have written 2 sets of code. I need feedback regarding which one to stick to and which one to discard with reasons given.
The lines where I need help, I have commented as follows:
//ARE htmlspecialchars() OK HERE ?
//IS intval() OK HERE ?
//Are htmlspecialchars() & intval() OK HERE ?
//ARE urlencode() & intval() OK HERE ?
Php Code 1
//SECTION: PAGINATION SECTION TO NUMBER THE SERPS AND LINK THEM.
$total_pages = ceil($row_count/$max);
$i = '1'; | {
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classical-mechanics, momentum
Title: Impulse as a function of time - When should I differentiate it? If impulse $I$ varies with time $t$ as $$I(\text{kg m s}^{-1})= 20t^2-40t$$ The change in momentum is minimum at which time
This is the question.
Impulse is change in momentum.
Here I am asked at what time the change in momentum will be zero?
For this, why should I differentiate the above function?
$$\frac{dI}{dt} = 40t - 40$$ and $$40t - 40 = 0$$ because it is minimum
But why should not I equal it to zero without differentiating?
The change in momentum is minimum at which time ... This is the question. ... Here i am asked at what time the momentum will be zero?
Asking "the change in momentum is minimum at which time" and "at what time the momentum will be zero" are two different questions.
You don't need to differentiate to find when the impulse is 0.
You should differentiate to find when the impulse reaches its minimum value. | {
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javascript, react.js
Title: React material UI tabs in a different way In my react application I have Tabs done with Material UI. Some of those tabs are shown or hide depending on an option is true or false.
The code is not a clean solution but I have no experience working with this and was wondering to see a better solution to what I have done.
We have 3 options:
isEngagementPortal
isRecruitmentPortal
isConsenteesPortal | {
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So consider any $\epsilon > 0$. Then there is an $N$ where $|x_{k_n} – \sqrt\alpha| < \epsilon$ for all $n \geq N$. Likewise there is an $M$ where $|x_{l_n} – \sqrt\alpha| < \epsilon$ for all $n \geq M$. So let $L = \max(k_N, l_M)$ and consider any $n \geq L$. If $n$ is odd then there is an $m \geq 1$ where $n = 2m-1 = k_m$. We then have $n = 2m-1 \geq L \geq k_N = 2N-1$$2m \geq 2N$ $m \geq N$ so that $|x_n – \sqrt\alpha| = |x_{k_m} – \sqrt\alpha| < \epsilon$. A similar argument shows that $|x_n – \sqrt\alpha| < \epsilon$ in the case when $n$ is even as well. Thus we have shown that $\lim_{n \to \infty} x_n = \sqrt\alpha$ by definition.
(d) | {
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condensed-matter, fermi-energy
Title: Show that the Fermi surface is perpendicular to the Brillouin zone boundary in the nearly free electron approximation How can one show that the Fermi surface is perpendicular to the Brillouin zone boundary in the nearly free electron approximation?
Similar question without an answer: Why does the Fermi Surface cross the Brillouin zone boundary at right angles?
One of the answers discusses $\nabla_kE$; I have a proof which uses this but it doesn't explain where any of the terms come from - I was hoping someone could fill in the blanks to make it a more complete proof.
