qid int64 1 4.65M | metadata listlengths 3 3 | prompt stringlengths 31 25.8k | chosen stringlengths 17 28.2k | rejected stringlengths 19 40.5k | domain stringclasses 28
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|---|---|---|---|---|---|
216,074 | [
"https://physics.stackexchange.com/questions/216074",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/97180/"
] | I read an example where someone was explaining how the law of conservation of energy does not have to be maintained within a rotating mass even though angular momentum is maintained. The given example is an ice skater who spins faster as she brings her arms inward. The energy used bringing her arms inward gets transfe... | Yes, the rotational kinetic energy decreases. The extra energy is converted to thermal energy in the wheel and environment.
If you imagine letting the weight go, it will slide across the surface of the wheel as it moves towards the edge. This sliding is motion against friction, so energy is lost there. Then the weight... | Wait...wait... what? No, no, no, no... No. If a body is spinning, supposing non frictional surfaces and all of that, the energy would not decrease (if there is no external force). The energy is always constant. In that kind of problems there is only rotational energy (there is no other energy):
$
\begin{equation}
E_{r... | https://physics.stackexchange.com |
421,838 | [
"https://softwareengineering.stackexchange.com/questions/421838",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/384459/"
] | In the past few months that I've been learning Javascript, I've wondered which is the better usage of functions:
Functions that perform actions based on their arguments with <strong>no return value</strong>:
<pre><code>const someName = 'John';
function sayHello(name) {
console.log(`Hello, my name is ${name}!`);
}
s... | The first variant works with side effects: calling the function 10 times will produce 10 lines in the console.
The second version is without side-effects: you can call it 10 times and 10 times you can do something or nothing with its result.
The latter is sometimes called a functional style. Now about preferences, the ... | <blockquote>
To my understanding, the latter functions are also considered "pure" functions since they do not mutate any variables (which are a core principle in functional programming).
</blockquote>
You're absolutely right.
<blockquote>
Does either style have any strict advantages, or is it all down to pers... | https://softwareengineering.stackexchange.com |
337,627 | [
"https://electronics.stackexchange.com/questions/337627",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/40382/"
] | I am designing a simple contact switch(tactile, which conducts when you pushes, and springs back to not-conducting when released) interface with a microcontroller.
It's GPIO has option for both internal pull-up and pull-down.
1) Which one should I use? For 2 layered board, pull-up makes me easier to do PCB artwork, s... | <blockquote>
1) Which one should I use?
</blockquote>
Whatever suits your overall design best
<blockquote>
1) For 2 layered board, pull-up makes me easier to do PCB artwork, since one-end of switch connects to GND.
</blockquote>
That is exactly the reason pull-ups are used more often than pull-downs (and some ... | Standard practice is to enable internal pull-up of ~100k with a debounce cap across switch such that RC=T > bounce time or use software debounce.
Depending of ESD risk the contact may also have a series current limiting R to allow the IC diodes rated for 5mA to do their job or better , add Transil or TVS protection.
| https://electronics.stackexchange.com |
595,274 | [
"https://physics.stackexchange.com/questions/595274",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/280346/"
] | I'm working on a project which uses cylindrical permanent magnets, and I'm trying to determine the expected magnetic field due to these magnets. One problem I run into is that these magnets are usually not completely horizontal above the point at which I want to calculate the expected magnetic field. Assuming the point... | If you are measuring the length of an object in <span class="math-container">$S$</span> or in <span class="math-container">$S'$</span>:
\begin{itemize}
\item $\Delta x$ is the distance between two events at the same time in frame $S$.
\item <span class="math-container">$\Delta x'$</span> is the distance between two eve... | I don't know if it helps, but one problem that I see with distances in relativity is how to measure it in typical examples:
A trip from earth to Alpha Centauri, that is 4 ly distance, at a speed of 0,5c, will take 8 years in earth time:
<span class="math-container">$t' = \gamma (t - vx) = 1,1547(8 - 0.5*4) = 6,9282$</s... | https://physics.stackexchange.com |
61,426 | [
"https://mechanics.stackexchange.com/questions/61426",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/10835/"
] | My truck had these fancy lug nuts and I accidentally broke one off and I don't know how to get the remnants off. Any ideas?
<img src="https://i.imgur.com/8Bb9gDZ.jpg" alt="Here's a picture">
| I would use a bit of pipe as a protective collar and drill out the remnants of the nut.
If you have the tools then making a washer in the end of the pipe with guide holes for the drill would be better...
Remove one of the other nuts to see how much clearance there is...
On one of my wheels this had to be done and th... | I think I'd take a small cold chisel and split what's left of the nut. If careful, you should be able to do this without damaging the lug. If if you do end up damaging the lug, they usually aren't that hard to replace. I'm not seeing as how you are going to get around doing damaging something, though ... either rim or ... | https://mechanics.stackexchange.com |
492,591 | [
"https://physics.stackexchange.com/questions/492591",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/234979/"
] | I'm learning about centripetal force and I was shown a scenario where a man was spinning a rope attached to a ball over his head. There's a centripetal acceleration toward the center and therefore a force must be acting in the same direction as the centripetal acceleration — the centripetal force. But I wonder if that'... | The centripetal force can be made up of any type of force, whether gravitational, friction or tension. The centripetal force is not a force type, it is just a net force that is always radial. So it is a sum of forces, no matter the type.
So yes, it is a tension force. It just acts as a centripetal force.
| The centripetal force is the force required to keep the ball rotating in a circle, by providing it the necessary centripetal acceleration. In this case this force is the tension in the rope, but of course in general the centripetal acceleration can be provided by forces of a different nature.
| https://physics.stackexchange.com |
424,908 | [
"https://mathoverflow.net/questions/424908",
"https://mathoverflow.net",
"https://mathoverflow.net/users/484326/"
] | In my research in a different field (representation theory), the following system of equations popped up:
<span class="math-container">$$
ax=by
$$</span>
<span class="math-container">$$
xy+a+b-ax=p
$$</span>
where <span class="math-container">$p\in\{0,1,2,3,4\}$</span> and <span class="math-container">$a,b,x,y$</span> ... | Here is solution in positive integers.
The equation <span class="math-container">$ax=by$</span> implies that there are four integers <span class="math-container">$u,v,w,t$</span> such that <span class="math-container">$a=uv$</span>, <span class="math-container">$x=wt$</span>, <span class="math-container">$b=uw$</span>,... | Here is the general solution for general value of <span class="math-container">$a$</span> and the set of values in <span class="math-container">$b$</span> which is dense in an infnite interval (dpending on <span class="math-container">$a$</span>). More precisely, solve the first equation with respect to <span class="ma... | https://mathoverflow.net |
244,562 | [
"https://mathoverflow.net/questions/244562",
"https://mathoverflow.net",
"https://mathoverflow.net/users/20282/"
] | I am trying to understand $\mathbb Q$-Gorenstein smoothings, and especially the third condition in the following definition.
<blockquote>
<strong>Definition.</strong> For a normal projective surface $X$ with quotient singularities, a $\mathbb Q$-Gorenstein smoothing is a one-parameter flat family of projective surf... | <strong>Question 1</strong>. The answer is <em>yes</em>, and the classical example is as follows. Is it possible to find a one-parameter family $\psi \colon \mathcal{X} \to \Delta$ such that $X_0$ is isomorphic to the cone over a rational normal curve $C_4 \subset \mathbb{P}^4$, whereas $X_t (t \neq 0)$ is isomorphic t... | Just a note on the construction of the example Francesco mentioned, since in my opinion it is very instructive.
Let $X$ be either the Veronese surface or a rational quartic scroll in $\mathbb P^5$. In the first case, it is $\mathbb P^2$ embedded via the global sections of $\mathscr O_{\mathbb P^2}(2)$ and in the secon... | https://mathoverflow.net |
4,589 | [
"https://earthscience.stackexchange.com/questions/4589",
"https://earthscience.stackexchange.com",
"https://earthscience.stackexchange.com/users/2721/"
] | Antarctica receives heat from the Sun every day, so how does it stay frozen?
I have some thoughts about the answer but I'm unsure of whether it is correct; I hope people here can clarify.
My idea: the heat that Antarctica receives from the Sun is always 'travelling' from one spot to another, but the heat does not st... | It doesn't stay frozen. Ice evaporates (or sublimates is the correct term) under direct sunlight, but that's at a molecular level, it doesn't melt, it goes from solid to gas under sunlight and in the cold, some of this newly formed water vapor goes back being to ice.
In an absolutely dry climate, well below freezing,... | userLTK has explained that not all of the ice in the Antarctic stays frozen all the time. But perhaps there's a more basic view needed : sunlight in temperate areas melts all of the ice quite quickly, so why doesn't the same happen in Antarctica?
There are a number of reasons, but the simplest (and probably most impor... | https://earthscience.stackexchange.com |
721,415 | [
"https://physics.stackexchange.com/questions/721415",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/342394/"
] | I have a question about standing waves on strings. I'll try to explain the best I can, I searched and researched the whole day yesterday but I am confused still:
<ol>
<li>Every frequency has a single, and only one possible wavelength. This is what I come across over and over again, with no other conditions mentioned. e... | You overlooked the fact the speed varies when tension varies. Note that since <span class="math-container">$v=f\lambda$</span> a variation in both <span class="math-container">$v$</span> and frequency <span class="math-container">$f$</span> can mean wavelength <span class="math-container">$\lambda$</span> stays constan... | Your logic and research are sound (pun intended), the last piece of the puzzle is the fact that the speed of sound is different in different materials and it changes when you change pressure/density of the material. To your specific questions:
<ol>
<li>That fixed reference wavelength you mention is for air at room tem... | https://physics.stackexchange.com |
69,518 | [
"https://stats.stackexchange.com/questions/69518",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/28577/"
] | I'm investigating using a trimmed mean to measure the location of various distributions. The distributions sometimes are heavily contaminated and sometimes not. Usually they follow something similar to a log-normal or possibly mixed log-normal distribution, but often the data is "all over the place".
I've looked at th... | If the underlying population is normally distributed without contamination then the sample mean is the best unbiased estimate (in the sense of the lowest mean square error) of the centre of the population distribution.
This is not always the case with other distributions, which might include those with contamination... | The efficiency of the trimmed mean depends on the shape of the distribution.
If the underlying distribution is very asymmetric -- say, Exponential -- then trimming will bias your mean in the negative direction.
Or, say, if the distribution is a mixture of two distributions with different means, trimming could remove ... | https://stats.stackexchange.com |
513,071 | [
"https://physics.stackexchange.com/questions/513071",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/246947/"
] | If I was looking towards the horizon while standing on an infinite, perfectly flat plane, what would I see?
| If you were looking straight ahead, so that your line of sight were parallel to the ground, then the horizon line would appear to be at eye height, in all directions.
| In theory you would see whatever is on the other side. It would be very small and anything at the same height as you would be level with you.
In practice it would appear very hazy because of all the dust and other pollutants in the atmosphere, and the slightly different refractive index of air masses at different tem... | https://physics.stackexchange.com |
84,531 | [
"https://mathoverflow.net/questions/84531",
"https://mathoverflow.net",
"https://mathoverflow.net/users/20262/"
] | The Kullback-Leibler Divergence (KLD) of two PMF's $P(x)$ and $Q(x)$ is $D(P||Q)=\sum_x P(x)\log(P(x)/Q(x))$, with the provisos that $0\cdot \log (0/p)=0$ and $p\cdot \log (p/0)=+\infty$ whenever $p>0$.
It is known that KLD is continuous at $(P,Q)$ if $Q$ is <em>strictly positive over all $x$'s</em>. What can be s... | In addition to the conventions you have mentioned, it is also assumed that $0\log(0/0)=0$.
With these conventions, I think, in the finite case, it is always true that $$\lim_{n\to \infty} D(P_n||Q_n)=D(P||Q)$$ As you said, if $Q(x)>0$ for all $x$, its immediate from the Dominated Convergence theorem.