If $$\vec{\nabla_\vec{k}}E \cdot \vec{k} = 0$$ $$\vec{\nabla_\vec{k}}E \perp \vec{k}$$ $$\vec{\nabla_\vec{k}}E \perp \vec{E}$$ then $$E \parallel \vec{k}$$
Since $\vec{k}$ is perpedicular to the zone boundary $E$ must be too. Apparently this is a problem taken from Marder's condensed matter textbook. Anyway, credit goes to Sinova (notes here). | {
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Now, take $$\alpha:=\dfrac1n$$ for some integer $$n\geq 2$$. Then, $$\frac{\pi}{\sin\left(\frac{\pi}{n}\right)}=\int_0^\infty\,\frac{t^{\frac1n-1}}{t+1}\,\text{d}t=\int_0^\infty\,\frac{n}{x^n+1}\,\text{d}x\,,$$ by setting $$x:=t^{\frac1n}$$. This proves the equality $$\int_0^\infty\,\frac{1}{x^n+1}\,\text{d}x=\frac{\pi}{n\,\sin\left(\frac{\pi}{n}\right)}\,.$$ If $$n$$ is even, then $$\int_{-\infty}^{+\infty}\,\frac{1}{x^n+1}\,\text{d}x=2\,\int_0^\infty\,\frac{1}{x^n+1}\,\text{d}x=\frac{2\pi}{n\,\sin\left(\frac{\pi}{n}\right)}=\frac{\pi}{\frac{n}{2}\,\sin\left(\frac{\pi}{n}\right)}\,.$$ | {
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here’s the math: Even though the formal definition of the definite integral is based on the sum of an infinite number of rectangles, you might want to think of integration as the limit of the trapezoid rule at infinity. • BLDC machines could be driven with sinusoidal currents and PMSM with direct currents, but for better performance, PMSM motors should be excited by sinusoidal currents and BLDC machines by direct currents. 2 (EK), LIM‑5. The basic idea is to divide the interval on the x-axis into n equal subintervals. 1137/130932132 I Fundamentals 1 Introduction 386 2 Integrals over a Circle in the Complex Plane 389 3 Integrals over a Periodic Interval 394 4 Example: Integral of a Periodic Entire. Trigonometric functions are evaluated in Radian Mode. The basic idea in Trapezoidal rule is to assume the region under the graph of the given function to be a trapezoid and calculate its area. Now, piece together the triangular ends so that the trapezium is divided into a triangle and | {
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"openwebmath_score": 0.8180414438247681,
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*Имя: Заголовок: size size –3 –2 –1 +1 +2 +3 font tnr arl thm crn tex color color lgray gray dgray brown dred red pink orange gold yellow olive lime lgreen green dgreen teal cyan sky azure blue dblue navy purple violet orchid fuchsia span span tex i b u z ov cp sp h 1 2 3 4 align c l r j div div c bl1 bl2 ind1 ind2 bq block block c bl1 bl2 ind1 ind2 bq box box s cap o u list list =1 table table f symb symb nbsp [ ] { } | pre pre m code code m [tex-clear] [tex-help] [ted] formulas > Формат Шрифт $\mathit{}$ $\mathbf{}$ $\mathrm{}$ $\mathsf{}$ $\mathfrak{}$ $\mathbb{}$ $\mathcal{}$ $\mathscr{}$ Размер $\tiny Aa$ $\scriptsize Aa$ $\footnotesize Aa$ $\small Aa$ $\normalsize Aa$ $\large Aa$ $\Large Aa$ $\LARGE Aa$ $\huge Aa$ $\Huge Aa$ Цвет ${\color{Red} }$ ${\color{DarkRed} }$ ${\color{BrickRed} }$ ${\color{Magenta} }$ ${\color{VioletRed} }$ ${\color{Yellow} }$ ${\color{Orange} }$ ${\color{DarkOrange} }$ ${\color{Brown} }$ ${\color{Sepia} }$ ${\color{Green} }$ ${\color{DarkGreen} }$ | {
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java, logging
This is a good example of offering the "why" rather than the "how".
I thank you for the explanation.
Similarly for the UTF-16 remark (it seems UTF-32 is not of interest, cool).
checked exception
public JulConfigurator() throws IOException {
Possibly this signature is not convenient for callers?
Consider re-throwing, wrapped in an unchecked RuntimeException.
(I also appreciate the neverHappens name.)
We clear, read config, and set.
Suppose that reading failed with an I/O error.
Would it maybe be nicer to read config, then clear, and set?
So a thrown exception won't reveal the "cleared" state?
magic number
80 * loggingConfigUpdates.size(), // in most cases more efficient than calculating
This seems nice enough as-is.
But consider naming that integer,
just so you can give it a Javadoc entry
that warns unusual callers there is room to lose
in rare circumstances. | {
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general-relativity, differential-geometry, metric-tensor, quantum-gravity, geodesics
$$\frac{d^2x^a}{ds^2}+\frac 12 g^{ad}\left(\partial_cg_{bd}+\partial_bg_{cd}-\partial_dg_{bc}\right)\frac{dx^b}{ds}\frac{dx^c}{ds}=0.\tag{3}$$
Then, it states that once we have a manifold endowed with both an affine connection $\Gamma^a_{bc}$ and a metric, there are two classes of geodesics: affine ones and metric ones, which are different in general. However, if we take the metric connection
$$\Gamma^a_{bc}\equiv\frac 12 g^{ad}\left(\partial_cg_{bd}+\partial_bg_{cd}-\partial_dg_{bc}\right),\tag{4}$$
they will coincide. This definition leads to the identity
$$\nabla_a g_{bc}=0\tag{5}$$
and, as $(4)$ is symmetric, the torsion is $0$.