The problem is... | I believe that the lower semicontinuity of KBD is proved in Cover-Thomas Information Theory book. Also in Kullback's information theory book.
| https://mathoverflow.net |
75,612 | [
"https://mathoverflow.net/questions/75612",
"https://mathoverflow.net",
"https://mathoverflow.net/users/17855/"
] | Let $G_1$ and $G_2$ be topological groups. Assume that there exists a continuous homomorphism $f : G_1 \rightarrow G_2$ which (ignoring the group structure) is a homotopy equivalence. If $BG_i$ is a classifying space for $G_i$, then we get an induced map $f_{\ast} : BG_1 \rightarrow BG_2$ which is a homotopy equivale... | The space $\Omega BG$ is, by categorical nonsense, a classifying space for principal $G$-bundles over $\Sigma X$ with a chosen trivialisation at the basepoint. Any such bundle can be trivialised over the upper and lower halves of $\Sigma X$, and the difference between the two trivialisations gives a map $X\to G$. One... | First of all let me point out that, to my knowledge, your statement is true for weak equivalences, and therefore for homotopy equivalences if your topological groups have the homotopy type of a CW-complex.
Now, I'll answer your question. By the very definition of classifying space there is a principal $G$-bundle
$$G\l... | https://mathoverflow.net |
45,273 | [
"https://mathoverflow.net/questions/45273",
"https://mathoverflow.net",
"https://mathoverflow.net/users/1353/"
] | Simplicial commutative rings are very easy to describe. They're just commutative monoids in the monoidal category of simplicial abelian groups. However, I just realized that a priori, it's not clear that even some of the simplest facts we can prove for ordinary commutative rings (in particular those that depend integ... | Most of the things that stop working are things related to procedures in commutative algebra that don't preserve exactness. The tensor product of simplicial modules always has to be the derived tensor product in order to be meaningful, etc.
One of the sticky points is that "free" is not the same as "polynomial" in hi... | Given a simplicial ring $A_\bullet$, it is standard that $\pi_0(A)$ is a ring and $\pi_n(A)$ is a module over it, so $A_\bullet$ is weakly contractible iff $\pi_0(A)=0$. Also, $\pi_0(A)$ is just the cokernel of $d_0-d_1:A_1\to A_0$. We can take any chain of face maps $A_n\to A_0$ and compose with the projection to $\... | https://mathoverflow.net |
16,810 | [
"https://chemistry.stackexchange.com/questions/16810",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/7256/"
] | I understand that a polar solvent will help dissociate the <span class="math-container">$\ce{HBr}$</span> into ions.
But why a protic solvent?
Why would we want a solvent that would encage the <span class="math-container">$\ce{Br}$</span> and <span class="math-container">$\ce{H}$</span> ions?
Why is the aprotic solvent... | <blockquote>
why a protic solvent?
</blockquote>
Protic solvents tend to have higher dielectric constants than typical, <strong>unreactive</strong>, non-protic solvents. Look at the following table.
<span class="math-container">\begin{array}{|c|c|c|}\hline
\text{Solvent} & \text{Dielectric constant} \\ \hline
\... | A polar protic solvent will help stabilize the carbocation that is formed in the process of electrophilic addition. When the nucleophilic $\pi$ bond grabs the hydrogen from the $\ce{HBr}$, one of the carbons that was part of the $\pi$ bond is left deficient of an octet.
| https://chemistry.stackexchange.com |
683,809 | [
"https://physics.stackexchange.com/questions/683809",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/299640/"
] | From what I have read it seems magnetic susceptibility and magnetic permeability both represent the level of a material's magnetic response to an external field.
Fundamentally, what is the difference between them?
| The important equation here is the difference between <span class="math-container">$\mathbf H$</span> and <span class="math-container">$\mathbf B$</span> fields (using boldface for vectors):
<span class="math-container">$$\mathbf B = \mu_0(\mathbf H +\mathbf M),$$</span>
where <span class="math-container">$\mathbf M$</... | There's a different definition for each one,
Magnetic permeability has to do with the property of a magnetic material to have its parts in a aligned magnetization
<span class="math-container">$$B=\mu H.$$</span>
Magnetic susceptibility have to do with other properties of the material, as refractive index or absorption
... | https://physics.stackexchange.com |
1,205,668 | [
"https://math.stackexchange.com/questions/1205668",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/222290/"
] | I tried turning it into an exp limit and using l'Hopital but I must have done some mistake because the limit to me results infinite whereas the answer is -1, can someone give a hint please
<img src="https://i.stack.imgur.com/0iHC6.gif" alt="enter image description here">
<img src="https://i.stack.imgur.com/0iHC6.gif... | There is, but as with most of the checks of the field axioms using Dedekind Cuts, it isn't pretty.
First recall that multiplication is given by, for $A,B$ positive
\begin{equation}
A\cdot B =\{a\cdot b \mid a\in A \wedge 0<a \wedge b \in B \wedge 0<b \} \cup \{ q\in \mathbb{Q}\mid q\leq 0\}.
\end{equation}
More ... | I tried to prove your above claim for positive cuts, that is, cuts containing some positive rationals. This is the first time I've tried to prove this, so I apologize in advance if it is a bit hard to follow or if it contains mistakes.
<blockquote>
Addition and multiplication of positive Dedekind cuts are defined as... | https://math.stackexchange.com |
66,882 | [
"https://physics.stackexchange.com/questions/66882",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/7769/"
] | <img src="https://i.stack.imgur.com/VPQaJ.png" alt="enter image description here">
I would like to put this into a differential equation. This is what I have.
$$r \times F = I \ddot\theta + \mu \dot\theta + k \theta$$
What I need verified:
<ul>
<li>$\text{Torque} = I\ddot\theta + \mu \dot\theta + k \theta$</li>
<li... | Is this the situation?
If yes then the friction force has to be proportional to the applied force $F$ and not $\omega$. With a perfectly relaxed rope, there is no contact and hence friction. What you include as a friction term is actually a rotational damper, which resists $\omega$. So you have a spring damper system ... | In other words, you're asking whether it is correct to say that $\tau = I \alpha + \mu \omega + k \theta$ (where $\alpha = \theta ''$ and $\omega = \theta'$) in the specific case of us having a rigit object with torsion, kinetic friction and inertia. However, your equation frictional force is wrong: it should be $\tau... | https://physics.stackexchange.com |
59,515 | [
"https://physics.stackexchange.com/questions/59515",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/22585/"
] | This is a pretty basic conceptual question about the conservation of linear momentum.
Consider an isolated system of 2 fixed-mass particles of masses $m_1$ and $m_2$ moving toward each other with velocities $v_1(t)$ and $v_2(t)$ respectively.
Now conservation of momentum says that at any point during the particles'... | I too will set $c=1$ and I'll ignore the mass and minus sign outside of the integral for simplicity since they don't affect Lorentz-invariance.
Let $x^\mu(\lambda) = (t(\lambda), x(\lambda)$) denote a parameterized path in two-dimensional Minkowski space. We can mathematically <em>define</em> the action of Lorentz ... | joshphysics's answer was excellent, and I'd like to draw attention to another aspect of the question.
Your action,
$S=-m\int\sqrt{1-u^{2}}dt$
Can be written:
$S=-m\int\sqrt{(dt)^{2}-(udt)^{2}}$
$=-m\int\sqrt{(dt)^{2}-(dx)^{2}} = -m\int ds$
And the transformed action $S' = -m \int ds'$.
So, for the action to be L... | https://physics.stackexchange.com |
96,622 | [
"https://physics.stackexchange.com/questions/96622",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/36746/"
] | The gravity at the centre of a star is zero as in the case of any uniform solid sphere with some mass. When a massive star dies, why does it give rise to a black hole at it's centre?
I know how to derive the field equations for gravity inside a star assuming the star as a uniform solid sphere of mass M and radius R. ... | It's because the value of the gravitational field at the center of a star is not the relevant quantity to describe gravitational collapse. The following argument is Newtonian.
Let's assume for simplicity that the star is a sphere with uniform density $\rho$. Consider a small portion of the mass $ m$ of the star that'... | Well, you're right that a particle sitting at the centre of a star (or generally the centre of any spherical distribution of matter) feels no net gravitational force. So, in the absence of other forces, it will simply continue to sit at the centre. But every other particle in the spherical distribution will feel a grav... | https://physics.stackexchange.com |
168,699 | [
"https://electronics.stackexchange.com/questions/168699",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/-1/"
] | What happens to the light bulbs if the power switch is connected. Will B shine brighter or will both? Or will nothing happen?
A & B are light bulbs.
<img src="https://i.stack.imgur.com/ua4Y1.png" alt="A & B are light bulbs">
| I'm assuming that all your batteries are of same voltage and are able to deliver arbitrary currents. Additionally I'm assuming the bulbs have equal inner resistance.
A and B divide the voltage exactly in half. So the potential on both terminals of the switch is the same in opened state. In this case closing it would h... | In a circuit that's driven by voltage sources, (i.e., almost all circuits), in this case the batteries, you have to look first at the voltages throughout. Figure out what the voltage is across each light bulb when the switch is open, and from that, figure out the current through each bulb. Then do the same thing with t... | https://electronics.stackexchange.com |
5,376 | [
"https://quantumcomputing.stackexchange.com/questions/5376",
"https://quantumcomputing.stackexchange.com",
"https://quantumcomputing.stackexchange.com/users/4974/"
] | I found something in a lecture on Simon's algorithm that I do not quite understand how to interpret. There the following is said:
<span class="math-container">$$\sum_{y\in\{0,1\}^n}|y\rangle\left(\sum_{x\in\{0,1\}^n} (-1)^{x\cdot y}|f(x)\rangle\right)$$</span>
So we assume a 1 to 1 function and <span class="math-cont... | In the first state you write they omitted to write the normalization factor. This is not rare to see, as one can usually easily deduce what the normalization should be from the context (though it might not be a very pedagogical choice).
To deduce the correct normalization in this case, you need only notice that, becau... | The first state in your question is not a valid quantum state as it is not normalized.
The result comes directly from the axioms of quantum mechanics. You just have to apply the Born rule. For a state <span class="math-container">$\sum_y ~ a_y |y\rangle$</span> the probability of measuring <span class="math-container"... | https://quantumcomputing.stackexchange.com |
1,355,375 | [
"https://math.stackexchange.com/questions/1355375",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/169954/"
] | Solve the problem :
$$ \begin{cases}
\frac{dx}{dt} + \frac{1}{t} \cdot x = {e^t}^2 , t>0 \\[2ex]
x(1) = 1 \end{cases}$$
I have solved it by restructuring which gives :
$$\frac{d}{dt} \cdot (tx) ={e^t}^2 \cdot t $$
Some calculations later we will have the solution :
$$ x(t) = \frac {1}{t}(\frac{{e^t}^2}{2} - ... | Let $h$ be an inverse for $f\circ f \circ g\circ g \circ f\circ f$.
$id=(f\circ f \circ g\circ g \circ f\circ f)\circ h=f\circ (f \circ g\circ g \circ f\circ f\circ h)$ implies that $f$ is surjective.
$id=h\circ (f\circ f \circ g\circ g \circ f\circ f)=(h\circ f\circ f \circ g\circ g \circ f)\circ f$ implies that $f$... | <ul>
<li>1) $r$ is by definition a <em>retraction</em> if $r\circ s=\text{id}$ for some
$s$.</li>
<li>2) $s$ is by definition a <em>section</em> if $r\circ s=\text{id}$ for some
$r$.</li>
<li>3) If $h$ is both a retraction and a section then $h$ is invertible:
let $h\circ s$ and $r\circ h$ be identities. Then $r=r\circ... | https://math.stackexchange.com |
387,808 | [
"https://stats.stackexchange.com/questions/387808",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/229979/"
] | I'm currently facing a new type of problem, and i have no idea how to solve it, so <strong>any suggestion will be really appreciated</strong> ! The problem is the following:
I have a matrix of temperatures, depending on two parameters (Alpha and Beta). We can plot this matrix with matplotlib, and we get :
[<img src="... | It depends upon what you know and the motivation as to why you are doing it. Since you are not concerned with any of the uncertainty about <span class="math-container">$\alpha$</span> and <span class="math-container">$\beta$</span>, we will remove that uncertainty by using the predictive distribution. It would solve ... | You have got a situation where the temperature (a 1D variable) maps to a 2D plane (alpha and beta).
For a single temperature, the alpha and beta can be anything along a single curve.
If you would be able to add something like a secondary variable then you could better estimate which alpha and beta on the curve are ... | https://stats.stackexchange.com |
256 | [
"https://stats.stackexchange.com/questions/256",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/217/"
] | What is the easiest way to understand boosting?
Why doesn't it boost very weak classifiers "to infinity" (perfection)?
| In plain English: If your classifier misclassifies some data, train another copy of it mainly on this misclassified part with hope that it will discover something subtle. And then, as usual, iterate. On the way there are some voting schemes that allow to combine all those classifiers' predictions in sensible way.
Beca... | Boosting employs shrinkage through the learning rate parameter, which, coupled with <em>k</em>-fold cross validation, "out-of-bag" (OOB) predictions or independent test set, determine the number of trees one should keep in the ensemble.
We want a model that learns slowly, hence there is a trade-off in terms of the com... | https://stats.stackexchange.com |
18,829 | [
"https://security.stackexchange.com/questions/18829",
"https://security.stackexchange.com",
"https://security.stackexchange.com/users/5400/"
] | I've got an 8U 19-inch server rack cabinet with two locks - one on the front panel, one on the rear panel. The locks are small cam locks, but the cam part is rather thin and flimsy-looking.
<img src="https://i.stack.imgur.com/QJdbr.gif" alt="Cam Lock">
I could easily break them open in a couple of seconds with a crow... | Your server rack should only be a small component of your overall security. Ideally, your supplemental security arrangement (such as the staff at a data center) should handle the heavy-lifting of keeping intruders out of your rack.
Ideally, the physical security on your rack should make intrusion slow, noisy, difficul... | <strong><h3>In a home/small office setting:</h3></strong>
One thing you can add is to anchor the rack to the floor. Also use Kensingtons to secure your hardware to the Anchor or the rack frame. Use front panels for your servers (these can be locked picked in under a minute if you are handy though) and consider puttin... | https://security.stackexchange.com |
357,143 | [
"https://mathoverflow.net/questions/357143",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | For each natural number <span class="math-container">$a$</span> consider the sequence <span class="math-container">$l(a):=\left(\frac{\gcd(a,b)}{a+b}\right)_{b \in \mathbb{N}}$</span>.
Then I have computed that for <span class="math-container">$k\ge 2, k \in \mathbb{R}$</span> and <span class="math-container">$p$</spa... | Yes, and yes.
1) We have
<span class="math-container">$$|l(a)|_k^k=\sum_{d\mid a}\left(\prod_{p\mid d}\left(1-\dfrac{1}{p^k}\right)\right)\left(\zeta(k)-\sum_{j=1}^{a/d}\dfrac{1}{j^k}\right)\;,$$</span>
which checks with your special cases.
2) Expand into partial fractions.
P.S. The coefficient of <span class="mat... | First of all, we consider <span class="math-container">$|L(a)|_k^k=\sum_{b=1}^{\infty} \frac{(a,b)^k}{b^k}$</span>. It is easy to see that <span class="math-container">$|l(a)|_k^k=|L(a)|_k^k-y$</span>, where <span class="math-container">$y=y(a)=\sum_{b=1}^a \frac{(a,b)^k}{b^k}$</span>. Also
<span class="math-container... | https://mathoverflow.net |
16,584 | [
"https://mathoverflow.net/questions/16584",
"https://mathoverflow.net",
"https://mathoverflow.net/users/4155/"
] | In the definition of vertex algebra, we call the vertex operator state-field correspondence, does that mean that it is an injective map??
Are there some physical interpretations about state-field correspondence ? Or why we need state-field correspondence in physical viewpoint??
Does it have some relations to highest ... | Yes, the state-field map $v\mapsto Y(v,z)$ is an injective map, since by the axioms of VOA, $Y(v,z)1|_{z=0}=v$.
The state-field correspondence appears in 2-dimensional field theory because such a field theory attaches an amplitude to a "pair of pants" (a 2-sphere with 3 holes). Namely, if you regard two of the holes ... | I want to elaborate a little on Pavel's excellent answer.
We can think (very schematically) of local operators in an n-dimensional
field theory the following way. We have an n-1 manifold M with some additional
structures (topological, conformal, metric etc), to which our field theory assigns a vector space Z(M) of s... | https://mathoverflow.net |
473,695 | [
"https://physics.stackexchange.com/questions/473695",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/228579/"
] | By the parallel axis theorem, a pendulum that rotates around a point <span class="math-container">$P$</span> and a distance <span class="math-container">$l$</span> from it's center, has kinetic energy <span class="math-container">$E_{kin}= \frac{\omega^2}{2}(\frac{2mR^2}{5}+ml^2)$</span>. Where R is the radius of the s... | The net electric field intensity <span class="math-container">$\vec E_{\rm net}(\vec r)$</span> at a position <span class="math-container">$\vec r$</span> is the vector sum of the electric field intensities produced at that point by each individual charge, <span class="math-container">$\vec E_{\rm net}(\vec r)= \vec E_... | Field intensity depends upon all charges in the surroundings and the presence of conductors too affects field intensity. However, flux at a "point" isn't quite meaningful I guess.
| https://physics.stackexchange.com |
179,595 | [
"https://physics.stackexchange.com/questions/179595",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/79217/"
] | It is obvious that dimensional analysis can be used to derive many classical mechanics equations (excluding constants). As long as all the dependent quantities are known.
My question is whether this is an accepted method to derive formulas or is calculus is a must? If so can it be used in advanced areas such as Quant... | Dimensional analysis can help to "guesstimate" the form of many important results but it can, for instance, not produce general solutions to equations of motion. It's an invaluable tool to understand the structure of physical theory, including quantum mechanics and relativity, and to check results for consistency, but ... | Yes it can!
However, the term <em>dimension analysis</em> needs to be seen in its/a context.
Buckinghams Pi-Theorem did not just emerge <em>out of the blue</em>. And, the reason it works is not pure luck. There is a well grounded physical/theoretical basis for it. And it is the basis which allowed for <em>dimesion an... | https://physics.stackexchange.com |
26,533 | [
"https://dsp.stackexchange.com/questions/26533",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/15030/"
] | I would like to know if the following method of 2x oversampling is correct:
Interpolate:
<ul>
<li>Take an original signal sampled at 44100Hz as input</li>
<li>Upsample by adding a zero after each original sample to get a signal twice as long</li>
<li>Filter the new signal using a low pass filter (cutoff of 44100Hz ba... | <strong>Interpolation (sampling frequency 44.1 kHz ➔ 88.2 kHz)</strong>
Your original 44.1 kHz sampled signal has frequencies up to 22.05 kHz, so you should lowpass filter at 22.05 kHz after dilution with zeros. Your filter should have a gain of 2. Otherwise the signal amplitude drops to half because you set half of t... | Yes, your method is correct, and will work just fine.
You can reduce the computational load by combining the upsampling (insertion of zeros) and low-pass filter into a single interpolating filter, and combining the low-pass filter and removal of samples into a single decimating filter, but that is not necessary to get... | https://dsp.stackexchange.com |
861,128 | [
"https://math.stackexchange.com/questions/861128",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/-1/"
] | <blockquote>
Let f(z) be analytic function and $\forall z=x+iy\in\mathbb C, u_x=u_y$ ($u_x=\frac{\partial f}{\partial x},u_y=\frac{\partial f}{\partial y}$. Prove that $f(z)=az+b$.
</blockquote>
I thought using Cauchy Riemann equations with the given equation: $$\begin{cases}u_x=u_y \\ u_x=v_y\\u_y=-v_x\end{cases}$... | From $u_x=u_y$ and $u_x=v_y$, you have $u_y=v_y$ which implies
$$ u=v+2c_1(x). $$
Similarly from $u_x=u_y$ and $u_y=-v_x$, you have $u_x=-v_x$ which implies
$$ u=-v+2c_2(y). $$
Thus
$$ u=c_1(x)+c_2(y), v=c_2(y)-c_1(x). $$
Now use $u_x=u_y$ to get $c_1'(x)=c_2'(y)$. Since $c_1(x)$ and $c_2(y)$ are functions of $x$ and $... | From Cauchy-Riemann we have $u_{xx} + u_{yy} = 0$, if now $u_x = u_y$, we have $$ u_{xx} = (u_x)_x = (u_y)_x = u_{xy} = (u_x)_y = u_{yy}$$
so $2u_{xx} = 0$, that is $u_{xx} = u_{yy} = u_{xy} = 0$. For $v$, we have
$$ v_{xx} = (v_x)_x = -(v_y)_x = -v_{xy} = -(v_x)_y = v_{yy} $$
which again gives $v_{xx} = v_{xy} = v_{y... | https://math.stackexchange.com |
66,195 | [
"https://dba.stackexchange.com/questions/66195",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/36118/"
] | I have two Postgres 9.1 installations. One works properly, the other does not.
On the working installation:
<pre><code>dc=# select * from pg_extension;
extname | extowner | extnamespace | extrelocatable | extversion | extconfig | extcondition
----------+----------+--------------+----------------+------------+-----... | On PostgreSQL 9.1, it is possible to get to this state without directly manipulating the catalogs.
I started from having <code>plpgsql</code> as an extension, and did the following:
<pre><code># DROP EXTENSION plpgsql CASCADE; -- do this only if you are prepared to lose your plpgsql functions, too
# \dx
... | I don't think that the server would allow you to drop the "plpgsql" extension. It seems a case of somebody manually deleting the entry from pg_extension catalog table.
You can recreate the extension if it is available in the pg_available_extensions table. If that doesn't work, you can try inserting the required row fo... | https://dba.stackexchange.com |
183,320 | [
"https://physics.stackexchange.com/questions/183320",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/70392/"
] | Consider I have a state represented by the Ket:
$$|\psi\rangle=\sum_i a_i |\phi_i\rangle$$
What are the physical interpretations of the coefficients $a_i$? My guess is that $|a_k|^2$ represents the probability that the 'paritcle' is in the state $ |\phi_k\rangle$ is this right? If so does it only hold for orthonormal ... | The coefficients $a_k$ quantity the projection of the state $|\psi\rangle$ onto the $k^\mathrm{th}$ basis state. So if you measure in that basis you would expect $|a_k|^2$ of the time to measure state $|\phi_k\rangle$. If you change the basis you will need to recalculate the projection coefficients.
If you are in a n... | It's convention to normalize the wave function, but this is purely something done to make calculations easier. States multiplied by a c number(complex number) are completely equivalent.
This is why we choose to normalize states (magnitude 1). It makes the calculations for things like the transitions probability betwee... | https://physics.stackexchange.com |
4,071 | [
"https://physics.stackexchange.com/questions/4071",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/1186/"
] | Here are some depictions of electromagnetic wave, similar to the depictions in other places:
<img src="https://idol.union.edu/malekis/Phys%20&%20Pol%202010/Images/e&mWave.gif" alt="enter image description here">
<img src="https://micro.magnet.fsu.edu/primer/java/wavebasics/basicwavesjavafigure1.jpg" alt="enter... | The depictions you're seeing are correct, the electric and magnetic fields both reach their amplitudes and zeroes in the same locations. Rafael's answer and certain comments on it are completely correct; energy conservation does <em>not</em> require that the energy density be the same at every point on the electromagne... | There is no contradiction with conservation law, you are just applying it wrongly. To do it right, you have to consider a small closed region and check whether the variation of energy inside this domain is the same as (minus) the energy flux through its boundaries. In the case of a electromagnetic wave, when the energy... | https://physics.stackexchange.com |
334,265 | [
"https://mathoverflow.net/questions/334265",
"https://mathoverflow.net",
"https://mathoverflow.net/users/136860/"
] | Let <span class="math-container">$X$</span> be a Banach space and <span class="math-container">$S\subseteq X$</span> be a subspace such that the unit sphere of <span class="math-container">$S$</span> is weakly compact. If <span class="math-container">$Y^*=X$</span> for some separable Banach space <span class="math-cont... | Assume that Samya Kumar Ray meant that the unit ball of <span class="math-container">$S$</span> is weakly compact. If <span class="math-container">$S$</span> is really a sphere, the fact that the answer is "Yes" follows from the argument outlined by Bill Johnson (and the additional assumptions are not needed).
The ans... | I found a proof using a theorem in "Topcis In Banach Space Theory" by Albiac and Kalton.