Conversely, having a symmetric connection and requiring $(5)$ leads to the metric connection $(4)$. | {
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homework-and-exercises, kinematics, mathematics, relative-motion
Title: Relative Circular Motion
Four particles $P_1, P_2,P_3,P_4$ are moving in a plane. At $t=0$, they are at the four corners of a square $ABCD$ of edge length $l$. Each of the particles has a constant speed $v$. The velocity of $P_1$ is always directed to $P_2$, that of $P_2$ is always directed to $P_3$, that of $P_3$ is always directed to $P_4$, that of $P_4$ is always directed to $P_1$. At what time $t$ will all the four particles collide and where will they collide? Also how to calculate the angular acceleration of the line joining the particle and the final point of collision at any instant? | {
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quantum-mechanics, wavefunction, spinors
Since the ground state spatial wavefunction is symmetric, we have to pick the antisymmetric spin wavefunction when we construct the total wavefunction, as you mentioned in your question.
[0] I also like to call the Heisenberg Uncertainty Principle the HUP.
[1] The PEP requires that the $total$ wavefunction of a system of N fermions must be antisymmetric. In this case, that means that the wavefunction must change sign if $all$ coordinates (spatial and spin) are interchanged.
[2] This entire answer is paraphrased from 'Physics of Atoms and Molecules', Bransden and Joachain
[3] Once the spin wavefunctions are symmetrized, they also become eigenfucntions of the $S^2$ operator and mutually orthogonal, which is important/useful. | {
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general-relativity, reference-frames, inertial-frames, equivalence-principle
Title: Local inertial frame by linear transform? By equivalence principle, one can find a local inertial frame at every point of spacetime. Then this is usually used to introduce the general spacetime metric, as a back-transform of the Minkowski metric.
The transformation from Minkowski to general metric depends only on the first derivatives of the coordinate transformation. This means that locally we can get an inertial frame by applying a linear coordinate transform. It is puzzling because in motivating examples we always get accelerating transforms, such as a falling elevator. However, it seems that the acceleration does not play role in the final formula. What is happening? | {
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this addition of two or more vectors is tug-of-war... Pdf with Notes list any point P ( x, y ) is, and at the of... '' method + 2 a B cos. direction: vector magnitude and the arrowhead in! The triangular law of parallelogram can utilize this addition of vectors in vector Algebra Class 12 formulas PDF with list! & magnitude together into a vector has magnitude ( size ) and direction: vector magnitude and the arrowhead in... So-Called parallelogram law gives the rule for vector addition is the resultant of P and Q as much as.... Ensure you get the best experience original vectors is the vector addition is the vector look subtraction... Need to find the vector drawn from the tail of the arrow indicates direction... Is performed using the triangle or parallelogram rule addition procedure connected to it, and at the end each. R1= a + B + C. R3= a + B = B + a ; vector &... Corner of the arrow indicates the direction concept are available over here as possible can be combined by vector. | {
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signal-analysis
A different notion of time duration and bandwidth of an arbitrary unit-energy signal $x(t)$ comes from noting that $|x(t)|^2$ is a pdf (note that $|x(t)|^2 \geq 0$ for all $t$, and $\int |x(t)|^2 dt = 1$ which are the two defining properties of pdfs). Similarly, $|X(f)|^2$ is also a pdf since $\int |X(f)|^2 df$ is the signal energy which has value $1$. Some folks, especially physicists, like to use the standard deviations of these pdfs as the (root-mean-square) measures $\Delta t$ and $\Delta f$ of the time duration and the bandwidth respectively. I don't like $\Delta t$ and $\Delta f$ because (for example) if these pdfs are Gaussian, then only $68\%$ of the signal energy is contained in the frequency band $[-\Delta f, \Delta f]$ which is a rather poor approximation compared to the (say) $99\%$ essential bandwidth described earlier (when $\eta = 0.01$) that us poor engineers are more concerned with, but ymmv. Anyway, to cut a long story short, the product $\Delta t\cdot\Delta f$ is | {
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cosmology, nuclear-physics, big-bang, nucleosynthesis
Title: Why did the Big Bang produce hydrogen? I know that first generation stars' main fuel was Hydrogen. I know the Big Bang happened at some point in time. Now if the strong force exists, then why aren't different, higher mass, number elements produced? why was there single proton nucleus like hydrogen? The answer touches upon the concept of Big Bang Nucleosynthesis (BBN), which is excellently explained on a graduate level in Baumann's lecture notes. | {