Theorem: Let <span class="math-container">$X$</span> be a Banach space. The Dual <span class="math-container">$X^*$</span> contains a sequence <span class="math-container">$(x_n^*)$</span> having the property <span class="math-cont... | https://mathoverflow.net |
3,894,961 | [
"https://math.stackexchange.com/questions/3894961",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/839704/"
] | In a country called Sevenland there are 15 cities. And every city has at least 7 highways connected to it. Prove that from any city we can go to any city using the highways
| There is.
<span class="math-container">$$mx+q=m(x-\mu_x)+(m\mu_x+q)$$</span> and an antiderivative is
<span class="math-container">$$m\frac{(x-\mu_x)^4}{4}+(m\mu_x+q)\frac{(x-\mu_x)^3}{3}.$$</span>
| <span class="math-container">$$I=\int (x-\mu_x)^2 \cdot (mx+q) dx$$</span>
Substitute <span class="math-container">$z=x-\mu_x$</span>:
<span class="math-container">$$I=\int z^2 (m(z+\mu_x)+q) dz$$</span>
<span class="math-container">$$I=\int mz^3+(m\mu_x+q)z^2)dz$$</span>
It's a polynomial.
| https://math.stackexchange.com |
218,236 | [
"https://stats.stackexchange.com/questions/218236",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/55946/"
] | I'm wondering if when it comes to predictive analytics, whether a lower test MSE is really all that matters. Should I not even look at residuals - other model diagnostics when it comes to prediction if I'm getting a lower test MSE?
Or does a lower test MSE model always satisfy the model assumptions? at least more than... | The formula is actually pretty straight forward. Consider the table from your question.
<blockquote>
The table states that there were a total <strong>90 observations</strong>
</blockquote>
Out of all 90 observations:
<ol>
<li><strong>76 times</strong>, no pizzas or squirrel</li>
<li><strong>9 times</strong>, pizz... | Maybe it's too late since this question was asked 5 years, 9 months ago. But I hope my explanation will help you to understand the phi coefficient in this book better. Things we know from this book are:
<ul>
<li><strong>The first variable</strong> is the squirrel.</li>
<li><strong>the second variable</strong> is the pi... | https://stats.stackexchange.com |
216,800 | [
"https://softwareengineering.stackexchange.com/questions/216800",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/-1/"
] | I couldn't think of a good way to word the title, sorry. But what I mean is, is it considered bad practice to do:
<pre><code>print get_array()[2]
</code></pre>
over:
<pre><code>output=get_array()
print output[2]
</code></pre>
(where get_array() is a function that returns an array, if that wasn't clear). Which metho... | Let me take a crack at this,
Think of the risks you're posing by accessing an array straight away.
<ul>
<li>Do you know for SURE, it's got data at the aforementioned index?</li>
<li>Is that data in the format you want?</li>
<li>If there was an Exception, like a null at that index, would your
program be able to reco... | This entirely depends upon what you are planning on doing with the array and what you should/can do if the element you expect to be at a certain position isn't there.
Frequently, when this is done, it is returning multiple values (such as a first, middle and last names) which are actually independent -- the array is ... | https://softwareengineering.stackexchange.com |
143,973 | [
"https://softwareengineering.stackexchange.com/questions/143973",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/42062/"
] | <strong>Scenario:</strong>
<ul>
<li>You push to production</li>
<li>The push broke multiple things</li>
<li>That same build did not break qa or dev</li>
<li>As a developer, you don't have prod access. </li>
<li>There is lots of pressure from <em>above</em> to get things working agian.</li>
</ul>
<strong>Specifics:</... | Grab as much information about the problem as you can (logfiles etc.) and then rollback the production servers to a working state. That's a pain from the developer's point of view of course, but is most likely a given.
Next, try and see if you can reproduce the problem in a development environment.
If you can, then f... | How <em>well</em> do you understand the problem? What's the risk that your hunch will make things worse? Is it possible to go back and reproduce the problem in DEV/QA regions? What can you do to sync your DEV/QA region to get it closer to PROD? Maybe you have to change some environmental or database settings, maybe you... | https://softwareengineering.stackexchange.com |
975,859 | [
"https://math.stackexchange.com/questions/975859",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/178310/"
] | So I do not understand the concept at all. Could somebody explain it to me, in very dumbed down terms, using the problem $x^2y + xy^2 = 6$?
All I have down is that it is equal to $4xy + x^2 + y^2 = 6$, and even that could be wrong. Help!
| <blockquote>
So I do not understand the concept at all. Could somebody explain it to me, in very dumbed down terms, using the problem $x^2y + xy^2 = 6$?
All I have down is that it is equal to $4xy + x^2 + y^2 = 6$, and even that could be wrong. Help!
</blockquote>
Yeap, it is. You're on the right track, applyi... | It would actually depends on whether you are differentiating with respect to x or with respect to y ( d/dx or d/dy ). If you are differentiating with respect to x, then you would have 4xy (dy/dx) + 2x + 2y (dy/dx) = 0. Basically every time you see a y, take the derivative of if and put in dy/dx. Then solve for dy/dx to... | https://math.stackexchange.com |
53,678 | [
"https://mechanics.stackexchange.com/questions/53678",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/37130/"
] | Car: BMW E46 3-series 318i (1998-2005 model)
I recently returned from working abroad for four weeks. Unfortunately I had to leave my car parked on the street for the duration (I usually do this two or three times per year).
<ul>
<li>Battery was completely drained past the point of no return (measured 5.2V). Replaced... | Fixed it. Took the Light Control Module out (a five minute job, as it's part of the headlight knob assembly) and noticed some damage to the PCB. Swapped it out for another one I got at the local scrappers for £5 and all problems have gone away. I assume that there was a short on the PCB that drained the battery.
The o... | The problem is most likely the turn signal stalk switch itself. The e46 uses the same relay for the hazards and the turn signals, and since the hazards work, the relay, wiring, hazard switch, and signals are all probably fine, leaving only the stalk switch.
The e46 also has parking lights which are turned on by leavi... | https://mechanics.stackexchange.com |
30,620 | [
"https://datascience.stackexchange.com/questions/30620",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/50899/"
] | I trained a classifier using TfidfVectorizer in Sklearn. I then pickled the model for future use.
The new x_test that I want to make predictions on, has more features than the x_train from the model. This is the resulting error:
<pre><code>ValueError: X has 4877 features per sample; expecting 2799
</code></pre>
Is t... | You should not experience this problem if you use TfidfVectorizer properly.
Demo:
<pre><code>In [58]: from sklearn.feature_extraction.text import TfidfVectorizer
</code></pre>
source text
<pre><code>In [59]: text = """I trained a classifier using TfidfVectorizer in Sklearn. I then pickled the model for future use.
... | I think you would need to delete exactly those features (columns) that are not known to your model.
Imagine that you trained your model on the following features:
<ul>
<li>human weight</li>
<li>human height</li>
<li>sex</li>
<li>age</li>
</ul>
and now you want to feed it a test data set containing the following feat... | https://datascience.stackexchange.com |
578,584 | [
"https://physics.stackexchange.com/questions/578584",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/62203/"
] | At the end of the day what the thermometer is measuring as temperature is energy of the air molecules (which could come in the form of kinetic energy). Now, imagine the following scenario :
<ol>
<li>Take a box with just one gas molecule (at speed x). It goes and hits the mercury of the thermometer. Thermometer will pro... | Assuming an ideal gas, if you are keeping the average speed of the molecules the same then you are holding the temperature of the gas constant. Assuming the container keeps the same volume, by the ideal gas law it must be that the pressure of the gas increases as you add more molecules.
Yes there are more molecules hit... | <blockquote>
Now double the density (but keep the speed of individual air molecules
the same). Fill the box with 2 million molecules, but keep the average
speed of the molecules the same. Will it record the same temperature?
</blockquote>
The actual temperature of the gas will be the same prior to making a reading, but... | https://physics.stackexchange.com |
854,279 | [
"https://math.stackexchange.com/questions/854279",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/63615/"
] | The notation is for the greatest common divisor. I know that
$$(a,b,c)=((a,b),c)=((a,c),b)=(a,(b,c))$$
Suppose $g=(a,b,c)$. Then $g\mid a,b,c$. Also, $g\mid(a,b),c$ and $g\mid(a,c),b$. Thus there exist integers $k,m$ such that
$$(a,b)=gk, (a,c)=gm$$
Then
$$((a,b),(a,c))=(gk,gm)=g(k,m)$$
Therefore, since $(k,m)=1$... | It's much simpler using the identities you already know (associativity, commutativity, etc)
$$((a,b),(a,c))\, =\, ((a,b),a,c)\, =\, (a,b,a,c)\, =\, (a,b,c)$$
<strong>Remark</strong> $\ $ By induction, in the same way, one can always "flatten" such gcd expressions.
| Your proof seems okay. This is probably the shortest one. But gonna be large because I am oversimplifying.
Let
$$a=\prod_{i=1}^{k}p_i^{\alpha_i},b=\prod_{i=1}^{k}p_i^{\beta_i},c=\prod_{o=1}^{k}p_i^{\gamma_i}$$
Now $\displaystyle \text{gcd}(a,b,c)=\prod_{i=1}^{k}p_i^{\min(\alpha_i,\beta_i,\gamma_i)}$
and $\displaystyle... | https://math.stackexchange.com |
2,776,133 | [
"https://math.stackexchange.com/questions/2776133",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/560857/"
] | I've really been stuck on this problem for a while. We have the equation: $s_t = (s_{t-1}/2)+3$. I need to show the steps it would take to show this can be written as: $s_t = 2^{-t}(s_0-6) +6$. I figure it has something to do with telescoping but I'm not sure how this would be done.
| <ol>
<li>The area of the rectangle $PQRS$ is the length of $RS$ multiplied by the length of $PS$. You are given the length of $RS$ as being $2p$. You want to find the length of $PS$. </li>
<li>Let $(x,y)$ be the coordinates of $P$. Since $P$ is on the graph, we must have that $y = x(8-x)$. So what we want to find is th... | Let $S(4-p,0)$, then $P(4-p,(4-p)(4+p))$ or $P(4-p,16-p^2)$. Then you have $A=SR\times SP$.
| https://math.stackexchange.com |
140,300 | [
"https://chemistry.stackexchange.com/questions/140300",
"https://chemistry.stackexchange.com",
"https://chemistry.stackexchange.com/users/70817/"
] | So the electron density is the function <span class="math-container">$\rho(\vec x)$</span> that associates a value of electrons per cubic angstrom, to each point <span class="math-container">$\vec x$</span> in the 3D space.
This information tells us how likely it is to find electrons at specific regions of space within... | This is standard for purifying substances.
To wash means to add your product solution to an aqueous solution (or just water, but frequently a saturated solution) to a separatory funnel. After shaking, you drain the lower layer (which is usually aqueous). This process removes water soluble impurities. This is frequently... | The solvent of this experiment should be non polar, and may be a hydrocarbon, or a chlorinated hydrocarbon. This organic phase may contain as impurities some acids and other polar substances soluble in water, that should be eliminated. This liquid is then mixed with an aqueous solution of soda <span class="math-contain... | https://chemistry.stackexchange.com |
375,170 | [
"https://physics.stackexchange.com/questions/375170",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/131490/"
] | When I was first introduced to Snell's Law, I was shown a derivation using Fermat's principle of least time. Using this same principle you can show that the angle of incidence must be equal to the angle of reflection. I was later again shown this, but instead of using Fermat's principle, all of this was derived using H... | If all you have is a basin of water at 310K, you cannot concentrate the temperature. The water is already at thermal equilibrium, so there is no way to extract energy from it in any way. That's the nature of entropy.
Now if you have that basin of water at 310K <strong>and</strong> a heat sink at a lower temperature,... | heat pumps do not rely on evaporative effects. in a heat pump, mechanical work is used to extract heat from a cold source and move it to a warm sink (think: refrigerator running backwards). Heat pumps can and are used to extract heat from a cold body of water and move it into a warmer space; in all such cases the amoun... | https://physics.stackexchange.com |
518,147 | [
"https://physics.stackexchange.com/questions/518147",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/249032/"
] | Let’s say there’s a planet 4 light years away from Earth and we send a rocket ship towards that planet at 99.9% light speed. We stay behind on Earth and watch the rocket ship travel towards the other planet.
Eventually we should be able to see our rocket ship reach it’s destination. How much time will have elapsed for... | <blockquote>
Will it appear as if the trip took 8 years to complete?
</blockquote>
Yes.
| It takes the spaceship 4 years to get there, and then it takes light from the spaceship getting there 4 years to get back, i.e. 8 years for an observer on Earth to see it land on the planet.
| https://physics.stackexchange.com |
732,638 | [
"https://math.stackexchange.com/questions/732638",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/130748/"
] | Q. Let n be any positive integer. Find all primitive pythagorean triples which have 2^n as a side.
So here is what I have;
We see that 2^n = 2∙2∙2∙∙∙2, n times, and is clearly an even number. Then we see 2^n can be the side x, for where x=2st, by our definition of primitive pythagorean triplet. That is 2^n=2st ⇒ 2^n... | Hint: So now you have $st=2^{n-1}$, with $s$ and $t$ relatively prime and of opposite parity. Can you figure out $s,t$ from that? There are not many choices.
| $$ a = k\cdot(m^2 - n^2) ,\ \, b = k\cdot(2mn) ,\ \, c = k\cdot(m^2 + n^2)\\
\implies b=2^n\\
\implies mnk=2^{n-1}\\
\implies k=\dfrac{2^{n-1}}{mn}$$
Thus,
$$a=\dfrac{2^{n-1}}{mn}\cdot(m^2 - n^2)=\dfrac{2^{n-1}m}{n}-\dfrac{2^{n-1}n}{m}\\
\implies b=\dfrac{2^{n-1}m}{n}+\dfrac{2^{n-1}n}{m}$$
Then, since $m$ and $n$ rel... | https://math.stackexchange.com |
95,463 | [
"https://mathoverflow.net/questions/95463",
"https://mathoverflow.net",
"https://mathoverflow.net/users/23240/"
] | Suppose that the ring homomorphism $R\rightarrow S$ is faithfully flat ($R$ and $S$ are Noetherian commutative rings). Let $A$ be an Artinian $R$-module. Do we have $0:_S(A\bigotimes_R S)=(0:_RA)S$.
I know this the case when $A$ is Noehterian. Also by purity I know that $\big(0:_S(A\bigotimes_R S)\big)\bigcap R=0:_RA... | No. Let $A=\mathbb{Z}[1/2]/\mathbb{Z}$. Let $R\to S$ be $\mathbb{Z}\to \mathbb{Z}_2\times \mathbb{Z}_3$, where $\mathbb{Z}_n$ denotes $\mathbb{Z}[1/n]$.
Then $Ann_{\mathbb{Z}}A=0$. But $(1,0)\in S$ kills $A\otimes_{\mathbb{Z}}S$.
| The following counterexample might be interesting too. There exists an unmixed d-dimensional commutative Noetherian local domain $(R,\mathfrak{m})$ such that its completion is not unmixed. Then $H^d_\mathfrak{m}(R)$ is a counterexample since the annihilator of $H^d_\mathfrak{m}(R)$ is the unmixed part of the zero ideal... | https://mathoverflow.net |
4,645,707 | [
"https://math.stackexchange.com/questions/4645707",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/1153517/"
] | As title, I'm wondering is there any way to show that <span class="math-container">$|P(z)|\leq |z^n|$</span> for <span class="math-container">$|z|\geq 1$</span>.
I attempt to divide <span class="math-container">$|z^n|$</span> on both side, and get
<span class="math-container">$$\bigg|\frac{P(z)}{z^n}\bigg| =\bigg |\fra... | Let <span class="math-container">$w=1/z$</span> and note that <span class="math-container">$P(z)=P(1/w)= a_0+a_1/w + \dots + a_n/w^n$</span> so <span class="math-container">$Q(w)=w^nP(1/w)$</span> is analytic in the unit disc including at <span class="math-container">$0$</span>. But on the unit circle <span class="math... | One has to consider analytic function <span class="math-container">$f(z) = P(z)/z^n$</span> on annulus <span class="math-container">$A(R) = \{{z:|z| >=1 , |z| <= R}\}$</span> where <span class="math-container">$R$</span> is large enough. Also, note that since <span class="math-container">$|P(z)| <=1$</span> on... | https://math.stackexchange.com |
589,892 | [
"https://electronics.stackexchange.com/questions/589892",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/297506/"
] | <pre><code> |================================= |------------|
Power Outlet 220V Large Cable | Water Pump |
|================================= |------------|
|
|
A small 3 watt LED? (o)=-----... | In order to define the parameters in a two port network using y, z, or h-parameters, you need to use short and open circuit conditions for the network. This is not ideal for transmission lines in general because the input impedance of a distributed parameter system is a function of <em>length</em>.
When you’re routing ... | Directly from Wikipedia:
<blockquote>
... S+parameters differ from Z and Y in the sense that S-parameters do not use open or short circuit conditions to characterize a linear electrical network; instead, matched loads are used. These terminations are much easier to use at high signal frequencies than open-circuit and s... | https://electronics.stackexchange.com |
479,047 | [
"https://physics.stackexchange.com/questions/479047",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/230132/"
] | Supernovae clouds are very colorful, and if I trust documentaries I watched, the colors are due to excitation of elements, as in fireworks. Since the Sun is mostly made of hydrogen, I suppose those lines should be very apparent but they are not so much, its light looking like a blackbody radiation. What contributes to ... | The sun's spectrum is a blackbody spectrum with absorption lines superimposed. The blackbody spectrum comes from the photosphere, which is the highest elevation at which the sun is opaque. It becomes opaque because it's ionized to form a plasma. A plasma is opaque because it has free charges that interact strongly with... | <blockquote>
What contributes to the rest of the spectrum up to the point it masks
hydrogen lines?
</blockquote>
It's basically due to the optics.
In the case of the sun, you're seeing the energy of the gas in the outer shell. This is highly random, moving in all directions and over a huge distribution of speeds.... | https://physics.stackexchange.com |
193,889 | [
"https://electronics.stackexchange.com/questions/193889",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/15575/"
] | I have a simple circuit arrangement of a 9V battery - 1k Ohm resistor - LED. This circuit has a current of 7.5 mA (measured between the LED and the battery). If there's voltage drop of 2V in the LED, does it mean that my LED has a (2 % 7.5)k Ohm resistance?
Thanks!
| Diodes are not ohmic. Resistors have a linear relationship between current and voltage. That is the relationship described by Ohm's law which you used in your question. Diodes look like this:
<img src="https://upload.wikimedia.org/wikipedia/commons/a/a5/Diode-IV-Curve.svg" alt="">
We normally model them as a simple v... | You should not consider LEDs (and other diodes) as having resistance, as they do not obey Ohm's Law. The voltage across a lit LED varies only slightly as the current varies. It is best to say that an LED has a (nearly) fixed voltage drop, which varies with the colour of the LED.
| https://electronics.stackexchange.com |
250,783 | [
"https://softwareengineering.stackexchange.com/questions/250783",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/139797/"
] | I've been learning about using a hashtable to efficiently check for items in a list without looping through the whole thing, but there's one thing that I don't get:
Why hashed keys?
It seems like:
<pre><code>var wordList = {
'aa' : ['aa'],
'aah' : ['aah'],
'ahhed' : ['aahed']
};
</code></pre>
Would wo... | Because you still need a way to search the associative array. The hash table is your search mechanism; it gives you O(1) performance for any given key search, by computing an index into the bucket containing your item.
What is your underlying search mechanism, if it's not a hash table? A Binary Search Tree? Tha... | Well, if you need to find something in your associative array, you need to iterate through each of the keys, and find equality. This means that in the worst case, you'll need to iterate through your whole collection to find the good key.
Accessing an array with an index (myArray[0] for example) is instant; it doesn't ... | https://softwareengineering.stackexchange.com |
4,178,082 | [
"https://math.stackexchange.com/questions/4178082",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/47771/"
] | I know that for any open cover <span class="math-container">$(\Omega_i)_{i\in I}$</span> of <span class="math-container">$\mathbb R$</span> we can find a <span class="math-container">$C^\infty$</span>-partition of unity subordinated to <span class="math-container">$(\Omega_i)_{i\in I}$</span>. Moreover, if <span class=... | There exists <span class="math-container">$\varphi \in C^\infty_c(\mathbb R)$</span> such that <span class="math-container">$\varphi>0$</span> on <span class="math-container">$(0,1),$</span> <span class="math-container">$\varphi = 0$</span> everywhere else, and <span class="math-container">$\int_0^1 \varphi =1.$</sp... | Why not use mollified characteristic functions? I.e.,
<span class="math-container">$$
\rho_k = \eta_{1/2} \ast \chi_{ (-k-1,k+1)}.
$$</span>
| https://math.stackexchange.com |
352,368 | [
"https://softwareengineering.stackexchange.com/questions/352368",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/195338/"
] | I've made a small change to an integration component and have prepared unit tests to cover my work. All new and existing unit tests are passing.
It will take a substantial amount of time to configure and run the component locally as I will need to restore databases, check firewall rules etc.
The definition of Done in... | <blockquote>
Is a unit test a better replacement for works-on-my-machine?
</blockquote>
Yes, it's absurdly better. Unless you've got some sort of containerization to guarantee the configuration of your environment, running on your local machine guarantees nothing. And even then, doing it by hand is just asking for o... | No. You need an integration or UI test to verify the whole thing works.
Ideally these are performed on some sort of test environment rather than your own machine though.
If you lack that, its probably worth going through the setup and testing it manually. After all its a one time thing for that system right?
Use a v... | https://softwareengineering.stackexchange.com |
461,610 | [
"https://electronics.stackexchange.com/questions/461610",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/122223/"
] | I was wondering the safety of using non-RoHS parts for hobby projects. I already use non-leaded solder, but some of the parts I have are not RoHS compliant. How much would I, and my family, be exposed to lead for parts like resistors, if I were to handle them? How much lead is actually in these parts that I would be ex... | It's good practice to avoid eating electronic components.
It's also good practice to wash your hands after handling electronic components, or anything for that matter, before handling food that you, or your family, are going to eat.
As long as you follow those two good practices, there is essentially no health differ... | RoHS and lead-free electronics are more about preventing the lead going into waste and/or in the environment and then in the water sources and/or the food chain.
A properly disposed off (i.e. recycled) electronics is safe with any lead content. Lead costs money and generally will be extracted from the waste along with... | https://electronics.stackexchange.com |
21,591 | [
"https://scicomp.stackexchange.com/questions/21591",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/18586/"
] | There are lot of articles being written about how the newly launched Intel Xeon Phi will steal the HPC\Super Computer market share from the competitors. Intel Knights is equipped with 72 cores and 4 sockets making it 288 core system. Whereas a single Gtx980 has 2048 CUDA cores. How can these two compete in terms of Com... | Like Brian said, the Xeon Phi cores are not at all comparable to the CUDA ones. The problem with the Phi is that it's somewhere between two horses.
If you are doing highly parallel floating point calculations, NVIDIA will provide you with something like 3 times the performance at 1/4th of the price. For double precis... | CUDA cores aren't at all comparable to the separate processor cores in the Xeon Phi coprocessors. The Phi coprocessor cores are full fledged processors that can have their own loops, branching, etc. while the CUDA cores are all executing the same operations on various slices of your data.
| https://scicomp.stackexchange.com |
556,759 | [
"https://physics.stackexchange.com/questions/556759",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/156987/"
] | I visited some other QA threads about this topic, and I don't understand why people think it's mysterious that the bucket knows about its rotation.
If a non-rotating bucket is all there is in the universe, then, initially, all the parts of the bucket are at rest wrt to each other.
But if we want to rotate that bucket... | In Newtonian mechanics (and also relativity and quantum mechanics), a hypothetical physicists sitting in the bucket would definitely be able to do an experiment to detect that the bucket is rotating. I'm not sure why that would be mysterious. It should be noted that the velocities of the particles involved (relative to... | Suppose that instead of talking about the bucket's angular velocity, you talked about its linear velocity. Then it would have indeed been the case that you can't speak of an absolute linear velocity in an empty universe. The paradox is why the same logic doesn't apply to angular velocity, since they're both "velocities... | https://physics.stackexchange.com |
267,210 | [
"https://dba.stackexchange.com/questions/267210",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/188730/"
] | I have the following schema/query where I basically need to filter parent table by some criteria and then collect aggregated data from its child table(s):
<pre><code>create table parent (id integer primary key, name text not null);
create table child (id integer primary key, pid integer not null references parent(id))... | For example you can do it this way:
<pre><code>select p.id, p.name,
COALESCE((select count(*) from child where p.id = pid), 0) AS cnt
from parent AS p
where name like '%xyz%'
</code></pre>
or this:
<pre><code>select p.id, p.name,
count(c.pid) AS cnt
from parent AS p
left join child AS c ON p.id = c.pid
where nam... | Did you try a lateral join?