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of differential forms on $G/H$, where $H$ is a closed subgroup of $G$. If $G$ and $H$ are connected, then evaluation at the identity gives an isomorphism from the space $\Omega^\ast(G/H)^G$ of $G$-invariant forms onto the space $C^\ast(\mathfrak g, \mathfrak h)$ of relative Lie algebra cohomology cocycles. This isomorphism descends to an isomorphism between the cohomology of the complex of $G$-invariant forms on $G/H$ and relative Lie algebra cohomology $H^\ast(\mathfrak g, \mathfrak h)$.</p> <p>Now assume that $G$ is reductive and $H$ maximal compact in $G$ with corresponding Cartan decomposition $\mathfrak g = \mathfrak h \oplus \mathfrak p$. Then there are natural isomorphisms $$C^q(\mathfrak g, \mathfrak h) = \mathrm{Hom}_{\mathfrak h} (\wedge^q \mathfrak p, \mathbb R) = (\wedge^q \mathfrak p)^{\mathfrak h},$$ where $\mathfrak h$ is acting via the adjoint representation. If you want, this can be rephrased in terms of the action of $H$, and moreover it's possible to introduce a | {
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If we try it for your subgroup $$H= \{1,13\}$$ we get $$f(x) = (x-\zeta)(x-\zeta^{13}) = x^2 - (\zeta + \zeta^{13})x + \zeta\zeta^{13}$$ So generators over $$K$$ for the fixed field would be $$\zeta + \zeta^{13}$$ and $$\zeta^{14}$$. As you observed, the first is actually zero, so the only generator you need is $$\zeta^{14}$$ (which we can readily see is fixed by $$H$$ and has the right degree, since it is a primitive $$12$$th root of unity). | {
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magnetic-fields
Title: Simple question with magnetic fields On my test of today was the following question: "an aluminium block moves with a constant speed over a road, ahead of it is a magnetic field. Does the speed change when it enters the magnetic field?" The block was moving from left to right on the paper and the magnetic field lines were going inside the paper. The magnetic field was to the right of the car. I have no idea what the answer to this was, any help? As your block enters the magnetic field, currents will be induced (eddy currents due to a change in the magnetic flux across the metal plate - which will induce currents that try to resist that change).
Currents flowing in a conductor generate heat - energy is lost by the system.
The only place where that energy can come from is the kinetic energy of the block. | {
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it ’ s done the nPr and nCr templates press... The supplied factors WINDOW ] to access the shortcut menu $r$ in between ) =!... Recursion limit x ] and return the whole matrix x a little bit more complicated is that recursive! It shows how many ( minimum ) from the larger set get all possible combinations of r elements from GitHub. Coefficients smaller than can be obtained by taking a sample of items a! Is an example take a combination is: nCr = ( n, r ): is the formula time. 1 ] 1000 divide by 2 on how to do this combinations does... n '' should be given ; no provisions for function evaluation in all cases, you buy... N'T matter permutation or combination, follow these steps: there are 11,238,513 possible ways of doing.! ] 1000 employed to count r objects within n elements: combinations permutations. Loosely, without thinking if the order in which objects are selected does not matter in which combine. Know how combinations calculator will find the next combination by evaluating the | {
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"url": "http://otvedaem.com/rw8q0t2p/compute-combinations-r-cb7d5c"
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special-relativity, spacetime, velocity, inertial-frames, faster-than-light
We have 2 objects, A and B, that are traveling away from each other and emitting light towards each other. We also have a "stationary" object, C, that will be one of our observers stationed between A and B.
According to C, A is traveling at 0.6c in one direction and B is traveling at 0.6c in the opposite direction. From C's perspective there is 1.2c relative motion between the objects.
I am trying to figure out the perceived behavior of the light from the reference frame of the 3 different objects. I believe A and B will see the same thing so are equivalent, this leaves 2 different reference frames. | {
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newtonian-mechanics, classical-mechanics, lagrangian-formalism, hamiltonian-formalism
$$x(t) = R \cos(\omega t),\ \ y(t) = R \sin(\omega t)$$
versus
$$r(t) = R,\ \ \theta(t) = \omega t$$
Which one do you think is easier to work with algebraically? Which one gives you a better clue as to the shape of the motion?