<pre><code>select parent.id, parent.name, q.cnt
from parent
left join lateral (
select count(*) cnt
from child ch
where ch.pid = parent.id
) q on true
where name like '%xyz%'
</code></pre>
| https://dba.stackexchange.com |
32,478 | [
"https://datascience.stackexchange.com/questions/32478",
"https://datascience.stackexchange.com",
"https://datascience.stackexchange.com/users/50451/"
] | Inertial measurement units (IMU), usually composed of accelerometers and gyroscopes; are well known to have inherent errors in their data, originating from bias, random walk noise, temperature dependence etc. creating a highly non-linear dependence. Typically, extended Kalman filters are used to estimate and remove the... | The only way to find out is to try it, but I doubt it. A Kalman makes a specific assumption about the "priors", i.e., about the nature of how the signals are related over time. This is based on knowledge about the physics of movement and how this affects the sensor values, combined with some assumptions about the lik... | <strong>Yes</strong> you can do sensor fusion, given that you have access to ground truth during training.
You should not try to model the errors with your RNN. Instead you should directly build a MISO RNN model (multiple inputs -> your sensors | single output -> the estimation of ground truth).
| https://datascience.stackexchange.com |
108,044 | [
"https://mathoverflow.net/questions/108044",
"https://mathoverflow.net",
"https://mathoverflow.net/users/16858/"
] | Let $G(N)$ be the congruence subgroup
$\big\{ \begin{pmatrix} a&b \\ c&d \end{pmatrix} \in SL_2(\mathbb{Z}) \ \ | \ \ a \equiv d \mod N \textrm{ and } b \equiv c\equiv 0 \mod N \big\}$.
$G(N) \backslash \mathbb{H}$ seems to parametrize elliptic curves with a cyclic subgroup and some extra data (I think its ... | Here's a very clunky answer:
For a particular elliptic curve $E$, the collection of bases $\{P,Q\}$ of the $N$-torsion $E[N]$ is acted upon (diagonally) by the group $(\mathbb{Z}/N\mathbb{Z})^\times$. This group has a subgroup $G$ consisting of elements $x$ with a lifting to an element $y\in (\mathbb{Z}/N^2\mathbb{Z}... | A disjoint union of copies of this space parameterizes elliptic curves with a choice of two disjoint (except for the identity) $N$-element cyclic subgroups and an isomorphism between them.
Proof: First we show that any two disjoint, except for the identity, subgroups must form a basis for the level $N$ structure. This... | https://mathoverflow.net |
15,827 | [
"https://dba.stackexchange.com/questions/15827",
"https://dba.stackexchange.com",
"https://dba.stackexchange.com/users/1285/"
] | There are many blog posts and best practice articles extolling the virtues of placing the SQL Server data file on one hard drive and the transaction log on another. The reason given is that that the database file will be experiencing random reads and writes while the transaction log will only have sequential writes.
... | Correct. In theory, if you have 100s of DBs you need 100s of drives, one for each log. In practice though one does not care for such case, cause when you have 100s of DBs you obviously don't expect top-notch TPC performance for <em>each</em> DB. You will likely have some DBs with high throughput and stringent SLAs and ... | The transaction log is exactly that... a running log of all transactions. As such it fills continuously in one direction until checkpointed and overwritten, or truncated and overwritten. The overwriting is sequential.
Consider your data files. A customer record may contain an order from 5 years ago, and one from 10 ye... | https://dba.stackexchange.com |
125,139 | [
"https://mathoverflow.net/questions/125139",
"https://mathoverflow.net",
"https://mathoverflow.net/users/32388/"
] | I want to calculate the dual space of $\mathcal{C}_0[a,b]$, that is the space of continuous functions on $[a,b]$ vanishing at $a$. I know that the dual space of $\mathcal{C}[a,b]$ (continuous functions) is the space of differences of Lebesgue-Stieltjes measure associated to increasing functions, left-continuous, and va... | Each (bounded linear) functional on $C[a,b]$ is also a functional on $C_0[a,b]$. Each function $f \in C[a,b]$ can be written as $f(x) = f_0(x) + f(a) \cdot 1$, where $f_0 \in C_0[a,b]$. On the other hand, each functional on $C_0[a,b]$ can be extended to a functional on $C[a,b]$ (Hahn-Banach). Therefore the answer is $(... | $C_0[a,b]^* = C[a,b]^*/C_0[a,b]^{ann}$ where $C_0[a,b]^{ann}$ is the annihilator of $C_0[a,b]$ in $C_0[a,b]^*$; the annihilator is 1-dimensional with basis $\delta_a$, the atomic measure at $a$, or the evaluation at $a$.
In your setup this corresponds to the Stieltjes integral with respect to the function
which is 1 at... | https://mathoverflow.net |
2,348,963 | [
"https://math.stackexchange.com/questions/2348963",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/15748/"
] | Q: A multiple choice exam has 4 choices for each question. A student has studied enough so that the probability they will know the answer to a question is 0.5, the probability that they will be able to eliminate one choice is 0.25, otherwise all 4
choices seem equally plausible.
If they know the answer they will get ... | Let A represent the event that the question is answered correctly
Let
X represent the event that the student knows the correct answer
Let Y
represent the event that the student is able to eliminate one choice
Let Z represent the event that the student is not able to eliminate
any choice
I interpret the s... | With
$A$: students answers correctly
$B$: student knew answer
what you want is $P(B|A)$, rather than $P(A|B)$
Now, we are given that:
$$P(B)= \frac{1}{2}$$
and hence
$$P(B^C)=1-\frac{1}{2}=\frac{1}{2}$$
Also:
$P(A|B)=1$ (if they knew the answer they give the correct answer)
and
$$P(A|B^C)=\frac{1}{4}\cdot \... | https://math.stackexchange.com |
159,456 | [
"https://physics.stackexchange.com/questions/159456",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/70783/"
] | I am not a physicist, but this question came to me and I need to answer it, and I think that you guys can help me.
Is it possible to calculate the energy in a spark? For example in a lighter with an 'electric ignition'.
If it is, how can I do that?
| One way is to connect the ignition to a high voltage (10kV) capacitor. Then the energy is:
$$E = \int VI d t = \frac{CV^2}{2},$$
where $C$ is its capacitance and $V$ its voltage, assuming that you connected it and did the measurements so that energy losses are negligible.
| When you create a spark you generate a voltage, $V$, between the two electrodes and a current, $I$, flows between them. Both the voltage and the current vary with time, so we need to write them as functions of time: $V(t)$ and $I(t)$.
If we have a current $I$ flowing across a voltage $V$, then the power is given by:
... | https://physics.stackexchange.com |
109,910 | [
"https://softwareengineering.stackexchange.com/questions/109910",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/785/"
] | Say you are given a mock-up of 25 screens of the visual states of your application. The expectation is that this is enough for us to be confident we can develop and hand it to the original stakeholder or customer as a finished application, and they will be satisfied. Naturally, you're going to end up asking the stakeho... | Some other things you may need are:
<ul>
<li>Usecases or Workflow descriptions: Just because you know what a screen looks like, do you know how bad input is handled? Do you know how to transition between screens in ALL cases? You could include error handling here as well.</li>
<li>High-level system description: Someth... | <strong>How to get people to understand that UI mocks aren't enough to create a working program:</strong>
I would handle this with an analogy. Since I'm a bit of a car nut, I'm going that route.
"Pretend I know nothing about cars. You hand me a few photos of a Ferrari. A couple from the outside and one from insi... | https://softwareengineering.stackexchange.com |
627,210 | [
"https://physics.stackexchange.com/questions/627210",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/236734/"
] | Suppose I have <span class="math-container">$U$</span> in it's natural variables that is <span class="math-container">$U(S,V)$</span> and lets say somehow I get the same internal energy in terms <span class="math-container">$U(V,T)$</span>, then does it make sense to say:
<span class="math-container">$$U(V,T) = U(S,V).... | We can't directly write <span class="math-container">$U(V,T)=U'(S,V)$</span>.
There should be a map from <span class="math-container">$\phi:(S,V)\to (V,T)$</span>
such that: <span class="math-container">$U'(S,V)=U(\phi(S,V))$</span>
Consider a parametrized curve <span class="math-container">$\gamma:t\to\mathbb R^2$</sp... | Yes. Both Eq.(1) and Eq.(2) are ok. They simply the calculus chain-rule and change variables. Nothing wrong with that. You don't need a thermodynamic property to validate these equations. It is rigorous mathematical relation.
<span class="math-container">\begin{align}
& f(x(\xi, \eta), y(\xi, \eta)) = f(\xi, \eta... | https://physics.stackexchange.com |
17,059 | [
"https://mechanics.stackexchange.com/questions/17059",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/10392/"
] | I have a diesel common-rail 1.5l engined car. Lately I am facing an issue where the RPM needle is bouncing in the tachometer when the car is idling. The normal idling RPM is around 820. When idling, I can see the RPM fluctuating between 800-1000 rpm. This fluctuation is more evident when the AC is switched on. I can ev... | The exact cause of the issue had been found to be that of a loose alternator belt.
When the engine was cold, the alternator had a slack in it and if the AC load is added on the engine, the rpm fluctuated.
Solution was simply to tension the alternator belt.
Well, thanks to all for sharing the knowledge.
| The Problem can be with the engine not getting enough ventilation.
<ul>
<li><strong>Problem:</strong> In your car the ECU is programmed to raise the rpm when it detects a stall or the RPM dropping down so if there is problem with your air filter which is not allowing much air into the engine and causing a stall but no... | https://mechanics.stackexchange.com |
3,985 | [
"https://mechanics.stackexchange.com/questions/3985",
"https://mechanics.stackexchange.com",
"https://mechanics.stackexchange.com/users/1838/"
] | I have a 1999 Toyota Corolla, which has a D, 2, and L gear. I also have a steep driveway to climb everyday. Which of these gears is most appropriate for going up steep inclines?
| Assuming that you have no faults with your transmission, it doesn't matter - an automatic transmission will automatically switch down gear as and when it needs to. All the '2' gear does is not let you go over 2nd gear - which if you were heading downhill could make your engine over-rev...generally not recommended.
So... | If you're carrying a high load, L is best.
The gears work as follows:
D = use whichever gear the computer decides/ Useful for everyday driving.
2 = use first or second, depending on speed. Useful when carrying high loads at low speeds.
L = stay in the lowest gear. Best for carrying high loads up steep inclines.
| https://mechanics.stackexchange.com |
31,275 | [
"https://mathoverflow.net/questions/31275",
"https://mathoverflow.net",
"https://mathoverflow.net/users/-1/"
] | Let $R$ be a nonzero commutative ring with $1$, such that all finite matrices over $R$ have a <em>Smith normal form</em>. Does it follow that $R$ is a principal ideal domain?
If this fails, suppose we additionally suppose that $R$ is an integral domain?
What can we say if we impose the additional condition that ... | The implication is false without the assumption that R is Noetherian, because finite matrices don't detect enough information about infinitely generated ideals.
For example, let R be the ring
$$
\bigcup_{n \geq 0} k[[t^{1/n}]]
$$
where $k$ is a field (an indiscrete valuation ring). Any finite matrix with coefficients... | If every matrix has a Smith normal form, then every finitely generated
$R$-submodule $M$ of $R^n$ satisfies $R^n/M$ is a finite
direct sum of modules isomorphic to $R/aR$. If $R$ is Noetherian
this implies that every finitely generated module is a direct sum of modules
of the form $R/aR$. So if $I$ is a maximal ideal o... | https://mathoverflow.net |
399,570 | [
"https://physics.stackexchange.com/questions/399570",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/178941/"
] | A man is standing on one side of a boat and the boat is stationary. We ignore friction between water and boat (and air friction). Thus there are no external forces on the man+boat system. So momentum is conserved, and centre of mass does not move. I understand that if the man moves to the other side the boat moves ... | The exact dynamics associated with each step will depend on how the man walks.
If he makes small jumps and stops after each jump, the boat will also stop after each jump. To stop after each jump, the man would have to grab something on the boat, in which case the boat will be stopped by that force, or land feet first,... | The dynamics of walking are quite complicated and I think this is clouding the issue somewhat. So imagine a similar experiment where the man is on a bicycle in the long, thin boat.
As he pedals, the wheels and act on the boat, which starts to slip "backwards" in the water. When he gets near the end of the boat, he has... | https://physics.stackexchange.com |
229,268 | [
"https://electronics.stackexchange.com/questions/229268",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/20711/"
] | Changing sampling rate is called up sampling or down sampling depending on which way or is done. If the factor is an even number then the process becomes very simple.
However, what term is used to change bit depth e.g 16 bit samples to 8 bit samples? Certainly this requires "re-quantization" rather than just throwing ... | Well, basically it DOES amount to simply chopping off the lower bits and discarding them.
Now it may help to amplify (multiply) the signal up to some amplitude so that the signal will be above your new, higher zero threshold.
In some cases "dithering" is used to introduce low-level random ("noise") factors to make ... | You are referring to "scaling". To go from 16 bits (arithmetic data, of course, not logical) to 8 is done by dividing by 256.
In some cases it's done by truncation, where the lsb's are simply discarded. If you want to be careful, you apply rounding to the lsb of the result, but then the result is the same as scaling.
| https://electronics.stackexchange.com |
364,717 | [
"https://softwareengineering.stackexchange.com/questions/364717",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/250257/"
] | I'm struggling with a very simple question:
I'm now working on a server application, and I need to invent a hierarchy for the exceptions (some exceptions already exist, but a general framework is needed). How do I even start doing this?
I'm thinking of following this strategy:
1) What is going wrong?
<ul>
<li>Somet... | <strong>General remarks</strong>
(a bit opinion-biased)
I'd typically not go for a detailed exception hierarchy.
Most important thing: an exception tells your caller that your method failed to complete its job. And your caller <strong>must</strong> get notice about that, so he doesn't simply continue. That works wit... | The main thing to keep in mind when designing an error response pattern is to make sure it's useful to callers. This applies whether you're using exceptions or defined error codes, but we'll restrict ourselves to illustrating with exceptions.
<ul>
<li>If your language or framework already provides general exception cl... | https://softwareengineering.stackexchange.com |
11,497 | [
"https://dsp.stackexchange.com/questions/11497",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/3802/"
] | In Harris Corner detection, is there any particular reason why this function is chosen:
$R=det(M)-k*trace(M)^2$
We want to a function to evaluate how fast E(u,v) fluctuate accross different direction, but can't we use other function such as:
$R=1-(\lambda_1+\lambda_2)^2$
| <blockquote>
can't we use other function such as: $R=1-(\lambda_1+\lambda_2)^2$
</blockquote>
This formula isn't as useful, because it doesn't differentiate between two equally large eigenvalues (a corner) and one twice as large eigenvalue plus one very small one (a straight line). So for example $\lambda_1 = 2, \la... | $M$ is the structure tensor. The points where the signal changes in two directions are the points for which both eigenvalues of $M$ are large. $R = det(M) - k*trace^2(M) = \lambda_1\lambda_2 - k(\lambda_1 + \lambda_2)^2$, so $R$ is large when both $\lambda_1$ and $\lambda_2$ are large.
| https://dsp.stackexchange.com |
19,618 | [
"https://scicomp.stackexchange.com/questions/19618",
"https://scicomp.stackexchange.com",
"https://scicomp.stackexchange.com/users/16325/"
] | It is well known that upwind schemes are stable when calculating convection flows with $|\text{Pe}|>2$, $\text{Pe}$ is the Peclet number. Why is that, and why is central difference unstable?
Is there any intrinsic reason there?
Any explanation, references, links will be helpful.
| The reasoning for the stability of upwind schemes based on an understanding of the characteristics of the hyperbolic equation(s). Characteristics are essentially the finite speeds at which information in a hyperbolic system travel, and are found via decomposing a hyperbolic system into independent hyperbolic PDEs.
Now... | An intuitive reason is that upwinding can be viewed as providing additional numerical diffusion, which is typically associated with stability in standard Finite Difference/Finite Element schemes. In finite differences, this means that the first order upwind scheme can be rewritten
$$
\frac{u_i-u_{i-1}}{h} = \frac{u_{i... | https://scicomp.stackexchange.com |
39,736 | [
"https://electronics.stackexchange.com/questions/39736",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/12116/"
] | I can't find a detailed answer to this question. What is the condition for a signal to be considered small, so that you have to use small signal modeling? Also how is this condition derived for both BJT and JFET.
| It's not that you <em>have</em> to use small signal modelling when the signal is small...it's that you <em>can</em> use small signal modelling when the signal is small. A small signal model will typically be much simpler to compute than a large signal model.
The reason the small signal model is simpler to compute, is ... | For a quantitative answer to complement The Photon's answer, consider the diode equation:
\$i_D = I_Se^{v_D/nV_T}\$
\$i_D = I_D + i_d, v_D = V_D + v_d \$
Taylor expand about the operating point \$V_D, I_D \$
\$I_D + i_d = I_Se^{V_D/nV_T} \cdot [1 + \frac{v_d}{nV_T} + \frac{1}{2}(\frac{v_d}{nV_t})^2 + ...] \$
For \... | https://electronics.stackexchange.com |
66,371 | [
"https://mathoverflow.net/questions/66371",
"https://mathoverflow.net",
"https://mathoverflow.net/users/15449/"
] | Hello,
I read that if $A\subset D$ is the heart of a bounded t structure, D a triangulated category, then D=D^b(A).
Have not been able to find a proper reference for this. Can anyone confirm this result?
Thanks!
| You're never going to find a reference because it's false. Just take $D$ to be the stable homotopy category of Postnikov pieces, i.e. spectra with finitely many non-trivial homotopy groups. Take $D_{\geq 0}$ (resp. $D_{\leq 0}$) the full subcategory of spectra with non-trivial homotopy groups concentrated in non-negati... | To add to what Fernando Muro said, there are examples where this is true. Beilinson showed in his paper "On the derived category of perverse sheaves" (Springer LNM 1289 pp. 27-41) that it is true when you are talking about the middle perverse t-structure in the constructible derived category of sheaves on schemes. I... | https://mathoverflow.net |
70,384 | [
"https://math.stackexchange.com/questions/70384",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/14712/"
] | If the probabilities that three children X, Y ,Z will get a ticket for a football game are 0.4, 0.3, 0.2 respectively, calculate the probability that,
(Assume that the events of X,Y,Z are independent)
1) None will get the ticket
2) Only one will get the ticket
3) At least one will get the ticket
4) All w... | I assume you know how to convert integers from base 10 to base 3, so this answer will address fractions between $0$ and $1$.
To say, for example, that $\frac{5}{8} = 0.625$ means that $\frac{5}{8} = 6 \frac{1}{10} + 2 \frac{1}{100} + 5 \frac{1}{1000}$. So to convert a fraction $\frac{a}{b}$ to ternary means we want t... | The easiest way to do it, I think, is to convert everything before the decimal point the regular way. Then you just repeat the following process:
<ol>
<li>Subtract 1 until you get between 0 and 1.</li>
<li>Multiply by 3.</li>
<li>The integer part of your answer is the next digit of the ternary expansion.</li>
<li>Rins... | https://math.stackexchange.com |
457,679 | [
"https://physics.stackexchange.com/questions/457679",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/221198/"
] | I'm doing the following problem:
<blockquote>
A castle on a cliff has a cannon 300m above sea level. The cannon can
shoot a 10kg iron ball with a velocity of 400 m/s . If the cannon is
raised to an angle 30º of above the horizon, calculate the following:
the final velocity of the cannon ball just before... | Velocity is a vector, and vectors have components. To find the magnitude of <span class="math-container">$V_{final}$</span> , we have to take the square root of both components squared.
<span class="math-container">$V_{final} = \sqrt{V_{x}^2+V_{y}^2}$</span>
Because <span class="math-container">$V_{y}$</span> is squa... | Interestingly, the angle of the cannon above the horizon doesn't matter here at all, assuming no losses due to air friction. The ball exits the cannon with a specific kinetic energy. When the ball hits the water, the potential energy from the 300m height difference gets converted into additional kinetic energy.
If yo... | https://physics.stackexchange.com |
99,818 | [
"https://electronics.stackexchange.com/questions/99818",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/37209/"
] | I am currently misunderstanding the relation between Ohm's Law and the law for conservation of energy. I am referring to the example (in the book "Foundations of Analog and Digital Electronic Circuits" - Anant Agarwal and Jeffrey H. Lang, page 97):
<img src="https://i.stack.imgur.com/mV8Jj.png" alt="Example Image from... | Nothing at all. The book is wrong.
Just the last line is wrong.. \$0.002v = 0.001v^2\$ divide both sides by \$v\$ and 0.001 and we get \$v = \$\$0.002\over 0.001\$ = 2.
| 2mA thru 1kohm implies 2V and the power is calculated by either: -
\$\dfrac{V^2}{R}\$ = 4mW or
\$I^2R\$ = 4mW
What's the problem?
Ah it's the book (idiots LOL)
| https://electronics.stackexchange.com |
201,664 | [
"https://stats.stackexchange.com/questions/201664",
"https://stats.stackexchange.com",
"https://stats.stackexchange.com/users/108573/"
] | I am trying to run the egger's test to check my meta analysis for publication bias.
My data consists of a correlation effect size and a sample size from each study.
I understand that the egger's regression is based on the individual standard error of the mean for each observation.
I need help to calculate that based o... | I can't find a citation for it, but Charlie Poole has called this phenomena "Directional publication bias" - there's a publication bias that's toward a particular finding (in this case, what's already published) that's beyond just what you'd expect to see with the usual significant/non-significant result publication bi... | You may also be interested in some of the following which discuss various features of selective reporting and citation distortions.
<pre>
@article{greenberg09,
author = {Greenberg, S A},
title = {How citation distortions create unfounded authority:
analysis of a citation network},
journal = {British Med... | https://stats.stackexchange.com |
622,475 | [
"https://electronics.stackexchange.com/questions/622475",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/309311/"
] | I was wondering regarding the requirement of earthing that is it dependent on the Input value of power or not?
If a device is powered using 24V, 1.5A adaptor then is it mandatory to provide earthing in the product?
Kindly provide the range of inputs in which earthing is required.
| It's <em>way</em> more complex than that.
Earthing requirements in fact depends on the local laws. In most parts of the world, if the equipment is not of a peculiar type (like medical) it is <em>not</em> required to provide an earth for such a kind of load <em>if</em> you ensure that double insulation is provided (and ... | It all depends on where your 24V comes from. SELV is isolated from the AC supply. PELV or FELV aren't, and probably need earthing unless your kit is all double insulated.
| https://electronics.stackexchange.com |
69,954 | [
"https://dsp.stackexchange.com/questions/69954",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/34155/"
] | I have an OFDM signal affected by AWGN, if I know the power of the gaussian noise, can I recover the OFDM signal? Can I perform deconvolution to recover the original signal?
thanks
| Let <span class="math-container">$\delta_\Delta(t) = \begin{cases}\frac{1}{\Delta} && -\frac{1}{2\Delta} \le t \le \frac{1}{2\Delta} \\ 0 && \mathrm{otherwise}\end{cases}$</span>.
Then just integrate it! <span class="math-container">$u_\Delta(t)$</span> must be zero for <span class="math-container">$t ... | I didn't look at how the function <span class="math-container">$\delta_\Delta(t)$</span> is defined in that lecture, but the convention is that it's a rectangular <em>pulse</em> of area being <span class="math-container">$1$</span>. The definition is :
<span class="math-container">$$\delta_\Delta(t) = \begin{cases}{ \f... | https://dsp.stackexchange.com |
56,462 | [
"https://cs.stackexchange.com/questions/56462",
"https://cs.stackexchange.com",
"https://cs.stackexchange.com/users/49740/"
] | What is an intuitive way of understanding what a push down automaton is capable of computing?
| Intuitively, a pushdown automaton uses a stack and using a stack we can do a depth first traversal of a parse tree. It means that we can accept strings which are in context free languages by using stack of a pushdown automaton (left-most derivation). This is not a rigorous proof that languages of pushdown automata are ... | Let's start with a finite automaton. Such a device can be viewed as a machine that has a fixed, finite number of boolean variables, like $s = $ "we've seen an even number of $0$'s in the input so far", or $s_i = $ "the input so far, when interpreted as a binary number, is congruent to $i\pmod 3$". Using such a machine,... | https://cs.stackexchange.com |
13,236 | [
"https://computergraphics.stackexchange.com/questions/13236",
"https://computergraphics.stackexchange.com",
"https://computergraphics.stackexchange.com/users/6496/"
] | I am working on the port of a demo from DXR to Vulkan Ray Tracing extension using GLSL.