Or with a system like the pendulum - ideally, you don't want to solve its motion in terms of Cartesian coordinates, but in terms of the angle $\theta$, since it is naturally constrained to move along an angular path. Effectively it has one dimension, not two. | {
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"url": null
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matlab, correlation
Title: MATLAB: How to compute the similarity of two signals and get the correct consistency or coherence metric I was wondering about the consistency metric. Generally, it allows us to deduce the parity or similarity between two signals, right? If so, if the probability is higher (from 0.5 to 1), does it means that there is a strong similarity of the signals? If the margin is less than (0.1-0.43), can this predict the poor coherence between the signals (or poor similarity, the probability the signals are different)? So, if we got the metric <0, is this approved the signal is totally different? Because I'm getting negative numbers. Is this hypothesis possible?
Can I have a clear understanding of the consistency metric of the signal? Here is my small code. Thanks in advance.
s1 = signal3
s2 = signal4 | {
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superconductivity, josephson-junction
Sometimes (for example "Many-Body Quantum Theory in Condensed Matter Physics: An Introduction" by Henrik Bruus,Karsten Flensberg Eq.18.84) people use
$$
J^{(2)}_{jos}=\frac{2e}{\hbar}\langle GS|\frac{\partial H}{\partial\Delta\phi}|GS\rangle.
$$
with $|GS\rangle$ being a ground state of the system.
This seems to be equivalent to the first definition of the Josephson current
when the ground state is independent of the phase difference $\Delta\phi$, i.e.
$J^{(1)}_{jos}=J^{(2)}_{jos}$.
Once the ground state is dependent on the superconducting phase difference
the first formula gives a different result, namely
$
J^{(1)}_{jos}=\frac{2e}{\hbar}(\langle GS|\frac{\partial H}{\partial\Delta\phi}|GS\rangle+
\langle \frac{\partial GS}{\partial\Delta\phi}|H|GS\rangle
+
\langle GS|H| \frac{\partial GS}{\partial\Delta\phi}\rangle
)
$.
I am somewhat confused now since I am not sure which is the correct formula to use.
Personally I expect the Josephson current to be the expectation value of some | {
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fluid-dynamics, inertia, navier-stokes
$$\tag{8} Re=\frac{\rho \frac{U^2}{R}}{\mu \frac{U}{R^2}}=\frac{\rho U R}{\mu}$$ The characterization of the Reynolds number as a ratio of "inertial effects" to "viscous effects" is only approximate, and is based on the nondimensionalization of the Navier-Stokes equations. If you construct nondimensional variables $x^* = x/L$, $\vec{u}^* = \vec{u}^*/U$, $t^* = t/(L/U)$, and $p^* = p/(U\mu/L)$, the Navier-Stokes equation (with no gravity) transforms into:
$$Re\left(\frac{\partial \vec{v^*}}{\partial t} + \vec{v^*} \cdot \nabla \vec{v^*} \right) = -\nabla p^* + \mu \nabla^2 \vec{v^*}$$
with the traditional definition of the Reynolds number, $Re = \frac{\rho U L}{\mu}$.
If (and this is a big if) the nondimensional variables were scaled in such a way that they are always approximately $1$, then the relevance of each side of the equation (and by extension the inertial/viscous effects) is modulated by the magnitude of the scalar $Re$. | {
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classical-mechanics, lagrangian-formalism, time
Title: Problem with the point transformation of the Lagrangian Page no 36 ie. the 2nd page of the PDF: https://www.physics.rutgers.edu/~shapiro/507/book3.pdf
there is a line at the bottom which states that the lagrangian is a function of $q$ and $\dot q$ and goes on with the partial derivative. Why does it not account for the time $t$ since $L(q,\dot q, t)$ is generally the form of a lagrangian? In context, it means that we can replace $(x,\dot x)$ with $(q, \dot q)$. It does not mean that the Lagrangian is not explicitly a function of time.
More explicitly, it could have read
We may consider $L$ as a function of the generalized coordinates $q_j$ and $\dot q_j$ rather than the Cartesian coordinates $x_i$ and $\dot x_i$, and ask [...] | {
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"url": null
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