In DXR/HLSL space, there are <em>RayTMin()</em> and R<em>ayTCurrent()</em> functions to retrieve the starting and the current end point of the ray (<em>Origin + (Direction * RayTMin)</em> and <em>Origin + (Direction * RayTCurrent)... | Others have interpreted your question as being about “progressive JPEG”, but “line by line from top to bottom” is <em>not</em> how progressive JPEG appears. Progressive JPEG organizes the data in the file so that low-detail data (the average color of 8×8 blocks) is stored before the data required for higher detail. A s... | What you are referring to is called a "progressive JPEG" file. This is a property of the way the file was compressed file which allows its decompression to be done in stages, such that a less-detailed version of the image can be shown despite not having the entire file. This technology was originally invented... | https://computergraphics.stackexchange.com |
47,305 | [
"https://dsp.stackexchange.com/questions/47305",
"https://dsp.stackexchange.com",
"https://dsp.stackexchange.com/users/34008/"
] | I have an USRP (B205mini) with an RX frequency of 900 MHz and a bandwidth of 100 MHz. I want to distinguish between two raw, unmodulated signals at respectively 875 and 925 MHz.
My approach would be to bandpass filter the output of the USRP, but I am not quite sure how to design and implement filters based on baseband... | So, after a search in the official sources of the scipy.signal.stft, I found the normalization.
They compute the scale factor as following:
<pre><code>scale = 1.0 / win.sum()**2
</code></pre>
where 'win' represents the window function selected.
Then, if the 'stft' mode is selected, the root from the scale is extract... | The $\texttt{scipy.signal.stft()}$ function returns the complex-valued STFT. You can see in the output that its datatype is $\texttt{complex64}$. You however, are taking the square of the absolute value of the complex-valued STFT coefficients, which is typically called the spectrogram.
| https://dsp.stackexchange.com |
358,919 | [
"https://physics.stackexchange.com/questions/358919",
"https://physics.stackexchange.com",
"https://physics.stackexchange.com/users/170120/"
] | Assume a rope on a smooth surface. If the rope is pulled from one side (force exerted on one side), where is the equal and opposite force? Why does the rope move? What I mean here is that there is no mass either side of the rope, it's just laying on the ground. I pick it up and then drag it. Shouldn't the force of tens... | Newton's Third Law says that for every force there is an equal and opposite force. However, it must be clear that these forces act on different bodies. For example, if you push a wall, you will feel a force against your hand, which is due to the wall. It is the wall's reaction to the force you are applying to it.
In ... | By pulling the rope, you are exerting a force on it, and so Newton's third law tells us that it too exerts an equal force on you but in the opposite direction. Obviously, this force is not very large, so it isn't enough to accelerate you by any significant amount.
| https://physics.stackexchange.com |
132,192 | [
"https://electronics.stackexchange.com/questions/132192",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/54539/"
] | On a computer power supply can I add 12 volts and 5 volts supply to get 17 volt supply? **Edited for clarification
| In short, no. Not if the 5V rail that you intend to use is the one available on the same PSU.
The reason for this is that every supply rail in that PSU (+12, -12, +5, -5, +3.3, etc) shares a common reference ground. If you attempt to stack the 5V on top of the 12V, you will instead short 12V directly to the common gro... | You cannot get something out of nothing! You only read 24V because you are using the -12V as the "ground" reference for your measurement device. If you actually put the measurement device's "negative" pin on the board's "ground" point, you would get the correct readings of + or - 12V.
You don't really "add" a 5V rail... | https://electronics.stackexchange.com |
60,757 | [
"https://mathoverflow.net/questions/60757",
"https://mathoverflow.net",
"https://mathoverflow.net/users/3891/"
] | I am a bit embarrassed to ask this question, but still: assume that I have
a finite morphism $\pi:X\to Y$ of affine algebraic varieties over a field (probably
finiteness is too strong an assumption, but it is true in my situation, so let
me assume it), which is an isomorphism
over an open subset $U$ of $Y$. Let $Z$ be ... | I don't think so. Let $Y$ be the plane curve $y_1^2=y_2^5$, let $X$ be the line with coordinate $x$, and define $\pi:X\to Y$ by $y_1=x^5,y_2=x^2$. It's an isomorphism outside the closed point $y_1=0=y_2$. The function $x^3$ vanishes on the scheme-theoretic preimage (that is, it belongs to the ideal of $k[x]$ generated ... | I was in fact pondering the same question just yesterday, and ended up with this: there is a thickening $Z'\subset X$ of $\pi^{-1}Z$ such that every regular function vanishing on $Z'$ comes from $Y$.
Proof is straight forward, but anyway: in terms of rings, let $\phi\colon A \subset B$ be a finite extension of rings, ... | https://mathoverflow.net |
347,451 | [
"https://softwareengineering.stackexchange.com/questions/347451",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/252261/"
] | Like this:
<pre><code>Campaign:
type: object
properties:
id:
type: string
description: "A GUID identifier"
referenceId:
type: string
description: "A consumers identifier they have used to map their own systems logic to this object."
name:
type: string
description: "'Great Campaign 2017' ... | <strong>This is not a problem; it is a necessity.</strong> The lack of this field would be problematic for integrating with customer systems.
There are plenty of common use cases for this sort of thing. For example, an API involving billing is likely to allow companies to specify their own invoice numbers, workforce m... | I don't think that there is a best practice regarding this. Holding an opaque <code>referenceId</code> in your system is required or not depending on your relation with the 3rd party clients.
Strictly speaking, most probably, it is not your system's responsibility to map between your model and the 3rd party model. It... | https://softwareengineering.stackexchange.com |
1,064,337 | [
"https://math.stackexchange.com/questions/1064337",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/190706/"
] | I was wondering whether a contour integral (over a simple, closed contour) changes if we change the differential to only the axis that contains the singularities. Intuitively, I would think there is no difference since the contour integral everywhere excluding the singularities is zero.
For example: Is $\int_C \frac{1... | It is true that in contour integration there is great freedom in choosing the shape of the contour. As long as the contour is closed, has the correct orientation (counter clockwise) and encloses the singularities of interest, all contours are in principle equivalent.
We can now see that there are two problems with you... | Replacing $dz$ with $dx$ makes a lot of difference. The integral with $dx$ will not be zero for holomorphic functions, in general. To see why, write $f=u+iv$. Then
$$
\int f\,dz = \int (u+iv)\,(dx+i\,dy) = \int(u\,dx-v\,dy)+i\int(v\,dx+u\,dy)
$$
Both integrals on the right are zero thanks to Green's theorem and Cau... | https://math.stackexchange.com |
567,495 | [
"https://math.stackexchange.com/questions/567495",
"https://math.stackexchange.com",
"https://math.stackexchange.com/users/101586/"
] | Show that $X_{n}=\sum_{k=0}^{n} \frac{1}{k!}$ and $X_{n}=\sum_{k=0}^{n} \rho^{k}$ are Cauchy sequences.
I know that for each sequence I have to show the following:
"$\forall \epsilon>0 \text{ }\exists \text{ } N_{\epsilon}=N(\epsilon) \in \mathbb{N}$ s.t. $\forall n \geq N_{\epsilon}$ , $ \left | X_{n}... | For the first we have that $\frac {1}{k!}<\frac {1}{k^2}$ for $k\geq 4$ and thus $\sum_{k=n+1}^{m} \frac {1}{k!}\leq \sum_{k=n+1}^{m} \frac {1}{k^2}$ and $\sum_{k=n+1}^{m} \frac {1}{k^2}$ converges and so the sequence $x_m=\sum_{k=n+1}^{m} \frac {1}{k^2}$ is Cauchy, and thus $y_m=\sum_{k=n+1}^{m} \frac {1}{k!}$ is u... | For the first series: $X_{n} = \sum^{n}_{k=0} \frac{1}{k!} $ you could use the following approximation:
$$
\left| X_{n} - X_{m} \right| = \left| \sum^{n}_{k=0} \frac{1}{k!} - \sum^{m}_{k=0} \frac{1}{k!} \right| = \left| \sum^{m}_{k=n+1} \frac{1}{k!} \right| \leq \left| \sum^{m}_{k=n+1} \frac{1}{e^{k}} \right|
$$
for a ... | https://math.stackexchange.com |
82,933 | [
"https://softwareengineering.stackexchange.com/questions/82933",
"https://softwareengineering.stackexchange.com",
"https://softwareengineering.stackexchange.com/users/22098/"
] | How to tackle 2-D and 3-D space in data ? lets say you are working on a power grid problem. You need to represent Towers; transmission lines; transformers and every thing else in a 2-D space. How would you design a Data Model for this 2-D space ? I can use a
<pre><code>class tower {
int x_cor;
int y_cor;
string powe... | I do a lot of work with Geographic Information Systems (GIS). Part of working in this domain requires handling and storing all sorts of spatial data, which we usually leave up to software vendors like ESRI or use open source solutions like GDAL. GDAL can also be plugged into C++ and python programs easily.
There are... | What I am going to say probably sounds very generic, and to a degree it is, but it can be applied to any engineering problem.
Software is generally used to deal with problems in the real world. In consequence it models those parts of the real world it deals with. The more accurate the model is, the better you can deal... | https://softwareengineering.stackexchange.com |
28,183 | [
"https://electronics.stackexchange.com/questions/28183",
"https://electronics.stackexchange.com",
"https://electronics.stackexchange.com/users/8698/"
] | I was reading in 8086 datasheet and I found this phrase that I couldn't understand in memory organisation :
<blockquote>
memory is logically divided into code, data, extra data, and stack
segments of up to 64K bytes each, with each <strong><em>segment falling on
16-byte boundaries</em></strong>.
</blockquote>
I... | This means that each segment starts at an address that is a multiple of 16. This is achieved as follows.
Addresses in 8086 are 20 bit long. Addresses are computed from a segment start and an offset, both are 16 bit. The 16-bit segment start is shifted left by 4, then the offset is added. These two operations are perfo... | Doing the math, 2<sup>16</sup>=64k, which means that a 64k segment can be addressed by a 16-bit value.
So if you have a set of 64k stack segments, you can select the single segment with a segment-address value and then the offset in the segment is a 16-bit address.
Note that they can be <em>up to</em> 64k, but also s... | https://electronics.stackexchange.com |
576,088 | [
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] | Suppose a conductor is placed in a non uniform external electric field. Why does the field inside the conductor remain zero?
| When you make such claims, you must keep one thing in mind - you are talking about steady state.
So why does the Electric Field inside the conductor become zero in steady state? If it was not zero the free electrons will still keep moving and hence the state will not be so steady. When you say steady state, you mean no... | In the absence of a source of power, any electric field inside a conductor will cause the free electrons to flow until the resultant field in the conductor is zero. In the absence of a field, the electric potential must be the same at all points in the conductor.
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323,973 | [
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] | The major pre-requisite in utilizing SSIS Catalog is enabling CLR Integration. The instance in question is running SQL Server 2014. I'm looking for feedback and resources I can mine which specifically covers best practices and security considerations for enabling CLR Integration on SQL Server 2014.
As I understand it, ... | Consider upgrading to 3.11.14. Apache Cassandra 3.11.2 is almost 5 years old, and I'm pretty sure the JNA library is included with it. That itself might fix this.
Otherwise, you should be able to clear out the <code>/tmp/jna*</code> files and restart.
It also might be that the Cassandra user doesn't have adequate per... | The <code>UnsatisfiedLinkError</code> happens because Cassandra doesn't have permissions to execute the shared libraries in the <code>/tmp</code> directory (mounted with the <code>noexec</code> option).
As a workaround, you can map the JNA temporary directory by adding the following line in Cassandra's <code>conf/jvm.o... | https://dba.stackexchange.com |
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